irregularity in its motion is ascribable to its Parallax And this will be so much the easier because the examination and reduction of it may be done with as great exactness as the observation can be made by the help only of Ruler and Compasses for all the distances will be set off by equal divisions of straight lines the line also of the periodick motion whether of the Comet or Planet especially if the observations be made when the body is near an opposition with the Sun which is much the best time will be with sufficient exactness taken for a straight line and the motion in that line may be supposed by equal spaces in equal times for the difference between the Tangents of the centesms of a degree to two degrees is not increased much more then 2 1745 that is not a quarter of a centesm of the hundredth part of a degree which is much more exact than I fear our observations will ever be Another way of finding the Parallax may be by the help of exact observations made by several persons at the same time in places much differing in Latitude though as near as may be under the same Meridian because of saving the trouble of Calculation and for being assured that the observations were both made exactly at the same time each person by the help of very long Telescopes observing the exact distance of the body from the small fixt Stars next adjoyning A third way of finding the Parallax of Comets is wholly new and though hypothetical as supposing the annual motion of the Earth and the motion of the Comet in a right line through equal spaces in equal times yet 't is founded upon a Problem in Geometry invented by the incomparable Mathematician Doctor C. Wren which is truly noble and wholly new and though it had been of no use in Astronomy deserves none of the meanest places in Geometry by the help of which which is much more than either of the other ways is capable of one may easily find the true parallax of the Comet from any four exact observations of it made at differing times in the same place Nor does it require so nice and accurate Instruments and Observators as are altogether necessary in the other ways The Problem as I received it is this Problema Datis quatuor lineis utcunque ductis quarum nec tres sunt parallelae neque ab eodem puncto ductae quintam ducere quae à quatuor primo datis in tres partes secetur ratione positione datas Sint in Figuris 13 14 15 16 17 18 quatuor rectae ADC BEC AE BD productae versus K γ φ M oportet quintam ducere ut KM quae secetur à primo datis in segmenta KN NO OM secundum datas rationes R S T. Fiat ut R ad S T simul sumptas ita CD ad CF. Rursus ut T ad S R simul sumptas ita EC ad CG ductis autens AGH BFH à mutua intersectione H ducantur H γ K H φ M parallelae nimirum lineis AC BC quae mediae interjacent inter extremas BD AE Denique inter puncta extremarum KM ducatur Recta secans medias in NO Dico segmenta KN NO OM esse in Data ratione RST Quoniam FD parallela est ipsi HK ergo ut CD ad CF ita K γ ad γ H quoniam γ N parallela est ipsi HM ergo ut K γ ad γ H ita KN ad NM ergo ut KN ad NM ita CD ad CF sed CD ad CF est ut R ad S T simul sumptas ergo KN est ad NM ut R ad ST simul sumptas Similiter quoniam EG parallela est ipsi MH φ O ipsi HK demonstratur MO esse ad OK ut T ad S R simul sumptas Quare tres KN NO OM erunt ad invicem ut R S T ergo ducitur linea KM cujus tria segmenta à quatuor lineis datis intercepta sunt in data Ratione R S T servata quidem positione sive rationum ordine R S T quod erat faciendum From the invention of which Problem 't will be very easie by any four observations Graphically to describe or Geometrically to calculate the true distance of the line of the trajection of the Comet and consequently to answer all those questions that can be demanded concerning the bigness of the body and head and concerning the bigness and length of the blaze and concerning the distance of it from the Earth in every part of its way when it was nearest the Earth when nearest the Sun where it cuts the Plain of the Ecliptick seen from the Sun and where seen from the Earth with what Angle it was inclined to the said Plain how swift the motion was that is what length it passed in what time when it must appear Stationary when Retrograde when disappear and the like According to this method I received at the same time whilst it yet appeared very visible to the Eye and was not Retrograde the way of the first Comet delineated by the said person which did very near solve all the appearances preceding and subsequent which I have therefore here annexed in the Table expressed in the 19.20 and 21. figures where in the 19. is delineated the Place of the Sun in the Center of the Circle ♈ N D I ♎ which represents the annual Orb of the Earth about the Sun the points between N and D represent the places of the Earth in that Orbit in the days of November and the lines drawn from them to the points in the straight line represent the lines in which the Comet appeared in respect to the Sun in like manner the points between D and I the places of the Earth in December and the lines drawn from them to the straight line as before the visible places of the Comet at those times c. The 20. figure represents singly the several Longitudes of the Comet at several times seen from the Earth And the 21. represents the several Latitudes at the several times together with the true distances of the Comet at those times both which are made out of the 19. figure where E at the end of the line represents the Center of the Earth from which to the figures in the prickt curve-line are the true distances of the Comet the Perpendiculars from those figures to the line E C are the signs of the Latitude of the Comet from the plane of the Ecliptick E C the aforesaid distances being made the Radii Now though according to my former Delineation the Comet seemed to take a circuit as if it would within three years return to its former position yet I am not wholly convinced that it moves in a circle or Ellipse but I rather incline to the incomparable Keplers opinion that its natural motion tends towards a straight line though in some other suppositions I differ from him As first that the Comet
may at all vary the Angle nor any unequal thickness in the Limb of the Quadrant but that the turning only of the Screw shall produce a variation and that exactly proportionate to the number of Revolutions and the parts thereof shew'd by the Index The way to know exactly what the obliquity of the Screw ought to be to make the Teeth upon the Limb perpendicular is to number how many Threads of the Screw there are in a known length and what the Compass of the said Screw or the Cylinder out of which it is made is and multiplying the said Compass by the number of Revolutions into a Product the Proportions of that Product to the known length will give the obliquity of the Screw the Product being the Radius and the known length the Tangent of obliquity thus Suppose in the length of 4 inches there be 83 Threads of the Screw and that the Compass of the Cylinder of the Screw be ⌊ 92 Centesms of an inch I multiply the ⌊ 92 by 83 the number of Revolutions and it giveth me 76 ⌊ 36 that is 76 inches and 36 Centesms of an inch making this Product the Radius and the known length viz. 4 inches the Tangent of the obliquity of the Thread of the Screw to the Axis thereof or of the Axis of the Screw to the Plain of the Quadrant The demonstration of this is so plain that I need not insist upon it for the length of the Thread of the Screw is the Secant the Compass of the Cylinder is the Radius and the bigness of the Thread or the Distance between two Threads is the Tangent in a right angled Triangle and the Screw is such a right angled Triangle wound about a Cylinder putting the Tangent thereof parallel to the Axis of the Cylinder and consequently in the Mechanical â—ryal of these Proportions the more Threads are taken to make that comparison or measurement the more exact is the inclination found The consideration of which doth plainly shew how exact a way of Division this by the help of the Screw is for the whole Quadrant is thereby resolved into one grand Diagonal the same with Triangle the length of the Thread upon the Compass of the Cylinder being the Diagonal and the Distance of the two ends of those Threads in a Line parallel to the Axis being the space to be divided by it and consequently by augmenting the bigness or Compass of the Cylinder and diminishing the Thread you may augment the Diagonal in any Proportion assigned Or by making the Hand or Index upon the end thereof of double treble quadruple decuple c. of the semi-Diameter of the Cylinder out of which the Screw is made you may duplicate triplicate quadruplicate decuplicate c. the said length of the Diagonal in Proportion to the space to be divided The next thing then to be described is the Screw-Frame made of Iron much of the shape represented by h h h in the first and 11 Figures This Frame by the help of a Screw through the aforesaid Plate whose head is expressed by the round head k is fixed on to the long Plate from the center and by the help of the Screw I is forced and kept down very close upon the edge of the Limb of the Quadrant the Frame hath 4 Collers for the Screw-Pin to run against which are indeed but half Collers serving only to keep the Screw steady two of these are made with most care marked with m m in the 11th Figure against m i doth rest the Shoulder of the Screw-Pin 3 which is kept close home against it by the Cylinder g g in the 10 and 11 Figures the sharp Conical Point of this Screw 9 9 goeth into the Conical hole at the end of the said Cylinder g g g. The shape of this Cylinder and the Screw by which it is forced against the end of the Screw 99 is represented in the 10th Figure 7 in the 9th Figure represents the Conical Point 3 the place lying against the Coller m i 6 the Screw that moves upon the edge of the Limb of the Quadrant 5 the Nut or Pinnion by which the Screw is turn'd by a Rod from the Center exprest alone in the 8th Figure but the manner how it lyes in the Frame is exprest by p p 0 0 0 in Fig. 1.0 0 0 representing the Rod p p the Handle by which it is turned q q the Nut or Pinnion that turneth the Pinnion 5 of the Screw s r the Collers or Holes that hold it fast to the moveable Plate or arm of the Quadrant s s representeth two small pieces that clip the edge of the Limb and serve to keep the Screw-Frame steady and true in its oblique posture and move equally on the Limb by a strong springing of one side of it t t representeth the Index-Plate which is divided into what number of parts are thought necessary 1 2 3 4 or 5 hundred parts according to the bigness of the Thread of the Screw at 6 a greater Thread requiring a more minute Division and a smaller Thread requiring a more gross These Divisions are pointed at by the Index 8 at the end of the Screw and the number of Revolutions or Threads are marked on the Limb of the Quadrant and pointed at by the Tongue e e upon the which is fastned a small Pin f serving to carry a Lens over the Point of the Tongue which maketh the number of Threads appear more plain and big The manner of doing which upon the Frame of the Screw is so easie that I shall not spend more time in the Explication thereof and the manner of making the whole Instrument will be easie enough to any ingenious Workman but if any person desire one of them to be made without troubling himself to direct and oversee a Workman he may imploy Mr. Tompion a Watchmaker in Water-Lane near Fleetstreet this person I recommend as having imploy'd him to make that which I have whereby he hath seen and experienced the Difficulties that do occur therein and finding him to be very careful and curious to observe and follow Directions and to compleat and perfect his Work so as to make it accurate and fit for use By the help of these Indices 't will be easie and plain to see how many Revolutions of the Screw and what parts of a Revolution make a Quadrant of a Circle and consequently 't will be easie to make a small Table which shall shew what parts of a Quadrant divided into Degrees Minutes and Seconds will be designed by the Revolutions and parts of the Revolutions of the Screw As for instance If I find that 1600 Revolutions and ⌊ 912 make a Quadrant then 17 ⌊ 788 Revolutions make a Degree and ⌊ 296 Millesms of a Revolution make a Minute and about 5 Millesms make a Second thence 't will be easie to find if you observe an Angle to contain 294 ⌊ 358 that is 294 Revolutions and 358 Millesms
