all of which join accurately on the spherical into 360 degrees. 4. From the poles D and surface, and cover the whole ball. To direct the E, fig. 2, with the interval of twenty-three deapplication of these gores, lines are drawn by a grees and a half describe arches ab; these semicircle on the surface of the ball, dividing it will be twelfth parts of the polar circles. 5. into a number of equal parts corresponding to After the like manner, from the same poles D those of the gores, and subdividing those again and E, with the interval of sixty-six degrees and answerably to the lines and divisions of the gores. a half reckoned from the equator, describe arches There remains only to color and illuminate the cd; these will be twelfth parts of the tropics. globe; and to varnish it, the better to resist dust, 6.Through the degree of the equator e, corremoisture, &c. The globe itself, thus finished, is sponding to the right ascension of any given star, hung in a brass meridian, with an hour circle, and the poles D and E, draw an arch of a circle; quadrant of altitude; and then fitted into a and, taking in the compasses the complement of wooden horizon. the declination from the pole D, describe an The following is the detailed mode of their arch intersecting it in i ; this point i will construction: be the place of that star. 7. All the stars of a constellation being thus laid down, the figure of Fig. 1. the constellation is to be drawn according to Bayer, Hevelius, or Flamstead. 8. Lastly, after the same manner are the declinations and right MAAN ascensions of each degree of the ecliptic, dg, to be determined. 9. The surface of the globe 23456789101112 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 Fig. 3. 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 fh 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 Astronomie, tom. 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 PC 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 KDI, which represent the parallels, are equal to the cotangents of the latiFrom the given diameter of the globe find a tudes, and the arches of each, as D I, are nearly right line A B, fig. 1 of the diagram above, equal equal to the number of the degrees of the to the circumference of a great circle, and divide breadth of the gore (which is usually thirty deit into twelve equal parts. 2. Through the se- grees) multiplied by the sine of the latitude: veral points of division, 1, 2, 3, 4, &c., with the thus, there will be found an intricacy in tracing interval of ten of them, describe arches mutually them; but the difficulty proceeds from the vaintersecting each other in D and E: these figures riation found in the trial of the gores when pasting or pieces duly pasted and joined together will them on the globe, and of the quantity that must make the whole surface of the globe. 3. Divide be taken from the paper, less on the sides than each part of the right line A B into thirty equal in the middle (because the sides are longer), to parts, so that the whole line AB, representing apply it exactly to the space that it should cover. tvz periphery of the equator, may be divided · "The method used among workmen to delineate ALDM_K Phiar the gores, and which is described by M. Bion, GEH, of the gore, are exactly equal to the (Usage des Globes, tom. 3) and by M. Robert quarter of the circumference of the globe, when de Vaugendy in vol. vii. of the Encyclopedie, is compared to the figure on the copper, or to the hardly geometrical, but yet is sufficient in prac- numbered sides shown in fig. 4. Mr. Bonne tice. Draw on the paper a line AC, equal to having made several experiments on the dimenthe chord of fifteen degrees, to make the half sions that gores take, after they had been parted breadth of the gore; and a perpendicular PC ready to apply to the globe, and particularly with equal to three times the chord of thirty degrees, the paper named jesus, that he made use of for a to make the half length: for these papers, the globe of one foot in diameter, found that it was dimensions of which will be equal to the chords, necessary to give to the gores on the copper the become equal to the arcs themselves when they dimensions shown in fig. 4. Supposing that the are pasted on the globe. Divide the height C Ý radius of the globe contained 720 parts, the half into nine parts, if the parallels are to be drawn breadth of the gore is AG=188 s, the distance in every ten degrees; divide also the quadrant AC for the parallel of ten degrees taken on the B E into nine equal parts, through each division right line L M is 12:81, the small deviation from point of the quadrant, as G: and through the the parallel of ten degrees in the middle of the corresponding point D of the right line CP, gore ED is four, the line ABN is right, the draw the perpendiculars HGF and DF, the radius of the parallel of ten degrees or of the meeting of which in F gives one of the points of circle CEF is 4083, and so of the others as the curve BEP, which will terminate the cir- marked in the figure. The small, circular cap, cumference of the gore. When a sufficient which is placed under H, has its radius 253 number of points are thus found, trace the out- instead of 547, which it would have if the sine line PIB with a curved rule. By this construc- of twenty degrees had been the radius of it. tion are given the gore breadths, which are ou the globe, in the ratio of the cosines of the lati Fig. 4. tudes; supposing these breadths taken perpen KasR. dicular to CD, which is not very exact, but it is 13. 