[ 5»7 ] 
Cafe XVII. Given m, p> r j Required n. 
Put L, for logarithm ; and L, for arith. comp, of a log. 
Since i 4 -r v> Therefore n 
P L,r -\- 1 
Cafe XVIII. Given a, p, r ; Required n _ 
Since i~ 4 -r — — - — . Therefore n — V.’ a ~ a 
a ~P r L,r+i 
Cafe XIX. Given p, m - } Required j?. 
Since A = (r i T — ) ^ 
Then (L, r + i* " =) L,m — L, p — L, A j 
Hence A, and A — i, are known. 
Alfo L, A — i -{- L, * -j- L, m = L, R — i 
(by Cafe 14th) : 
Hence (B — 1), and r -f- ij are known. 
Therefore n — • » 
L, r + x 
Cafe XX. Given a , m, r j Required 
Since (A =) — - T — — 1 -f- P". 
Therefore n = b^±±.i=h?. 
Lj 1 i~ r 
XLIV. ^ 
