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
fourth as the Root of 64. that is of 19+17+15+13 at the end of the tenth or whole as the Root of 100. that is as equal to 100. Now since the Velocity is in the same proportion to the root of the space as the root of the space is to the time it is easie to determine the particular time in which every one of these spaces are passed for dividing the spaces by the Velocities corresponding the quotients give the particular times To explain this more intelligibly let A in the fourth figure represent the end of a Spring not bent or at least counterpoised in that posture by a power fixt to it and movable with it draw the line A B C and let it represent the way in which the end of the Spring by additional powers is to be moved draw to the end of it C at right Angles the Line C δ D d and let C D represent the power that is sufficient to bend or move the end of the Spring A to C then draw the Line D A and from any point of the Line A C as B B. Draw Lines parallel to C D cutting the Line D A in E E the Lines B E B E will represent the respective powers requisite to bend the end of the Spring A to B which Lines B E B E C D will be in the same proportion with the length of the bent of the Spring A B A B A C. And because the Spring hath in every point of the Line of bending A C a particular power therefore imagining infinite Lines drawn from every point of A C parallel to C D till they touch the Line A D they will all of them fill and compose the Triangle A C D. The Triangle therefore A C D will represent the aggregate of the powers of the Spring bent from A to C and the lesser Triangles A B E A B E will represent the aggregate of all the powers of the Spring bent from A to B B and the Spring bent to any point of the Line A C and let go from thence will exert in its return to A all those powers which are equal to the respective ordinates B E B E in the Triangles the sum of all which make up the Triangles A B E A B E. And the aggregate of the powers with which it returns from any point as from C to any point of the space C A as to B B is equal to the Trapezium C D E B C D E B or the excesses of the greater Triangles above the less Having therefore shewn an Image to represent the flexure and the powers so as plainly to solve and answer all Questions and Problems concerning them in the next place I come to represent the Velocities appropriated to the several powers The Velocities then being always in a subduplicate proportion of the powers that is as the Root of the powers impressed and the powers imprest being as the Trapezium or the excess of the Triangle or square of the whole space to be past above the square of the space yet unpassed if upon the Center A and space A C C being the point from which the Spring is supposed let go a Circle be described as C G G F and ordinates drawn from any point of C A the space to be past as from B B to the said Circle as B G B G these Lines B G B G will represent the Velocity of the Spring returning from C to B B c. the said ordinates being always in the same proportion with the Roots of the Trapeziums C D E B C D E B for putting A C = to a and A B = b B G will always be equal to the square of the ordinate being always equal to the Rectangle of the intercepted parts of the Diameter Having thus found the Velocities to wit B G B G A F to find the times corresponding on the Diameter A C draw a Parabola C H F whose Vertex is C and which passeth through the point F. The Ordinates of this Parabola B H B H A F are in the same proportion with the Roots of the spaces C B C B C A then making G B to H B as H B to I B and through the points C I I F drawing the curve C I I I F the respective ordinates of this curve shall represent the proportionate time that the Spring spends in returning the spaces C B C B C A. If the powers or stiffness of the Spring be greater than what I before supposed and therefore must be expressed by the Triangle C de A. then the Velocities will be the Ordinates in an Ellipse as C γ γ N greater than the Circle as it will also if the power be the same and the bulk moved by the Spring be less Then will the S-like Line of times meet with the Line A F at a point as X within the point F. But if the powers of the Spring be weaker than I supposed then will C δ e e A represent the powers and C γ γ O the Ellipsis of Velocity whose Ordinates B γ B γ A O will give the particular Velocities and the S-like Line of time will extend beyond N. The same will happen supposing the body moved by the Spring to be proportionately heavy and the powers of the Spring the same with the first And supposing the power of the Spring the same as at first bended only to B 2 and from thence let go B 2 E A is the Triangle of its powers the Ordinates of the Circle B g L are the Lines of its Velocity and the Ordinates of the S-like Line B i F are the Liues of time Having thus shewed you how the Velocity of a Spring may be computed it will be easie to calculate to what distance it will be able to shoot or throw any body that is moved by it And this must be done by comparing the Velocity of the ascent of a body thrown with the Velocity of the descent of Gravity