a EIGHTH REPORT — 1838. 



express the mutual action of the particles of ordinary and solid bodies, 

 being perhaps of some such form as the following : — 



_C r\'' — ( ^ ^*' 



rf(r)=-a.b ^' + a,b, ^'' ' (18.) 



h and bf being each greater than unity, and ff, ff,, h, h, being some large 

 jjositive numbers, while a and a^ are constant and positive multipliers, 

 and e is, as before, the mean or average interval between two adjacent 

 particles. With such a law there would be a nearly constant repulsion, 



if a be greater than a^, and if ff be less than ff,, as long as — is sensi- 

 bly less than unity; but the force would rapidly change, as the distance 

 r approached to p e, and would then become a nearly constant attraction, 

 until r became nearly = g^e ; it would then diminish rapidly, and soon 

 become insensible. Sir William Hamilton did not, however, intend to 

 exclude the hypothesis, that the function r f(r) may contain several 

 alternations of such repulsive and attractive terms, — much less did he 

 deny that at great distances it may reduce itself to the law of the in- 

 verse square. 



On the Propagation of Light in Crystals. By Prof. Sir W. R. 

 Hamilton, F.R.S. 



By continuing to modify the analysis of M. Cauchy in the manner 

 already explained, he had succeeded in deducing, more satisfactorily 

 than had in his opinion been done before, from dynamical principles, 

 a large and important class of the phenomena of light in crystals ; 

 though much still remained to be done before it could be said that a 

 perfect theory of light was obtained. He had employed, for the pur- 

 poses of calculation, the supposition that the arrangement of the parti- 

 cles of the ether in a crystal differs from an exactly cubical arrangement 

 only by very small displacements, caused by the action of the particles of 

 the crystalline body ; and had attended only to those indirect or reflex 

 iiffects of the latter particles which are owing to the disturbances which 

 they produce in the arrangement of the former particles : but he did 

 not mean to assert that he had established any strong physical pro- 

 bability for this being the true modus operandi in crystals, though 

 he thought the hypothesis had explained so much already that it de- 

 served to be still further developed. 



On some Points connected with the Theory of Light. By Professor 

 Powell, F.K.S. 



At the last meeting, the author dwelt on the importance of extending 

 .observations on the refractive indices for the standard rays to more 

 highly dispersive media. In prosecuting these inquiries, he has to re- 



