96 
Mr. Christie on the mutual action of 
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 — = ^ in the 
“ 3 
equation (i) we have 
-I- cf + e=zMa .... (2). 
If we indicate the values of c and a, in the successive ob¬ 
servations, by r,, &c. and a^, a^^, a^^^, &c. and eliminate 
p and £ from three equations of the form (2), then 
M = -;-r-p^-- . (3). 
a (c, — c ) — a (c, — c ) + fl, (c — c ) ' ' 
I m' m ^ I n’ ^ I ^ 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 — r, 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 
a 
consecutive observations are excluded is 23-314. 
The mean value of M being obtained, the value of p will 
be found by eliminating t from two equations of the form 
(2), and we have thus, 