allowance being also made for the Resistance and impediment of the medium through which it passes For instance suppose a Bow or Spring fixed at 16 foot above a Horizontal floor which is near the space that a heavy body from rest will descend perpendicularly in a second of time If a Spring deliver the body in the Horizontal line with a Velocity that moves it 16 foot in a second of time then shall it fall at 16 foot from the perpendicular point on the floor over which it was delivered with such Velocity and by its motion shall describe in the Air or space through which it passes a Parabola If the Spring be bent to twice the former Tension so as to deliver the body with double the Velocity in a Horizontal Line that is with a Velocity that moves 32 foot in a second then shall the body touch the floor in a point very near at 32 foot from the aforesaid perpendicular point and the
Instrument to adjust it upon that Frame the whole Table and Quadrant being so counterpois'd as to be easily moveable and fixt in any posture But Hevelius is pleas'd as I said before wholly to lay aside all manner of Wooden Instruments as useless and to indeavour the obtaining of Instruments of Brass or Iron Nam sayes he pag. 136. cùm longâ experientiâ probe tandem didicerim multo securius esse ex solido prorsus metallo obtinere Instrumenta tum quo majora ampliora eo esse accuratiora absolutiora adhaec prioribus admodum Tichonicum constructis plurima deesse quibus ditari merito deberent quod iisdem de causis omnino necessum sit ut parte corrigerentur meliorentur tam quà eorum materiam fructuram commotionem facilitandam divisionem quam alia diversa subsidia adminicula quo sic aptius exquisitius promptius minorique labore c. ac temporis dispendio possent Astris exponi observationésque peragi Idcirco omnem curam atque operam pro tenui ingenii mei facultatúmque mearum modulo à Deo concesso reliqua sublimioribus ingeniis at que ampliori fortunâ Viris five posteritati nostrae relinquens adhibui quo minora tam lignea universa ab Astris planè removerem atque in ejus locum ex puro solidóque metallo organa mihi compararem quidem ejusmodi quae insigni amplitudine essent conspicua simul commoditate regendi simul aliquanto accuratioribus adhuc divisionibus ad paulò subtiliores observationes obtinendas gauderent His Reasoning indeed is very good that since he had from much and long experience learn'd that Instruments of Wood after Ticho's manner were not to be trusted to by reason of their warping and shrinking and consequently that Instruments of solid Metall were much to be preferred before them and also that the larger the Instruments were the more exactly they could be made and divided and that the more easie they were to be moved and the more steddy and sure they were to be fixt in any position the more convenient they were for use he had therefore rejected all those Instruments which he had made after Ticho's way and had indeavoured to procure for his own use such as were compleat both for their matter and form having caused them to be made of Mettal that which could not be subject to the inconvenience of warping swelling or shrinking with the variety of Weather or length of Time And likewise of such a bigness as was capable of receiving more nice and curious Divisions and in the dividing them had found such contrivances and used such diligence that they were more then ordinarily true and exact As far as he has gone on with these Designs he seems to have been even profuse in his expences and exceeding bountiful of his own care labour and diligence but I could have wish'd heartily that it had been some other way imploy'd Those Instruments which he chiefly laboured to perfect he professes to be Quadrants Sectants and Octants after Ticho's manner rejecting all other Instruments of whatsoever Figures whether Radii Astrolabs Zodiacal or Aequinoctial Rings Parallactical Instruments or Hoops as more troublesome and less accurate But whether he hath in this his choice been rightly advised I shall hereafter have more occasion to examine when I come to describe an Apparatus of Instruments necessary for such a one as designs to promote and perfect the knowledge of the Coelestial Bodies and their motions wherein I shall shew that of some Instruments rejected by him there is a use absolutely necessary The Instruments therefore that he begins with are three small Quadrants of Brass the first of two foot the second of eighteen inches and the third of one foot Radius Each of these Instruments he sayes were made somewhat larger then common Quadrants to wit of an arch of 110 degrees which is to no other end but only in order to shew the subdivisions of each degree of the Quadrant by the help of a new invented Perpendicular of Brass wherewith each of them was furnisht This Invention is by him highly extoll'd for most excellent and usefull and to that end is made use of for the division of all his other Instruments both great and small Hear what he sayes of it Quiscunque hujus rei to wit the new way of subdividing the degrees of the Quadrant primus fuerit repertor sublimes profecto cogitationes exercuit hoc ipso ad congruentem effectum deducendo inter praestantissima