352 
MR. R. A. FISHER ON THE MATHEMATICAL 
ellipses are coaxial, the deviations of r and v being uncorrelated ; in the case of Type VII. 
we put v = 0, in the determinant given above, which then becomes 
r -11 V + 2 
r + 4 
0 
r+1 
r + 2 
0 
2r +1 
r + 4 
0 
' 1 
r + 2 
r+1 
r -f- 2 
0 
¥ (£ 
o 
F 
0 
1 
r + 2 
0 
2 J 
F (- 
and falls in the two factors 
r+1 \ _ (v —1 
-2 r + 4 
- F 
v + 1 r + 2 ^ / r \ 
. 2r + 4 -2/ 
r+l~ 
so that 
n<r ( = 
2 r + 2 
•3 _ V 
'r\ 
r + 2 F ) — 2 r +1 r + 4 
and 
Tirr? = 
4 r +1 r + 2 
r+1 r + 2 2 {hr)- f (k)\ -2 r + 4 
1 
2 / \2 / 
The corresponding expressions for the method of moments are 
)trr„ 
3 r 2 r-2' (r 2 + r+10 ) 
8 r-1r-3r-5 
and 
n«r. 
2 _ 2 rr-1' r —3 (r 2 —r + 18) 
r-5 r-7 
Since for moderately large values of r, we have, approximately, 
_ r 
r + 2" F ( } ~ ) — 2 r+ 1 r + 4 = yr ( 1 — _ -- 2 /> 
2/ 3 \ 5 r + 2 J 
16 
1 
r+1 r + 2 F 
V— 1 
F - -2 r+1 r + 4 = 6- 
r + 2 
2 ? 
and 
