326 PROCEEDINGS OF THE AMERICAN ACADEMY. 



sixteen azimuths around a circumference. At the date of the observa- 

 tions, 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 sec- 

 ond, the ratio of the squares of the velocities is 0.72 X 10 8 . The length 

 of path of a ray in our apparatus was 3224 centimeters, in which distance 

 there are contained 5.5 X 10 7 wave lengths of sodium light. The expected 

 effect being doubled by rotation through 90, the displacement of fringes ex- 

 pected on the simple kinematic theory will be 1 1 X 10 7 -f- 0.72 X 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 87654321 



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 circum- 

 ference ; 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 sub- 

 tracting 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 X 10" 4 ; afterwards, it was 329 x 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 



