Sbptember 28, 1917] 



SCIENCE 



301 



the slope of the curve at each intersection 

 increases towards a finite limit as r ap- 

 proaches zero. This slope df/dr is the re- 

 storing force per unit displacement, and 

 its square root determines the natural fre- 

 quency of oscillation of the electron.' We 

 thus have a picture of a system which, con- 

 sistently with recognized principles of me- 

 chanics and electromagnetics, would give 

 a series of spectral lines analogous to the 

 series which are known for various elements. 

 The limiting value of df/dr as r approaches 

 zere determines the limiting frequency of 

 the series. In the case of Balmer's hydro- 

 gen series this limiting frequency is equal to 

 one foui'th of the fundamental frequency 

 which Eyd'berg has found associated with 

 the series of a large number of elements. 

 It has been argued that the existence of 

 this fundamental frequency speaks for sim- 

 ilarity of constitution of different atoms. 

 Is it not simpler to assume that it is char- 

 acteristic of the one thing which is common 

 to all atoms emitting light, namely, the elec- 

 tron? 



The condition which we have imposed 

 regarding the slope of our curve at its in- 

 tersections does not determine the area 

 which will lie under any section of it. As 

 the curve is drawn, the area under the r 

 axis between r^ and r„, r^ and rj, etc., is 

 greater than the area above the axis. In 

 other words, the potential energy of the 



3 It 'will of course be understood that, owing to 

 its much smaller mass, it is the electron that os- 

 cillates and not the positive particle. I am refer- 

 ring above to oscillations in the line of centers. 

 In general the oscillations of an object which is 

 held in space in a fixed position by constraints 

 which differ in different directions will be re- 

 solved by either mathematical or physical analysis 

 to give three frequencies corresponding to the 

 three axes of constraint. If the constraint along 

 two of these axes is the same the corresponding 

 two frequencies wiU be identical. I venture to 

 offer this as an explanation of the well-known fact 

 that the lines of a series spectrum occur often as 

 pairs or triplets. 



system increases as the positive particle 

 is brought from r^ to r„, from r, to r^, and 

 so on. If now we fix the form of the curve 



so that I /(iris proportional to the differ- 

 ence between the values for r„ and rm of 

 {df/dry^, the potential energy of our sys- 

 tem at any point of equilibrium is a linear 

 function of the frequency which is char- 

 acteristic of that position of equilibrium. 

 We then have what is, to my mind, a very 

 suggestive explanation of the Einstein 

 photo-electric equation. If an electron 

 moving with a given velocity meet a posi- 

 tive particle, the latter would penetrate 

 the electron field to one of the positions 

 of equilibrium, and the electron would os- 

 cillate with a frequency depending solely 

 upon the equilibrium position it reaches 

 and therefore upon its original kinetic en- 

 ergy. The higher the original velocity, the 

 higher the frequency it is capable of excit- 

 ing. On the other hand, if we assume the 

 presence of atoms in which the electrons 

 are in various positions of equilibrium 

 with respect to the positive particle, and 

 these atoms are subjected to light of a given 

 frequency, the electron which possesses this 

 as its natural frequency will oscillate with 

 greater and greater amplitude until it is 

 able to leave its position of unstable equi- 

 librium and will then be ejected from the 

 atom, acquiring a kinetic energy equal to 

 the potential energy of its original position. 

 On our assumptions the relation between 

 frequency and velocity will be quantita- 

 tively that given by the Einstein equation. 

 In the time which has been allotted to me 

 I can not further elaborate the^e points, 

 but I hope that I have succeeded in ma- 

 king it seem plausible that some model of 

 a static atom, perhaps only roughly re- 

 sembling the one that I have outlined to 

 you, may be expected to give at least as 

 satisfactory an explanation of the phe- 

 nomena of spectroscopy, and of the rela- 



