606 M- BIOT ON THE APPLICATION OF CIRCULAR POLARIZATION 



ployment, and he might have added, very inexact. But there is here 

 on the part of M. Chevreul some error, though undoubtedly an invo- 

 luntary one ; for I have never proposed or employed such a method, 

 which may be proved by consulting my formulae. It is true that they 

 contain the density of the solutions observed, as they also enter into 

 the determination of numerous other physical results ; as, for example, 

 into the calculation of refractive power, and of capillary forces ; though 

 certainly it has never been said that these phaenomena are estimated 

 or measured by the density. So in the phaenomena of circular polari- 

 zation there exists for each active substance a necessary mathematical 

 relation between its power of molecular rotation ; the thickness through 

 which it is observed, whether insulated or in solution ; the angular de- 

 viation which it produces of the plane of polarization of a simple 

 ray of a given nature ; and lastly, the actual density of the solution in 

 which the substance exists, as well as its ponderable proportion in that 

 solution*. Of these five elements, four being given, the fifth is de- 

 duced by necessity from the mathematical relation; and if this unknown 

 fifth be, for example, the ponderable proportion of the active substance, 

 it may indeed be obtained by calculation, in which the density will 

 enter as one of the elements. But it will not be from this density, at 

 least not from it alone, that the proportion will be estimated. It is even 

 evident from the formulae that in aqueous solutions greatly diluted, the 

 density of which consequently scarcely differs from unity, this element 

 preserves scarcely any influence upon the ponderable proportion, because 

 it only affects the decimals of a very distant order. For example, Avhen 

 I say, as I can say, that by means of the apparatus which I now employ 

 the presence of two thousandths in weight of cane sugar, or one of dex- 

 trine, in an aqueous solution may immediately be rendered sensible and 

 appreciable, it is not certainly from the density that such results are 

 obtained ; for at such degrees of dilution the densities of the solutions 

 differ so little from unity, that the observation of the density might be 

 entirely dispensed with, and unity be substituted in its place, without 

 the ponderable proportions of the substances being affected by it in an 

 observable degree. The estimation of the ponderable proportion by 

 the density must not therefore be attributed to me, for it does not in 

 any degree belong to me, and the supposition that it does would lead 

 to a veiy false idea of my processes. 



After having thus considered the objections which M. Chevreul 



♦ Not only is the mathematical relation of which I am treating established 

 in my memoir of the oth of October, 1S32, printed among those of the Aca- 

 demy ; it is also mentioned in the memoir upon grape sugar which has served 

 specially as a text to M. Chevreiil's dissertation. Vide the Nouvelles Annates 

 flu Miixpinn d'Hisloire Nalin-flle, vol. ii. p. 97, in a note. The numeincal table 

 in the foilowir)g page is mathematically deduced from that relation. 



