444 SCIENCE PROGRESS 



sponding to the arc temperature (say 2730 abs.). The value of 

 (/i 2 — 1) is then reduced to one-tenth of its previous value, and, 

 with this modification, the theory gives k = 3, i.e. the sur- 

 rounding medium must be regarded as extending to within a 

 distance of three times the molecular radius from the vibrating 

 molecule; but at this temperature the average distance apart 

 of the molecules is about sixty times the molecular radius. It 

 seems, then, as though the above estimate of k is much too 

 small, and if a larger value be substituted in the formula for d\ 

 the displacement obtained is much smaller than the observed 

 value. 



Moreover, if this theory were true, the displacement should 

 vary with the nature of the gas surrounding the arc. In fact, 

 for a gas //. is nearly unity, and (fi— 1) varies as the density 

 (Gladstone and Dale's Law), so that the displacement obtained 

 should be proportional to the density of the surrounding gas. 

 For example, in the case of arcs in atmospheres of air and 

 carbon dioxide at the same pressure, the displacements should 

 be respectively in the ratio of 2:3, whereas Rossi was unable 

 to obtain any differences in the displacements in the two cases 

 beyond the limits of experimental error. Gale and Adams did 

 indeed find an effect in the case of the enhanced lines of titanium, 

 but it was in a direction opposite to that given by the above 

 formula. Another objection to the theory is that experiment 

 -shows that the displacement varies accurately as the pressure. 

 Now, for a gas (/x 2 — 1) is proportional to the density or pressure, 

 and k 3 may be expected to vary approximately inversely as the 

 pressure, so that this theory requires a displacement varying 

 as the square of the pressure. Further, other things being 

 equal, dx. is proportional to \ and this has been disproved by 

 experiment. 



It must be concluded that although the effect of the surround- 

 ing medium pictured by Larmor and Fitzgerald must exist, the 

 resulting displacement is many times smaller than that experi- 

 mentally observed, and that an explanation of the facts must be 

 sought in another direction. 



A different theory which was advanced by Humphreys 1 

 attempted to explain the effect by means of the mutual inter- 

 action of atomic magnetic fields, in a manner analogous to the 

 Zeeman effect. It is well known that the periods of the radia- 



1 Astroph. Journ. 23, p. 233, 1906. 



