end that the Reader may know that those Axioms are not indemonstrable therefore not Principles of Demonstration and from hence learn to be wary how he admits any thing for a Principle which is not at least as evident as these are Greater is defined to be that whose Part is Equal to the Whole of another Now if we suppose any Whole to be A and a Part of it to be B seeing the Whole B is Equal to it self and the same B is a Part of A therefore a Part of A will be Equal to the Whole B. Wherefore by the Definition above A is Greater then B which was to be proved CHAP. IX Of Cause and Effect 1 Action and Passion what they are 2 Action and Passion Mediate and Immediate 3 Cause simply taken Cause without which no Effect follows or Cause Necessary by Supposition 4 Cause Efficient and Material 5 An Entire Cause is alwayes sufficient to produce its Effect At the same instant that the Cause is Entire the Effect is produced Every Effect has a Necessary Cause 6 The Generation of Effects is Continual What is the Beginning in Causation 7 No Cause of Motion but in a Body Contiguous and Moved 8 The same Agents and Patients if alike disposed produce like Effects though at different times 9 All Mutation is Motion 10 Contingent Accidents what they are 1 A Body is said to Work upon or Act that is to say Do some thing to another Body when it either generates or destroys some Accident in it and the Body in which an Accident is generated or destroyed is said to Suffer that is to have something Done to it by another Body As when one Body by putting forwards another Body generates Motion in it it is called the AGENT and the Body in which Motion is so generated is called the PATIENT so Fire that warms the Hand is the Agent and the Hand which is warmed is the Patient That Accident which is generated in the Patient is called the EFFECT 2 When an Agent and Patient are Contiguous to one another their Action and Reason are then said to be Immediate otherwise Mediate and when another Body lying betwixt the Agent and Patient is Contiguous to them both it is then it self both an Agent and a Patient an Agent in respect of the Body next after it upon which it Works and a Patient in respect of the Body next before it from which it suffers Also if many Bodies be so ordered that every two which are next to one another be contiguous then all those that are betwixt the first and the last are both Agents and Patients and the first is an Agent onely and the last a Patient onely 3 An Agent is understood to produce its determined or certain Effect in the Patient according to some certain Accident or Accidents with which both it and the Patient are affected that is to say the Agent hath its Effect precisely such not because it is a Body but because such a Body or so Moved For otherwise all Agents seeing they are all Bodies alike would produce like Effects in all Patients and therefore the Fire for example does not warm because it is a Body but because it is Hot nor does one Body put forward another Body because it is a Body but because it is moved into the place of that other Body The Cause therefore of all Effects consists in certain Accidents both in the Agents and in the Patient which when they are all present the Effect is produced but if any one of them be wanting it is not produced and that Accident either of the Agent or Patient without which the Effect cannot be produced is called Causa sine qua non or Cause Necessary by Supposition as also the Cause Requisite for the Production of the Effect But a CAUSE simply or An Entire Cause is the Aggregate of all the Accidents both of the Agents how many soever they be and of the Patient put together which when they are all supposed to be present it cannot be understood but that the Effect is produced at the same instant and if any one of them be wanting it cannot be understood but that the Effect is not produced 4 The Aggregate of Accidents in the Agent or Agents requisite for the production of the Effect the Effect being produced is called the Efficient Cause thereof and the Aggregate of Accidents in the Patient the Effect being produced is usually called the Material Cause I say the Effect being produced for where there is no Effect there can be no Cause for nothing can be called a Cause where there is nothing that can be called an Effect But the Efficient and Material Causes are both but Partial Causes or Parts of that Cause which in the next precedent article I called an Entire Cause And from hence it is manifest that the Effect we expect though the Agents be not defective on their part may nevertheless be frustrated by a defect in the Patient and when the Patient is sufficient by a defect in the Agents 5 An Entire Cause is alwayes sufficient for the production of its Effect if the Effect be at all possible For let any Effect whatsoever be propounded to be produced if the same be produced it is manifest that the Cause which produced it was a sufficient Cause but if it be not produced and yet be possible it is evident that something was wanting either in some Agent or in the Patient without which it could not be produced that is that some Accident was wanting which was requisite for its Production and therefore that Cause was not Entire which is contrary to what was supposed It follows also from hence that in whatsoever instant the Cause is Entire in the same instant the Effect is produced For if it be not produced something is still wanting which is requisite for the production of it and therefore the Cause was not Entire as was supposed And seeing a Necessary Cause is defined to be that which being supposed the Effect cannot but follow this also may be collected that whatsoever Effect is produced at any time the same is produced by a Necessary Cause For whatsoever is produced in as much as it is produced had an Entire Cause that is had all those things which being supposed it cannot be understood but that the Effect follows that is it had a Necessary Cause And in the same manner it may be shewn that whatsoever Effects are hereafter to be produced shall have a Necessary Cause so that all the Effects that have been or shall be produced have their Ne cessity in things antecedent 6 And from this that whensoever the Cause is Entire the Effect is produced in the same instant it is manifest that Causation and the Production of Effects consist in a certain continual Progress so that as there is a continual Mutation in the Agent or Agents by the working of other Agents upon them so also the Patient upon
which they work is continually altered and changed For example as the Heat of the Fire encreases more and more so also the Effects thereof namely the Heat of such Bodies as are next to it again of such other Bodies as are next to them encreases more more accordingly which is already no litle argument that all Mutation consists in Motion onely the truth whereof shall be further demonstrated in the ninth Article But in this Progress of Causation that is of Action and Passion if any man comprehend in his imagination a part thereof and divide the same into parts the first part or Beginning of it cannot be considered otherwise then as Action or Cause for if it should be considered as Effect or Passion then it would be necessary to consider something before it for its Cause or Action which cannot be for nothing can be before the Beginning And in like manner the last part is considered onely as Effect for it cannot be called Cause if nothing follow it but after the last nothing follows And from hence it is that in all Action the Beginning and Cause are taken for the same thing But every one of the intermediate parts are both Action and Passion and Cause and Effect according as they are compared with the antecedent or subsequent part 7 There can be no Cause of Motion except in a Body Contiguous and Moved For let there be any two Bodies which are not contiguous and betwixt which the intermediate Space is empty or if filled filled with another Body which is at Rest and let one of the propounded Bodies be supposed to be at Rest I say it shall always be at Rest. For if it shall be Moved the Cause of that Motion by the 8th Chapter 19th Article will be in some external Body and therefore if between it and that external Body there be nothing but empty Space then whatsoever the disposition be of that external Body or of the Patient it self yet if it be supposed to be now at Rest we may conceive it wil continue so til it be touched by some other Body but seeing Cause by the Definition is the Aggregate of all such Accidents which being supposed to be present it cannot be conceived but that the Effect will follow those Accidents which are either in external Bodies or in the Patient it self cannot be the Cause of future Motion and in like manner seeing we may conceive that whatsoever is at Rest will still be at Rest though it be touched by some other Body except that other Body be moved therefore in a contiguous Body which is at Rest there can be no Cause of Motion Wherefore there is no Cause of Motion in any Body except it be Contiguous and Moved The same reason may serve to prove that whatsoever is Moved will alwayes be Moved on in the same way and with the same Velocity except it be hindered by some other Contiguous and Moved Body and consequently that no Bodies either when they are at Rest or when there is an interposition of Vacuum can generate or â—â—tinguish or lesson Motion in other Bodies There is one that has written that things Moved are more resisted by things at Rest then by things contrarily Moved for this reason that he conceived Motion not to be so contrary to Motion as Rest. That which deceived him was that the words Rest and Motion are but contradictory Names whereas Motion indeed is not resisted by Rest but by contrary Motion 8 But if a Body work upon another Body at one time and afterwards the same Body work upon the same Body at another time so that both the Agent and Patient and all their parts be in all things as they were and there be no difference except onely in time that is that one Action be former the other later in time it is manifest of it self that the Effects will be Equal and Like as not differing in any thing besides time And as Effects themselves proceed from their Causes so the diversity of them depends upon the diversity of their Causes also 9 This being true it is necessary that Mutation can be nothing else but Motion of the Parts of that Body which is Changed For First we do not say any thing is Changed but that which appears to our Senses otherwise then it appeared formerly Secondly both those Appearances are Effects produced in the Sentient therefore if they be differeÌ„t it is necessary by the preceding article that either some part of the Agent which was formerly at Rest is now Moved and so the Mutation consists in this Motion or some part which was formerly Moved is now otherwise Moved and so also the Mutation consists in this new Motion or which being formerly Moved is now at Rest which as I have shewn above cannot come to pass without Motion and so again Mutation is Motion or lastly it happens in some of these manners to the Patient or some of its parts so that Mutation howsoever it be made will consist in the Motion of the parts either of the Body which is perceived or of the Sentient Body or of both Mutation therefore is Motion namely of the parts either of the Agent or of the Patient which was to be demonstrated And to this it is consequent that Rest cannot be the Cause of any thing nor can any Action proceed from it seeing neither Motion nor Mutation can be caused by it 10 Accidents in respect of other Accidents which precede them or are before them in time upon which they do not depend as upon their Causes are called Contingent Accidents I say in respect of those Accidents by which they are not generated for in respect of their Causes all things come to pass with equal necessity for otherwise they would have no Causes at all which of things generated is not intelligible CHAP. X. Of Power and Act. 1 Power and Cause are the same thing 2 An Act is produced at the same instant in which the Power is Plenary 3 Active and Passive Power are parts onely of Plenary Power 4 An Act when said to be Possible 5 An Act Necessary and Contingent what 6 Active Power consists in Motion 7 Cause Formal and Final what they are 1_COrrespondent to Cause and Effect are POWER and ACT Nay those and these are the same things though for divers considerations they have divers names Forwhensoever any Agent has all those Accidents which are necessarily requisite for the production of some Effect in the Patient then we say that Agent has Power to produce that Effect if it be applyed to a Patient But as I have shewn in the precedent Chapter those Accidents constitute the Efficient Cause and therefore the same Accidents which constitute the Efficient Cause constitute also the Power of the Agent Wherefore the Power of the Agent and the Efficient Cause are the same thing But they are considered with this difference that Cause is so called in respect of the Effect already
Syllogisme and they deceived not others oftner then they were themselves deceived For the force of that famous argument of Zeno against Motion consisted in this Proposition Whatsoever may be divided into parts infinite in number the same is infinite which he without doubt thought to be true yet neverthelesse is false For to be divided into infinite parts is nothing else but to be divided â—â—â—o as many parts as any man will But it is not necessary that a Line should have parts infinite in number or be infinite because I can divide and subdivide it as often as I please for how many parts soever I make yet their number is finite but because he that sayes Parts simply without adding how many does not limit any number but leaves it to the determination of the Hearer therefore we say commonly a line may be divided infinitely which cannot be true in any other sense And thus much may suffice concerning Syllogisme which is as it were the first Pace towards Philosophy in which I have said as much as is necessary to teach any man from whence all true argumentation has its force And to enlarge this Treatise with all that may be heaped together would be as superfluous as if one should as I said before give a young child Precepts for the teaching of him to goe for the Art of Reasoning is not so well learned by Precepts as by Practice and by the reading of those books in which the Conclusions are all made by severe Demonstration And so I pass on to the way of Philosophy that is to the Method of Study CHAP. VI. Of Method 1 Method and Science defined 2 It is more easily known concerning Singular then Universall things That they are and contrarily it iâ— more easily knowne concerning Universall then Singular things Why they are or what are their Causes 3 What it is Philosophers seek to know 4 The first Part by which Principles are found out is purely Analyticall 5 The highest Causes and most Universall in every kind are knowne by themselves 6 Method from Principles fonnd out tending to Science simply what it is 7 That Method of Civill and Naturall Science which proceeds from Sense to Principles is Analytical and againe that which begins at Principles is Syntheticall 8 The Method of searching out whether any thing propounded be Matter or Accident 9 The Method of seeking whether any Accident be in this or in that Subject 10 The Method of searching after the Cause of any Effect propounded 11 Words serve to Invention as Markes to Demonstration as Signes 12 The Method of Demonstration is Syntheticall 13 Definitions onely are Primary and Universal Propositions 14 The Nature and Definition of a Definition 15 The Properties of a Definition 16 The Nature of a Demonstration 17 The Properties of a Demonstration and Order of things to be demonstrated 18 The Faults of a Demonstration 19 Why the Analyticall Method of Geâ—metricians cannot be treated of in this place 1 FOr the understanding of Method it will be necessary for me to repeat the definition of Philosophy delivered above Chap. 1. Art 2. in this manner Philosophy is the knowledge we acquire by true Ratiocination of Appearances or apparent Effects from the knowledge we have of some possible Production or Generation of the same and of such Production as has been or may be from the knowledge we have of the