of a Revolution that the Content of that Angle in Degreess Minutes and Seconds is 16 Degrees 32 Minutes and 47 Seconds which is plain enough and much less subject to mistake then the common way made use of I shall therefore proceed to The third particular wherein this Instrument excels all others and that is That one Observator with a single glance of his eye at the same moment doth distinctly see that both the Sights of the Instrument are exactly directed to the desired Points of the two Objects and this though they be removed by never so great an Angle nay though they are opposite to each other directly in a Line This I question not will by all that know any thing of Instruments or celestial Observations be accounted one of the greatest helps to such Observations that was ever found out For whereas other Instruments require two Observators for taking a Distance in the Heavens and Ticho generally made use of four amongst which there was necessary so unanimous a concurrence in their readiness and certainty that the failure of any one spoyl'd all the rest and made the Observation become uncertain and of no use and such Instruments as were contrived for one Observator were accompany'd with so great difficulty in the adjusting to both the Objects being both in a continual and swift motion and but one to be seen at once that they were generally left off and dis-used there being so vast a trouble and fatigue of looking now upon one then upon another by many repeated tryals and so many new settings of the Instrument to the Objects in motion before the Sights could be adjusted besides the great uncertainty at the best of several Minutes of truth In this way the Observator has no farther trouble then first to set the Plain of the Quadrant in the Plain of the Objects and by the Screw to move the arm of his Instrument till he perceive both the Objects to touch each other in those Points he would measure the Distance between That this is so he will easily perceive when he understands the method of so adapting two Telescopes that by looking in at one small hole in the side of one of them he will be able to see both those Objects distinctly to which they are directed how much soever separated The way then of doing it is in short this Joyn them together at one end by a hollow Joynt that has a hole through it about ¾ of the hollow of the Tubes prepare two square Tubes of Wood Brass Iron c. of what length you please and directly against the Center of this hole in the Joynt make a small hole about the bigness of the blackest part or pupil of the eye so as the eye looking in at that hole may see perpendicularly into the lower Tube then obliquely place two pieces of reflecting Metal very well and truely polisht so as to reflect the Axis of both those Tubes perpendicular or at right Angles which is by fixing the Plain of the Plates inclined to the said Axis in an Angle of 45 Degrees let the upper reflex Plate reach from the upper side of the Tube so low as to touch the Axis or middle of the Tube and let the lower extend over the whole Tube from the top to the bottom and from one side to the other These will be known to be duely placed if looking in at the small hole against the Center of the Joynt the two round holes of the Tube do appear to the eye to coallesce into one and that the eye sees directly through the lengths of them both alike Then into these Tubes fit two Telescopes with convex Eye-Glasses and cross Threads for Sights in their Foci that they may be both of them at due distance from the eye looking in at the side-hole then opening those Tubes upon the said Joynt to any Angle and looking in at the side hole you shall plainly distinguish at once both the Objects that are brought into the Tubes directly and reflected up to the eye That this may be the plainer understood I shall add a Delineation thereof in plano Let a a b b in the 12th Figure represent the upper Tube and c c c c the lower Tube and let d d represent that part of the Joynt which belongs to the lower Tube at one end by which they are joyn'd together and can be open'd in the manner of a Sector Let i represent the hollow or center of this Joynt which communicates the Cavities of the two Tubes Let e e represent that part of the said Joynt which belongs to the upper Tube being only a hole through the lower side big enough to incompass the Cylinder d d of the lower Tube and let r r represent a Plate screw'd or pinn'd on to keep the parts of the Joynt together instead of rivetting Let s represent the hole in the side by which the Eye h is to look in and f the reflex Mettal in the upper Tube reaching only half way the Tube and g g the reflex Mettal in the under Tube reaching over the whole Cavity then will n o and p represent the Eye-Glass Sight-Threads and Object-Glass of the upper Tube and k l and m the same parts in the lower and whatever Angle the Tubes make to each other whilst they open upon the before-mention'd Joynt the Eye h looking in at s will see directly by the Axis of them both and see the Sight-Threads distinctly crossing the Points of the Objects whose