Arms to any angle may not vary the centre of the Ball or Cross out of the point where the two Axes cut each other Both these Arms are to be made so as to be inclined to any angle that is that the Axis of the Medium taken hold of by the Arms of Iron may be made to incline to the axis of the Rod on which they are in any angle desired and being set to that Angle to be steadily fixed which may be done by a pin screw or wedge the way I make use of for the Azimuth-Instrument described in the 73 p. of my Animadversions is this which is delineated and explained in the 9th Fig. where G represents a socket of Brass movable cylindrically round about the end or neck B of the Axis or Rod B B the same with a b in the 22 Fig. of my Animadversions and fixable in any posture desired by help of a side-Screw h such as is very commonly made use of for most Instruments that are fixed upon the end of a three legg'd Staff and is commonly called a Cylinder and Socket this Socket of Brass hath a small Rod of Iron k fixed into it at k which is near the middle of its concave part through this Rod there is made a small eye or hole and through that hole a wedge-like pin m being thrust serves to keep the Semicircular Iron-arms C C steady and fixed in any posture they shall be rectified to The Semicircular-arms C C are to be made of very good Iron or rather Steel and to have a channel or grove quite through the middle of one of them and extending the whole length of a quadrant of a Circle namely from n to o because according to the variety of occasions it may be varied to any point between n and o and 't is to be observed that the Iron-rod k must be so far fixed out of the axis of the Socket g as n is distant from i or o from p the middle of the Iron-arms between i and i that so when there is occasion the Centre-hole or hands i may be moved to p and fastned At q must be made a Joynt in the Semicircular-arms so that when the end n of the Arms is fixed in or near k the other arm C may fall back from the point i otherwise the circular motion in many cases cannot be continued quite round and communicated from one Rod to the other by help of the Medium or Plate x. The several pieces of this Joynt as they are apart and distinct you may see in the 9th Figure and as they are joyned all together sit for motion you may see in the tenth Figure to which also the description of every part is adjoyned in words referred to by the help of Literal marks I hope will make it sufficiently plain to any Artist to understand Thirdly The medium Ball or Cross X must be made of a bigness suitable to the Arms and Cylinders and great care must be had that all the ends points or handles lie exactly in the same plain and that they be all equally distant from their Center at least that any two opposite ones be so made because it is not absolutely necessary that they should be so all four though in most cases it be best and farther the Handles or Pivots ought to be exactly round conical or cylindrical and the middle lines of them to cut each other at right angles or upon a square and in general that all things about the said Joynt be so contrived and wrought that the Axis of the two Rods may alwaies cut each other in the centre of the medium Cross or Plate and that the said Centre whatever change happens to the Joynt may alwaies keep exactly in the same very point without any alteration The shape of this Medium may be either a Cross whose four ends hath each of them a Cylinder which is the weakest way 't is described in the 9 and 10th Figures by the Cross X or secondly it may be made of a thick plate of Brass upon the edge of which are fixed four Pivots which serve for the handles of the Iron-arms to take hold of this is much better than the former but hath not that strength and steadiness that a large Ball hath which is the way I most approve of as being strong steady and handsome these are delineated in the aforesaid Figures by X x and X x x. If it be an Elliptical Dial to be described by the Orthographical projection the former way for describing Tangent Dials gives the lines that divide the Ellipsis of the Equinox in its true proportions and if you would have the Lines that divide the Ellipsis of either Tropick or of any other parallel Circle you must rectifie the Semicircular Arms C C of the Axis B B to the degree of the declination of that Parallel and them proceeding as before you have the Lines which from the aforesaid Circle divide the Ellipsis of that Parallel accordingly Perpendiculars also let fall from the ends of the Cross 11 give the true Ellipsis in the Orthographical projection answering to that Parallel These Lines thus found are the true azimuth Lines of the points or divisions of that Parallel and are this way traced out exactly without any trouble of Calculation which for some purposes in Surveying Navigation c. are of very great use as I shall afterwards shew The Universality of this Contrivance for resolving almost all Spherical Questions makes it of very great use in Navigation if it be adapted as it ought to be especially for the Common Sea-mans use who with a very few Rules will be able immediately to find the hour and azimuth of any point in the Heaven sufficiently accurate for most Observations that can be made at Sea of which more hereafter For making the Hand or Index of a Clock move in the shadow of the Style made upon the Face of the Dial and exposed to the Sun this Joynt being made to joyn the arbor of the Wheel that goeth round in twenty four hours with the arbor of the hand performeth it without any other Wheel or Pinion in the Dial or Face part of the Clock if the Arbor of the Clock that should have carried the Hand round in twenty four hours be made to have the same inclination to the plain of the Dial that the Axis hath whether parallel to the Axis or not it matters not at all so that the Hand be rectified accordingly as it ought to be and that the Style of the Dial ariseth from the centre of the Dial out-through which the Arbor is produced for carrying the Hand and placed in its Parallel respect to the Axis as it ought to be for a Tangent Dial. For the shadow-Line of the Axis upon the plain of the Dial being alwaies carried round the centre of a Dial in a plain which passeth through the Axis or Style and maketh equal progressions about it in equal spaces
of Time and unequal progressions upon the Dial-plain according to the proportion of Inclination and the whole Revolution being performed in twenty four hours and the Hand of the Clock upon the Face of the Dial being alwaies moved in a plain which passeth through the Arbor of the Clock and maketh equal progressions in equal spaces about the said Arbor but unequal progression about the Centre of the Dial according to the differing Inclinations And those Inclinations being both in the Sun-Dial and Clock-Dial the same it will follow that the Hand of the Clock must alwaies move in the shadow of the Style if the Hand be once rectified to the true Plain and the Axis or Arbor make its Revolution as it ought to do in twenty four hours If it be further desired for the ease of taking Azimuths and Altitudes that the Arm of the Azimuth quadrant that is once adjusted to the Coelestial Object should by the aforesaid Joynt or Instrument be kept alwaies respecting and following the said Object in its Diurnal motion it may be very easily performed by the help of a small perpendicular Ruler whose lower end is Joynted into either of the Arms 11 of the circular Plate X in the 22 and 23d Figure of my Animadversions and the upper end joynted into the movable Arm at the same distance from the Centre of the Quadrant that the lower end is from the centre of the Plate X and that the centre of the Quadrant be set exactly perpendicular over the centre of X but then the divisions by the help of the Screw cannot be made use of because the Clock-work it self is to turn and move the Arm But it may be done by any Quadrant where the minute Divisions are performed by the help of Diagonals For the Arms of the Circular-plate 11 being alwaies moved in the superficies of the Cone described by the radiation from the Coelestial Object to the centre of the Plate X that is to say the Line that passes through the Centre of the said Plate and through the two Points 11 being alwaies directed to the Coelestial Object if the Arm of the Quadrant be moved perpendicular over it and parallel to it that also must be alwaies directed to it And hence it may very easily be conceived how the aforesaid Semicircular Arms may be readily and certainly rectified to any Coelestial Object that is by fixing Telescopes or Common-sights upon the Circular-plate so as the Axis of them may be parallel to the Line through 11 and loosing the Screw h to rectifie it to the