48 On FresnePs Theory of Double Refraction. 



the Russian corruptions Feodor, Marpha, &c. for Theodore, 

 Martha), so that all the labial aspirates would approximate to 

 dentals, and on this principle might it be that the liquid 

 aspirate Nh approaches the next order of gutturals. 



Should this paper be admitted, I shall hereafter consider 

 some objections that have been communicated to me, and pro- 

 ceed to an attempted analysis of vowel sounds. 



C. B. Cayley. 



XI. On FresnePs Theory of Double Refraction. 

 By Archibald Smith. 



To the Editors of the Philosophical Magazine and Journal. 



Gentlemen, 



TN an article on FresnePs Theory of Double Refraction, in 

 the Supplement to the December Number of the Philo- 

 sophical Magazine, Mr. Moon has quoted part of an article 

 of mine in the first volume of the Cambridge Mathematical 

 Journal, in which the following passage occurs : — " Let the 

 particle receive a small displacement, the projections of which 

 on the co-ordinate axes are S.r, %/, Iz. Then supposing the dis- 

 placement to be very small, the force of restitution may be 

 taken as 'proportional to it, so that we have," &c. I am not 

 surprised that Mr. Moon should remark on this passage, 

 " what is meant by the mysterious principle ' supposing the 

 displacement to be very small, the force of restitution may be 

 taken as proportional to it,' I profess myself unable to under- 

 stand." 



The clause in italics, which was added to my manuscript 

 when it was sent to the press, to remove, I believe, what was 

 thought an abruptness in the reasoning, is certainly incorrect 

 when applied to a doubly refracting medium. What was in- 

 tended to be expressed, no doubt, was, that in the case sup- 

 posed terms involving powers of &r, ty, 8z higher than the first 

 might be neglected. But this expression is only equivalent to 

 the other in the case of a singly refracting medium. I may 

 mention that in the middle of page 7 of the article in the 

 Cambridge Mathematical Journal, the word " rays " was, 

 by a mistake, substituted for i( waves." These mistakes are 

 corrected in the second edition of the first volume of the 

 Cambridge Mathematical Journal which is now printing. As 

 they have been noticed in your Journal, I shall feel much 

 obliged by your inserting this explanation when you can afford 

 space for it. 



Your obedient Servant, 

 25 Old Square, Lincoln's Inn, Dec. 20. ARCHIBALD Smith. 



