Title , preface , globes , definitions , spheres , orrery , Bion & Stone
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Duke of Argyll and Greenwich, &c. Lord Steward of his Majesty's Houshold. [...] In Your Family it was, I first caught an Affection for Mathematicks; and it was under Your Countenance, that I took occasion to Cultivate them. [...] |
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THETRANSLATOR'sP R E F A C E.T H E Masters in Mathematicks have not been wanting in their Respect to the rest of Mankind: They have frankly communicated their Knowledge to the World; and have published Treatises in every Branch of their Art: insomuch, that a Man who has a Disposition to this Study, will find himself abundantly supplied with Helps, to what Part soever he applies himself. There seems, then, but little wanting to Mathematicks, considered as a Science: If there be any Defect, 'tis when considered as an Art. I mean, Mathematicks appears more accessible, as well as more extensive, on the Side of their Theory than on that of their Practice. Not that the latter has been less laboured by Authors than the former, but because a sufficient Regard does not seem to have been had to the Instruments, whereon it wholly depends. MATHEMATICAL INSTRUMENTS are the Means by which those Sciences are rendered useful in the Affairs of Life. By their Assistance it is, |
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B O O K VI.Of the Construction and Uses of AstronomicalInstruments.
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ADDITIONS of English Instruments.
Of Globes, Spheres, [...]
S E C T I O N I.
[ Plate XVII, p. 180a ] |
There are ten eminent Circles upon the Globe, six of which are called greater, and the four other lesser Circles. |
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Definition XI. And the Space contained between two such Parallels, is called a Climate: These Climates begin at the Equator; and when we go North or South, till the Day becomes half an Hour longer than it was before, they say we are come into the first Climate; when the Days are an Hour longer than they are under the Equator, we are come to the Second Climate, &c. these Climates are counted in Number 24, reckoned each ways from the Poles. The Inhabitants of the Earth are divided into three sorts, as to the falling of their Shadows. Definition XII. Amphiscii, who are those which inhabit the Torrid Zone, or live between the Equator and Tropicks, and consequently have the Sun twice a Year in their Zenith; at which time they are Ascii, i. e. having no Shadows, the Sun being vertical to them: these have their Shadows cast to the Southward, when the Sun is in the Northern Signs, and to the Northward when the Sun is in the Southern Signs reckoned in respect of them. Definition XIII. Heteroscii, who are those whose Shadows fall but one way, as is the Case of all such as live between the Tropicks and Polar Circles; for their Shadows at Noon are always to the Northward in North Latitude, and to the Southward in South Latitude. Definition XIV. Periscii, are such Persons that inhabit those Places of the Earth that lie between the Polar Circles and the Poles, and therefore have their Shadows falling all manner of ways, because the Sun at some time of the Year goes clear round about them. The Inhabitants of the Earth, in respect of one another, are also divided into three Sorts. Perioecei, who are such as inhabiting the same Parallel (not a great Circle) are yet directly opposite to one another, the one being East or West from the other exactly 180 Degrees, which is their Difference of Longitude. Now these have the same Latitude and Length of Days and Nights, but exactly at contrary Times; for when the Sin riseth to one, it sets to the other. Antoeci, who are Inhabitants of such Places, as being under a Semi-Circle of the same Meridian, do lie at equal Distance from the Equator, one towards the North, and the other towards the South. Now these have the same Degree of Latitude, but towards contrary Parts, the one North and the other South; and therefore must have the Seasons of the Year directly at contrary Times one to the other. Antipodes, who are such as dwell under the same Meridian, but in two opposite and equidistant Parallels, and in the two opposite Points of those two Parallels; so that they go Feet against Feet, and are distant from each other an intire Diameter of the Earth, or 180 Degrees of a great Circle. These have the same Degree of Latitude, but the one South, the other North, and accounted from the Equator a quite contrary way; and therefore these will have all things, as Day and Night, Summer and Winter, directly contrary to one another. Bring the Place to the Brass Meridian, and the Degrees of that Circle, intercepted between the Place and the Equinoctial, are the Latitude of that Place either North or South. Then to fit the Globe so that the wooden Horizon shall represent the Horizon of that Place, elevate the Pole as many Degrees above the wooden Horizon, as are contain'd in the Latitude of that Place, and it is done; for then will that Place be in the Zenith. If after this you rectify the Globe to any particular time, you may by the Index know the time of Sun-rising and Setting