Distances are to be measured These being thus explain'd I suppose it will be no difficult matter for any man to conceive how these may be apply'd to the above-described Quadrant for 't is but supposing c c the upper side of the under Tube in this Figure to represent a p a p the fixt side arm of the Quadrant and d d the Joynt of this to represent d d the Joynt of the Quadrant and b b the under side of the upper Tube to represent c c c the moveable arm of the Quadrant and applying two Tubes to these parts and fitting them with reflecting Plates Eye-Glasses Sight-Threads and Object-Glasses at due Distances the whole will be performed These Tubes thus fitted will serve to take any Angle less then a Quadrant to what exactness is desired but for bigger Angles the Contrivance must be somewhat varied the Description of which I shall now add Let either of the two Tubes for the Sights be made double the length of the other that is let it be as long behind the Center as before it and make the Reflex-Glass that it may be turned round and reflect the Ray exactly backwards as before it did forward then fix into this other half of the Tube a Telescope-Sight in all things fitted adjusted and like the other two then adjust them that they may look forwards and backwards in the same like which being done the Reader will easily understand how any Angle may be taken even to
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
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
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
R I say the Superficies thereof shall be in the Horizontal Line O Z for since the upper Hemisphere is half the weight of the under the two quadrantal Wedges P O H and H O R must necessarily counterpoise the quadrantal Wedge R O Z of the Oyl Thirdly Suppose that more than half the said Oyl or liquid Pabulum be consumed and that there be only left enough to fill the Wedge B O Z I say the counterpoising upper Hemisphere now made the under and placed in the Position A H C R B O A shall exactly counterpoise the said Wedge of Liquor so as that the Superficies thereof shall be in the Line O Z for the Wedge R O B of the aforesaid upper Hemisphere doth counterpoise the Wedge C O R on the other side of the Perpendicular and the double Wedge A O H and H O C will counterpoise the Wedge B O Z. Nor can the Superficies of the Liquor be any whit higher or lower than the Line O Z for if it be any whit higher as at E F the Liquor must necessarily overpoise the aforesaid Wedge A O C by all the weight of the Liquor contained in F G O Z F. And if it be any whit lower as at I K the Wedge K I B must be too light for the counterpoising Wedge A O C by the weight of the Liquor contained in the space Z O T K Z since I just now shewed that A O C did just counterpoise Z O B which was the thing to be proved Now though in this Instance I have chosen to explicate I have made choice of a Globe yet that form is not necessary but it may be made of any Figure whatsoever that is turned upon an Axis or Poles so as wheresoever the said Figure be cut by a Plain to which the Axis is Perpendicular the Superficies of the said Figure shall describe a Circle the Center whereof is in the said Axis whether the said Figure be a Cylinder Cone or any other Conoeidical mixt or otherwise regular or irregular figure Such as the Figures A B C D E F G which represent the Section of the said Vessel through the Axis The second way for the poysing the Liquor and keeping the Superficies thereof always to an equal height is this Make a Concave Receptacle for the Oyl or Liquor of a Hemispherical Semicylindrical Semiconical or of any other half-round hollow Figure where the turned Figure is cut in two parts per Axin and whereof the Axis is placed Horizontal and the plain Section per Axin likewise Horizontally so as it may be filled with any Liquor up to that Plain and that the Liquor may not be apt to dash be shaken or filter over it will be convenient to extend the brims of that Receptacle somewhat above the half-Round that there may be about half or three quarters of an Inch of space above the Superficies of the Oyl vacant or empty And that upon whatever Plain the foot stand the Plain per Axin may stand Horizontal it will be good to suspend the Receptacle in the same manner as a Sea-mans Compass is suspended within a frame Fix this Receptacle or the Frame that is to keep the Receptacle Horizontal upon a convenient Pedestal and fit within the Hollow or Concavity of the Receptacle a half-round solid poise turned of the same form with the hollow of the Receptacle and cut exactly through the Axis in two equal parts Let this solid poise be made exactly half the weight of the Liquor that is to be poised and fit to it two Pivots or Pins at each end of the Axis which may be exactly in the Poles of the half-Round and fit to those Pins make two holes in the Centers of the Ends of the Concave Receptacle in which the Pins may freely move and suffer the half-Round poise to move round within the hollow of the Receptacle according as the quantity of the Oyl or Liquor is increased or