37 
6. Or we may assume yb = (cos x)"; whence 
(5 =—2msec?2, r= = k=- 2m, and 0-g¢=c,+¢ tanz. 
In this case the general formula (3) becomes 
[(D+9)(D + ¢+e.4+ ¢tan 2)-(n+1)(c+n) sec? a]y= Xx. 
By putting ¢=c,, and c=0, this is reduced to 
{(D + &) (D + c)-—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. 
