of Thermodynamics. 243 



space ; but the scale of absolute temperature is defined as being 

 so graduated that the whole actual energy of the matter within 

 the space is the product of the absolute temperature, the mass of 

 matter, and some function of the sort and distribution of the 

 matter ; therefore the half -square of the velocity of the particle 

 which at any instant occupies a given position in the space consi- 

 dered is equal to the absolute temperature multiplied by some func- 

 tion of that position, and of the sort and distribution of the matter. 

 9. Suppose now that the dimensions of the limited space in 

 which the moving matter is enclosed, and the distribution of 

 that matter, undergo an indefinitely small change by the appli- 

 cation of suitable forces, and that after that process the motion 

 becomes steady as it was before. Then the dimensions and 

 position of each circulating stream will have been altered; and 

 the work done in effecting that alteration will consist of energy 

 converted between the forms of potential energy of the applied 

 forces, and actual energy of the molecular motions — that is, 

 between the forms of mechanical energy and of heat. Consider 

 now a point in one of the circulating streams before the change, 

 and let fall from it a perpendicular upon the same stream after 

 the change. The work done in shifting the path of the particle 

 which at any instant occupies that point, is the product of the 

 perpendicular displacement of the stream into the force exerted 

 along that perpendicular. But the perpendicular displacement 

 of the stream is a function of the position of the point shifted, 

 the distribution of matter in the space, and the change of dimen- 

 sions and distribution ; and the force is equal and opposite either 

 to the centrifugal force of the particle or to one of its components, 

 and is therefore proportional to the square of the velocity of the 

 particle, and to some function of its position and of the sort and 

 distribution of matter in the body. Therefore the energy trans- 

 formed in shifting the path of any particle is proportional to the 

 square of its velocity, and to some function of its position, of the 

 sort and distribution of matter in the space considered, and- of the 

 change in dimensions of that space and in the distribution of the 

 matter. 



10. But the square of the velocity of the particle which at 

 any instant occupies a given position has already been shown 

 to be proportional to the absolute temperature, and to some 

 function of that position and of the sort and distribution of the 

 matter ; therefore, if sensible heat consists in any kind of steady 

 molecular motion within limited spaces, the conversion of energy 

 during any change in the dimensions of such spaces, and in the distri- 

 bution of matter in them, is the product of the absolute temperature 

 into some function of that change and of the sort and distribution 

 of the matter. 



R2 



