1887.] 



On certain Definite In 



481 



x = m + 



y = n + 



z = r + 



x = m •{- 



y = 71 + 



z = r+ 



2 B 2 2rAj ^ 



2 C 3 2»A A/V 

 m 3 --± 5-2/+- 



Bj B 



B 



- , C 9 2mBi B, 9 1 * 

 wHt- ; — -» + ■ 1/m2 1 



A x A x 'A 



B2_2w_C n . (V, "I * 

 X A 



Hence we have the sum of the integrals (supposed to be taken 

 within the proper limits) — 



dx 



+ \ dx 



+ dx 



2 B 2 2rA T , A^l * 



0, o, 



. A„ 2«C, CVH 1 



Bi B^ ~Bf J 



C, 2mB! B, „ 11 



it "17 Aj } 



. B 3 2mC lj _C 1 .^\! 



r rr~xr + a7/ ' 



expressed by elliptic functions. 



As a final example take the following : — 



Let- 



Then since 



2 M 2 



