656 BELL SYSTEM TECHNICAL JOURNAL 



mechanics is yet incomplete. It has been applied with success to many 

 problems, but there are situations — those involving the Spinning 

 Electron, for instance — in which the way to apply it is not yet clear, and 

 many theorists are groping. The new theory is still plastic; many 

 minds, perhaps the hands of many experimenters, have yet to work 

 upon it before it is molded into its final shape. 



Classical Mechanics and Wave-Mechanics 

 The underlying principles of "classical" or "Newtonian" mechanics 

 may be stated in several alternative ways, each of which is especially 

 well adapted to certain particular classes of problems. The most 

 familiar of the statements is Newton's own. Unfortunately, it is 

 another and less current which is the most expedient for the problems 

 with which we have to deal. This formulation I will derive from 

 Newton's, by imagining a particular extremely simple mechanical 

 system and using Cartesian coordinates. 



Conceive then a particle of mass m and charge e, moving in an 

 electrostatic field of which the potential is a function U{x, y, z) of 

 the coordinates.^ Its momentum is a vector of which the components 

 are mx, my, mi. These are called the momenta with respect to the 

 coordinates x, y, z, and are designated by px, py, pz. The force upon 

 the particle is the negative of the product of e into the gradient of the 

 potential, a vector of which the components are dU/dx, dU/dy, dU/dz. 

 Newton's way of stating the underlying principles of mechanics 

 then gives: 



dpjdt = pz = - edU/dx; py ^ - edU/dy, pz = — edU/dz. (1) 



Multiplying the members of these three equations by x, y and z 

 respectively, and adding, we find: 



^^^m(^x +y -f- z) ^\dx dt^ dy dt^ dz dtj' ^^^ 



On the left we have the rate of change of the kinetic energy T of the 

 particle as it travels along its path. To interpret the right-hand 



chanics and geometrical optics on the one hand and wave-mechanics and diffraction- 

 theory on the other. I have not yet found this comparison helpful, and therefore 

 cannot present it in a convincing manner. 



1 wish to acknowledge the valuable assistance of my colleague Mr. L. A. MacColl 

 in preparing the mathematical portions of this paper. 



2 The reader will doubtless recognize that I am leading up to the case of the 

 electron traveling in the field of a nucleus; I must therefore recall that in the case 

 of the electron the charge e is intrinsically negative, and that according to the 

 classical electromagnetic theory equation (1) should contain a term describing the 

 reaction of the emitted radiation upon the electron— a term which is omitted in all 

 contemporary atomic theories. 