Object by the sight and then immediately to fix it in the said posture by the aforesaid Screw the Clock-work of the said Instrument having been before that put into motion The reason of all which will easily appear to any one that throughly considers that all Celestial Objects seem by the diurnal motion of the Earth to move equally from East to West about the Axis of it and would all do exactly so were they not somewhat varied by their own proper periodical revolutions which though it doth indeed make a real difference between their velocities about the Axis of the Earth yet that difference is but small and the same circular Pendulum will serve both for the Sun Moon Planets and Stars if at least the Pendulum p in the fifteenth Figure be a little lengthened or shortened by lifting up or letting down the Rod q q in proportion as the Body k moves swifter or flower And 't will not be difficult to mark upon the Rod q q the appropriated length of the Pendulum for the Sun Moon or Stars but this only by the by If in the next place it be desired that the Hand of the Clock should be alwaies carried round upon the face of the Clock in the shadow of a Style perpendicular to that plain by reason that the declination of the Sun daily varieth the angles of the shadow about that Style varieth also and consequently the inclination of the plate of the Joynt to the Axis or Arbor must vary also and that variation must alwaies be the same with the variation of the declination of the Sun which is twenty waies mechanically performable in Clock-work so that the motion shall be performed by the Clock-work alone without touching it with the hand All the other directions that are requisite to adjust the Clock-work to such a Dial is only to make the Arbor of the Clock-work to have the same inclination to the plain of the Dial that the Axis of the Earth or a line paralel to it hath and rectifying the Hand into the true plain of the Axis or Inclined arbor the equality of the motion of the Clock-work according to the diurnal and annual motion of the Sun we suppose also to be provided for If the Hand of the Clock be desired to be moved in the shadow of any other streight Style howsoever inclined to the plain of the Dial then must there be another Joynt like the former added to the end of that Axis which was perpendicular to the plain of the Dial and all the three Axes must be scituate in respect of the Plain in which the Hand on the end of the last is to move that the inclination of the said Axes to each other may represent the inclination of the Axis to the perpendicular axis of the Plain and of that perpendicular Axis to the axis of the Style Or which is somewhat shorter and may be made handsome enough Let the two ends of the Hand represent the two points of the second circular Plate or Globe extended long enough to reach to the hour Circle then let the axis of this second Arm be placed in the axis of the inclined Style and let the axis of equal motion representing the axis of the diurnal motion of the Earth be placed with such inclination to it as the axis of the Earth hath to the oblique Axis or Style of the Dial and the motion will be most exactly performed mechanically and according to the truth of Geometry and Calculation Now in all these motions care must be taken to provide that the inclination of the declination of the Sun from the Equinoctial be exprest by the ends 11 in the 22 and 23 Figures of the second Plate of my Animadversions of the Cross taken hold of by the semicircular arms c d upon the end of the first Axis that is that the said arms may by their revolution make the line of the Cross describe such a cone about the first Axis as the motion of the Sun doth about the axis of the Earth making the centre of the Earth the apex of that Cone which will be done if the said semicircular Arms be moved and set to the declination of the Sun for that day Or that an additional motion be added to the first Axis that the Clock it self may perform it This may be done twenty waies easily enough which I suppose will be sufficiently
to return or bend upwards again So that the Plain of the upper Superficies of the Oyl may cut that end of the Siphon where the flame is between the top of the mouth of it next the Socket and the return thereof upwards then by a counterpoise so suspend this Siphon that it may follow the Oyl as it wasts and fit into the return of the Siphon a Socket and Wick for the flame to be continued A contrivance somewhat of this kind you have in divers Authors and therefore I shall spend less time in the description thereof Let A A A A in the Sixth Figure then represent a large Cylindrical Viol of Glass through the mouth B of which the Cavity thereof may be filled with Oyl and also the end D and float C of a convenient Siphon may be put in This Siphon D D D P G must be made long enough that the float C may reach the bottom of the Vessel when the Oyl is spent and the other end thereof must be so curved that the knee of the Siphon P may be below the Superficies of the Oyl E F and yet that the Socket H made for holding the Wick for the flame I may be somewhat above it this Siphon D D D P G with its Socket and float should be so counterpoised with a weight M hung over a Pulley K by a string L that the float may not sink deep into the Surface of the Liquor but swim as it were at the top This done if the Wick I be lighted the Surface of the Oyl will be kept always at the same distance below the flame that it was first put at In the first third fourth and fifth ways the flame of the Lamp descends equal spaces with the Superficies of the Oyl in the Vessel and therefore though for some uses it be very convenient as in annealings where things are to be cooled by degrees yet for many other it is not Especially in Lamp Furnaces where the same heat is to be continued and in some cases gradually increased For such cases therefore the first and second ways will be very convenient In some other cases the sixth and seventh ways which do much the same thing The sixth way then is this Through an arm or Siphon like the Branch of a Lamp hung against a Wall fixed in any convenient place the Oyl from the Receptacle is continually and equally supplied to the flame of the Lamp by the raising of the Receptacle as fast as the Oyl wasts so as to keep the Superficies of the Oyl alway in the same Horizontal Plain The Receptacle is raised by a Counterpoise hung upon a Fusey which Fusey is a part of an Archimedean Spiral Let C C then in the seventh Figure represent the Receptacle for the Oyl being a Cylindrical or Prismatical Vessel of what Bigness or Length you please to this by two Ears at L L fasten two Lines or Ropes K K the ends of both which are fastned to the Wheel or Pulley G though one of them do run over the Pulley F. Fit into this Receptacle is made a Cylindrical or Prismatical Plug A A which is fixed in some convenient place so as not to rise or sink and through the middle thereof passeth a Siphon B B B the one end whereof extended like the branch of a Candle or Lamp sustains the Socket D for the Flame E which is fed with Oyl through the Siphon B B B by the rising Receptacle C C. To the side of the Pulley G is fastned a Fusey H made with very great care of one Revolution of an Archimedean Spiral not beginning from the Center but from some convenient distance from it where the weight I hanging may just counterpoise the Receptacle C C when quite empty of Oyl the other hanging counterpoise Tangent to the largest part of this Spiral must be so far distant from the Center of the Wheel G that the same weight I may just counterpoise the said Receptacle filled top-full of Oyl and the Fusey must be filed true to a Spiral drawn with great care of one Revolution between those two points I say here of one Revolution because I have supposed the Wheel or Pulley G big enough by one Revolution of it to draw up the Receptacle the whole space it is to be raised for if the said Pulley be so small as to require two three four or more Revolutions then must the piece of the Spiral between those points be drawn of two three four or more Revolutions proportionably which being very Artificially and Mechanically performed the Receptacle C C will be raised by the same Degrees by which the Oyl is consumed at E and the upper Superficies thereof shall always be in the same Horizontal Line MM. The Geometrical and Mechanical Reason of which being so very plain I hope I shall not need to spend any more time in the explication thereof than only to say that by means of the Archimedean Spiral-Fusey the Power of the weight I upon the Pulley G decreaseth in the same proportion as the weight of the Oyl in the Receptacle C C is diminished by its consumption The seventh way then is by a Cylindrical