CONTEMPORARY ADVANCES IN PHYSICS 105 



in which c stands for the speed of light in vacuo; ^ for vjc; and Wo 

 for a constant. The ratio of E to c^ is the function of v and mo which 

 this equation defines, and is denoted by m and called the mass of the 

 particle: it is in this sense that mass and energy are equivalent. 

 We may (mentally) divide the mass of the moving particle into two 

 terms mo and {ni — mo), and the energy into two terms moC- and 

 (m — mo)c^. We may further call mo the rest-mass and moc"^ the 

 energy associated with the rest-mass; and we may call (m — n?o)c^ 

 the kinetic energy and (m — mo) the mass associated with the kinetic 

 energy or the extra mass due to the motion of the particle. Such will 

 be the terminology used in these articles, although this definition of 

 kinetic energy is only approximately the same as the classical and 

 familiar one.^ 



Returning to the argument about the transmutation of light into 

 electrons, or more precisely, of a photon into an electron-pair : conserva- 

 tion of mass and energy is attainable, for the two electrons may have 

 such speeds — call them ^\C and ^iC — that the sum of mo(l — ^i')~'^''^c'^ 

 and mo(l — ^'^)~^^H^ is equal to the energy hv of the photon. But 

 the demand for conservation of momentum makes apparently serious 

 trouble. If we assume that a photon voyaging through the depths of 

 space suddenly converts itself spontaneously into a pair of electrons, 

 and if then we attempt to impose both conservation of momentum 

 and conservation of energy, the equations lead us straightway into an 

 inescapable muddle, in which the original assumptions contradict each 

 other. We are driven therefore to infer that the imagined process is 

 impossible. But this seeming catastrophe of the theory turns out to 

 be a blessing. What is observed is not after all the transmutation of 

 a photon in the depths of empty space, but a process which occurs in 

 the depths of plates of lead and other heavy elements. If we suppose 

 that such a transmutation occurs near to a massive nucleus, then this 

 may receive some of the energy and some of the momentum of the 

 photon; and the equations show that the momentum which it takes 

 may be quite sufficient to permit the process to occur, while the 

 energy which it takes is so small that for practical purposes we may 

 still pretend that the whole of the energy of the photon is divided 

 between the electrons (though we certainly should not forget about 

 the small fraction which goes to the nucleus). All the principles are 

 thus fulfillable: conservation of charge requires that there should be 



^ The classical definition of kinetic energy is {'\./2)inv^; the present or relativistic 

 definition, viz. {ni — mo)c^, is an infinite series of which the first term is identical with 

 the classical definition. The difference between the two definitions increases as the 

 speed of the particle increases, but so far as I know there has not yet been an actual 

 case in which it is of practical importance. 



