CONTPJBUTIONS TO THE THEOEY OF EVOLUTION. 
449 
Accordingly we shall write Type VI. in the form 
y = . 
and take the range from a to oo. 
Differentiating to find the position of the mode we have 
(xx.). 
For the moments about the origin : 
a[x 
. = I 2/0 — 
Put o/.r = s, hence 
a/x „ 
= (' 
.! A 
_ J/o _ 
•5i-92-»-2 
(1 —zY‘(h 
= ® - -Zo - « - r + X) 
_ yp r(/7i - ga - n -1) r(/?3 + i) 
Hence we deduce 
a = 
2/o r (/?! - /Zs - 1) T (g2 + 1) 
({91-92-> 
r(?i) 
(xxi.). 
y-z 
H = 
= 
-1) 
i'h - 23 - 2) (2i - 23 - 2) 
«*l2i-l)(2i-2)(2i-3) 
(2i - 23 - 2) (2i - 23 - 3) (2i - 23 “ I) 
_ cViZi - l)(^i - 2) {q^ - 3) fa - 4) _ 
(2i - 23 - 2) (2i - 23 - 3) (2i -22-4) (2i - 23 - 3) 
(xxii.). 
Now if we compare these results with those on p. 368 of the earlier memoir we see 
that the one set can he at once deduced from the other by writing = — q^, m„ = ^o. 
Thus with this interchange the whole of that solution holds, if we hear in mind that 
the range is now from x = a to co . 
We easily find : 
r = — -h + 2 
3 ]\T 
VOL. CXCVIT,—A. 
C = 1 - 9l + ^3 - <1\^Z 