or Prismatical Plug fitted into a Cylindrical or Prismatical Receptacle and let down into it by a Counterpoise hung upon a Spiral Fusey the Oyl is so raised in that Receptacle as always to stand Brimfull or to the same Horizontal height till the whole Oyl be consumed The contrivance of this way will be very easily understood by any one that shall peruse the Delineation in the eighth Figure and examine it by this following description Let A A in the eighth Figure then represent a Cylindrical or Prismatical Receptacle standing fixt upon a Table or Pedestal from the side of which issues a hollow Arm or Branch B B bearing the Socket for the Wick C where the flame D is continued Into the Cavity of this Receptacle is fitted a Cylindrical or Prismatical Plug E E big enough to fill the whole capacity thereof and yet not so close but that it may freely slip up and down the Cavity of the said Receptacle without sinking Let this Plug be made considerably heavier than the Oyl of the Receptacle that is let the Counterpoise L hanging upon the little Wheel M just reduce its gravity to be equal to that of the Oyl then let the point I where the Perpendicular toucheth the Spiral be so far removed from the Center of the Wheel H that the counterpoise L may just take off its whole gravity and suffer it to have no degree of gravity or pressure downwards Then draw the Spiral n o p according to the direction I gave in the former way and the effect will be produced The Geometrical and Mechanical Demonstration of which is very plain to any one that shall consider that As the Plug E E by sinking into the Receptacle A A so far as to raise the Oyl to the Horizontal Superficies M
fourth as the Root of 64. that is of 19+17+15+13 at the end of the tenth or whole as the Root of 100. that is as equal to 100. Now since the Velocity is in the same proportion to the root of the space as the root of the space is to the time it is easie to determine the particular time in which every one of these spaces are passed for dividing the spaces by the Velocities corresponding the quotients give the particular times To explain this more intelligibly let A in the fourth figure represent the end of a Spring not bent or at least counterpoised in that posture by a power fixt to it and movable with it draw the line A B C and let it represent the way in which the end of the Spring by additional powers is to be moved draw to the end of it C at right Angles the Line C δ D d and let C D represent the power that is sufficient to bend or move the end of the Spring A to C then draw the Line D A and from any point of the Line A C as B B. Draw Lines parallel to C D cutting the Line D A in E E the Lines B E B E will represent the respective powers requisite to bend the end of the Spring A to B which Lines B E B E C D will be in the same proportion with the length of the bent of the Spring A B A B A C. And because the Spring hath in every point of the Line of bending A C a particular power therefore imagining infinite Lines drawn from every point of A C parallel to C D till they touch the Line A D they will all of them fill and compose the Triangle A C D. The Triangle therefore A C D will represent the aggregate of the powers of the Spring bent from A to C and the lesser Triangles A B E A B E will represent the aggregate of all the powers of the Spring bent from A to B B and the Spring bent to any point of the Line A C and let go from thence will exert in its return to A all those powers which are equal to the respective ordinates B E B E in the Triangles the sum of all which make up the Triangles A B E A B E. And the aggregate of the powers with which it returns from any point as from C to any point of the space C A as to B B is equal to the Trapezium C D E B C D E B or the excesses of the greater Triangles above the less Having therefore shewn an Image to represent the flexure and the powers so as plainly to solve and answer all Questions and Problems concerning them in the next place I come to represent the Velocities appropriated to the several powers The Velocities then being always in a subduplicate proportion of the powers that is as the Root of the powers impressed and the powers imprest being as the Trapezium or the excess of the Triangle or square of the whole space to be past above the square of the space yet unpassed if upon the Center A and space A C C being the point from which the Spring is supposed let go a Circle be described as C G G F and ordinates drawn from any point of C A the space to be past as from B B to the said Circle as B G B G these Lines B G B G will represent the Velocity of the Spring returning from C to B B c. the said ordinates being always in the same proportion with the Roots of the Trapeziums C D E B C D E B for putting A C = to a and A B = b B G will always be equal to the square of the ordinate being always equal to the Rectangle of the intercepted parts of the Diameter Having thus found the Velocities to wit B G B G A F to find the times corresponding on the Diameter A C draw a Parabola C H F whose Vertex is C and which passeth through the point F. The Ordinates of this Parabola B H B H A F are in the same proportion with the Roots of the spaces C B C B C A then making G B to H B as H B to I B and through the points C I I F drawing the curve C I I I F the respective ordinates of this curve shall represent the proportionate time that the Spring spends in returning the spaces C B C B C A. If the powers or stiffness of the Spring be greater than what I before supposed and therefore must be expressed by the Triangle C de A. then the Velocities will be the Ordinates in an Ellipse as C γ γ N greater than the Circle as it will also if the power be the same and the bulk moved by the Spring be less Then will the S-like Line of times meet with the Line A F at a point as X within the point F. But if the powers of the Spring be weaker than I supposed then will C δ e e A represent the powers and C γ γ O the Ellipsis of Velocity whose Ordinates B γ B γ A O will give the particular Velocities and the S-like Line of time will extend beyond N. The same will happen supposing the body moved by the Spring to be proportionately heavy and the powers of the Spring the same with the first And supposing the power of the Spring the same as at first bended only to B 2 and from thence let go B 2 E A is the Triangle of its powers the Ordinates of the Circle B g L are the Lines of its Velocity and the Ordinates of the S-like Line B i F are the Liues of time Having thus shewed you how the Velocity of a Spring may be computed it will be easie to calculate to what distance it will be able to shoot or throw any body that is moved by it And this must be done by comparing the Velocity of the ascent of a body thrown with the Velocity of the descent of Gravity allowance being also made for the Resistance and impediment of the medium through which it passes For instance suppose a Bow or Spring fixed at 16 foot above a Horizontal floor which is near the space that a heavy body from rest will descend perpendicularly in a second of time If a Spring deliver the body in the Horizontal line with a Velocity that moves it 16 foot in a second of time then shall it fall at 16 foot from the perpendicular point on the floor over which it was delivered with such Velocity and by its motion shall describe in the Air or space through which it passes a Parabola If the Spring be bent to twice the former Tension so as to deliver the body with double the Velocity in a Horizontal Line that is with a Velocity that moves 32 foot in a second then shall the body touch the floor in a point very near at 32 foot from the aforesaid perpendicular point and the
