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all of which join accurately on the spherical surface, and cover the whole ball. To direct the application of these gores, lines are drawn by a semicircle on the surface of the ball, dividing it iuto a number of equal parts corresponding to those of the gores, and subdividing those again answerably to the lines and divisions of the gores. There remains only to color and illuminate the globe; and to varnish it, the better to resist dust, moisture, &c. The globe itself, thus finished, is hung in a brass meridian, with an hour circle, quadrant of altitude; and then fitted into a wooden horizon.
The following is the detailed mode of their construction:—
From the given diameter of the globe find a right line A B, fig. 1 of the diagram above, equal to the circumference of a great circle, and divide it into twelve equal parts. 2. Through the several points of division, 1,2, 3, 4, &c., with the interval of ten of them, describe arches mutually intersecting each other in D and E : these figures or pieces duly pasted and joined together will make the whole surface of the globe. 3. Divide each part of the right line A B into thirty equal parts, so that the whole line A B, representing lL« periphery of the equator, may be divided
into 360 degrees. 4. From the poles D and E, fig. 2, with the interval of twenty-three degrees and a half describe arches ab; these will be twelfth parts of the polar circles. 5. After the like manner, from the same poles D and E, with the interval of sixty-six degrees and a half reckoned from the equator, describe arches cd; these will be twelfth parts of the tropics. 6.Through the degree of the equator e, corresponding to the right ascension of any given star, and the poles D and E, draw an arch of a circle; and, taking in the compasses the complement of the declination from the pole D, describe an arch intersecting it in i; this point i will be the place of that star. 7. All the stars of a constellation being thus laid down, the figure of the constellation is to be drawn according to Bayer, lievelius, or Flamstead. 8. Lastly, after the same manner are the declinations and right ascensions of each degree of the ecliptic, dg, to be determined. J). The surface of the globe thus projected on a plane is to be engraven on copper, to save the trouble of doing this over again for each globe. 10. A ball in the mean time is to be prepared of paper, plaster, &c, as before directed, and of the intended diameter of the globe; on this, by means of a semicircle and style, is the equator to be drawn; and through every thirtieth degree a meridian. The ball thus divided into twelve parts, corresponding to the segments before projected, the latter are to be cut from the printed paper, and pasted on the ball. 11. Nothing now remains but to hang the globe as before in a brazen meridian and wooden horizon; to which may be added a quadrant of altitude made of brass, and divided in the same manner as the ecliptic and equator. If the declinations and right ascensions of the stars be not given, but the longitudes and latitudes in lieu thereof, the surface of the globe is to be projected after the same manner as before; except that, in this case, D and E, fig. 2, are the poles of the ecliptic, and f h the ecliptic itself; and that the polar circles and tropics, with the equator g d, and parallels thereof, are to be determined from their declinations.
M. De La Lande, in his Astronomic, torn. 3, p. 736, suggests the following method :—'To construct celestial and terrestrial globes, gores must be engraven, which are a kind of projection, or enclosure of the globe, fig. 3, similar to what is now to be explained. The length P C of the axis of this curve is equal to a quarter of the circumference of the globe; the intervals of the parallels on the axis PC are all equal, the radij of the circles K D I, Which represent the parallels, are equal to the cotangents of the latitudes, and the arches of each, as D I, are nearly equal to the number of the degrees of the breadth of the gore (which is usually thirty degrees) multiplied by the sine of the latitude: thus, there will be found an intricacy in tracing them; but the difficulty proceeds from the variation found in the trial of the gores when pasting them on the globe, and of the quantity that must be taken from the paper, less on the sides than in the middle (because the sides are longer), to apply it exactly to the space that it should cover. The method used among workmen to delineate the gores, and which is described by M. Bion, (Usage de3 Globes, torn. 3) and by SI. Robert de Vaugendy in vol. vii. of the Encyclopedie, is hardly geometrical, but yet is sufficient in practice. Draw on the paper a line A C, equal to the chord of fifteen degrees, to make the half breadth of the gore; and a perpendicular P C equal to three times the chord of thirty degrees, to make the half length: for these papers, the dimensions of which will be equal to the chords, become equal to the arcs themselves when they are pasted on the globe. Divide the height C P into nine parts, if the parallels are to be drawn in every ten degrees; divide also the quadrant B E into nine equal parts, through each division point of the quadrant, as G: and through the corresponding point D of the right line C P, draw the perpendiculars HGF and DF, the meeting of which in F gives one of the points of the curve B E P, which will terminate the circumference of the gore. When a sufficient number of points are thus found, trace the outline P I B with a curved rule. By this construction are given the gore breadths, which are ou the globe, in the ratio of the cosines of the latitudes; supposing these breadths taken perpendicular to C D, which is not very exact, but it is impossible to