242 Dr. Rankine on the Second Law 



of any kind of molecular motion whatsoever, and it therefore 

 affords of itself no reason for preferring one supposition as to 

 the kind of molecular motion which constitutes sensible heat to 

 another. 



4. But if there be molecular motions in bodies, it is certain 

 that, although all such motions are capable of conversion into 

 that which constitutes sensible heat, some of them are not ac- 

 companied by sensible heat. For example, the motion (supposed 

 to be vibratory and wave-like) which constitutes radiance, whether 

 visible or invisible, is not accompanied by sensible heat, and 

 only produces sensible heat by its absorption ; that is, in the 

 language of hypothesis, by its conversion into some other kind 

 of motion ; while, on the other hand, in the production of radi- 

 ance, sensible heat disappears. 



5. The object of the present paper is to give an elementary 

 proof of the proposition, thai the second law of thermodynamics 

 follows from the supposition that sensible heat consists in any kind 

 of steady molecular motion within limited spaces. 



6. The term " steady motion " is here used in the same sense 

 as in hydrodynamics, to denote motion, whether of a continuous 

 fluid or of a system of detached molecules, in which the velocity 

 and direction of motion of a particle depend on its position only; 

 so that each particle of the series of particles which successively 

 pass through a given position, assumes in its turn the velocity 

 and direction proper to that position. In other words, steady 

 motion may be defined as motion in a set of streams of invariable 

 figure. 



When steady motion takes place in matter that is confined 

 within a limited space, the streams in which the particles move 

 must necessarily return into themselves, and be circulating 

 streams, being in that respect of the nature of whirls, eddies, or 

 vortices. 



7. Steady motion keeps unaltered the distribution of the den- 

 sity of the moving matter; and it therefore keeps unaltered the 

 forces depending on such distribution, whether of the nature of 

 pressure or of attraction. In that respect it differs from unsteady 

 motion, such as vibratory and wave-like motion. 



8. Conceive a limited space of any figure whatsoever to be 

 filled with matter in a state of steady motion. The actual energy 

 of any particle of that matter is the product of its mass into the 

 half-square of its velocity ; and the actual energy of the whole 

 mass of matter is the sum of all those products; and because of 

 the steadiness of the motion, the actual energy of the particle 

 which at any instant whatsoever occupies a given position is 

 some definite fraction of the whole actual energy, depending upon 

 that position, and upon the distribution of matter within the 