Instrument to adjust it upon that Frame the whole Table and Quadrant being so counterpois'd as to be easily moveable and fixt in any posture But Hevelius is pleas'd as I said before wholly to lay aside all manner of Wooden Instruments as useless and to indeavour the obtaining of Instruments of Brass or Iron Nam sayes he pag. 136. cùm longâ experientiâ probe tandem didicerim multo securius esse ex solido prorsus metallo obtinere Instrumenta tum quo majora ampliora eo esse accuratiora absolutiora adhaec prioribus admodum Tichonicum constructis plurima deesse quibus ditari merito deberent quod iisdem de causis omnino necessum sit ut parte corrigerentur meliorentur tam quà eorum materiam fructuram commotionem facilitandam divisionem quam alia diversa subsidia adminicula quo sic aptius exquisitius promptius minorique labore c. ac temporis dispendio possent Astris exponi observationésque peragi Idcirco omnem curam atque operam pro tenui ingenii mei facultatúmque mearum modulo à Deo concesso reliqua sublimioribus ingeniis at que ampliori fortunâ Viris five posteritati nostrae relinquens adhibui quo minora tam lignea universa ab Astris planè removerem atque in ejus locum ex puro solidóque metallo organa mihi compararem quidem ejusmodi quae insigni amplitudine essent conspicua simul commoditate regendi simul aliquanto accuratioribus adhuc divisionibus ad paulò subtiliores observationes obtinendas gauderent His Reasoning indeed is very good that since he had from much and long experience learn'd that Instruments of Wood after Ticho's manner were not to be trusted to by reason of their warping and shrinking and consequently that Instruments of solid Metall were much to be preferred before them and also that the larger the Instruments were the more exactly they could be made and divided and that the more easie they were to be moved and the more steddy and sure they were to be fixt in any position the more convenient they were for use he had therefore rejected all those Instruments which he had made after Ticho's way and had indeavoured to procure for his own use such as were compleat both for their matter and form having caused them to be made of Mettal that which could not be subject to the inconvenience of warping swelling or shrinking with the variety of Weather or length of Time And likewise of such a bigness as was capable of receiving more nice and curious Divisions and in the dividing them had found such contrivances and used such diligence that they were more then ordinarily true and exact As far as he has gone on with these Designs he seems to have been even profuse in his expences and exceeding bountiful of his own care labour and diligence but I could have wish'd heartily that it had been some other way imploy'd Those Instruments which he chiefly laboured to perfect he professes to be Quadrants Sectants and Octants after Ticho's manner rejecting all other Instruments of whatsoever Figures whether Radii Astrolabs Zodiacal or Aequinoctial Rings Parallactical Instruments or Hoops as more troublesome and less accurate But whether he hath in this his choice been rightly advised I shall hereafter have more occasion to examine when I come to describe an Apparatus of Instruments necessary for such a one as designs to promote and perfect the knowledge of the Coelestial Bodies and their motions wherein I shall shew that of some Instruments rejected by him there is a use absolutely necessary The Instruments therefore that he begins with are three small Quadrants of Brass the first of two foot the second of eighteen inches and the third of one foot Radius Each of these Instruments he sayes were made somewhat larger then common Quadrants to wit of an arch of 110 degrees which is to no other end but only in order to shew the subdivisions of each degree of the Quadrant by the help of a new invented Perpendicular of Brass wherewith each of them was furnisht This Invention is by him highly extoll'd for most excellent and usefull and to that end is made use of for the division of all his other Instruments both great and small Hear what he sayes of it Quiscunque hujus rei to wit the new way of subdividing the degrees of the Quadrant primus fuerit repertor sublimes profecto cogitationes exercuit hoc ipso ad congruentem effectum deducendo inter praestantissima inventa meritissimo refertur quod etiam minora Instrumenta remotis omnibus transversalibus Lineis in singula minuta corúmque particulas minimas subdividi liceat He seems indeed both here and elsewhere in many other places of his Book to be highly possest with admiration of the sublimity subtilty and extream usefulness of this invention and seems very much concern'd that the Author thereof should not certainly be known but dares not father it upon any one positively He sayes that one Benedictus Hedreus in a Work of his which he published Anno 1643. about the new and accurate Structure of the Geometrical Astrolab describes it but he gathers that he was not the Inventor himself but rather that he got both this Invention and the whole Quadrant which he describes out of the Observatory or rather Repository of Ticho Brahes Instruments for that it seems Ticho was the Inventor of this way of division and yet as I noted before he prefer'd the way by Diagonals much before it whatever Reason Hevelius had to be of a contrary Judgment What this way is I shall by and by explain But in the mean time I am sorry to find Hevelius joyning with Hedreus in the Opinion or Demonstration as Hevelius calls it that the Sub-divisions by Diagonals is not capable of a Geometrical demonstration especially in lesser Instruments which have need of many Circles I confess I understand not their meaning nor reasoning nor why it should be less demonstrable in lesser then in greater Instruments since 't is very easily demonstrable both in greater and lesser Instruments and as Geometrical as any other way of Division whatsoever the Diagonal Line being alwayes a piece of a Tangent Line that is to say the spaces between the Parallel Circles upon the Diagonals are alwayes to be in proportion to the difference of some Tangent Lines and the different distance of those Circles from the Center are alway in proportion of some Secants And the way of finding what those Tangents or Secants are and consequently what must be those Distances of the Parallel Circles I mentioned briefly before and shall now more fully demonstrate From which I will make it evident that the Theory was not as Hedreus and Hevelius have supposed uncapable of Calculation or Mechanical Demonstration But first give me leave to shew you what way Ticho Brahe made use of to demonstrate or rather to find out the true Angle unto each equal
parts of a Revolution and both these in Characters large and distinct enough and therefore the certainty and truth of this Assertion cannot be further doubted The way then for these Divisions is this Make a Frame of a Quadrant of hammer'd Iron after the manner expressed in the first Figure and in the Center hereof fix or raise a hollow Cylinder whose hollow may be about a 40th part of its Radius and whose convex part may be about a 30th leave this standing above the Plain of the Quadrant about 1 90 part of the Radius let the out-side of this Cylinder be made as exactly round as 't is possible to be turned or wrought then make a Ruler or Plate with a round hole in it at one end turned groun'd and fitted exactly about the above-mention'd Cylinder and as long as you design the Telescope for the Sights of the Quadrant this by a Screw on the top thereof must be kept close and steady upon the said Cylindeer Upon the end next the Limb is to be fitted a Socket or Frame with Screws to carry the Screw-Frame steady and firm according to the contrivance exprest in the first and 11 Figures this Plate must be filed or bended at that part of it which touches the Limb of the Quadrant so as to lye obliquely to the Plain of the Quadrant and to be parallel to the Plain of the Frame which carries the Screw and upon the part beyond the Limb must be fixt with a Screw k the Frame h h h which carries of the Screw 9 9 9 and the Index Plate t t the contrivance of this Frame h h is to keep the Screw 9 9 9 close against and very steady to the Limb of the Quadrant and is moved to and fro upon the Limb of the Quadrant b b b by the help of the Screw turning upon and against the edge of the Quadrant and this Screw by reason of its distance from the center and eye the reason of the placing of which in that place you will understand by and by being too far off to be reached by the hand is turned by a small Rod of Iron 0 0 0 in the first and 11 Figures lying by the side of the Ruler or Plate which hath a small Wheel q q at the end next the Limb by which the Screw is turn'd round with it and hath a small Handle or Windle p p next the Center by which it is made convenient to be so turned round Upon the end of the above-mention'd Screw-Frame h h is fixed a round Plate t t which is divided into 1 2 3 4 or 5 hundred equal parts according as it is in bigness and as it shall be thought convenient which Divisions are numbred and marked accordingly serving to shew what part of a Revolution is made of the aforesaid Screw for the end of the Screw 9 9 9 coming out through the middle thereof and a Hand 8 being fastned upon the said end every turn of the Screw doth make a Revolution of the Index upon the said Plate and consequently the motion of the arm made by one turn of the Screw is actually and sensibly divided into 1 2 3 4 or 5 hundred equal parts which is so exceeding exact and withal so Mathematically and Mechanically true that 't is hardly to be equallized by any other way of proceeding This Description will be much better understood by the Explication of the Figure and the several parts thereof Let a a a a a c. represent the