Displacement of Spectral Lines produced by Pressure. 565 

 absence of other matter, evidently 



19 9 9 



■±1^^ _ e" 

 X 2 m\i ' 



(14) 



Calling BX the increase in wave-length produced by the 

 medium, we have 



~= 1 ,;° e2 3 V 2 [8L 1 4l-26L 2 /« 3 ]. . . (15) 



Neglecting the second term and replacing 1^ by fju 2 — l/lwo, 

 this becomes 



X 67rV« 3 l ; 



With the exception of a all the quantities in equation (16) 

 are known with considerable accuracy. That a is indefinite 

 has already been pointed out, but there is little doubt that 



3 x 10 " 8 may be taken as an upper limit for it (cf. Jeans's 



4 Dynamical Theory of Gases,' chap. xix.). 



The theory may now be tested by seeing whether it affords 

 an explanation of the shift of spectral lines observed when 

 they are produced in the arc in a gas at high pressures. 

 The only factor in equation (16) which involves the pressure 

 is fi 2 — 1 , which is proportional to the pressure. Hence SX 

 will always be proportional to the pressure. It will also be 

 noticed that SX is always positive, so that the shift is always 

 towards the side of longer wave-length. Although a number 

 of interesting relationships between the displacements of the 

 different lines have been observed, these two, that the dis- 

 placement is in the direction of greater wave-length and is 

 proportional to the external pressure, appear to have been 

 established experimentally with greater certainty than the 

 others. 



The next question is as to whether the magnitude of the 

 calculated effect is great enough to account for the observed 

 displacements. The minimum value of the shift per atmo- 

 sphere for a line of wave-length X = 4x 10~ 5 cm. on the basis 

 of the preceding theory will be obtained if the following 

 values are substituted for the various constants in equation 



(16) : — = l'8xl0 7 , ^ 2 -l = 5'9xl0-\ * = 3xl0- 10 s 



y mc 



c = 3 x 10 10 , and a^3 x 10 8 . The value of //, 2 — 1 is the value 

 of this quantity at the temperature of the arc. This has 



