30 PROFESSOR KELLAND, ON MOLECULAR EQUILIBRIUM. 



To find the conditions of equilibrium of a particle of caloric. 



6. Let x, y, z be the co-ordinates of a particle of caloric measured 

 from any point as origin, x, y, % those of another particle, D the 

 density of the caloric estimated by the number of particles in a given 

 volume in the neighbourhood of the former particle : D' the correspond- 

 ing quantity for the latter; let also X, Y, Z be the co-ordinates of 

 a particle of matter supposed spherical, and collected at its centre of 

 gravity in all cases in which its own attraction or repulsion is to be 

 calculated; call P the mass of an atom of caloric, M that of an atom 

 of matter, each estimated by the attraction or repulsion exerted by it 

 on a unit of either caloric or matter at the distance unity : let V be 

 the sum of each particle of caloric, divided by its distance from that 

 whose co-ordinates are x, y, z; U the sum of each particle of matter 

 divided by its distance from the same point ; also, let r be the former 

 distance, R the latter corresponding to the particles respectively, whose 

 co-ordinates are x ', y, %'; X, Y, Z, then 



y = p rrr dx ' dy'dz-H 



R 



I have adopted integrals for the caloric, as it is supposed that the 

 particles are so near each other, that the variation of action due to the 

 .situation of a particle with respect to those immediately surrounding it, 

 forms no important element in the calculation. I shall have occasion 

 to mention this subject more explicitly in the sequel. 



In order to fix the ideas, let it be supposed that x', y, z; X, Y, Z 

 are in advance of xy%, so that 



r = \/V - xf + {y' — yf + (%' - zf, 



R = V(X- xf + (Y- yf + (Z- %f ; 



then the action of the caloric on the particle in question parallel 



dV 

 to the axis of x is P. -7—, and since the force is repulsive, it tends to 



