OF ERROES OF JUDGMENT AND ON THE PERSONAL EQUATION. 
239 
The coiTelation in the relative judgments of two observers, 1 and 2, both referred 
to a standard observer 3, is given by 
P.S’ 13 — 
b { (Pai (^.3 ) ilhi (‘^’s '^'2))} 
. (iii-)- 
So far as 1 can make out it is usually assumed that is zero, and the existence, 
if ?'io, &c., be zero, of very sensible values in the case of yOg, j.j has always been 
disregarded. 
The probable errors"^ of personal equations, variability in judgments, and 
correlations in judgments, as determined by the forrnulre (i.) (ii.) (iii.) above, are :— 
Per cent, o 
•>) 55 
?5 55 
5 ’ 55 
5 5 5 5 
5 ’ *5 
5 5 5 5 
5 5 5 5 
fpol = ’67449 (T^J^n 
Pm = ’67449 a-Q^I^/n 
p^\ 6/*449 ^\^j 
Oq! = ’67449 o-Qi/y/2n 
o-Qo = '67449 <T|;,2/\/2n 
cToi = ’67449 cToi/y/’in 
= -67449 (1 ->*,/)/v")! 
As) 13 ~ ’67449 (I pg, ip)l\/n 
\ 
\ 
/ 
, (iv.). 
If any investigation of personal equation is to have validity these probable errors 
must be small relatively to the quantity measured. Accordingly, no determination 
of personal equation is of the slightest value which does not give cr as well as for 
without this we do not know the weight to be attributed to the determination of p. 
My own experience would seem to show that ten to thirty olrservations, on which 
number some estimates of personal equation have lieen formed, are very insufficient. 
Further, astronomers rarely publish the data on which the personal equation has been 
determined so as to enable one to judge of its degree of stability, or of the degree 
of independence in the judgments of different observers. 
We shall have to investigate whether there are methods of finding ct-q^ and (T^^„ 
when only the relative personal equations and relative varial^ilities are given, and we 
shall have to see how the correlation of absolute and relative judgments may be 
determined. 
Personally it appears to me that without a knowledge of all these quantities we 
cannot profitably combine the observations of difterent observers or determine their 
individual independence and stability of judgment. 
* ‘ Phil. Trans.,’ A, vol. 191, pp. 239-245, 
