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



well-marked displacement towards the region of longer wave- 

 length. The existence of an effect of this kind was first 

 placed beyond doubt by the work of Humphreys and Mohler*, 

 and we owe most of our knowledge of it to their investigation 

 and the subsequent papers of Humphreys f. 



The present paper deals with the theory of this second 

 non-selective effect of pressure. Although the calculations 

 which follow do not, on account of the limitations imposed 

 by our ignorance of atomic structure, lead to an exact 

 numerical evaluation of the effects, they, nevertheless, afford 

 results of such a definite nature as to make it extremely 

 probable that the explanation of the phenomena is to be sought 

 along the lines indicated. 



§2. Outline of the Method. 



Briefly stated, the theory to be developed attributes the 

 displacement of spectral lines produced by pressure to the 

 effect of sympathetic vibrations occurring in the surrounding- 

 atoms. The fact that an atom A is emitting light shows that 

 it is surrounded by an alternating field of electric force. 

 This alternating electric field will produce forced vibrations 

 of equal period and, under certain conditions, of like phase 

 in neighbouring atoms. The electric field due to the forced 

 vibrations will react on the emitting electron in the atom A, 

 and, as will be shown, in such a way as to increase the period 

 of the latter. It will be necessary, then, to calculate the 

 reaction at A due to the forced vibrations set up in an atom 

 at B by a given vibration at A, to sum this up for all the 

 atoms B which occur, and to find .the effect of the resultant 

 reaction on the period of A. 



§ 3. The Reaction at A. 



If we are to arrive at results which can be tested numeri- 

 cally it will be necessary to forego generality to the extent 

 of making some hypothesis about the mechanism of the 

 emitting system in A. We shall suppose that the spectral 

 lines are emitted by a vibrating electric doublet within the 

 atom A, as this hypothesis appears to combine simplicity and 

 general applicability to the greatest extent. To be more 

 precise, we shall assume that the electrons emitting light are 

 oscillating about equilibrium configurations under forces 



* Astrophys. Journal, vol. iii. p. 114 (1896). 



f Ibid. vol. iv. p. 249 (1896) ; vol. vi. p. 169 (1897) ; vol. xxii. p. 217 

 (1905) j vol. xxiii. p. 233 (1906). 



