446 
PROF. KARL PEARSON ON SKEW VARIATION. 
where* 
b — ijcr { ($\ (wii + 071-2 + 4 )" + 1 6 (wij + 7Y\j2 4“ 3)} ' 2 . 
V* _ N 
r (m 1 + m 2 + 2) 
a ™ 1 a .™ 2 b mml r (m,+ l) T (m 2 + l)’ 
on substitution for a x and a 2 as above. 
Now put m 1 + m 2 = 0, or m 2 = —ntj = m, say. 
Then 
N . T (2) / 6(m+l) \ m ( b(l-m) _ ' 
hr ( 1 + m) r (1 — m) \ 2 / \ 2 
while 
b = wo- { 16 / 3 , + 48 } 1/2 = 2<r{(3 1 + 3)' / \ 
It remains to find m. 
Now m 1 and m 2 are the roots oft 
where 
m 2 — (r— 2) m + e—r +1 = 0, 
6 (/3,—/3 X — l) o 
3/3, — 2/3 2 + 6 
__ (m 1 + m 2 +2) 8 _ 
4 (w,-km 2 + 4) 2 /(mi + wi 2 + 3) 
Hence, when m, + rn 2 = 0, we have 
and 
Whence 
or 5/3 2 —6/3, — 9 = 0, the Udine, 
e= 3/(A + 3). 
m 2 =l—e or m = + A/ —^ 
“ V 3 + /3, 
But F (2) = 1, and it is well known that 
mi 
r ( 1 +m) r (1 —on) = — 
sin ??i7r 
Thus 
y 
N 
sm 
v: 
& _ _ _ 
3 + /3, I / q~ (y/ 3 +/3, + -y//3,) + 
:7T(T 
Pa 
c (p3+A“ PA) — ic 
This is the full equation to the B-line J-curve, the mean being origin.{ It requires 
for its determination only a knowledge of /3,, but we must be also certain that the 
* Loc. cit., p. 369. 
t Loc. cit., pp. 368-9. Deduced at once from m' 2 - rm’ + e = 0 by putting ni = m + 1. 
X The sign of *Jfl 1 in <r( \/3 + /3i± d/fi) must be determined from that of /x 3 . 
