62 Mr. G. F. C. Searle on the Impulsive 



speed of light be arrested by an obstacle, it only communicates 

 a finite part of its infinite momentum to the obstacle. From 

 Table II. we see that the momentum communicated to the 

 obstacle is- equal to that possessed by the sphere when moving 

 at a speed, of about 0*87 v. 



The " impulse " of the force required, to suddenly give the 

 sphere a velocity equal to that of light is Px + M l? and thus is 

 infinite. 



When the sphere is stopped, the pulse ceases to cut the 

 sphere after a time 2a/v, and then no force is required to 

 hold the sphere at rest. 



But when the sphere is started into motion at the speed of 

 light, the sphere is always just enclosed in its own pulse, and 

 consequently the force required to maintain its motion does 

 not vanish until the motion has continued for an infinite 

 time. 



The component in the direction opposite to the sphere's 

 motion of the electric force in the pulse is * 



QusmO 



Jil = jr^ — -. ^r sm V 



2Kra{v — ucosv) 



provided r be very great compared with a. When u=v and 

 is very small, 



Kra 



If x be measured along the direction of motion from the 

 centre of the sphere, the retarding mechanical force expe- 

 rienced by the sphere in consequence of the action of the 

 pulse tends to the value 



Km' 2a ' Kar 

 •or to the value Q 2 



ILavt* 



%) — a 



when t, the time since the sphere was started, tends to 

 infinity. I stated this result in a review of Dr. Heaviside's 

 'Electromagnetic Theory' in the 'Physical Review/ July 

 1900, where, however, by some error the result is printed 

 Q 2 /2avt f. 



When a charged sphere is suddenly set into motion with 

 velocity u at the time £ = 0, the force required to maintain 

 that velocity does not cease until t = 2a/(v — u), i. e. until the 



* Phil. Mag. January 1907, p. 124. 



t The printers did not furnish me with a " proof " of the review. 



