﻿HOWARD: ANNUAL PARALLAX 



187 



Proper Motion. The effect of proper motion on the distance 

 between the stars is shown in the formula 



The development of this formula is given in Chauvenet, Vol. I, 

 p. 695. 



The distance between the stars is affected by refraction, the 

 correction of which is completely discussed in Chauvenet, Vol. II. 



0'-s=Ap = sX [tan^ Z cos- (p - q) + lY 



This is the formula used in computing the differential refraction 

 in almost all of these observations. When these observations were 

 begun no barometer was at hand, so Professor Comstock's formula 

 was used instead. 



983 6 



r = tau Z 



460+ i 



983 b 1 



Thus X . 



460 + 1 206265 



This gives the refraction correct to the third decimal. 



Aberration. The effect of abereation on the distance between 

 the stars is fully discussed in Chauvenet, Vol. II. 



ACT = yc + 



Now (7 represents the true distance between the stars; but in these 

 reductions (J was taken to be the mean of the apparent distances. 

 This may be done without sensible error. Applying the above 

 corrections and reducing, the final formula for the conditional 

 equation may be obtained : 



^ + ry+ cp+ n = 0 



In the above formula T is the fractional part of the year from 

 the time of observation to the assumed epoch, January 1, 1907. 



Temperature Coefficient of the Micrometer Screw. Satisfactory 

 results in parallax work can not be hoped for without a thorough 

 knowledge of the effect of temperature on the micrometer screw; 

 consequently the temperature coefficient was carefully determined. 



At various times and temperatures, 383 observations in all were 

 made for the value of the screw. Many of these observations were 

 made on nights too poor for other work, and as the results were not 

 consistent, a number of them were rejected, which limited the range 

 of temperature. 



