58 PROFESSOR KELLAND, ON MOLECULAR EQUILIBRIUM. 



Moreover the density of the caloric at any point 



■wA e~ ae 



~ q 6 (1 - <?-<")* 



We see, then, that the density of caloric is not a proper measure 



of the temperature, although if e be small, the variation of density 



will be a proper measure of that of the temperature ; each depending 



c~ ae 

 on — — , or on the density of the material particles, which result I 



e 



obtained in a popular manner in my Theory of Heat, p. 166, and 

 found some remarkable consequences to accrue from it. 



36. From the expression for the force, it follows directly that 

 if q increase, which it must do if the temperature be increased in 

 whatever way that increase be measured, the attractive force diminishes, 

 but this diminution will also be accompanied by a diminution of the 

 repulsive force provided a increase, and that too, not by the variation of 



the common factor e~ aa - —-^ , but by the diminution of -=7= — - . 



a 2 * • (1 — e ) 



Hence, we perceive that the same series of particles will by an increase 

 in their mutual distances, exert actions on any one particle just 

 sufficient to retain it in equilibrium, notwithstanding that the quantity 

 of caloric has been increased. This fully explains the necessity of ex- 

 pansion by heat. 



37. It was my original intention in drawing up the present Memoir, 

 to have extended the investigations to a set of combinations of particles, 

 such as I have supposed to unite in the formation of crystals in my 

 Theory" of Heat, p. 174, but the subject is so extensive, that I am at 

 present obliged to postpone it for want of time. I will only make 

 one remark on the subject, which is this, that if in a binary combi- 

 nation the lines joining the centres of each pair of particles are 

 parallel to one another, it is obvious, that the attractive force on a 



