2 
Putting n = 1 we have :• 
1 K P 
= — . log 
p-iw C P-w 
K 
C 
P-\w i 
2 log 
P 
1 
1 
• • P - + P - f w + • • ' + 
p- 
w 
1 
p - 
- (n — 
1 ) w 
log 
p 
1 
p 
— nw 
p 
- 
log 
P 
p 
— w 
Putting P — (n — w = A, and writing the series the other 
way about : — 
1 + + . . . . + I 
A A + w A + ( n — 1) w 
A + Q - |) w 
= A — \ v) 
. , A + (n — w -r, -r 
l A + (» - 1) u ,} • A + {n _ i)w Formula I. 
The best results are obtained when A is much greater than w. 
An empirical variation of Formula I was obtained as follows: — 
The denominator of the above was observed to equal 
w . log 
— w . log 1 + 
A + (n — f ) w 
w 
'w 
A + (n — I) W\( A + tn — ijw) h 
(A/w + n — 1 ) 
A + (n — f ) w 
- " los (' + ir « + ?. - 1) ) 
which is the limit, when n is infinite, 
= w. log e. 
= w, if hyperbolic logarithms are used. 
The expression then becomes : — 
1 lo* A + ( n ~ * )J? 
w ge A — \ w 
Then, as a first approximation, we have : — 
1 1 
(A/w + n — 1 ) 
■i +' 
A A + w 
+ . • • + 
A + (n — 1) w 
= - . log, 
w 
i + 
1 loo- A + ( n - §) w 
~ w oe A — i w 
n w 
A - \ w 
