applicable to Heat. 123 



proportional to the absolute temperature. From this theorem, in 

 conjunction with that of the equivalence of heat and work, I have, 

 in the subsequent portion of that treatise, deduced various con- 

 clusions concerning the deportment of bodies towards heat. As 

 the theorem of the equivalence of heat and work may be reduced 

 to a simple mechanical one, namely that of the equivalence 

 of vis viva and mechanical work, I was convinced a priori that 

 there must be a mechanical theorem which would explain that 

 of the increase of the effective force of heat with the temperature. 

 This theorem I think I shall be able to communicate in what 

 follows. 



Let there be any system whatever of material points in sta- 

 tionary motion. By stationary motion I mean one in which the 

 points do not continually remove further and further from their 

 original position, and the velocities do not alter continuously in 

 the same direction, but the points move within a limited space, 

 and the velocities only fluctuate within certain limits. Of this 

 nature are all periodic motions — such as those of the planets 

 about the sun, and the vibrations of elastic bodies, — further, 

 such irregular motions as are attributed to the atoms and mole- 

 cules of a body in order to explain its heat. 



Now let m, m\ m", &c. be the given material points, x, y, z, 

 x \ y'y z *> d\ y", z", &c. their rectangular coordinates at the 

 time /, and X, Y, Z, X', Y', Z', X", Y", Z", &c. the components, 

 taken in the directions of the coordinates, of the forces acting 

 upon them. Then we form first the sum 



2LU/ + \dt) T U/ J' 



for which, v, v 1 , v n , &c. being the velocities of the points, we may 

 write, more briefly, 



Z 2 V > 



which sum is known under the name of the vis viva of the 

 system. Further, we will form the following expression : — 



-^(Xx+Yy + Zz). 



The magnitude represented by this expression depends, as is 

 evident, essentially upon the forces acting in the system, and, if 

 with given coordinates all the forces varied in equal ratio, would 

 be proportional to the forces. We will therefore give to the mean 

 value which this magnitude has during the stationary motion of 

 the system the name of Virial of the system, from the Latin 

 word vis (force) . 



