Prof. MacCullagh on the Dispersion of Optic Axes, tyc. 293 



veys of the great lines of subterranean movement, may here- 

 after enlarge the limited view now presented of a part of the 

 Malvern hills, into a general contemplation of the agency of 

 heat during the Palaeozoic periods in the great physical re- 

 gion between the vale of the Severn and the coasts of Wales. 

 But to state such a speculation without the data which have 

 been collected for its illustration, would be useless or injuri- 

 ous, and the constitution of even the Malvern chain itself is 

 sufficiently varied in its different parts, to induce a long pause 

 before the apparently proved high antiquity of the northern 

 sienites should be implicitly extended even to the southern 

 portion of the same chain. 

 Malvern, Sept, 19, 1842. 



L. On the Dispersion of the Optic Axes, and of the Axes of 

 Elasticity, in Biaxal Crystals. By James MacCullagh, 

 LL.D., M.R.I.A., Fellow of Trinity College, and Professor 

 of Mathematics in the University of Dublin*. 



TN the last Number of the Philosophical Magazine (p. 228), 

 -■- there appeared an extract from the Proceedings of the Royal 

 Irish Academy, containing a notice of a memoir which I had 

 the honour of reading to that body on the 24th of May, 1841 ; 

 and in the concluding paragraph of the notice a brief allusion 

 is made to a K mathematical hypothesis" by which I had con- 

 nected the laws of dispersion and those of the elliptic polari- 

 zation of rock-crystal with the other laws that were there an- 

 nounced. My present object is to indicate the development 

 of that hypothesis, with reference more particularly to the 

 subject of dispersion in crystals, and to communicate a very 

 simple result which I have lately had occasion to obtain from 

 it. The result is remarkable as embracing and explaining a 

 class of intricate phaenomena which hitherto have not been 

 connected with any theory, or rather have stood in opposition 

 to all theories ; I mean the phaenomena of the dispersion of 

 the optic axes, and of the axes of elasticity (as they are called) 

 in biaxal crystals. 



The name of axes of elasticity was given by Fresnel to three 

 rectangular directions, which, according to his theory, exist in 

 every crystallized medium, and which are distinguished by the 

 property, that if a particle of the medium be slightly displaced 

 in the direction of any one of them, the elastic force thereby 

 called into play will act precisely in the line of the displace- 



. * Communicated by the Author. 



