46 
Proceedings of the Royal Society of Edinburgh. [Sess. 
This would correspond to the case in which the electrons were arranged 
at the corners of a tetrahedron of length of edge equal to L. Then (3) 
becomes 
I = I' W2 (1 + cos* fl)(4 + 12 ... (6) 
In fig. 4 this expression has been graphed for different values of 6. The 
curve A gives the first factor alone, the distribution of the scattered 
energy on the assumption that the four electrons scatter independently. 
The curves B, C, D, E, and F give the expression for 2&L = 100, 50, 10, 5, 
and ^ respectively. They explain the extra-radiation quite satisfactorily ; 
when the wave-length is very short there is an extra-radiation confined 
to a small region round about 6=180°; as the wave-length increases 
this extra-radiation widens out, until in the case of F it spreads over the 
whole 360° and we pass over to the case represented by formula (5). 
The radii of F are four times the radii of A within the limits of accuracy 
of the diagram. No matter what the value of 2&L, the radius has always 
the same value for 6 — 180°. 
In the ideal case represented in the diagram L has the same value 