Frame of the Quadrant consisting of 5 Bars radiating from the Center steadyed all of them by a Quadrantal Limb and a straight subtending Chord Bar this whole Frame is to be made of very good Iron partly welded and partly sodered together with Brass the breadth of the Bars may keep the same Proportions express'd in the Figure and the thickness may be about 180 part of the Radius in large Instruments In the Center of this out of the solid Bar is to be raised a Cylinder as d d expressed above more plainly in the 2d Figure the out-side of this Cylinder is to be turned and wrought as Founders do their Stopcocks as exactly as possibly it can be and the end of the Iron Plate or moveable arm c c c c shaped as is expressed in the 3d. and first Figure must be bored and wrought upon it very well so as they may turn exactly true evenly and smoothly without any manner of sticking or shaking which a good Workman will easily perform This arm being put on the Cylinder is screwed down fast by the help of a Screw-Plate expressed in the 4th and first Figures by e e which hath two notches in it f f by means whereof a Handle g g in the 6th Figure doth readily screw and unscrew it as there is occasion Between this screw'd Plate and the hole of the Plate c c c c is a thin Brass Plate let on upon an 8 sided part of the Cylinder that so the turning of the Plate c c c c may not have any power to unscrew the Plate e e which otherwise it is very apt to do Why this Center is thus made and a hole left in the middle thereof you will shortly understand more plainly Upon the Iron Limb of the Quadrant last mention'd is screw'd and rivetted a Limb of fine Brass first cast into that shape and then very well hammer-hardned and filed represented in the Figure by b b b b This as I said by many holes drilled through the Iron and the Brass is screwed and rivetted upon the iron Limb so as about half an inch in a Quadrant of 5 foot Radius doth over-hang the iron Limb and the ends thereof extend a considerable deal longer then the Quadrant the reason and use of which you will by and by understand when I give the Description of the Screw-Frame The edge of this Brass Limb must be by the help of the Plate c c c c and a File or Plain cut very exactly round to answer the Center of the Quadrant and the upper side thereof must be plained exactly smooth and flat upon which Plain-side the Loop-holed Plate c c c c must move as is visible in the Figure This Plate at i i must be wrenched or wreithed so that the Plain thereof must stand parallel to the Plain of the Index-Frame and by the wrâ—â—thing of it at i i as aforesaid there is room left for the Screw to lye obliquely without the Screws touching the aforesaid Plate or grating against it The reason why I put the Screw obliquely to the Plain of the Quadrant is that that part of the Thread which toucheth the edge of the Limb may be exactly at right Angles or perpendicular to that Plain and consequently that the Teeth upon the said edge may likewise be exactly cross or perpendicular also and consequently that no bending of the Rule c c c c to the end of which the Frame of the Screw is fastned
of a Revolution that the Content of that Angle in Degreess Minutes and Seconds is 16 Degrees 32 Minutes and 47 Seconds which is plain enough and much less subject to mistake then the common way made use of I shall therefore proceed to The third particular wherein this Instrument excels all others and that is That one Observator with a single glance of his eye at the same moment doth distinctly see that both the Sights of the Instrument are exactly directed to the desired Points of the two Objects and this though they be removed by never so great an Angle nay though they are opposite to each other directly in a Line This I question not will by all that know any thing of Instruments or celestial Observations be accounted one of the greatest helps to such Observations that was ever found out For whereas other Instruments require two Observators for taking a Distance in the Heavens and Ticho generally made use of four amongst which there was necessary so unanimous a concurrence in their readiness and certainty that the failure of any one spoyl'd all the rest and made the Observation become uncertain and of no use and such Instruments as were contrived for one Observator were accompany'd with so great difficulty in the adjusting to both the Objects being both in a continual and swift motion and but one to be seen at once that they were generally left off and dis-used there being so vast a trouble and fatigue of looking now upon one then upon another by many repeated tryals and so many new settings of the Instrument to the Objects in motion before the Sights could be adjusted besides the great uncertainty at the best of several Minutes of truth In this way the Observator has no farther trouble then first to set the Plain of the Quadrant in the Plain of the Objects and by the Screw to move the arm of his Instrument till he perceive both the Objects to touch each other in those Points he would measure the Distance between That this is so he will easily perceive when he understands the method of so adapting two Telescopes that by looking in at one small hole in the side of one of them he will be able to see both those Objects distinctly to which they are directed how much soever separated The way then of doing it is in short this Joyn them together at one end by a hollow Joynt that has a hole through it about ¾ of the hollow of the Tubes prepare two square Tubes of Wood Brass Iron c. of what length you please and directly against the Center of this hole in the Joynt make a small hole about the bigness of the blackest part or pupil of the eye so as the eye looking in at that hole may see perpendicularly into the lower Tube then obliquely place two pieces of reflecting Metal very well and truely polisht so as to reflect the Axis of both those Tubes perpendicular or at right Angles which is by fixing the Plain of the Plates inclined to the said Axis in an Angle of 45 Degrees let the upper reflex Plate reach from the upper side of the Tube so low as to touch the Axis or middle of the Tube and let the lower extend over the whole Tube from the top to the bottom and from one side to the other These will be known to be duely placed if looking in at the small hole against the Center of the Joynt the two round holes of the Tube do appear to the eye to coallesce into one and that the eye sees directly through the lengths of them both alike Then into these Tubes fit two Telescopes with convex Eye-Glasses and cross Threads for Sights in their Foci that they may be both of them at due distance from the eye looking in at the side-hole then opening those Tubes upon the said Joynt to any Angle and looking in at the side hole you shall plainly distinguish at once both the Objects that are brought into the Tubes directly and reflected up to the eye That this may be the plainer understood I shall add a Delineation thereof in plano Let a a b b in the 12th Figure represent the upper Tube and c c c c the lower Tube and let d d represent that part of the Joynt which belongs to the lower Tube at one end by which they are joyn'd together and can be open'd in the manner of a Sector Let i represent the hollow or center of this Joynt which communicates the Cavities of the two Tubes Let e e represent that part of the said Joynt which belongs to the upper Tube being only a hole through the lower side big enough to incompass the Cylinder d d of the lower Tube and let r r represent a Plate screw'd or pinn'd on to keep the parts of the Joynt together instead of rivetting Let s represent the hole in the side by which the Eye h is to look in and f the reflex Mettal in the upper Tube reaching only half way the Tube and g g the reflex Mettal in the under Tube reaching over the whole Cavity then will n o and p represent the Eye-Glass Sight-Threads and Object-Glass of the upper Tube and k l and m the same parts in the lower and whatever Angle the Tubes make to each other whilst they open upon the before-mention'd Joynt the Eye h looking in at s will see directly by the Axis of them both and see the Sight-Threads distinctly crossing the Points of the Objects whose Distances are to be measured These being thus explain'd I suppose it will be no difficult matter for any man to conceive how these may be apply'd to the above-described Quadrant for 't is but supposing c c the upper side of the under Tube in this Figure to represent a p a p the fixt side arm of the Quadrant and d d the Joynt of this to represent d d the Joynt of the Quadrant and b b the under side of the upper Tube to represent c c c the moveable arm of the Quadrant and applying two Tubes to these parts and fitting them with reflecting Plates Eye-Glasses Sight-Threads and Object-Glasses at due Distances the whole will be performed These Tubes thus fitted will serve to take any Angle less then a Quadrant to what exactness is desired but for bigger Angles the Contrivance must be somewhat varied the Description of which I shall now add Let either of the two Tubes for the Sights be made double the length of the other that is let it be as long behind the Center as before it and make the Reflex-Glass that it may be turned round and reflect the Ray exactly backwards as before it did forward then fix into this other half of the Tube a Telescope-Sight in all things fitted adjusted and like the other two then adjust them that they may look forwards and backwards in the same like which being done the Reader will easily understand how any Angle may be taken even to