with the Inhabitants of that Place, and consequently the present Length of their Day and Night, &c. Bring the Places severally to the Brass Meridian, and then the Number of Degrees of the Equinoctial, which are between the Meridian of each Place, are their Difference of Longitude either East or West. But if you reckon it from any Place where a first Meridian is supposed to be placed, you must bring the first Meridian to the Brazen one on the Globe; and then turn the Globe about till the other Place come thither also: reckon the Number of Degrees of the Equinoctial intercepted between the first Meridian, and the proper one of the Place, and that is the Longitude of that Place, either East or West. Bring the Sun's Place found in the Ecliptick on the Terrestrial Globe to the brazen Meridian, and note what Degree of the Meridian it cuts; then by turning the Globe round about, you will see what Places of the Earth are in that Parallel of Declination (for they will all come successively to that Degree of the brazen Meridian); and those are the Places and Parts of the Earth to which the Sun will be Vertical that Day, whose Inhabitants will then be Ascii; that is, their erect Bodies at Noon will cast no Shadow. |
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Seek the Day of the Month upon the Horizon, observing the Difference between the Julian and Gregorian Calendars; and then against the said Day you will find, in the Circle of Signs, The Sign and Degree the Sun is in the said Day. This being done, find the same Sign and Degree upon the Ecliptick on the Superficies of the Globe, and the Sun's place will be had. Note, If the Sun's place be required more exactly, you must consult an Ephemeris for the given Year, or else calculate it from Astronomical Tables. Bring the Sun's Place for that Day to the Meridian, and then the Degrees of the Meridian, reckoned from the Equinoctial either North or South to the said Place, shew the Sun's Declination for that Day at Noon, either North or South, according to the time of the Year, viz. from March the 10th to September the 12th, North; and from thence to March again, South. Having rectified the Globe to the Latitude of the Place, that is, moved the brazen Meridian till the Degree of Latitude thereon be cut by the Plane of the wooden Horizon, bring the Sun's Place to the said Horizon either on the East or West side, and the Degrees of the Horizon, reckoned from the East Point, either North or South, give the Amplitude sought, and at the same time you have in the Circle of Rhumbs the Point that the Sun rises or sets upon. Bring the Sun's Place to the brazen Meridian, and the Degrees intercepted between the beginning of Aries, and that Degree of the Equinoctial which comes to the Meridian with the Sun, is the Right Ascension; which if you would have in time, you must reckon every 15 Degrees for one Hour, and every Degree four Minutes. Note, The Reason of bringing the Sun's place to the Meridian in this Use, is to save the trouble of putting the Globe into the Position of a Right Sphere: for properly Right Ascension is that Degree of the Equinoctial, which rises with the Sun in a Right Sphere. But since the Equator is always at Right Angles to the Meridian, if you bring the Sun's place thither, it must in the Equinoctial cut his Right Ascension. Having rectified the Globe to the Latitude, bring the Sun's Place to the East-side the Horizon, and the Number of Degrees intercepted between that Degree of the Equinoctial, which is now come to the Horizon and the beginning of Aries, is the Oblique Ascension. Now the lesser of these two Ascensions being taken from the greater, the Remainder is the ascensional Difference; which therefore is the Difference in Degrees between the Right or Oblique Ascension, or the Space between the Sun's Rising or Setting, and the Hour of six. Wherefore the ascensional Difference being converted into Time, wille give the time of the Sun's Rising and Setting before or after six. Having first brought his Place to the Meridian, and the Hour-Index to twelve at Noon, bring his Place afterwards to the Horizon, either on the East or West-side thereof; then the Hour-Index will either shew the time of his Rising and Setting accordingly. Now the time of the Sun's Setting being doubled, gives te Length of the Day; and the time of his Rising doubled, gives the Length of the Night. Bring his Place to the Meridian above the Horizon, for his Noon Altitude, which will shew the Degrees thereof, reckoning from the Horizon; and to find his midnight Depression below the North Point of the Horizon, the Point in the Ecliptick opposite to the Sun's present Place, must be brought to the South part of the Meridian above the Horizon, and the Degrees there intercepted between the Point and the Horizon, are his midnight Depression. Rectify the Globe, that is, bring the Sun's Place to the Meridian, and set the Hour-Index to twelve, and raise the Pole to the Latitude of the Place above the Horizon. This being done, fit the Quadrant of Altitude, that is, screw the Quadrant of Altitude to |
