268 



the discussion of the properties of this function occupies the 

 remainder of the former paper. As the six quantities used in 

 this function are not the same as the three quantities used 

 by Professor Mac Cullagh in his researches in Physical 



Optics, 



dri dZ, dZ> d%, d^ drt 

 dz dy ' dx dz' dy dx ' 



Mr. Haughton was led to suppose that the laws of the op- 

 tical medium were quite distinct from those of solid and fluid 

 bodies ; and that, consequently, the molecular action in that 

 medium is of a more general character, and is not confined 

 to molecular forces acting in the line joining the molecules. 

 In the present paper Mr. Haughton shows that this prima 

 facie view of the subject requires some restriction, and that 

 Professor Mac Cullagh's equations, so far as they belong to 

 the propagation of waves, may be deduced from the simple 

 assumption offerees in the line joining the molecules; while 

 the equations containing the laws of reflexion and refraction 

 cannot be deduced from any such hypothesis. The object of 

 Mr. Haugh ton's paper is, however, more general, and in- 

 cludes the discussion of the laws of propagation of plane waves 

 in bodies of the most complicated molecular structure ; from 

 which are deduced the laws of bodies whose molecular action 

 is more simple, and consists of simple attractions or repulsions 

 between the molecules. 



In an indefinitely extended body, no external forces acting, 

 the most general function for the internal forces will be 



V= F (oi, 02, as, /3i, ^1, 1^3, 71, 725 73) ; 

 where 



d^ dl d^ 



^^=^' ^^ = ^' ^'^di' 

 dZ, dZ dZ, 



'^'^Tx' ^^ = ^' "^'^Tz' 



