172 



has been shown that the ultimate particles of our atmosphere com- 

 pose such an aether. But if our atmosphere is the luminiferous aether, 

 we must next inquire whether it does pervade space. Omitting 

 variations of temperature, and merely considering the atmosphere as 

 subject to the two forces of elasticity and gravity, we have for the 

 equation of a column of air on a unit of surface, 



7 qaP- , 1 dp kqa? , 7 p 



dp= — Z — pdz, or — -i-=:— ^ — , where «=—. 

 z* p dz z" p 



Integrating this, we find thatp and p, though they become extremely 

 small, never vanish ; and therefore, if these laws are absolutely true, 

 our atmosphere does pervade space. 



It may be well to obviate the objection, that black substances 

 radiate heat best, and white substances light. This arises from 

 employing the same word radiation to denote two different things : 

 by radiated heat is meant heat given out from a heated body ; by 

 radiated light is meant the secondary radiation from the surface of 

 a body exposed to light. 



If Sir J. Leslie's experimental calculation of the heat lost from 

 the sun be correct, there is no need of any theories to account for its 

 generation. 



From the foregoing arguments and facts, it was urged that mo- 

 tions and forces, which certainly exist in cases of combustion, would 

 produce phsenomena exactly similar to those of heat, and therefore 

 that part of the phsenomena usually attributed to heat are due to 

 this motion ; and if part of them, probably the whole. And further, 

 that if the phsenomena of radiation of heat are explained by this 

 motion of the particles of matter, light is simply radiated heat of 

 considerable intensity ; and that imponderable substances, whether 

 under the names of aether, caloric, or phlogiston, are equally ima- 

 ginary. 



Also, a paper was read " On the Question — What is the Solution 

 of a Differential Equation ?" By Professor De Morgan. 



This paper is a short supplement to § 3 of a paper on some points 

 of the integral calculus (Camb. Trans, vol. ix. part 2). It discusses 

 the principles on which such an equation as y'- = a q , giving 



(y — ax + b)(y + ax +c)=0, 



is generally affirmed to be completely solved when b = c. It dwells 

 on the distinction between a relation and an equation, which may 

 express the alternative of one or more relations ; it points out several 

 cases in which conclusions applicable to the simple relation only are 

 affirmed of any equation ; and, with reference to the question asked 

 in the title, discusses the manner in which the answer depends on 

 the cross-question, what degree of discontinuity is allowed to be im- 

 plied in the word solution ? 



