46 Mr. Earnshaw on the Motion of Luminous Waves. i 



sin 3^+ 0'00115cos3£— 0'00715sin4£ 



+ 0-00686 cos 4£, 

 temp, froml = 48 o. 266 + 3 o. 0257sin ^ + 44 o 53 f) + o. 4265 

 noon = h J v ' 



sin (2 * + 46° 14') + 0° '1302 sin (3 t 



+ 1 79° 30') + 0*0099 sin (4 t + 1 36° 50'). 



The quantities c, E, and e are the only ones wherein the 

 separate values in each combination disagree, but this is not 

 very material, owing to the smallness of these quantities. 



London, April 29, 1842. S. M. D. 



XL On the Motion of Luminous Waves in an Elastic Me- 

 dium, consisting of a system of detached particles, separated 

 by finite intervals. By S. Earnshaw, M.A. of St. John's 

 College, Cambridge. 



THE equations obtained at the close of my last communi- 

 cation on this subject (vol. xx. p. 373) involve six co- 

 efficients, A, B, C, D, E, F. From the peculiar manner in 

 which they enter those equations it is known, that if the co- 

 ordinate axes be turned through proper angles, their directions 

 still remaining rectangular, the equations will assume the 

 forms 



d?z=-k*Sj, 4Sm~'& : » d^^-lcit 



These show that vibrations of m parallel to any one of the 

 axes of dynamical symmetry cannot be affected by vibrations 

 which are parallel to the other axes. Simple as these equa- 

 tions are, they have precisely the same degree of generality as 

 the original ones, for the motion of the particle m. It might 

 not happen that the axes of dynamical symmetry for every 

 particle would be parallel to those for m, and that the same 

 position of the coordinate axes would reduce the equations of 

 motion for the other particles of the medium to the same form, 

 and cause them to have the same coefficients as for m. A 

 condition equivalent to mechanical homogeneity of the me- 

 dium must be fulfilled that this may be the case. It is neces- 

 sary therefore to appeal to experiment for license in this 

 matter. By experimental means we learn that the positions 

 of the axes of elasticity for waves of a given length are fixed, 

 and that the velocity of transmission of such waves is uniform, 

 and that both these properties are independent of the thick- 

 ness of the medium : hence we may assume that fc l £ 2 k 3 have 

 constant values through the whole interior of a medium, and 

 that the equations in the simple forms above given are appli- 

 licable to, and fully represent all the properties of, the trans- 



