POOR, THE FIGURE OF THE SUN 391 



series of observations], — was taken as standard. With the personal equa- 

 tions so determined, the observations were reduced, and the results showed 

 periodic variations, which at first sight bore some resemblance to the vari- 

 ations in the sun-spot frequency. 



During the period 1862-72 this resemblance was more striking than in 

 periods before and after those dates. In investigating the probability of 

 a connection between the diameters as observed in each series, and the 

 number of sun-spots, Auwers assumed that, if present, such connection 

 could be expressed by the equation 



V = X + A.y 



where V is the residual obtained by subtracting the mean of all the horizon- 

 tal diameters from the mean of each year, and A is a number arbitrarily 

 obtained for each year by Auwers, from Wolf's "relative number" for that 

 year and from the observed magnetic variations during that year. From 

 such equations for each year, as given by the Greenwich and Washington 

 observations for the central period, Auwers found by least squares the 

 values 



x= +0.030 

 y=— 0.500 



with a weight of 2.73 and a mean error of 0.198 for y. Thus y was over 

 twice its mean error, a result which seemed to confirm a connection between 

 the observed diameter and the sun-spot period. 



Auwers also plotted the yearly residuals of the Greenwich and W'ash- 

 ington observations in connection with the sun-spot curve, and the rela- 

 tion between the two was again clearly indicated. Thus the observations, 

 when interpreted graphically or mathematically, point toward a close 

 connection between the variations in the diameter and those in the number 

 of visible sun-spots. 



Not content with this conclusion, Auwers proceeded further and inves- 

 tio'ated the various series of observations made by the individual observers. 

 In tliese indixidual series of residuals he found variations, some abrupt, 

 some periodic. These changes in an observer's residuals he now assumes 

 as due to changes in the personal equations rather than to changes in the 

 measured quantity. When abrupt changes in the residuals are found, 

 corresponding abrupt changes in the observers' personal equations are as- 

 sumed; when gradual periodic changes in the residuals are seen, corre- 

 sponding periodic changes in the personal equation are taken. Thus, in his 

 second or definitive reduction of the Greenwich and Washington observa- 



