558 Sir E. Rutherford and Mr. H. Robinsou on Mass and 



ol particle in the portion of the field between the slit and 

 photographic plate is 



d 2 y HE 

 ax* mv 



and dy^ _ ^ _,_ _E 



dx 



a mv Jo 



The final deflexion of the a particle at the photographic 

 plate is then 



E C l2 C x 



Vh=Pah+ — \ ) H-dxdx 



E/^ C*i E C h 



— — -7 \ ocHdx-\ \ (L — x)Kdx. 



mvl iJo mv Jo 



the first integral being taken between the source and the 

 slit, the second between the slit and photographic plate. If 

 we make H constant, the last equation reduces to 



and the expression -^~ — will be recognized as the approxi- 



-'Vh m 

 mate formula for the radius of the circle passing through the 

 source and the slit and corresponding to a deflexion of y u on 

 the photographic plate. 



It will be seen from the above expression that the effect 

 of the variability of the field can be taken into account by 

 deducing a mean effective field which would produce the 

 same deflexion. This mean would be a weighted mean for 

 the fields at all points along the path of the a particle, the 

 weight attached to a value between the source and the 



slit being proportional to p times the distance x from the 



1 

 source, and in the region between the slit and photo- 

 graphic plate proportional to (J2~~x)i the distance from the 

 photographic plate. 



This shows that slight variations of the magnetic field over 

 the regions near the source and the photographic plate will 

 only involve very small corrections in the result; but that it 

 is important to have the field as uniform as possible in the 

 regions close to the slit. This condition was satisfied in the 

 present experiments, the apparatus being so arranged that 

 the slit was situated between the centres of the two large 

 pole-pieces of the magnet. 



