6 E. L. De Forest—Law of Error in Target-Shooting. 
which referred to the free axes become 
w= 9°38, = 12°85, (21) 
Comparing these with (20), we see that the actual distance of the 
centre of gravity from the centre of the target is too great to be 
considered accidental, and we infer as in the former case, that to rep- 
resent the probabilities of future shots, the vertex of the probability 
surface should remain at the centre of gravity, and not be changed 
to the centre of the target, unless the aim is also changed. 
The probable difference in this case between p,” and p,” is by (16) 
A= 537°2. (22) 
The actual difference however is 
7698-0 — 4894-0 = 2804:0, 
a value so much greater that we are obliged to conclude that it is 
probably not accidental. 
This is what might be expected from the results already oheed 
with the same kind of weapon at shorter range. If there is really a 
greater liability to error in one direction than in another, it will nat- 
urally show itself at all ranges, with only such differences as might 
occur by accident. The angles which the direction of greatest error 
makes with the X axis at the two ranges here considered 
g' +90°= 114°31' and @’+ 90°=119°56', 
are not very different from each other. 
Didion finally gives the codrdinates of the trajectories of 100 can- 
non balls fired, under constant charges and angles of elevation, at 
distances of 200, 400 and 600 metres. The heights are reckoned, 
not from the centre of a target, but from the plane of the platform 
on which the gun-carriage stands. By an easy reduction, we get the 
coordinates « and v referred to axes taken horizontally and vertically 
through the centre of gravity, and expressed in metres. For 200 
metres range, we find 
fobs] 1182; [v?] = 16°39, [uv] = — 0°18, 
and (6) gives 
gi= 2° 15’, p' + 90°= 92° 15’, _ (23) 
Then by (9), 
[x] = 11°81, [y"] = 16-40, 
and by (10), 
“9 2="1198, p= "1657. 
The probable difference between ,* and p,” is by (16) 
A*=-0192. (24) 