the Zenith, or in our Latitude screw it so that the divided Edge cut 51 deg. 32 min. on the Meridian reckoned from the Equinoctial. Then turn the Globe about till the Index shews the given time, and stay the Globe there; after which, bring the Quadrant of Altitude to cut the Sun's Place in the Ecliptick, and then that Place or Degree of the Ecliptick will shew the Sun's Altitude on the Quadrant of Altitude. Rectify the Globe, and fit the Quadrant of Altitude. Then bring the Quadrant to cut the true East Point, and turn the Globe about till the Sun's Place in the Ecliptick cuts the divided Edge of the Quadrant of Altitude; for then that Place will shew the Altitude, and the Index the Hour. Set the Quadrant of Altitude to the Azimuth given, and turn the Globe about till his Place in the Ecliptick touches the divided Edge of the Quadrant; so shall that Place give the Altitude on the Quadrant, and the Hour-Index the Time of the Day. Bring the Star to the brazen Meridian, and then the Degrees intercepted between the Equinoctial and the Point of the Meridian cut by the Star, gives its Declinations. And the Meridian cuts, and shews its Right Ascension on the Equinoctial, reckoning from the beginning of Aries. Bring the Solstitial Colure to the brazen Meridian, and there fix the Globe; then will the Pole of the Ecliptick be just under 23 deg. 30 min. reckoning from the Pole above the North Point of the Horizon, and upon the same Meridian; there screw the Quadrant of Altitude, and then bring its graduated Edge to the Star assigned, and there stay it: so will the Star cut its proper Latitude on the Quadrant, reckoned from the Ecliptick; and the Quadrant will cut the Ecliptick in the Star's Longitude, or its Distance from the first Point of Aries. Rectify the Globe, and Hour-Index, and bring the Star to the East or West part of the Horizon, or to the brazen Meridian, and the Index will shew accordingly the time of the Star's rising, setting or culminating, or of its being on the Meridian. Rectify the Globe, and fit the Quadrant of Altitude, and set the Globe, by means of the Compass, due North and South; then turn the Globe and Hour-Index to the Hour of the Night assigned; so will the Globe, thus fixed, represent the Face or Appearance of the Heavens for that time: whereby you may readily see what Stars are in or near the Horizon; what are on or near the Meridian; which are to the North, or which to the South, &c. and the Quadrant of Altitude being laid over any particular Star, will shew its Altitude and Azimuth, or on what Point of the Compass it is, whereby any Star may easily be known; epsecially if you have a Quadrant to take the Altitude of any real Star supposed to be known by the Globe, to see whether it agrees with that Star which is its Representative on the Globe or not. Rectify the Globe, and fit the Quadrant of Altitude; then move the Globe backwards or forwards, till the Quadrant cuts the Star in its given Altitude: for then the Hour-Index will shew the Hour of the Night. And thus may the Hour of the Night be known by a Star's Azimuth, or its Azimuth by its Altitude. If the Stars lie both under the same Meridian, bring them to the brazen Meridian, and the Degrees of the said Meridian comprehended between them, are their Distance. If they are both in the Equinoctial, or have both the same Declination, that is, are both in the same Parallel, then bring them one after another to the brazen Meridian, and the Degrees of the Equinoctial intercepted between them, when thus brought to the Meridian severally, are their Distance. |
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If the Stars are neither under the same Meridian or Parallel, then either lay the Quadrant of Altitude from one to the other (if it will reach) and that will shew the Distance between them in Degrees; or else take the Distance with Compasses, and apply that to the Equinoctial, or to the Meridian. This Method of Proceeding will also shew the Distance of any two Places on the Terrestrial Globe in Degrees. Wherefore to find how far any Place on the Globe is from another, you need only take the Distance between them on the Globe with a Pair of Compasses, and applying the Compasses to the Equator at the beginning of Aries, or at the first Meridian, you will there find the Degrees of their Distance, which multiply'd by 70, and that will be their Distance in Miles. |
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Upon the Surface of this Ball are drawn Meridians, Parallels, &c. as likewise as many Kingdoms, Countries, Seas, &c. with their Names, as can conveniently be depicted thereon. This Sphere revolves about the said Axis, between the Meridian, and by this means not only shews the Sun's diurnal and annual Course, &c. about the Earth, according to the Ptolemaick Hypothesis, which supposes the Earth to be at rest, and the Sun to move about the same; but likewise by it any Problem relating to the Sun, may be solved, that can be done by the Globes. And this any one that knows the Use of the Globes may likewise do. Of the common Copernican Sphere. This Sphere stands upon four brass or wooden Feet, upon each of which are fixed the four ends of a brass or wooden Cross, upon which Cross is fastened a large hollow brass or wooden Circle, whose Center is exactly over the Center of the Cross. Upon the upper Plane of this Circle are the Calendars, and Circle of Signs described, the