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
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
the motion of the ascending stream or beard being but slow there needs no very quick supply of other parts We see also into what a vast quantity of smoke a small parcel of a combustible body may be turn'd From all which particulars 't is not unlikely but that the Comet may be a body moved with a regular circular or elliptical motion as the Planets are that it may be a body of such a constitution as that the fluid Aether through which it passes may dissolve it much after the manner as a meâ—struum such as Aquafortis Spirit of Niter c. does a dissoluble body that by this means there may be a slow but continual eruption of somewhat opacous parts which may by their dissolution afford a sufficient quantity of light to make as great an appearance as any of the Comets that this stream or beard may by the resistance of the Aether be a little deflected back wards in the same manner as an ascending stream of smoke will be by the resistance of the Air if the burning body be mov'd this or that way through it that the body of the Comet may be both as ancient and as lasting as the world and that this which has lately appeared may have appeared heretofore and may likewise hereafter appear again that 't is probable the nearest distance of it was much greater than that of the Moon that the length of its Beard was longer than its distance from the Earth and consequently several times longer than the distance between the Earth and the Moon that its visible way among the Stars was very differing from a great circle especially towards the latter end when it became retrograde that its way through the Aether could not be supposed equal in a straight line though it might be supposed equal in a curve or circle that the exact way of it could not be certainly determined by the best Observations I have yet met with and that therefore the best help we have to ghess of its way and distance is by its manner of moving as to appearance among the fixed Stars which I have already shewn to be explicable by various Hypotheses for both the Earth and Comet may be supposed to be moved either both one way or contrary ways or cross ways the Earth may be supposed to stand still and the Comet only to be moved and the like These Requisites therefore being hitherto wanting in the Observations I have met with of this Comet all that can be said of it will at best be but conjectural and hypothetical since nothing can be reasonably built upon those Observations where the truth of them is dubious wanting therefore sound materials to work upon in this Comet I had recourse to the Observations of the noble Dane Tycho Brahe being sufficiently satisfied both of the ability industry and veracity of that excellent Author who left nothing unattempted for the perfecting of such Observations as seem'd to him requisite for the compleating a History of that Comet which appeared in 1577. And from those Observations of his I endeavoured to trace the way of it according to several hypotheses and found that supposing the Earth not to be moved with an annual motion but only a diurnal about its own Axis the way of Comets will fall in a line very near approaching the nature of a circle though neither into an exact circle nor an exact ellipse and therefore seems irregular and not at all probable Again supposing it moved about the Sun as Tycho has done we find from his Calculation of it he was fain to allow it a quicker and slower motion in its Orbit to solve the Phaenomena which seems to me but a shift that will serve to help out any lame Hypothesis whatsoever And that granted and the Parallax of the Comet unknown I will undertake very easily to make out almost any Hypothesis which is the fault also of Mr. Horox his Hypothesis wherein he supposes the Earth to be moved about the Sun and the Comet like a Rocket to be shot out of the Sun and by degrees to return to it again in which Hypothesis indeed there seems to be much more reason for aninequality of motion though not in the manner as he has placed it 't was very rational that the motion of it at first if cast out of the Sun should be very swift but then it ought likewise to have accelerated its motion in the same manner in its return back to it again which it does not in his Hypothesis for a stone or any other heavy body being shot up into the Air does make its return back again to the Earth almost by the same degrees of velocity by which it ascended from it almost I say because the resistance of the Air does so far impede the motion of the body through it that it never suffers it to acquire the same degree of velocity with which it was first shot upward This is sufficiently evident from a Pendulum which if it be thrown upwards and be suffered to return back it will never rise again on the opposite side to an equal height with that it descended from on that side towards which it was thrown but besides in his Hypothesis he seems to take no notice at all of the Latitude of the Comet which seemed to carry it much farther off from the Sun when he supposes it to be returning nearer And indeed upon the whole his Hypothesis seems rather a product of chance than of any contrivance For he in endeavouring to set off the Longitude of the Comet according to Tycho's Tables and to trace its way by supposing the Earths annual motion making use always of the same Radius to set off the aspect or apparent angle of it with the Sun his line of Chords he made use of did always direct the point of his Compasses to the place where he situates the Comet as may be easily found by examining the ninth figure where you may find that he places the Comet always equally distant from the Earth and that distance is always equal to the distance of the Sun which has so many inconveniencies and improbabilities that I shall not insist farther on it especially since I do not find that he bestowed any farther pains in explicating or cultivating this his Hypothesis than only the bare delineation of this ninth figure But to return to Tycho's Hypothesis if that be true why did not the Comet again appear after a certain space of time and why could not he have foretold when it should again appear as well as he could predict the appearance of Venus about whose Orb he supposes it to circulate I shall pass by several other very material objections that might be made against that his supposition because many of them might be made also against his Hypothefis of the Heavens in general which I shall the rather omit because I do not find he has many followers in that supposition the generality of
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
of Art doth often prove without the conjunction of the study of Nature and upon what rational grounds it was that Sir John Cutler the Patron and Founder of this Lecture proceeded in joyning the contemplation of them both together The next thing was the Instrument for the making of this observations such a one as should not be lyable to any of the former exceptions nor any other new ones that were consideâ—able To this purpose I pitched upon a Telescope the largest I could get and make use of which I designed so to fix upright as that looking directly upwards I could be able certainly to observe the transits of any Stars over or near the Zenith and furnishing it with perpendiculars and a convenient dividing Instrument I should be able not only to know exactly when the Star came to cross the Meridian but also how far it crossed it from the Center or Zenith point of Gresham Colledge either towards the North or towards the South All which Particulars how I performed I shall now in order describe and this somewhat the more distinctly that such as have a desire to do the like may be the more ready and better inabled to proceed with the same First then finding a Tube would be very troublesome to the Rooms through which it past especially if it were placed pretty far in the Room and that one wanted so free an access as was necessary if it were planted nigh the wall and that there was no absolute necessity of such an intermediate Tube supposing there were a cell to direct the eye fixt to the Eye Glass and that there were some short cell to carry the Object Glass in at the top so as to keep it steady when raised upward or let downwards the light in the intermediate Rooms not at all hindring but rather proving of good use to this purpose for seeing the Mensurator I opened a passage of about a foot square through the roof of my lodgings see the Fourth Figure and there in fixt a Tube a a perpendicular and upright of about ten or twelve foot in length and a foot square so as that the lower end thereof came through the Ceiling and was open into the Chamber underneath This Tube I covered with a lid at the top q housed so as to throw off the rain and so contrived as I could easily open or shut it by a small string n o p which came down through the Tube to the place where I observed Within this perpendicular Tube a a I made another small square Tube b b fit so as to slide upwards and downwards as there was occasion and by the help of a skrew to be fixt in any place that was necessary Within this Tube in a convenient cell c was fixt the Object Glass of the Telescope that which I made use of was thirty six foot in length having none longer by me but one of sixty foot and so too long to be made use of in my Rooms the manner of fixing which was this The Glass it self was fixed into a cell or frame of Brass so exactly fitted to it that it went in stiff and to fill up all the Interstitia's there was melted in hard Cement this cell had a small barr that crossed under the center of the Glass or the aperture thereof in which barr were drill'd two small holes at equal distance from the middle of the Glass through which the upper ends of the two perpendiculars d d were fastned and in the fixing this brass cell or frame into the square Tube that was to slide up and down care was taken to make the barr lye as exactly