Displacement of Spectral Lines produced by Pressure. 561 

 is displaced. The above equations give 



a 2 = - p (-3i» + | (1-5^) ^j 



where x—x' , y—V f 



u= — — and v = u — — . 



and 



(6) 



Higher terms in %ji\ have been neglected. 



The next step is to calculate the reaction on the vibrating 

 electron due to the induced doublet —a^e, —a 2 i;e, at x\ y. 

 The part of the potential at %' +%, y' arising from this cause 

 is evidently 



where r? = {x -.,/- (1-%)!)*+ (y-y' + arf)». . (7) 



By varying the potential energy we find the force in the 

 direction of x on the negative electron at x +^,y' arising 

 from the 5th electron in the atom B to be 



.^ fZKu _ J^ (1 _ 15M 2) + f*f (i_45u 2 + 144?/-108u 6 ) } . 



In evaluating this expression terms in f 2 have been retained 

 except in the final result. The force due to all the doublets in 

 the atom at B will be obtained by summing up the above 

 expression for all the electrons that occur. Denoting %\ s by 

 L L and 2xf by L 2 , the extra force on the electron at A due 

 to the doublets induced in the atom at B 



= e 2f^J«_?Ll (1 _ 15((2) + & {1 _ 45((2+Uiul _ 108w 6 ) l 

 I l\ T\ >\ J 



... (8) 



This is the effect due to one atom, the effect for the whole 

 of the surrounding gas will be obtained by multiplying this 

 by the number of atoms in the element of volume and inte- 

 grating over all the atoms which occur. If v is the number 

 of atoms in unit volume, we find for the x component of the 

 force 



-2 W 2 i *drS~du l^f - @£ (1-15*0 + ^i(l-±ou 2 



J a J+l ( ? 'l' r i V l 



+ 144w 4 -108^) 



= ?w*J [81*4 1-26^] . (9) 



