14 
PROFESSOR G. H. DARWIE" ON THE MECHANICAL CONDITIONS OF 
we have 
and 
c"' — u . 
%D 
P 
9 
U. 
But it may easily be seen that 2^'a^j9r^ is a particular solution of the problem ; 
hence, u is a factor by which the particular solution is to be multiplied to obtain the 
general solution. The function u is given by 
J- .( 22 ) 
U — 2 o — 
1 2 
2^" 
A table of the values of u is given below, showing how the general solution shades 
off into the particular solution. This function, v,, is also tabulated by Ritter, and I 
made use of its value, when x = 1, to determine the value of 77 , with which the 
integration is to. begin. I find, however (see Table I.), that, when x = 1, = 1‘0063, 
in place of 1’031, as given by him. 
The last row in Table I. gives the ratio of the central density oj to iv, the density 
at the distance r; this ratio is equal to 
