r,72 Mr Greenhill, Integrals dx. [Mar. 8, 1880. 



and 



,2 „:„2 I xi 



o(l-A;'sm'(/))* 



is obtained by writing (1 - F sin^)* for x in the preceding ex- 

 pression. 



Similarly ' 



— 3 



o(l -^^sin»3 

 1 dx 



^ x~^dx 



'^}x\/(\ + n^ + 'M'z-z^) 



1 + ^2 



dz dz 



3 Jz-^n Jz+2n 



^n] z V(l + n^ - z) W.2 + i (1 + n^)X + f (1 - w^)1 



can be written down. 



Many more examples of the same kind can be collected from 

 the papers of L. Konigsberger on the " Reduction of Abel's inte- 

 grals to elliptic and hyperelliptic integrals," in Crelle and the 

 Mathematische Annalen. 



(5) H. MiDDLETON, On a metJiod of constructing an electrical 

 telescope, and the application of the py^inciijle to the theory of 

 vision. 