diminished Fit to this Receptacle a neck and socket fit for the Wick and flame of the Lamp and the same operation will be performed by this as by the first contrivance to wit the Oyl will be kept always to the same height in the Receptacle This will be easier understood by explaining a Designation thereof which is shadowed forth in the fourth Figure Where A A A represents a Pedestal which may be made with three claws or toes to make it stand the steadier and evenner upon any Plain or Table B B represent one of the Semicircular Arms that are fix'd to the top of the Pedestal this hath two holes in it at the ends or extremities as at C is one the other hole being in the other arm which goes behind the Globe and therefore cannot be seen is supposed to be Diametrically opposite to this at C. These two holes are the Center holes in which two small Pins or Centers fastned into two opposite points of the Hoop or Frame are made fit to move by which means the said Hoop is preserved in an horizontal Position D D is this Hoop or Frame which is made to incompass the Vessel or Receptacle of the Oyl and is shaped exactly like it This is made strong enough of Brass Iron Silver or other material to bear the Receptacle Poise and Oyl without bending and hath as I said before two Pins or Gudgeons at C and opposite to it Diametrically or Semicircularly upon which the said Hoop always hangeth Horizontally It hath also on each side in the middle between the aforesaid Pivots two Centers as at F and E to receive the ends of the Axis of the Receptacle appearing at F and E by which the said Receptacle is always free to hang plumb or in its Perpendicularity so as that the upper edge thereof at F F will always lie Horizontally One of these Pivots namely that on the Right hand is the Pipe to convey the Oyl to the Socket of the Lamp I in which is fitted a Wick of Cotton to serve for the flame K G G represents the Vessel or Receptacle of Oyl which is here described Hemispherical that being the most capacious uniform Figure but may be of any other qualified as those I mentioned in the first contrivance The Brims of this are extended somewhat higher than a Semicircle namely to F F to keep the Oyl from flashing or filtring over This is always kept full with Oyl or other Liquor to the Horizontal prick'd Line L L which passeth through the Center or Axis of its Cavity by the Counterpoise moved on the Center C. H H H represents that Counterpoise which is made exactly half the weight of the Oyl or Liquor and the Center of gravity of it must be somewhere in the Line M M and it ought to be fitted as exactly into the hollow of the Receptacle as it is possible that there may be left as little space as may be between its convex sides and the Concave of the Receptacle
but yet so much must be left that it may move very freely upon its Center C a whole Semicircle This done and the Receptacle being filled with Oyl the same effect will follow as in the first contrivance and the Demonstration of it being much the same I shall not now spend time to explain it But rather proceed to the description of a third way of keeping the Liquor counterpoised to the same level The third way then is Take any round Vessel whose Concavity and Convexity is turned upon an Axis and suspend that Vessel upon two small Pivots but yet big enough to bear the said Vessel filled with Oyl c. fastned in the Poles of that Axis and leave or cut open a sixth part more or less as you please of the side thereof that thereby any thing may be put into or taken out of the Cavity of the Vessel then poise the Vessel exactly on those Centers that no side be heavier than the other then fit into it a float of Brass Silver Tin Lead c. Convex on the under side so as just to fill to the Cavity of the Vessel And on the upper side Plain or Convex or any other convenient Figure it matters not much Make this float as heavy as you can at the bottom and as light as may be at the top but yet of such weight as may well float upon the top of the Oyl c. Let one end of this be fastned by a wire or string so as that end thereof may always touch that point of the Concave of the Vessel to which it is tied and that the rest thereof may turn and follow the sinking of the Oyl and through the end of it near the place where it is fastned let a Pipe go through it to receive the Wick which Pipe hath no communication with the Cavity of the hollow float This done fill the Vessel as full as convenient with Oyl and light the Wick and you shall find that as the fire consumeth the Oyl the Vessel will turn upon its Poles and keep the Superficies of the Oyl always at the same distance from the flame that it was put at at first till the whole be consumed This will be made more conceivable by a figure and explanation thereof which therefore take as follows in the fifth figure A C B B represents a hollow Vessel the Cavity whereof is very exactly turned upon an Axis whose Poles are in P the space between A and B in the side thereof is left open into the Cavity of it This Vessel is suspended upon its Poles at P so as to be free to move round upon them