Displacement of Spectral Lines produced by Pressure. 569 



importance for the present investigation are therefore those 



n-\- 1 

 which involve cos /3(r — r 2 ) 4- 9 ir. 



The behaviour of series (22) is best illustrated by con- 

 sidering a numerical example such as might occur in nature. 

 The greatest discrepancy between the cases of the fixed and 

 moving atoms will arise when the moving atom is displaced 

 from a distance equal to the free path in a direct line until it is 

 in contact with the fixed atom. The mean free path at the 

 temperature of the arc and a pressure of 10 atmospheres will 

 be about 10 ~ 5 cm., so that r = 10_5 cm. r 1 is determined by 

 the dimensions of the atom, and is, as we have seen, nearly 

 equal to 3 x 10 -8 cm. We shall take v = 10 5 cms. per sec, 

 which is very near the true value under the conditions 

 described, and, as illustrative numbers, /3=5xl0 10 and 

 y=6 x 10 1( >. The last two numbers correspond to vibrations 

 of optical wave-length 3*77 X 10~ 5 cm. and 3*14 xlO -5 cm. 

 respectively. With these numbers the first series in (22) is 

 equal to 



\ A-^ x 4-05 x 10i 2 [cos /3(r -r{) + '0091 sin )S(r — ^) 



-•000122 cos /SOo-rO- -00000205 sin£(r -r 1 )+ . . .] 



It remains to consider the unintegrated part of (22). The 

 dotted curve in fig. 2 is supposed to represent the graph of 



y— +(/3 + ry) 2 " n r- n_1 . The integrand is evidently a sinuous 

 curve bounded by the two dotted lines as shown in the figure. 

 Since the areas below the axis of r are to be reckoned nega- 

 tive, the value of the integral cannot be greater than the 



