566 Prof. 0. W. Richardson on a Theory of the 



been taken to be approximately 2730° absolute. These 

 numbers give S\/\ = 1'07 X 10 -5 . This is a minimum value 

 because 3 x 10~ 8 cm. is a maximum value for u. Humphreys'* 

 measurements of a large number of iron lines ranging around 

 X = 4 x 10~ 5 cms. at a pressure of 37 atmospheres give values of 

 S\/\ varying between 2 x 10 ~ 6 and 4 X 10 -7 . Thus the shift 

 given by formula (16) varies from 5 to 25 times that observed 

 experimentally. If we had taken the more probable value 

 1'5 X 10~ 8 cm. instead of the superior limit 3 x 10~ 8 cm. for 

 a, these factors would have been increased to 40 and 200 

 respectively. Thus the difficulty on the electrostatic resonance 

 theory is not to account for the existence of the effect, but 

 to explain why it is as small as the experiments show 

 it to be. 



§ 5. The Motion of the Atoms. 



The fact that the observed displacement is so much smaller 

 than that demanded by the preceding calculation, suggests 

 the advisability of looking further into the assumptions 

 which underlie that calculation. The first point which seems 

 to require attention is the question of the error which has 

 been introduced by neglect of the motion of the atoms. So 

 far the atoms of the gas have been treated as though they 

 were stationary, and effects due to their motion have been 

 left out of consideration. We have supposed that the forced 

 vibrations excited in an atom at any instant were the same 

 as if the atom had remained fixed for an indefinite time in 

 that position ; although, as a matter of fact, the atom must, in 

 general, have just moved from a position where the forcing 

 field was either weaker or stronger. It may be suspected 

 that this is the reason for the discrepancy between the 

 observed and calculated values, but the following discussion 

 of a simple case seems to show that, with the values of the 

 physical quantities which occur in nature, the assumption 

 of instantaneous equilibrium gives a close approximation to 

 the truth. 



The case we shall take as an illustration is the following: — 

 The emitting atom A is supposed to be fixed at the origin of 

 coordinates, and the emitting electron in it to be constrained 

 so that its displacement f at time t is given by £=fo cos i^« 

 The moving atom B is supposed to contain one electron which 

 is initially at rest, its subsequent displacement being denoted 



* Astrophys. Journal, vol. xxii. p. 217 (1905). 



