( 608 ) 
Suppose that 4 successively becomes equal to 
Ll eee tay es eee ses Oee Oe 
where A and 4’ denote any pair of consecutive values of h, and 
consider the expression 
hh’ (—])rh 1 
He) = Er = —* [log | £ (9) + Lien] — 
Dac i L 
h=h"" | h Es 
— = ae Grs(c*) . 
h—hv À 
Obviously we may write also 
hah’ (—1)h Ë eae 
H,(e)= =: = | es (c*) — log | 5 (s) | — Lie ales 
and, from what has been proved before, we infer that Hs (c) approxi- 
mately obeys the relation 
A, te) =e Hy (é): 
It is by means of this equation that we are able to find 
= p-* as soon as = pl be given. 
p<e pce 
The choice of 4 and h' is quite arbitrary. If desired we may take 
h' = h'"; in general it will be advisable to determine 4" by the con- 
1 
dition that cl is just a little less than 5, in order to avoid the 
1 
application of the approximation formula for Gis (el) in cases where 
1 
ch is too small a number. 
It will be seen from the following examples that the formula may 
be relied on, if a not too close approximation is required. 
1. pS = 146 Ae, Sp = se, SS pe eee 
pce pce 
ta Hr: HRE 
1 5 
Ho (©) = 34 — [— log 2 + Li(e°)] + Db log 2 + Li(e2)] + 
1 ] 1 1 
+= [—log2+ iel + = 0+ LI + I= — 1.08524. 