same as on the Horizon of the Globes. Close within the inside of this Circle is fitted a flat moveable Rundle, whose Center is common with the Center of the Cross. The outmost Limb of this Rundle is divided into 24 equal Parts, representing the 24 Hours of Day and Night, numbered from the Index (of which more hereafter) towards the Right-hand with Numerical Letters from I to XII, and then beginning again with I, II, &c. to XII again. There is a round Wheel fixed upon the Cross, under the said Rundle, whose Convex Side is cut into a certain Number of Teeth. Thro the Rundle, the Wheel on the Cross, and the Cross itself, is fitted a perpendicular Axis, about which the Rundle moves. This represents parts of the Axis of the Ecliptick, and at the top thereof is placed a little Golden Ball, representing the Sun. On the under side of the moveable Rundle moves another Wheel, whose Convex Side is cut into Teeth, and as the Rumble is turned about upon its Center, this Wheel is also turned about upon its Center, by the falling in of the Teeth on that Wheel fixed on the Cross. Likewise near the outmost Limb of the Rundle is fitted another Wheel, into which is fitted a Pedestal, holding up a Sphere of several Parts, having a Terrestrial Globe inclosed therein, as shall be shewn hereafter. The outmost Limb of this Wheel is likewise cut into Teeth, fitted into the Teeth of the fixed Wheel; and so as the Rundle moves round, this Wheel is carried about, and with it likewise the Earth, and all the Circles fastened upon the aforesaid Pedestal. |
On one side of this Rundle is fastened a little round Pin to turn about the Rundle by, and near this Pin, is an Index upon the Rundle, reaching to the outward Limb of the great hollow Circle, and so at once may be applied to the Day of the Month in both Calenders, and also to the Degree of the Ecliptick the Sun is in that Day at Noon. Note, This Index is called the Index of the moveable Rundle. On each side of the Cross is placed a Pillar, supporting a broad Circle, representing the Zodiack, with the Ecliptick in the middle |
thereof, as in the Ptolemaick Sphere. Note, This is called the Zodiack, in the Use of the Sphere. Upon the aforesaid Pedestal are fastened two Circles cutting each other at Right Angles, representing the two Colures so placed, that the Points wherein they intersect each other stand directly upwards and downwards, and represent the Poles of the Ecliptick, the uppermost being the North, and the other the South. One of these Colures, viz. the Solstitial, hath a small Hour-Circle placed thereon, at the extremity of the Axis of the Earth. In the middle, between the two Poles of the Ecliptick, is a Circle broader than the Colures, cutting them at Right Angles; and this represents the Ecliptick, so called in the Use of the Sphere, and is divided into Degrees, figured with the Names and Characters of the Signs, and having on the inward edge thereof several of the most notable fixed Stars, with the Names affixed to them, and each Star placed to the Degree and Minute of Longitude thereon, that it hath in the Heaven. Oblique to this Ecliptick 23½ Degrees, on the inside, is fitted a thin Circle, representing the Equinoctial, and is divided into 360 Degrees, and having two parallel lesser Circles at 23½ Degrees equally distant therefrom, representing the Tropicks. On the inside of all these Circles, two thin Semi-circles (called Semi-circles of Latitude) are fitted in the Poles of the Ecliptick, so as one of them may move thro one half of the Ecliptick, viz. from Cancer thro Aries to Capricorn; and the other from Cancer thro Libra to Capricorn: the former of these may be called the vernal Semi-circle of Latitude, and the other the autumnal Semi-circle of Latitude. On the edge of these Semi-circles are depicted thee same fixed Stars in their proper Longitude and Latitude, as are placed on the ecliptick Circle aforesaid, with their several Names affixed to them. Thro the solstitial Colure at 23½ Degrees from each Pole of the Ecliptick, goes a Wire, representing the Earth's Axis, having an Index placed on the end thereof, for pointing at the Hour, on the Hour-Circle placed on the solstital Colure, as aforesaid. In the middle of this Axis is fixed a round Ball, representing the Earth, having Meridians, Parallels, &c. and the Bounds of the Lands and Waters depicted thereon, as also the Names of as many Countries and Towns as can be placed with conveniency thereon. And in two opposite Points of the Equinoctial of this Ball, viz. 90 Degrees distant from the first Meridian, are fixed two small Pins, whereon a moveable Horizon is placed, in the East and West Points thereof; so that these Pins serve for an Axis to the Horizon: for on these Pins the Horizon may be elevated or depressed to any Degree the Pole is elevated above the Horizon. This Horizon slides on the North and South Points, within a brazen Meridian, hung upon the Axis of the Earth. Round this Meridian, on the outmost Side, is made a Groove, having a small brass Ring fitted therein, so as the upper side thereof is even with the upper side of the brazen Meridian. This small brass Ring is fastened to two opposite Points in the Horizon, viz. in the North and South, and serves as a Spring to keep