Effects METHOD therefore in the Study of Philosophy is the shortest way of finding out Effects by their known Causes or of Causes by their known Effects But we are then said to know any Effect when we know that there be Causes of the same and in what Subiect those Causes are and in what Subiect they produce that Effect and in what Manner they work the same And this is the Science of Causes or as they call it of the 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 All other Science which is called the 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 is either Perception by Sense or the Imagination or Memory remaining after such Perception The first Beginnings therefore of Knowledge are the Phantasmes of Sense and Imagination and that there be such Phantasmes we know well enough by Nature but to know why they be or from what Causes they proceed is the work of Ratiocination which consists as is said above in the 1. Chap. 2. Art in Composition and Division or Resolution There is therefore no Method by which we find out the Causes of things but is either Compositive or Resolutive or partly Compositive and partly Resolutive And the Resolutive is commonly called Analyticall Method as the Compositive is called Syntheticall 2 It is common to all sorts of Method to proceed from known things to unknown and this is manifest from the cited Definition of Philosophy But in Knowledge by Sense the whole object is more known then any part thereof as when we see a Man the Conception or whole Idea of that Man is first or more known then the particular Ideas of his being figurate animate and rationall that is we first see the whole Man and take notice of his Being before we observe in him those other Particulars And therefore in any knowledge of the 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 or that any thing is the beginning of our search is from the whole Idea and contrarily in our knowledge of the 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 or of the Causes of any thing that is in the Sciences we have more knowledge of the Causes of the Parts then of the Whole For the Cause of the Whole is compounded of the Causes of the Parts but it is necessary that we know the things that are to be compounded before we can know the whole Compound Now by Parts I do not here mean Parts of the thing it self but Parts of its Nature as by the Parts of Man I do not understand his Head his Shoulders his Arms c. but his Figure Quantity Motion Sense Reason and the like which Accidents being compounded or put together constitute the whole Nature of Man but not the man himselfe And this is the meaning of that common saying namely that some things are more knowne to us others more known to Nature for I do not thinke that they which so distinguish mean that something is known to Nature which is known to no man and therefore by those things that are more known to Us we are to understand things we take notice of by our Senses and by more known to Nature those we acquire the knowledge of by Reason for in this sense it is that the Whole that is those things that have Universal Names which for brevities sake I call Universall are more knowne to us then the Parts that is such things as have Names lesse Universal which I therefore call Singular and the Causes of the Parts are more known to Nature then the Cause of the Whole that is Universalls then Singulars 3 In the Study of Philosophy men search after Science either Simply or
distance and the Magnitude and Splendor be seen in more lines and distances then one as it is in Reflection or Refraction then neither that Splendor nor apparent Magnitude are in the Sun it self and therefore the Body of the Sun cannot be the Subject of that Splendor and Magnitude And for the same reasons the Aire and other parts will be rejected till at last nothing remain which can be the Subject of that Splendor and Magnitude but the Sentient it selfe And this Method in regard the Subject is divided into parts is Analitycall and in regard the Properties both of the Subject and Accident are compared with the Accident concerning whose Subject the enquiry is made it is Syntheticall 10 But when we seek after the Cause of any propounded Effect we must in the first place get into our Mind an exact Notion or Idea of that which we call Cause namely that A Cause is the Summe or Aggregate of all such Accidents both in the Agents and the Patient as concurre to the producing of the Effect propounded all which existing together it cannot be understood but that the Effect existeth with them or that it cannot possibly exist if any one of them be absent This being known in the next place we must examine singly every Accident that accompanies or praecedes the Effect as farre forth as it seemes to conduce in any manner to the production of the same and see whether the propounded Effect may be conceived to exist without the existence of any of those Accidents and by this meanes separate such Accidents as do not concurre from such as concurre to produce the said Effect which being done we are to put together the concurring Accidents and consider whether we can possibly conceive that when these are all present the Effect propounded will not follow and if it be evident that the Effect will follow then that Aggregate of Accidents is the entire Cause otherwise not but we must still search out and put together other Accidents For example if the Cause of Light be propounded to be sought out first we examine things without us and find that whensoever Light appeares there is some principall Object as it were the fountaine of Light without which we cannot have any perception of Light and therefore the concurrence of that Object is necessary to the generation of Light Next we consider the Medium and find that unlesse it be disposed in a certaine manner namely that it be transparent though the Object remain the same yet the Effect will not follow and therefore the concurrence of Transparency is also necessary to the generation of Light Thirdly we observe our own Body and find that by the indisposition of the Eyes the Brain the Nerves and the Heart that is by Obstructions Stupidity and Debility we are deprived of Light so that a fitting disposition of the Organs to receive impressions from without is likewise a necessary part of the Cause of Light Again of all the Accidents inhaerent in the Object there is none that can conduce to the effecting of Light but onely Action or a certain Motion which cannot be conceived to be wanting whensoever the Effect is present for that any thing may shine it is not requisite that it be of such or such â—agnitude or Figure or that the whole Body of it be moved out of the place it is in unlesse it may perhaps be said that in the Sun or other Body that which causeth Light is the light it hath in it selfe which yet is but a trifling exception seeing nothing is meant thereby but the Cause of Light as if any man should say that the Cause of Light is that in the Sunne which produceth it it remaines therefore that the Action by which Light is generated is Motion only in the parts of the Object Which being understood we may easily conceive what it is the Medium contributes namely the continuation of that Motion to the Eye and lastly what the Eye and the rest of the Organs of the Sentient contribute namely the continuation of the same Motion to the last Organ of Sense the Heart And in this manner the Cause of Light may be made up of Motion continued from the Original of the same Motion to the Original of Vitall Motion Light being nothing but the alteration of Vitall Motion made by the impression upon it of Motion continued from the Object But I give this onely for an example for I shall speak more at large of Light and the generation of it in its proper place In the mean time it is manifest that in the searching out of Causes there is need partly of the Analyticall and partly of the Syntheticall Method of the Analyticall to conceive how circumstances conduce severally to the production of Effects and of the Syntheticall for the adding together and compounding of what they can effect singly by themselves And thus much may serve for the Method of Invention It remaines that I speake of the Method of Teaching that is of Demonstration and of the Meanes by which we demonstrate 11 In the Method of Invention the use of words consists in this that they may serve for Marks by which whatsoever we have found out may be recalled to memory for without this all our Inventions perish nor will it be possible for us to go on from Principles beyond a Syllogisme or two by reason of the weaknesse of Memory For example if any man by considering a Triangle set before him should find that all its angles together taken are equall to two right angles and that by thinking of the same tacitely without any use of words either understood or expressed and it should happen afterwards that another Triangle unlike the former or the same in different scituation should be offered to his consideration he would not know readily whether the same property were in this last or no but would be forced as often as a different Triangle were brought before him and the difference of Triangles is infinite to begin his contemplation anew which he would have no need to do if he had the use of Names for every Universal Name denotes the conceptions we have of infinite Singular things Neverthelesse as I said above they serve as Markes for the helpe of our Memory whereby we register to our selves our own Inventions but not as Signes by which we declare the same to others so that a man may be a Philosopher alone by himselfe without any Master Adam had this capacity But to Teach that is to Demonstrate supposes two at the least and Syllogisticall Speech 12 And seeing Teaching is nothing but leading the Mind of him we teach to the knowledge of our Inventions in that Track by which we attained the same with our own Mind therefore the same Method that served for our Invention will serve also for Demonstration to others saving that we omit the first part of Method which proceeded from the Sense of Things to Universal Principles which
produced and Power in respect of the same Effect to be produced hereafter so that Cause respects the Past Power the Future time Also the Power of the Agent is that which is commonly called Active Power In like manner whensoever any Patient has all those Accidents which it is requisite it should have for the production of some Effect in it we say it is in the Power of that Patient to produce that Effect if it be applyed to a fitting Agent But those Accidents as is defined in the precedent Chapter constitute the Material Cause and therefore the Power of the Patient commonly called Passive Power and Material Cause are the same thing but with this different consideration that in Cause the Past time and in Power the Future is respected Wherefore the Power of the Agent and Patient together which may be called Entire or Plenary Power is the same thing with Entire Cause for they both consist in the Sum or Aggregate of all the Accidents as well in the Agent as in the Patient which are requisite for the production of the Effect Lastly as the Accident produced is in respect of the Cause called an Effect so in respect of the Power it is called an Act. 2 As therefore the Effect is produced in the same instant in which the Cause is Entire so also every Act that may be produced is produced in the same instant in which the Power is Plenary And as there can be no Effect but from a Sufficient and Necessary Cause so also no Act can be produced but by Sufficient Power or that Power by which it could not but be produced 3 And as it is manifest as I have shewn that the Efficient and Material Causes are severally and by themselves parts onely of an Entire Cause and cannot produce any Effect but by being joyned together so also Power Active and Passive are parts onely of Plenary and Entire Power nor except they be joyned can any Act proceed from them and therefore these Powers as I said in the first Article are but conditionall namely the Agent has Power if it be applyed to a Patient and the Patient has Power if it be applyed to an Agent otherwise neither of them have Power nor can the Accidents which are in them severally be properly called Powers nor any Action be said to be Possible for the Power of the Agent alone or of the Patient alone 4 For that is an Impossible Act for the production of which there is no Power Plenary For seeing Plenary Power is that in which all things concurre which are requisite for the production of an Act if the Power shall never be Plenary there will always be wanting some of those things without which the Act cannot be produced wherefore that Act shall never be produced that is that Act is IMPOSSIBLE And every Act which is not Impossible is POSSIBLE Every Act therefore which is Possible shall at some time be produced for if it shall never be produced then those things shall never concurre which are requisite for the production of it wherefore that Act is Impossible by the Definition which is contrary to what was supposed 5 A Necessary Act is that the production whereof it is Impossible to hinder and therefore every Act that shall be produced shall necessarily be produced for that it shall not be produced is Impossible because as is already demonstrated every Possible Act shall at some time be produced Nay this Proposition What shall be shall be is as necessary a Proposition as this A Man is a Man But here perhaps some man may ask whether those Future things which are commonly called Contingents are Necessary I say therefore that generally all Contingents have their Necessary Causes as is shewn in the preceding Chapter but are called Contingents in respect of other Events upon which they do not depend as the Rain which shall be to morrow shall be Necessarily that is from necessary Causes but we think and say it happens by chance because we doe not yet perceive the Causes thereof though they exist now for men commonly call that Casuall or Contingent whereof they do not perceive the necessary Cause and in the same manner they use to speake of things past when not knowing whether a thing be done or no they say it is possible it never was done Wherefore all Propositions concerning Future things contingent or not contingent as this It will rayne to morrow or this To morrow the Sun will rise are either necessarily true or necessarily false but we call them Contingent because we doe not yet know whether they be true or false whereas their Verity depends not upon our Knowledge but upon the foregoing of their Causes But there are some who though they confess this whole Proposition To morrow it will either rain or not rain to be true yet they will not acknowledge the parts of it as To morrow it will rain or To morrow it will not rain to be either of them true by it self because they say neither this nor that is true determinately But what is this determinately true but true upon our knowledge or evidently true and therefore they say no more but that it is not yet known whether it be true or no but they say it more obscurely and darken the Evidence of the truth with the same words with which they endevour to hide their own ignorance 6 In the 9th Article of the precedent Chapter I have shewn that the Efficient Cause of all Motion and Mutation consists in the Motion of the Agent or Agents And in the first Article of this Chapter that the Power of the Agent is the same thing with the Efficient Cause From whence it may be understood that all Active Power consists in Motion also and that Power is not a certain Accident which differs from all Acts but is indeed an Act namely Motion which is therefore called Power because another Act shall be produced by it afterwards For example if of three Bodies the first put forwards the second and this the third the Motion of the second in respect of the first which produceth it is the Act of the second Body but in respect of the third it is the Active Power of the same second Body 7 The Writers of Metaphysiques reckon up two other Causes besides the Efficient and Material namely the ESSENCE which some call the Formal Cause and the End or Final Cause both which are nevertheless Efficient Causes For when it is said the Essence of a thing is the Cause thereof as to be Rational is the Cause of Man it is not intelligible for it is all one as if it were said To be a Man is the Cause of Man which is not well said And yet the knowledge of the Essence of any thing is the Cause of the knowledge of the thing it selfe for if I first know that a thing is Rational I know from thence that the same is Man but this is no
