SOME coxTr.Mi'oK.tKy .inr.ixcr.s i.\ riivsics ni m)? 



This st't of natural fri-(|Ufiuii>s whitli hartled all the etTorls to 

 fxplaiii it, the set oonstituliiiK the two siiu[)iest of all spectra (the 

 siH'ctriini of atomic hyiIro^;eii .iiul the spectrum of ioni/ed heliumV 

 is given by the formula 



. = r('\-\) .-(6) 



the different lines being obtained by assigning different integral 

 values to the parameters in and n; lines corresponding to values of m 

 ranging from 1 to 5 inclusive, and to values of n ranging from 2 to 40 

 inclusive, have already been obser\ed, and there is no reason to doubt 

 that lines corresponding to much higher values of m and n actually 

 are emitted, but are too faint to be detected with our apparatus. 

 The constant R has one value for hydrogen, another almost exactly 

 four times as great for ionized helium. 



Here, then, is the problem in its simplest presentation : How can a 

 model for a hydrogen atom be constructed, which shall emit rays of 

 the fretpiencies given by the formula ((>), only these and no others.'' 

 The obvious answer "By constructing a mechanical framework 

 having precisely these natural frequencies" is practically excluded; 

 it seems infeasible. Something radically different must be done. 

 The achievement of Niels Bohr consisted in doing a radically different 

 thing, with such a degree of success that the extraordinary divergence 

 of his ideas from all foregoing ones was all but universally condoned. 

 I do not know how Bohr first approached his theory; but it will do 

 no harm to pretend that the manner was this. 



Look once more at the formula for the frequencies of the h\drogen 

 spectrum. It expresses each frequency as a difference between two 

 terms, and the algebraic form of each term is of an extreme sim- 



the hydrogen spectrum is this, that it specifies infinitely many frequencies within 

 finite inter\'als enclosing certain critical values, such as R, 4H, 9R, and so forth. 

 I'oincari' is said to have proved that the natural frequencies of an clastic medium 

 with a rigid Ixjundary cannot display this feature, so long as the displacements are 

 governed by the familiar equation (ftfr rf/- = *V-«. For a membrane this equation 

 is tantamount to the statement that the restoring-force acting upon an element 

 of the membrane is proportional to the curvature of the membrane at that element. 

 Kitz was able to show that the natural frequencies of a square membrane would con- 

 form to the formula (6), »/ the restoring-force upon each clement of the membrane, 

 instead of l)eing profmrtional to the curvature of the membrane at that element, 

 delJended in an exceedingly involved and artificial manner ui)on the curvature of 

 the membrane elsewhere. He ajjologized abundantly for the extraordinary character 

 of the pro(x-rties with which he had l)een obliged to endow this membrane, in order 

 to arrive at the desired formula: but his procedure might have proved unsuspectedly 

 fruitful, if Bohr's interpretation had not supplanted it. 



