96 On the Variatiojis hi Personal Equation 
Experiment G. 
At the end of the section deaUng with the reduction of the observations 
for this experiment the conchision reached was that Rja' and R^' were not 
significantly negative; no difficulty therefore arises in fitting a curve of the form 
y = r//* to the values of R^.' given in the 6th row of Table XIV, p. 80. This 
was effected by the method of least squares, with the result 
R/ = -C673 X (-TOn/- (Ivii). 
In the 7th row of Table XIV are given the values of Hk calculated from this 
equation, and in the 8th row the differences 
(Rk from observations) — (R^;' from curve). 
If these differences are compared with the probable errors of R^', it will be 
seen that the fit is very satisfactory, for the later calculated values of R^;' are in 
any case uncertain ; Rjo' and R,/ were indeed not used in the least square 
solution as they were known to have too high negative values. 
Experiment D. 
On p. 85 it was suggested that R^ would approach the value + ■354 as k 
increased. In this case a curve of the form 
R^. = -354 + qr^, 
was fitted to the calculated values of R^. The fitting was carried out by moments. 
Making R^; — '354 = z, we have 
V (z) - qr J — — = N, say, where s is the luimber of ordinates, or 12 
i {zk) = q {r + 2/-- + 37" + . . . + sr*) = N x /j,,' 
, 1 sr* /, ••• 
whence fj-i = , , , (Ivin), 
1 - r 1 — ?•'' \ /' 
and is the distance of the mean from an origin at unit distance from the first 
ordinate qr, 
^ = 2'- 1^7 (Hx). 
The constants yu,/ and iVare known; solving (Iviii) by approximation we have r, 
and then (lix) gives q. 
The values are = •1153) 
r = -812lj' 
and finally, R^. = '354 + -1153 (■8121)* .(Ix). 
Then using the approximate relation 
R,' = (R, - ■354) X '-Lj^L-^ 
—which is a modified form of Equation (xliii) — we obtain for R/ the equation 
Rfc'=-1785 (-8121)* (Ixi). 