that the Proportion of the first Antecedent to the first Consequent is the same with that of the second Antecedent to the second Consequent And when four Magnitudes are thus to one another in Geometrical Proportion they are called Proportionals and by some more briefly Analogisme And Greater Proportion is the Proportion of a Greater Antecedent to the same Consequent or of the same Antecâ—dent to a Less Consequent and when the Proportion of the first Antecedent to the first Consequent is greater then that of the second Antecedent to the second Consequent the four Magnitudes which are so to one another may be called Hyperlogisme Less Proportion is the Proportion of a Less Antecedent to the same Consequent or of the same Antecedent to a Greater Consequent and when the Proportion of the first Antecedent to the first Consequent is less then that of the second to the second the four Magnitudes may be called Hypologisme 5 One Arithmetical Proportion is the Same with another Arithmetical Proportion when one of the Antecedents exceeds its Consequent or is exceeded by it as much as the other Antecedent exceeds its Consequent or is exceeded by it And therefore in four Magnitudes Arithmetically Proportional the sum of the Extremes is equal to the sum of the Means For if A. B C. D be Arithmetically Proportional and the Difference on both sides be the same Excess or the same Defect E then B+C if A be greater then B will be equal to A − E+C and A+D will be equal to A+C − E But A − E+C and A+C − E are equal Or if A be less then B then B+C will be equal to A+E+C and A+D will be equal to A+C+E But A+E+C and A+C+E are equal Also if there be never so many Magnitudes Arithmetically Proportional the Sum of them all will be equal to the Product of half the number of the Terms multiplyed by the Sum of the Extremes For if A. B C. D E. F be Arithmetically Proportional the Couples A+F B+E C+D will be equal to one another and their Sum will be equal to A+F multiplyed by the number of their Combinations that is by half the number of the Terms If of four Unequal Magnitudes any two together taken be equal to the other two together taken then the greatest and the least of them will be in the same Combination Let the Unequal Magnitudes be A B C D and let A+B be equal to C+D let A be the greatest of them all I say B will be the least For if it may be let any of the rest as D be the least Seeing therefore A is greater then C and B then D A+B will be greater then C+D which is contrary to what was supposed If there be any four Magnitudes the Sum of the greatest and least the Sum of the Means the difference of the two greatest and the difference of the two least will be Arithmetically Proportional For let there be four Magnitudes whereof A is the greatest D the least and B and C the Means I say A+D B+C A − B. C − D are Arithmetically Proportional For the difference between the first Antecedent and its Consequent is this A+D − B − C and the difference between the second Antecedent and its Consequent this A − B − C+D but these two Differences are equal and therefore by this 5th Article A+D B+C A − B. C − D are Arithmetically Proportional If of four Magnitudes two be equal to the other two they will be in reciprocal Arithmetical Proportion For let A+B be equal to C+D I say A. C D. B are Arithmetically Proportional For if they be not let A. C D. E supposing E to be greater or less then B be Arithmetically Proportional and then A+E will be equal to C+D wherefore A+B and C+D are not equal which is contrary to what was supposed 6 One Geometrical Proportion is the same with another Geometrical Proportion when the same Cause producing equal Effects in equal Times determines both the Proportions If a Point Uniformly moved describe two Lines either with the same or different Velocity all the parts of them which are contemporary that is which are described in the same time will be Two to Two in Geometrical Proportion whether the Antecedents be taken in the same Line or not For from the point A in the 10 Figure at the end of the 14 Chapter let the two Lines A D A G be described with Uniform Motion and let there be taken in them two parts AB AE and again two other parts AC AF in such manner that AB AE be contemporary and likewise AC AF contemporary I say first taking the Antecedents AB AC in the Line AD and the Consequents AE AF in the Line AG that AB AC AE AF are Proportionals For seeing by the 8th Chapter and the 15 Article Velocity is Motion considered as determined by a certain Length or Line in a certain Time transmitted by it the quantity of the Line AB will be determined by the Velocity and Time by which the same AB is described and for the same reason the quantity of the Line AC will be determined by the Velocity and Time by which the same AC is described and therefore the proportion of AB to AC whether it be Proportion of Equality or of Excess or Defect is determined by the Velocities and Times by which AB AC are described But seeing the Motion of the Point A upon AB and AC is Uniform they are both desribed with equal Velocity and therefore whether one of them have to the other the Proportion of Majority or of Minority the sole cause of that Proportion is the difference of their Times and by the same reason it is evident that the proportion of AE to AF is determined by the difference of their Times onely Seeing therefore AB AE as also AC AF are contemporary the difference of the Times in which AB and AC are described is the same with that in which AE and AF are described Wherfore the proportion of AB to AC and the proportion of AE to AF are both determined by the same Cause But the Cause which so determines the proportion of both works equally in equal Times for it is Uniform Motion and therefore by the last precedent Definition the proportion of AB to AC is the same with that of AE to AF and consequently AB AC AF. AF are Proportionals which is the first Secondly taking the Antecedents in different Lines I say AB AE AC AF are Proportionals For seeing AB AE are described in the same Time the difference of the Velocities in which they are described are the sole Cause of the proportion they have to one another And the same may be said of the proportion of AC to AF. But seeing both the Lines AD and AG are passed over by Uniform Motion the difference of the Velocities in which AB AE are described will be the same with the
which it is inscribed so that the Complement of the Spiral that is that space in the Circle which is without the Spiral Line is double to the space within the Spiral Line In the same manner if there be taken a mean proportional every where between the Semidiameter of the Circle which contains the Spiral and that part of the Semidiameter which is within the same there will be made another figure which will be half the Circle And to conclude this Rule serves for all such Spaces as may be described by a Line or Superficies decreasing either in magnitude or power so that if the proportions in which they decrease be commensurable to the proportions of the times in which they decrease the magnitudes of the figures they describe will be known 12 The truth of that proposition which I demonstrated in the second Article which is the foundation of all that has been said concerning Deficient Figures may be derived from the Elements of Philosophy as having iâ—â— original in this That all equality and inequality between two effects that is all Proportion proceeds from and is determined by the equal and unequal causes of those effects or from the proportion which the causes concurring to one effect have to the causes which concurre to the producing of the other effect and that therefore the proportions of Quantities are the same with the proportions of their causes Seeing therefore two Deficient Figures of which one is the Complement of the other are made one by motion decreasing in a certain time and proportion the other by the loss of Motion in the same time the causes which make and determine the quantities of both the figures so that they can be no other then they are differ onely in this that the proportions by which the quantity which generates the figure proceeds in describing of the same that is the proportions of the remainders of all the times and altitudes may be other proportions then those by which the same generating quantity decreases in making the Complement of that Figure that is the proportions of the quantity which generates the Figure continually diminished Wherefore as the proportions of the quantity in which Motion is lost is to that of the decreasing quantities by which the Deficient Figure is generated so will the Defect or Complement be to the Figure it self which is generated 13 There are also other quantities which are determinable from the knowledge of their causes namely from the comparison of the Motions by which they are made and that more easily then from the common Elements of Geometry For example That the Superficies of any portion of a Sphere is equal to that Circle whose Radius is a straight Line drawn from the Pole of the portion to the Circumference of its base I may demonstrate in this manner Let B A C in the 7 Figure be a portion of a Sphere whose Axis is A E whose base is B C let A B be the straight line drawn from the Pole A to the base in B and let A D equal to A B touch the great Circle B A C in the Pole A. It is to be proved that the Circle made by the Radius A D is equal to the Superficies of the portion B A C. Let the plain A E B D be understood to make a revolution about the Axis A E it is manifest that by the straight line A D a Circle will be described and by the arch A B the Superficies of a portion of a Sphere and lastly by the Subtense A B the Superficies of a right Cone Now seeing both the straight line A B and the arch A B make one and the same revolution and both of them have the same extreme points A and B the cause why the the Spherical Superficies which is made by the arch is greater then the Conical Superficies which is made by the Subtense is that A B the arch is greater then A B the Subtense and the cause why it is greater consists in this that although they be both drawn from A to B yet the Subtense is drawn straight but the arch angularly namely according to that angle which the arch makes with the Subtense which angle is equal to the angle D A B for an angle of contingence adds nothing to an angle of a Segment as has been shewn in the 14 Chapter at the 16th Article Wherefore the magnitude of the angle D A B is the cause why the Superficies of the portion described by the arch A B is greater then the Superficies of the right Cone described by the Subtense A B. Again the cause why the Circle described by the Tangent A D is greater then the Superficies of the right Cone described by the Subtense A B notwitstanding that the Tangent and the Subtense are equal and both moved round in the same time is this that A D stands at right angles to the Axis but A B obliquely which obliquity consists in the same angle D A B. Seeing therefore the quantity of the angle D A B is that which makes the excess both of the Superficies of the Portion and of the Circle made by the Radius A D above the superficies of the Right Cone described by the subtense A B it follows that both the Superficies of the Portion and that of the Circle do equally exceed the Superficies of the Cone Wherefore the Circle made by A D or A B and the Spherical Superficies made by the arch A B are equal to one another which was to be proved â—4 If these Deficient Figures which I have described in a 〈◊〉 were capable of exact description then any number of mean proportionals might be found out between two straight lines given For example in the Parallelogram A B C D in the 8th Figure let the three-sided figure of two Means be described which many call a Cubical Parabola and let R and S be two given straight lines between which if it be required to find two mean proportionals it may be done thus Let it be as R to S so B C to B F and let F E be drawn parallel to B A and cut the crooked line in E then through E let G H be drawn parallel and equal to the straight line A D and cut the Diagonal B D in I for thus we have G I the greatest of two Means between G H and G E as appears by the description of the figure in the 4th Article Wherefore if it be as G H to G I so R to another line T that T will be the greatest of two Means between R and S. And therefore if it be again as R to T so T to another line X that will be done which was required In the same manner four mean proportionals may be found out by the description of a three-sided figure of four Means and so any other number of Means c. CHAP. XVIII Of the Equation of Straight Lines with the
nothing but perturbed Light is comprehended Wherefore the Phantasme of a Lucid Body is Light and of a coloured Body Colour But the Object of Sight properly so called is neither Light nor Colour but the Body itself which is lucid or enlightned or coloured For Light and Colour being Phantasmes of the Sentient cannot be Accidents of the Object Which is manifest enough from this that Visible things appear oftentimes in places in which we know assuredly they are not and that in different places they are of different colours and may at one and the same time appear in divers places Motion Rest Magnitude and Figure are common both to the Sight and Touch and the whole appearance together of Figure and Light or Colour is by the Greeks commonly called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 and by the Latines Species and Imago all which names signifie no more but Appearance The phantasme which is made by Hearing is Sound by Smell Odour by Tast Savour and by Touch Hardness and Softness Heat and Cold Wetness Oiliness and many more which are easier to be distinguished by sense then words Smoothness Roughness Rarity and Density refer to Figure and are therefore common both to Touch and Sight And as for the Objects of Hearing Smel Tast and Touch they are not Sound Odour Savour Hardness c. but the Bodies themselves from which Sound Odour Savour Hardness c. proceed Of the causes of which and of the manner how they are produced I shall speak hereafter But these Phantasmes though they be effects in the Sentient as Subject produced by Objects working upon the Organs yet there are also other effects besides these produced by the same Objects in the same Organs namely certain Motions proceeding from Sense which are called Animal Motions For seeing in all Sense of external things there is mutual Action and Reaction that is two Endeavours opposing one another it is manifest that the motion of both of them together will be continued every way especially to the confines of both the Bodies And when this happens in the internal Organ the Endeavour outwards will proceed in a solid Angle which will be greater and consequently the Idea greater then it would have been if the impression had been weaker 11 From hence the Natural cause is manifest First why those things seem to be greater which caeteris paribus are seen in a greater Angle Secondly why in a serene cold night when the Moon doth not shine more of the fixed Stars appear then at another time For their action is less hindred by the serenity of the Aire and not obscured by the greater Light of the Moon which is then absent and the Cold making the Air more pressing helpeth or strengtheneth the action of the Stars upon our Eies in so much as Stars may then be seen which are seen at no other time And this may suffice to be said in general concerning Sense made by the Reaction of the Organ For as for the place of the Image the deceptions of Sight and other things of which we have experience in our selves by Sense being they depend for the most part upon the Fabrick it self of the Eie of Man I shall speak of them then when I come to speak of Man 12 But there is another kind of Sense of which I will say somthing in this place namely the Sense of Pleasure and Pain proceeding not from the Reaction of the Heart outwards but from continual action from the outermost