126 The Rev. S. Haughton on a Classification of Elastic Media, 



Hence the simplest form of the function -will be 



The axes of co-ordinates are in this formula the axes of elasticity. 



SECTION IV. EQUATIONS OF A SYSTEM WHOSE MOLECULES ATTRACT AND REPEL 



EACH OTHER. 



The third form of the function F, which possesses the property of repro- 

 ducing itself by a transformation of co-ordinates, is given by equation (22), 



V = F{a, jS,y, u,v, iv). 



The six variables contained in this function are the quantities upon which a 

 change in the distance between the molecules depends ; hence the variation of 

 this function will express the virtual moments of a system of forces tending to 

 alter this distance. In my former commvmication* I have made use of this func- 

 tion, using definite integrals to represent the coefficients ; the equations thus 

 found contain a smaller number of constants, than if the coefficients had been 

 assumed to be arbitrary, without any relation expressed by definite integrals. I 

 shall here use the function in its most general form, as the use of definite inte- 

 grals may, perhaps, involve an hypothesis which would be too restricted to 

 represent all the bodies whose molecular forces act in the line joining the 

 molecules. 



The following relations will exist, in consequence of the form of the function, 



(29) 



These equations will reduce the equations of motion (5) to the following : 

 * Transactions of the Royal Irish Academy, yd. xxi. p. 151. 