and exactly poised as no one side thereof be heavier than another To the hollow of this Vessel is fitted a float D of Brass Latton Silver Lead c. whose underside is made of a Convexity just fit for the Concavity of the Vessel as may be seen at K D I and the upper straight or Plain Let this float be made somewhat lighter than the Oyl or Liquor on which it is to swim so that a part thereof may float above the Superficies thereof Let one end thereof E be fastned to the side of the Vessel a little below the Brim B through the end of this float is put a Pipe and Wick h for the flame i then pouring in Oyl by the open side A Q B fill the same till it carry the float up to touch the hollow of the Vessel then light the Wick and you will find that the Lamp will consume the Oyl and this contrivance will continually supply it till the whole be consumed and the Poise be moved to touch the Concave of the aforesaid Vessel for when the Vessel is filled up to f g the float D will touch at O and E and the Cavity above f g being empty the Vessel will be as is described in the Figure the open part A B being upwards And as the flame consumeth the Oyl the side of the Vessel B will descend downward towards B 1 and so by B 1 B 2 B 3 to B 4 where the whole quantity of Oyl will be consumed and the bottom of the float will touch the hollow side of the Vessel in all which gradual wasting of the Oyl the Superficies thereof will lie at the same distance below the upper side of the float D that it had at first and consequently at the same distance from the bottom of the flame The reason of all which will be very easie to be understood by any one that shall seriously on this Delineation consider that the float D must necessitate the Vessel A C B to move on its Axis B according as its Oyl wasts because one end thereof E being fastned to the brim of the Vessel B the other end O being loose will as the Oyl wasts descend towards N whence the end E must hang heavier on the brim B and consequently must move it down towards B till the upper side f g of the float be reduced to a Parallelism with the Superficies of the remaining Oyl and the end E have no gravitation on the brim B which motion will be continued as the Oyl wasts and the brim B will be moved downwards by the points B 1 B 2 B 3 to B 4. I shall not therefore spend any more time in the Geometrical demonstration thereof but proceed to explain a fourth way by which the Flame and Superficies of the Oyl keep always at the distance they were first put at The Fourth way then is the making the Socket of the Wick to swim upon the top of the Oyl so that the Socket may sink as well as the Oyl by reason it is sustained by that and by that only The Vessel or Receptacle is generally made of Glass and it is best of a Hemispherical Figure the light casting it self through the body of the Oyl as well as of the Glass This is so plain and obvious and so commonly used and practised that I need not spend more time in the explanation or demonstration thereof but proceed to describe a Fifth way The Fifth way then is much upon the same principle with the Fourth but avoids several inconveniences to which that is subject For whereas the Flame in the Fourth is necessitated to be within the capacity or the Receptacle in this Fifth it may be at any distance and so is made much more convenient to be come at and to be dressed and trimmed Take then a Vessel of Glass Cylindrical is best as a Glass Bottle and fit to it a Siphon long enough to draw the Oyl from the bottom of the said Vessel make the one end of this Siphon extend at what distance you think convenient for the placing the flame of the Lamp and so order it that it may always draw from the Receptacle by its arms to feed the flame which it will do if the end of the Siphon be made where the Socket of the Lamp is placed
to return or bend upwards again So that the Plain of the upper Superficies of the Oyl may cut that end of the Siphon where the flame is between the top of the mouth of it next the Socket and the return thereof upwards then by a counterpoise so suspend this Siphon that it may follow the Oyl as it wasts and fit into the return of the Siphon a Socket and Wick for the flame to be continued A contrivance somewhat of this kind you have in divers Authors and therefore I shall spend less time in the description thereof Let A A A A in the Sixth Figure then represent a large Cylindrical Viol of Glass through the mouth B of which the Cavity thereof may be filled with Oyl and also the end D and float C of a convenient Siphon may be put in This Siphon D D D P G must be made long enough that the float C may reach the bottom of the Vessel when the Oyl is spent and the other end thereof must be so curved that the knee of the Siphon P may be below the Superficies of the Oyl E F and yet that the Socket H made for holding the Wick for the flame I may be somewhat above it this Siphon D D D P G with its Socket and float should be so counterpoised with a weight M hung over a Pulley K by a string L that the float may not sink deep into the Surface of the Liquor but swim as it were