To perform this problem you should never seek the altitude of the star when it is within an hour or two of the meridian, because at that time the altitude varies so very little. When you have gotten the altitude, then seek what is the star's hour, that is, its equatorial distance from the meridian at that altitude, which may be done by the globe, or any quadrant, or by the analemma, just as you would seek the sun's hour if its altitude were given: After this, seek the difference between the sun's right ascension for that day and the star's right ascension, and by comparing this difference with the star's hour you will find the true hour of the night. Note, This method of operation though it be true in theory, yet it is tedious and very troblesome in practice. The most usual ways therefore of finding the hour of the night by the star's (whether they are on the meridian or not) is by making use of a large globe, or the instrument called a nocturnal, wherein the most remarkable stars are fixed in their proper degrees of declination and right ascension: And their relation to the sun's place in the ecliptic and to his right ascension every day in the year being so obvious, makes the operation of finding the true hour very easy and pleasant. SECT. XXI.-Tables of the Sun's Declination, and of the Declination and Right Ascension of several remarkable fixed Stars, together with some Account how they are to be used. THE resolution of some of the astronomical problems by geometrical operations on the analemma requires the knowledge of the true place of the sun, his right ascension or his declination at any given day of the year. But since the knowledge of his declination is of most easy and convenient use herein, and since his true place in the ecliptic as well as his right ascension may be nearly found geometrically when his declination is given, (except when near the solstices) I have not been at the pains to draw out particular tables of the sun's place, but contented myself with tables of declination for every day in the year, and tables of right ascension for every tenth day. These are sufficient or a young learner's practice in his first rudiments of astronomy. Those who make a further progress in this science and would attain greater exactness, must seek more particular tables relating to the sun in other larger treatises. Here let these few things be observed. I. These tables shew the declination of the sun each day at noon; for it is then that the astronomer's day begins. If you The sun or star's horizontal distance from the meridian is the azimuth : It is the equatonal distance from the meridian which is called the sun or -star'> hour, would therefore know the sun's declination, suppose at six o'clock in the morning of any given day, you must compare the declination for that day with the sun's declination the foregoing day, and make a proportionable allowance, viz. three-fourth parts of the difference of these two declinations. If at six in the afternoon, you must compare it with the following day, and allow in the same manner one-fourth part. If II. These tables are fitted for the meridian of London. you would know therefore the sun's declination the same day at noon at Port Royal in Jamaica, you must consider the difference of longitude. Now that place being about 75 degrees westward from London, that is, five hours later in time, it is but seven o'clock in the morning there when it is noon at London; and you must make a proportionable allowance for the difference of the sun's declination by comparing it with that of the foregoing day. If that place had the same longitude eastward from London, it would be five o'clock in the afternoon there; and then you must compare the sun's present declination with that of the day following, and make allowance for the five hours, i. e. almost difference of the two declinations. But if you would know the sun's declination at any place, and at any hour of the day at that place; find what hour it is at London at the given hour at that place, and find the declination of the sun for that hour at London by note the first. of the Note, These allowances must be added or substracted according as the sun's declination is increasing or decreasing. Yet in any of these geometrical operations the difference of the sun's declination at other hours of the day or at other places of the world is so exceeding small that it is not sufficient to make any remarkable alterations, except when the sun is near the equinoxes; and then there may be some allowances made for it in the manner I have described; nor even then is there any need of any such allowances except in places which differ from London near 5 or 6 hours in longitude. III. Let it be noted also, that as the place of the sun, so consequently his declination and right