analogy, and leads the mind in a wrong direction. To speak 
of storms coming from a certain quarter also misleads, as the 
cause of storms is to he found in the part towards which the 
wind blows. In conclusion it was suggested that aeronauts, 
when ascending into the higher regions to ascertain the state 
of the atmosphere in those regions, should, in addition to the 
ordinary instruments, use a wet bulb thermometer in con- 
junction with a dry one, in order that the hygrometrical state 
of the upper regions may be ascertained.* 
A Paper was read entitled “ Note on a Differential 
Equation,” by Arthur Cayley, Esq., F.R.S. 
The investigation was suggested by Mr. Harley’s remarks 
on the Theory of the Transcendental Solution of Algebraical 
Equations, communicated to the Society at the meeting of 
the 4th February last. 
The equation y—u-\-ay" (which is used instead of Mr. 
Harley’s equation y n — ny-f (n — 1) #=0) gives by Lagrange’s 
theorem an expression for y in the form of an infinite series, 
and by means of his series it is shown that y satisfies the 
differential equation 
f d 1 f n cl 2»— 11 *-i 
{•‘w.f y= na \^r[ «■ y- 
([ m ] v denotes as usual the factorial m (m — 1). . (m — v+1)). 
It is remarked that the equation may be written in the 
form 
d , ,/ d \ 2 . "- 1 / d \ 
«0 + Gl Ufa + U ifa) •”+«»-! M [fa) 
and the law of the coefficients is obtained. 
* Mr. Welsh employed the wet bulb thermometer in his balloon ascents —Phil. 
1'ka.ns., 1853. Pt. 3. — En. 