prescribe a rigid operation sufficient to make a plane which shall cover a curved surface, and that on a right line A B shall make lines PA, PC, PB, equal among themselves, as they ought to be on the globe. To describe the circle K D I, which is at thirty degrees from the equator, there must be taken above D a point which shall be distant from it the value of the tangent of sixty degrees, taken out either from the tables, or on a circle equal to the circumference of the globe to be traced; this point will serve as a centre for the parallel D I, which should pass through the point D, for it is supposed equal to that of a cone circumscribing the globe, and which would touch at the point D. The meridians may be traced to every ten degrees, by dividing each parallel,, as K I, into three parts at the points L and M, and drawing from the pole P, through all these division points, curves, which represent the intermediate meridians between P A and P B (as B R and S T, fig. 4). The ecliptic A Q may be described by means of the known declination from different points of the equator that may be found in a table: for ten degrees, it is 3° 58'; for twenty degrees, 7° 5C — B Q; for thirty degrees, 11° 29', &c. It is observed, in general, that the paper on which charts are printed, such as the colombier, shortens itself J, part of a line in six inches upon an average, when it is dried after printing; this inconvenience must therefore be corrected in the engraving of the gores: if, notwithstanding that, the gores are found too short, it must be remedied by taking from the surface of the ball a little of the white with which it is covered; thereby making the dimensions suitable to the gore as it was printed. But what is singular is, that in drawing the gore, moistened with the paste to apply it on the globe, the axis G H lengthens, and the side A K shortens, in such a manner that neither the length of the side A C K nor that of the axis
G E H, of the gore, are exactly equal to the quarter of the circumference of the globe, when compared to the figure on the copper, or to the numbered sides shown in fig. 4. Mr. Bonne having made several experiments on the dimensions that gores take, after they had been parted ready to apply to the globe, and particularly with the paper named jesus, that he made use of for a globe of one foot in diameter, found that it was necessary to give to the gores on the copper the dimensions shown in fig. 4. Supposing that the radius of the globe contained 720 parts, the half breadth of the gore is A G ~ 188 jjj, the distance A C for the parallel of ten degrees taken on the right line LM is 12-8l, the small deviation from the parallel of ten degrees in the middle of the gore E D is four, the line A B N is right, the radius of the parallel of ten degrees or of the circle C E F is 4083, and so of the others as marked in the figure. The small, circular cap, which is placed under II, has its radius 253 instead of 547, which it would have if the sine of twenty degrees had been the radius of it.
Mr. George Adams, late mathematical instrument maker to his majesty, made some useful improvements in the construction of globes. His globes, like others, are suspended at their poles in a strong brass circle, and turn therein upon two iron pins, which are the axis. They have besides a thin brass semi-circle, moveable about the poles, with a small, thin, sliding circle upon it. On the terrestrial globe, the thin brass semicircle is a moveable meridian, and its small sliding circle the visible horizon of any particular place to which it is set. On the celestial globe, the semi-circle is a moveable circle of declination, and its small annexed circle an artificial sun or planet. Each globe has a brass wire circle, placed at the limits of the twilight, which, together with tbe globe, is set in a wooden trame, supported by a neat pillar and claw, with a magnetic needle at its base. On the terrestrial globe the division of the earth into land and water is laid down from the latest discoveries; there are also many additional circles, as well as the rhumb-lines, for solving all the necessary geographical and nautical problems. On the celestial globes, all the southern constellations, observed at the Cape of Good Hope by M. de la Caille, and all the stars in Mr. Flamstead's British Catalogue, are accurately laid' down and marked with Greek and Roman letters of reference, in imitation of Bayer. Upon each side of the ecliptic are drawn eight parallel circles, at the distance of one degree from each other, including the zodiac; and these are crossed at right angles with segments of great circles at every fifth degree of the ecliptic, for the more readily noting the place of the moon, or of any planet upon the globe. The author has also inserted, from Ulugh Beigh, printed at Oxford in 1665, the mansions of the Moon of the Arabian Astronomers, so called, because they observed the moon to be in or near one of these every night during her monthly course round the earth, to each of which the Arabian characters are fixed. On the strong brass circle of the terrestrial globe, and about twenty-three degrees and a half on each side of the north pole, the days of each month are laid down according to the sun's declination; and this brass circle is so contrived, that the globe may be placed with the north and south poles in the plane of the horizon, and with the south pole elevated above k. The equator, on the surface of either globe, serves the purpose of the horary circle, by means of a semi-circular wire placed in the plane of the equator, carrying two indices, one of which is occasionally to be used to point out the time. A farther account of these globes, with the method of using them, will be found in Adams's Treatise on their Construction and Use.