it to the Degree of the Meridian you elevate the Horizon to. Upon two Pins on this small Ring, are likewise fastened two Semi-circles of Altitude, yet not so fastened, but that they may move as upon Centers, the one moving from North to South, thro the East-side of the Horizon, and the other the same way thro the West-side. This Motion is performed upon the two Pins aforesaid, as upon two Poles, which they represent, viz. the Poles of the Horizon, and therefore are so placed, that they may divide the upper and lower half of the Horizon into two equal Parts, and as the Horizon is moved, slide always into the Zenith and Nadir, and so become the Poles of the Horizon. These two Semi-circles of Altitude are divided into twice 90 Degrees, numbered at the Horizon upwards and downwards, and ending at 90 in the Zenith and Nadir. The Use of the common Copernican Sphere. Bring the Index of the moveable Rundle to the Day of the Month, and elevate the Horizon to the Latitude of the Place; then bring the Meridian to the Sun's Place in the Ecliptick, and the Index of the Hour-Circle to 12. Lastly, Bring the Center of the Earth, the Sun, or Golden Ball, in the Sphere, and the Sun in Heaven into a Right Line. Then will the Earth be rectified to its Place in Heaven, the Horizon to its Latitude on Earth, the Circles on the Sphere agreeable to those in Heaven, and the whole correspondent with the Heavens for that Day at Noon. Rectify the Earth's place (according to Use I.) and then you will have the Sun's place in the Zodiack; then bring the Meridian to the Sun's place in the Ecliptick on the Sphere; and the Number of Degrees comprehended between the Equinoctial and the Sun's place, are the Sun's Declination for that Day at Noon. |
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Rectify the Earth's place to the Day of the Month, and bring the Meridian to the Sun's place in the Ecliptick; and the Number of Degrees on the Equinoctial contained between the vernal Colure, and the Sun's place, are the Right Ascension sought. Now to find the Oblique Ascension, turn the Earth till the East side of the Horizon stands against the Sun, and the Degree of the Equinoctial then at the Horizon, shews the Oblique Ascension. Bring the Index of the Rundle to the Day of the Month, and rectify the Horizon to the Latitude of the Place. This being done, bring the Meridian to the Sun's place in the Ecliptick, and the Number of Degrees on the Meridian comprehended between the Horizon and the Sun's place, gives the Meridian Altitude sought. Bring the Index of the moveable Rundle to the Day of the Month, and rectify the Horizon, and Hour-Index: then turn the Earth till the Hour-Index comes to the given Hour of the Day, and bring the vertical Circle to the Sun's place, and the Number of Degrees of the vertical Circle that transite the Sun's place, are his Altitude above the Horizon. Bring the Index of the Rundle to the Day of the Month, and rectify the Horizon and Hour-Index (as by Use I.) then turn the Earth till you can fit the Horizon to the given Altitude upon the vertical Circle, directly against the Sun's place; then the Hour-Index will give the Hour of the Day, respect being had to the Morning or Afternoon. Bring the Index of the moveable Rundle to the Day of the Month, and rectify the Horizon and Hour-Index (as by Use I.) then bring the vertical Circle to the East Point of the Horizon, if it be the Sun's Easting you would enquire; or to the West Point of the Horizon, if it be the Sun's Westing. This being done, turn the Earth till the vertical Circle comes to the Sun's place; then will the Index point to the Hour of the Day. Bring the Index of the moveable Rundle to the Day of the Month, and rectify the Horizon, and Hour-Index. Then turn the Earth Eastwards, till some part of the East-side of the Horizon stands directly against the Sun's place; then will the Hour-Index point to the time of the Sun's rising. Again, Turn the Earth till some part of the West-side of the Horizon stands directly against the Sun's place, then the Index of the Hour-Circle will shew the time of the Sun's seting. Bring the Index of the moveable Rundle to the Day of the Month, and rectify the Horizon and Hour-Index. Then turn the Earth till the Hour-Index points to the Hour of the Day given. This being done, bring the vertical Circle to the Sun's place, and the Number of Degrees of the Horizon, that the vertical Circle cuts, counted from the East Point, either Northwards or Southwards, are the Degrees of the Sun's Azimuth before Noon. Or the Number of Degrees of the Horizon that the vertical Circle cuts, counted from the West-side of the Horizon, either Northwards or Southwards, give the Sun's Azimuth after Noon. Bring the Index of the moveable Rundle to the Day of the Month, and rectify the Hour-Index; then seek the Sun's Declination, and turn the Earth eastwards till the Index points to the given Hour; so shall the Number of Degrees of the Equinoctial that the Meridian passes thro while the Earth is thus turning, be the Number of Degrees of Longitude, eastwards from your Habitation, the Place shall have in the Parallel of the Sun's Declination. Now if you open a Pair of Calliper Compasses to 90 Degrees on the Equinoctial, and place one Foot in this Point of the Earth thus found, and turn the other Foot round about the Earth, all the Places that the Foot passes thro will at that time have the Sun in their Horizon. |
