974 



Mr. S. Smith on Initial 



Hence it appears that if" a does not exceed the value *13 

 the relation (5) is very approximately true. The larger 

 values of! a given in Table I. are too large, but if these values 



of a are taken as first approximations to evaluate 



n x -f n 2 + n 3 

 (//,), and these values substituted in (4), more accurate values 



of a can be found. The values of — thus obtained are given 



V 

 in the last column of Table II., and for the sake of com- 

 parison the corresponding values of — in Table I. are re- 

 written in the fifth column. P a 

 The following table gives a comparison of the values of - 



obtained by this method with those found by F. W. Wheatley *, 

 who made use of a more direct method. 



Table III. 



z 



P 



40 



50 



60 



70 



•212 

 •226 



a 

 P 



f Wheatley ... 

 [Smith 



•019 

 •021 



•055 

 •065 



•118 

 •134 





If the values of a, for larger values of — , found by Prof. 



P 



Townsendf are used to evaluate /jl from (3), and /x is also 

 found by substituting values of u and p in (4), another 

 interesting comparison may be made. 



Table IV. 



z 



p 



z 



k 



/a from (3) 



fi from (4) 



p=2 mm. 

 2^=3 mm. 



| 100 

 1 120 



100 



1-25 

 1-33 

 1-87 



•573 

 •556 

 •606 



•576 

 •528 

 •591 



* Phil. Mag-. Dec 1913. 

 t Phil. Mag. June 1902. 



