CONTEMPORARY ADVANCES IN PHYSICS 183 



another of the "permitted" momenta defined by equations (43) and 

 (44). 



Examining equation (44), one sees how this definition of the per- 

 mitted momenta may be stated. The quantity on the left of (44) is 

 the product of the momentum of the particle, by the distance which it 

 traverses each time it performs its cycle. '^ This product must be 

 equal to an integer multiple of the Planck constant //. 



Now the quantum-theory of the atom developed fifteen years ago 

 by Bohr, Sommerfeld and W. Wilson — the first and greatest of the 

 forward steps in the contemporary conquest of the problem of atomic 

 structure — was based on the assumption that an electron perfomiing a 

 cyclic motion must perform it in such a way, that its momentum 

 conforms to a condition of which equation (44) is but a special case. 

 This is the condition alwavs written thus: 



/ 



pdq — 7ih, w = 1, 2, 3 . . . (45) 



If the electron is oscillating to and fro in a straight line through a 

 position of equilibrium, q stands for its distance from that position and 

 p for its momentum, and the integral is taken once around a complete 

 oscillation. It is evident that (44) is the special form of this equation 

 for the case in which the force acting on the electron is vanishingly 

 small until it hits the wall and then suddenly becomes enormous. If 

 the electron is revolving in an orbit in two or three dimensions, there 

 are two or three equations like (45) all postulated at once; but I shall 

 not take up such more complicated cases. 



Summarizing the outcome of this section in a phrase: if we associate 

 waves of wave-len»th X with corpuscles of momentum hi\, and stationary 

 waves in an enclosure with corpuscles flying hack and forth between its 

 walls, then the condition that the waves must fulfil to form a stationary 

 system is equivalent to the quantum -condition imposed upon the corpuscles. 



This is an illustration of wave-mechanics. How extraordinarily 

 fruitful and valuable such comparisons have proved in the hands of 

 Louis de Broglie, of Schroedinger, Rose, Fermi and Sommerfeld — to 

 name only a few — I have shown in part, in earlier issues of this journal. 

 Here it must suffice to say that Schroedinger developed the principle 

 into a form suitable for predicting the stationary states of atoms; Bose 

 constructed out of it a competent theory of radiation in themial equili- 



'^ It travels a distance d in the forward sense with a momentum p, and then an 

 equal distance in the backward or negative sense with a momentum of equal amount 

 but reversed sign, so that the total product of distance by momentum is 



t>d + (- p)(-d) = 2dp. 



