390 MR. J. C. MAXWELL GAENETT ON 



Thus in fig. 3 the microscope is along Oy, in fig. 6 along Ox, while in figs. 5 and 4 

 the tube lies in the intermediate positions, namely, 6 = 90, (j> = - 45 respectively. 



It will now be shown that the figs. 3-6 are completely accounted for if the particles 

 are spheres small compared with a wave-length, i.e., appreciably smaller than O'l /u,. 



From equations (7) the character of the light emitted by such a sphere in the 

 direction 0, tf> (fig. 1) is determined by the electric force E L whose composition is : 



X L = 0, Y! = B cos cos <f>, Z x = B sin <j> ..... (8), 

 where 



-D 47r 2 a 3 N 2 1 , ,. , x, 



-"- f '~ r / c }}- 



Suppose first that, as in the case corresponding to fig. 3, the microscope tube is 

 along Oy (fig. 1), the centre of the field then corresponds to 6 = 90, ^> = 90. 



The fig. 7 represents the direction of E 1; as deduced from equation (8), for positions, 

 the co-ordinates of which are 0, <f>, the centre of the diagram corresponding to 



Fig. 7. 



= (f) = 90, the axis of y. The same figure will therefore represent the directions 

 of the electric vector in various parts of the second focal plane of the microscope. 



From equation (8) it appears that when either = 90 or < = 90, we shall have 

 YL=:O, and therefore Ej becomes (0, 0, Zj) and only has a component in the direction <f>. 

 This is represented by the arrows for positions on the axes in fig. 7. 



In the middle of the quadrants the directions of the electric vector are no longer 

 parallel to the axis of < but are tilted as in the figure, being tilted in the same 

 manner in opposite quadrants. 



Now the planes of polarisation are perpendicular to the electric vector, and the 

 small lines in fig. 3 are perpendicular to the arrows in fig. 7. When, therefore, the 

 incident light is polarised in the plane of incidence, the appearances are accounted for 

 if the particles are small spheres. 



Next consider the case corresponding to fig. 6, when the microscope tube is 

 above Ox. The centre of the field is then = 90, <j> = 0. The arrows represent the 

 direction of Ej in various parts of the field. All these arrows point nearly towards 

 the centre. Along the two axes they point accurately towards the centre. There is 

 no force at the centre, for then both Y, and Z l vanish. Consequently, a black spot 

 should appear at the centre, if the particles were spheres. Finally, lines perpendicular 

 to the arrows in fig. 8 are parallel to the lines in fig. 4. Consequently, in this case 

 also the appearances are explained by supposing the particles to be spheres. 



