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XX. Note on Mr. Earnshaw's Paper in Phil. Mag. for 

 April 1842. By Professor Powell. 



To the Editors of the Philosophical Magazine and Journal. 

 Gentlemen, 

 T DID not happen to see your Number for April till a few 

 days ago, or I should long before this have addressed to 

 you the very brief remarks which I now feel called upon to 

 offer in consequence of certain observations in a paper inserted 

 in the Number referred to, (S. 3. vol. xx. p. 304) " On the 

 Theory of the Dispersion of Light," by Mr. Earnshaw. 



I am truly glad to see that a mathematician of such emi- 

 nence has felt interested in the subject, and has given his at- 

 tention to what I have published upon it : there is nothing I 

 more desire than fair discussion : no one can have read my 

 treatise on the Dispersion, I trust, without perceiving that I am 

 no prejudiced undulationist, and that so far from asserting 

 that that theory has explained the dispersion, I on the con- 

 trary expressly point out the extent to which it does apply, 

 and the precise degree and nature of its failure* So far then 

 Mr. Earnshaw and myself are quite agreed. 



But in the mode in which he sets about the more particular 

 proof of this assertion, there are I confess several particulars 

 which strike me as being, to say the least, extraordinary over- 

 sights on the part of so able a mathematician, who seems to have 

 read my treatise, though I can only imagine, too cursorily to 

 perceive wherein it differs from certain earlier researches, on 

 a reference to which his whole objections seem founded. 



More precisely : Mr. Earnshaw points out certain imper- 

 fections in a formula which he assumes as that I have adopted 

 for the dispersion ; he contends that this formula is theoreti- 

 cally defective, and also that it is discordant with the results 

 of observation ; and enormously so in the case of the more 

 highly dispersive media. 



Now all this is precisely 'what I have stated in my work on 

 Dispersion, where (in section vi.) he and your readers will 

 find the nature of the formula fully discussed; the formula on 

 which he has commented being avowedly but an approximate 

 one, which applies nearly for low dispersive substances, and 

 which I so applied in my earliest researches, but which I long 

 since discarded for a more accurate one. This simple circum- 

 stance then renders all his elaborate criticisms superfluous. 

 My published volume contains my latest view of the whole 

 subject, and supersedes all my previous researches ; while it in- 

 vestigates the entire series of experimental results by one uni- 



