8 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 65 



But, as we have just seen, the mutual interference of these orbits, 

 even if they each contained several electrons, would make their indi- 

 vidual persistence impossible, and so the system would at once drift 

 into chaotic motion. Let us therefore consider what modifications 

 the supposition that there is this chaotic motion in the atom would 

 make in Langevin's results. 



It would not affect that part of the superstructure of his theory 

 which deals with the orbits altogether statistically, for chaotic 

 motion, from a statistical standpoint, is certainly equivalent to motion 

 in a great many separate orbits whose axes are uniformly distributed 

 in three dimensions. But for those parts of his work which deal with 

 the Zeeman effect, or presuppose in any way the existence of sepa- 

 rate definite periods of vibration in the atom, as, for example, where 

 he says that the constancy of wave-lengths of spectrum lines shows 

 that the interior of the atom is not much affected by temperature 

 changes — for those parts, the assumption of motion in separate orbits 

 is essential, and those parts would therefore have to be abandoned. 



Again, in the case of either supposition, while the difficulty about 

 accelerated motion of classical electrons being accompanied by con- 

 tinual radiation may be obviated by supposing that the atom contains 

 so large a number of electrons that the compensation among their 

 chance motions reduces the average radiation to an inappreciable 

 amount, we still have the difficulty that for these compensations to 

 be even approximately complete the number of electrons would have 

 to be much greater than the number actually believed to be present 

 in many atoms : this difficulty is thus similar to one that Thomson's 

 theory encounters. Apart from this difficulty of the allowable 

 number of electrons, the theory labors under the following dilemma : 

 If the internal compensation is not complete, the radiation will be 

 continual and promiscuous and will rapidly exhaust the atom's store 

 of energy : if the compensation is complete, it does not seem possible 

 to imagine any additional mechanism in such an atom that could 

 explain the phenomena of radiation. We may notice also in passing 

 that chaotic motion seems to be quite inadmissible from a chemical 

 standpoint. 



But in spite of the existence of such substantial objections to his 

 fundamental assumption, even when it is replaced by the less objec- 

 tionable one of chaotic motion, the superstructure of Langevin's 

 theory is in excellent accord with the facts. The circumstance, then, 

 that the substitution of the magneton here described for Langevin's 

 electron in orbital motion not only removes all of the difficulties just 



