The dawn of astronomy / A study of the temple-worship and mythology of the ancient Egyptians

by Sir Norman Lockyer

We can say then that a star of a certain declination will rise or set at such an azimuth, if we reckon from the N. point of the horizon, or at such an amplitude if we reckon from the equator. This will apply to both north and south declinations.

The following table gives for Thebes the amplitudes of rising or setting (north or south) of celestial bodies having declinations from 0° to 64°; bodies with higher declinations than 64° never set at Thebes if they are north, or never rise if they are south, as the latitude (and therefore the elevation of the pole) there is nearly 26°.

Amplitudes at Thebes.

Declination.	Amplitude.		Declination.	Amplitude.		Declination.	Amplitude.
°	°	′	°	°	′	°	°	′
0	0	0	22	24	33	44	50	25
1	1	7	23	25	41	45	51	41
2	2	13	24	26	49	46	52	57
3	3	20	25	27	58	47	54	14
4	4	26	26	29	6	48	55	32
5	5	33	27	30	15	49	56	51
6	6	40	28	31	23	50	58	12
7	7	47	29	32	32	51	59	34
8	8	53	30	33	41	52	60	58
9	9	59	31	34	51	53	62	23
10	11	6	32	36	1	54	63	51
11	12	13	33	37	11	55	65	21
12	13	20	34	38	21	56	66	54
13	14	27	35	39	31	57	68	31
14	15	34	36	40	42	58	70	12
15	16	41	37	41	53	59	71	59
16	17	49	38	43	5	60	73	55
17	18	56	39	44	17	61	76	1
18	20	3	40	45	30	62	78	25
19	21	10	41	46	43	63	81	19
20	22	17	42	47	56	64	85	42
21	23	25	43	49	10

The absolute connection, then, between the declination of a heavenly body and the amplitude at which it rises and sets is obvious from the above table: given the declination we know the amplitude; given the amplitude we know the declination.

Suppose we were dealing with a sea horizon: all the bodies rising or setting at the same instant of time would be in a great circle round the heavens, for the plane of the sensible horizon is parallel to the geocentric one.

But there are some additional points to be borne in mind. Ordinarily we should determine that the amplitude being so and so, the declination of the body which rose or set with that amplitude would be so and so, taking the horizon to be an all-round horizon like a sea one. But that would not be quite true, because we generally see the sun, to take an instance, some little time before it really rises and after it has set, owing to refraction. So that if we see the sun setting, say, north of west, we know that when we see it setting it appears really a little further to the north than it actually was at the moment of true sunset, because refraction gives us the position of the sun just below the true horizon. That is one point that we have to consider. Another is that, of course, we as a rule do not deal with sea horizons. Here we find a hill, there some other obstacle; so that it is necessary to make a correction depending on the height of the hill or other obstacle above the sea-or true-horizon at the place. Only when we take these things completely into consideration, can we determine absolutely the declination, or distance from the celestial equator, of the body at the moment of rising or setting. Still, it is worth while noting that when only approximations are required, the refraction-and hill-corrections have a tendency to neutralise each other in the northern hemisphere. Refraction will tend to carry the sunrise or sunset place more to the north, hills will cause the body to appear to rise or set more to the south.

DIAGRAM SHOWING THE VARIOUS AMPLITUDES AT WHICH STARS OF DIFFERENT DECLINATIONS RISE AND SET IN DIFFERENT LATITUDES.

It is important to point out that these corrections vary very considerably in importance according to the declination of the star with which we have to deal. With a high north or south declination the amplitude increases very rapidly, and the more it increases the more the corrections for refraction and elevation above the true horizon to which I have referred become of importance. In all cases the correction has to be made so that the amplitude will be increased or decreased from the true amplitude by this effect of refraction, according as the body—whether sun or star—is seen to the north or south of the equator.