506 



SCIENCE 



[N. S. Vol. LI. No. 1325 



but of very little fundamental significance. 

 Eecently, however, tliis data has furnished 

 e^ddenee of great importance as to the struc- 

 ture of matter and the mechanism of radi- 

 ation. This is largely due to two funda- 

 mental laws: Planck's law of radiation in 

 quanta, and Bohr's law of constant angular 

 momenta. 



According to the first law the amount of 

 energy radiated from an atom is proportional 

 to the frequency at which it is radiated, the 

 constant h being the factor of proportionality. 

 In other words the atom changes from one 

 state into another when it radiates, and the 

 difference between the energy it possessed be- 

 fore and after the radiation equals the fre- 

 quency of vibration multiplied by h, thus : 

 ;». = JTi — W,. 



According to this conception the terms in 

 the combination law represent the energy of 

 the atom in its various states of equilibrium 

 divided by h, plus, of course, an additive con- 

 stant. 



The complete expression of the law is 

 rhv ^Wi — W,, 

 where t denotes any whole number, but spec- 

 trum lines cori-esponding to values of t greater 

 than 1 have not been observed. They may be 

 very faint, except, perhaps, in the infra red 

 spectrimi. The chance of t's being greater 

 than unity (in black body radiation) is verj' 

 small for high frequencies of vibration. 



Extraordinary success has attended the ap- 

 plication of Bohr's theory to the case of a 

 single electron revolving about an atomic 

 nucleus. In this theorj' the angular mo- 

 mentum of the electron equals some whole 

 number multiplied by a universal constant, 

 h/^TT, thus 



■mi'a = T{h/2T). 



The value of the universal angular mo- 

 mentum may be regarded as chosen to fit the 

 facts, i. e., to give the correct value for the 

 Eydberg fundamental frequency, or we may 

 assume, with William Wilson, that a certain 

 integral equation, occurring in tlie theory of 

 quanta, expressed in generalized coordinates, 

 namely, 



/: 



[ = T7i, 



applies to the revolving electron. Since the 

 force acting on the electron is a central force, 

 the angular momentum p is constant, and, if 

 we take the integral over a complete period 

 during which the angle q varies by 27r, we 

 have 



2irmva = rh. 



As an example of the application of Bohr's 

 theory let us consider the values of the Eyd- 

 berg constant for hydrogen and for ionized 

 helium. In each case a single electron revolves 

 about an atomic nucleus. The theory assumes 

 that the attraction between them is given by 

 Coulomb's law, and from this together with 

 the two laws mentioned above the various un- 

 known quantities can be calculated, including 

 the frequency of the emitted radiation. 

 Since the helium nucleus is nearly four times 

 as heavy as the hydrogen nucleus, the common 

 center of gravity, about which the electron 

 and the nucleus revolve, is slightly nearer 

 the center of the helium nucleus, than is the 

 case with hydrogen. Bohr predicted that on 

 account of this fact certain lines in the hy- 

 drogen spectrum should have wave-lengths 

 slightly longer than certain lines in the en- 

 hanced helium spectrum, and experiments 

 prove this to be true. Further, the ratio of 

 the mass of the electron to that of the hydro- 

 gen atom, and the ratio of the charge to the 

 mass of the electron can be calculated from 

 accurate measiu-ements of the wave-lengths 

 of these lines. The values of these ratios 

 calculated from data obtained by Pashen are 

 very nearly the same as the values deduced 

 from other methods of experiment. In fact^ 

 granting the general truth of the theory, they 

 are, perhaps, the most accurate estimates we 

 have of these important ratios. 



The Eydberg constant for the spectra of 

 ordinary helium, in which we may suppose 

 that there is one electron revolving in an inner 

 ring about the nucleus, appears to be slightly 

 less than that for the spectrmn of ionized 

 helium. Bohr's theory would seem to account 

 for some such decrease in the value of the 

 constant, for the influence of this electron on 