Mr. G. Wright, of London, has simplified the construction of the hour-circle. There are engraved on his globes two hour-circles, one at each of the poles; which are divided into a double set of twelve hours, as usual in the common brass ones, except that the hours are figured round both to the right and left. The hour-hand or index is placed in such a manner under the brass meridian, as to be moveable at pleasure to any required part of the hour-circle, and yet remain there fixed during the revolution of the globe on its axis, and is entirely independent of the poles of the globe. In this manner, the motion of the globe round its axis carrying the hour-circle, the fixed index serves to point out the time, the same as in the reverse way by other globes. There is an advantage in having the hour-circle figured both ways, as one hour serves as a complement to XII. for the other, and the time of the sun rising and setting, and vice versa, may be both seen at the same time on the hour-circle. In the problems generally to be performed, the inner circle is the circle of reckoning, and the outer one only the complement.
In the Philosophical Transactions for 1789,
p. 1, Mr. Smeat on has proposed some improvements of the celestial globe, especially with respect to the quadrant of altitude, for the resolution of problems relating to the azimuth and altitude. The difficulty, he observes, that has occurred in fixing a semi-circle, so as to have a centre in the zenith and nadir points of the globe, at the same time that the meridian is left at liberty to raise the pole to its desired elevation, I suppose, has induced the globe makers to be contented with, the strip of thin flexible brass, called the quadrant of altitude; and it is well known how imperfectly it performs its office. The improvement I have attempted, is in the application of a quadrant of altitude of a more solid construction; which being affixed to a brass socket of some length, and this ground, and made to turn upon an upright steel spindle, fixed in the zenith, steadily directs the quadrant, or rather arc, of altitude to its true azimuth, without being at liberty to deviate from a vertical circle to the right hand or left; by which means the azimuth and altitude are given with the same exactness as the measure of any other of the great circles.
Of The Use Of The Globes.
We subjoin the principal problems which exemplify the use of these elegant and important scientific instruments.
Sect. I.—Of The Use Of The Terrestrial
Prob. I. To rectify the globe.—The globe being set upon a true plane, raise the pole according to the given latitude; then fix the quadrant of altitude in the zenith; and, if there be any mariner's compass upon the pedestal, let the globe be so placed that the brazen meridian may stand due south and north, according to the two extremities of the needle, allowing for its variation.
Prob. II. To find the longitude and latitude of any place.—Bring the given place to the brazen meridian, and the degree it is under is the latitude; then observe the degree of the equator under the same meridian, and you wiU have the longitude.
Prob. III. The longitude and latitude of any place being given, to find that place on the globe.— Bring the degree of longitude to the brazen meridian; find upon the same meridian the degree of latitude, whether south or north, and the point exactly under that degree is the place desired.
Prob. Iv. The latitude of any place being given, to find all those places that have the same latitude.—The globe being rectified (Prob. I.) according to the latitude of the given place, and that place being brought to the brazen meridian, make a mark exactly above the same, and, turning the globe round, all those places passing under the said mark have the same latitude with the given place.