10 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 DI, which is at thirty degrees from the equator, there must be taken above D a point which shall be distant froin 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 DI, 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 171,25 every ten degrees, by dividing each parallel, as 1979 KI, into three parts at the points L and M, and drawing from the pole P, through all these division points, curves, which represent the inter 4083; che mediate meridians between PA and PB (as BR and ST, 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° 50' =BQ; for thirty degrees, 11° 29', &c. It is observed, in general, Mr. George Adams, late mathematical instruthat the paper on which charts are printed, such ment maker to his majesty, made some useful as the colombier, shortens itself t part of a line improvements in the construction of globes. His in six inches upon an average, when it is dried globes, like others, are suspended at their poles after printing; this inconvenience must there- in a strong brass circle, and turn therein upon fore be corrected in the engraving of the gores: two iron pins, which are the axis. They have if, notwithstanding that, the gores are found too besides a thin brass semi-circle, moveable about short, it must be remedied by taking from the the poles, with a small, thin, sliding circle upon surface of the ball a little of the white with it. On the terrestrial globe, the thin brass semiwhich it is covered; thereby making the dimen- circle is a moveable meridian, and its small sions suitable to the gore as it was printed. But sliding circle the visible horizon of any particuwhat is singular is, that in drawing the gore, lar place to which it is set. On the celestial moistened with the paste to apply it on the globe, the semi-circle is a moveable circle of globe, the axis G H lengthens, and the side AK declination, and its small annexed circle an artishortens, in such a manner that neither the ficial sun or planet. Each globe has a brass length of the side ACK nor that of the axis wire circle, placed at the limits of the twilight, 23.7 80.2 420 125.0 26,3 162 18.5.5 | D4 AN 128./ Ecliptic / 1883 which, together with the globe, is set in a wooden p. 1, Mr. Smeat on has proposed some improve trame, supported by a neat pillar and claw, with ments of the celestial globe, especially with rea magnetic needle at its base. On the terres- spect to the quadrant of altitude, for the resolutrial globe the division of the earth into land tion of problems relating to the azimuth and and water is laid down from the latest disco. altitude. The difficulty, he observes, that has veries; there are also many additional circles, as occurred in fixing a semi-circle, so as to have a well as the rhumb-lines, for solving all the ne centre in the zenith and nadir points of the cessary geographical and nautical problems. On globe, at the same time that the meridian is left the celestial globes, all the southern constella- at liberty to raise the pole to its desired elevations, observed at the Cape of Good Hope by tion, I suppose, has induced the globe makers M. de la Caille, and all the stars in Mr. Flam- to be contented with, the strip of thin flexible stead's British Catalogue, are accurately laid brass, called the quadrant of altitude ; and it is down and marked with Greek and Roman letters well known how imperfectly it performs its of reference, in imitation of Bayer. Upon each office. The improvement I have attempted, is side of the ecliptic are drawn eight parallel in the application of a quadrant of altitude circles, at the distance of one degree from each of a more solid construction; which being other, including the zodiac; and these are crossed affixed to a brass socket of some length, and at right angles with segments of great circles at this ground, and made to turn upon an upevery fifth degree of the ecliptic, for the more right steel spindle, fixed in the zenith, steadily readily noting the place of the moon, or of any directs the quadrant, or rather arc, of altitude planet upon the globe. The author has also to its true azimuth, without being at liberty inserted, from Ulugh Beigh, printed at Oxford to deviate from a vertical circle to the right in 1665, the mansions of the Moon of the Arabian hand or left; by which means the azimuth and Astronomers, so called, because they observed the altitude are given with the same exactness moon to be in or near one of these every night as the measure of any other of the great cirduring her monthly course round the earth, to cles. each of which the Arabian characters are fixed. OF THE USE OF THE GLOBES. On the strong brass circle of the terrestrial globe, and about twenty-three degrees and a half on We subjoin the principal problems which exeach side of the north pole, the days of each emplify the use of these elegant and important month are laid down according to the sun's scientific instruments. declination; and this brass circle is so contrived, that the globe may be placed with the north and Sect. I.