the earth’s annual motion is equal to
h cos b1, = h { cos D1 sin P sin [☉ – ✻] – sin D1 cos P}, where
— sin D1 = sin 23° 38' cos ☉.
In this formula ☉ denotes the right ascension of the sun, P and the same magnitudes as before, and h=20″·4 the velocity of the earth expressed by the angle it subtends at the centre of a circle whose radius is the velocity of light. The total correction of the angle ϕ, therefore, will be
Δϕ=24″·9 [cos b1 + n cos b],
since
X=nh and 40″·8 tan Θ =24″·9.
If by means of this last formula, and under different assumptions for the value of n, we calculate the correction for each angle ϕ in Table III., and afterwards add these corrections to their respective angles, the resulting values of ϕ + Δϕ, subtracted from the assumed true value of 2Θ4, that is to say, from
ϕ0=62° 55′ 41″, will give the following:
Table IV.
|
ϕ0–ϕ. |
ϕ0–(ϕ+Δϕ). | |||
|
n = 0. |
n = 1/3. |
n = 1/2. |
n = 1. | |
|
″ |
″ |
″ |
″ |
″ |
|
+ 3 |
+ 3 |
+ 4 |
+ 4 |
+ 7 |
|
–11 |
+ 9 |
+ 5 |
+ 3 |
– 2 |
|
–26 |
– 3 |
– 6 |
– 7 |
–13 |
|
–19 |
+ 2 |
– 1 |
– 3 |
– 9 |
|
–10 |
–17 |
–14 |
–12 |
– 8 |
|
–18 |
– 7 |
–10 |
–10 |
–12 |
|
–26 |
– 5 |
–10 |
–10 |
–16 |
The sums of the squares of the differences are respectively 2267, 462, 419, 427, 719.
So far as we can conclude from the above observations, the influence of the earth’s annual motion appears to be verified; that of the motion of the solar system is less perceptible. Nevertheless it is obvious that if we were to assume that motion to be zero, or to be equal to that of the earth in its orbit, the agreement between the observations would be worse than under the assumption that the magnitude of the motion in question is
somewhat more than one-third of that of the earth. Between this result, and what we already know of the motion of the solar system through astronomy, there is no great divergence.
I hope during the present year, however, to be able to continue my spectrum–experiments, and to have a better opportunity of determining, numerically, the magnitude of the motion of the solar system. In the present paper my object has merely been to show the possibility of solving, optically, this interesting problem in physical astronomy.