ascension for every day do vary something every year by reason of the odd five hours and forty-nine minutes over and above 365 days, of which the solar year consists. Therefore it was proper to represent the sun's declination every day for four years together, viz. the three years before leap-year, and the leap-year itself. For in the circuit of those four years the sun returns very nearly to the same declination again on the same day of the year, because those odd five hours and 49 minutes do in four years time make up 24 hours, or a whole day (wanting but four times eleven, i. e. 44 minutes ;) which day is super-added to the leap-year, and makes the 29th of February, as hath been said before. It is true, that in a considerable length of time these tables will want further correction, because of those 44 minutes which are really wanting to make up the super-added day in the leapyear. But these tables will serve sufficiently for any common operations for forty or fifty years to come, provided you always consult that table which is applicable to the current year, whether it be a leap-year, or the first, the second, or the third year after it. IV. Observe also these tables of the sun's declination are sometimes reduced (as it were) to one single scale. And for this purpose men generally choose the table of declination for the second after leap-year, and this is called the mean declination, that is, the middle between the two leap years. This is that account of the sun's place and declination, &c. which is made to be represented on all mathematical instruments, viz. globes, quadrants, projection of the sphere, and graduated scales, &c. and this serves for such common geometrical practices in astronomy without any very remarkable error. Concerning the table of the fixed stars, let it be remembered that they move slowly round the round the globe eastward in circles parallel to the ecliptic, and therefore they increase their longitude 50 seconds of a minute every year, that is, one degree in seventy-two years. But their latitude never alters, because they always keep at the same distance from the ecliptic. Let it be noted also, that this slow motion of the fixed stars causes their declination and their right ascension to vary (though very little) every year. Their right ascension necessarily changes because their longitude changes, though not exactly in the same quantity. And though their latitude never alters, because latitude is the distance from the ecliptic, yet their declination must alter a little, because it is their distance from the equator. But the tables of their right ascension, which I have here exhibited, will serve for any common practices for at least twenty years to come, and their declination for near fifty years, without any sensible error in such astronomical essays as these. It may be proper here to give notice to learners, that the same stars may have north latitude and south declination; such are all those that lie between the equator and the southern half of the ecliptic; but all those stars which lie between the equator and the northern half of the ecliptic, have south latitude and north declination. A TABLE OF THE SUN'S DECLINATION For the Year 1753, BEING The First after Leap-Year, which will serve for near 50 Years. Janu. Febr. Mar. |April May June July Aug. Sept. | Oct. Nov. Dec. S. S. S.* N. N. N. N. N. N*. S. S. Day. | 0522 23 22 40 22 5622 S d. m.d. m. d. m.d. m. d. m. d. m. d. m.d. m.d. m.d. m.d. w.d. m. 122 59 16 5707 24 04 4315 1222 08 23 0717 59 08 10 03 2014 36 21 55 2 22 55 16 4007 0105 06 15 30 22 1623 05 17 4307 4803 4314 5522 04 522 48 16 2206 38 05 29 15 48 22 23 22 5917 2807 2604 0715 14 22 13 422 41 16 0406 1505_5216 3022 54 17 1207 04 04 30 15 32 22 21 5 22 35 15 4605 5106 14 16 622 2715 28/05 2806 37 16 722 19 15 0905 0507 0016 822 1114 5004 4207 22 17 1322 54 22 922 0314 31 04 1807 44 17 28 22 5922 1021 54 14 1104 55 08 07 17 4423 04 22 36 22 48 16 5606 4204 5315 51 22 28 4322 4216 3906 1905 16 16 09 22 36 1720 59 11 4901 0910 37 19 IS 20 27 11 2800 4510 5819 39 23 2621 0113 0201 4409 47 19 22 23 26 19/20 14/11 0600 2211 1919 5223 2720 20 20 01 10 45 N. 0211 5920 05 23 28 20 21 19 48 10 2200 25 12 00 20 1723 2920 28 12 0200 3410 5220 05 23 29 2219 3410 0000 4812 20 20 29 23 28 20 1511 4200 10/11 14 20 16 25 28 23 19 2009 3901 1212 40 20 40 23 27 20 0311 22 S. 1211 34 20 29 23 28 2419 0609 1601 3613 00 20 51 23 26 19 5011 0100 5611 55 20 41 23 27 2518 5108 54 01 5913 19 20 02 23 25 19 37 10 4100 59 12 16 20 5323 25 26 18 3608 3102 25 13 5921 1223 24 19 24 10 2001 25 12 36 21 27 18 2108 0902 4613 58 21 1109 5901 4612 5721 2818 0507 4603 0114 1721 3223 1918 5709 37 02 10 13 1721 25 23 18 297 49 13 3314 36 21 4223 1518 43 09 1602 3313 3721 36 23 14 03 5614 5421 51 23 11 18 28 08 5502 5713 5721 46 23 10 01 19 |