-OF THE USE OF THE TERRESTRIAL south poles in the plane of the horizon, and with GLOBE. the south pole elevated above it. The equator, PROB. I. To rectify the globe. The globe on the surface of either globe, serves the purpose being set upon a true plane, raise the pole acof the horary circle, by means of a semi-circular cording to the given latitude; then fix the quadwire placed in the plane of the equator, carrying rant of altitude in the zenith; and, if there be two indices, one of which is occasionally to be any mariner's compass upon the pedestal, let the used to point out the time. A farther account of globe be so placed that the brazen meridian may these globes, with the method of using them, will stand due south and north, according to the two be found in Adams's Treatise on their Construction extremities of the needle, allowing for its variaand Use. tion. Mr. G. Wright, of London, has simplified PROB. II. To find the longitude and latitude the construction of the hour-circle. There of any place.-Bring the given place to the braare engraved on his globes two hour-circles, one zen meridian, and the degree it is under is the at each of the poles; which are divided into a latitude; then observe the degree of the equator double set of twelve hours, as usual in the under the same meridian, and you will have the common brass ones, except that the hours are longitude. figured round both to the right and left. The Prop. III. The longitude and latitude of any hour-hand or index is placed in such a manner place being given, to find that place on the globe. under the brass meridian, as to be moveable at Bring the degree of longitude to the brazen mepleasure to any required part of the hour-circle, ridian ; find upon the same meridian the degree and yet remain there fixed during the revolution of latitude, whether south or north, and the of the globe on its axis, and is entirely inde- point exactly under that degree is the place dependent of the poles of the globe. In this sired. manner, the motion of the globe round its axis ProB. IV. The latitude of any place being carrying the hour-circle, the fixed index serves given, to find all those places that have the same to point out the time, the same as in the reverse latitude --The globe being rectified (Prob. I.) way by other globes. There is an advantage in according to the latitude of the given place, and having the hour-circle figured both ways, as one that place being brought to the brazen meridian, hour serves as a complement to XII. for the make a mark exactly above the same, and, turnother, and the time of the sun rising and setting, ing the globe round, all those places passing and vice versa, may be both seen at the same under the said mark have the same latitude with time on the hour-circle. In the problems gene- the given place. rally to be performed, the inner circle is the Prob. V. Two places being given on the circle of reckoning, and the outer one only the globe, to find the distance between them.-If the complement. places are under the same meridian, that is, have In the Philosophical Transactions for 1789, the same longitude, their difference of latitude, reckoning sixty-nine miles and a half to a degree, horizon (or by proper tables of the sun's annual will give the distance. motion) on what days he passes through the If they have the same latitude, but differ in aforesaid points of the ecliptic; for those are the longitude, their distance may be found by their days required, in which the sun is vertical to the difference of longitude, reckoning the number of given place. miles in a degree of longitude in their common PROB. XI. The month and the day being parallel of latitude, according to the table given given, to find by the globe those places of the above. northern frigid zone, where the sun begins then to If they differ both in latitude and longitude, shine constantly without setting; as also those lay the graduated edge of the quadrant of alti- places of the southern frigid zone, where he then tude over both the places, and the number of begins to be totally absent.-The day given degrees intercepted between them will give their (which must be always one of those either bedistance from each other, reckoning every de- tween the vernal equinox and the summer solgree to be sixty-nine English miles and a half. stice, or between the autumnal equinox and the PROB. VI. To find the sun's place in the ecliptic winter solstice), ônd (Prob. VI.) the sun's place at any time. The month and day being given, in the ecliptic, and marking the same, bring it to look for the same upon the wooden horizon; the brazen meridian, and reckon the like numand opposite the day you will find the sign and ber of degrees from the north pole towards the degree in which the sun is at that time; which equator, as there is between the equator and the sign and degree being noted in the ecliptic, the sun's place in the ecliptic, making a mark where same is the sun's place, or nearly, at the time the reckoning ends. Then turn the globe round, desired. and all the places passing under the said mark PROB. VII. The month and day being given, are those in which the sun begins to shine