North and South as could be though that were not altogether so absolutely necessary to this observation These perpendiculars d d fastned to the barr hung 36 foot and better in length and had at the lower ends of them two balls of lead e e as big as the Silks could bear by which the lowest parts of this Instrument were adjusted as I shall by and by explain But first I must acquaint the Reader that I opened a so perpendicularly under this Tube a hole r r a foot square in the floor below which with shutters could be closed or opened upon occasion by this means I had a perpendicular Well-hole of about forty foot long from the top of a to the lower floor s s. Upon the second floor s s I fixed the frame that carried the Eye-glass and the other Apparatus fit to make this observation I made then a Stool or Table such as is described in the same Fourth Figure i h h i having a hole through the top or cover thereof h h of about nine inches over the middle of which I placed as near as I could perpendicularly under the middle of the Object Glass in the cell above and then nailed the frame fast to the floor by the brackets i i that it could not stir underneath the cover of this Table I made a slider g g in which was fixed in a cell an eye Glass f so as that I could through the eye Glass moved to and fro see any part of the hole in the Table that I desired without stirring the stool from its fixtness This was necessary because many Stars which were forerunners of this Star in Draco and served as warning to prepare for the approaching Star went pretty wide from the parallel that passed over our Zenith by this means also I took notice of the Star it self at above half a degree distance from the Zenith to the East and so followed the motion of it with my eye Glass and also with my measuring Clew and at the same time told the Seconds beat by a Pendulum Clock and so was very well prepared to take notice of all things necessary to compleat the observation but might have been otherwise surprised by the suddain approach and swift motion of the said Star The measuring Instrument or Mensurator was a round thin plate or circle of Brass delineated in the Seventh Figure the aperture a b of which was about nine inches over crossed in the middle by two very small hairs a b and c d which served to shew the Zenith point at e by which the Star was to pass there were also two other small hairs f g and i h drawn parallel to that which was to represent the East and West line that past under our Zenith these cut the Clue that represented the Meridian or North and South Line at the places k and l where the perpendicular points were made by the two long plumb lines This Instrument was produced on the side a to n n e being made fifteen times the length of e m so that e m being one inch and two thirds e n was twenty five inches at n the line n e was crost by a rule of about 3½ foot long o p which from the point n was divided each way into inches and parts each inch being subdivided into thirty parts which
then either of those two of Ticho Brahe or this set down by Hevelius which is much the same with one of those which was 100 years since made use of by Ticho and described and is by him attributed to an English Mathematicians But because this industrious and careful Person put himself to the trouble of making and examining the Divisions himself I could heartily have wisht he had thought upon some such way as this which I here describe and call a Compendium of Diagonal Divisions it being a way whereby as 89 90 of the trouble is saved in performing the manual operation thereof so I judg it to be much more certain exact and plain then the other way of Diagonals My Reason for the first is plain The Division of one Degree serving for the whole ninety And my Reasons for the second are First Because it is much plainer to be distinguished then by the help of the edge of a Ruler lying over the Diagonals one being able to see but one part of the Diagonal And Secondly I think it much better then a small fiducial Thread which is very apt to be bended and broken if it lyes close to the Superficies of the Diagonal and if it lyes at a distance a skew glance of the eye will much alter the seeming intersection of the Diagonals which in this way are both prevented The way then in short is nothing but this Take a thin piece of clear Looking-glass Plate well smoothed and polished on both sides and large enough one way to cover the whole breadth of the Rim of the Quadrant on which the Diagonals were to be made and the other way to cover two or three Degrees this I do the bigger that the sides of the Arm may not shadow or darken the Divisions and numbrings Suppose a a a a in the 29th Figure Plate 2. to represent such a Plate upon this Plate describe with great care a Degree of the Quadrant you would have divided and compleat it with all its parallel Circles and Diagonals as you would have done any one Degree upon the Quadrant and if the Rim of the Quadrant be very broad in proportion to its Radius you may by the Table of natural Secants or Tangents set the parallels at their due Distances but if the Rim be narrow 't will be sufficiently accurate to make their Distances equal These Divisions must be done with Compasses pointed with small Diamant Points in the manner of those wherewith Glasiers cut their Glass The Glass being thus divided and lined number the Diagonals and place it in the Frame of the Ruler with the lined side next the Quadrant so that moving it to and fro the side of the Glass may immediately touch the Brass Rim of the Quadrant This Brass Rim must be divided into 90 equal parts or Degrees and at each Division straight Lines drawn from the Circumference to wards the Center the whole breadth of the Limb at least as much as is made use of for the Glass-Plate for the breadth of the Diagonals the Frame to carry this Plate is a convenient Cavity left in the moveable Arm of the Quadrant the whole manner of which will be better understood by the Delineation thereof to which I shall therefore refer the Reader The Distances of the parallel Circles if unequal may be easily set down true according to the numbers of natural Tangents or Secants with a pair of Compasses contrived like Beam-Compasses but having its Points to be set at any distance desired by the help of a Screw moving upon one side of the Beam which I may have occasion to describe elsewhere more properly and therefore will here omit it Next If this way had not pleased I could have wished he had known this following which is altogether as easie and as Geometrically true which I have contrived and have made small Instruments thereby to shew very minute Divisions very easily and very plainly I strike then upon the Limb of the Quadrant I would divide being first made exceeding smooth and plain a Circute very fine and as lightly as possibly I can so it be but discernable and by the help of a very large Quadrantal Dividing Plate of ten foot Radius I divide the said Quadrant in the faint Circle above-mention'd into 90 parts or Degrees then by a peculiar contrivance of a very curious Point that strikes with a Spring which I describe in another Discourse the said Degrees are marked upon the Plate by curious small round and deep holes these are by another Line without it which is divided and figured the Common way distinguished and numbred by Figures according to the Common manner Then for the sub-Divisions I make a small Hold-fast by a Screw which is fixed on to the moveable Arm of the Quadrant this serves to hold the end of a Diagonal Hair the other end of which is strain'd over the Supplementary Degree till it lyeth directly over some prickt-Hole of the curious Divisions on the Limb of the Quadrant this gives me the sub-Divisions of the Quadrant to what accurateness I desire The Supplementary Degree is a Degree of a very large Circle put on upon a small Rule fixed on to the side of the moveable Arm whose Magnitude and Distance is found by this Proportion as the Distance between the end of the small Hold-fast and the pointed Circle is to the Radius of that Circle so make the Distance between the said End and the Supplementary Circle to the Radius of that Circle This will be more plain by a Scheme Let a a a in the 32th Figure represent a Quadrant b b b a very fine Circle struck on the Limb of the Quadrant from the Center l which by a large Quadrant of 10 foot Radius I divide into Degrees and by a springing Point strike so many small Points and number them to 90. beginning at m and numbring towards i. Let d d represent the moveable Arm c c the hold-fast fixed upon the side of that Arm which by a small Screw pincheth and holds fast a very fine Hair at k ee the small Ruler fixed at right Angles with the Line l k f in this Line through the Points l and k I take a Point as f and through f I strike a part of a Circle f g whose Center is somewhere in the Line f k l produced which I find by resolving this Proportion as k i is to l i so will k f be to the Radius of the Supplementary Circle f g which will fall somewhere in f k l produced towards l then take a Degree of that Circle which will extend from f to g and divide it into as minute Divisions as are necessary and number them from f to g. Now to find what Angle the Sight d d maketh with the Sight m m I strain the Hair h k till I find it lye over the next Division Point towards the right hand and observe in the Ruler e e what part of a
Distance which I find set down at the latter end of his Mechanicks as a Supplement to the rest Divisionis puncta habentis transversalia modus talis est ut 34 exprimit figura in qua singula denominata per Lincolas in decem interstitia aequalia discriminatum punctis notata sunt sicque regula fiducioe quodcunque horum inter observandum transiens ip sum minutum gradus quòd quaerebatur promit aut aliquotam ejus partem prout ab hoc vel illo puncto removeri discernitur Ut vero hoc etiam demonstratum hic addam ob sciolos fortè quosdam qui ea quae non satìs capiunt carpunt sic habe In Figura 34. Sit A centrum Instrumenti ejusque Semidiamiter A O assumitur autem O I Particula in qua divisio ista per lineas transver sas fit ea proportione quae est 1 ad 48. qualis in meis Instrumentis ut plurimum usurpatur Cúmque A I ponatur partium 10000000000. integri canonis majoris Rhetici erit earundem O I 208333333 utpote pars quadragesima octava radii Arcus I E sit 20′ IV. 10′ horum sinus 29088779 Y I. Sinus autem secundus corundem 42308. V Y. qui additus N V quod aequale est O I facit N Y 208375641. In triangulo igitur NYI ad Y rectangulo nota sunt duo Latera N Y Y I. quare datur basis I N 210396208. una cum angulo NIY 82° 3′ 10″ 47‴ sui additus YIA 89° 50′ conficit N I A. 171° 53′ 10″ 47‴ Basis verò N I in triangulo rectangulo N V I dividatur in decem partes aequales ut conveniant uni minuto 21039621 representatae per I B. Moxque in triangulo obliquengulo BIA dantur duo latera IB IA. radius una cum angulo BIA qui idem est cum NIA 171° 53′ 10″ 47‴ prius reperto quare innotescit angulus IAB 1′ 1″ 7‴ qui tantummodo 1′ esse deberet ità ut major sit saltem 1″ 7‴ differentia sanè insensibili similiter si F I assumatur noven particularum erunt eae 189356587 habebimusque rursus triangulum F I A in quo dantur duo latera FI modo dictum una cum