EQUATIONS OF ELECTRON MOTION 177 



upon the special forms which the Hamiltonian function and equation (45) 

 assume in those coordinates. Hence the proof already given applies imme- 

 diately to the present general case. 



Similar remarks apply also to the case in which // does not involve the 

 time explicitly, and in which we write 



IV = S - Et, 



where S is the complete solution (without the additive arbitrary constant) 

 of the equation 



Hix\ x\ .v^ dS/dx\ dS/dx^ dS/dx^) = E. 



Bibliography 

 Works dealing with Newtonian particle dynamics: 



P. Appell, Traite de Mecanique Rationnelle, Vol. 1, 5th ed., Paris, Gauthier-Villars, 



1926; 

 E. T. Whittaker, A Treatise on the Analytical Dynamics of Particles and Rigid Bodies, 



3rd ed., Cambridge University Press, 1927. 



Works dealing with the fundamental physical aspects of electron motion 



N. R. Campbell, Modern Electrical Theory, 2nd ed., Cambridge University Press, 1913; 

 J. H. Jeans, The Mathematical Theory of Electricit}- and Magnetism, 5th ed., Cambridge 



University Press, 1925; 

 H. A. Lorentz, The Theory of Electrons, 2nd ed., Leipzig, B. G. Teubner, 1916; 

 0. W. Richardson, The Electron Theor\- of Matter, Cambridge University Press, 1914. 



Works dealing with relativistic dynamics 



A. S. Eddington, The Mathematical Theorv of Relativitv, 2nd ed., Cambridge University 



Press, 1937; 

 W. PauH, Relativitatstheorie, Leipzig, B. G. Teubner, 1921; 

 H. Weyl, Raum-Zeit-Materie, 4th ed., Berlin, Julius Springer, 1921. 



Works dealing with the Calculus of Variations 



G. A. Bliss, Calculus of Variations, Chicago, Open Court Publishing Company, 1925; 

 E. Goursat, Cours d'Analjse Mathematique, Vol. Ill, 3rd ed., Paris, Gauthier-Villars, 

 1923. (See also Vol. I, translated by E. R. Hedrick under the title A Course 

 in Mathematical .Analysis, Ginn and Co., 1904.) 



Works on the tensor calculus 



P. Appell, Traite de Mecanique Rationnelle, Vol. 5, Paris, Gauthier-Villars, 1926; 

 .\. S. Eddington, The Mathematical Theory of Relativity, see above; 

 J. A. Schouten and D. J. Struik, Einfiihrung in Die Neueren Methoden der Differential- 

 geometrie, Vol. I, Groningen, P. Noordhoff, 1935. 



