E. L. De Forest—Law of Error in Target-Shooting. 5 
Therefore, when p,’ and p,° are computed as in (10), if the proba- 
bility of error in the and y directions is really the same, the proba- 
ble difference between p,* and p,’, occurring from accidental causes, 
will be 
26 
Vn 
or, if we take approximately &°=4(p,’+9,°), 
. 5 2 2 
Aa 674 (p+ Ps ) (16) 
Vn 
To apply this to the case in hand, we substitute for p,* and p,” their 
numerical values as in (10), and so get for the probable difference 
A? = 48°64. (17) 
A* = 6745 
(15) 
The actual value 
: 474°24 — 332°03 = 142°21, 
is so much larger that we are obliged to conclude that in this case it 
is probably not an accidental but a real difference, likely to affect the 
distribution of future shots in the same way. Hence (1) is the 
proper formula to use, and the codrdinate axes ought to be taken not 
horizontally and vertically, but coincident with the free axes of the 
group of shot-marks. 
Didion also gives a table of the positions of the shot-marks made 
by firing a pistol, apparently similar and with equal charge, 250 
times at 100 metres distance, aiming at a point 1°47 m. above the 
centre of the target. By the same procedure as before, we find 
u’| = 1892560 v’| = 1742890, uv | = — 301980 
5} b) 
where u and v are expressed in centimetres. The inclinations of the 
free axes to the U axis then are by (6) 
gp! = 29° 56, gp’ + 90° = 119° 56’, (18) 
and with codrdinates referring to these axes we have by (9) 
[a7] = 1218600, [y*] = 1916800, 
so that the squared q. m. errors are by (10) 
p= 4894°0, p, = 76980. (19) 
The semi-axes of the ellipse of probable error in the position of the 
centre of gravity are by (11) 
G&= 6:21, 6 = 6°53. (20) 
But the horizontal and vertical codrdinates of the centre of the tar- 
get are 
Ti (er Oi == 15°82, 