at the top This done if the Wick I be lighted the Surface of the Oyl will be kept always at the same distance below the flame that it was first put at In the first third fourth and fifth ways the flame of the Lamp descends equal spaces with the Superficies of the Oyl in the Vessel and therefore though for some uses it be very convenient as in annealings where things are to be cooled by degrees yet for many other it is not Especially in Lamp Furnaces where the same heat is to be continued and in some cases gradually increased For such cases therefore the first and second ways will be very convenient In some other cases the sixth and seventh ways which do much the same thing The sixth way then is this Through an arm or Siphon like the Branch of a Lamp hung against a Wall fixed in any convenient place the Oyl from the Receptacle is continually and equally supplied to the flame of the Lamp by the raising of the Receptacle as fast as the Oyl wasts so as to keep the Superficies of the Oyl alway in the same Horizontal Plain The Receptacle is raised by a Counterpoise hung upon a Fusey which Fusey is a part of an Archimedean Spiral Let C C then in the seventh Figure represent the Receptacle for the Oyl being a Cylindrical or Prismatical Vessel of what Bigness or Length you please to this by two Ears at L L fasten two Lines or Ropes K K the ends of both which are fastned to the Wheel or Pulley G though one of them do run over the Pulley F. Fit into this Receptacle is made a Cylindrical or Prismatical Plug A A which is fixed in some convenient place so as not to rise or sink and through the middle thereof passeth a Siphon B B B the one end whereof extended like the branch of a Candle or Lamp sustains the Socket D for the Flame E which is fed with Oyl through the Siphon B B B by the rising Receptacle C C. To the side of the Pulley G is fastned a Fusey H made with very great care of one Revolution of an Archimedean Spiral not beginning from the Center but from some convenient distance from it where the weight I hanging may just counterpoise the Receptacle C C when quite empty of Oyl the other hanging counterpoise Tangent to the largest part of this Spiral must be so far distant from the Center of the Wheel G that the same weight I may just counterpoise the said Receptacle filled top-full of Oyl and the Fusey must be filed true to a Spiral drawn with great care of one Revolution between those two points I say here of one Revolution because I have supposed the Wheel or Pulley G big enough by one Revolution of it to draw up the Receptacle the whole space it is to be raised for if the said Pulley be so small as to require two three four or more Revolutions then must the piece of the Spiral between those points be drawn of two three four or more Revolutions proportionably which being very Artificially and Mechanically performed the Receptacle C C will be raised by the same Degrees by which the Oyl is consumed at E and the upper Superficies thereof shall always be in the same Horizontal Line MM. The Geometrical and Mechanical Reason of which being so very plain I hope I shall not need to spend any more time in the explication thereof than only to say that by means of the Archimedean Spiral-Fusey the Power of the weight I upon the Pulley G decreaseth in the same proportion as the weight of the Oyl in the Receptacle C C is diminished by its consumption The seventh way then is by a Cylindrical or Prismatical Plug fitted into a Cylindrical or Prismatical Receptacle and let down into it by a Counterpoise hung upon a Spiral Fusey the Oyl is so raised in that Receptacle as always to stand Brimfull or to the same Horizontal height till the whole Oyl be consumed The contrivance of this way will be very easily understood by any one that shall peruse the Delineation in the eighth Figure and examine it by this following description Let A A in the eighth Figure then represent a Cylindrical or Prismatical Receptacle standing fixt upon a Table or Pedestal from the side of which issues a hollow Arm or Branch B B bearing the Socket for the Wick C where the flame D is continued Into the Cavity of this Receptacle is fitted a Cylindrical or Prismatical Plug E E big enough to fill the whole capacity thereof and yet not so close but that it may freely slip up and down the Cavity of the said Receptacle without sinking Let this Plug be made considerably heavier than the Oyl of the Receptacle that is let the Counterpoise L hanging upon the little Wheel M just reduce its gravity to be equal to that of the Oyl then let the point I where the Perpendicular toucheth the Spiral be so far removed from the Center of the Wheel H that the counterpoise L may just take off its whole gravity and suffer it to have no degree of gravity or pressure downwards Then draw the Spiral n o p according to the direction I gave in the former way and the effect will be produced The Geometrical and Mechanical Demonstration of which is very plain to any one that shall consider that As the Plug E E by sinking into the Receptacle A A so far as to raise the Oyl to the Horizontal Superficies M