Prob. V. Iwo places being given on the globe, to find the distance between them.—If the places are under the same meridian, that is, have the same longitude, their difference of latitude, reckoning sixty-nine miles and a half to a degree, will give the distance. If they have the same latitude, but differ in longitude, their distance may be found by their difference of longitude, reckoning the number of miles in a degree of longitude in their common parallel of latitude, according to the table given above. If they differ both in latitude and longitude, lay the graduated edge of the quadrant of altitude over both the places, and the number of degrees intercepted between them will give their distance from each other, reckoning every degree to be sixty-nine English miles and a half. Prob. VI. To find the sun's place in the ecliptic at any time.—The month and day being given, look for the same upon the wooden horizon; and opposite the day you will find the sign and degree in which the sun is at that time; which sign and degree being noted in the ecliptic, the same is the sun's place, or nearly, at the time desired. ProB. VII. The month and day being given, as also the particular time of that day, to find those places of the globe to which the sun is in the meridian at that time.—The pole being elevated according to the latitude of the place where you are, bring the said place to the brazen meridian, and setting the index of the horary circle at the hour of the day, in the given place, or where you are, turn the globe till the index points at the upper figure of XII; which done, fix the globe in that situation, and observe what places are exactly under the upper hemisphere of the brazen meridian; for those are the places de
sired. Prop. VIII. To know the length of the day and night in any place of the earth at any time. —Elevate the pole (Prob. I.) according to the latitude of the given place; find the sun's place in the ecliptic (Prob. VI.) at that time; which being brought to the east side of the horizon, set the index of the horary circle at noon, or the upper figure of XII; and, turning the globe till the aforesaid place of the ecliptic touch the western side of the horizon, look upon the horary circle; and where the index points, reckon the number of hours to the upper figure of XII; for that is the length of the day; the complement of which to twenty-four hours is the length of the night. Prob. IX, To know by the globe what o clock it is in any part of the world at any time, provided you know the hour of the day where you are at the same time.—Bring the place in which you are to the brazen meridian, the pole being raised (Prob. I.) according to its latitude, and set the index of the horary circle to the hour of the day at that time. en bring the desired place to the brazen meridian, and the index will point out the hour at that place. Prob. X. A place being given in the torrid zone, to find the two days of the year in which the sun shall be vertical to the same.—Bring the given place to the brazen meridian, and mark what degree of latitude is exactly above it. Move the globe round, and observe the two points of the o that | through the said degree of latitude. Find upon the wooden
horizon (or by proper tables of the sun's annual motion) on what days he passes through the aforesaid points of the ecliptic; for those are the days required, in which the sun is vertical to the given place. Prob. XI. The month and the day being given, to find by the globe those places of the northern frigid zone, where the sun begins then to shine constantly without setting; as also those places of the southern frigid zone, where he then begins to be totally absent.—The day given (which must be always one of those either between the vernal equinox and the summer solstice, or between the autumnal equinox and the winter solstice), find (Prob. VI.) the sun's place in the ecliptic, and marking the same, bring it to the brazen meridian, and reckon the like number of degrees from the north pole towards the equator, as there is between the equator and the sun's place in the ecliptic, making a mark where the reckoning ends. }. turn the globe round, and all the places passing under the said mark are those in which the sun begins to shine constantly without setting, upon the given day. For solution of the latter part of the problem, set off the same distance from the south pole upon the brazen meridian towards the equator, as was in the former case set off from the north; then marking as before, and turning the globe round, all places passing under the mark are those where the sun begins its total disappearance from the given day. PRob. XII. A place being given in either of the frigid zones, to find by the globe what number of days the sun constantly shines upon the said place, and what days he is absent, as also the first and last day of his appearance.—Bring the given place to the brazen meridian, and observing its latitude (Prob. II.), elevate the globe accordingly; count the same number of degrees upon the meridian from each side of the equator, as the place is distant from the pole; and, making marks where the reckonings end, turn the globe, and carefully observe what two degrees of the ecliptic pass exactly under the two points marked on the meridian : first for the northern arch of the circle, namely, that comprehended between the two degrees marked, which, being reduced to time, will give the number of days that the sun constantly shines above the horizon of the given place; and the opposite arch of the said circle will, in like manner, give the number of days in which he is totally absent, and also will point out which days those are. And in the interval he daily will rise and set. PRob. XIII. The month and day being given, to find those places on the globe to which the sun, when on the meridian, shall be vertical on that day.— The sun's place in the ecliptic being found (Prob. VI.), bring the same to the brazen meridian, on which make a small mark exactly above the sun's place. Then turn the globe; and those places which have the sun vertical in the meridian, will successively pass under the said mark. PRob. XIV. The month and day being given, to find upon what point of the compass the sun then rises ...? sets in any place.—Elevate the pole according to the latitude of the place, and, finding the sun's place in the ecliptic at the given time, bring the same to the eastern side of the horizon, and it will show the point of the compass upon which he then rises. By taming the globe till his place coincides with the western side of the horizon, you may also see upon that circle the exact point of his setting.
