1

2. On the 13th of February 1810, at 9 m. 54 sec. past seven o'clock in the evening, at Greenwich, there was an emersion of the second satellite of Jupiter; where was the eclipse visible? Jupiter's longitude at that time being O signs 21° 28′; and his declination 1° 7' south.

3. On the 17th of March 1810, at 50 m. 34 sec. past six o'clock in the evening, at Greenwich, there was an emersion of the second satellite of Jupiter; where was the eclipse visible? Jupiter's longitude at that time being O signs 27° 18′; and his declination being 1° 1' south.

4. On the 30th of August 1810, at 16 m. 42 sec. past one o'clock in the morning, at Greenwich, there was an emersion of the first satellite of Jupiter; where was the eclipse visible? Jupiter's longitude at that time being 2 signs 0° 17′ and his declination 1°2′ south.

3. On the 19th of August 1810, there was an emersion of the third satellite of Jupiter at 26 m. 53 sec. past three o'clock in the morning, at Greenwich; where was the eclipse visible? Jupiter's longitude at that time being 1 sign 29 deg. 44 min. and his declination 1 deg. 2 min south.

6. On the 5th of November 1810, there was an emersion of the third satellite of Jupiter at 29 min. 24 sec. past eleven o'clock in the evening, at Greenwich; where was the eclipse v ible? the longitude of Jupiter being 1 sign 29 deg. min. and his declination 1 deg. 7 min. south.

PROBLEM LVIII.

To place the terrestrial globe in the sun-shine, so that it may represent the natural position of the earth. Rule. If you have a meridian line* drawn upon a horizontal plane, set the north and south points of the wooden horizon of the globe directly over this line; or,

*As a meridian line is useful for fixing a horizontal dial, and for placing a globe directly north and south, &c. the different methods of drawing a line of this kind will precede the problems on dialling.

place the globe directly north and south by the mariner's compass, taking care to allow for the variation; bring the place in which you are situated to the brass meridian, and elevate the pole to its latitude; then the. globe will correspond in every respect with the situation of the earth itself. The poles, meridians, paraliel circles, tropics, and all the circles on the globe, will correspond with the same imaginary circles in the heavens; and each point, kingdom and state, will be turned towards the real one, which it represents.

While the sun shines on the globe, one hemisphere will be enlightend, and the other will be in the shade: thus, at one view may be seen all places on the earth which have day, and those which have night.*

If a needle be placed perpendicularly in the middle of the enlightened hemisphere (which must of course be upon the parallel of the sun's declination for the given day), it will cast no shadow, which shows that the sun is vertical at that point; and if a line be drawn through this point from pole to pole, it will be the meridian of the place where the sun is vertical, and every place upon this line will have noon at that time; all places to the west of this line will have morning, and all places to the east of it afternoon. Those inhabitants who are situated on the circle which is the boundary between light and shade, to the westward of the meridian where the sun is vertical, will see the sun rising; those in the same circle to the eastward of this meridian will see the sun setting. Those inhabitants towards the north of the cire which is the boundary between light and shade, w perceive the sun to the southward of them, in the h izon; and those who are in the same circle towards, he south, will see the sun in a similar manner to the north of them.

If the sun shine beyond the north pole at the given time, his declination is as many degrees north as he

* For this part of the problem, it would be more convenient if the globe could be properly supported without the frame of it, because the shadow of its stand, and that of its horizon, will darken several parts of the surface of the globe, which would otherwise be enlightened.

shines over the pole; and all places at that distance from the pole will have constant day, till the sun's declination decreases, and those at the same distance from the south pole will have constant night.

If the sun do not shine so far as the north pole at the given time, his declination is as many degrees south as the enlightened part is distant from the pole; and all places within the shade, near the pole will have constant night, till the sun's declination increases northward. While the globe remains steady in the position it was first placed, when the sun is westward of the meridian, you may perceive on the east side of it, in what manner the sun gradually departs from place to place as the night approaches; and, when the sun is eastward of the meridian, you may perceive on the western side of it, in what manner the sun advances from place to place as the day approaches.

PROBLEM LIX

The latitude of a place being given, to find the hour of the day at any time when the sun shines.

