Mr. Earnshaw on the Motion of Luminous Waves. 49 



the experimental dispersion of light. The only reference to 

 that communication which I have yet seen, is in the postscript 

 of Professor Kelland's letter in your Journal of the present 

 month, where, after admitting that all the values of q given in 

 his memoir on Dispersion are erroneous, the Professo states 

 that the error is of no importance, seeing that the fo nulse 

 are of necessity capable of fulfilling the conditions requinted.of 

 them. This must be admitted, I think, to be ratfcer an un- 

 usual mode of disposing of a matter of such importance as the 

 numerical verification of his theory. Am 1 to understand 

 him to say, that his formulae are of necessity capable of pro- 

 ducing correct results even if the data employed be erroneous? 

 May I not then ask, what is the nature of the connexion of 

 these formulae with theory ? and in what degree is his theory 

 supported and strengthened by coincidences obtained from such 

 formulae ? I take it for granted that the results were consi- 

 dered as strengthening the theory in some way, else why 

 have they been published both in Professor Kelland's me- 

 moir and in other places in connexion with theory ? Now I 

 showed, and Professor Kelland has now allowed, that funda- 

 mental errors were made in the application of the data ; and 

 the results thus obtained were announced as proofs of the 

 soundness of the theory. I wish to ask, then, how the results 

 could have any power at all in confirming the theory, if the 

 formulae were of necessity capable of producing correct results 

 from correct or incorrect data indifferently ? 



I am aware that the position which I have taken in the 

 present paper touching the transversality of vibrations is al- 

 ready by anticipation controverted in Professor Kelland's 

 letter to Mr. O'Brien (p. 377), where we read, that "if the 

 law " of molecular force " be that of the inverse square of the 



distance the vibrations are transversal only." I regret 



that the necessity of defending my own investigations from 

 implied error prevents me from letting this statement pass 

 without comment. I have turned to the part of the memoir 

 to which the Professor has directed attention, and shall here 

 state in as few words as possible the objections which seem to 

 me to lie against the conclusion there come to ; merely pre- 

 mising, that if I have misunderstood the nature of the reason- 

 ing, 1 am open to correction. My objections are 



1st. I find it stated that "v and o" are possible and equal, 

 but o' impossible and of a different magnitude ;" and thence 

 it is inferred that " attractive forces give rise to transversal 

 vibrations only." Now it appears to me that, admitting the 

 former part of this to be true, there is some error in the in- 

 ference. For since y v' v" are the velocities of the wave, and 



Phil. Mag. S. 3. Vol. 21. No. 135. July 1842. E 