radio I A. angulo F I A ab iisdem comprehenso velut antea exurgitque angulus I A F 9′ 1″ 6‴ qui debebat esse 9′ exacte deficiente in ultimo minuto F N. 1″ 6‴ Porrò ut circa medium idem tentetur quod nunc apud extremitates fecimus inveniuntur eadem qua antea primo Angulus NAH 5′ 3″ 6‴ abundans 3″ 6‴ Secundo Angulus N A H 4′ 56″ 55‴ deficiens 3″ 5‴ Patet itaque quod maxima differentia five adjectiva five ablativa in hac pragmatia proveniat minimum quid ultra 3″ quam subtilitatem visus acumen discernere in quocunque tandem instrumento nullatenus sustinet quae etiam per se otiosa est quare frustra nodum in Scirpo quaerunt si qui hanc nostram satis accuratam distributionis formam cavillari praesumant By which 't is evident that Ticho understood an inequality and what it was and that it was insensible and so not to be regarded Now 't is to me very wonderful indeed that Ticho having thought of a way of calculating this inequality should not think of an easie expedient of reforming it by putting the Parallel Circles at unequal but their due proportionate distances And 't is much more strange that Hevelius should still affirm it to be a way not Geometrical For to any one that considers this proportion the inclination of a Diagonal Line being given to find the true distances of the Parallel Circles that shall divide any assignable part thereof in any proportion assigned Nothing can be more easie and for more expedition use may be made of the Table of Natural Tangents which is ready calculated to hand For instance Let B C represent a Diagonal Line subtending an angul of 10◠at the Center A produce the said Line BC to F and let full a Perpendicular from the Center A to E. Suppose then the Angle at B to be one Degree then is B E the Tangent of 89° to the Radius A E. and E C is the Tangent of 88. 50′ and the differences between the Tangents of 88 50 88 51.88 52.88 53.88 54.88 55.88 56.88 57. 88 58.88 59. and 89. gives the Distances of the several Circles C. 1 2 3 4 5 6 7 8 9 B. desired Since the Reading of this Lecture Dr. Wallis hath also described another way of finding these Distances which he hath communicated in a Letter to Hevelius and I have prevailed with the said Doctor to permit it to be here printed being very ingenious and accurate and proceeding by a differing method Dr. Wallis his Letter to Hevelius SED est cur communi omnium Literatorum nomine rebus praesertim caelicis addictorum reddam gratias tum ob immensos in tanto apparatu sumptos erogatos tam praetiosum conquirendo supellectilem Astronomicam graphice hic descriptam tum ob indefessos labores insomnes noctes diesque occupatissimos coelestis acquirendis observationibus impensos quarum vim ingentem The saurum supra aurum margaritus praetiosum erudito orbi jam ante dederis plura daturus indies verum non est ut sperem me verbis aequare posse tua merita qui ex privato penu sumptos plane Regios erogasti onusque suscepisti non infeliciter Herculeis Humeris ne Atlanteis dicam formidandum Oper is partem maximam jam evolvi miratus inibi tanta molis Instrumentorum ingeniosissimum regimen subtilissimam divisionum administrationem cum pari diligentia conjunctam in Regulis Dioptris solicite curandis quidem si hoc deesset reliquus in cassum caederet labor quippe exiguus vix evitabilis in Regulis aut Dioptris error totum Instrumentum vitiaret omnesque inficeret observationes sed singulis immorari non licet unum tamen est quod attingam breviter nempe divisiones per Line as Diagonales circulos in limbo concentricos oblique secantes Hanc dividendi methodum jam diu receptam ipse retines quidem merito circulosque hos concentricos aequalibus intervallis disjunctos habes quod quamvis in exiguorum aut etiam mediocrium Instrumentorum limbis latioribus aliquid erroris possit inducere in tuis tamen tantae amplitudinis Instrument is cum limbis exiguae latitudinis quod turecte mones nihil quicquam erit discriminis quod in sensus occurrere possit Hac tamen occasine libet hic subjicere quod ea de rejam olim circa A. 1650. aut 1651. meditatus sum atque apud auversaria mea nunc reperio nempe si quis vellet minoris Instrumenti limbum latiorem Lineis Diagonalibus sic dividere quibus intervallis oporteat concentricos illos circulos disponere ut angulos invicem aequales designarent
set to the Objects will continue to be so for as long a time as shall be desired without at all requiring the help of any one hand of the Observator though he be but one My way then in short is this I make an Axis of very dry and strong Dram-Fir of a bigness thick enough for its length to desend it from bending at the lower end of this I fix into the middle of it well bound and hoop'd about with Iron a Center or Point of Steel very well turn'd hardned and sharp which is to move in a conical hole fit to receive it of as good and well hardned Steel at the other end of this Rod I fix another piece of Steel into the middle thereof that immediately contiguous to the Wood hath a Neck very well turn'd and hardned a little tapering from the Wood outward which is to be moved in a Collar fit for it as I shall shew by and by and at a convenient Distance from the said Neck as at somewhat more then half the Radius of the Instrument is made a Cylindrical Neck fitted with a Collar of Brass with a Joynt and other Apparatus large enough to carry the Table and Instrument firm and true without sliding or yielding in its Socker after it be once set This Axis by the Collar and conical hole below I place parallel to the Axis which by some tryals is easily enough adjusted about the Cylindrical Neck at the upper end of this Axis is a Socket of Brass fastned with a Screw which Socket claspeth in a Joynt a short Arm which hath at one end a Ball that is fitted into a Socket that is fixed under the Table and Frame of the Quadrant and at the other end a Counterpoise of Lead to ballance the weight of the whole Apparatus about the Quadrant upon the middle Line of the long Axis then the Table and Quadrant is rectifi'd so as to lye in the Plain of the two celestial Objects whether Planets or fixt Stars and by the small Screws in the Sockets it is fixt in that Plain What further adjusting is requisite is done by the help of small Screws in the Quadiant it self which are easily enough conceiv'd without Description The Table being adjusted to the Plain of the Objects with the Quadrant on it and all counterpois'd pretty near by the poises underneath the Table and the fixed Sight directed to one of the said Objects the said Table and Instrument continues to be in that Plain so long as is desired without any father trouble to the Observer though the Objects continually change their places and the fixt Sight remains directed at one of the Objects till the other can be found by the moveable Sight To effect which motion of the Table and Instrument a Watch-work is fitted to the Axis so as to make it move round in the same time with a diurnal revolution of the Earth and consequently to keep even pace with the seeming motion of the fixt Stars the manner of doing which is thus About some part of the Axis where 't is most convenient for the Room in which 't is to be used six an Octant of a Wheel of 3 foot Radius let the Rim of this be turn'd true to the Centers of the Axis and cut the edge there of into 360 Teeth there being so many half minutes of an hour in the 8th part of a whole Revolution though these minutes and hours which respect the fixt Stars will be considerably shorter then the solar hours then sit a Worm or Screw to these Teeth that one revolution of the Worm being made in ½ a minute may move one Tooth forward the revolution of the Worm is adjusted by a circular Pendulum which is carried round by a Flie moved in the form of a one wheel'd Jack from a swash toothed Wheel fastned upon the shank of the Worm or Screw above-mention'd the weight that carries round this Wheel must hang upon the shank of the Worm and must be of about a 3d. or 4th part of the weight of the Quadrant and Table that it may carry it round steadily and strongly and the circular Pendulum must be so order'd that the Observator may at any time of his Observation either shorten or produce the length thereof so as to make it move quicker or slower as there shall be occasion which is done by sliding the hole upon which the Pendulum makes its conical motion a little higher or lower without listing up or letting down the Pendulum or else by winding up the Thread of the Pendulum a little shorter or letting it down a little longer by the help of a Cylinder above the hole or apex of the Cone in which the Pendulum is moved This whole Contrivance will be somewhat better understood by a Delineation Let a b then in the 15th Figure represent the Axis of Fir or Iron c the conical Point at the bottom d the conical center or hole in which it is to move e the Collar above in which the tapering Neck of the iron Par f is to be moved The Axis of this is to be placed as exactly as may be parallel to the Axis of the Earth at the end or head of the Iron f g is fitted a Socket b h with a Screw 4 which will fix it to the head in any posture This Socket hh in the 15 and 16 Figures hath a large Joynt to be stiffned by a Screw 5 in which Joynt is moved a strong Bar of Iron about 4 foot in length to wit 2 foot on each side of the Joynt the one end 6 hath a large weight or counter poise of Lead 8 which serveth to counter ballance the whole weight of the Frame and Instrument upon the other and can be screw'd either nearer to or farther from the Joynt as there shall be occasion for poising at the other end of the Iron is a large Ball of Iron 7 to which is fitted also a Socket of Brass 9 with a Screw to fix it and move it as there shall be occasion This Socket is fastned under the middle of a Table s s upon the plain side of which the Quadrant is to lye Upon some convenient part of this Axis is fixed an Octant or Sextant of a Circle represented in the 15th Figure edge-ways and in the 17th Figure broad-ways by 3 3 ii whose circular edge 3 3 is cut into Teeth as before is directed unto these is adjusted a Worm or Screw k which is the Axis or Arbor of the Wheel PII this Wheel is moved round by the weight x whose Line is coiled round the Barrel u u and with it it turneth round the Flie n n by the help of a Screw m fixed upon the Arbor o o in the manner of the Flie of a one wheel'd Jack this Flie moveth circularly the Pendulum p p in the 15th and 29th Figures which is shortned or lengthned by slipping up and down the Cylinder q q the Thread of the
