Editorial 
525 
Integrating by parts we find : 
( ... 3.1 io, if 5 be even 
= |...4.2Z„if5beodd 
Now Xo = e - i'^'du = , 
and Li— \ ue du = l, 
Jo 
thus Mp is determined, and will depend on whether ii + p be even or odd. 
But ^/=2/oy ^'^=^oy ("-1)^-' 
7) — 1 
Hence ix.! = M^jM^ = a^ ^^ (xi). 
To find the modal value % we must differentiate (v), and we have 
(n - 2) 2"-^e ~ ' ^ - -4 2»-=e " ' ^ = 0, 
o- 
which gives 
^ = 
a result in agreement with the mean 2 of the approximate solution (vi), as we 
should anticipate. 
It now remains to find if/ and absolutely 
Suppose n even, then 
i:,,^_^ = (« - 2)(m-4) ... 2 X 1 ] 
Ln-, = {n-^){n-o)... 1 xy/; 
'IT ( (xiii)- 
Hence for n even 
2,=^ fl, = Ml Ma = ~, ^ ' ... ta/ - (xiv A). 
Again for n odd 
2 
Z„_i = (n-2)C«-4)...lxy^ 
X„_2 = (?i - 3) (/I - 5) ... 2 X 1, 
and hence 
^ — — ' (XIVB). 
V»i(n-3)(w- 6) ... 2 V 2 
67—2 
