846 M. G» Wertheim on the double Refraction 



indices of refraction is sensibly the same for the two substances. 

 For the plate of spar we have 



rf=L„(I.-I„); 



substituting this value in the equation (1), we find 



P=E.Lo.La; 



and for the unit of surface, 



P==E. 



It would therefore be necessary to apply to the plate of crown a 

 pressure of 6220 kilogrammes to each square millimetre of the 

 transverse section perpendicular to the thickness ; that is to say, 

 a pressure more than a thousand times greater than that which 

 would crush the glass to pieces. 



It now remains to compare the value of the double refraction 

 which we have just found for plate glass, with that which results 

 from the investigations of M. Neumann. After having shown 

 that the temporary optic axes are represented by the following 

 expressions, — 



C = 0' + qu+p^+py, 



in which the quantity 0' differs infinitely little from the velocity 

 Oo of light in isotropic bodies, and where a, y8, 7 represent the 

 proportional changes of length in the directions of the three 

 mechanical axes ; M. Neumann seeks to determme the values 

 of/? and q. 



To find two equations between p and q, he employs two dif- 

 ferent processes, but both of them based on the use of formulae 

 generally admitted for the flexure of prismatic bodies. 



In the first process, we determine in the medial plane the 

 flexure assumed by the band of curved glass, and the distances 

 of the neutral axis from two points«which possess the same tint, 

 corresponding to a certain thickness of air as determined by the 

 table of Newton ; of these two points, one is above the neutral 

 axis in the compressed portion of the band, and the other at an 

 equal distance below the axis" in the dilated portion. 



Assuming that a very small parallelopiped, placed at one of 

 these points, will sufi'er the same linear changes as if it had been 

 compressed or dilated by a force equal to that which results from 

 the flexure, we can find, by known formulae, the relation between 

 the double refraction and the mechanical linear change ; we have 

 hence the value oip—q. 



The second process is based on the method of displacement of 

 fringes, as in the experiment of M. Arago. Of two rays which 

 interfere, one has passed through the dilated, and the other 