the extent of two right ones For 't is plain enough that the two Tubes I first described apply'd to the Quadrant will measure any Angle to a Quadrant or right Angle and 't will be as easie to understand how by the help of the Reverse-Tube any Angle between a Quadrant and two right Angles may be measured To make this a little plainer to the Reader let c c c c c in the 12th Figure represent the under Tube or fixed Sight s the hole or Eye-cell t r a round piece carrying the reflex Mettal g g this is made to turn round and the reflecting Mettal g g being fixed to it within the Tube is carried round also with it Let s i k l m x represent the Ray passing forwards by the Eye-Glass Thread-Sight and Object-Glass then this round piece t r being turned and made r t as in the 13th Figure is represented and with it the reflecting Mettal g g here marked q q being turned also the Line s q k l m y will represent the Ray reflected and passing backwards by the reflex-Mettal q q Eye-Glass k Thread-Sight l and Object-Glass y. The measure of the Angle is found by the same Apparatus or Screw-Plate for as much as the Screw-Plate would shew the Angle less then a Quadrant if the fore-part of the Tube were used by so much is the Angle more then a Quadrant if the reverse or back part of the Tube be used and the same reason of the accurateness and certainty for the one is good for the other without being lyable to any manner of Objection or Inconvenience It remains therefore now only to shew First How these two Perspective or Telescope Sights placed within the same Tube may be made to look exactly forwards or backwards in the same Line And secondly How they shall be adjusted to the Telescope fixt upon the moveable arm of the Quadrant so as to know when the Division-Angle begins and when they are open'd to a Quadrant right Angle or 90 Degrees for unless these be ascertain'd and fixt to as great a measure of accurateness as the contrivance of the Screw is capable of dividing or the Telescope-Sights are capable of distinguishing or the Perpendicularity ascertain'd all the pains care industry and curiosity bestow'd about the other are of no use First then For fixing the Thread-Sights of the two Telescopes within the same Tube so as to look directly forward and backwards care must be taken that every one of the four Glasses that is to say the two Object-Glasses and the two Eye-Glasses must be so steadily and securely fixt into the Tube that they cannot by any means be stirr'd or removed the manner of doing which I suppose so exceeding easie that I need not spend time in describing a way to do it Next Sufficient care must be taken of the stiffness of the Tubes that they may not warp or bend Thirdly One of the Thread-Sights must be fixt as firmly and securely as the Glasses and so that the crossing of the Threads may be as near as possible in the Axis of the Object and Eye-Glass the other Thread-Sight must be left free till by several tryals it be found to stand exactly in the same Line with the first the manner of doing which I shall now describe There being two Threads which cross each other the one Perpendicular and the other Horizontal care must be taken that both these lye exactly in the same Lines with the Horizontal and Perpendicular Threads in the other Sights and in order thereunto there must be two Frames of Brass represented in the 29 and 30 Figures of the 2d Plate of the bigness of the hollow of the Tube these must have groves made in the Tube fit to receive them in which they may by the help of Screws be moved and made to slide to and fro as there is occasion for their adjusting Next They must lye so close together that the Hairs may touch each other And thirdly They must cross exactly in the Focus of the Object and Eye-Glass One of these Frames must carry the Perpendicular Thread and by a Screw in the side of the Tube must be moveable to the right or left side as there is occasion the other Frame must carry the Horizontal Thread and by a Screw in the top of the Tube must be made to rise or fall in the Tube as there is need The Mechanical Fabrick of which is so easie that I hope I need not spend time in the further Description thereof but refer the Reader to the 29 and 30 Figures These things being thus done from the top of some Turret or any other Station where two opposite places at a considerable distance as half a mile or a mile or two can be plainly seen find out two Points which at the first looking through your Glasses you find to be shewn out by the Crosses of the Thread-Sights then note those Points very diligently that you may be sure to find them and know them again when you have removed the Glasses this done turn the ends of the Tube and if you were looking Eastwards and Westwards turn that part towards the East which before looked Westwards and vice versâ and find out the two Points you saw in the former Observation then directing that part that hath the fixt Threads to the Point that was seen before by the moveable Threads find out the other Point which you will be sure to see within the compass of your Eye-Glass and observe how far the cross Threads are now removed from it either Northwards or Southwards upwards or downwards then as near as you can by your judgement half that Difference and by the Screws move the Frames that the Threads may stand in the middle between the two Points then take notice again of the Points shewn by the Threads and turn the Tube again Do this so many times till you find upon converting the Tubes that you see the same Points to be marked by the Crosses of the Thread-Sights with which end soever you look on them and then the Tube will be exact and fit for use The reason of this adjusting will be sufficiently plain to any one that shall consider the 14th Figure Where let v represent the middle of the Tube t u b or the place of the Eye and let w represent the Object seen Westwards and e the Object Eastwards at the first view then keeping the middle of the Tube exactly upon the same Point u turn the end of the Tube t towards the East and the end b towards the West and find out first the Eastern Object e and finding the other Cross to direct now to the Point p and not to w divide the Distance between the Point w and the Point p as exactly as you can in half which if you chance to hit exactly at first it will be the middle Point m but if you do not but you rectifie it only to r then by the
R I say the Superficies thereof shall be in the Horizontal Line O Z for since the upper Hemisphere is half the weight of the under the two quadrantal Wedges P O H and H O R must necessarily counterpoise the quadrantal Wedge R O Z of the Oyl Thirdly Suppose that more than half the said Oyl or liquid Pabulum be consumed and that there be only left enough to fill the Wedge B O Z I say the counterpoising upper Hemisphere now made the under and placed in the Position A H C R B O A shall exactly counterpoise the said Wedge of Liquor so as that the Superficies thereof shall be in the Line O Z for the Wedge R O B of the aforesaid upper Hemisphere doth counterpoise the Wedge C O R on the other side of the Perpendicular and the double Wedge A O H and H O C will counterpoise the Wedge B O Z. Nor can the Superficies of the Liquor be any whit higher or lower than the Line O Z for if it be any whit higher as at E F the Liquor must necessarily overpoise the aforesaid Wedge A O C by all the weight of the Liquor contained in F G O Z F. And if it be any whit lower as at I K the Wedge K I B must be too light for the counterpoising Wedge A O C by the weight of the Liquor contained in the space Z O T K Z since I just now shewed that A O C did just counterpoise Z O B which was the thing to be proved Now though in this Instance I have chosen to explicate I have made choice of a Globe yet that form is not necessary but it may be made of any Figure whatsoever that is turned upon an Axis or Poles so as wheresoever the said Figure