IN THE INTERIOR OF TRANSPARENT BODIES. 403 



f(r + p) (5jj + Sa) = f(r) $X + Sa) + -f'(r)$x($x$a + fyd/3 + &*$y). 



Hence, transforming in the same manner the similar quantities in the 

 equation (A), and observing that by the condition of previous equi- 

 librium we have 



^mf{r) Sx + 2,j» ( 0(r') Ax = 0, 



the equation (A) becomes 



£j = -2m {f( r )U + -f(r)Sx($xSa + hylfl + Hly)\ ) 



*~ r ! (J?). 



+ 2,m t {<p(r') Aa + -,$' if) Ax(Ax Aa + AyA(l + AssA 7 )} \ 



(7. I shall now proceed to put these equations in the form of 

 partial differential equations, in order to make them more manageable. 

 I must first observe, that a, /3, 7, a /9 (3 t , y /t x, y, ft, x t , y t , ss,, &c. are 

 quantities which, at first sight, do not appear capable of continuous 

 variation, since they belong to a set of discontinuous points : but not- 

 withstanding this, we are evidently quite at liberty to look upon 

 these quantities as continuous variables; for instance, we may suppose 

 that a is a continuous function of x, y, ss, t, having the proper value 

 when x, y, z become the co-ordinates of any particle of ether : for, 

 originally, we only assumed that a has certain values when x, y, z 

 belong to any particle of ether, but we made no assumption whatever 

 respecting the values of a when x, y, 1 do not belong to any particle 

 of ether, and therefore we may suppose these values such, that a 

 shall be a continuous function of x, y, z, t for all values of x, y, z, 

 and the same is true of /3, 7, &c. It is just on the same principle 

 that we may draw a continuous curve through any series of detached 

 points. 



In reducing the equation (2?) to the form of a partial differential 

 equation, I shall first omit the part under the sign S /9 and afterwards 

 restore it; this will be found the simplest course to pursue. 



§ 8. To put the equation (B) in the form of a partial differential 

 equation, omitting the part under the sign S y . 



