Electromagnetic Theory of Light. 



231 



If the symbols p, 7, 8, o; /3, e be arranged in this cyclic 

 order (counter-clockwise in fig. 1) uniformly round a circle, 

 it will be noticed that the three pairs of corresponding vectors 

 mentioned in Prop. II. are thosa at extremities of diameters. 

 And further : — 



Prop. III. When so arranged, each vector is the vector- 

 product of its two neighbours taken in the cyclic order named. 

 That is to say, p = Yey, y = Y p8, &c. 



For some purposes — especially to see easily the simplifi- 

 cations which occur when B is parallel to H — it is better to 



Fis-. 2. 



illustrate this by fig. 2. The curved lines of this figure are 

 meant to represent quadrantal arcs on a sphere (looked at 

 from the outside), and the points marked p, y, . . . . are the 

 points where lines from the centre parallel respectively to the 

 vectors p, 7, . . . . meet the sphere. 



When B is parallel to H it will be noticed that fig. 2 becomes 

 fig. 3. 



Fig. 3. 

 P 



In fig. 4 the plane of the paper is taken as the plane which, 

 in fig. 3, contains p, cr, e, 8. In this case ft and 7 must be 

 drawn upwards from 0. The figure indicates the mutual 



