154 H. Crew — Rotation of the Sun. 



of the prism being that in which two fine plumb lines, the one 

 before, the other behind, the prism, were brought to coinci- 

 dence. Having obtained this angle (by formula given below), 

 we have but to add to it the parallactic angle, and the position 

 angle of the sun, with their proper signs, to obtain the required 

 angle, viz : the angle which the projected axis of the sun makes 

 with the slit. This angle must finally be corrected for the in- 

 clination of the solar axis to the plane of the ecliptic ; a correc- 

 tion never amounting to one per cent. 



Theory and Observations. — Let V= velocity of light, 186328 miles 



per sec. (Newconib and Michelson). 

 A = wave length of ray observed (Rowland's Standards). 

 v'-v" = relative linear velocity of the two limbs of the sun at the 



equator. 

 j=heliocentric latitude of any point on the sun's limb at which 



the slit of the spectroscope is tangent ; call this the " latitude 



of observation." 

 /J= displacement of the line as measured on the micrometer. 

 c=value of one revolution of the micrometer screw in Angstrom's 



units, for the line observed. 

 A=half the angle subtended at the center of the sun's image by 



the length of slit covered by the image, 

 ^^inclination of plane of solar equator to plane of eliptic. 

 <5D=angular semi-diameter of the sun. 

 «=linear velocity of the earth in its orbits, expressed in miles 



per second. 



Thenj by Doppler's principle, we have 



cJV 1 A /l — «in 2 v cos 2 6 



V '-v"=y • " r • V1 *™ X C ° S +asin cp 



A cos x cos h cos x cos d 



where the factor '/cos. h is the correction for the overlapping 

 of the sun's image on the slit ; this correction is sufficiently 

 approximate except for very high latitudes, where a slight cor- 

 rection depending upon ^ must be introduced. The factor in- 

 volving the radical is the correction for the inclination of the 

 solar axis to the plane of the ecliptic. The addition of the last 

 term on the right (first suggested by Prof. Oliver) reduces the 

 velocity from the synodic to the true period* of rotation. The 

 correction due to the rotation of the earth is so small as to be 

 negligible. 



The following are two specimens of the individual observa- 

 tions ; the quality of the one being above, that of the other be- 

 low, the average. 



* In comparing my final results with those of Young and Vogel it must be 

 borne in mind that they have not made this reduction, and that therefore their 

 values are for the synodic period. 