part of the Organ towards the Heart For the original of Life being in the Heart that motion in the Sentient which is propagated to the Heart must necessarily make some alteration or diversion of Vital Motion namely by quickning or slackening helping or hindering the same Now when it helpeth it is Pleasure and when it hindereth it is Pain Trouble Grief c. And as Phantasmes seem to be without by reason of the Endeavour outwards so Pleasure and Pain by reason of the Endeavour of the Organ inwards seem to be within namely there where the first Cause of the Pleasure or Pain is as when the Pain proceeds from a Wound we think the Pain and the Wound are both in the same place Now Vital Motion is the Motion of the Bloud perpetually circulating as hath been shewn from many infallible signes and marks by Doctor Harvey the first Observer of it in the Veins and Arteries Which Motion when it is hindered by some other Motion made by the action of sensible Objects may be restored again either by bending or setting straight the parts of the Body which is done when the Spirits are carried now into these now into other Nerves till the Pain as farre as is possible be quite taken away But if Vital Motion be helped by Motion made by Sense then the parts of the Organ will be disposed to guide the Spirits in such manner as conduceth most to the preservation and augmentation of that motion by the help of the Nerves And in animal motion this is the very first Endeavour and found even in the Embrio which while it is in the wombe moveth its limbes with voluntary motion for the avoiding of whatsoever troubleth it or for the pursuing of what pleaseth it And this first Endeavour when it tends towards such things as are known by experience to be pleasant is called APPETITE that is an Approaching and when it shuns what is troublesome AVERSION or Flying from it And little Infants at the beginning and as soon as they are born have appetite to very few things as also they avoid very few by reason of their want of Experience and Memory therefore they have not so great a variety of animal Motion as we see in those that are more grown For it is not possible without such knowledge as is derived from Sense that is without Experience and Memory to know what will prove pleasant or hurtful onely there is some place for conjecture from the looks or aspects of things And hence it is that though they do not know what may do them good or harm yet sometimes they approach and sometimes retire from the same thing as their doubt prompts them But afterwards by accustoming themselves by little and little they come to know readily what is to be pursued and what to be avoided and also to have a ready use of their Nerves and other Organs in the pursuing and avoiding of good and bad Wherefore Appetite and Aversion are the first Endeavours of Animal Motion Consequent to this first Endeavour is the Impulsion into the Nerves and Retraction again of Animal Spirits of which it is necessary there be some Receptacle on place neer the original of the Nerves and this Motion or Endeavour is followed by a swelling and Relaxation of the Muscles and lastly these are followed by Contraction and Extension of the limbes which is Animal Motion 13 The Considerations of Appetites and Aversions are divers For seeing Living Creatures have sometimes Appetite and
reach the Zodiack of the fixed Starres wil fall stil upon the same fixed Starres because the whole Orbe a b c d is supposed to have no magnitude at all in respect of the great distance of the fixed Starres Supposing now the Sun to be in c it remains that I shew the cause why the Earth is neerer to the Sunne when in its annual motion it is found to be in d then when it is in b. And I take the cause to be this When the Earth is in the beginning of Capricorn at b the Sunne appears in the beginning of Cancer at d then is the midst of Summer But in the midst of Summer the Northern parts of the Earth are towards the Sunne which is almost all dry land containing all Europe and much the greatest part of Asia and America But when the Earth is in the beginning of Cancer at d it is the midst of Winter and that part of the Earth is towards the Sunne which contains those great Seas called the South Sea and the Indian Sea which are of farre greater extent then all the dry Land in that Hemisphere Wherefore by the last Article of the 21 Chapter when the Earth is in d it will come neerer to its first Movent that is to the Sunne which is in t that is to say the Earth is neerer to the Sunne in the midst of Winter when it is in d then in the midst of Summer when it is b and therefore during the Winter the Sunne is in its Perigaeum and in its Apogaeum during the Summer And thus I have shewn a possible cause of the Excentricity of the Earth which was to be done I am therefore of Keplers opinion in this that he attributes the Excentricity of the Earth to the difference of the parts thereof and supposes one part to be affected and another disaffected to the Sunne And I dissent from him in this that he thinks it to be by Magnetick virtue and that this Magnetick virtue or attraction and thrusting back of the Earth is wrought by immateriate Species which cannot be because nothing can give motion but a Body moved and contiguous For if those Bodies be not moved which are contiguous to a Body unmoved how this Body should begin to be moved is not imaginable as has been demonstrated in the 7th Article of the 9th Chapter and often inculcated in other places to the end that Philosophers might at last abstain from the use of such unconceiveable connexions of words I dissent also from him in this that he says the similitude of Bodies is the cause of their mutual attraction For if it were so I see no reason why one Egg should not be attracted by another If therefore one part of the Earth be more affected by the Sunne then another part it proceeds from this that one part hath more water the other more dry land And from hence it is as I shewed above that the Earth comes neerer to the Sunne when it shines upon that part where there is more water then when it shines upon that where there is more dry Land 9 This Excentricity of the Earth is the cause why the way of its annual motion is not a perfect Circle but either an Elliptical or almost an Elliptical line as also why the Axis of the Earth is not kept exactly parallel to it self in all places but onely in the Equinoctial points Now seeing I have said that the Moon is carried about by the Earth in the same manner that the Earth is by the Sunne and that the Earth goeth about the Sunne in such manner as that it shews sometimes one Hemisphere sometimes the other to the Sunne it remains to be enquired why the Moon has alwayes one and the same face turned towards the Earth Suppose therefore the Sunne to be moved with Simple Motion in the little Circle f g h i in the fourth figure whose Center is t and let ♈ ♋ ♎ ♑ be the annuall Circle of the Earth and a the beginning of Libra About the point a let the little Circle l k be described and in it let the Center of the Earth be understood to be moved with Simple motion and both the Sunne the Earth to be moved according to the order of the Signes Upon the Center a let the way of the Moon m n o p be described and let q r be the Diameter of a Circle cutting the Globe of the Moon into two Hemispheres whereof one is seen by us when the Moon is at the full and the other is turned from us The Diameter therefore of the Moon q o r will be perpendicular to the Straight Line t a. Wherefore the Moon is carried by reason of the Motion of the Earth from o towards p. But by reason of the motion of the Sunne if it were in p it would at the same time be carried from p towards o and by these two contrary Movents the straight line q r will be turned about and in a Quadrant of the Circle m n o p it will be turned so much as makes the fourth part of its whole conversion Wherefore when the Moon is in p q r will be parallel to the straight line m o. Secondly when the Moon is in m the straight line q r will by reason of the motion of the Earth be in m o. But by the working of the Suns motion upon it in the quadrant p m to◠same q r will be turned so much as makes another quarter of its whole conversion When therefore the Moon is in m q r will be perpendicular to the straight line o m. By the same reason when the Moon is in n q r will be parallel to the straight line m o and the Moon returning to o the same q r will return to its first place and the Body of the Moon will in one entire period make also one entire conversion upon her own Axis In the making of which it is manifest that one and the same face of the Moon is always turned towards the Earth And if any Diameter were taken in that little Circle in which the Moon were supposed to be carried about with simple motion the same effect would follow for if there were no action from the Sun every Diameter of the Moon would be carried about always parallel to it self Wherefore I have given a possible cause why one and the same face of the Moon is alwayes turned towards the Earth But it is to be noted that when the Moon is without the Ecliptick we do not alwayes see the same face precisely For we see onely that part which is illuminated But when the Moon is without the Ecliptick that part which is towards us is not exactly the same with that which is illuminated 10 To these three simple motions one of the Sunne another of the Moon and the third of the Earth in their own little Circles f g h i l k q r together with the Diurnal
which being done the Excentricity of the Earth will be cf. Seeing therefore the annual motion of the Earth is in the Circumference of an Ellipsis of which ♑ ♋ is the greater Axis ab cannot be the lesser Axis for ab and ♑ ♋ are equal Wherefore the Earth passing through a b will either pass above ♑ as through g or passing through ♑ will fall between c and a it is no matter which Let it pass therefore through g and let gl be taken equal to the straight line ♑ ♋ and dividing gl equally in i gi will be equal to ♑ ♋ il equal to f ♋ and consequently the point i will cut the Excentricity cf into two equal parts and taking ih equal to if hi will be the whole Excentricity If now a straight line namely the line ♎ i ♈ be drawn through i parallel to the straight lines ab and ed the way of the Sunne in Summer namely the Arch ♎ g ♈ will be greater then his way in Winter by 8 degrees and ¼ Wherefore the true Aequinoxes wil be in the straight line ♎ i ♈ and therefore the Ellipsis of the Earths annual motion will not pass through a g b l but through ♎ g ♈ l. Wherfore the annual motion of the Earth is in the Ellipsis ♎ g ♈ l and cannot be the Excentricity being salved in any other line And this perhaps is the reason why Kepler against the opinion of all the Astronomers of former time thought fit to bisect the Excentricity of the Earth or according to the Ancients of the Sunne not by diminishing the quantity of the same Excentricity because the true measure of that quantity is the difference by which the Summer Arch exceeds the Winter Arch but by taking for the Center of the Ecliptick of the great Orbe the point c neerer to f so placing the whole great Orbe as much neerer to the Ecliptick of the fixed Stars towards ♋ as is the distance between c i. For seeing the whole great Orbe is but as a point in respect of the immense distance of the fixed Starres the two straight lines ♎ ♈ and ab being produced both wayes to the beginnings of Aries and Libra will fall upon the same points of the Sphere of the fixed Stars Let therefore the Diameter of the Earth mn be in the plain of the Earths annual motion If now the Earth be moved by the Sunnes simple motion in the Circumference of the Ecliptick about the Center i this Diameter will bee kept alwayes parallel to itself and to the straight line gl But seeing the Earth is moved in the Circumference of an Ellipsis without the Ecliptick the point n whilst it passeth through ♎ ♑ ♈ will go in a lesser Circumference then the point m and consequently as soon as ever it begins to be moved it will lose its parallelisme with the straight line ♑ ♋ so that mn produced will at last cut the straight line gl produced And contrarily as soon as mn is past ♈ the Earth making its way in the internal Ellipticall line ♈ l ♎ the same mn produced towards m will cut lg produced And when the Earth hath allmost finished its whole circumference the same mn shall againe make a right angle with a line drawn from the center i a little short of the point from which the Earth began its motion And there the next yeare shall be one of the Aequinoctial points namely neer the end of ♠the other shall be opposite to it neer the end of ♓ And thus the points in which the Days and Nights are made equall doe every year fall back but with so slow a motion that in a whole year it makes but 51 first minutes And this relapse being contrary to the order of the Signes is commonly called the Praecession of the Aequinoxes Of which I have from my former Suppositions deduced a possible cause which was to be done According to what I have said concerning the cause of the Excentricity of the Earth and according to Kepler who for the cause thereof supposeth one part of the Earth to be affected to the Sunne the other part to be disaffected the Apogaeum Perigaeum of the Sunne should be moved every year in the same order and with the same velocity with which the Aequinoctiall points are moved and their distance from them should allwayes be the quadrant of a circle which seems to be otherwise For Astronomers say that the Aequinoxes are now the one about 28 degrees gone back from the first Star of Aries the other as much from the beginning of Libra So that the Apogaeum of the Sunne or the Aphelium of the Earth ought to be about the 28th degree of Cancer but it is reckoned to be in the 7th degree Seeing therefore we have not sufficient evidence of the 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 that so it is it is in vaine to seek for the 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 why it is so Wherefore as long as the motion of the Apogaeum is not observable by reason of the slownesse thereof and as long as it remaiues doubtful whether their distance from the Aequinoctiall points be more or lesse then a quadrant precisely so long it may be lawfull for me to thinke they proceed both of them with equall velocity Also I doe not at all meddle with the causes of the Excentricities of Saturne Jupiter Mars and Mercury Neverthelesse seeing the Excentricity of the Earth may as I have shewne be caused by the unlike constitution of the several parts of the Earth which are alternately turned towards the Sunne it is credible also that like effects may be produced in these other Planets from their having their Superficies of unlike parts And this is all I shall say concerning Sidereal Philosophy And though the causes I have here supposed be not the true causes of these Phaenomena yet I have demonstrated that they are sufficient to produce them according to what I at first propounded CHAP. XXVII Of Light Heat and of Colours 1 Of the immense Magnitude of some Bodies and the unspeakable Littleness of others 2 Of the cause of the Light of the Sun 3 How Light heateth 4 The generation of Fire from the Sunne 5 The generation of Fire from Collision 6 The cause of Light in Glow-wormes Rotten Wood and the Bolonian Stone 7 The cause of Light in the concussion of Sea-water 8 The cause of Flame Sparks and Colliquation 9 The cause why wet Hay sometimes burns of its own accord Also the cause of Lightning 10 The cause of the force of Gunpowder and what is to be ascribed to the Coals what to the Brimstone and what to the Nitre 11 How Heat is caused by Attrition 12 The distinction of Light into First Second c. 13 The causes of the Colours we see in looking through a Prisma of Glass namely of Red Yellow Blue and Violet Colour 14 Why the Moon and the Starres appear redder in the Horizon then in
