37 
6. Or we may assume vy = (cos x)"; whence 
(5) =— 2m sec? 2, 7 = - k=- 2m, and 0-g=c,+¢ tan2. 
Tn this case the general formula (3) becomes 
[(D+9)(D + ¢+e.4etan2)-(n+1)(c+n) sec? a] y= X. 
By putting ¢ =c,, and c=0, this is reduced to 
{(D + ¢) (D+ &)-n (n+1) sec? x} y= X, 
which is the equation solved by Dr. Hargreave at p. 52, in 
the Paper already referred to, and from a particular case of 
which he derives the solution of the equation of Laplace’s 
functions. 
Sir Robert Kane read a paper by the Rev. Professor Callan, 
on the results of a series of experiments on the decompo- 
sition of water by the iron galvanic battery, with the view of 
obtaining a brilliant lime light. 
