PROBLEM VI. The day of the which the sun on TERRESTRIAL GLOBE. year being given, to note all places to that day does not set, and those places where the sun does not rise; and to record his elevations at noon and midnight in the longitudes of the former places; and his depressions below the horizon at noon and midnight, in the longitudes of the latter. Learn Polar Circles, (def. 68); Periscii, (def. 75). RULE.-Rectify the globe for the north or south declination of the sun: then, as will be seen, all places not more degrees from the enlightened pole than are equal to the sun's declination, or (which is the same thing) all places having latitude in the summer hemisphere greater than the complement of his declination, cannot lose his beams; whilst those having corresponding latitude in the other hemisphere, cannot receive them. 2. Bring the given place, whether elevated or depressed, to that semicircle of the brass meridian which is graduated from the equator towards the poles; and reckon the number of degrees, the shorter way, between the place and the upper surface of the wooden circle, or "terminator:" this will give the elevation or depression of the sun at that place at the mid-day of its longitude. 3. Bring the given place to that semicircle of the brass meridian which is graduated from the poles towards the equator; and the number of degrees reckoned, as before, between the place and the terminator, will give the elevation or depression of the sun at the midnight of the longitude of that place. ***The pupil will still bear in mind, that every place less than 18° depressed, has twilight. 1. Find what places are having continuous sun-light at midnight of the 28th of May; and, of these find, at each of the undermentioned places, the elevation of the sun at mid-day, when their inhabitants see the sun southward ; and his elevation at midnight, when they look at him across the north pole, and see him northward :— North Cape of Lapland; north point of Nova Zembla; north point of Spitzbergen; south point of Nova Zembla? North Cape Lapland, noon 41°; midnight 3°. North point of Nova Zembla, noon 351°; midnight 84°, &c., &c., &c. 2. Find what are the depressions or elevations of the sun at these places on the 5th of November; both when it is noon, and when it is midnight, at all places corresponding with them, severally, in longitude, and therefore in time? 3. On the 20th of February, 1823, Captain Weddell reached 7410 of south latitude.* Find the altitude of the sun on this occasion, at noon, when his crew looked northward at the sun; and its depression at midnight, when they looked across the south pole towards that luminary, and, consequently, saw its light strongly reflected upon the clouds near the south point of their horizon? 4. What would have been the elevation and depression of the sun at noon and at midnight, to his crew, had they remained in that latitude until the equinox (March 21st); and would they have had any real night during the twentyfour hours of that day? 5. Find how much London is depressed below the terminator at midnight of the 21st of March, or of the 23d of September; and how far the sun must shine over the north pole (i. e., how much the north pole must be inclined towards the sun,) in order that London may be within the twilight limit at that hour? 6. What must be the north declination of the sun, that is, how far must the north pole of our earth incline into his beams, in order that the following places may have no real night during a portion of the summer:-Paris, Madrid, Rome, Edinburgh:—and at which of them cannot that circumstance occur? * Any longitude in the given latitude may be taken. MERIDIAN ALTITUDE AND LONGITUDE. 125 PROBLEM VII. TERRESTRIAL GLOBE. Given the longitude and the sun's meridian altitude on a certain day, to find the place where the observation was made. Read and explain, H, given with the diagram on page 19. Read page 49 in explanation of page 48. RULE.-Since there are always 90° between the horizon and the zenith, the complement of the altitude of any heavenly body, or what it wants of 90°, is equal to the zenith distance; hence,— Find the sun's declination. Subtract the meridian altitude from 90°, and it will show the meridian zenith distance. Bring the given longitude to the brass meridian; then, if the sun was south, and the place consequently north of where it was vertical, count the degrees of this zenith distance northward from the sun's declination, and it will show the zenith of the required place. If the sun was north of the place of observation, count southward of the sun's declination in like manner. 1. 20th May, 1839, longitude 64 W. Sun's meridian altitude 7710 and south of the place: where was I ? 2. At sea, 3d March, in longitude 52° W. I observed the sun when on the meridian and north of my zenith, to have an altitude of 81°: where was the ship? Find the places at which the following observations were made on the days prefixed : 3. 6th July; Greenwich chronometer showing 20m. past 9 in the morning; sun on the meridian and south, at 481° altitude. 4. 18th Sept.; London time, as shown by my watch, being 8m. past 5, P. M.; sun on the meridian, and south of me; altitude 74°. 5. 15th Oct.; 13m. past 11, P. M. I observe an immersion of Jupiter's 1st satellite; time given for this in the Ephemeris, (London,) 10 o'clock, P. M.; altitude of sun last noon 64°, and north. 6. On the 27th May, 1840, at Greenwich; (but on 26th May where I was ;) I observed an immersion of Jupiter's second satellite; exact time at the place 50m. past 11, and latitude, as determined by the stars that evening, and by the sun at the last noon, 20 S. Refer to page 34 of White's Ephemeris, given on our pages 52 and 53, and determine my station? PROBLEM VIII. CELESTIAL GLOBE. Having a given day, to find at what time a certain star comes to the meridian. Learn Aspect, (def. 89); Read page 50 in explanation of page 51. Explain the "Speculum Phænomenorum,' on page 52, by attention to page 53. RULE. Find the sun's right ascension, and note whether the star (above the horizon or below it) be situated E. or W. of the plane of the meridian, when the sun is coinciding with it. Find the right ascension of the star, and subtract the less R. A. from the greater: then, if the remainder be less than 180°, when turned into time it will show how much earlier or later than noon the given star culminates. If the remainder be greater than 180°, subtract it from 360°, and what then remains, when turned into time, is the distance from noon. If the star be west of the sun it CULMINATIONS OF STARS, ETC. 127 will have culminated before noon; if to the east of the sun, it will culminate after noon. If the R. A. be given, as it frequently is, in time, subtract the hours and minutes of the one, from the hours and minutes of the other: then, if the remainder be less than 12 hours, it is the difference of earlier or later culminating : If the remainder be greater than 12 hours, subtract it from 24 hours, and what then remains is the difference of R. A., or of the time of culminating. The Problem may be performed mechanically by means of the sun's place and the index, as in the next Problem; but the questions are so put as to elicit the difference of Right Ascension, and impress the cause of the daily alteration of that difference. 1. There are three stars a, B, y, of the 2nd. magnitude, in the constellation Andromeda : find the difference of their Right Ascension and that of the sun, on 21st March, and on the 4th April, (just a fortnight after); and the precise times of each of these stars coming to the meridian on these two days? 2. On 6th July, 1840, the planets had very nearly the following R. A. :— 3. On the 10th March, at what time does Sirius, (a of Canis Major,) come to the meridian? 4. On the same day when do Altair, (a of Aquila,) and Regulus, (a of Leo Major,) culminate ? 5. Find at what time Betelgeux, and Castor, and Vega, culminate at any place on the 22d of December? |