Reflecting-plates that make those flexures The third and fourteenth Figures represent the Tube shortned by two or three reflections and so serves to shorten the Tube by two thirds only These are of use for a very strong Eye and with a small aperture of the Object-Glass and when the Sun is near the Horizon or its light is a little diminished by a Fogg thin Clouds or the like If it be thought more convenient to have this long Tube to lie alwaies Horizontal and consequently that there should be no need of having a Pole or Engine to raise the Tube It may be framed somewhat like that in the fourth Figure where the same Letters answer to all the parts above-mentioned or else like that in the sixth Figure the Letters of both which being the same with the former will easily explain them Now in all these and 20 other contrivances of this nature with one two three or four Reflecting-plates which may be presently thought of the sight is directed exactly at the Sun so that there will be little difficulty of finding it after the Glasses are fixt to their due lengths and positions I explained also at the same time to the Royal Society at their publick Meeting at Arundel-house several other waies of facilitating the use of very long Glasses for other Objects in the heaven by the help of one Reflecting plate only and that was by a Tube fixed either perpendicularly horizontally or obliquely for it mattered not whether as to the seeing the Object in any part of the Heaven supposing other circumstances hindred not and the object could be as easily found as by the common Telescopes of the same length But of these elsewhere These contrivances with four Reflections may be made use of by such whose sight is weak but such as can endure it somewhat brighter and would see the parts more strong may make use of one of three Reflections only like that of Fig. 14. which doth best suit my eye Next this Helioscope may be made by Reflection only without any Refraction and that may be done either in the manner of that in the seventh Figure when a b represents a concave surface of a black Glass whose focus is o which for Instance we will suppose at the distance of forty foot c d represents a clear plate of Glass of two flat surfaces which are made not parallel but a little inclining so as the reflection from that side which is furthest from the concave may be cast another way and not fall at all upon the third Reflecting-plate ◠ζ and because the wedg-like form of this transparent plate of Glass c d will cause a refraction and consequently a coloration of the Ray therefore there must be another wedg-like Plate exactly as may be like the former which at some distance as at m p where the reflection will not come to fall upon the Plate ◠ζ must be so fixed that the thinnest part of this may lie just upon the thickest part of c d and the thickest of this over the thinnest of that by which means both the false reflections and refractions will be removed From ◠ζ that Rays are reflected to γ θ and from γ θ to o the focus and so through the lens z to the eye x. This I take to be the best by Reflection but it may be twenty other waies contrived which I shall not now spend more time in describing it being so easie a matter from the consideration of these I have mentioned to make an hundred other variations of the principle To this Helioscope may be fitted Instruments for measuring the Maculae faculae and Nebulae visible in the body of the Sun as also the spaces passed by them in a day two three ten c. together with the variation of their Figures and Magnitudes but the diameter of the body of the Sun will be better taken by the following Instrument And by reason that it will be often necessary to draw their figures more exactly the Engine that I have described in my Animadversions in the 67 68 and 69 pages may be made use of to keep the Helioscope alwaies directed at the body of the Sun which will be no small ease to an Observer that is to delineate the figures on Paper When the brightness and radiation of the Moon Venus or Jupiter do somewhat offend the eye they will presently lose their beards and look very distinct if one reflection from glass be made use of in the Telescope Another Instrument I promised to describe is for taking any such Diameters transits or distance to the certainty of a second Minute by which more may be done for the finding the Parallax of the superiour Planets and the Longitude on the Earth then hath been ever yet done by all the Instruments that have been used in the World 1. This is made exactly in all particulars like the Quadrant as to its hollow centre Screwd-limb Screw-frame and long Rod to turn the Screw from the Centre and that the Screw-frame may be kept down the truer upon the edge of the Limb there should be made a small Arm to clasp behind the inward limb of the Instrument after the manner represented in the 8th Figure by w by which means the Screw will be kept close steady and eaven to the outward edge of the Limb. The Letters in this 8th Figure being the same with those of the 1 and 11th Figures of the Animadversions and representing the same parts need no further explanation 2. Instead of this Screw upon a circular Limb a Screw may be made to move upon a straight Limb or Ruler the end of which must move upon Centres or Rowlers the centres or axes of which Rowlers must be exactly in the same line when both the Perspective-sights are adjusted to the same Object and the divisions began The same thing may be done by a straight Screw in the manner of a pair of dividing Compasses where the same care must also be had that the axes of the Rowlers must be exactly in the same line and the sides of the Incompassing-screw being made of steel must be made to spring about the long Straight-screw this long Screw must be made of steel of half an inch of diameter at least if it be made 18 inches long and 't will be best to screw it with a small thred otherwise it will be apt to be moved out of a straight by screwing a large thred and the thred whether greater or less must be made by degrees with a pair of cutting-stocks that may be set closer every time of screwing The manner of contriving the Centres and Sockets may be seen in the 12 and 13 Figures where the 13 represents it in an end way Prospect and the 12 in a lateral or side-Prospect 1 is the Rowler of the upper Tube and 2 of the under 33 the Screws to fasten them in the holes 44 the incompassing or Socket-screw which springeth close to the Cylinder
5 6 the Cylinderical smooth Socket which guides the Cylindricalscrew so as to make its Axis pass exactly over the center of the Rowler 22 and which by means of a Ring 7 on the screw keepeth the pointed-end thereof 8 against the stay or portance 9 't is not difficult how to make a Dividing-plate and an Hand or Index thereunto nor how it may be turned from the centre of the two Tubes by a long Rod as in the 8th Figure nor vvill it be difficult after it is known by Observation how many Revolutions and vvhat part of a Revolution answers to five whole degrees to calculate a Table of Subtenses which shall shew vvhat part thereof goeth to make the subtense of every Minute and Second of the said angle 3. The same thing in the year 1665 I performed by a Rowler rowling upon the limb of the Quadrant by the help of two Wires vvhich vvere coyled about those Rowlers and the ends thereof were fastned upon the limb of the Quadrant for by a large index on the end of this Rowler I was able to move the arm of the Instrument to any fifth Second of the Quadrant vvith great ease and certainty I also at the same time made another Frame with a straight Screw vvhich opened to five degrees only vvith Tumbrels or Rowlers like a pair of dividing Compasses after the same manner vvith this I have newly described for taking Diameters or Distances to five degrees and by the help of very curious Lines drawn upon a smooth Glass-plate and Points very curiously made at every five degrees on the limb of the Quadrant or Instrument on vvhich it vvas fixt and the help of a very deep Plano convex lens vvhose plain side vvas turned downwards towards the Plate and the convex side towards the eye the said Frame vvas moveable from five degrees to five degrees upon the whole limb of the Quadrant or Instrument by vvhich Instrument I could vvith great ease actually and accurate divide an angle into every five Seconds and consequently take any angle to the accurateness of sive Seconds for removing the Frame to the next division less than the Angle desired and then by the Glass fixing one of the Arms that had the plate exactly over the hole or point of division by the Screw the remaining part of the Angle could be exactly measured As to the method of dividing any of these the best vvay vvill be to measure upon some Plain 1000 1500 or 2000 foot in length by two Rods of twenty foot long a piece or else by Wires strained vvith vveights the vvay of which I shall shortly describe Beginning from the very centre of the Instrument and at the end thereof to set up so many Deal-boards joyned to the end of each other in a streight line or else to strain a pretty big Line vvhich shall cut the measured line of distance from the center of the Instrument at Right-angles and then by a Table of natural tangents according to the distance from the centre of the Quadrant put as Radius to set and mark off upon those Boards or Lines the divisions of Degrees and Minutes by Compasses or Rules as exactly as may be and mark them accordingly that the Degrees may be distinguished very plainly from the Minutes Then having adjusted the Instrument so as to see the beginning of those Divisions through both the Tubes at once to set both the Indices to o or the beginning of the divisions then keeping the undermost of the two Tubes fixt to the same place so as still to respect the same point or beginning of the Divisions upon the Boards or Line by the help of the Rod to turn the Screw or Rowl till you find the upper Tube to respect the first minute and then the first degree and so till you see the last minute of the five vvhole degrees or vvhatever Angle else you design it to take in then for the first and third way reckon how many vvhole Revolutions and vvhat part of a Revolution goeth to make up that vvhole Angle and subdivide the same by a small Table into Minutes and Seconds and you vvill presently find by the Trial that you vvill be able to divide to a strange accurateness upon those Boards by the help of your Tubes and Screw even at the distance of 1000 1500 or 2000 foot and even almost to equalize the Divisions by your Compasses when at the very Boards And by this you may easily examine whether your Instrument doth make the sub-divisions exactly or not which will be a great confirmation of the certainty and truth of your Instrument But for the second way by streight Screws the Table of Sub-division into degrees minutes and seconds must be proportioned according to the length of Subtenses answering to the Radius which is the distance of the centre of the Rowlers from the centre of the Instrument Now because in an Instrument of this bigness it will be somewhat troublesome to turn the whole Angle by the help of the Screw upon the Limb vvhich I find also is somewhat troublesome in the Instrument of three foot Radius vvhen the Angle is large therefore for preventing of that trouble and to be able immediately to open the Instrument to the Angle desired or very near it The Screw l in the first Figure of my Animadv at the end of the moveable Arm is made by unscrewing to draw off the long Screw from touching the threds on the Limb which being done the Arm is at liberty to be moved to any part of the Quadrant when by returning the Screw l the Screw-frame and Screw is brought down again to take hold of the Threds of the Limb of the Instrument The only care to be taken in this action is that neither the Index e e be at all moved out of its posture to the Index-frame h h nor the Index 8 be moved at all about the rod of the Screw 999. It matters not at all though the Screw-rod 999 be turned round or moved so as it be done by the Rod 000 and the handle thereof p p or by the small handle x at the end of the Screw-rod and that the Index 8 being very stiffly fixt to the said Rod be moved round with it by the same motion without varying its position to the Rod for being again brought down by the return of the Screw l to take hold of the Threds of the Limb into which it must be steadily guided by hand the Index e e will shew upon the Limb the number of Threds or Revolutions from the beginning and the Index 8 will shew what part of a Revolution there is to be joyned to it I hope I shall not need to spend time to explicate how the Centre of these Tubes are to be made nor how the Glasses and Thred-sights are to be fixt nor need I much to shew how the Tubes may be stiffned to keep them from warping very much A small matter of
