H. Crew — Period of Rotation of the Sun. 207 



direction of motion. The prism was by Steinheil and gave 

 very perfect definition. 



The Fahrenheit heliostat, with two mirrors, used in the first 

 series, was replaced by a better instrument of the Foucault 

 pattern. 



Two of Professor Rowjand's gratings were used. That desig- 

 nated as "No. 1," I had used before. It was four inches long, 

 ruled with 14,436 lines to the inch, and gave superb definition 

 in the 4th order. The other, "No. 2," was a six-inch grating, 

 with 7218 lines to the inch, and gave fair definition in the 8th 

 order. 



The objectives of the collimator and telescope had each a 

 clear aperture of six and one-half inches. The angle between 

 their optical axes remained constant, the grating being movable. 



In the first series, the grating was so placed that its normal 

 and the diffracted ray were both on the same side of the inci- 

 dent ray, a position which shall be denoted by "right;" while, 

 in the second series, the normal and the diffracted ray were on 

 opposite sides of the incident ray, a position called "left." 

 This change, as we shall presently see, has a very decided 

 effect on the result. 



The method of observation was very simple. The adjust- 

 ment of the instrument having been tested as accurately as 

 could be, by setting on an atmospheric line, the cross hairs 

 were then set on the solar line whose displacement was to be 

 measured, and the micrometer read. The sun's image was 

 then shifted by a cord convenient to the observer at the eye- 

 piece, and the micrometer read for the opposite limb. Ten 

 settings of this kind were made in succession, and then a new 

 latitude was chosen. 



Formula. 



The value of the relative linear velocity of the two limbs at 

 the equator, v' — v", was computed from the following formula 

 which, together with the method of obtaining the heliocentric 

 latitude, was sufficiently discussed in connection with the first 

 series.* 



,, c V A 1 a/ 1 — sin a y cos r 



v'—v" = = • r- *— ,, +2a sin a> 



A cos j cos h cos x cos " 



* Professor Oliver has been kind enough to call my attention to an error in the' 

 formula as used in the computation of the first series, viz : the omission of the factor 

 " 2 " from the last term of the right-hand member, the effect of which was to make 

 the result there given some three per cent smaller than it should have been. 



The corrected value from the previous measurements is 



v' — v" = 2 - 565 mi. per sec. 

 and daily angular motion at equator = 838'. 



