PROFESSOR KELLAND, ON MOLECULAR EQUILIBRIUM. 43 



the medium, be less than that without. I shall not attempt to justify 

 this hypothesis, or to prove that its apparent complexity, as compared 

 with the received one, affords a strong a priori argument against its 

 correctness. The only way to obtain final accuracy, is to subject to 

 rigid calculation any hypothesis which may suggest itself, and to retain 

 that which gives results consistent with facts. And should it be found 

 that a little difficulty attaches itself to the one in question, we may ex- 

 pect either that the difficulty itself will vanish, or the hypothesis will be 

 found unnecessary from after-attention to a more simple one. I may 

 state, that I have spent a considerable portion of time in trying other 

 hypotheses, but at present can find none which so apparently coincides 

 with known phenomena as that which I have just stated. 



23. Let us then determine the conditions of equilibrium of a 

 system in which the atoms of caloric are repulsive to those of matter. 



Assume the density of the external caloric to be q, and that of the 

 internal q', so that by writing q — q for D, we may adapt some of our 

 previous investigations to this case. 



where V has reference to every particle. 



But p = \cq*\ 



dp , da' 



' = co — — 



dx * dx * 



d£ = P fdU dV\ 

 dx c \dx dx I ' 



dD _ dq^ _ d£ ' P fdU + dV\ + ety 

 dx ~ dx dx c \ dx dx) dx' 



Now if there were no material particle, we should have 



dx c dx ' 



where V t is the quantity which V becomes for a homogeneous medium 

 of density q\ if then we assume V I -V=V; where V is the function 



F2 



