APPLICABLE TO MATHEMATICS, &C. 371 



Agreeably to what has been before stated, 

 there are as many values of o) that will make 



-H^ ^= to nothing, as there are roots of 



the equation F(.r) = . 



Hence, at each of these values of cT, which we 

 shall call Xi, d\, .1-3, &c. &c., an equilibrium 

 will take place ; or two particles placed re- 

 spectively at distances cZ\ , a.\ , x^ , &c. &c. from 

 each other will have no tendency to approach or 

 recede. 



This circumstance, or property of the roots of 

 equations, will explain, beautifully, the reason 

 why the same material particles combine in 

 various proportions, and by that means produce 

 combinations which possess various and distinct 

 properties. 



Chemical union I shall propose to call Che- 

 mical equilibrium, which takes place when the 

 particles of matter are forced into the different 

 roots of the equation F(ci')=0. 



The forces required to overcome the attractive 

 force when disturbed by a small quantity h after 



