140 VARIABLE MASS [CH. xiv. 



that the magnetic and electric fields are superposed in 

 the same direction, their lines of force being coincident. 



Under these circumstances the particles will 

 describe the beginning of a spiral, being curved 

 round the magnetic lines and deflected along the 

 electric lines, until they escape from the combined 

 field and travel in their deflected direction to the 

 photographic plate as target. The slow-moving 

 particles, if any, will presumably strike the bounding 

 surfaces and be stopped, only the very rapid ones 

 will reach the plate; which is protected from alpha-rays 

 by aluminium foil, while the undeflected gamma-rays 

 would probably mark the direct line of fire, and thus 

 give the geometrical "origin" of the curve or trace 

 which would be found on the plate after long ex- 

 posure, a curve which we may write yf(^)-> where 

 y signifies the electric deflexion and x the magnetic. 



This method may be called the method of the 

 crossed spectra. 



The theory can then be expressed somewhat as 

 follows : 



Let the measured coordinates of any point in the 

 spectrum, as developed on the photographic plate, be 



y ' x being the magnetic deflexion, 

 and y the electric. 



These deflexions may be taken to represent 

 inversely the radii of curvature r and r f produced 

 in the rays by the respective fields H and E, 

 in accordance with the simple mechanical equations 



mu 2 , mu 2 



TT , -r, 



u.e}u, and 7- = Le, 



T 



if. XT fJLtiU U 



wherefore 



y r E 



