the Colours of Mixed Plates. 867 



the summation of the effects of the individual boundaries in 

 the film leads to results in close agreement with the features 

 of the halo already described. 



The foregoing treatment also enables us at once to explain 

 the increased intensity of the halo in certain directions in 

 the case of films containing elongated boundaries. In so 

 far as relates to the general configuration of the halo, the 

 aro-umentsof the preceding paragraph apply mutatis mutandis 

 also in the case of such films, and it is clear why the distor- 

 tion of the boundaries leaves the circular form and positions 

 of the rings in the diffraction-halo unaffected ; the only 

 difference is as regards the relative intensity of the halo along 

 different radii, which depends on the aggregate length of the 

 scattering elements effective along the respective directions. 

 If we divide up each boundary in the film into n parts, such 

 that the successive normals at the points of division make 

 angles ot' 27rjn with each other, the aggregate scattering- 

 effect of each of the n groups of: parallel elements in the film 

 in the planes respectively normal to them would be the same, 

 provided the average length of an element in each of the n 

 groups were the same. The latter condition is satisfied, 

 provided the boundaries in the film show no bias towards 

 elongation in any particular direction. But if they do show 

 such bias, the average length of an element is greatest in 

 respect of the groups running parallel to the general direc- 

 tion of elongation, and least in the groups running transverse 

 to such direction. From this, it follows that the intensity of 

 the halo should be greatest in the plane perpendicular to 

 the direction of elongation, and least in the plane parallel to 

 it. This is exactly what is observed. The intensities should, 

 in fact, be quantitatively proportional to the square of the 

 average length of an element in each group. 



5. Mathematical Theory : Normal Incidence. 



We have now to consider the explanation of the unsym- 

 metrical scattering by the laminar boundaries in a mixed 

 plate, and to express the results in quantitative form. No 

 rigorous treatment of the problem of diffraction by plane 

 transparent laminss bounded by edges appears as vet to have 

 been put forward. In practice, the precise shape of the 

 difr'r acting-edge should obviously have a considerable in- 

 fluence in determining the manner in which it scatters light 

 in direction* much removed from that of regular propagation 

 of the incident waves. For instance, the strise in mica are 



