6 Prof. Powell on the Demonstration of FresnePs Formulas 



. ^8. It may here be observed, that if we admit equal densities, 

 we must nevertheless suppose some retarding power in the sether 

 within the denser medium. It is still conceivable that this may 

 follow the same law as that of increased density, and that thus 

 Fresnel's formula might still apply. 



Or again, this reduces itself to the condition, that for perpen- 

 dicular incidence we should have 



W /^' 



which might be simply the original condition, without involving 

 the division by /x*, as above, and might be dependent directly on 

 some hypothesis assumed as to the constitution of the sether. 



19. Expressing FresnePs values by roman letters, and com- 

 paring with Maccullagh's, we have 



m _ m 1 

 m^ m^ fA^' 



20. According to the view of Cauchy, the density is diminished 



in the denser medium. If we suppose it diminished, according 



to the same law, 



8 a 1 m q cos i 



KT = /tt' and — =fi^ . 



Of Mf cosr 



21. Mr. Power, taking a for the distances of the molecules 

 without, and a^ within, the medium, obtains what is equivalent to 



m __ al^v cos i 8^v cos i 



a^Vy cos r SpVf cos r ' 



but having avoided any assumption of the law of refraction at 

 the outset, he deduces (§§ 18, 28) the value 



which seems irreconcileable with the admitted principle /a=-, 



unless by supposing S=8., which would agree with Maccullagh's 



W 1 

 view. Or if we could have ^ = — ^, the expression would agree 



with FresnePs view ; or if ^ =/Lt^, with that of diminished den- 

 sity. But as neither of these suppositions seem reconcileable 

 with admitted principles, it will not be material to discuss them 

 further. 



Equivalent Vibrations. 

 22. As to the general nature of the vibratory forces concerned, 

 it wiU be on all hands admitted that the vibratory force of the 



