J30 Mr» Henchel on the Action of [Fiiji. 



C. sin.'^ (M k tt) + C\ sin.^ (M Ic'tt) + &c. (a) 



Now, suppose M to begin from zero, and to pass, by a varia- 

 tion either in the direction of the ray or thickness of the medium, 

 or both, through all gradations of value, to infinity, or to ita 

 ipaximura, if not susceptible of infinite increase : then we see that 

 ipr every value of M a certain pecuHar tint will arise, and that, 

 provided M commence at zero and continue increasing, the same 

 |uccession of tints will invariably be developed in the same order, 

 Consequently, if we fix upon any two tints m this scale of colour, 

 or any two values of M, the same succession and the same num- 

 ber of alternations of colour must invariably intervene betweea 

 them, however we pass from one to the other. 



In a crystal with two or more axes, the value of M for any ray 

 C must of course be zero in the direction of the axis, and, there- 

 fore, if the same supposition of the independence of M on c be 

 (i^ade, the same conclusions should follow ; namely, first, that 

 the extraordinary ray must always vanish in the pole, whatever 

 be the thickness of the plate ; and, secondly, that the same suc- 

 cession and number of alternations of colour should intervene 

 between the pole and any assigned unequivocal tint, such as 

 black, or the pure brilliant green of the third order of Newton's 

 scale. Both these conclusions are totally at variance with the 

 facts above detailed, as to the developement of colour in the 

 poles, and the situation in the order of the rings of what we have 

 called the virtual poles. Hence we are necessitated either to 

 give up the theory of alternate polarisation altogether, or to 

 ^dmit the dependence of the multiplier M on f, or on the nature 

 of the ray. Let us see to what this will lead us. 



According to the theory of the polarised rings, if extended to 

 crystals with two axes, the number of periods performed in a 

 ^iven space (= 1) by a molecule of a given colour, transmitted 

 in a direction making angles 5, 6^, with the axes, can only be a 

 functiop of the form /r, 4^ (d, &'), k depending on the intensity of 

 the polarising force ; or, as before, being a function of c, the 

 nature of the ray, and of the intrinsic energy of the molecules of 

 the crystal. Now if we call t the thickness of the plate, and ^ 



the angle of refraction, is the length of the path described, 



sind, therefore, we must have for the number of periods 



COS. (p ^ ^ ' ^ ' 



SO that the value of M must be ' , which must be a func- 



tipn, of c. Now t is obviously independent of it ; and if we neg- 

 lect at pre&ent the very trifling effect at moderate incidences of 

 the ordinary dispersive powers of the media examined,* 9 is so also. 



* It is easy to see that in the two, dasses of crystals above described, the effects of 

 the dispersive powers will be opposite to each other, in one opposing, and in the other 



