Prof. Kelland on the explanation of Dispersion. 375 



present purpose that I direct attention simply to that form of 

 the hypothesis which I gave in my treatise on ' The Theory 

 of Heat.' From the difficulty of accounting for the want of 

 dispersion in a vacuum, I was led to attribute to the imme- 

 diate presence of the material particles, an influence on the 

 velocity of transmission, exerted in a two-fold manner: — 1. by 

 their vibrations along with the particles of aether: 2. by the 

 actions which they put in play, or rather (which is really the 

 same thing) exclude, through the particles of ffither which 

 they displace (Arts. 161, 162). 



Of the two hypotheses now mentioned, the former leads to 

 a very satisfactory explanation of the phaenomena of disper- 

 sion, provided the difficulty which is alluded to can be got 

 over. That this can be done, M. Cauchy endeavours to show 

 by calculations based on a certain assumed law of force. But, 

 even if it cannot, the latter hypothesis, which arises out of the 

 former, leads very simply to the desired conclusion, inasmuch 

 as it introduces into our equations of motion a term depending 

 on the action of the aether which would occupy the place of 

 a material particle, in addition to other terms similar to those 

 which apply to a vacuum. It happens that \.\\e foiin of the 

 result deduced from the second hypothesis differs in no ma- 

 terial respect from that which arises out of the first (Theoi'y 

 of Heat, p. 154). 



2. We shall be able to ascertain the exact nature of Mr. 

 O'Brien's hypothesis, as well by an examination of the equa- 

 tions which result from the supposition that the particles of 

 matter are absolutely fixed, as from the more general equa- 

 tions. We ai-e desirous, indeed, of avoiding all incidental 

 remarks relative to the correctness of the equations themselves, 

 and this we could not do at present in regard to the more 

 general ones, nor, in fact, can we admit anything coricerning 

 these equations until the legitimacy of the hypothesis, that 

 a^, ^1, 7, may be regarded as independent of the sign 2, has 

 been proved. It is evident, that, except in this particular, the 

 equations differ from those which I deduced on the same hy- 

 pothesis (with a limitation) in the Transactions of the Cam- 

 bridge Phil. Soc, vol. vi. pp. 239, 245, &c., only in appear- 

 ance. But the results with which we are concerned, are those 

 which appear at the top of p. 210 of Mr. O'Brien's paper. 

 Now it will readilj' appear to tiiose conversant with the sub- 

 ject, that these equations difler from the ordinary ecjuations of 

 motion of a vibrating system, only in having the additional 

 terms — C«, — C/3, — C7. The otiier parts of the expres 

 sions for the forces are identical with those always given in 

 similar cases; and they will be found at p. 135, vol. iv. of 



