488 G. H. KNIBBS AND F. W. BARFORD. 
The constant nis determined by the equation 
log yo — y, = nu” (ke? — 1) logieina2 ee (33) 
which gives n since all the other quantities are known. 
Lastly B is obtained from the equation 
log B = log y, |= me” log ie .f hee (34) 
This is the solution when a single set of three points is 
taken. Ifit is required to approximately fit a large number 
of sets of points, the following method of obtaining the 
constants may be adopted. 
Using Y» as an abbreviation for log y. — log y,, etc., we 
Shall have 
pe — *x 
Ya 
Calculating p from the geometric mean of s such sets of 
quantities the previous equation (32) becomes 
op el WS 
ws TL 
from which the mean value of p may be determined. 
The value of n given by (33) may be written 
1 ¥, 
1h — = 
32 
a(kP?- 1) loge «(kP—1) loge 
The mean value of n is consequently given by 
a pe Uy Yo ee pe Ih V9 
a GR Sate — 1) AS eh ee 
n® 
Lastly, the value of B was given by (84). 
The mean value is given by 
log B = & | 2 log (yy2y3) — Mn X;{ af (kh? +k +1)} | sae (37) 
In the case when A, however, is not 0, it will be necessary 
by graphic or difference methods to ascertain the value of 
y for the asymptotic line y = A. If this cannot be done 
the original equation is inappropriate. 
* is equal to unity for Naperian logarithms, and to 2°302586...... for 
common logarithms. The value of M in the last line is 1//. 
