IMMERSIONS, ETC., OF JUPITER'S SATELLITES. 157

burgh; and what the times of culmination of Mars, Saturn, and Uranus?

3. What was the time of Saturn's rising on the 25th June, 1840 (for his place see our page 51); and what were his azimuth and altitude at half-past 9 P. M., when I was viewing his ring?

***Whether, under some circumstances, the morning star may be seen or, whether it even rise before the sun, although to the west of that luminary, may depend upon the latitude of the place and the planet's declination: This may be illustrated by the following:

4. Venus's longitude, on the 21st March, was 20° in and her latitude 1° south: at what times* will she rise on the morning of that day at Madrid, latitude 40°; Land's End, latitude 50°; Petersburgh, latitude 60°; and at the north part of Lapland, latitude 70° ?

PROBLEM XIX.

TERRESTRIAL GLOBE.

Having the instant of the immersion or emersion of a satellite of Jupiter, to determine those situations from which may be viewed.

it

Read again p. 53, in explanation of p. 52, and p. 50, in explanation of p. 51.

These eclipses furnish an excellent means of determining longitude, since, on account of Jupiter's distance, no change of place on the earth can effect the apparent relative positions of him and his moons, (M on. p. 18); but to observe them with precision, a telescope of considerable magnifying power must be used, and such a telescope requires perfect steadiness: hence these phenomena are not available on ship-board.

"the

To have an eclipse of a satellite of Jupiter distinctly visible, sun must be at least 8° below the horizon, and Jupiter not less than 8° above it at the same time.t" Hence we will take the following method:

RULE 1.-If the latitude and longitude of Jupiter be

* 1t will be recollected that the first point of Aries (the sun's place) rises at 6 o'clock every where on that day.

+ Nautical Almanac.

P

given, find by the celestial globe his R. A. and declination, and elevate the pole to his declination. Find, from the difference of Jupiter's R. A. and the sun's, the time of his last being on the meridian,* and reckon the hours between this time and the time of the immersion, &c. Bring the place, the time of which is given, to the brass meridian, and set the index to 12, (as a mark). Cause the globe to rotate eastward so many hours as the time of immersion, &c. is past the previous culmination of Jupiter :-All places now above the terminator are those to which the planet's beams are extending:-Note down the principal of them, excepting those which, not being more than 8° above the terminator, do not have him sufficiently elevated.

2. Now, elevate the pole (north or south accordingly) to the sun's declination; bring the sun's “ place" to the brazen meridian, set the index to 12, and turn the globe as many hours eastward as the time of the immersion, &c. is past the last noon. This will show the position of the earth's surface with regard to sunlight at the time of the immersion, &c; and all places now above the terminator, or within 8° below it, which have been inserted in the foregoing list, must be struck out of it, as having the phenomenon hidden from them by daylight: the remaining places only being those at which it may be viewed.

1. I find (on p. 52) that there was an emersion of 's first satellite at 15d. 11h. 13m. 40s. of June; or about past 11 P.M. of 15 June; and, looking at p. 51, I find that his R. A. is then 14h. 30m. and his declination about 13° S. Find, from these data, from what situations this emersion might have been viewed?

Here having elevated the S. pole 1340, and having found that the O's R. A. is 859 or 5h. 40m.; and that, consequently, 24 was on the meridian, 8h. 50m. after the O, or at 50m. past 8 P.M., I bring Greenwich to the brass meridian, set the index to 12, (as a mark,) and turn the globe 2h. 24m. eastward, such being the interval between

*This time of culminating will not differ materially in one day; we take the last culmination to avoid the inconsistency of reversing the globe's motion.

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the time of 4's being on the meridian, and the emersion's taking place. I now note down the places above the terminator, as being those that have 4 above their horizon, omitting all within 8° of the terminator; they are the following:-South America, North America, except the N. W.; Africa and Madagascar, except the eastern parts, and all western Europe.

But, following the 2d section of the rule, I find that it is needful to strike out North America, the West Indies, and the N. W. of South America, as well as the extreme north of Europe; since they were in sun-light, or strong twilight, at the time of this eclipse.

