193 



analogy, and leads the mind in a wrong direction. To speak 

 of storms coming /ro^Ti a certain. quarter also misleads, as the 

 cause of storms is to be 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-\-a\f' (which is used instead of Mr. 

 Harley's equation if — ny-\-{ii — 1) a;=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 



(imY denotes as usual the factorial m (m — I) . . (m — v+l) J . 

 It is remarked that the equation may be written in the 

 form 



and the law of the coefficients is obtained. 



* Mr. Welsh employed the wet bulb thermometer in his balloon ascents.— Phil. 

 Trans., 1853. Pt 3.— Ed. 



