Page:MillerContraction.djvu/6

sixteen azimuths around a circumference. At the date of the observations, the annual motion of the earth, together with the motion of the solar system, may be taken as 33.5 kilometers a second. It is assumed that the solar system is moving towards a point whose right ascension is 277.5°, and whose north declination is 35°, with a velocity of eleven miles a second. The velocity of light being 300,000 kilometers a second, the ratio of the squares of the velocities is $0.72\times 10^{8}$. The length of path of a ray in our apparatus was 3224 centimeters, in which distance there are contained $5.5\times 10^{7}$ wave lengths of sodium light. The expected effect being doubled by rotation through 90, the displacement of fringes expected on the simple kinematic theory will be $11\times 10^{7}\div 0.72\times 10^{8}$. This is 1.5 wave length.

As was indicated, there were two times in the day when observation was advisable. The direction of the motion with reference to a fixed line on the floor of the room being computed for the two hours, we were able to superimpose those observations which coincided with the line of drift for the two hours of observation. Doing this, and subtracting a constant so as to make the algebraic sum of the observations equal to zero, we get a certain result. Then adding the first term to the ninth, and so on, since the effect repeats itself in a circumference, we get our final result, as follows: —

Result of observations at various azimuths.

Azimuths	8 || 7 || 6 || 5 || 4 || 3 || 2 || 1
Wave lengths	+0.0075	+0.0088	+0.0113	-0.0102	-0.0123	+0.0027	-0.0021	-0.0062

Azimuth mark 1 denotes that the telescope of the apparatus was directed N. 29° E.; 3, N. 16° W.; 5, N. 61° W., &c.

These numbers may be confidently pronounced to be due to errors of observation. We computed from them several curves of the theoretical form, having their origin at sixteen equidistant points in the half circumference; this was done by the method of least squares. The most probable of these curves had an amplitude of 0.0073 wave lengths, and its zero was half-way between the azimuths marked 4 and 5. The average of the given observations is 0.0076 wave lengths; after subtracting the ordinates of the computed curve, the mean residual was 0.0066 wave lengths. The sum of the squares of the residuals before was $565\times 10^{-4}$; afterwards, it was $329\times 10^{-4}$.

We may therefore declare that the experiment shows that if there is any effect of the nature expected, it is not more than the hundredth part