be cut by a Plain to which the Axis is Perpendicular the Superficies of the said Figure shall describe a Circle the Center whereof is in the said Axis whether the said Figure be a Cylinder Cone or any other Conoeidical mixt or otherwise regular or irregular figure Such as the Figures A B C D E F G which represent the Section of the said Vessel through the Axis The second way for the poysing the Liquor and keeping the Superficies thereof always to an equal height is this Make a Concave Receptacle for the Oyl or Liquor of a Hemispherical Semicylindrical Semiconical or of any other half-round hollow Figure where the turned Figure is cut in two parts per Axin and whereof the Axis is placed Horizontal and the plain Section per Axin likewise Horizontally so as it may be filled with any Liquor up to that Plain and that the Liquor may not be apt to dash be shaken or filter over it will be convenient to extend the brims of that Receptacle somewhat above the half-Round that there may be about half or three quarters of an Inch of space above the Superficies of the Oyl vacant or empty And that upon whatever Plain the foot stand the Plain per Axin may stand Horizontal it will be good to suspend the Receptacle in the same manner as a Sea-mans Compass is suspended within a frame Fix this Receptacle or the Frame that is to keep the Receptacle Horizontal upon a convenient Pedestal and fit within the Hollow or Concavity of the Receptacle a half-round solid poise turned of the same form with the hollow of the Receptacle and cut exactly through the Axis in two equal parts Let this solid poise be made exactly half the weight of the Liquor that is to be poised and fit to it two Pivots or Pins at each end of the Axis which may be exactly in the Poles of the half-Round and fit to those Pins make two holes in the Centers of the Ends of the Concave Receptacle in which the Pins may freely move and suffer the half-Round poise to move round within the hollow of the Receptacle according as the quantity of the Oyl or Liquor is increased or diminished Fit to this Receptacle a neck and socket fit for the Wick and flame of the Lamp and the same operation will be performed by this as by the first contrivance to wit the Oyl will be kept always to the same height in the Receptacle This will be easier understood by explaining a Designation thereof which is shadowed forth in the fourth Figure Where A A A represents a Pedestal which may be made with three claws or toes to make it stand the steadier and evenner upon any Plain or Table B B represent one of the Semicircular Arms that are fix'd to the top of the Pedestal this hath two holes in it at the ends or extremities as at C is one the other hole being in the other arm which goes behind the Globe and therefore cannot be seen is supposed to be Diametrically opposite to this at C. These two holes are the Center holes in which two small Pins or Centers fastned into two opposite points of the Hoop or Frame are made fit to move by which means the said Hoop is preserved in an horizontal Position D D is this Hoop or Frame which is made to incompass the Vessel or Receptacle of the Oyl and is shaped exactly like it This is made strong enough of Brass Iron Silver or other material to bear the Receptacle Poise and Oyl without bending and hath as I said before two Pins or Gudgeons at C and opposite to it Diametrically or Semicircularly upon which the said Hoop always hangeth Horizontally It hath also on each side in the middle between the aforesaid Pivots two Centers as at F and E to receive the ends of the Axis of the Receptacle appearing at F and E by which the said Receptacle is always free to hang plumb or in its Perpendicularity so as that the upper edge thereof at F F will always lie Horizontally One of these Pivots namely that on the Right hand is the Pipe to convey the Oyl to the Socket of the Lamp I in which is fitted a Wick of Cotton to serve for the flame K G G represents the Vessel or Receptacle of Oyl which is here described Hemispherical that being the most capacious uniform Figure but may be of any other qualified as those I mentioned in the first contrivance The Brims of this are extended somewhat higher than a Semicircle namely to F F to keep the Oyl from flashing or filtring over This is always kept full with Oyl or other Liquor to the Horizontal prick'd Line L L which passeth through the Center or Axis of its Cavity by the Counterpoise moved on the Center C. H H H represents that Counterpoise which is made exactly half the weight of the Oyl or Liquor and the Center of gravity of it must be somewhere in the Line M M and it ought to be fitted as exactly into the hollow of the Receptacle as it is possible that there may be left as little space as may be between its convex sides and the Concave of the Receptacle
but yet so much must be left that it may move very freely upon its Center C a whole Semicircle This done and the Receptacle being filled with Oyl the same effect will follow as in the first contrivance and the Demonstration of it being much the same I shall not now spend time to explain it But rather proceed to the description of a third way of keeping the Liquor counterpoised to the same level The third way then is Take any round Vessel whose Concavity and Convexity is turned upon an Axis and suspend that Vessel upon two small Pivots but yet big enough to bear the said Vessel filled with Oyl c. fastned in the Poles of that Axis and leave or cut open a sixth part more or less as you please of the side thereof that thereby any thing may be put into or taken out of the Cavity of the Vessel then poise the Vessel exactly on those Centers that no side be heavier than the other then fit into it a float of Brass Silver Tin Lead c. Convex on the under side so as just to fill to the Cavity of the Vessel And on the upper side Plain or Convex or any other convenient Figure it matters not much Make this float as heavy as you can at the bottom and as light as may be at the top but yet of such weight as may well float upon the top of the Oyl c. Let one end of this be fastned by a wire or string so as that end thereof may always touch that point of the Concave of the Vessel to which it is tied and that the rest thereof may turn and follow the sinking of the Oyl and through the end of it near the place where it is fastned let a Pipe go through it to receive the Wick which Pipe hath no communication with the Cavity of the hollow float This done fill the Vessel as full as convenient with Oyl and light the Wick and you shall find that as the fire consumeth the Oyl the Vessel will turn upon its Poles and keep the Superficies of the Oyl always at the same distance from the flame that it was put at at first till the whole be consumed This will be made more conceivable by a figure and explanation thereof which therefore take as follows in the fifth figure A C B B represents a hollow Vessel the Cavity whereof is very exactly turned upon an Axis whose Poles are in P the space between A and B in the side thereof is left open into the Cavity of it This Vessel is suspended upon its Poles at P so as to be free to move round upon them and exactly poised as no one side thereof be heavier than another To the hollow of this Vessel is fitted a float D of Brass Latton Silver Lead c. whose underside is made of a Convexity just fit for the Concavity of the Vessel as may be seen at K D I and the upper straight or Plain Let this float be made somewhat lighter than the Oyl or Liquor on which it is to swim so that a part thereof may float above the Superficies thereof Let one end thereof E be fastned to the side of the Vessel a little below the Brim B through the end of this float is put a Pipe and Wick h for the flame i then pouring in Oyl by the open side A Q B fill the same till it carry the float up to touch the hollow of the Vessel then light the Wick and you will find that the Lamp will consume the Oyl and this contrivance will continually supply it till the whole be consumed and the Poise be moved to touch the Concave of the aforesaid Vessel for when the Vessel is filled up to f g the float D will touch at O and E and the Cavity above f g being empty the Vessel will be as is described in the Figure the open part A B being upwards And as the flame consumeth the Oyl the side of the Vessel B will descend downward towards B 1 and so by B 1 B 2 B 3 to B 4 where the whole quantity of Oyl will be consumed and the bottom of the float will touch the hollow side of the Vessel in all which gradual wasting of the Oyl the Superficies thereof will lie at the same distance below the upper side of the float D that it had at first and consequently at the same distance from the bottom of the flame The reason of all which will be very easie to be