sidered as quite decisive. Last midsummer the weather was unfavourable to my observations, and at the end of October the latter were not sufficiently numerous to furnish an answer even to the first of the above questions.
I should not in fact have alluded to the subject had not M. Babinet, in the Academy of Sciences, proposed a method of determining the translatory motion of the solar system identical with the one which, two years ago, I submitted to the Royal Scientific Society of Upsala.
A small difference exists, however, in our calculations. I had assumed the motion of the grating to have no influence on the angle Θ, whereas Babinet introduces, on this account, the correction
h (1 – cos Θ) tan Θ.
The truth of this formula may in fact be readily established by help of the adjoining figure, in which e sin Θ denotes the distance traversed by light during the time that the grating describes the distance — h e sinΘ in a direction contrary to that of the incident rays. The difference of path for the two interfering waves will consequently, through the motion of the grating, be diminished by
he (1 – cos Θ) sin Θ,
a magnitude which, when equated to
– e cos Θ dΘ,
gives
dΘ = – h(l – cos Θ) tan Θ.
The value of dΘ will, of course, be positive when the instrument moves in the same direction as the light.
The expression thus obtained, added to the one in the formula (1), gives for the total variation of the angle Θ the value
AΘ=(h–h′) tan Θ; and if, moreover, h= – h′= 20″·4, and 2Θ=62° 55′41″,
then will
Δ2Θ=49″·8.
Hence in the special case under consideration, the variation of the angle 2Θ is increased by 7″·2 in consequence of the motion of the grating.
The observations on which the numerical values of Table I.
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