218 



Mr Greenhill, On the Rotation of a [March 20, 



G 

 Table of Values of j — in region I, 



G 

 47779 



in region II, 



- — in region III. 

 4nrp J 



Putting, with Riemann, 



D = 3a i -(c 2 -a 2 )(a 2 -b 2 ) 

 = 4a 4 -a 2 (& 2 + c 2 ) + 6V, 

 then we may write 



b 2 - c 2 Deo 2 _ a a r abc\d\ t b 2 4a 2 + & 2 -c 2 \ 



d'-b 2 2tt P ~ (C +a +/i) J P(b*+\) W+\ c 2 +~X )> 



b 2 -c 2 D(o 2 _ 2 /2 , f°° abcXd X ( c 2 4a 2 -6 2 +c i 

 c^^2^p~ (a+ +/i) Jo P(c'+XjU 2 + X~' 

 and therefore Riemann's S and T are 



(O 2 rr, 6>J 



b 2 + \ 



S= 



4>abc (c 2 + a 2 + fi)' 



T = 



±abc(a 2 + b 2 + fj,)' 



The remainder of the notation of this paper can be identified 

 with Riemann's notation, by putting 



JP = a >i> 



'- 2ho 

 P ~b 2 + C 



9 = K> 



n , 2ca » 



r=o> 3 ; 

 2ab 



c* + a 



r 



g' = -2bct;, h' 



Icarj , 



fc=A a ; 



// = - 2ab£ 