understood by any one that shall seriously on this Delineation consider that the float D must necessitate the Vessel A C B to move on its Axis B according as its Oyl wasts because one end thereof E being fastned to the brim of the Vessel B the other end O being loose will as the Oyl wasts descend towards N whence the end E must hang heavier on the brim B and consequently must move it down towards B till the upper side f g of the float be reduced to a Parallelism with the Superficies of the remaining Oyl and the end E have no gravitation on the brim B which motion will be continued as the Oyl wasts and the brim B will be moved downwards by the points B 1 B 2 B 3 to B 4. I shall not therefore spend any more time in the Geometrical demonstration thereof but proceed to explain a fourth way by which the Flame and Superficies of the Oyl keep always at the distance they were first put at The Fourth way then is the making the Socket of the Wick to swim upon the top of the Oyl so that the Socket may sink as well as the Oyl by reason it is sustained by that and by that only The Vessel or Receptacle is generally made of Glass and it is best of a Hemispherical Figure the light casting it self through the body of the Oyl as well as of the Glass This is so plain and obvious and so commonly used and practised that I need not spend more time in the explanation or demonstration thereof but proceed to describe a Fifth way The Fifth way then is much upon the same principle with the Fourth but avoids several inconveniences to which that is subject For whereas the Flame in the Fourth is necessitated to be within the capacity or the Receptacle in this Fifth it may be at any distance and so is made much more convenient to be come at and to be dressed and trimmed Take then a Vessel of Glass Cylindrical is best as a Glass Bottle and fit to it a Siphon long enough to draw the Oyl from the bottom of the said Vessel make the one end of this Siphon extend at what distance you think convenient for the placing the flame of the Lamp and so order it that it may always draw from the Receptacle by its arms to feed the flame which it will do if the end of the Siphon be made where the Socket of the Lamp is placed
Pulse it is propagated to 4 below c before the other side of the Pulse touches the Superficies at d the Pulse therefore 44 55 66 c. becomes Oblique to the tendency of the Radiation and by the Superficies ef it is reflected by 77 77 77 till it touches the second refracting Superficies g h where it is observable that the same side of the Ray that entred first the Superficies c d enters first into the Superficies g h in the same manner as if it had proceeded on by the straight Lines f m e l till it met with a Parallel Superficies l m to the first c d for the Ray between the two Parallel Lines f h e g hath the same inclination and respect to the Refracting Superficies h g that the Ray between f m and e l would have to the Superficies m l supposing there were no Reflecting Superficies at e f. I shall not need I hope more particularly to demonstrate every part of this Explanation the very observing the Delineation of the Scheme being enough to make it plain to any one never so little versed in Geometry from which he will plainly perceive that what I endeavour to demonstrate was really so and that I did understand what scope my Demonstration aimed at so far as to hit the Mark which was to shew that Colours were generated where according to Des Cartes own Principles there could be no Rotation of the Globuli Now though the Learned Doctor would not admit of this Demonstration to be sufficient to do the work yet he says Pag. 252. Veruntamen dissimulandum non est non pauca me meapte opera excogitasse quibus pro persuasissimo habeo eorum motus rotationes modis pure mechanicis semper fieri non posse And in prosecution of the destruction of this Rotation of the Globuli which he hath hitherto seemed to defend he adds four several Arguments I shall not now stay to repeat them But whosoever will please to read what the Learned Doctor hath suapte opera excogitated against the Cartesian Hypothesis and set down in the 252 253 254 and 255. pages And compare them with what I have said in the forementioned place to wit at the latter end of the 60. and the beginning of the 61. pages of my Micrographia may plainly find the Arguments brought by the Doctor do very little if at all differ from those I there published I could heartily therefore have wished that the Learned Doctor had made use of some other Mediums to prove the Existence of an Hylarchick Spirit and not have medled with Arguments drawn either from Mechanicks or Opticks for I doubt that such as understand those subjects well will plainly see that there is no need of any such Hylarchick Spirit and if there be no need of it but that all the Phenomena may be done without it then it is probable that there is none there for Natura nihil agit frustra It had been much easier to have proved the existence of it by Arguments drawn from subjects we less perfectly understand as from the generation nutrition vegetation and propagating of Vegetables and animal substances for there the manner of the progress of Nature being infinitely more curious and abstruse and further removed beyond the reach of our senses and understandings one may more boldly assert strange things of this Hylarchick Spirit without fear of controul or contradiction and from whence possibly it may never lie within the power of Reasoning to banish him But to leave this Digression and return to the use of these water-poises A fifth effect may be for washing and refining of Earth Clays Powders and the like the clear water by these contrivances being made to run over gently at the top and so leaving all the settlement from the water at the bottom By any one of these with a receptacle Cistern added to it the stream of water from that Cistern may be accelerated or retarded by any degrees desirable This doth depend partly from the proportion of the Tap of the Receptacle Cistern to the Tap of the counterpoised Cistern and partly from the shape and make of the Receptacle Cistern by the proportion and shape of which the stream of Liquor through the Tap of the Receptacle Cistern may be modulated at pleasure as any one a little versed in Hydrostaticks will easily perceive and demonstrate A sixth effect may be for governing the heat of Lamps for Distillations Digestions Fermentations Putrefactions Dissolutions hatching the Eggs of Birds or Insects accelerating and seasoning or timing the growth of Plants nealing of Glasses and Metals by the gradual access of the heat so as to make them fit for stronger degrees or by the gradual recess to bring them out of the greater degrees to make them tough and capable to receive the cold of the Air. It would be too long to give instances of contrivances for every of these operations but the skilful Mechanist Philosopher or Chymist will easily supply his own desires by some one of these I have instanced in or at least by a composition of them I shall therefore only add a description of a Clepsydra or time-keeper or two and so leave this subject for the present A description of a new sort of Clepsydra THis contrivance is nothing else than that Two of the second sort of Vessels are so contrived as to run into each other and to empty themselves and be filled alternately and their bigness or capacity and the hole through which the Liquor is vented are so proportioned as to be emptying the space of an hour which is easie enough and may be adjusted to what accurateness is desired Then the convex Superficies of the Cylindrical poise is divided into sixty equal parts by straight Lines drawn upon its Surface Parallel to the Axis and to each other these lines by the sinking or turning of the said poise denote the minutes and if smaller Divisions of time be desired the spaces between them may be divided by other smaller Parallel Lines denoting the parts of each minute to what niceness is desired One of these Cylindrical Receptacles may be fixt and the other by an easie apparatus may be made to rise a little when it is top-full and fall a little when quite empty below the Level of the other that is fixt The Chanel between them through which the water is to run out of the one into the other may be a small pipe with a hole in it of a bigness proportioned as I said above to let the Liquor run out of one into the other in the time desired and its ends may be fastned to the two Receptacles by a part of the neck of a bladder or gut so that it may be limber and may always have a Declivity into the Vessel that is to be filled the Declivity need not be above half an Inch. The Liquor used in it may be Water Oyl or any other Liquor that doth not easily evaporate But