of Light jivoduced by Quartz : Part II. 323 



sets, of which one set will be spherical and the other sphe- 

 roidal. 



Let f^p ?y, denote the displacements connected with the 

 former, and rjg, ^, those connected with the latter; then 

 1 =>!/ + 12 5 ?= ^/ + ?2> ^^^ 'he equations (22.) resolve 

 themselves into 



)), = a^ sin )-^{^v^t—x) \ , 



'Ja = «2 sin J — — (I'a ^ — J^) )• 3 

 L \ J 



?2 = F2 «2 sin \"77 (^2 ^ - .2^) -^j- . 



From these expressions it appears, that, in each set of 

 waves, the revolutions of the molecules are elliptical. And, 

 since the equations (31.) show that p^ is nearly the negative 

 reciprocal of p^, it also appears, from these expressions (33.), 

 that the greater axis of the ellipse of revolution in one of the 

 sets of waves has the same direction as the lesser axis of that 

 in the other, and that the revolutions connected with the one 

 set are performed in an opposite direction to those connected 

 with the other. We have seen that, when x coincides with 

 the axis of the crystal, we have p, = — Ij Pa = 1> hence we 

 perceive that the ellipses are then changed into circles ; the 

 motions constituting the two rays being expressed by the 

 equations (23.). All these deductions are verified by the ex- 

 periments of Mr. Airy. 



Having thus, by the aid of certain probable suppositions 

 respecting the relative values of the arbitrary quantities, 

 brought our formulae to express the laws of the refraction of 

 quartz, we may in conclusion obsei ve, that our general in- 

 tegrals are susceptible of extensive application ; and I think 

 I shall be able to show, in another paper, that they are ade- 

 quate to explain the cause of the absorption of light. It is 

 immediately obvious, from the equations (18.), that, for media 

 possessing, in any degree, the elliptically polarizing structure, 

 the dispersion-formula must be different from that which has 

 hitherto been used. I am, Gentlemen, yours, &c., 



Littlemoor, Clitheroe, March 20, 1839. JoHN ToVEY. 



P.S. In the last paper, page 169, line next above the equa- 

 tion {\2.), for b' read b; p. 171, for A3 in the second line 

 of (18.) read A'^; and p. 174, line \0,for correctly rearf ap- 

 proximately. 



V2 



