^W6 Mr. Herschel on the Action cf [MARCff, 



of the constancy of this coefficient, and we are, therefore, autho- 

 rized to take sin. 9 x sin. 6' as the general value of %|/ (fl, 6'). The 

 observations on Rochelle salt, presently to be noticed, confirm 

 this law.* If we denote by / the minimum length of a douVjle 

 oscillation, or the space passed over during one complete period 

 1^.-% ray transmitted at right angles to both axes, we have /c jss 



J ; and consequently ^ = r, I = ht. If we substitute for A antt 



tttheir values above found, we obtain 



/ = 0-00076497 inch 



Tor the minimum length of a period performed by a mean redrs^ 

 in mica. 



Resuming our general equations (b) and (d) if we substitute 



Ae value now determined for <4., and write j, for -, we have 



/' . COS. 9' . sin. 9 . sin. 6' = / . cos. <p . sin. (9 — 3^ a + I if). 

 sin. (5' 4- Sa + 54»); (g) 



whence it is easy to derive (independent of any approximation) 



COS. 2 (a + Ja) = cos. 2 (£>' + 2 - ^^^' . sin. fl . sin. S': (h) 



^ * I COS. <p 7 \ / 



while our approximate equation (d) furnishes the following very 

 convenient formula for incidences nearly perpendicular 



^ I — I' sin. $ . sin. d' , .. 



sm, 8 a = — =— . — -. — - — (i) 



I sin, Ha ^ ' 



The simplest supposition we can frame relative to the values 

 <5f the constant elements /, I' is their proportionality to those of 

 c, d, or the lengths of the fits of easy reflection and transmission. 

 This cannot certainly be far from the truth in crystals with one 

 -axis, in which the coincidence of the tints, with those of New- 

 ton's scale, is for the most part exact. In sulphate of lime too, 

 and mica, the only crystals with two axes which have been exa- 

 mined with sufficient exactness, and under the proper circum- 



• When B = 6', as in crystals with one axis' we have ^^ (9, 9') = sin. 9", a result long 

 aince confirmed by the accurate experiments of Brewster and Biot. The velocity of the 

 extraordinary ray in such crystals is given by the formula v^ = V + a . sin. B\ Fol- 

 lowing this analogy, we may conclude that in crystals with two axes we should have v* 

 = V^ + a. sin. . sin. 9'. Now this is precisely the expression at which M. Biotha« 

 recently arrived. This very simple and elegant result was communicated to me by that 

 eminent philosopher in the spring of this year, and subsequently in a letter of May 2. 

 His memoir on the subject which appears (by the Ann. de Chim.) to have been read to 

 the Institute in April, I have not seen, nor do I know by what precise steps he was led 

 to it, but presume it nmst have been by some consideiations of the nature above 

 described. In the foregoing investigation of the law of periodicity, I beg leave, there- 

 fore, to disclaim all intention of arrogating to myself any share in this beautiful discovery, 

 Init have thought it necessary to state the steps in the text, in order to demonstrate a 

 truth essential to the investigations that follow, which could not have been taken fbr 

 granted, or deduced by any legitimate reasoning, independent of experiment, from the 

 equation t* = V + a . sin. 9 . sin. 9', by reason of our ignorance of the nature and 

 ■mode of action of the polarising forces ; and have purposely abstained from entering any 

 ■fttrther into the general laws 6f douWe refraction and polarisation than I could possildy 

 jtvoid. 



