144 PHILOSOPHICAL SOCIETY OF WASHINGTON. 
be; but it may, or rather must, happen sometinies that the most 
n n 
probable increase of the sum of 2? and y’ or [2*]_ + [y] consistent 
Nap Nes; 
with (25’) is << (n —n,,) 6’,b being the smaller limit. Such a re- 
sult cannot be accepted, being contradictory to the fact that there 
are n—n,, shots at a greater distance than 6. The following 
method gives plausible results in that case. Assume 
[y7], + = yy) 8? 
(4 ee (25,”) 
as first approximate value in (25,’), and if ¢,<(<,) adopt (<,) as 
final value of «,: but if ¢,>(¢,), then proceed in approximating to 
e, by (25,’). The solution of (25,’) gives, as heretofore, the best 
value of ¢,. Among the target records of the international shoot- 
ing match of 1874, at Creedmoor, there are 9 with lost shots, 5 of 
which give too small an increase of sum of squares, and this means 
that from the record of the hitting shots it would not appear prob- 
able that so many shots were lost. 
Instead of the squares, we may, however, employ first powers of 
distances; and I shall develop the requisite formule for a circular 
target and equal precisions. 
Nap 
n R ee s? 
We have [s], k= nf 8 pid e 22 
> 
0 
iss 2 
an(— 27 ae NF Re | 
oe ~_ Be si by (13) 
ry, * (n ay ils 
eee )n a (26) 
if N p=, this becomes ¢ = ae . ; (27) 
a | Soe 
The quantity ae rad VE (28) 
: 
