3l6 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 52 



IV. MATHEMATICAL THEORY, 



I. NOTATION. 



c = velocity of light. A = yiF {l^ — b-) 



e = charge on each particle. £ = Yz I'^H. 



E = energy of n particles. 

 F=- electrostatic field strength. 

 H = magnetic field strength. 



/= distance from cathode to screen. 

 ni ^= mass of each particle. 



« = number of particles. 



q=zne ^^ charge on n particles. 



p = radius of curvature of path in magnetic field. 



z/ = velocity of particles. 



V= cathode fall. 



X = electrostatic deflection on screen. 

 y = magnetic deflection on screen. 

 AXn = shift of line Xn in Angstrom units or tenth-meters. 



2. EQUATIONS. 



e v^ 

 (i) -^^ ==^; W4(43i); 85(464, 894); W5(56o, 258); Ew3(309). 



Kinetic energy of rays : 



(2) E=^yz nmv^. 



(3) E = '^^^- from definition of q. 



(4) E = neV; from (i) and (2). 



!a ^^ some number greater than one. 

 « = heat, in absolute mechanical units, generated 

 by ;/ particles striking an obstacle. 

 Velocity of rays : 



m 



(I) v=^ 



(6) z/ = a^/2 ^ . — ;froni (2) and (5): Ewi(i84). 



\ q m 



f^H e 



(7) v^^y'^^^ ■ W4(43i); W5(56i, 261); 84(603). 



4Fy 



(8) r=-^; from (7) and (i). 



(9) ^ = y • ,1= Tm3(565). 

 .(II) v=flp-^: Tm3(564). 



Y12) v=J ^^^'-^'\ ' : W5(56i,26i); Si(346); Tm3(564). 



\ 2X VI 