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Round the Plane of the Ecliptick, are placed several of the most noted fixed Stars, according to their true Longitude; and along the two Semi-circles of Latitude, are the same Stars placed according to their Latitude from the Ecliptick. Whence if you would find the true place of any given Star in the Sphere; First seek the Star in the Ecliptick, and likewise the same Star on one of the Semi-circles of Latitude, and bring the edge of that Semi-circle to the Star in the Ecliptick; then will the Star on the Semi-circle of Latitude stand in the same Place and Situation on the Sphere, that it does in Heaven. Bring the proper Semi-circle of Latitude to the Star on the Ecliptick, and the Meridian to the Star on the Semi-circle of Latitude; and then the Number of Degrees on the Meridian, comprehended between the Equinoctial and the Star, are its Declination. Likewise the Degree of the Equator, cut by the Meridian, is the Star's right Ascension. But to find a Star's oblique Ascension, rectify the Horizon (as by Use I.) and bring the proper Semi-circle of Latitude to the Star in the Ecliptick, and turn the East-side of the Horizon to the Star; then will the Degree of the Equator cut by the Horizon be the Star's oblique Ascension. Bring the Index of the moveable Rundle to the Day of the Month, and rectify the Horizon and Hour-Index; then bring the proper Semi-circle of Latitude to the Star on the Ecliptick, and the East-side of the Horizon to the Star; this being done, the Hour-Index will shew the Hour the Star rises at: and if you bring the West-side of the Horizon to the Star, the Index of the Hour-Circle will shew the Time that the Star sets. Bring the Index of the moveable Rundle to the Day of the Month, and rectify the Horizon and Hour-Index; then turn the Earth till the Index of the Hour-Circle comes to the Hour of the Night, and observe the Altitude of the Star, and what Point of the Compass it bears upon. Afterwards bring the vertical Circle to the same Point of the Compass, and number the Star's Altitude on the vertical Circle, and try with the Semi-circle of Latitude what Star you can fit to that Altitude, for that is the Star in the Heavens. Bring the Index of the moveable Rundle to the Day of the Month, and rectify the Horizon and Hour-Index; afterwards bring the Star to its place, and the vertical Circle to its known Degree of Azimuth. This being done, turn the Earth till the vertical Circle comes to the Star; then the Index of the Hour-Circle will shew the Hour of the Night, and the Degree of the vertical Circle cut by the Star will be its Almicanter. The Description and Use of the Copernican Sphere, called the Orrery. The Outside of this Instrument, as appears by the figure thereof, is very beautiful, the Frame being of fine Ebony adorned with 12 Silver Pilasters, in the form of Caryatides; and with all the Signs of the Zodiack cast of the same Metal, and placed between them: the Handles are also of Silver finely wrought, with very nice Joints. On top of the Frame, which is exactly Circular, is a broad Silver Ring, on which the Figures of the twelve Signs are exactly graved, with two Circles accurately divided; one shewing the Degrees of each Sign, and the other the Sun's Declination against his place in the Ecliptick each Day at Noon. The aforesaid Silver Plate, represents the Plane of the great Ecliptick of the Heavens, or that of the Earth's annual Orbit round the Sun; which, as it passes thro the Center of the Sun, so its Circumference is made by the Motion of the Earth's Center; and which, for the better advantage of view and sight, is in the Figure placed parallel to the Horizon. |
S is a large gilded Ball, standing up in the middle, whose Support AB makes with the Plane of the Ecliptick an Angle of about 82 Degrees. This Support represents the Sun's Axis continued, about which he revolves in about 25 Days, and the Golden Ball represents the Sun itself placed pretty near the Center of the Earth's Orbit; so that |
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when the Instrument is set a going, the Excentricity of the Earth, and the other Planets, may be in the same proportion as they are in the Heavens. The two little Balls M and V, which stand upon two Wires at different Distances from the Sun, represent Mercury and Venus: The reason why they are placed upon the said two Wires, is only that their Centers may be sometimes in, and always pretty near the Plane of the great Ecliptick; and this Position is contrived in order to shew what Appearances they do really exhibit in their several Revolutions round the Sun. The Globe E is of Ivory, and represents the Earth. The Pin or Wire that supports it, represents the Earth's Axis continued, and makes an Angle of 66½ Degrees, with the Plane of the Ecliptick. And as the Earth in each of her annual Revolutions round the Sun, always keeps her own Axis parallel to itself; so when this Instrument is set a going, the little Ivory Earth will likewise do so too, in its Revolutions round the Golden Sun