PROCEEDINGS 
OF 
THE ROYAL IRISH ACADEMY. 
1846-7. No. 57. 
November 30th, 1846. (Stated Meeting.) 
REV. HUMPHREY LLOYD, D.D., President, in the 
Chair. 
Thomas Moore, Esq., having been specially recommended 
by the Council, was elected an Honorary Member. 
The Rev. William Roberts, F,.T.C.D., read a paper on 
_ the definite integral 
4 ‘ log(1 + m sin?¢) 
o V(L— Fsin’g) “® 
It is clear that the only admissible values of x (real) are those 
of the parameter of an elliptic function of the third kind, to 
the modulus 4, namely, cot?0, — 1+ k*sin?@, and — ?sin’9, 
_ where k’ is the complement of k. The value of the definite 
__ integral may, in each of these cases, be expressed by elliptic 
_ functions of the first and second kinds, and by the remarkable 
-.., E($) dp ae 
pemepecendant Y ( a Wada Paty) by the aid of which fune- 
_ tions of the third species, with a logarithmic parameter, can be 
VOL, Ill. 2c 