conas also the particular time of that day, to find stantly without setting, upon the given day. For those places of the globe to which the sun is in the solution of the latter part of the problem, set off meridian at that time. The pole being elevated the same distance from the south pole upon the according to the latitude of the place where you brazen meridian towards the equator, as was in are, bring the said place to the brazen meridian, the former case set off from the north ; then and setting the index of the horary circle at the marking as before, and turning the globe round, hour of the day, in the given place, or where you all places passing under the mark are those are, turn the globe till the index points at the where the sun begins its total disappearance upper figure of XII; which done, fix the globe from the given day. in that situation, and observe what places are Prob. XII. A place being given in either of the exactly under the upper hemisphere of the frigid zones, to find by the globe what number of brazen meridian; for those are the places de- days the sun constantly shines upon the said place, sired. and what days he is absent, as also the first and PROB. VIII. To know the length of the day last day of his appearance.—Bring the given place and night in any place of the earth at any time. to the brazen meridian, and observing its latitude -Elevate the pole (Prob. I.) according to the (Prob. II.), elevate the globe accordingly; count latitude of the given place; find the sun's place the same number of degrees upon the meridian in the ecliptic (Prob. VI.) at that time; which from each side of the equator, as the place is being brought to the east side of the horizon, set distant from the pole; and, making marks where the index of the horary circle at noon, or the the reckonings end, turn the globe, and carefully upper figure of XII; and, turning the globe till observe what two degrees of the ecliptic pass exthe aforesaid place of the ecliptic touch the actly under the two points marked on the meriwestern side of the horizon, look upon the horary dian: first for the northern arch of the circle, circle; and where the index points, reckon the namely, that comprehended between the two number of hours to the upper figure of XII; degrees marked, which, being reduced to time, for that is the length of the day; the comple- will give the number of days that the sun conment of which to twenty-four hours is the length stantly shines above the horizon of the given of the night. place; and the opposite arch of the said circle PROB. IX. To know by the globe what o clock will, in like manner, give the number of days it is in any part of the world at any time, pro- in which he is totally absent, and also will point vided you know the hour of the day where you are out which days those are. And in the interval at the same time.-Bring the place in which you he daily will rise and set. are to the brazen meridian, the pole being raised PROB. XIII. The month and day being given, (Prob. I.) according to its latitude, and set the to find those places on the globe to which the sun, index of the horary circle to the hour of the when on the meridian, shall be vertical on that day.-day at that time. Then bring the desired place The sun's place in the ecliptic being found to the brazen meridian, and the index will point (Prob. VI.), bring the same to the brazen meriout the hour at that place. dian, on which make a small mark exactly above PROB. X. A place being given in the torrid the sun's place. Then turn the globe; and those zone, to find the two days of the year in which the places which have the sun vertical in the merisun shall be vertical to the same.-Bring the dian, will successively pass under the said mark. given place to the brazen meridian, and mark PROB. XIV. The month and day being given, what degree of latitude is exactly above it. to find upon what point of the compass the sun then Move the globe round, and observe the two rises and sets in any place.- Elevate the pole acpoints of the ecliptic that pass through the said cording to the latitude of the place, and, finding degree of latitude. Find upon the wooden the sun's place in the ecliptic' at the given time, bring the same to the eastern side of the horizon, vertical at the given hour, if the place be in the and it will show the point of the compass upon northern hemisphere, elevate the north pole as which he then rises. By turning the globe till many degrees above the horizon as are equal to his place coincides with the westeru side of the the latitude of that place; if the place be in the horizon, you may also see upon that circle the southern hemisphere, elevate the south pole acexact point of his setting. cordingly, and bring the said place to the brazen PROB. XV. To know by the globe the length meridian. Then, all those places which are in of the longest and shortest days and nights in any the western semicircle of the horizon have the part of the world.