238 Mr. J. J. Thomson on the Electric and Magnetic 



wave-length was the length of the tube, and so, by Stokes's 

 law, could not produce a luminous phosphorescence. 



It may be useful to form a rough estimate of the electro- 

 motive force which could be produced by a moving particle. 



By equation (1) we see, if the particle be moving parallel 

 to the axis of x with velocity p, that the greatest value of F 

 at a point distant R from the centre of the particle is 



/l a 2 \ 



Now the greatest value of e, as before, is K x 3 x 10 12 x a 2 , 



hence the greatest value of F at the surface of the particle 

 _ 3x4xl0 12 pq 



)™2 

 5 x 9 x 10 20 



Now during the collision let us represent p by p Q cos kr, where 



-j- is less than the period of vibration of green light ; R must 



be therefore at least 3 x 10 15 ; for a particle of air a is of the 

 order 10" 7 . Substituting, we get 



dF 4x10* . - 



^ = -l5^10^ R ^ SinR ^ 



or the maximum value of -^ is 



at, 



4x3xl0 20 



Now at present we know nothing about p ; but it must be 



very much greater than the mean velocity of the air-molecules, 



which is about 5 x 10 4 ; if we substitute this value for it ; we 



d¥ 

 get the maximum value of -=-- or the maximum electromotive 



force to be about 4 x 10 4 , or about g^oo °f a volt per centi- 

 metre. Now, for sunlight the maximum electromotive force 

 is about 6 volts per centimetre (Maxwell's ' Electricity and 

 Magnetism,' § 793) ; and when we consider the immense num- 

 ber of particles which must be striking the glass at each in- 

 stant, we have no difficulty in conceiving that the magnitude of 

 the electromotive force due to the moving particle may be suffi- 

 cient to cause phosphorescence. To show the rapidity with 



