SECT. I.] FORM OF SOLUTION IN CASE CONSIDERED. 359 



Let us represent now the integral = Idre ^ from r = R to r = oo 



JfJ 

 by T/T (R], and we shall have 



HLt _, x 



cDs + ^jm 



CD 



y_ _HLt 



hence u, which is equivalent to&quot; eTcDS t is expressed by 



and 



The function denoted by i/r (7?) has been known for some time, 

 and we can easily calculate, either by means of convergent series, 

 or by continued fractions, the values which this function receives, 

 when we substitute for R given quantities; thus the numerical 

 application of the solution is subject to no difficulty 1 . 



1 The following references are given by Riemann: 



Kramp. Analyse des refractions astronomiques et terrestres. Leipsic and Paris, 



An. vii. 4to. Table I. at the end contains the values of the integral / e 

 from k = 0-00 to fc = 3 -00. 



Legendre. Traite desfonctions elliptiques et des integrates Euleriennes. Tomen. 



