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LXV. On the Laws of Trafismission of Light and Heat in 

 una-ystallized Media. By P. Kelland, B.A.^ Fellow and 

 Tutor of Queen's College, Cambridge, afid Member of the 

 Cambridge Philosophical Society.^ 



T^HE difficulties under which a mechanical theory labours 

 -■ must necessarily be owing, in the outset, to a view of the 

 subject not sufficiently simple. In the memoir \ from which 

 the following pages are extracted, I have endeavoured to re- 

 duce the equations of motion of a series of particles trans- 

 mitting vibrations, to the most simple possible Ibrm ; and from 

 that form to deduce, conversely, conclusions with respect to 

 the action of the particles themselves. Whether indeed a more 

 general form of the solution of the resulting equations may 

 not be the correct one, is another question, which I have dis- 

 cussed in a memoir lately presented to the Cambridge Philo- 

 sophical Society. It would be out of place again to give a 

 historical view of the subject, as it has been ably done by Pro- 

 fessor Powell, in his " Abstract of M. Cauchy's ViewsJ." I 

 have satisfied myself with developing my views as briefly as 

 I can. 



In order to reduce the investigation to the simplest possible 

 form, I will suppose the particles symmetrically arranged with 

 respect to the three coordinate axes, and conceive the trans- 

 mission to take place along one of these axes, that of x. It 

 is clearly requisite that such an hypotliesis should be made 

 when we treat of media not crystallized. 



Let X, y, z be the coordinates of the particles P under con- 

 sideration : when at rest 



x-\-lx, y-^ly, ;s-\-lz those of Q. 

 r the distance P Q, 

 i^nd at the end of the time t, let 



x-\-a, 3/ + /3, sf+y be the coordinates of P, 

 x + a + ^^ + ^a> 3/ + /3 + ^y + a/3, ^ + 7+82 + ^7 those of Q, 

 r + g the distance P Q. 

 .Also let (r <^{x)) represent the attraction at the distance r. 



Then denoting by the symbol X the sum of all functions si- 

 milar to that which follows that symbol, we have 



= X<^(r + Vi{Zx-^la). 



dt' 



• Communicated by the Author. 



t Transactidns of the Camb. Phil. Society, vol. vi. part 1. 

 t This abstract will be found in Lond. and Edinb. Phil. Mag. vol. vi. 

 p. ]6 ^/ seq, — Edit. 



