726 Sir J. J. Thomson on some Optical Effects 



where x, y are the coordinates of the centre of 

 figure referred to axes through the centre of mass 



x%e = Xex' 



y%e = %ey' : 

 hence we see 



sLey'Xex'z' = x yl{%e) 2 = Xex'Xey'z' = Xez'Xex't/ ; 



(5) if there is a plane of symmetry in the molecule : 

 for if this plane be taken as the plane z f = Q, 



2**' -0, Xex'z' = 0, 2,ey'z' = 0, 



and hence Q = 0. 



It follows from this that if all the atoms in a 

 molecule are in one plane, the molecule cannot 

 when in solution give rise to optical rotation. 



It should be noticed that molecules when in a crystalline 

 arrangement could produce optical rotation when they could 

 not do so in solution, it being assumed that the molecules 

 are not distorted by solution. We have seen that when in 

 solution, either dynamical or electrical symmetry is fatal to 

 rotation. Whereas in the crystalline arrangement rotation 

 would in general exist, unless the molecule was symmetrical 

 dynamically as well as electrically. For rotation to be 

 absent in the crystalline arrangement the coefficients of 

 h 2 i h 2 i h 2 i hhi hh> hh in the expression for Q (p. 725) must 

 all vanish. Two important cases in which this condition is 

 fulfilled are (I) when the centre of the electrical charges 

 coincides with the centre of mass ; (2) when the molecule is 

 symmetrical about an axis. 



For the present I shall confine myself to the case of 

 rotation in solutions, as this is the one to which the attention 

 of investigators has in the main been directed. As most 

 of these have occupied themselves with substances which 

 contained asymmetric carbon atoms, it is interesting to com- 

 pare the value and sign of Q for two molecules (i.) and (ii.), 

 where (ii.) is such that its masses and electrical charges 

 occupy positions which are the images of their positions 

 in (i.) in a mirror placed in one of the principal planes of (i.) . 

 Let us take this plane as the plane z' — 0. The coordinates 

 of the masses and charges on (ii.) will be those of the 

 corresponding mass of (i.) with the sign of the z 1 coordinate 

 reversed. Thus %ex', Xey' will be unaltered, while %ez l will 

 change sign. Again, %ex ] y ] will be unaltered, while %ex'z' 

 and %ey'z / will change sign : hence we see that Q will have 



