0(b PROCEEDINGS OP THE AMERICAN ACADEMY 



The probable error, e, of the resultant value of t may be found 

 from n, the number of residuals, their magnitudes r, and their 



T 



weights a. The value of each expressed in minutes will be -, but 



since a weight of a should be assigned to it, we must write a X - = r . 

 The sum of all these terms will be 2r, and the sum of their weights 



S45 Sr 

 ^a. The probable error will therefore be, e = , — . We can- 



y ?i - 1 2a 



not determine 1r directly, since r has not been computed. If t is not 



very large, 2i? will not greatly exceed 1r ; we shall not therefore 



0.845 •2R 



cause a large error if we write e = — ^ . The probable error 



® '\/n -1 2a ^ 



thus found will be somewhat too large, so that the substitution from 



which it results cannot exaggerate the accuracy of the observations. 



yR 



— equals the average deviation D, and if n is large we may write 



0.845 WnD 

 e = 



2a 



To apply this method we must determine the values of i? and a 

 corresponding to each set. The light corresponding to the time of 

 each observation was read off from the light curve, and subtracted 

 from the observed brightness. The value of a was determined as 

 follows : A silk thread was kept stretched perfectly straight by making 

 it the string to a bow of whalebone. It was then laid upon the curve 

 60 as to be tangent in turn to the points whose abscissas differ by 

 twenty-five minutes. The ordinates of the points where the thread 

 intersected two vertical lines, whose abscissas differed one hundred 

 minutes, were next read. The difference in these ordinates, divided 

 by one hundred, gave the change in magnitude per minute or a. 

 Table III. gives, in the first and second columns, tlie corresponding 

 times and values of a derived in this way, fiom the portion of the 

 light curve preceding the minimum. Points were next plotted with 

 the times as abscissas, and the values of a as ordinates, and a smooth 

 curve drawn through them. The ordinates of this curve are given 

 in the third column, and the residuals found from tlie observed values 

 of a in the fourth column. The close agreement testifies to the 

 smoothness of the curve and the precision of the measures. From 

 the curve thus found, the values of a were read for each set. The 

 last three columns corres[)ond to the portion of the curve following 

 the minimum. 