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
figure Now though the Comets appearance be this way caused and so a man might conceive the Globous body would in a little time by so copious an emanation be consumed yet I do not believe that it doth in a short time wast and disperse the whole Ball nor can I conceive that the disappearing of those blazing bodies toward the latter end does depend upon their dissolution though possibly that may somewhat diminish them but that rather is to be ascribed to their distance and position in respect of us Though this I remember I observed very manifestly in that of 1664. that the body toward the latter end of its appearing was very much less in proportion to the radiations about it than it seemed to be at the beginning but whether that might not be partly ascribed to the great distance it then was from us and the turning of the head pretty near towards us and thence the spreading of the Tail appearing beyond it might add to the breadth of the radiation about the Nucleus I will not positively determine Now though for explication sake I have compared the parts separated from the body of the Comet to blazing Granadoes or Fire-balls yet I would not be understood to suppose these parts so separated to be of any very large bulk for I see no necessity to suppose them bigger than the Atoms of smoke or the particles of any other steaming body or than the parts of the Air which make the body of it appear thick and hazy nor do I believe that all the light of the Star head and blaze does depend only upon the shining of the dissolving body and particles thereof but I do suppose that it doth proceed both from the reflection of the Sun-beams from those parts and also from an innate and momentaneous light produced by the action of dissolution wrought on the parts by the incompassing Aether It may possibly seem very difficult to suppose that the dissolution of the parts of the Nucleus by the incompassing Aether should cause or impress so violent a motion into the separated parts as to make them depart from it to the space of four or five Diameters before it be over-powered by the power of Levitation from the body of the Sun and so deflected into a parabolical line upwards It may likewise seem strange to suppose that the Aether should have such power in it as first to dissolve a body into it self and secondly to cause a shining and thirdly to cause a Levitation of the dissolved parts upwards whereas I supposed before and I think 't is very manifest that they cause a gravitation downwards towards the Center of the Sun But to these for explication I answer that we need not go far for instances to make these things probable the Atmosphere about the Earth as I have formerly mentioned in my Micrographia I take to be nothing else but the dissolution of the parts of the Earth into the incompassing Aether for the proof of which I could bring many arguments were it here a proper place by which I could most evidently demonstrate the thing to be as I have asserted It is here evident that this Aether doth take up the particles of bodies to a very great distance from the surface from which they were separated and it doth not only raise them but susteins them at those heights nor is this peculiar only to the Aether when a menstruum but to all dissolving menstruums in general As to give one instance in stead of many we find that Gold the heaviest of all Terrestrial bodies we yet know being dissolved by Aqua Regis is taken up into it and kept suspended therein though the parts of the Gold be fifteen times heavier than the parts of the Aqua Regis So Pit-coal though very heavy is yet taken up into the Air and kept suspended therein though it will be found to be some thousands of times more ponderous than the menstruum of the Air that keeps it suspended Many reasons I could produce to shew the great power of the Aether and the universality of its activity almost in all sensible motions but reserving them for another Discourse hereafter I shall at present only mention those suppositions which seem to have the greatest difficulty in this Theory viz. how the dissolution of the parts of the Star by the incompassing Aether should cause light and secondly how it should cause an actual Levitation of the dissolving particles upwards For the explication of these two difficulties I must at present crave favour to explain them by examples taken from operations of Nature in the Atmosphere wherein we live very similar and analogous to them First for the production of light we find that the Air incompassing the steams of bodies prepared by heat or otherwise and made fit for dissolution doth so operate upon them as to make them fly and part asunder with a very impetuous motion insomuch that the small particles or Atoms of the dissolved bodies do not only leave one another but depart and dart out with so great an impetuosity as to drive off all the incompassing Air from their Center from whence they flew and this I take to be the cause not only of their Light but also of their Levity upwards this may be seen very plainly by the small parts of crackling Char-coal which upon the blowing them with Bellows and so crowding a great quantity of the fresh menstruum on them fly and dart asunder with great celerity and noise but is abundantly more evident in the kindling of Gun-powder where the impetuosity is so very great as to drive away not only all the incompassing Air but all other bodies though never so solid that hinder its expansion in the performing of which operation the Aether hath a great share as I may hereafter shew 't is very probable that the Aether in the same manner dissolving the particles of the Star causeth the Atoms thereof to fly asunder with so great an impetuosity as to leave a vacuity even of the parts of the Aether which flying asunder doth not only cause light by impressing on the Aether a stroke or pulse which propagates every way in Orbem but maketh such an agitation of the the Aether as causes a rarefaction in the parts thereof whilst the parts that are once actually separated by continual rebounding one against another before they come to be at rest and quietly to touch each other prolong that first separation or vacuity between them This Explication though it be somewhat difficult yet I hope it is intelligible and may be with probability enough supposed to be the true cause of the appearance whilst there is nothing therein supposed which is not manifestly the method of Nature in other operations and though the supposition even of the Aether may seem to be a Chimera and groundless yet had I now time I could by many very sensible and undeniable experiments prove the existence and reality thereof and
be glad to understand I would willingly also be informed whether my Letter of the second of December mention'd above be come to your hands and how those Observations do please the Gentlemen of your Society and also to understand the receipt of this The manner how the said Mr. Leeuwenhoeck doth make these discoveries he doth as yet not think fit to impart for reasons best known to himself and therefore I am not able to acquaint you with what it is but as to the ways I have made use of I here freely discover that all such persons as have a desire to make any enquiries into Nature this way may be the better inabled so to do First for the manner of holding the liquor so as to examine it by the Microscope I find that the way prescribed by Mr. Leeuwenhoeck is to include the same in a very fine pipe of glass and then to view it by the help of the Microscope for by placing that at a due distance whatever is contained in the said liquor will most easily be discovered The liquor will most easily insinuate it self into the cavity of the said pipe if the end thereof only be just put within the liquor This as it is exceedingly convenient for many trials so is it not very difficult to prepare but because every one is not instructed how to proceed in this matter and it may cause him more trouble than needs to procure them I will here describe the way and so much the rather because the same apparatus will serve for the preparing of Microscopes as I shall afterwards shew Provide then a box made of tin with a flat bottom and upright on all sides let this have fixed within it to the bottom a small piece of tin hollowed like a ridg tile so that the wiek of the Lamp may lie and rest upon it and let the Tin-man fix on it a cover of tin so that there may be only left one part of the aforesaid box open to wit where the bent tin piece and the wiek do lie and come above the sides this cover may be turned back on its hinges when there is occasion to raise the wiek or put in more oyl c. but for the most part ought to lie flat and covered for whilst it is using it is necessary to keep the flame from spreading too much and taking fire all over This box must stand within another box of tin made large enough to contain it the use of which is to keep the former Lamp box from fowling the board or table on which it stands This stands upon a board about one foot square into which is fastned a standard or stick upright cleft so as to pinch and hold the sodering pipe between its clefts which may be fastned with a screw or a slipping ring through which pipe blowing with your breath the flame will be darted forward with great swiftness and brightness if then into this flame you hold a small piece of a glass pipe made of white glass for green glass or coarser glass will not be melted easily in this flame and keep it turning round between your fingers and thumbs you shall find that the flame will in a very short time melt the middle part of the said pipe so that if you remove it out of the flame and draw your hands one from another you may easily draw the former pipe into a very small size which will yet remain hollow though drawn never so small The best Oyl for this purpose is good clean Sallat Oyl or Oyl Olive but high rectified Spirit of Wine is yet better and cleanlier but much more chargeable and for most uses the Oyl Olive will serve This I have set down because many who are far off in the Country cannot have the convenience of going to a Lamp-blower as oft as they have occasion for such pipes which if they provide themselves with small white glass pipes from the Potters they may accommodate themselves withal though they have nothing but a large