266 Prof. Kelland's Reply to some Objections against the 



a theory which has succeeded so well in accounting for a great 

 variety of intricate and delicate phenomena" (Earnshaw, p. 

 304), is strengthened by the removal of any obstacle, and con- 

 sequently by bringing under it the explanation of the pheno- 

 menon of dispersion. But has the phenomenon been ex- 

 plained ? I answer, most assuredly. It is done as satisfactorily 

 as almost any one phenomenon in nature is explained. Its 

 doubtful nature, the "uncertainty J" which I mentioned in my 

 'Theory of Heat' as attached to it, is referable, not to the kindof 

 explanation, but to its detail. Nay, even Mr. Earnshaw himself 

 appears to look for a complete explanation to the very quarter 

 at which he aims his objections. Unless Mr. Earnshaw adopts 

 the hypothesis that the particles of matter are at rest, there is 

 no difference whatever between the hypothesis of Mr. O'Brien, 

 which he designates as a " more promising one," and my own. 

 Are my equations then incorrect, and why ? I see them open 

 at p. 248 of vol. vi.of the Transactions of the Camb. Phil. Soc, 

 they are certainly not of exactly the same form as Mr. 

 O'Brien's ; but his are only approximations. 1 do not say 

 that even then they are identical, the difference probably will 

 be removed by supposing B and B equal in the latter. So far 

 as I am concerned with the numerical verification of the for- 

 mulas for dispersion (which occupies between five and six 

 pages in my Memoir), I may state that it is essential to show 

 that our results are in the form which the phenomena require 

 they should be : and having premised this, I will gladly answer 

 the questions which Mr. Earnshaw puts me in p. 49. 



" Am I to understand him to say, that his formule are of 

 necessity capable of producing correct results even if the data 

 employed be erroneous ?" Yes : but the data are not erro- 

 neous. 



" May I then ask, what is the nature of the connexion of 

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

 supported and strengthened by coincidences obtained from 

 such formule?" The numerical verifications were used, as 

 is stated at the place, as a test of the general accuracy of the 

 deductions. Let me quote my own words. " Results more 

 nearly agreeing might doubtless be obtained by proceeding to 



one place further in the expansion of sin — °, but the above 



will suffice to establish the general accuracy of the formula" 

 (p. 174). " If, however, it were requisite to determine accu- 

 rately the values of/>, a , . . . . of course the plan to be adopted 

 would be that of introducing seven constants, and determining 

 their values from the seven given equations" (pp. 172-3). 

 " I wish to ask, then, how the results could have any power 



