temporarily produced in Isotropic Bodies. 343 



we have ' ta 



P to 



E.Lo.La' - 



for feeble charges, we can construct upon the curve the ratio of 

 the veritable ordinate to that which would be furnished by the 

 coefficient of elasticity which corresponds to the dotted line. 



But neglecting these small differences, and remarking that for 

 all the substances which we have examined, 8 may always be 

 neglected in comparison with unity, we obtain, by substituting 

 in the preceding equation the value of 8, the equation 



±^=E:ra(oro> • • • • (^) 



which contains our propositions 1, 2, 3 and 5. 



pT- and pT- are the two indices of refraction Iq and I^ ; and for 

 d^ +1 and La=l, we have P = C, and consequently 



I.=I.+ §, (2) 



where it is necessary to take the sign — for traction, and the 

 sign -I- for pressure. It now remains to find the values of !« 

 and E. 



M. Dutirou has determined the indices of refraction of the 

 glasses derived from the same manufactories as those which I 

 have employed ; I might therefore have made use of his results. 

 But notwithstanding the identity of origin, the densities of my 

 glasses differ notably from those found by M. Dutirou. These 

 differences indicate corresponding differences in the composition, 

 and I have thought it necessary, wherever such differences ap- 

 peared, to ascertain by direct experiment the refractive index of 

 the substance. For this purpose a prism was cut from the mass 

 from which the corresponding parallelopiped was taken, and by 

 means of the goniometer of M. Babinet, the index for the mean 

 yellow ray was determined; this suffices in the case before us, 

 the difference !«— lo, which it is our object to find, being inde- 

 pendent of the length of the undulation. Fluor-spar and rock- 

 salt are bodies of such constant properties, that I have been able 

 with safety to make use of the indices given by Sir David 

 Brewster; but I have deemed it necessary to determine the 

 index of inactive alum, on account of the peculiar properties 

 which it exhibits. 



The coefficient of mechanical elasticity has been found for 

 each substance by means of the transversal vibrations of a thin 

 plate, sufficiently long, which we were careful to take from the 