it follows necessarily from hence that by reason of the fermentation of the whole Aire of which I have spoken in the 21 Chap. some of those Atomes meeting with others will cleave together by applying themselvs to one another in such manner as is agreeable to their motions and mutual contacts and seeing there is no Vacuum cannot be pulled asunder but by so much force as is sufficient to overcome their Hardness Now there are innumerable degrees of Hardness As for example there is a degree of it in Water as is manifest from this that upon a plain it may be drawn any way at pleasure by ones finger There is a greater degree of it in clammy liquors which when they are poured out doe in falling downwards dispose themselves into one continued thred which thred before it be broken will by little and little diminish its thickness till at last it be so small as that it seems to break onely in a point and in their separation the external parts break first from one another and then the more internal parts successively one after another In Wax there is yet a greater degree of Hardness For when we would pull one part of it from another we first make the whole mass slenderer before we can pull it asunder And how much the harder anything is which we would break so much the more force we must apply to it Wherefore if we go on to harder things as Ropes Wood Metals Stones c. reason prompteth us to believe that the same though not alwayes sensibly will necessarily happen and that even the hardest things are broken asunder in the same manner namely by Solution of their continuity begun in the outermost Superficies and proceeding successively to the innermost parts In like manner when the parts of Bodies are to be separated not by pulling them asunder but by breaking them the first separation will necessarily be in the convex Superficies of the bowed part of the Body and afterwards in the concave Superficies For in all bowing there is in the convex Superficies an endeavour in the parts to go one from another and in the concave Superficies to penetrate one another This being well understood a reason may be given how two Bodies which are contiguous in one common Superficies may by force be separated without the introduction of Vacuum though Lucretius thought otherwise believing that such separation was a strong establishment of Vacuum For a Marble Pillar being made to hang by one of its bases if it be long enough it will by its own weight be broken asunder and yet it will not necessarily follow that there should be Vacuum seeing the solution of its continuity may begin in the Circumference and proceed successively to the midst thereof Lastly Wine is not so easily congeled as Water because in Wine there are particles which being not fluid are moved very swiftly and by their motion congelation is retarded but if the Cold prevail against this motion then the outermost parts of the Wine will be first frozen and afterwards the inner parts whereof this is a signe that the Wine which remains unfrozen in the midst will be very strong 9 Another cause of Hardness in some things may be in this manner If a soft Body consist of many hard particles which by the intermixture of many other fluid particles cohaere but loosely together those fluid parts as hath been shewn in the last Article of the 21 Chapter will be exhaled by which means each hard particle will apply it self to the next to it according to a greater Superficies and consequently they will cohaere more closely to one another that is to say the whole mass will be made Harder 10 Again in some things Hardness may be made to a certain degree in this manner When any fluid substance hath in it certain very small Bodies intermingled which being moved with simple motion of their own contribute like motion to the parts of the fluid substance and this be done in a small enclosed space as in the hollow of a little Sphere or a very slender Pipe if the motion be vehement and there be a great number of these small enclosed Bodies two things will happen the one that the fluid substance will have an endeavour of dilating it self at once every way the other that if those smal Bodies can no where get out then from their reflexion it will follow that the motion of the parts of the enclosed fluid substance which was vehement before will now be much more vehement Wherefore if any one particle of that fluid substance should be touched pressed by some external Movent it could not yeild but by the application of very sensible force Wherefore the fluid substance which is enclosed and so moved hath some degree of Hardness Now greater and less degree of Hardness depends upon the quantity and velocity of those small Bodies and upon the narrowness of the place both together 11 Such things as are made Hard by sudden heat namely such as are hardned by fire are commonly reduced to their former soft form by Maceration For fire hardens by Evaporation and therefore if the evaporated moisture be restored again the former nature and form is restored together with it And such things as are frozen with Cold if the Wind by which they were frozen change into the opposite quarter they will be unfrozen again unless they have gotten a habit of new motion or endeavour by long continuance in that hardness Nor is it enough to cause thawing that there be a cessation of the freezing Wind for the taking away of the Cause doth not destroy a produced effect but the thawing also must have its proper cause namely a contrary Wind or at least a Wind opposite in some degree And this we finde to be true by experience For if Ice be laid in a place so well enclosed that the motion of the Aire cannot get to it that Ice will remain unchanged though the place be not sensibly cold 12 Of Hard Bodies some may manifestly be bowed others not but are broken in the very first moment of their bending And of such Bodies as may manifestly be bended some being bent do as soon as ever they are set at liberty Restore themselves to their former posture others remain still bent Now if the cause of this Restitution be asked I say it may be in this manner namely that the particles of the bended Body whilest it is held bent do nevertheless retain their motion and by this motion they restore it as soon as the force is removed by which it was bent For when any thing is bent as a plate of steel and as soon as the force is removed restores it self again it is evident that the cause of its restitution cannot be referred to the ambient aire nor can it be referred to the removal of the force by which it was bent for in things that are at rest the taking away of impediments is
not a sufficient cause of their future Motion there being no other cause of Motion but Motion The cause therefore of such Restitution is in the parts of the Steel it self Wherefore whilest it remains bent there is in the parts of which it consisteth some motion though invisible that is to say some endeavour at least that way by which the restitution is to be made and therefore this endeavour of all the parts together is the first beginning of Restitution so that the impediment being removed that is to say the force by which it was held bent it will be restored again Now the motion of the parts by which this is done is that which I called Simple Motion or Motion returning into it self When therefore in the bending of a plate the ends are drawn together there is on one side a mutual compression of the parts which compression is one endeavour opposite to another endeavour and on the other side a divulsion of the parts The endeavour therefore of the parts on one side tends to the restitution of the plate from the middle towards the ends and on the other side from the ends towards the middle Wherefore the impediment being taken away this endeavour which is the beginning of restitution will restore the plate to its former posture And thus I have given a possible cause why some Bodies when they are bent Restore themselves again which was to be done As for Stones seeing they are made by the accretion of many very hard particles within the Earth which particles have no great coherence that is to say touch one another in small latitude and consequently admit many particles of aire it must needs be that in bending of them their internal parts will not easily be compressed by reason of their hardness And because their coherence is not firm as soon as the external hard particles are disjoyned the aethereal parts will necessarily break out and so the Body will suddenly be broken 13 Those Bodies are called Diaphanous upon which whilest the Beams of a lucid Body do work the action of every one of those Beams is propagated in them in such manner as that they still retain the same order amongst themselves or the inversion of that order and therefore Bodies which are perfectly Diaphanous are also perfectly homogeneous On the contrary an Opacous Body is that which by reason of its heterogeneous nature doth by innumerable reflexions and refractions in particles of different figures and unequal hardness weaken the Beams that fall upon it before they reach the Eie And of Diaphanous Bodies some are made such by Nature from the beginning as the substance of the Aire and of the Water and perhaps also some parts of Stones unless these also be Water that has been long congeled Others are made so by the power of Heat which congregates homogeneons Bodies But such as are made Diaphanous in this manner consist of parts which were formerly Diaphanous 14 In what manner Clouds are made by the motion of the Sunne elevating the particles of Water from the Sea and other moist places hath been explained in the 26th Chapter Also how Clouds come to be frozen hath been shewn above at the 7th Article Now from this that Aire may be enclosed as it were in Caverns and pent together more and more by the meeting of ascending and descending Clouds may be deduced a possible Cause of Thunder and Lightening For seeing the Aire consists of two parts the one Aethereal which has no proper motion of its own as being a thing divisible into the least parts the other Hard namely consisting of many hard Atomes which have every one of them a very swift simple motion of its own whilest the Clouds by their meeting do more and more straighten such Cavities as they intercept the Aethereal parts will penetrate and pass through their watry substance but the hard parts will in the mean time be the more thrust together and press one another and consequently by reason of their vehement motions they will have an endeavour to rebound from each other Whensoever therefore the compression is great enough and the concave parts of the Clouds are for the cause I have already given congeled into Ice the Cloud wil necessarily be broken this breaking of the Cloud produceth the first clap of Thunder Afterwards the Aire which was pent in having now broken through makes a concussion of the Aire without and from hence proceeds the roaring and murmur which follows and both the first Clap and the Murmur that follows it make that noise which is called Thunder Also from the same Aire breaking through the Clouds and with concussion falling upon the Eie proceeds that action upon our Eie which causeth in us a perception of that Light which we call Lightening Wherefore I have given a possible cause of Thunder and Lightening 15 But if the Vapours which are raised into Clouds do run together again into Water or be congeled into Ice from whence is it seeing both Ice and Water are heavy that they are sustained in the Aire Or rather what may the cause be that being once elevated they fall down again For there is no doubt but the same force which could carry up that Water could also sustain it there Why therefore being once carried up doth it fall again I say it proceeds from the same Simple Motion of the Sunne both that Vapours are forced to ascend and that Water gathered into Clouds is forced to descend For in the 21th Chapter and 11th Article I have shewn how Vapours are elevated and in the same Chapter and 5th Article I have also shewn how by the same motion Homogeneous Bodies are congregated Heterogeneous dissipated that is to say how such things as have a like nature to that of the Earth are driven towards the Earth that is to say what is the cause of the descent of Heavy Bodies Now if the action of the Sun be hindered in the raising of vapours and be not at all hindered in the casting of them down the Water will descend But a Cloud cannot hinder the action of the Sunne in making things of an earthly nature descend to the Earth though it may hinder it in making Vapours ascend For the lower part of a thick Cloud is so covered by its upper part as that it cannot receive that action of the Sunne by which Vapours are carried up because Vapours are raised by the perpetual fermentation of the Aire or by the separating of its smallest parts from one another which is much weaker when a thick Cloud is interposed then when the Skie is cleere And therefore whensoever a Cloud is made thick enough the water which would not descend before will then descend unless it be kept up by the agitation of the Winde Wherefore I have rendred a possible cause both why the Clouds may be sustained in the Aire and also why they may fall down again to the Earth which was propounded to
in like manner is followed by the noxious matter contained in CB by this means the pit is for that time made healthful Out of this History which I write onely to such as have had experience of the truth of it without any designe to support my Philosophy with Stories of doubtful credit may be collected the following possible cause of this Phaenomenon namely that there is a certain matter fluid most transparent and not much lighter then water which breaking out of the Earth fills the Pit to C and that in this matter as in water both Fire and Living creatures are extinguished 15 About the nature of Heavy Bodies the greatest difficulty ariseth from the contemplation of those things which make other Heavy Bodies ascend to them such are Jet Amber and the Loadstone But that which troubles men most is the Loadstone which is also called Lapis Herculeus a stone though otherwise despicable yet of so great power that it taketh up Iron from the Earth and holds it suspended in the aire as Hercules did Antaeus Nevertheless we wonder at it somewhat the less because we see Jet draw up Straws which are Heavy Bodies though not so Heavy as Iron But as for Jet it must first be excited by rubbing that is to say by motion to and fro whereas the Loadstone hath sufficient excitation from its own nature that is to say from some internal principle of motion peculiar to it self Now whatsoever is moved is moved by some contiguous and moved Body as hath been formerly demonstrated And from hence it follows evidently that the first endeavour which Iron hath towards the Loadstone is caused by the motion of that aire which is contiguous to the Iron Also that this motion is generated by the motion of the next aire and so on successively till by this succession we find that the motion of all the intermediate air taketh its beginning from some motion which is in the Loadstone it self which motion because the Loadstone seems to be at rest is invisible It is therefore certain that the attractive power of the Loadstone is nothing else but some motiō of the smallest particles thereof Supposing therefore that those small Bodies of which the Loadstone is in the bowels of the Earth composed have by nature such motion or endeavour as was above attributed to Jet namely a reciprocal motiō in a line too short to be seen both those stones wil have one the same cause of attraction Now in what manner and in what order of working this cause produceth the effect of attraction is the thing to be enquired And first we know that when the string of a Lute or Viol is stricken the Vibration that is the reciprocal motion of that string in the same straight Line causeth like Vibration in another string which has like tension We know also that the dregs or small sands which sink to the bottom of a Vessel will be raised up from the bottom by any strong and reciprocal agitation of the water stirred with the hand or with a staff Why therefore should not reciprocal motion of the parts of the Loadstone contribute as much towards the moving of Iron For if in the Loadstone there be supposed such reciprocal motion or motion of the parts forwards and backwards it will follow that the like motion will be propagated by the aire to the Iron and consequently that there will be in all the parts of the Iron the same reciprocations or motions forwards and backwards And from hence also it will follow that the intermediate aire between the Stone and the Iron will by little and