- Elevate the pole according sun rising to them at that time, and those in the to the latitude of the given place, and bring the eastern semicircle have it setting: to those under first degree of Cancer, if in the northern, or Ca- the upper semicircle of the brass meridian it is pricon, if in the southern hemisphere, to the noon; and to those under the lower semicircle eastern side of the horizon. Then, setting the it is midnight. All those places which are above index of the horary circle at noon, turn the globe the horizon are enlightened by the sun, and have about till the sign of Cancer touches the western the sun just as many degrees above them as they side of the horizon, and observe upon the horary themselves are above the horizon; and this height circle the number of hours between the index may be known, by fixing the quadrant of altitude and the upper figure of XII, reckoning them ac- on the brazen meridian over the place to which cording to the motion of the index; for that is the sun is vertical; and then, laying it over any the length of the longest day, the complement of other place, observing what number of degrees which to twenty-four hours is the extent of the on the quadrant are intercepted between the said shortest night. The shortest day and longest place and the horizon. In all those places that night are only the reverse of the former. are eighteen degrees below the western semicircle PROB. XVI. The hour of the day being given of the horizon the morning twilight is just beginat any place, to find those places of the earth where ning; in all those places that are eighteen it is either noon or midnight, or any other parti- degrees below the eastern semicircle of the horicular hour, at the same time.-- Bring the given zon the evening twilight is ending; and all place to the brazen meridian, and set the index those places that are lower than eighteen degrees of the horary circle at the hour of the day in that have dark night. place. Then turn the globe till the index points. If any place be brought to the upper semicirat the upper figure of XII, and observe what cle of the brazen meridian, and the hour-index be places are exactly under the upper semicircle of set to the upper figure of XII, or noon, and then the brazen meridian ; for in them it is mid-day the globe be turned round eastward on its axis,at the time given. Which done, turn the globe when the place comes to the western semicircle till the index points at the lower figure of XII; of the horizon, the index will show the time of and whatever places are then in the lower semi- the sun's rising at that place; and when the circle of the meridian, in them it is midnight at same place comes to the eastern semicircle of the given time. After the same manner we may the horizon the index will show the time of the find those places that have any other particular sun's setting. hour at the time given, by moving the globe till To those places which do not go under the the index points at the hour desired, and observ- horizon, the sun sets not on that day : and, to ing the places that are then under the brazen those which do not come above it, the sun does meridian. not rise. PROB. XVII. The day and hour being given, Prob. XIX. The month and day being given, to find by the globe that particular place of the with the place of the moon in the zodiac, and her earth to which the sun is vertical at that time.- true latitude, to find the exact hour when she will The sun's place in the ecliptic (Prob. VI.) being rise and set, together with her southing, or coming found, and brought to the brazen meridian, make to the meridian of the place.-The moon's place in a mark above the same; then (Prob X.) find the zodiac may be found by an ordinary almanack; those places of the earth in whose meridian the and her latitude, which is her distance from the sun is at that instant, and bring them to the bra- ecliptic, by applying the semicircle of position zen meridian ; which done, observe that part of to her place in the zodiac. For the solution of the earth which falls exactly under the aforesaid the problem, elevate the pole (Prob. II.) accordmark in the brazen meridian; for that is the parti- ing to the latitude of the given place; and the cular place to which the sun is vertical at that time. sun's place in the ecliptic at the time being Prob. XVIII. The day and hour at any place (Prob. VI.) found, and marked, as also the being given, to find all those places where the sun moon's place at the same time, bring the sun's is then rising, or setting, or in the meridian ; con- place to the brazen meridian, and set the index sequently all those places which are enlightened at of the horary circle at noon; then turn the globe that time, and those which have twilight, or dark till the moon's place successively meet with the night.—This problem cannot be solved by any eastern and western side of the horizon, as also globe fitted up in the common way, with the the brazen meridian; and the index will point hour-circle fixed upon the brass meridian, unless at those various times the particular hours of her the sun be on or near either of the tropics on the rising, setting, and southing given day. But by a globe fitted up with the hour-circle on its surface below the meridian, it SECT. 11 it Sect. II.—DIRECTIONS FOR USING THE CEmay be solved for any day in the year, according LESTIAL GLOBE. to the following method. We shall now proceed to the use of the ceHaving found the place to which the sun is lestial globe, premising, that as the equato, |