are based were all (with a few exceptions) made at or near midday. On this account I thought that the corrections due to the motion of the instrument might be neglected in calculating the results, since in the final mean such corrections must, for the most part, disappear.
In proof of the accuracy of the theory here established, I will give a few of the observations made last year at the commencement of October. They have reference to the double line D in the fourth interference spectrum. The light was always incident from south to north. The second telescope and the grating were readjusted every day.
Table III.
|
Time of observation, in 1862. |
2Θ4=ϕ. |
Remarks. | |
|
h |
° ′ ″ | ||
|
Oct. 5 |
11·4 A.M. |
62 55 38 |
Mean of three observations. |
|
3·58 p.m. |
62 55 53 | ||
|
5 P.M. |
62 56 7 |
Mean of six observations. | |
|
Oct. 9 |
3·74 p.m. |
62 56 0 |
Mean of six observations. |
|
Oct. 11 |
9·5 A.M. |
62 55 51 |
Mean of two observations. |
|
1 P.M. |
62 55 58 | ||
|
3·75 p.m. |
62 5 6 7 | ||
From the mean value of the wave-lengths corresponding to the line D given in Table I. we deduce
2Θ4=62°55′ 41″·2=ϕ0;
and since this value must be very nearly free from any error due to the motion of the instrument, it ought to agree with that furnished by the observations in Table III., after applying to the latter the corrections due to the motion of the instrument.
If X be the velocity of the solar system in a direction determined by the coordinates of the equator,
D=34°·5 and A=259°·8,
the magnitude of the motion of the instrument from north to south, due to the motion of the solar system, will be
X cos b=X[cos D sin P cos (A – ✻) – sin D cos P],
where P denotes the altitude of the pole, and ✻ the sidereal time of the observation.
For Upsala, therefore, we shall have the formula
X [0·713 cos (259°·8 – ✻) – 0·284].
The velocity of the instrument, in the above direction, due to
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