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



dV^O, ^=0, ^=0; 

 rfa, ' dpi dys 



and the function V will become 



r=F(a„a„§,,p,,y„r2)- 



But, as I have already shown, such a form must be assumed, as will reproduce 

 itself by transformation of co-ordinates. The only function which satisfies this 

 condition is the function (21), 



V=FiX, Y,Z). 



This function, deduced in a different manner, has been used by Professor 

 Mac Cullagh in his mechanical theory of light ; and for the discussion of its 

 properties and the laws of propagation, reflection, and refraction, deduced from 

 it, I shall refer to his memoir in the Transactions of the Royal Irish Academy.* 

 As, however, I shall have occasion to use them hereafter, I shall here state the 

 differential equations of motion, and the conditions at the limits. On account 

 of the form of the function, the following relations exist : 



(27) 



