236 Mr. D. L. Webster on the Theory of the 



from the origin, and z > 0, the electric vector radiated from an 

 electron at x, y, z, is in the -ry direction, of intensity, 



6 2 JjJ rt-r'-x \ m 



±irmr' J \ T /' KJ 



where r' is the distance from the electron to the point x, y, z. 

 For the electron at the origin, letting E 1 = e 2 E /47r???r, this 

 reduces to 



Mtt) (*> 



Neglecting small quantities of the second order, (2) becomes 



^ f ( t-r-*(i-*> s e )+ My (3) 



If now the electron at the origin is to be re-enforced by the 



one at x, y, z, the times of arrival at r, 6, -^ of their scattered 



radiations must differ by less than T, so that the point x, y, z 

 must at least lie between the planes, 



x(l — cos#)— £sin 0= — JT,"\ ,^v 



and A'(l — cos ^)— ^sin^= +^T,J 



Q 



the distance between these planes being T/2 sin ^, and their 



direction being parallel to the y axis and to the bisector of 

 the angle between the x axis and the radius vector r. 



This, however, is not the only limitation on the space 

 available for re-enforcing electrons, for there is also the 

 limitation due to the second order terms, neglected in (3j. 

 But since the limits thereby imposed may be widened inde- 

 finitely by making r large enough, we shall disregard this 

 limitation. 



But another limitation, that cannot be disregarded, is 

 imposed by the irregularities of the primary pulse, due to 

 the disturbing effects of electrons near the —x direction 

 from the region considered. To determine the shape of the 

 space to which we are limited by this effect, we have no data 

 except the fact that each electron disturbs the primary 

 pulse only throughout a very sharp cone with its apex at the 

 electron and its axis in the x direction from it. For a rough 

 approximation we may assume the region to be a sphere with 

 a number of these practically cylindrical pieces cut out of it; 

 and for purposes of computation the result may be assumed 

 to be a spheroid, flattened in the x direction, with its centre 

 at the origin. 