candle and a tobacco-pipe instead of the aforesaid apparatus though not altogether so conveniently But I would rather advise them to have a Lamp made which most Tin-men know how to fit and prepare and so it will not need much more description But this way of Mr. Leeuwenhoecks of holding the liquors in small glass pipes though it be exceedingly ingenious and very convenient for many examinations yet for divers others 't is not so well accommodated as this which I contrived my self for my own trials at least for those Microscopes I make use of what it may be for those which Mr. Leeuwenhoeck uses I know not I take then instead of a glass pipe a very thin plate of Muscovy glass this serves instead of the moveable plate which is usually put upon the pedestal of Microscopes but because the common pedestal hitherto made use of in Microscopes is generally not so convenient for trials of this nature I lay those by and instead thereof I fix into the bottom of the Tube of the Microscope a cylindrical rod of Brass or Iron Upon this a little socket is made to slide to and fro and by means of a pretty stiff spring will stand fast in any place This hath fastned to it a joynted arm of three or four joynts and at the end a plate about the bigness of a half crown with a hole in the middle of it about three quarters of an inch wide upon this plate I lay the Muscovy glass and upon that I spread a very little of the liquor to be examined then looking against the flame of a Candle or a Lamp or a small reflection of the Sun from a globular body all such parts of the liquor as have differing refraction will manifestly appear By this means I examined the water in which I had steeped the pepper I formerly mentioned and as if I had been looking upon a Sea I saw infinite of small living Creatures swimming and playing up and down in it a thing indeed very wonderful to behold If the flame of the candle were directly before the Microscope then all those little Creatures appeared perfectly defin'd by a black line and the bodies of them somewhat darker than the water but if the candle were removed a little out of the axis of vision all those little Creatures appeared like so many small pearls or little bubbles of air and the liquor in which they swimmed appeared dark but when the water began to dry off the bending of the superficies of the liquor over their backs and over the tops of other small motes which were in the water made a confused appearance which some not used to these kind of examinations took to be quite differing things from what they were really and the appearances here are so very strange that to one not well accustomed to the phaenomena of fluids of differing figures and refractions the examinations of substances this way will be very apt to mis-inform
rather than instruct him especially of such substances as are not perfectly fluid and will not readily and naturally smooth their own superficies such as Tallow concreted Oyls Marrow Brains Fat inspissated juyces c. for if those substances be so examined by spreading them upon this plate and be looked upon against the candle or other small defined light all the inequalities left on the surface by the spreading do by the refractions of the rays of light render such odd appearances that they will easily deceive the examinator and make him to conceive that to be in the texture of the part which is really no where but in the make of the superficies of it This therefore as another great inconvenience to be met with in Microscopical Observations I prevent by these ensuing methods First all such bodies as Fat Oyl Brains Rhobs Pus tough concreted Flegm and the like whose surfaces are irregular and ought to be reduced to smoothness before they can be well examined I order in this manner First I provide a very clear and thin piece of looking-glass plate very smooth and plain on both sides and clean from foulness upon the surface of this I lay some of those substances I last mentioned then with such another piece of Looking-glass plate laid upon the said substance I press it so thin as not only to make the surfaces of it very smooth but also to make the substance of it very thin because otherwise if the substance be pretty thick as suppose as thick as a piece of Venice paper if it be a whitish substance the multitudes of parts lying one upon another in such a thickness do so confound the sight that none of them all can be distinctly seen but if by squeezing the said plates hard and close together it be reduced to a twentieth part perhaps of that thickness the substance may be well looked through and the constituent parts may be very plainly discovered Thus also 't is very visible in the Globules of milk and blood discovered by the ingenious Mr. Leeuwenhoeck for when either of those substances are thick the multitude of those little Globules confound and thicken the liquor so as one cannot perceive any thing until it be run very thin for then all the remaining Globules with their motions may very distinctly be apprehended This therefore is an expedient by which thousands of substances may be examined and therefore the more fit to be communicated that there may be the greater number of observers well accommodated for such trials These plates therefore may be contrived so as to be pinched together by the help of screws and a frame that thereby they may be forced the closer and the evener together as there shall be occasion and may be kept firm and steady in that posture and then that it may some ways or other be conveniently fastned to the former plate so as to be moved this way or that way steadily as there shall be occasion But there are other substances which none of these ways I have yet mentioned will examine and those are such parts of animal or vegetable bodies as have a peculiar form figure or shape out of which if it be put the principal thing looked after is destroyed such are the Nerves Muscles Tendons Ligaments Membranes Glandules Parenchymas c. of the body of Animals and the Pulps Piths Woods Barks Leaves Flowers c. of Vegetables Some of these which are not made by dissection or separation from other parts may be viewed alone but there are others which cannot be well examined unless they be made to swim in a liquor proper and convenient for them as for instance the parts of flesh muscles and tendons for if you view the fibres of a muscle encompassed only with the air you cannot discover the small parts out of which it is made but if the same be put into a liquor as water or very clear oyl you may clearly see such a fabrick as is truly very admirable and such as none hitherto hath discovered that ever I could meet with of which more hereafter when I shew the true mechanical fabrick thereof and what causes its motion Thus if you view a thred of a Ligament you shall plainly see it to be made up of an infinite company of exceeding small threads smooth and round lying close together each of which threads is not above a four hundredth part of the bigness of a hair for comparing those of Beef with a hair of my head which was very fine and small viz. about a 640. part of an inch I found the Diameter thereof to be more than twenty times the Diameter of these threads so that no less than 163 millions besides 840 thousands of these must be in a ligament one inch square I shall not here enlarge upon the admirable contrivance of Nature in this particular nor say any thing farther of the reason of the greater strength of the same substance drawn into smaller than into greater threads but only this in general that the mechanical operations of these minute bodies are quite differing from those of bodies of greater bulk and the want of considering this one thing hath been the cause of very great absurdities in the Hypotheses of some of our more eminent modern Philosophers For he that imagines the actions of these lesser bodies the same with those of the larger and tractable bodies will indeed make but Aristotles wooden hand at best This put me in mind likewise of advertising the Experimenter that he provide himself with instruments by which to stretch and pull in pieces any substance whilst the same is yet in view of the Microscope of which there may be many which any one will easily contrive when he hath this hint given him of the usefulness thereof in the examination of the texture of several substances as of Tendons Nerves Muscles c. those I have made use of were made to open like a pair of Tobacco Tongues by two angular plates of thin brass rivetted together which by pinching the opposite end would either open or shut at the other as I had occasion These having a part extended between the two tops were fixt at a due distance from the object-glass that the body extended between them might be distinctly seen then with my finger squeezing together the opposite ends the other ends opened by which means how the parts stretched and shrunk might be plainly discovered Now as this is of use for some kind of substances so the two glass plates are for others and particularly for squeezing of several substances between them so as to break them in pieces as those little Creatures in pepper-water or the Globules in blood milk flegm c. whereby the parts within them may yet farther be enquired into as Mr. Leeuwenhoeck I find hath done by his latest Observations Whether he makes use of this way or some other I know not Having thus given a description of the appurtenances
by the Ancients which being once found and Tables thereof calculated I shall anon shew a way how to calculate the power they have in shooting or casting of Arrows Bullets Stones Granadoes or the like From these Principles also it will be easie to calculate the proportionate strength of the spring of a Watch upon the Fusey thereof and consequently of adjusting the Fusey to the Spring so as to make it draw or move the Watch always with an equal force From the same also it will be easie to give the reason of the Isochrone motion of a Spring or extended string and of the uniform sound produced by those whose Vibrations are quick enough to produce an audible sound as likewise the reason of the sounds and their variations in all manner of sonorous or springing Bodies of which more on another occasion From this appears the reason as I shall shew by and by why a Spring applied to the balance of a Watch doth make the Vibrations thereof equal whether they be greater or smaller one of which kind I shewed to the right Honourable the Lord Viscount Brounker the Honourable Robert Boyle Esq and Sir Robert Morey in the year 1660. in order to have gotten Letters Patents for the use and benefit thereof From this it will be easie to make a Philosophical Scale to examine the weight of any body without putting in weights which was that which I mentioned at the end of my description of Helioscopes the ground of which was veiled under this Anagram c e d i i n n o o p s s s t t u u namely Vt pondus sic tensio The fabrick of which see in the three first figures This Scale I contrived in order to examine the gravitation of bodies towards the Center of the Earth viz. to examine whether bodies at a further distance from the Center of the Earth did not lose somewhat of their power or tendency towards it And propounded it as one of the Experiments to