(G), 



AT THE SURFACE OF AN UNCRYSTALLIZED BODY. 15 



Comparing this with the equation {F), we see that 



N=M, N'=M', and— , = -. 



M n 



(12.) In our ignorance of the constitution of the liminiferous ether, it is natural to 

 assume that it is of the same nature as ordinary elastic fluids, and that it accordingly obeys 

 the common law of elasticity ; we shall, in the first instance, make this assumption, and there- 

 fore put Jlf = iV, M'=N', and M'=eM, where c=— , a quantity not differing much from 



n 



unity ; and then the equations (E) and (F) become 

 da dy /da dy'\\ 



dz dx \dz dx ) I 



i^ + tL = J^+tL\\ 



dss dy \dz dy J j 



Ida d/3 dy\ (da rf/3' dy'\ 



\dx dy dzj \dx dy dz / 



Further, if we neglect the variation of temperature, and therefore put e= I, these equations, 

 in virtue of the equations (D) differentiated with respect to x and y, assume the simple forms 



da _ da' d/3 _ d/3' dy _ dy' 



dz dz ' dz dz ' dz dz ' 



(13.) The equations of connection just obtained, along with the equations of motion given 

 in the Cambridge Transactions, Vol. vii. p. 409, are sufficient to solve all problems respecting 

 the propagation of waves from one medium into the other. We shall assume that these equations 

 of motion hold up to the very plane of separation : which of course is not accurately true, 

 since there will most probably be a variation of density in the media in the immediate vicinity 

 of that plane. If we describe two planes parallel to the plane of separation, one above it and 

 the other below it, including between them the slice of the two media in which this variation 

 of density is sensible, it is easy to see that, in consequence of the smallness of the sphere of 

 action of the molecular forces compared with the length of a wave, the thickness of this slice 

 will be extremely small compared with the length of a wave. Indeed, if one medium exercised 

 a sensible action only upon those particles of the other which are immediately contiguous to 

 the plane of separation, the thickness of this slice would be actually zero. We shall therefore 

 consider this slice to be of insensible thickness, and regard it as a physical plane. This being 

 assumed, we may, without sensible error, suppose that the equations of motion hold up to the 

 very plane of separation. All therefore that is proved of the propagation of waves in a sym- 

 metrical medium in the Cambridge Transactions, Vol. vii. p. 41 6, &c., we shall assume to be 

 true up to the very plane of separation. 



We shall in the following Section, use the equations of connection in their simplest form, 

 viz. (Z)) and (7) ; and afterwards, in Section vii., shew how we must proceed when they are 

 taken in their most general form, viz. (Z>), (E), {F). 



