8 M. L. A. Colding on the Universal Powers of 



If all these last equations are added, and if we put dq + dq' -f dq" 

 + • • * — dq l} then we get 



*-*•{(*- 9)* + ( Y -30^+( z - S)4 ( 8 ) 



in which ^/ y denotes the whole increment of energy which all 

 the material parts together yield to the material resistances, and 

 £ denotes summation. 



If there are no other resistances than those given in the system 

 of material points in question, we have 



which shows that the system docs not lose any energy on account 

 of the internal resistances. 



The energy imparted to the material resistances by the system 

 during the time t may, conformably to formula (8), be expressed 



qi =Xm (jx«fe + Ydy + Z&) - g 2 ^ + jf +i ^ + const. (9) 



If now we compare what has been set forth in equations (1) 

 to (7) above, then we perceive that the whole internal energy 

 which is contained in a system of material points may in all 

 cases be represented by 



w=iXm{^ —^ J + C, . . . (10) 



C being an arbitrary constant. 



Hence results that when the energy of a body manifests itself 

 under the shape of heat, then the contained quantity of heat may 

 always be expressed by the vis viva contained in the material par- 

 tides of the body, as we mean by vis viva half the amount of all 

 the masses of the material particles, each multiplied by the square 

 of its own velocity. 



In a note by Ampere, " Sur la Chaleur et sur la Lumiere 

 considered commes resultant de mouvemens vibratoires "*, the 

 author has set forth the idea that, while all rays of light and 

 heat advance in waves through the aether, the propagation of heat 

 in bodies depends upon the vibrations of the atoms and their 

 propagation from particle into particle. Thus, looking upon heat 

 as a motion of atoms, the author compares the quantity of heat 

 contained in bodies with the vis viva of the atoms, and thereafter 

 shows that the general equations for the propagation of heat in 

 a body must also hold true for the propagation of the vis viva. 

 As I think I have proved in the above that the internal energy of 

 a body must necessarily be equal to the vis viva contained in the 

 * Annates de Chimie et de Physique, vol. lviii. p. 432. 