little be thrust away and the aire being thrust away the Bodies of the Loadstone and the Iron will necessarily come together The possible cause therefore why the Loadstone and Jet draw to them the one Iron the other Strawes may be this that those attracting Bodies have reciprocal motion either in a straight line or in an Elliptical line when there is nothing in the nature of the attracted Bodies which is repugnant to such a motion But why the Loadstone if with the help of Cork it float at liberty upon the top of the water should from any position whatsoever so place it self in the plain of the Meridian as that the same points which at one time of its being at rest respect the Poles of the Earth should at all other times respect the same Poles the cause may be this That the reciprocal motion which I supposed to be in the parts of the Stone is made in a line parallel to the Axis of the Earth and has been in those parts ever since the Stone was generated Seeing therefore the Stone whilest it remains in the Mine and is carried about together with the Earth by its diurnal motion doth by length of time get a habit of being moved in a line which is perpendicular to the line of its reciprocal motion it will afterwards though its axis be removed from the parallel situation it had with the axis of the Earth retain its endeavour of returning to that situation again and all endeavour being the beginning of motion and nothing intervening that may hinder the same the Loadstone will therefore return to its former situation For any piece of Iron that has for a long time rested in the plain of the Meridian whensoever it is forced from that situation and afterwards left to its own liberty again will of it self return to lie in the Meridian again which return is caused by the endeavour it acquired from the diurnal motion of the Earth in the parallel circles which are perpendicular to the Meridians If Iron be rubbed by the Loadstone drawn from one Pole to the other two things will happen one that the Iron will acquire the same direction with the Loadstone that is to say that it will lie in the Meridian and have its Axis and Poles in the same position with those of the Stone the other that the like Poles of the Stone and of the Iron will avoid one another and the unlike Poles approach one another And the cause of the former may be this that Iron being touched by motion which is not reciprocal but drawn the same way from Pole to Pole there will be imprinted in the Iron also an endeavour from the same Pole to the same Pole For seeing the Loadstone differs from Iron no otherwise then as Ore from Metal there will be no repugnance at all in the Iron to receive the same motion which is in the Stone From whence it follows that seeing they are both affected alike by the diurnal motion of the Earth they will both equally return to their situation in the Meridian whensoever they are put frō the same Also of the later this may be the cause that as the Loadstone in touching the Irō doth by its action imprint in the Iron an endeavour towards one of the Poles suppose towards the North Pole so reciprocally the
be so stretched as that there be left in it no boâ—ome at all for otherwise the straight lines LP MQ BK will not be perpendicular to the plain of the Sayl but falling below P Q and K will drive the Ship backwards But by making use of a small Board for a Sayl a little Waggon with wheels for the Ship and of a smooth Pavement for the Sea I have by experience found this to be so true that I could scarce oppose the board to the winde in any obliquity though never so small but the Waggon was carried forwards by it By the same 6th Theoreme it may be found how much a stroke which falls obliquely is weaker then a stroke falling perpendicularly they being like and equal in all other respects Let a stroke fall upon the Wall AB obliquely as for example in the straight line CA in the 3d figure Let CE be drawn parallel to AB DA perpendicular to the same AB equal to CA let both the velocity time of the motion in CA be equal to the velocity time of the motion in DA. I say the stroke in CA will be weaker then that in DA in the proportion of EA to DA. For producing DA howsoever to F the endeavour of both the strokes will by the 6th Art proceed from A in the perpendicular AF. But the stroke in CA is made by the concourse of two motions in CE and EA of which that in CE contributes nothing to the stroke in A because CE and BA are parallels and therefore the stroke in CA is made by the motion which is in EA onely But the velocity or force of the perpendicular stroke in EA to the velocity or force of the stroke in DA is as EA to DA. Wherefore the oblique stroke in CA is weaker then the perpendicular stroke in DA in the proportion of EA to DA or CA Which was to be proved 9 In a full Medium all Endeavour proceeds as far as the Medium it self reacheth that is to say if the Medium be infinite the Endeavour will proceed infinitely For whatsoever Endeavoureth is Moved and therefore whatsoever standeth in its way it maketh it yeild at least a little namely so far as the Movent it self is moved forwards But that which yeildeth is also moved and consequently maketh that to yeild which is in its way and so on successively as long as the Medium is full that is to say infinitely if the full Medium be infinite which was to be proved Now although Endeavour thus perpetually propagated do not alwayes appear to the Senses as Motion yet it appears as Action or as the efficient cause of some Mutation For if there be placed before our Eyes some very little object as for example a small grain of sand which at a certain distance is visible it is manifest that it may be removed to such a distance as not to be any longer seen though by its action it still work upon the organs of sight as is manifest from that which was last proved that all Endeavour proceeds infinitely Let it be conceived therefore to be removed from our Eyes to any distance how great soever and a sufficient number of other grains of sand of the same bigness added to it it is evident that the aggregate of all those sands will be visible and though none of them can be seen when it is single and severed from the rest yet the whole heap or hill which they make wil manifestly appear to the sight which would be impossible if some action did not proceed from each several part of the whole heap 10 Between the degrees of Hard and Soft are those things which we call Tough Tough being that which may be bended without being altered from what it was and the Bending of a Line is either the adduction or diduction of the extreme parts that is a morion from Straightness to Crookedness or contrarily whilest the line remains still the same it was for by drawing out the extreme points of a line to their greatest distance the line is made straight which otherwise is Crooked So also the Bending of a Superficies is the diduction or adduction of its extreme lines that is their Dilatation and Contraction 11 Dilatation and Contraction as also all Flexion supposes necessarily that the internal parts of the Body bowed do either come neerer to the external parts or go further from them For though Flexion be considered onely in the length of a Body yet when that Body is bowed the line which is made on one side will be convex and the line on the other side will be concave of which the concave being the interiour line will unless something be taken from it and added to the convex line be the more crooked that is the greater of the two But they are equal and therefore in Flexion there is an accession made from the interiour to the exteriour parts and on the contrary in Tension from the exteriour to the interiour parts And as for those things which do not easily suffer such transposition of their parts they are called Brittle and the great force they require to make them yield makes them also with sudden motion to leap asunder and break in pieces 12 Also Motion is distinguished into Pulsion and Traction And Pulsion as I have already defined it is when that which is moved goes before that which moveth it But contrarily in Traction the Movent goes before that which is moved Nevertheless considering it with greater attention it seemeth to be the same with Pulsion For of two parts of a hard Body when that which is foremost drives before it the Medium in which the motion is made at the same time that which is thrust forwards thrusteth the next and this again the next and so on successively In which action if we suppose that there is no place void it must needs be that by continual Pulsion namely when that action has gone round the Movent will be behind that part which at the first seemed not to be thrust forwards but to be drawn so that now the Body which was drawn goes before the Body which gives it motion and its motion is no longer Traction but Pulsion 13 Such things as are removed from their places by forcible Compression or Extension and as soon as the force is taken away doe presently return and restore themselves to their former situation have the beginning of their restitution within themselves namely a certain motion in their internal parts which was there when before the taking away of the force they were compressed or extended For that Restitution is motion and that which is at rest cannot be moved but by a moved and a Contiguous Movent Nor doth the cause of their Restitution proceed from the taking away of the force by which they were compressed or extended for the removing of impediments hath not the efficacy of a cause as has
at severall times is by Vehemence made stronger and more praedominant than the rest which deprives us of the Sense of other Phantasmes no otherwise then the Sun deprives the rest of the starres of light not by hindering their action but by obscuring and hiding them with his excesse of brightnesse 7. But the motion of the Organ by which a Phantasme is made is not commonly called Sense except the Object be present And the Phantasme remaining after the Object is removed or past by is called Fancy and in latine Imaginatio which word because all Phantasmes are not Images doth not fully answer the signification of the word Fancy in its generall acceptation Neverthelesse I may use it safely enough by understanding it for the Greek 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 IMAGINATION therefore is nothing else but Sense decaying or weakned by the absence of the Object But what may be the cause of this decay or weakning Is the Motion the weaker because the Object is taken away If it were then Phantasmes would alwayes and necessarily be less cleare in the Imagination then they are in Sense which is not true For in Dreams which are the Imaginations of those that sleep they are no less clear then in Sense it self But the reason why in men Waking the Phantasms of things past are more obscure then those of things present is this that their Organs being at the same time moved by other present Objects those Phantasmes are the lesse praedominant Whereas in Sleep the passages being shut up externall action doth not at all disturbe or hinder internall motion If this be true the next thing to be considered will be whether any cause may be found out from the supposition whereof it will follow that the passage is shut up from the externall Objects of Sense to the internall Organ I suppose therefore that by the continuall action of Objects to which a Reaction of the Organ and more esqecially of the Spirits is necessarily consequent the Organ is wearied that is its parts are no longer moved by the Spirits without some pain and consequently the Nerves being abandoned and grown slack they retire to their fountain which is the cavity either of the Brain or of the Heart by which means the action which proceeded by the Nerves is necessarily intercepted For Action upon a Patient that retires from it makes but little Impression at the first and at last when the Nerves are by little and little slackâ—ed none at all And therefore there is no more Reaction that is no more Sense till the Organ being refreshed by Rest and by a supply of new Spirits recovering strength and motion the Sentient awaketh And thus it seems to be alwayes unless some other praeternatural cause intervene as Heat in the internal parts from lassitude or from some disease stirring the Spirits and other parts of the Organ in some extraordinary manner 8 Now it is not without cause nor so casual a thing as many perhaps think it that Phantasmes in this their great variety proceed from one another and that the same Phantasmes sometimes bring into the mind other Phantasmes like themselves and at other times extreamly unlike For in the motion of any continued Body one part followes another by cohaesion and therefore whilst we turne our Eies and other Organs successively to many Objects the motion which was made by every one of them remayning the Phantasmes are renewed as often as any of those motions comes to be praedominant above the rest and they become praedominant in the same order in which at any time formerly they were generated by Sense So that when by length of time very many Phantasmes have been generated within us by Sense then allmost any thought may arise from any other thought in so much that it may seeme to be a thing indifferent and casuall which thought shall follow which But for the most part this is not so uncertain a thing to waking as to sleeping men For the thought or Phantasme of the desired End brings in all the Phantasmes that are meanes conducing to that end and that in order backewards from the last to the first and againe forwards from the beginning to the End But this supposes both Appetite and Judgement to discerne what meanes conduce to the end which is gotten by Experience and Experience is store of Phantasmes arising from the sense of very many things For 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 and Meminisse Fancy and Memory differ onely in this that Memory supposeth the time past which Fancy doth not In Memory the Phantasmes we consider are as if they were worne out with time but in our Fancy we consider them as they are which distinction is not of the things themselves but of the considerations of the Sentient For there is in Memory something like that which happens in looking upon things at a great distance in which as the small parts of the Object are not discerned by reason of their remotenesse so in Memory many accidents and places and parts of things which were formerly perceived by Sense are by length of time decayed and lost The perpetuall arising of Phantasmes both in Sense and Imagination is that which we commonly call Discourse of the Mind and is common to men with other living Creatures For he thta thinketh compareth the Phantasmes that passe that is taketh notice of their likenesse or unlikenesse to one another And as he that observes readily the likenesses of things of different natures or that are very remote from one another is said to have a good Fancy so he is said to have a good Judgement that finds out the unlikenesses or differences of things that are like one another Now this observation of differences is not perception made by a common Organ of Sense distinct from Sense or Perception properly so called but is Memory of the differences of particular Phantasmes remaining for some time as the distinction between Hot and Lucid is nothing else but the Memory both of a Heating and of an Enlightning Object 9 The Phantasmes of men that sleep are DREAMS Concerning which we are taught by experience these five things First that for the most part there is neither order nor coherence in them Secondly that we dream of nothing but what is compounded and made up of the Phantasmes of Sense past Thirdly that somtimes they proceed as in those that are drowsy from the interruption of their Phantasmes by little and little broken and altered through sleepiness and sometimes also they begin in the midst of sleep Fourthly that they are clearer then the Imaginations of waking men except such as are made by Sense itself to which they are equal in clearness Fifthly that when we dream we admire neither the places nor the looks of the things that appear to us Now from what hath been said it is not hard to shew what may be the causes of these Phaenomena For as for the first seeing all Order and Coherence proceeds from frequent
