Astronomy Explained Upon Sir Isaac Newton's Principles / And made easy to those who have not studied mathematics

by James Ferguson

Time	Motion.			Time	Motion.			Time	Motion.
Hours	Degrees	Minutes	Seconds	*Min.	Deg.	Min.	Sec.	*Min.	Deg.	Min.	Sec.
				Sec.	Min.	Sec.	Th.	Sec.	Min.	Sec.	Th.
				Th.	Sec.	Th.	ʺʺ	Th.	Sec.	Th.	ʺʺ
1	15	2	28	1	0	15	2	31	7	46	16
2	30	4	56	2	0	30	5	32	8	1	19
3	45	7	24	3	0	45	7	33	8	16	21
4	60	9	51	4	1	0	10	34	8	31	24
5	75	12	19	5	1	15	12	35	8	46	26
6	90	14	47	6	1	30	15	36	9	1	29
7	105	17	15	7	1	45	17	37	9	16	31
8	120	19	43	8	2	0	20	38	9	31	34
9	135	22	11	9	2	15	22	39	9	46	36
10	150	24	38	10	2	30	25	40	10	1	39
11	165	27	6	11	2	45	27	41	10	16	41
12	180	29	34	12	3	0	30	42	10	31	43
13	195	32	2	13	3	15	32	43	10	46	46
14	210	34	30	14	3	30	34	44	11	1	48
15	225	36	58	15	3	45	37	45	11	16	51
16	240	39	26	16	4	0	39	46	11	31	53
17	255	41	53	17	4	15	41	47	11	46	56
18	270	44	21	18	4	30	44	48	12	1	58
19	285	46	49	19	4	45	47	49	12	17	1
20	300	49	17	20	5	0	49	50	12	32	3
21	315	51	45	21	5	15	52	51	12	47	6
22	330	54	13	22	5	30	54	52	13	2	8
23	345	56	40	23	5	45	57	53	13	17	11
24	360	59	8	24	6	0	59	54	13	32	13
25	376	1	36	25	6	16	2	55	13	47	16
26	391	4	4	26	6	31	4	56	14	2	18
27	406	6	32	27	6	46	7	57	14	17	21
28	421	9	0	28	7	1	9	58	14	32	23
29	436	11	28	29	7	16	11	59	14	47	26
30	451	13	56	30	7	31	14	60	15	2	28

Accelerations of the Fixed Stars.

D.	H.	M.	S.
1	0	3	56
2	0	7	52
3	0	11	48
4	0	15	44
5	0	19	39
6	0	23	35
7	0	27	31
8	0	31	27
9	0	35	23
10	0	39	19
11	0	43	15
12	0	47	11
13	0	51	7
14	0	55	3
15	0	58	58
16	1	2	54
17	1	6	50
18	1	10	46
19	1	14	42
20	1	18	38
21	1	22	34
22	1	26	30
23	1	30	26
24	1	34	22
25	1	38	17
26	1	42	13
27	1	46	9
28	1	50	5
29	1	54	1
30	1	57	57

[PLATE III].
An absolute Turn of the Earth on it’s Axis never finishes a
solar day.
Fig. II.

222. Thus it is plain, that an absolute turn of the Earth on it’s Axis (which is always completed when the same Meridian comes to be parallel to it’s situation at any time of the day before) never brings the same Meridian round from the Sun to the Sun again; but that the Earth requires as much more than one turn on it’s Axis to finish a natural day, as it has gone forward in that time; which, at a mean state is a 365th part of a Circle. Hence, in 365 days the Earth turns 366 times round it’s Axis; and therefore, as a turn of the Earth on it’s Axis compleats a sidereal day, there must be one sidereal day more in a year than the number of solar days, be the number what it will, on the Earth, or any other Planet. One turn being lost with respect to the number of solar days in a year, by the Planet’s going round the Sun; just as it would be lost to a traveller, who, in going round the Earth, would lose one day by following the apparent diurnal motion of the Sun: and consequently, would reckon one day less at his return (let him take what time he would to go round the Earth) than those who remained all the while at the place from which he set out. So, if there were two Earths revolving equably on their Axes, and if one remained at A until the other travelled round the Sun from A to A again, that Earth which kept it’s place at A would have it’s solar and sidereal days always of the same length; and so, would have one solar day more than the other at it’s return. Hence, if the Earth turned but once round it’s Axis in a year, and if that turn was made the same way as the Earth goes round the Sun, there would be continual day on one side of the Earth, and continual night on the other.

To know by the Stars whether a Clock goes true or not.

223. The first part of the preceding Table shews how much of the celestial Equator passes over the Meridian in any given part of a mean solar day, and is to be understood the same way as the Table in the 220th article. The latter part, intitled, Accelerations of the fixed Stars, affords us an easy method of knowing whether or no our clocks and watches go true: For if, through a small hole in a window-shutter, or in a thin plate of metal fixed to a window, we observe at what time any Star disappears behind a chimney, or corner of a house, at a little distance; and if the same Star disappears the next night 3 minutes 56 seconds sooner by the clock or watch; and on the second night, 7 minutes 52 seconds sooner; the third night 11 minutes 48 seconds sooner; and so on, every night, as in the Table, which shews this difference for 30 natural days, it is an infallible Sign that the machine goes true; otherwise it does not go true; and must be regulated accordingly: and as the disappearing of a Star is instantaneous, we may depend on this information to half a second.

Pl. VI.

J. Ferguson inv. et delin.