266 On the Transformation of a certain Differential Equation, 



45 centimetres long as in a tube of 90 centimetres. He ranks 

 carbonic acid as low as air, and makes bromine-vapour a greater 

 absorbent than nitrous acid, whereas the absorption by the com- 

 pound gas is vastly greater than that by the elementary one. 

 The heat rendered latent by the evaporation of his bromine, aug- 

 mented the effect which in reality he was measuring. In fact 

 all the differences between the German philosophers and myself 

 appear to be strictly accounted for by reference to a source of 

 error which the application of plates of rock-salt enabled me 

 from the outset to avoid*. 



Roval Institution, 

 March 1862. 



XXXVI. Note on the Transformation of a certain Differential 

 Equation, By A. Cayley, Esq.f 



r g^HE differential equation 



if we put therein id = 2.r 2 +l (i= */ — \ as usual), becomes 

 dx z ax 



In fact an integral of the second equation is ( v 1 -\- a? + w) 2m ) 

 this is 



= ( ^/(2a? 2 +l) 2 -l + 2x 2 + l) m ; 



or putting i9 = 2x 2 + l, it is 



which is 



= {i(VW+l+6)) m >, 

 so that an integral of the transformed equation in 6 is 



= {VW+l + 0) m . 



And writing in the second equation 6 for x, and J m for m, we 



* I should be willing to pay a heavy price for a clear specimen of this 

 substance. Results of the very highest interest are, I believe, quite within 

 the reach of any experimenter who may be fortunate enough to possess a 

 suitable prism and one or two lenses of transparent rock-salt ; and I am 

 practically disabled at the present moment through my inability to procure 

 a moderate quantity of this precious material. A pair of plates, or even 

 one plate, of rock-salt, 3 inches in diameter and an inch thick, would also 

 be of the greatest use to me. 



f Communicated by the Author. 



