FE. L. De Forest—Law of Error in Target-Shooting. " 
The actual difference is greater, being 
1657 — +1193 = “0464, 
We omit the discussion for the 400 and 600 metre ranges, since the 
shots here are apparently the same as those used at 200 metres, and 
the differences in relative position for the same shot at different 
ranges seem to be largely due to accidental variations in the projec- 
jectile or the powder. From the three series of trials retained, 
namely, two of pistol shots and one of cannon shots, it appears that 
the test requires us to use formula (1), and to make the codrdinate 
‘axes coincide with the free axes. This therefore, it seems to me, 
had better be generally done when accuracy is desired, unless indeed 
our results should hereafter be invalidated by those of other and 
more extended experiments. 
We might also inquire what are the probable values, arising from 
accidental causes, of the cubes of the c. m. inequalities in x and y, 
when the law of error in either direction is suspected to be unsym- 
metrical. This question finds an answer in my article on the Unsym- 
metrical Probability Curve, Analyst, vol. x, p. 74. See also Trans. 
of the Conn. Academy, vol. vi, part. 1. For determining a, and a, 
the easiest way will perhaps be to compute the values of [z*], [v’], 
[wv] and [wv*]. Then from (8) we have 
[a*|=[2"]cos*—' + [v*]sin’g’ ) 
+8sing'cosq ([u’v]cosq’ +[uv’|sing’) 
[y'I=[0"]eos* p! —[u']sin’ g' 
—3sing'cosp'([uv* ]cosp'—[w*v ]sing’) | 
and a, and a, are obtained like @ in Analyst, ix, p. 161. For ex- 
ample, from the first table here tried we get 
(25) 
[u*] = 322100, [uv] = — 9600, 
[v*] = 264700, [ wv" | = 37400, 
and consequently by (7) and (29) 
[x] = 269207, [y*] = 133301, 
and the cubed inequalities are 
elem a = 2153°8, te aa = 1066'5. (26) © 
From accidental causes alone, they would probably be something like 
(G1) =+ e745 p.4/ 2 = + 1413°7, | 
ee (27) 
(6,2) = + 6745p,°4/ 19 = 4 2413-1. | 
2 
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