inventa meritissimo refertur quod etiam minora Instrumenta remotis omnibus transversalibus Lineis in singula minuta corúmque particulas minimas subdividi liceat He seems indeed both here and elsewhere in many other places of his Book to be highly possest with admiration of the sublimity subtilty and extream usefulness of this invention and seems very much concern'd that the Author thereof should not certainly be known but dares not father it upon any one positively He sayes that one Benedictus Hedreus in a Work of his which he published Anno 1643. about the new and accurate Structure of the Geometrical Astrolab describes it but he gathers that he was not the Inventor himself but rather that he got both this Invention and the whole Quadrant which he describes out of the Observatory or rather Repository of Ticho Brahes Instruments for that it seems Ticho was the Inventor of this way of division and yet as I noted before he prefer'd the way by Diagonals much before it whatever Reason Hevelius had to be of a contrary Judgment What this way is I shall by and by explain But in the mean time I am sorry to find Hevelius joyning with Hedreus in the Opinion or Demonstration as Hevelius calls it that the Sub-divisions by Diagonals is not capable of a Geometrical demonstration especially in lesser Instruments which have need of many Circles I confess I understand not their meaning nor reasoning nor why it should be less demonstrable in lesser then in greater Instruments since 't is very easily demonstrable both in greater and lesser Instruments and as Geometrical as any other way of Division whatsoever the Diagonal Line being alwayes a piece of a Tangent Line that is to say the spaces between the Parallel Circles upon the Diagonals are alwayes to be in proportion to the difference of some Tangent Lines and the different distance of those Circles from the Center are alway in proportion of some Secants And the way of finding what those Tangents or Secants are and consequently what must be those Distances of the Parallel Circles I mentioned briefly before and shall now more fully demonstrate From which I will make it evident that the Theory was not as Hedreus and Hevelius have supposed uncapable of Calculation or Mechanical Demonstration But first give me leave to shew you what way Ticho Brahe made use of to demonstrate or rather to find out the true Angle unto each equal
long it may contain two whole Minutes of such a Circle between f and f and one between 4 and 4 and consequently the said Glass may be set Horizontal to the certainty of a Second which is hardly to be ascertain'd any other way But there remains yet one great Difficulty how to be able to make such a Curviture for though the thing be true in theory yet is it not without some trouble put in practice Very few Glass Canes are so conveniently bent as is desirable and 't is as difficult to find them true straight To prevent this If Glass Canes be used there must be much care taken and many tryals made for the finding what pieces and what side of those pieces will be most fit for this purpose for our Glass-House Workmen know not yet a way certainly to draw them of this or that curviture or straightness nor are they easily ground into a straightness or curviture by the Glassgrinder afterwards though that can be done with some trouble But diligence and tryal will quickly find some piece or other that will be sufficiently exact for any tryal among those which are only drawn at the Glass-House I made use of one of another form such as is described in the 25th Figure which I found to do exceeding well the dark part representing the Water and the lighter part the Air. This was made of two Glasses drawn in distinct Pipes at the Glass-House but joyn'd together in the Lamp and the upper part of the larger or under Tube was incurvated with its convexity downwards so that the Water touched the middle part and the bubbles of Air at each end thereof communicated together by the small Pipe above I tryed also another way by which I was more certain of the truth of the Curvity and could make the Curvity of a greater Circle This was by a long piece of a Looking-Glass-Plate ground very smooth and polished which by the help of Screws I bent upon the circular edges of a brass prismatical Box and cemented the same very tight with hard and soft Cement this Plate had a hollow Channel ground in it the length thereof which serv'd to keep the bubble in the middle By this means 't is not difficult to bend such a Plate into the Curviture of a Circle of 50 60 100 1000 foot Radius and the Brass Box can easily be made to fill or empty as there shall be occasion for the use thereof so that the Bubble may be at any time left of what bigness shall be desired It will be convenient also to varnish the in-side of this Brass Box with Lacker-Varnish very thick and close both to keep it from rustâ—ng and also to preserve it from being corroded by Aqua fortis whensoever there shall be occasion to put it in for the cleansing he inward tarnish and foulness of the Glass-Plate This Curvity of the upper side of the Level may be made by grinding the under side of such a long Plate of Looking Glass upon a