of Reflexion and Befraction. 291 



possible and impossible parts of either (1.) or (2.), we deter- 



B C 



mine ^^ and — also. Thus by two sets of observations we 



B' n ■^ 



may determine all the unknown constants which enter into our 

 equations. We have also an equation of condition, namely, 



which must turn out true if our theory be correct. 



The simplest way, perhaps, to test the truth of our theory 

 would be this : to find from observation several corresponding 

 values of the two quantities 



and to try whether they vary with the angle of incidence or 

 not ; and whether they are always equal to each other or not. 

 If they turn out to be invariable and always equal to each 

 other, it is clear we have a very decisive proof of the correct- 

 ness of the above results, and vice versa; especially, because 

 there are only three distinct unknown constants involved in 

 the above equations. 



7. The method here explained of determining Q and < by 

 repeated metallic reflexions is not so well-adapted to test the 

 truth of the above formulae as another method which gives the 

 following result, 



Q.-.y-^^ tan j^+ v'-ltany 

 \/ — 1 tan j8 tany— 1 

 where /3 and y are two angles which may be immediately ob- 

 served for any angle of incidence we please. The considera- 

 tion of this method I shall reserve for my next communica- 

 tion, and now briefly prove the laws of reflexion and refraction 

 here stated. 



8. If ^, rj, ^ be the displacements of any element of the 

 aethereal fluid from its position of rest, it appears, as in art. 19, 

 that the material particles will bring into play upon that ele- 

 ment a resisting force, the components of which (parallel to 

 the three axes) are 



"Pd^^^dn Fdn d^ri Prf? rf2^ 

 ~dr^^dfi' Tf^^Jf' "dT^^lt^'' 



where PsCj— CaW^ + C^w'* ... , Q=C2-C4 wH CgW* ... , 



Cj, C2, Cg, &c. being constants depending upon the constitu- 



2 nt 

 tion of the aether and of the transparent substance, and — the 



n 



periodic time of the aethereal vibrations. 



Hence the general equations of motion, for transversal vi- 



X 2 



