M. Cauchy's View of the Undulator-y Theory of Light, 107 



The cabinet of Natural History under the direction of M. 

 Voltz, at Strassburg, contains an alloy of copper and tin in 

 acicular crystals, the composition of which, according to the 

 analysis of M. Roth, is expressed by the formula 2 Sn Cu. 

 Some of these crystals, which were given me for the purpose 

 of having their form determined, are regular six-sided prisms, 

 cleavable with some difficulty in a direction perpendicular to 

 the axis of the prism. No rhombohedral faces or cleavage 

 could be detected. 



XVII. An Abstract of the essential Principles of ^. Cauchy's 

 View of the Undtilatory Theory,, leading to an Explanation 

 of the Dispersion of Light ; with Remarks. By the Rev, 

 Baden Powell, M.A., F.R.S., Savilian Professor of Geo- 

 metry^ Oxford. 



[Continued from p. 25.] 



Integration of the Equations of Motion, 



TN order to proceed to the integration of the equations (12.), 

 ■*• M. Cauchy adopts the principle, (or at least one which 

 comes to the same thing,) that whatever may be the values of 

 the functions ^ ») 5 which will verify those equations, they may 

 always be developed in some serieses of algebraic functions of 

 xy z, which may be considered as formed by adding together 

 the serieses for the sine and cosine of quantities involving those 

 functions of xy z, with certain arbitrary quantities uvw, and 

 certain coefficients d e f g h i, functions of /. Using the sym- 

 bol i' to signify the sum of a number of such terms, we shall 

 thus have 



J = 2!{d cos {uxi-vy-\-wz) + g sin{ux + vy-\-wz)} 



ri = S{e cos (ux-\-vy-\-wz) -i- h sin {ux + vy + wz)} {IS.) 



?= Su cos (ux-\-vy-i-w;::) + i sm (ux-\-vy + w z)} 



Now the arbitrary quantities n v w may be assumed, so that 

 we have 



w 1 



j._a, J- -0, ^ ^ ., ^ ^^^^ 



and a^ + b' + c^ = 1 ; 



that is, these quantities may represent the cosines of the in- 

 clinations to the three axes, of a line passing through the 

 origin, which we will call O P. 

 And if we write, for abbreviation, 



ax -\- by -\- cz = g, (15.) 



P2 



