CONTEMPORARY ADVANCES IN PHYSICS 661 



interconnections between the classical mechanics and the new, which 

 such a procedure might mask. I can refer the reader to Schroedinger's 

 own attempts to interpret W, some of which will figure in the last 

 section of this article; or I can invite him to grow his own conception 

 of W. This last in fact is what I will do. 



Now if it is proposed to regard the fundamental dynamical equation 

 (13) as the description of a family of wave- fronts perpetually wandering 

 through space with the speed E/V2m(£ — V) — and this is precisely 

 what is proposed — then the description is obviously incomplete; for 

 it omits to state the wave-length of these waves or the frequency of 

 whatever be the vibrating thing which manifests itself by the waves, 

 and indeed if the frequency were separately stated there would be no 

 place for it in such an equation as (13). That equation, in fact, may 

 be compared with the bare statement that the ripples traveling over 

 the water of a pond from the place where a stone fell in are circles 

 expanding at a given speed, or that the sound-waves proceeding 

 through air from a distant source are plane waves traveling about 

 340 metres per second. To describe the ripples or the sound-waves 

 completely it is essential to discover some ampler equation; a like 

 extension is necessary here. 



In treating familiar vibrating mechanical systems, stretched strings 

 and tensed membranes and the like, it is customary to employ the 

 general Wave-Equation 



in which V^ stands for the Laplacian differential operator (page 671); 

 ^ stands for the sidewise displacement of the string or distortion of 

 the membrane or whatever it is that is transmitted as a wave; and 

 u for the speed of propagation of the wave. It is furthermore cus- 

 tomary to supplement this by the equation 



d'^^/dt^ = - 47r2,/2^, (17) 



in which v stands for the frequency of the vibration; combining 

 which with (16), one obtains 



47r2v2 4^2 



V2^ -f yfe2^ = V^vEr + ZZLl ^ = V2^ + -^ ^ = 0, (18) 



U" X- 



in which X = u/v stands for the wave-length of the wave-motion. 



All of these matters will be developed at length in the following 

 section. At this point it is necessary only to return to the description 