of this Evocation and Swelling and such as agreeth with the rest of the Phaenomena of Heat may be thought to have given the cause of the Heat of the Sunne It hath been shewn in the 5 article of the 21 chapter that the fluid Medium which we call the Aire is so moved by the simple circular motion of the Sunne as that all its parts even the least do perpetually change places with one another which change of places is that which there I called Fermentation From this Fermentation of the Aire I have in the 8 article of the last chapter demonstrated that the water may be drawn up into the clouds And I shall now shew that the fluid parts may in like manner by the same Fermentation be drawn out from the internall to the externall parts of our Bodies For seeing that wheresoever the fluid Medium is contiguous to the Body of any living creature there the parts of that Medium are by perpetuall change of place separated from one another the contiguous parts of the living creature must of necessity endeavour to enter into the spaces of the separated parts For otherwise those parts supposing there is no Vacuum would have no place to go into And therefore that which is most fluid and separable in the parts of the living creature which are contiguous to the Medium will go first out and into the place thereof will succeed such other parts as can most easily transpire through the poâ—es of the skin And from hence it is necessary that the rest of the parts which are not separated must all together be moved outwards for the keeping of all places full But this motion outwards of all parts together must of necessity press those parts of the ambient Aire which are ready to leave their places and therefore all the parts of the Body endeavouring at once that way makes the Body swell Wherefore a possible cause is given of Heat from the Sunne which was to be done 4 We have now seen how Light and Heat are generated Heat by the simple motion of the Medium making the parts perpetually change places with one another and Light by this that by the same simple motion Action is propagated in a straight line But when a Body hath its parts so moved that it sensibly both Heats and Shines at the same time then it is that we say Fire is generated Now by Fire I do not understand a Body distinct from matter combustible or glowing as Wood or Iron but the matter it self not simply and always but then onely when it shineth and heateth He therefore that renders a cause possible and agreeable to the rest of the Phaenomena namely whence and from what action both the Shining and Heating proceed may be thought to have given a possible cause of the generation of Fire Let therefore ABC in the first Figure be a Sphere or the portion of a Sphere whose Center is D and let it be transparent and homogeneous as Cristal Glass or Water and objected to the Sunne Wherefore the foremost part ABC will by the simple motion of the Sunne by which it thrusts forwards the Medium be wrought upon by the Sun-beams in the straight lines EA FB and GC which straight lines may in respect of the great distance of the Sunne be taken for parallels And seeing the Medium within the Sphere is thicker then the Medium without it those Beams will be refracted towards their perpendiculars Let the straight lines EA and GC be produced till they cut the Sphere in H and I and drawing the perpendiculars AD and CD the refracted Beams EA and GC will of necessity fall the one between AH and AD the other between CI and CD Let those refracted Beams be AK and CL. And again let the lines DKM DLN be drawn perâ—endicular to the Sphere and let AK and CL be produced till they meet with the straight line BD produced in O. Seeing therefore the Medium within the Sphere is thicker then that without it the refracted line AK will recede further from the perpendicular KM then KO will recede from the same Wherefore KO will fall between the refracted line and the perpendicular Let therefore the refracted line be KP cutting FO in P and for the same reason the straight line LP will be the refracted line of the straight line CL. Wherfore seeing the Beams are nothing else but the Wayes in which the motion is propagated the motion about P will be so much more vehement then the motion about ABC by how much the base of the portion ABC is greater then the base of a like portion in the Sphere whose Center is P and whose magnitude is equal to that of the little Circle about P which comprehendeth all the Beams that are propagated from ABC and this Sphere being much less then the Sphere ABC the parts of the Medium that is of the Aire about P will change places with one another with much greater celerity then those about ABC If therefore any matter Combustible that is to say such as may be easily dissipated be placed in P the parts of that matter if the proportion be great enough between AC and a like portion of the little circle about P wil be freed from their mutual cohaesion and being separated will acquire simple motion But vehement simple motion generates in the beholder a Phantasm of Lucid and Hot as I have before deâ—onstrated of the simple motion of the Sunne and therefore the combustible matter which is placed in P will be made Lucid and Hot that is to say will be Fire Wherefore I have rendered a possible cause of Fire which was to be done 5 From the manner by which the Sunne generateth Fire it is easy to explaine the manner by which Fire may be generated by the collision of two Flints For by that Collision some of those particles of which the stone is compacted are violently separated and thrown off and being withall swiftly turned round the Eie is moved by them as it is in the generation of Light by the Sunne Wherefore they shine and falling upon matter which is already halfe dissipated such as is Tinder they throughly dissipate the parts thereof and make them turn round From whence as I have newly shewn Light and Heat that is to say Fire is generated 6 The shining of Glow-worms some kinds of Rotten Wood and of a kinde of stone made at Bolognia may have one common cause namely the exposing of them to the hot Sunne We finde by experience that the Bolonian stone shines not unless it be so exposed and after it has been exposed it shines but for a little time namely as long as it retains a certain degree of heat And the cause may be that the parts of which it is made may together with heat have Simple Motion imprinted in them by the Sunne Which if it be so it is necessary that it shine in the dark as
But in the mean time the hard particles which are mingled with the Aire and are agitated as I have supposed with Simple Motion wil not pass through the water of the clouds but be more straightly compressed within their cavities And this I have demonstrated at the 4th and 5th Articles of the 22th Chapter Besides seeing the Globe of the Earth floateth in the Aire which is agitated by the Sunnes Motion the parts of the Aire resisted by the Earth will spread themselves every way upon the Earths Superficies as I have shewn at the 8th Article of the 21th Chapter 5 We perceive a Body to be Hard from this that when touching it we would thrust forwards that part of the same which we touch we cannot do it otherwise then by thrusting forwards the whole Body We may indeed easily and sensibly thrust forwards any particle of the Aire or Water which we touch whilst yet the rest of its parts remain to sense unmoved But we cannot do so to any part of a stone Wherfore I define a Hard Body to be that whereof no part can be sensibly moved unless the whole be moved Whatsoever therefore is Soft or Fluid the same can never be made Hard but by such motion as makes many of the parts together stop the motion of some one part by resisting the same 6 These things premised I shall shew a possible cause why there is greater Cold neer the Poles of the Earth then further from them The motion of the Sunne between the Tropicks driving the Aire towards that part of the Earths Superficies which is perpendicularly under it makes it spread it self every way and the velocity of this expansion of the Aire grows greater and greater as the Superficies of the Earth comes to be more and more straightned that is to say as the Circles which are parallel to the Aequator come to be less and less Wherefore this expansive motion of the Aire drives before it the parts of the Aire which are in its way continually towards the Poles more and more strongly as its force comes to be more and more united that is to say as the Circles which are parallel to the Aequator are less and less that is so much the more by how much they are neerer to the Poles of the Earth In those places therefore which are neerer to the Poles there is greater Cold then in those which are more remote from them Now this expansion of the Aire upon the Superficies of the Earth from East to West doth by reason of the Sunnes perpetual accession to the places which are successively under it make it Cold at the time of the Sunnes Rising and Setting but as the Sunne comes to be continually more and more perpendicular to those cooled places so by the Heat which is generated by the supervening Simple Motion of the Sunn that Cold is again remitted and can never be great because the action by the which it was generated is not permanent Wherefore I have rendred a possible cause of Cold in those places that are neer the Poles or where the obliquity of the Sunne is great 7 How Water may be congeled by Cold may be explained in this manner Let A in the first figure represent the Sunne and B the Earth A will therefore be much greater then B. Let EF be in the plain of the Equinoctial to which let GH IK and LC be parallel Lastly let C and D be the Poles of the Earth The Aire therefore by its action in those parallels will rake the Superficies of the Earth and that with motion so much the stronger by how much the parallel Circles towards the Poles grow less and less From whence must arise a Wind which will force together the uppermost parts of the water and withal raise them a little weakning their endeavour towards the Center of the Earth And from their endeavour towards the center of the Earth joyned with the endeavour of the said Wind the uppermost parts of the water will be pressed together and coagulated that is to say the top of the water will be skinned over and hardned And so againe the Water next the top will be hardned in the same manner till at length the Ice be thick And this Ice being now compacted of little hard Bodies must also containe many particles of ayre received into it As Rivers and Seas so also in the same manner may the Clouds be frozen For when by the ascending and descending of severall Clouds at the same time the Air intercepted between them is by compression forced out it rakes by little little hardens them And though those smal drops which usually make Clouds be not yet united into greater Bodies yet the same Wind will be made by it as water is congeled into Ice so will Vapours in the same manner be congeled into Snow From the same cause it is that Ice may be made by art and that not farre from the fire For it is done by the mingling of Snow and Salt together and by burying in it a small vessell full of Water Now while the Snow and Salt which have in them a great deale of aire are melting the aire which is pressed out every way in Wind rakes the sides of the Vessel and as the Wind by its motion rakes the Vessell so the Vessell by the same motion and action congeles the Water within it We find by experience that Cold is allwayes more Remisse in places where it raynes or where the weather is cloudy things being alike in all other respects then where the aire is cleare And this agreeth very well with what I have sayd before For in cleare weather the course of the Wind which as I sayd even now rakes the Superficies of the Earth as it is free from all interruption so also it is very strong But when small drops of water are either rising or falling that Wind is repelled broken and dissipated by them and the lesse the Wind is the lesse is the Cold. We find also by experience that in deep Wells the Water freezeth not so much as it doth upon the Superficies of the Earth For the Wind by which Ice is made entring into the Earth by reason of the laxity of its parts more or lesse loseth some of its force though not much So that if the Well be not deep it will freeze whereas if it be so deep as that the Wind which causeth cold cannot reach it it will not freeze We find moreover by experience that Ice is lighter then Water The cause whereof is manifest from that which I have already shewn namely that Aire is received in and mingled with the particles of the Water whilest it is in congeling 8 We have seen one way of making things Hard namely by Congelation Another way is thus Having already supposed that innumerable Atomes some harder then others and that have several simple motions of their own are intermingled with the aethereal substance
be done 16 Granting that the Clouds may be frozen it is no wonder if the Moon have been seen eclipsed at such time as she hath been almost two degrees above the Horizon the Sunne at the same time appearing in the Horizon for such an Eclipse was observed by Mestline at Tubing in the year 1590. For it might happen that a frozen Cloud was then interposed between the Sunne and the Eie of the Observer And if it were so the Sunne which was then almost two Degrees below the Horizon might appear to be in it by reason of the passing of his Beams through the Ice And it is to be noted that those that attribute such refractions to the Atmosphere cannot attribute to it so great a refraction as this Wherefore not the Atmosphere but either Water in a continued Body or else Ice must be the cause of that refraction 17 Again granting that there may be Ice in the Clouds it will be no longer a wonder that many Sunnes have sometimes appeared at once For Looking-glasses may be so placed as by reflections to shew the same object in many places And may not so many frozen Clouds serve for so many Looking-glasses and may they not be fitly disposed for that purpose Besides the number of Appearances may be encreased by refractions also and therefore it would be a greater wonder to me if such Phaenomena as these should never happen And were it not for that one Phaenomenon of the new Starre which was seen in Cassiopaea I should think Comets were made in the same manner namely by Vapours drawn not onely from the Earth but from the rest of the Planets also and congeled into one continued Body For I could very well from hence give a reason both of their Haire and of their motions But seeing that Starre remained sixteen whole moneths in the same place amongst the fixed Starres I cannot believe the matter of it was Ice Wherefore I leave to others the disquisition of the cause of Comets concerning which nothing that hath hitherto been published 〈…〉 the bare Histories of them is worth considering 18 The Heads of Rivers may be deduced from Rain-water or from melted Snowes very easily but from other causes very hardly or not at all For both Rain-water and melted Snowes run down the descents of Mountains and if they descend onely by the outward Superficies the Showres or Snowes themselves may be accounted the Springs or Fountains but if they enter the Earth descend within it then wheresoever they break out there are their Springs And as these Spings make small streams so many small streams running together make Rivers Now there was never any Spring foūd but where the Water w ch flowed to it was either further or at least as farre from the center of the Earth as the Spring it self And whereas it has bin objected by a great Philosopher that in the top of Mount-Cenis which parts Savoy from Piemont there Springs a River which runs down by Susa it is not true For there are above that River for two miles length very high hils on both sides which are almost perpetually covered with Snow from which innumerable little streams running down do manifestly supply that River with water sufficient for its magnitude CHAP. XXIX Of Sound Odour Savour and Touch 1 The definition of Sound and the distinctions of Sounds 2 The cause of the degrees of Sounds 3 The difference between Sounds Acute and Grave 4 The difference between Clear and Hoarse Sounds whence 5 The Sound of Thunder and of a Gunne whence it proceeds 6 Whence it