Prob. XV. To know by the globe the length of the longest and shortest days and nights in any part of the world.—Elevate the pole according to the latitude of the given place, and bring the first degree of Cancer, if in the northern, or Capricon, if in the southern hemisphere, to the eastern side of the horizon. Then, setting the index of the horary circle at noon, turn the globe about till the sign of Cancer touches the western s-de of the horizon, and observe upon the horary circle the number of hours between the index and the upper figure of XII, reckoning them ac, cording to the motion of the index; for that is the length of the longest day, the complement of which to twenty-four hours is the extent of the shortest night. The shortest day and longest night are only the reverse of the former.
Prob. XVI. The hour of the day being given at any place, to find those places of the earth where it is either noon or midnight, or any other particular hour, at the same time.—Bring the given place to the brazen meridian, and set the index of the horary circle at the hour of the day in that place. Then turn the globe till the index points at the upper figure of XII, and observe what places are exactly under the upper semicircle of the brazen meridian; for in them it is mid-day at the time given. Which done, turn the globe till the index points at the lower figure of XII; and whatever places are then in the lower semicircle of the meridian, in them it is midnight at the given time. After the same manner we may find those places that have any other particular hour at the time given, by moving the globe till the index points at the hour desired, and observing the places that are then under the brazen meridian.
Prob. XVII. The day and hour being given, to find by the globe that particular place of the earth to which the sun is vertical at that time.— The sun's place in the ecliptic (Prob. VI.) being found, and brought to the brazen meridian, make a mark above the same; then (Prob X.) find those places of the earth in whose meridian the sun is at that instant, and bring them to the brazen meridian; which done, observe that part of the earth which falls exactly under the aforesaid mark in the brazen meridian; for that is the particular place to which the sun is vertical at that time.
Prob. XVIII. The day and hour at any place being given, to find all those places where the sun is then rising, or setting, or in the meridian; consequently all those places which are enlightened at that time, and those which have twilight, or dark night.—This problem cannot be solved by any globe fitted up in the common way, with the hour-circle fixed upon the brass meridian, unless the sun be on or near either of the tropics on the given day. But by a globe fitted up with the hour-circle on its surface below the meridian, it may be solved for any day in the year, according to the following method.
Having found the place to which the sun is
vertical at the given hour, if the place be in the northern hemisphere, elevate the north pole as many degrees above the horizon as are equal to the latitude of that place; if the place be in the southern hemisphere, elevate the south pole accordingly, and bring the said place to the brazen meridian. Then, all those places which are in the western semicircle of the horizon have the sun rising to them at that time, and those in the eastern semicircle have it setting: to those under the upper semicircle of the brass meridian it is noon; and to those under the lower semicircle it is midnight. All those places which are above the horizon are enlightened by the sun, and have the sun just as many degrees above them as they themselves are above the horizon; and thisheight may be known, by fixing the quadrant of altitude on the brazen meridian over the place to which the sun is vertical; and then, laying it over any other place, observing what number of degrees on the quadrant are intercepted between the said place and the horizon. In all those places that are eighteen degrees below the western semicircle of the horizon the morning twilight is just beginning; in all those places that are eighteen degrees below the eastern semicircle of the horizon the evening twilight is ending; and all those places that are lower than eighteen degrees have dark night.
If any place be brought to the upper semicircle of the brazen meridian, and the hour-index be set to the upper figure of XII, or noon, and then the globe be turned round eastward on its axis,— when the place comes to the western semicircle of the horizon, the index will show the time of the sun's rising at that place; and when the same place comes to the eastern semicircle of the horizon the index will show the time of the sun's setting.
To those places which do not go under the horizon, the sun sets not on that day: and, to those which do not come above it, the sun does not rise.
Prob. XIX. The month and day being given, with the place of the moon in the zodiac, and her true latitude, to find the exact how when she will rise and set, together with her southing, or coming to the meridian of the place.—The moon's place in the zod iac may be found by an ordinary almanack; and her latitude, which is her distance from the ecliptic, by applying the semicircle of position to her place in the zodiac. For the solution of the problem, elevate the pole (Prob. II.) according to the latitude of the given place; and the sun's place in the ecliptic at the time being (Prob. VI.) found, and marked, as also the moon's place at the same time, bring the sun's place to the brazen meridian, and set the index' of the horary circle at noon; then turn the globe till the moon's place successively meet with the eastern and western side of the horizon, as also the brazen meridian; and the index will point at those various times the particular hours of her rising, setting, and southing.
Sect. II.—Directions For Using The CeLestial Globe.
We shall now proceed to the use of the celestial globe, premising, that as the cquato-.