48 SOME REMARKS, &c. 



tion in the function which expresses the mutual action of the 

 molecules, the body may pass into a new state of equilibrium in 

 which the average distance between adjacent molecules may be 

 increased or diminished. If such an explanation could be esta- 

 blished, we should have a case of the action of (force) 2 . 



11. In conclusion, it may be well to remark that mathe- 

 matical analysis is conceivably as applicable to these new 

 modes of action of matter on matter as to ordinary questions in 

 dynamics. It is, however, easily seen that as in these we deal 

 chiefly with differential equations of the second order, and in 

 merely cinematical questions with equations of the first only, so 

 contrariwise when we introduce higher powers of force (so to 

 call them) we shall correspondingly have to do with equations 

 of higher orders. I venture to predict with a degree of confi- 

 dence, which doubtless I shall not communicate to many, that if 

 we ever succeed in establishing a mathematical theory of che- 

 mistry, it will be as much conversant with equations of the third 

 or of a higher order, as physical astronomy is with equations 

 of the second. 