is that Pipes by blowing into them have a clear Sound 7 Of Reflected Sound 8 From whence it is that Sound is Uniform and Lasting 9 How Sound may be helped aud hindered by the Wind. 10 Not onely Aire but other Bodies how hard soever they be conveigh Sound 11 The causes of Grave and Acute Sounds and of Concent 12 Phaenomena for Smelling 13 The first Organ and the generation of Smelling 14 How it is helped by Heat and by Wind. 15 Why such Bodies are least smelt which have least intermixture of Aire in them 16 Why Odorous things become more Odorous by being bruised 17 The first Organ of Tasting and why some Savours cause Nauseousness 18 The first Organ of Feeling and how we come to the knowledge of such Objects as are common to the Touch and other Senses SOUND is Sense generated by the action of the Medium when its motion reacheth the Eare and the rest of the Organs of Sense Now the motion of the Medium is not the Sound it self but the cause of it For the Phantasme which is made in us that is to say the Reaction of the Organ is properly that which we call Sound The principal distinctions of Sounds are these First that one Sound is stronger another Weaker Secondly that one is more Grave another more Acute Thirdly that one is Clear another Hoarse Fourthly that one is Primary another Derivative Fifthly that one is Uniform another not Sixthly that one is more Durable another less Durable Of all which distinctions the members may be subdistinguished into parts distinguishable almost infinitely For the variety of Sounds seems to be not much less then that of Colours As Vision so Hearing is generated by the motion of the Medium but not in the same manner For Sight is from Pressure that is from an Endeavour in which there is no perceptible progression of any of the parts of the Medium but one part urging or thrusting on an other propagateth that action successively to any distance whatsoever whereas the motion of the Medium by which Sound is made is a Stroke For when we Hear the Drumme of the Eare which is the first Organ of Hearing is stricken and the Drumme being stricken the Pia Mater is also shaken and with it the Arteries which are inserted into it by which the action being propagated to the Heart it self by the reaction of the Heart a Phantasm is made which we call Sound and because the reaction tendeth outwards we think it is without 2 And seeing the effects produced by Motion are greater or lesse not onely when the Velocity is greater or less but also when the Body hath greater or less Magnitude though the Velocity be the same a Sound may be greater or lesse both these wayes And because neither the greatest nor the least Magnitude or Velocity can be given it may happen that either the motion may be of so small velocity or the Body it self of so small magnitude as to produce no Sound at all or either of them may be so great as to take away the Faculty of Sense by hurting the Organ From hence may be deduced possible causes of the strength and weakness of Sounds in the following Phaenomena The first whereof is this That if a man speak through a Trunk which hath on end applyed to the mouth of the Speaker and the other to the eare of the
in all Concussion a reciprocation of Motion forwards and backwards in the parts stricken for opposite motions cannot extinguish one another in an instant as I have shewn in the 11th Art of the 8th Chap. it follows necessarily that the Sound will both continue and grow weaker and weaker till at last the action of the reciprocating aire grow so weak as to be unperceptible Wherefore a possible cause is given both of the first fierce Noyse of the Thunder and also of the Murmur that follows it The cause of the great Sound from a discharged piece of Ordnance is like that of a Clap of Thunder For the Gunpowder being fired doth in its endeavour to go out attempt every way the sides of the metal in such manner as that it enlargeth the Circumference all along and withall shortneth the axis so that whilest the peece of Ordnance is in discharging it is made both wider and shorter then it was before and therefore also presently after it is discharged its wideness will be diminished and its length encreased again by the restitution of all the particles of the matter of which it consisteth to their former position And this is done with such motion of the parts as are not onely very vehement but also opposite to one another which motions being communicated to the Aire make impression upon the Organ and by the reaction of the Organ create a Sound which lasteth for some time as I have already shewn in this Article I note by the way as not belonging to this place that the possible cause why a Gun recoyles when it is shot off may be this That being first swoln by the force of the fire and afterwards restoring it self from this restitution there proceeds an endeavour from all the sides towards the cavity and consequently this endeavour is in those parts which are next the breech which being not hollow but solid the effect of the restitution is by it hindered and diverted into the length and by this means both the breech and the whole Gun is thrust backwards and the more forcibly by how much the force is greater by which the part next the breech is restored to its former posture that is to say by how much the thiner is that part The cause therefore why Gunnes recoyle some more some less is the difference of their thickness towards the breech the greater that thickness is the less they recoyl and contrarily 6 Also the cause why the Sound of a Pipe which is made by blowing into it is nevertheless Clear is the same with that of the Sound which is made by collision For if the breath when it is blown into a Pipe doe onely rake its concave Superficies or fall upon it with a very sharp angle of incidence the Sound will not be Clear but Hoarse But if the angle be great enough the percussion which is made against one of the hollow sides will be reverberated to the opposite side and so successive repercussions will be made from side to side till at last the whole concave Superficies of the Pipe be put into motion which motion will be reciprocated as it is in Collision and this reciprocation being propagated to the Organ from the reaction of the Organ will arise a Cleare Sound such as is made by Collision or by breaking asunder of hard Bodies In the same manner it is with the Sound of a Mans voice For when the breath passeth out without interruption and doth but lightly touch the cavities through which it is sent the Sound it maketh is a Hoarse Sound But if in going out it strike strongly upon the Larinx then a Clear Sound is made as in a Pipe And the same breath as it comes in divers manners to the Palate the Tongue the Lips the Teeth and other Organs of Speech so the Sounds into which it is articulated become different from one another 7 I call that Primary Sound which is generated by motion from the sounding Body to the Organ in a straight line without reflexion and I call that Reflected Sound which is generated by one or more reflexions being the same with that we call Echo and is iterated as often as there are reflexions made from the Object to the Eare. And these reflexions are made by Hils Wals and other resisting Bodies so placed as that they make more or fewer reflexions of the motion according as they are themselves more or fewer in number and they make them more or less frequently according as they are more or less distant from one another Now the cause of both these things is to be sought for in the situation of the reflecting Bodies as is usually done in Sight For the Lawes of Reflexion are the same in both namely that the Angles of Incidence and Reflexion be equal to one another If therefore in a hollow Elliptique Body whose inside is well polished or in two right Parabolical Solids which are joyned together by one common base there be placed a Sounding Body in one of the Burning Points the Ear in the other there will be heard a Sound by many degrees greater then in the open Aire and both this and the burning of such combustible things as being put in the same places are set on fire by the Sun-beams are effects of one and the same cause But as when the visible Object is placed in one of the Burning Points it is not distinctly seen in the other because every part of the Object being seen in every line which is reflected from the Concave Superficies to the Eie makes a confusion in the Sight so neither is Sound heard articulately and distinctly when it comes to the Eare in all those reflected lines And this may be the reason why in Churches which have arched rooffs though they be neither Elliptical nor Parabolical yet because their figure is not much different from these the voice from the Pulpit will not be heard so articulately as it would be if there were no vaulting at all 8 Concerning the Uniformity and Duration of Sounds both which have one common cause we may observe that such Bodies as being stricken yeild an unequal or harsh Sound are very heterogeous that is to say they consist of parts which are very unlike both in figure and hardness such as are Wood Stones and others not a few When these are stricken there follows a concussion of their internal particles and a restitution of them again But they are neither moved alike nor have they the same action upon one another some of them recoyling from the stroke whilest others which have already finished their recoylings are now returning by which means they hinder and stop on another And from hence it is that their motions are not only unequal and harsh but also that their reciprocations come to be quickly extinguished Whensoever therfore this motion is propagated to the Eare the Sound it makes is Unequal and of small Duration On the contrary if a Body
that is stricken be not onely sufficiently hard but have also the particles of which it consisteth like to one another both in hardness and figure such as are the particles of Glass and Metals which being first melted do afterwards settle and harden the Sound it yeildeth will because the motions of its parts and their reciprocations are like and Uniform be Uniform and pleasant and be more or less Lasting according as the Body stricken hath gteater or less magnitude The possible cause therefore of Sounds Uniform and Harsh and of their longer or shorter Duration may be one and the same likeness and unlikeness of the internal parts of the Sounding Body in respect both of their figure and hardness Besides if two plain Bodies of the same matter and of equal thickness do both yeild an Uniform Sound the Sound of that Body which hath the greatest extent of length will be the longest heard For the motion which in both of them hath its beginning from the point of percussion is to be propagated in the greater Body through a greater Space and consequently that propagation will require more time and therefore also the parts which are moved will require more time for their return Wherefore all the reciprocations cannot be finished but in longer time and being carried to the Eare will make the Sound last the longer And from hence it is manifest that of hard Bodies which yeild an Uniform Sound the Sound lasteth longer which comes from those that are round and hollow then from those that are plain if they be like in all other respects For in circular lines the action which begins at any point hath not frō the figure any end of its propagation because the line in which it is propagated returns again to its beginning so that the figure hinders not but that the motion may have infinite progression whereas in a plain every line hath its magnitude finite beyond which the action cannot proceed If therefore the matter be the same the motion of the parts of that Body whose figure is round and hollow wil last longer then of that which is plain Also if a string which is stretched be fastned at both ends to a hollow Body and be stricken the Sound will last longer then if it were not so fastned because the trembling or reciprocation which it receives from the stroke is by reason of the connexion communicated to the hollow Body and this trembling if the hollow Body be great will last the longer by reason of that greatness Wherefore also for the reason above mentioned the Sound will last the longer 9 In Hearing it happens otherwise then in Seeing that the action of the Medium is made stronger by the Wind when it blows the same way and weaker when it blows the contrary way The cause whereof cannot proceed from any thing but the different generation of Sound and Light For in the generation of Light none of the parts of the Medium between the object and the Eie are moved from their own places to other places sensibly distant but the action is propagated in spaces imperceptible so that no contrary Wind can diminish nor favourable Winde encrease the Light unless it be so strong as to remove the Object further off or bring it nearer to the Eie For the Wind that is to say the aire moved doth not by its interposition between the object and the eie worke otherwise then it would doe if it were stil and calme For where the pressure is perpetuall one part of the aire is no sooner carried away but another by succeeding it receives the same impression which the part carried away had received before But in the generation of Sound the first collision or breaking asunder beateth away driveth out of its place the nearest part of the aire and that to a considerable distance and with considerable velocity and as the circles grow by their remotenesse wider and wider so the aire being more more dissipated hath also its motion more more weakned Whensoever therfore the air is so stricken as to cause Sound if the Wind fall upon it it will move it all neerer to the Eare if it blow that way and further from it if it blow the contrary way so that according as it blowes from or towards the Object so the Sound which is heard will seeme to come from a neerer or remoter place and the action by reason of the unequall distances be strengthened or debilitated From hence may be understood the reason why the voice of such as are said to speake in their bellies though it be uttered neer hand is neverthelesse heard by those that suspect nothing as if it were a great way off For having no former thought of any determined place from which the voice should proceed and judging according to the greatesse if it be weake they thinke it a great way off if strong neer These Ventriloqui therefore by forming their voice not as others by the emission of their breath but by drawing it inwards doe make the same appear small and weake which weaknesse of the voice deceives those that neither suspect the artifice nor observe the endeavour which they use in speaking and so instead of thinking it weake they thinke it farre off 10 As for the Medium which conveighs Sound it is not Aire onely For Water or any other Body how hard soever may be that Medium For the Motion may be propagated perpetually in any hard continuous Body but by reason of the difficulty with which the parts of hard Bodies are moved the motion in going out of hard matter makes but a weak impression upon the Aire Nevertheless if one end of a very long and hard beam be stricken the eare be applyed at the same time to the other end so that when the action goeth out of the beam the aire which it striketh may immediately be received by the eare and be carried to the Tympanum the Sound will be considerably strong In like manner if in the night when all other noyse which may hinder Sound ceaseth a man lay his eare to the ground he will hear the Sound of the steps of Passengers though at a great distance because the motion which by their treading they communicate to the earth is propagated to the eare by the uppermost parts of the earth which receiveth it from their feet 11 I have shewn above that the difference between Grave and Acute Sounds consisteth in this that by how much the shorter the time is in which the reciprocations of the parts of a Body stricken are made by so much the more Acute will be the Sound Now by how much a Body of the same bigness is either more heavy or less stretched by so much the longer will the reciprocations last and therefore heavier and less stretched Bodies if they be like in all other respects will yeild a Graver Sound then such as be lighter and more stretched 12 For the finding out