[ 595 



LXVU. On Non-Radiating Atoms. 

 By Sir Joseph Larmor *. 



IS it possible to have orbital systems of electrons which 

 do not radiate unless when disturbed ? To the first 

 order, which neglects atomic size compared with lengths of 

 wave, the condition of absence of radiation is (' JEther and 

 Matter,' 1900, § 153) that the vector sum %ev, where v is 

 acceleration of the electron e, must vanish. It might appear 

 that, when pushed to the second order, an infinite number 

 of other conditions would be required in order to annul 

 radiation in all directions. But that seems not to be so. 

 The additional conditions are that for any direction of 

 radiation, say that of x, the quantities Xeyx and %ezx shall 

 vanish. These are obviously satisfied for every direction if 

 for any one set of coordinates (x, y, z) the nine expressions 

 of this type, including ^e'xx, Xe'yy, Xezz, all vanish. 



The twelve conditions in all are, in fact, parallel to those of 

 astatic equilibrium (cf. Routh's ' Statics '). It may be noted 

 that the latter nine involve, by additions, that the magnetic 

 moment of the atom remain fixed in magnitude and direction : 

 as a consequence, if the atom has a permanent magnetic 

 moment, any rotational motion which changes the direction 

 of that moment will be obstructed and resisted by radiation. 

 This may preclude the existence of a permanent moment : 

 or it may have a bearing on equipartition troubles. Atoms, 

 for instance of permanent symmetry with regard to three 

 planes, can readily be imagined for which the radiation is 

 residua], of the third order, in fact is so small that it ranks 

 with such residual effects as are masked by electrodynamic 

 relativity. An atomic orbital structure could subsist only 

 at or near one of this set of configurations that do not 

 radiate : by intense shock it can perhaps be imagined as 

 pushed over from one of them into another, with loss of 

 energy that goes in part into the disturbing system, and in 

 part into radiation. 



* Communicated to the British Association, Sept. 1921. 



