348 G. H, KNIBBS. 
The mean of these is n = 1°83], log k’,,(a) = 4°664, (6) 4°735 
Of the wholeseries(A) ,, 1°840, 4674 
bP) 
It should be noticed here that ike value of &' is greatly affected 
by the index m of the radius, and inasmuch as the value of that 
index is very uncertain the satisfactory numerical evaluation of 
k’ is impossible until m and its variation-law have been ascertained 
by sufficiently accurate experiments. In order to learn how far 
the slight indication of progression in Table K. is affected by 
considering m constant, formula (33) was applied to the values of 
k’, m being determined by the general formule (37), (38), with © 
the results above shewn, indicating no progression. If however, 
the results be taken from Table A. in groups of five, arranged 
with increasing values of n, the means of the very divergent 
results are as follows :— 
Table L. 
Mean n 1:754 1-796 1-866 1:956 mean 1°843 
» log ky 4651 4705 4679 4768 ,, 4701 
indicating very distinctly an increase with n. These results are 
shewn by crosses (+) in the figure. Accepting the mean values 
in the above table, and reducing by formule (35) and (36), § 17— 
q for m = 1-843 being 0:202—we find log &’, has the value 4°664 
while when n = 1 its value is 3836. Hence in order that the 
general formula may shew the progression above indicated, and at 
the same time be true for the first régime, we may put 
log &, = [1++256 (nm - 1)] log ( ey iki (39) 
or putting 8 for 0- 256 and & for gp/8, 
Be ee ccc (40) 
so that & is the rationalized coéfficient, and p = s(n - 1)" * 
empirical. The value of & for p = 1 is 6851 with the centimetre 
as unit. 
Until more accurate experiments are to hand, the relations 
between p and q cannot be satisfactorily studied. It may possibly 
be desirable to omit the f term and substitute » for 7,- 
a 
