96 
Mr. Christie on the mutual action of 
a 
5 m, n 
l p t +c S ’ 
That an estimate may be formed of the degree of coinci- 
dence, I shall give the comparison of the observations with 
the results obtained in both cases. Putting — = a in the 
equation ( 1 ) we have 
(/> "1“ C Y H - £2 = M a .... (2). 
If we indicate the values of c and a , in the successive ob- 
servations, by c lt c u , c m , &c. and a t , a lt , a tlli See. and eliminate 
p and £ from three equations of the form ( 2 ) , then 
A>r ( c / c m ^ ‘ ( c l c rl) " ^ C m C rD . , 
M = 7 — 7 • ( 3 ). 
a (c, — c ) — a (c, — c ) + a, (c — c ) v ' 
71 v l m ' m v / n’ ^ l K m n> 
Since, in determining the value of M from this formula by 
means of the observations, errors of observation to the same 
extent would be the more sensible the less the intervals 
c . — c , c. — c , c — c , between the observations, instead 
of employing all the possible combinations of the observa- 
tions, in order to deduce the mean value of M, I have excluded 
all combinations in which two consecutive observations en- 
tered. This however makes but a very small difference in 
the results, since the mean value of M deduced from the 
thirty-five combinations of the seven observations is 23-362, 
and its value deduced from the ten combinations in which 
consecutive observations are excluded is 23-314. 
The mean value of M being obtained, the value of p will 
be found by eliminating s from two equations of the form 
(2), and we have thus, 
P 
M(a z 
C l ” 
c 
m 
) 