Convex Glass-Tool of 50 60 100 1000 foot Radius and polishing the samé accordingly of that Figure The Curvity of the said Plate is express'd in the 26th Figure Now what by this way may be done with Water and Bubbles of Air the same may be done with the same Glasses turned upside-down by the help of an exactly round and polisht Cylinder or Globule of Glass Chrystal Cornelian Agate or other exceedingly hard and close Stone after the manner represented in the 27th Figure for the Ball or Cylinder will naturally roll to the lowest part of the Concavity and there stand But in the doing of this great care must be taken that the Globule be exactly round and polisht and that they Concavity of the Plate be as smooth and well polisht and that they be both very clean and free from dust otherwise the Cylinder or Globule will be apt to stand in a place where it should not and consequently produce considerable errors And here I cannot omit to take notice of a very curious Level invented by Sr. Chr. Wren for the taking the Horizon every way in a Circle Which is done by a large Concave ground and polisht on a very large Sphere and the Limb of it ground and polisht on a flat for by placing the same Horizontal and rectifying it by a small quantity of Quick-silver poured into the Concavity thereof 't will be easie by looking by the flat polisht Limb to discover the true Horizon The only inconvenience I find in it is that the ☿ hath some kind of sticking to the Glass but a small Chrystal Bowl I suppose may remedy that inconvenience and make it fit for use The 5th thing wherein this Instrument is made to excell others is in its easinesses to be adjusted to the Objects and in this that being once adjusted the whole Instrument is so order'd as that it will remain constant to those Objects though they are moved The want of this is so great an inconvenience in all other Instruments hitherto made use of that almost all Observations have been thereby vitiated And Hevelius to prevent and obviate this hath found out many contrivances but they are such as though they do it in part yet 't is but in part and that with much trouble and inconvenience I need not spend time to shew how many inconveniences his way by 4 several Hand-Screws to be managed by 2 Observators at the least is subject to they are indeed so many and so great that it was not without very good reason that he so often appeals to experience for the truth is there was great need of long practice and much experience to be able to make an Observation in that way well the removal of every one of those Screws having an influence upon every one of the other so as no Screw could be turn'd but the whole Instrument was put out of its due situation and both the Objects being continually in motion the whole Instrument was to be rectifi'd every moment There was therefore necessary so great a judgement and dexterity to manage every one of those Screws that without an acquired habitude and handiness by long practice and experience nothing could be done to any certainty nay not even to that little accurateness that the common Sights are able to reach But this though it were a very great unhappiness to Hevelius that he was not furnished with better Contrivances yet it no ways tends to his dispraise for his most extraordinary and indefatigable care pains and industry is so much the more to be admired esteem'd and honour'd and will be so much the more by such as have by experience found the difficulty of making any one Observation certain in that way But that he or any other that hath a mind to make further Tryals and Observations may be freed from this intollerable trouble and difficulty I have thought of this following Instrument by means whereof the Quadrant being once adjusted and
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
it remains that I come to the description of the Microscope it self which is the principal instrument and without which all the rest are insignificant The Microscopes then I design here to describe are only of two kinds either single or double The single Microscope I call that which consisteth only of one glass though it have a double refracting superficies and the double one I call that which is compounded of two glasses though it hath for the most part a quadruple refraction of the Rays The single Microscope then consisteth of one small lens so fastened into a cell that the eye may come conveniently to look through the middle part or Axis of it of these there are various sorts as double Convexes or plain Convexes or perfectly spherical I shall not need to describe the common lenses which are every where made use of for this purpose being plano-convexes of Spheres about half an inch Diameter save only this that 't is best to turn the plain side towards the object and the convex to the eye nor shall I say much concerning those double Convex Glasses there being no great difficulty in the making or using of them but that the smaller the sphere is in which they are made the nearer do they bring the object to the eye and consequently the more is the object magnified and the better and truer they are polisht in the Tool the more clear and distinct doth the object