2 
Proceedings, in the Monthly Notices of the Royal Astrono- 
mical Society, and in the Astronomische Nachrichten. 
Mr. Thomas Garrick was elected Treasurer of the Society 
in place of the late Mr. Worthington, F.R.A.S. 
A long conversation took place on the high rate of mor- 
tality which has prevailed in Manchester and Salford for 
some time past, and an opinion was generally expressed that 
its true causes had not yet been clearly indicated. In spite 
of their excellent systems of street paving and sewering, 
their plentiful supply of pure water, and wholesale but pro- 
bably not well considered interference with private petties, 
ashpits, and water closets, the death rate of these towns 
continued to show a steady increase, and still stood above 
that of any other town in the United Kingdom. 
“On Convertent Functions.” By Chief Justice Cockle 
F.R.S., &c., President of the Queensland Philosophical 
Society. Communicated by the Rev. Robert Harley, 
F.R.S. 
The theory of the conversion of integrals, of which I have 
given outlines (see supra vol. vii., p. 67; Phil. Mag. for 
July and December, 1867) will, I believe, be found to give 
an additional means of finitely solving differential equations. 
It is not necessarily restricted to the case in which tfie in- 
tegral to be converted is a single integral. Thus suppose 
that we have given the double integral 
J'dv fdu ' (f) ( x , v, u) 
or, more shortly, 
fdv Jdu ’ (f) , 
we first treat 
M' 
u 
by forming the convertent equation 
df 
du 
SF W) s “S = *"'( 2 > 
where the coefficients F (a, b) are functions of x and v only 
(excluding u) and the a’s and the b’s are zeros or any posi- 
