384 Mr. E. Edser. An Extension of 



As we are here concerned only with forced vibrations, and there- 

 fore the particular integral of the above equation alone is required, 

 we may write the solution to the above equation 



m i - lp > < 12 >' 



where D x 1 indicates the inverse of the operator D 1? and 



T) I *_ I 



dt~ m dt Ti 2 



Similarly the equation to the atomic vibration along the axis of 

 the molecule will be of the form 



The particular integral of this equation may be written 



(Dr'P). (13), 



where Do" 1 is the inverse of the operator D 2 , and 



D 2 ~'*4.xA+ IT 



rf^m #~ T./ 



T 2 = 27T v /(K 2 m). 



It has been assumed that the coefficient of viscosity is the same 

 for both kinds of vibration. 



Now the component of 2pv x contributed by the two atoms com- 

 posing the molecule under consideration will obviously be obtained 

 by differentiating with regard to time, the expression 



Eliminating and AZ by the aid of (12) and (13), this expressioi 

 becomes 



^21 {sin 2 (Dr 1 ?) + cos 2 (D a -'P) }. 



1Yl> 



Hence employing precisely similar reasoning to that used in 4, 

 we finally determine that 5Zqv x will be obtained* by differentiating 

 with regard to time the expression 



* [Added June 13. The possible presence of free ions, considered merely as 

 isolated charged atoms, is not considered capable of materially affecting the dis- 

 persion formula for light waves. This would follow no less from theoretical con- 

 siderations than from sucli facts as that the absorption of dilute sulphuric acid is 

 not appreciably different from that of pure water. For very long electrical waves 

 the case would be different.] 