S. The little Ball m standing upon a Wire, represents the Moon, and ab is a Silver Circle representing her Orbit round about the Earth, the Plane whereof always passes thro the Center of the Earth; and there are several Figures graved upon it, shewing the Moon's Age, from one New Moon to the other. One half of the Moon's Globe is white, and the other black, that so her Phases may be represented: for this Instrument is so contrived, that this little Moon will turn round its own Axis, at the same time as it moves in the Silver Orbit round the Earth E. The whole Movement, which consists of near 100 Wheels, is covered by a great Brass Plate, having a hole in it, and there is a moveable Index on the Silver Ecliptick, on the former of which, are the common Solar Years denoted; and by taking the Instrument to pieces, it may be set to this present time; and the Planets, by means of an Ephemeris, may be set to any particular time also. So that if a Weight or Spring, as in a Clock, were applied to the Axis of the Movement, so as to make it move round once in just twenty-four Hours, the representative Planets in the Instrument, viz. Mercury, Venus, the Earth, and the Moon, would all perform their Motions round the Sun, and one another, exactly in the same Order as their Originals do in the Heavens; and so the Aspects, Eclipses, &c. of the Sun and Planets, would thereby be shewn for ever. But because this would be instructive only in that slow and tedious way, to such as could have daily recourse to it, therefore there is a Handle fitted to it, by which the Axis may be swiftly turned round; and so all the Appearances shewn in a very little time: for by turning the Handle backwards or forwards, what Eclipses, Transits, &c. have happened in any time past, or what will happen for any time to come, will be shewn, without doing any injury to the Instrument. One entire Turn of the Handle of this Instrument, answers to the diurnal Motion of the Earth about its Axis, and is measured by means of an Hour-Index, placed at the Foot of the Wire whereon the Earth is fixed, moving once round in the same time. Also observe that the Contrivance of this Instrument is such, that the Motion may be made to tend either way, forwards or backwards; and so the Handle may be turned about till the Earth be brought to any Degree or Point of the Ecliptick required. Again, As the Earth moves round, by turning the Handle, the Moon's Orbit rises and falls about 5 Degrees above and below the great Ecliptick, that so her North or South Latitude may be exactly represented; and there are two little Studs placed in two opposite Points of the Moon's Orbit, representing the Moon's Nodes. Now if the Handle, one Turn of which answers to one Natural Day, or twenty-four Hours, be turned twenty-five times about, then the Sun will have moved once round about its Axis. Again, 365 ¼ of the Turns of the Handle will carry the Earth quite round the Sun; 88 will carry Mercury quite round; 244 will make Venus move once round the Sun; and about 27 ¼ Turns will carry the Moon round the Earth in her Orbit, which will likewise at the same time always turn the same Hemisphere towards the Earth. And by thus revolving the Earth and Planets round the Sun, the Instrument may be brought to exhibit Mercury, and sometimes Venus, as directly interposed between the Earth and the Sun; and then they will appear as Spots in the Sun's Disk: and this Instrument shews also very clearly the Difference between the Geocentrick and Heliocentrick Aspects, according as the Eye is placed in the Center of the Earth or Sun. This Instrument likewise very plainly shews the Difference between the Moon's Periodick and Synodick Months, and the reason thereof; for if the Earth be set to the first Point of Aries, at which time suppose the first New Moon happens, and afterwards the Handle be turned 27 ¼ times about, we shall have the second New Moon; and if at the Earth's place in the Ecliptick where this last New Moon happens, some Mark be made, and then the Handle be turned 27 ¼ times more, the Moon will be exactly brought again to interpose between the Earth and the Sun, that is, it will be New Moon with us: but the Line of the Syzygy will not be right against the aforesaid Mark in the Ecliptick, but behind it; and it will require two Days time, or two Turns more of the Handle, before it gets thither. The reason of this is plain, because in this 27 ¼ Days, the Earth advances so far forwards in her annual Course, as is the Quantity of the Difference in time between the Moon's two Months. |
