300 Dr. Beer on the deduction of PresnePs construction from 



P=27w^S^.Ay.A2'{MAa?+vAy + w;A2r}2&c. 



The most natural way of presenting a symmetrical medium 

 possessing two axes to the mind, that is, a medium which is 

 built symmetrically as regards three principal sections which 

 stand pei-pendicular to each other, is that in it the particles in 

 three groups of parallel lines, which stand perpendicular to the 

 three sections respectively, are at equal distances from each other. 

 If we suflfer the axes of our system of coordinates to run parallel 

 with the normals to the principal sections, with the so-called 

 principal axes of the medium, and denote the distance between 

 two neighbouring particles in the direction of these axes by Sx, 

 Bi/, Sz, then the coordinates of a particle, according to this me- 

 thod of representation, will be 



Aa7=w.8.r, Ay = n.Bi/, Az=p.Bz, 

 where wi, n, and jo denote whole numbers. 



In a medium characterized as we have supposed, the particles 

 whose coordinates possess the same absolute value arrange them- 

 selves by eights which lie in the corners of a parallelopiped, the 

 centre of which coincides with the origin of coordinates, and the 

 edges of which run parallel with the axes of coordinates. For 

 eveiy such eight particles the sum of the members 



^.Ax'^.AyKAz^ and ^.Aa?°.A2/*.A^. 



is evidently equal to zero when one of the exponents, «, b or c, 

 is an odd number ; thus in this case we obtain generally 



S ^ . Aaf, AyKAz' = 0, S ^ . Aa?«. Ay*. A^ = ; 



and according to this, the coefficients for the ellipsoid of polari- 

 zation passes into the following : 



L=2m.^S-r^ + -^.AxA- {u^Ax^+v^Ay'^+w^Az^jkc. 



P=2.2m.^2^.Ay«.A^^vw;&c. 



For the sake of brevity let us set 

 im2£:.A.-f^, lm%L.^,^=,^ lm^^.^z^=? 



lmZ-^.AfA2^=A lm2^.Aa^.A.'=^, im2^.A*»Ay^=y 

 imS^.A^-/, lm%^,^/=q^ |mS^3-^='-^ 



