358 G. H. KNIBBS. 



To eliminate m and n we then proceed as follows : — 

 Omitting in as the suffix unity, which is the same throughout, 



Y 2l = mlogq + nx^f—1) (26a) 



Y m = m log q + nx l 'q ]l (q v —l) (26b) 



the factor for Y i3 being q 2p instead of q" in the right-hand 

 member. Hence 



'r„ — r„ = log to///*) = nx^f—lf (28) 



Similarly 



Y u - r»= log (i h uJu 2 d = nxW-W (28a) 



Consequently, 



(F«- Y 32 )/(F 32 - Y a ) = {na?(q>- DY}/{«sW-l f } = q p ...(29) 



or = log i/ 2 + log ? / 4 -2 log i/ 3 (29a) 



log iy, + log //,- 2 log ;/., 



Prom this p may be found, since q is known. It is obvious 

 that it is indifferent whether Naperian or common logarithms 

 are used. 



When ji has been obtained, we have from (28) 



= ii (log ;,, -h log u, - 2 log |/ 2 _) (30) 



^(q"-l) 2 ' 



n = 'il 10 ? //, r log // ; - 2 log /,,) ^te.) 



M equals unity if Naperian logarithms are used, but if com- 

 mon logarithms are used, /* = 2'3025850930 approximately. 

 Then n and p being known, m may be determined from 

 (26a), which gives 



m = Ml °" '-l^ lo S .'/.) ~ "■v"(f/'; - 1) (3i) 



/'• tog q 

 the same remark applying to /* as before. Then finally, 



log A = log 1/,-m log x x + Mwrc" (32) 



in which M=l//*or 0*4342944819 approximately, if Briggsian 

 (common) logarithms are used, or unity if Naperian 

 logarithms are used. 