2. Suppose that on the 21st December, in a certain year, there will be an immersion of a satellite of Jupiter at 5 A.M. (Greenwich time); and that Jupiter's R. A. is 150° or 10h., and his declination 12° N. From what situations may this immersion be viewed? (a)

3, On 4th August 4's longitude being 11 signs 14° and his latitude 11° south, there was an eclipse of his second satellite when it was 10 o'clock at night at Petersburgh. Where might it have been viewed? (b)

4. June 8, 9h. 39m. 8s. 4's 1 Sat. emers. (see p. 52.) Find 's R. A. and declination from p. 51 (c); and from these data determine the situations from which this emersion might have been visible?

5. In 1838, January 17, 19h. 14m. 34s.; 4's 1 Sat. Im. R. A. 11 h. declination 52° north. Find where this immersion was visible?

(a) Here Jupiter will culminate hours before the sun; but the immersion will take place only 7 hours before the sun culminates. (b) Here (from his longitude and latitude) I find Jupiter's R. A. will be such that he culminates - before the sun; but the eclipse takes place 10 hours after the sun culminates; hence the difference between the times of Jupiter's culmination and the eclipse of his satellite will be 10 hours added to hours.

(c) It must be remembered that the R. A. is given for every day; but declination (as well as longitude and latitude) for every 6th day only; in this case we must take the declination given for the 7th day, as the nearest to the 8th day.

CELESTIAL GLOBE.

Exercises, chiefly recapitulatory, on the Right, Oblique, and Parallel positions of the Sphere.

RIGHT SPHERE.-Latitude 0; the poles in the horizon. Repeat def. 49.

1. What inhabitants of the earth have this position of the sphere; and what stars are constantly above or below their horizon?

2. What (strictly speaking, and also disregarding refraction) is the diurnal arc of any fixed star at the equator: and is the diurnal arc of a star as shown by the index of a globe strictly correct?-(See def. 83 and its note.)

4. What is the diurnal arc of the pole-star at the equator, supposing the polar-point not to be elevated by refraction?-(See 5th question of Prob. V. p. 77.)

5. What (invariably) is the diurnal arc of the sun there? -(See def. 84.)

6. What is the diurnal arc of the moon there;* and why does it differ from the diurnal arc of the sun, and still more from the diurnal arc of a fixed star?—(See def. 88, and its note.)

7. What is meant by the right ascension (R. A.) of the sun, or of a star, or planet?

8. In strictness, does the R. A. of the for any day coincide with that degree of the equinoctial which culminates with him? why, or why not?

9. Find, by the globe, whether the declination of a star, &c., affect its R. A. (for instance B Auriga and Betelgeux.) and how much longer the day is at the equator when the has 2340 north declination, than when he has 2310 south declination ?

* The moon, if watched, will be found, night after night, to have removed about 13° (nearly 24 times her apparent diameter) to the east of the position she occupied amongst the stars at the same hour of the night before: hence the earth must turn about 50 minutes more, to bring her to the meridian, after the star with which she last came to the meridian has arrived there.

POSITIONS OF THE SPHERE.

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10. Find, by the globe, the difference in a right sphere between the rising or setting amplitude of any heavenly body and its declination?

11. On what two days is the O vertical at the equator; and when he is on the meridian but not vertical, what is his depression from the zenith (i. e. his "meridian zenith distance") always equal to ?

12. Suppose a house at Quito to stand with its façade duly north, during which months in the year is the back of it entirely shaded; and out of which windows must the inhabitant look to see the full moons of those months?

13. What is the greatest meridian zenith distance of the sun at the equator; what, consequently, his least meridian altitude; and on what two days of the year does this occur?

OBLIQUE SPHERE.-The north or south pole elevated according to the latitude.

Repeat def. 51.

1. How many degrees does the altitude of the pole-star change, in the course of the sidereal day, at any place having an oblique sphere ?-(See explanation to question 1 on page 96.)

2. What is the diurnal arc of any star in the equinoctial to the inhabitants of an oblique sphere ?

3. Find (by bringing them severally to the meridian) what are the right ascensions of 8 of Orion, a of Orion, (Betelgeux,) and Castor, (a of Gemini,) and what are the oblique ascensions of these three stars in latitude 37° north, and their several ascensional differences?-(Def. 56 and note.)

4. Find, by using the index, how long these several stars are above the horizon in that latitude; and contrast their several "descensional differences" with their several "ascensional differences"?

5. Turn into time the sum of the ascensional and descensional differences of either of these two northern stars (Castor and Betelgeux); and compare that time with the