appear but to make any of a Sphere less than 1 10 of an inch in Diameter is exceeding difficult by reason that the glass becomes too small to be tractable and 't is very difficult to find a cement that will hold it fast whilst it be completed and when 't is polisht 't is exceeding difficult to handle and put into its cell besides I have found the use of them offensive to my eye and to have much strained and weakened the sight which was the reason why I omitted to make use of them though in truth they do make the object appear much more clear and distinct and magnifie as much as the double Microscopes nay to those whose eyes can well endure it 't is possible with a single Microscope to make discoveries much better than with a double one because the colours which do much disturb the clear vision in double Microscopes is clearly avoided and prevented in the single The single Microscope therefore which I shall here describe as it is exceeding easie to make so is it much more tractable than the double Convex glasses made the common way by working them in a hollow Hemisphere with water and sand for those supposing them made with all the accurateness imaginable will be far short from being so well polisht as these and wanting the stem or handle which these have they are infinitely troublesome to remove or place or to cleanse when there shall be occasion Take then a small rod of the clearest and cleanest glass you can procure free if possible from blebbs sands or veins then by melting it in the flame of a Lamp made with Spirit of Wine or the cleanest and purest Sallet Oyl draw it out into exceeding fine and small threads then take a small piece of these threads and in the same flame of the aforesaid Lamp melt the end of it till you perceive it to run into a little ball or globule of the bigness desired then suffer it to cool and handling it by the aforesaid thread of glass which is as it were a handle to it fix it with a little wax upon the side of a thin plate of Brass Silver or the like that the middle of it may lie directly over the middle of a small hole pricked through the said thin plate with a needle then holding this plate close to the eye look through the said little hole and thereby you may also see very clearly through the aforesaid Globule fixed with wax on the side that is from the eye if then either by a little joynted arm or by a little soft wax and a needle or a thin plate of Muscovy glass you fix the object you would examine so that it may be at a due distance from the said little Globule you will perceive the minute parts thereof very distinct The focus of a sphere looked on by the naked eye is about half the radius of the sphere without the superficies of it but this is varied much by the age of the eye that looks through it by the imagination also of the person and by the differing specifique refraction of the glass made use of By this means I have prodigiously magnified some small bodies insomuch that I have been able to see and distinguish the particles of bodies not only a million of times smaller than a visible point but even to make those visible whereof a million of millions of them would hardly make the bulk of the smallest visible sand so prodigiously do these exceeding little Globules of glass inlarge the prospect of humane sight into the more private recesses of nature If the things to be viewed be liquors they may be included either in those little pipes of Mr Leeuwenhoeck I newly mentioned or else they may be put upon exceeding thin plates of Muscovy glass or Selenites and the other side of the plate may be made to touch the Globule or at least be fixed at such distance as may make the parts of the liquor distinct If you make use of a Looking-glass plate to spread the liquor upon you would examine you may turn the liquor towards the Globule and you may therein easily see all the parts very distinctly without at all hurting the prospect by the interposition of the Muscovy glass which though it be exceeding clear especially if the plates be very thin yet hath it some flaws and some opacoufnesses in it which do somewhat cloud the prospect If further you would have a Microscope with one single refraction and consequently capable of the greatest clearness and brightness that any one kind of Microscopes can possibly be imagined susceptible of when you have fixt one of these little Globules as I have directed and spread a little of the liquor upon a piece of Looking-glass plate then apply the said plate with the liquor next to the Globule and gently move it close to the Globule till the liquor touch which done you will find the liquor presently to adhere to the Globule and still to adhere to it though you move it back again a little by which means this liquor being of a specifique refraction not much differing from glass the second refraction is quite taken off and little or none left but that of the convex side of the Globule next the eye by which means as much of the inconvenience of refraction as is possible is removed and that by the easiest and most practicable expedient that can be desired I could add various other ways of making these Globular bodies both of glass and other substances