of the Newtonian Law of Molecular Action. 441 



cular action, it is needless to enter further upon the inferences 

 from them which the Professor in various parts of his letters 

 has placed in opposition to my results. 



It now only remains to reply to the accusation (p. 267) that 

 I have fallen into an error in turning the equations of motion 

 into that form, from which I drew all my inferences. I can 

 assure the Professor that I did not lay my investigations be- 

 fore the public, without having first carefully revised them, 

 compared them with what other persons have written on the 

 same subject, and satisfied myself as to the cause of difference 

 where any existed. The Professor may therefore for the 

 future take it for granted that I have seen and examined the 

 equations in M. Cauchy's Memoire sur la Dispersion de la 

 Lumiere, to which he refers me for correction. I fear it will 

 give to my letter an air of great sameness if I again ac- 

 cuse the Professor of misunderstanding what he has under- 

 taken to criticise. I shall not, however, make the charge 

 without bringing forward the proof of it. The Professor tells 

 me that the coefficient of a certain term of my equations dif- 

 fers in appearance from the corresponding coefficient in M. 

 Cauchy's equations ; and his inference is, therefore these co- 

 efficients are not equal, and therefore mine are erroneous. 

 Now I ask, how does the Professor know that these coeffi- 

 cients are not equal ? I admit that they appear to the eye to 

 be different, but the symbol 2) in M. Cauchy's differs entirely 

 from the same symbol in mine. M. Cauchy's coefficients have 

 been brought into the state referred to by reductions sug- 

 gested by theoretical considerations ; but my coefficients were 

 brought into the state in which I leave them by reductions 

 effected upon experimental grounds. j If M. Cauchy's differ in 

 value from mine they disagree with experiment, and are there- 

 fore to be rejected, as will be made manifest by the following 

 process, which applies equally to M. Cauchy's equations and 

 mine own. But I will first state the matter in another way. 

 In my investigations (March, p. 372), A represents the value 

 of 2 {m' <4 2 F (R)}, the summation represented by 2 ex- 

 tending to all particles in the rth wave surface, and in all other 

 surfaces the particles of which are in the same state of dis- 

 placement as in the rth. Also A represents the value of 



2% f A r sin 2 — -J, 2 now denoting summation for all the 



values of r in one wave's length. The limiting value of r in 

 performing the operation 2 is therefore the number of par- 

 ticles in a wave's length, which number in any conceivable 

 geometrical arrangement of the particles depends upon the 



