Kirchhojf's Formulation of the Principle of Huygeus. 2(31 



angular momentum by variation of mass, but must assume 

 a force component in the direction of motion. 



21. The considerations of § 20 make it clear that we 

 cannot look to the electromagnetic energy of the electron 

 itself as the source from which the energy lost by radiation 

 is derived. There remain three possible sources to be dis- 

 cussed : (1) external electromagnetic energy, (2) internal 

 nonelectromagnetic energy of the electron, and (3) external 

 nonelectromagnetic energy ; but the consideration of these 

 sources must be reserved for a future communication. 



In conclusion we may summarize the results of the present 

 investigation as follows : — 



(1) Bohr's hypothesis A is incompatible with the electro- 

 magnetic equations of Maxwell and Hertz, together with the 

 Poynting energy flux for the free gather, at least for the 

 case of uniform circular motion of the electron, and almost 

 certainly for any other motion of translation. 



(2) The hypothesis A can be rendered compatible by a 

 restatement postulating no change in the electromagnetic 

 energy of the electron in spit? of the emission of radiant 

 energy. For neither the acceleration energy, nor the 

 electrostatic energy of an expanding electron, is available 

 as a source of the radiant energy. 



XXIII. On Kirchhojf's Formulation of the Principle of 

 Huygens. By Prof. A. Anderson *. 



rpHE usual method of establishing KirchhofFs formula 

 -A- is to start with a function V(x, y, z, t) of the 

 co-ordinates of a point and the timej that satisfies the 



equation 



d ~ = a 2 V 2 V 

 dP V ' 



and to show that, if t— - be written for t in V, we get 



a 



a new function of x, y, z, r, and t, which satisfies a certain 

 differential equation. A closed surface is then drawn 

 bounding a space at every point of which the differential 

 equation holds, and a point is taken in this space. 

 Both sides of the equation are then integrated throughout 

 the space between the closed surface and the surface of 

 a small sphere whose centre is 0. This leads to an 

 expression for the value of V at the point in the 



* Communicated by the Author. 