Rule 1. Place the north and south points of the horizon of the globe directly north and south upon a horizontal plane, by a meridian line, or by a mariner's compass, allowing for the variation, and elevate the pole to the latitude of the place; then, if the place be in north latitude, and the sun's declination be north, the sun will shine over the north pole; and if a long pin be fixed perpendicularly in the direction of the axis of the earth, and in the centre of the hour circle, its shadow will fall upon the hour of the day, the figure XII of the hour circle being first set to the brass meridian. If the place be in north latitude, and the sun's declination be above ten degrees south, the sun will not shine upon the hour circle at the north pole.

Rule 2. Place the globe due north and south upon a horizontal plane, as before, and elevate the pole to the latitude of the place; find the sun's place in the ecliptic, bring it to the brass meridian, and set the index of the hour circle to XII; stick a needle perpendicularly in the sun's place in the ecliptic, and turn the globe on its axis till the needle casts no shadow; fix the globe in

this position, and the index will show the hour before 12 in the morning, or after 12 in the afternoon.

Rule 3. Divide the equator into 24 equal parts from the point Aries, on which place the number VI; and proceed westward VII, VIII, IX, X, XI, XII, I, II, ÎII, IV, V, VI, which will fall upon the point Libra, VII, VIII, IX, X, XI, XII, I, II, III, IV, V ;* clevate the pole to the latitude, place the globe due north and south, upon a horizontal plane, by a meridian line, or a good mariner's compass, allowing for the variation, and bring the point Aries to the brass meridian; then observe the circle which is the boundary between light and darkness westward of the brass meridian, and it will intersect the equator in the given hour in the morning; but, if the same circle be eastward of the brass meridian, it will intersect the equator in the given hour in the afternoon.

Or, Having placed the globe upon a true horizontal plane, set it due north and south by a meridian line; elevate the pole to the latitude, and bring the point Aries to the brass meridian, as before; then tie a small string, with a noose, round the elevated pole, stretch its other end beyond the globe, and move it so that the shadow of the string may fall upon the depressed axis; at that instant its shadow upon the equator will give the hour.t

PROBLEM LX.

To find the sun's altitude by placing the globe in the sun-shine.

Rule. Place the globe upon a truly horizontal plane, stick a needle perpendicularly over the north pole,‡ in

* On Adams' globes the antarctic circle is thus divided, by which the problem may be solved.

†The learner must remember that the time shown in this problem is solar time, as shown by a sun-dial; and, therefore, to agree with a good clock or watch, it must be corrected by a table of equation of time. See a table of this kind among the succeeding problems.

It would be an improvement on the globes were our instrument makers to drill a very small hole in the brass meridian over the north pole.

the direction of the axis of the globe, and turn the pole towards the sun, so that the shadow of the needle may fall upon the middle of the brass meridian; then elevate or depress the pole till the needle casts no shadow; for then it will point directly to the sun; the elevation of the pole above the horizon will be the sun's altitude.

PROBLEM LXI.

To find the sun's declination, his place in the ecliptic, and his azimuth, by placing the globe in the sun

shine.

Rule. Place the globe upon a truly horizontal plane, in a north and south direction by a meridian line, and elevate the pole to the latitude of the place; then, if the sun shine beyond the north pole, his declination is as many degrees north as he shines over the pole; if the sun do not shine so far as the north pole, his declination is as many degrees south as the enlightened part is distant from the pole. The sun's declination being found, his place may be determined by Prob. XX.

Stick a needle in the parallel of the sun's declination for the given day, and turn the giobe on its axis till the needle casts no shadow; fix the globe in this position, and screw the quadrant of altitude over the latitude; bring the graduated edge of the quadrant to coincide with the sun's place, or the point where the needle is fixed, and the degree on the horizon will show the azimuth.

PROBLEM LXII.

To draw a meridian line upon a horizontal plane, and to determine the four cardinal points of the horizon. Rule 1. Describe several circles from the centre of the horizontal plane, in which centre fix a straight wire

* On Adams' globes the torrid zone is divided into degrees by dotted lines, so that the parallel of the sun's declination is instantly found in using other globes, observe the declination on the brass meridian, and stick a needle perpendicularly in the globe under that degree.