II. Grew — Period of Rotation of the Sun. 211 



ds = ± 1-25X10X0-000019 = 0-000238 centimeters. 



COS z 



. • . dm = -4- 0-0052 X micrometer revolutions. 



cos r 



For either grating in the position " right," the value of 



COS i 



was approximately, for all lines observed, - 84. 



cos r 



rev. 



:-.. dm — -4- 0-0044 



COS % 



But in the position "left," — -- = 1-19, 

 r cos r 



rev. 



.-. dm =- 0-0062 



The divergence between the first series and the second, due 

 to this cause, would therefore be that produced by a difference 



rev. 



of 0-0106 in the micrometer readings. Kow the mean value 

 of the displacement due to rotation, for latitudes less than 30°, 



rev. rev. 



was 0-099 ; for latitudes between 30° and 75°, was 0-060. So 

 that the heating effect would explain for lower latitudes a 

 divergence of 11 per cent, and for higher latitudes, a differ- 

 ence of 18 per cent between the results of the first and 

 second series. It is thus fully competent, on the assumptions 

 we have made, to explain the discrepancy between a velocity 

 of 2-565 mi. per sec, obtained in the first series, and 2-173 mi. 

 per sec, obtained in the second. 



0*0044 



Dividing this error in the ratio , we have for a final value 



& 0-0062' 



v' — v" = 2-403 ± 0-026 mi. per sec, 



which corresponds to a sidereal period of 26-23 days, or a daily 

 angular motion of 824/. 



It is to be observed that this result is independent of any 

 assumption as to how much the slit is heated. The divergence 

 between the two series has simply been divided in the ratio of 



- for the position " right " to for the position " left." 



cos r ° cos r 



To determine the change of angular velocity with latitude, 

 I have drawn through the observations of the second series the 

 straight line which most nearly represents them, and find by 

 the method of least squares its equation to be : 



= 802 / (l — 0-002061°) 



where d is the daily angular motion, and X the heliocentric 

 latitude, expressed in degrees. This would indicate accelera- 

 tion as we approach the equator. The first series gave : 



6 = 838' (1+0-00335 1°). 