be tried at the top of the Pike of Teneriff and attempted the same at the top of the Tower of St. Pauls before the burning of it in the late great Fire as also at the top and bottom of the Abby of St. Peters in Westminster though these being by but small distances removed from the Surface I was not able certainly to perceive any manifest difference I propounded the same also to be tried at the bottom and several stations of deep Mines and D. Power did make some trials to that end but his Instruments not being good nothing could be certainly concluded from them These are the Phenomena of Springs and springy bodies which as they have not hitherto been by any that I know reduced to Rules so have all the attempts for the explications of the reason of their power and of springiness in general been very insufficient In the year 1660. I printed a little Tract which I called An Attempt for the explication of the Phenomena c. of the rising of water in the pores of very small Pipes Filtres c. And being unwilling then to publish this Theory as supposing it might be prejudicial to my design of Watches which I was then procuring a Patent for I only hinted the principle which I supposed to be the cause of these Phaenomena of springs in the 31 page thereof in the English Edition and in the 38 page of the Latine Edition translated by M. Behem and printed at Amsterdam 1662. But referred the further explication thereof till some other opportunity The Principles I then mentioned I called by the names of Congruity and Incongruity of bodies And promised a further explanation of what I thereby meant on some other occasion I shall here only explain so much of it as concerns the explication of this present Phaenomenon By Congruity and Incongruity then I understand nothing else but an agreement or disagreement of Bodys as to their Magnitudes and motions Those Bodies then I suppose congruous whose particles have the same Magnitude and the same degree of Velocity or else an harmonical proportion of Magnitude and harmonical degree of Velocity And those I suppose incongruous which have neither the same Magnitude nor the same degree of Velocity nor an harmonical proportion of Magnitude nor of Velocity I suppose then the sensible Universe to consist of body and motion By Body I mean somewhat receptive and communicative of motion or progression Nor can I have any other Idea thereof for neither Extention nor Quantity hardness nor softness fluidity nor fixedness Rarefaction nor Densation are the proprieties of Body but of Motion or somewhat moved By Motion I understand nothing but a power or tendency progressive of Body according to several degrees of Velocity These two do always counterballance each other in all the effects appearances and operations of Nature and therefore it is not impossible but that they may be one and the same for a little body with great motion is equivalent to a great body with little motion as to all its sensible effects in Nature I do further suppose then that all things in the Universe that become the objects of our senses are compounded of these two which we will for the present suppose distinct essences though possibly they may be found hereafter to be only differing conceptions of one and the same essence namely Body and Motion And that there is no one sensible Particle of matter but owes the greatest part of its sensible Extension to Motion whatever part thereof it ows to Body according to the common notion thereof Which is that Body is somewhat that doth perfectly fill a determinate quantity of space or extension so as necessarily to exclude all other bodies from being comprehended within the same Dimensions I do therefore define a sensible Body to be a determinate Space or Extension defended from being penetrated by another by a power from within To make this the more intelligible Imagine a very thin plate of Iron or the like a foot square to be moved with a Vibrative motion forwards and backwards the flat ways the length of a foot with so swift a motion as not to permit any other body to enter into that space within which it Vibrates this will compose such an essence as I call in my sense a Cubick foot of sensible Body which differs from the common notion of Body as this space of a Cubick foot thus defended by this Vibrating plate doth from a Cubick foot of Iron or the like throughout solid The Particles therefore that compose all bodies I do suppose to owe the greatest part of their sensible or potential Extension to a Vibrative motion This Vibrative motion I do not suppose inherent or inseparable from the Particles of body but communicated by Impulses given from other bodies in the Universe This only I suppose that the Magnitude or bulk of the body doth make it receptive of this or-that peculiar motion that is communicated and not of any other
Line of the motion of the body so shot shall be moved in a Parabola or a Line very near it I say very near it by reason that the Impediment of the medium doth hinder the exactness of it If it be delivered with treble quadruple quintuple sextuple c. the first Velocity it shall touch the floor at almost treble quadruple quintuple sextuple c. the first distance I shall not need to shew the reason why it is moved in a Parabola it having been sufficiently demonstrated long since by many others If the body be delivered by the Spring at the floor but shot by some Angle upwards knowing withwhat Velocity the same is moved when delivered and with what Inclination to the Perpendicular the same is directed and the true Velocity of a falling body you may easily know the length of the Jactus or shot and the time it will spend in passing that length This is found by comparing the time of its ascent with the time of the descent of heavy bodies The ascent of any body is easily known by comparing its Velocity with the Angle of Inclination Let a b then in the fifth Figure represent 16 foot or the space descended by a heavy body in a second minute of time If a body be shot from b in the Line b f with a Velocity as much swifter than that equal motion of 16 foot in a second as this Line b f is longer than a b the body shall fall at e for in the same space of time that the oblique equal motion would make it ascend from b d to a c will the accelerated direct motion downward move it from a c to b d and therefore at the end of the space of one second when the motions do equal and balance each other the body must be in the same Horizontal Line in which it was at first but removed asunder by the space b e and for the points it passeth through in all the intermediate spaces this method will determine it Let the Parallelogram a b p q then represent the whole Velocity of the ascent of a body by an equal motion of 16 foot in a second and the Triangle p q r represent the whole Velocity of the accelerated descending motion p b is then the Velocity with which the body is shot and p is the point of rest where the power of Gravity begins to work on the body and make it descend Now drawing Lines parallel to a q r as s t u s t gives the Velocity of the point t ascending and t u the Velocity of the same point t descending Again p b s t signifies the space ascended and p t u the space descended so that subtracting the descent from the ascent you have the height above the Line b d the consideration of this and the equal progress forwards will give the intermediate Velocities and determine the points of the Parabola Now having the Jactus given by this Scheme or Scale appropriated to the particular Velocity wherewith any body is moved in this or that line of Inclination it will be easie to find what Velocity in any Inclination will throw it to any length for in any Inclination as the square of the Velocity thus found in this Scale for any inclination is to the square of any other Velocity so is the distance found by this Scale to the distance answering to the second Velocity I have not now time to inlarge upon this speculation which would afford matter enough to fill a Volume by which all the difficulties about impressed and received motions and the Velocities and effects resulting would be easily resolved Nor have I now time to mention the great number of uses that are and may be made of Springs in Mechanick contrivances but shall only add that of all springy bodies there is none comparable to the Air for the vastness of its power of extention and contraction Upon this Principle I remember to have seen long since in Wadham Colledge in the Garden of the learned Dr. Wilkins late Bishop of Chester a Fountain so contrived as by the Spring of the included Air to throw up to a great height a large and lasting stream of water Which water was first forced into the Leaden Cistern thereof by two force Pumps which did alternately work and so condense the Air included into a small Room The contrivance of which Engine was not unknown to the Ancients as Hero in his Spiritalia does sufficiently manifest nor were they wanting in applying it to very good uses namely for Engines for quenching fire As Vitruvius by the help of the Ingenious Monsieur Clande Perraults interpretation hath acquainted us in the Twelfth Chapter of his Tenth Book where he endeavours to describe Ctesibius his Engine for quenching fire Not long since a German here in England hath added a further improvement thereof by conveying the constant stream of water through Pipes made of well tanned and liquored Leather joyned together to any convenient length by the help of brazen Screws By which the stream of water may be conveyed to any convenient place through narrow and otherwise inaccessible passages The ingenious Dr. Denys Pappin hath added a further improvement that may be made to this Ctesibian Engine by a new and excellent contrivance of his own for making of the forcing Syringe or Pump which at my desire he is pleased to communicate to the Publique by this following Description which he sent me some time since Dr. Pappins Letter containing a Description of a Wind-Fountain and his own particular contrivance about the forcer of its Syringe SInce the Artificial Fountain you have seen at Mr. Boyles which was of my making upon his desire hath been so pleasing to you as to make you desire to see my description thereof I cannot doubt but the same will be as grateful also and well received by the Publick especially when they shall therein find a remedy for one of the greatest inconveniences of forcing Pumps which are of so great use for raising of water and quenching of fires This was the occasion of my sending you this present description which would not have been thus prolix had it been only for your self In the Figure then A A is the Receptacle or body of the Fountain careful sodered in all places B B is the Pump C C the Plug or forcer D a Pipe in the middle of the Plug which is perfectly shut and stopped when the Plate E E is forced down upon it E E is the Plate with a hole in the middle upon which is sodered a Pipe F which serves for a handle to move the Plug up and down G is a Cock at the top of the Pipe which serves to moderate the Jetto or stream H H is a Valve at the bottom of the Pump which openeth outward for the passage of the water out of the Pump into the Fountain or Receptacle I I is a Cross at the top of the Plug to hinder