142 PHILOSOPHICAL SOCIETY OF WASHINGTON. 
which formule afford a comparison between the precisions of 
sighting and leveling. We have then 
el: =] 24 gf 
c= Jit = ory . as 
This formula, although laborious for practical use, is the most 
rigorous measure of skill in shooting, and there is no need of other 
formule except when shots are lost. In that case it requires an 
important modification, whereby it loses in rigor if the number of 
lost shots is considerable. Assuming the precisions of sighting 
and leveling equal, then the reduced distance r in (12) will be the 
actual distance s of a shot; and if the target is circular, of limiting 
radius R, we have 
nD R j & 
[s*], Ser oF fi ee 
o 
Bays . eG 
=n} — 2 ze <A bah =)! 
ke? 
Now by (18) fe G. ft 
therefore [2], # on, gee (n — Np ) R 
"R 
and wis Le ota (n Tee )e (23) 
2n 2 
This formula reverts, of course, to (22), ifn =n # and it makes 
the most probable sum of the squares of the lost shots 
ny oe ae R 
[s iM 5 (n n eh 
R R 
and since ( a Ni is the smallest possible actual value of 
this quantity ; this expression for it is quite plausible. 
The targets used by the National Rifle Association are rectan- 
gular. (At long range they are 12 feet wide and 6 feet high). 
ae 