If the Handle be turned about till the Conjunction or Opposition of the Sun and Moon happens in or near the Nodes, then there will be an Eclipse of the Sun of Moon. But in order yet further to shew the Solar Eclipses, and also the several Seasons of the Year, the Increase and Decrease of Day and Night, and the different Lengths of each in different parts of our Earth, there is a little Lamp contrived to put on upon the Body of the Sun, which casting, by means of a Convex Glass, (the Room wherein the Instrument is, being a little darkened) a strong Light upon the Earth, will shew at once all these things: First, how one half of our Globe is always illuminated by the Sun, while the other Hemisphere is in the dark, and consequently how Day and Night are formed by the Revolution of the Earth round her Axis. Also by turning round the Handle, you will see how the Shadow of the Moon's Body will cover some part of the Earth, and thereby shew, that to the Inhabitants of that part of the Earth there will be a Solar Eclipse. When the Earth is brought to the first Degree of Aries or Libra, the reason of the Equality of Days and Nights all over the Earth, will be plainly shewn by this Instrument; for in these Positions, as the Earth turns about her Axis, just one half of the Equator, and all Parallels thereto, will be in the Light, and the other half in the Dark; and therefore the Days and Nights must be every where equal: for the Horizon of the Earth's Disk will be parallel to the Plane of the Solstitial Colure.*) And when the Earth is brought to Cancer, the Horizon of the Disk, or that Plane which divides the Earth's enlightened Hemisphere from the darkened one, will not then be parallel to, but lie at Right Angles to the Plane of the Solstitial Colure. The Earth being now in Cancer, the Sun will appear to be in Capricorn, and consequently it will be our Winter Solstice. And as the Earth is turned either way about its Axis, the entire Northern frigid Zone, or all Parts of the Earth lying within the Artick Circle, are in the dark Hemisphere; and by making a Mark in any given Parallel, by the Earth's Diurnal Revolution, you will know how much longer the Nights are than the Days in that Parallel. And the contrary of this will happen, when the Earth is brought to Capricorn. Therefore this Instrument delightfully and demonstratively shews, how thereby all the Phenomena of the different Seasons of the Year, and the Varieties and Vicissitudes of Night and Day, are solved and accounted for. |
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[ *) See Lansbergen's figure, in Blaeu, 1634 (part 2, title page). J. T. Desaguliers described his orrery in: A course of experimental philosophy, London 1734. 2nd ed. (1745) I: 448-66, pl. 30-32. Add.: II (1744), 552-5.] Nicholas Bion was engineer for mathematical instruments to the King of France. It is surprising how little is known about his life beyond the fact his workshops were in Paris. He was very famous, but it is difficult to determine if his fame rests on the quality of his instruments or because he wrote this respected book. Only a few of his original instruments appear to have survived. Edmund Stone (ca. 1700-1768), was the son of a gardener to the Scottish Duke of Argyle. At the age of 8, another servant taught him to read. Shortly thereafter he noticed an architect, working on the Duke's house, using instruments and making calculations. Inquiring about these, he learned of the existence of arithmetic and geometry and purchased a book on the subject. When he was 18 and a gardener on the estate, the Duke saw a copy of Newton's Principia in the grass. Assuming it was from his library, the Duke called a servant to return it and was very surprised when the young gardener intervened claiming it was his own. The Duke became his patron and provided him with employment that would allow time for study. Stone became a Fellow of the Royal Society in 1725. The patronage continued until the Duke's death in 1743. The work is encyclopaedic and gives descriptions of the mathematical instruments commonly available at the beginning of the 18th century. It is composed of a preface giving definitions of mathematical terms, followed by eight separate books: rulers, and protractors; the sector containing a line of equal parts, line of planes, line of polygons, line of chords, line of solids, and line of metals, the compass (including both proportional compass and beam compass); surveying devices (quadrants, chords, chains, and sighting devices); water levels and gunner's instruments (gunner's compass and quadrant); astronomical instruments (large quadrants and micrometers for measuring); navigational instruments, including, for example, the Jacob's staff, and the mariner's quadrant, sundials of all forms at all orientations, the nocturnal, and a water clock. Stone also added, as an example of the power of the instruments, a short section on "The Use of the Sector in the Construction of Solar Eclipses" in which he details the path, across Europe, of the Moon's shadow for the eclipse of May 11, 1724 the year after the publication of this translation. In the appendix he describes and illustrates Isaac Newton's Reflecting Telescope as improved by Mr. Hadley, and prints Newton's own description of the Telescope. Newton was a member of the Royal Society until his death in 1727 and would undoubtedly have known Edmund Stone. This work is actually a translation of the second (1716) edition of Bion. It includes the additional chapters on fortification, and the pendulum clock from that edition. This translation appeared at the same time as Bion's third French edition. [...] The book was printed for John Senex, (1690-1740), a well known Engraver, Map, Print, Instrument and Globe seller, publisher, surveyor and geographer to Queen Anne. He engraved the plates for this edition [...]. Source: Bell Book Collection.
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