[PLASKETT-DELURY | THE SOLAR ROTATION 55 
20. From these mean values about one-third of which are due 
to Method I of reduction and two-thirds to Method II, the law of 
variation of latitude has to be obtained. Many different forms con- 
taining both sine and cosine terms of the latitude in different powers 
were tried and, although some gave close agreement, none, on the 
whole, were as good as the simple Faye formulæ 
V —\(a +b cos 9) cos ¢ 
= 
Sear COsey: 

Using the method of least squares to determine the constants the 
following formule were obtained. 
. f[V =( 1.504 + .509 cos? ¢) cos @ 
à 
; EN = ( 1.448+ .523 cos g) cos ¢ 
pones 11) ee 
ne f V=(1.421+ .599 cos @) cos ¢ 
Re nr 
From these formule the values in columns headed “Computed” 
and “Residual” in the preceding tables (Table IX) were obtained. 
The residuals in Series I and III are satisfactorily small and show no 
tendency to systematic arrangement of sign. In Series II, however, 
they are considerably larger and systematically grouped as to sign, 
indicating the necessity of an additional term in the Faye formula. 
If the observations of Series I and III are grouped together we 
get formule which represent the observations in both series nearly as 
well as the separate formule. The difference between the formule 
for Series I and III above is probably due to the small number of 
latitudes observed (only three) in Series III, in which case a small 
deviation of one of the values would make a large change in the co- 
efficients. The formule from both Series 
f V = (1483 + .532 cos? g) cos ¢ 
Series I and III (combd.) | €= 10°32 + 4°.05 cos? © 
may therefore be considered as the formule obtained from Plaskett’s 
measurements. Series II is not included in this on account of the 
systematic difference and because another term would be necessary to 
obtain reasonable agreement between the observed and computed 
values. However, if we compare the co-efficients from Series II with 
those from Series I and III combined we find them practically the 
same except for the difference in the first terms which is in line with 
