274 Prof. L. Natanson on the Molecular Theory 



It will save needless repetition if it is understood that ira 

 obtaining these results no approximation has been employed; 

 they are exact consequences of the initial equations from 

 which they are derived. The importance of a distinction 

 between exact relations and those which (at great distances- 

 from the vibrator) hold true approximately does not appear 

 to be always fully appreciated. 



§ 3. Suppose we had a material medium, that is an immense 

 collection of very minute, equal, simple linear vibrators dis- 

 tributed at random through space. Consider the surface of 

 the medium as plane ; taking it for the plane z = 0, refer 

 everything to rectangular axes «i', ?/, z, the positive part of z. 

 being measured vertically upwards through the medium. 

 Below the boundary plane conceive a void region extending 

 to infinity in the negative direction of the axis of z. Suppose 

 also that the material medium is unlimited in the positive 

 direction of the axis of z. 



Let an infinite train of homogeneous electromagnetic waves- 

 (proceeding from vacuum in the positive direction of the 

 axis of z) be externally incident on the surface of the medium. 

 Suppose the components of its electric and magnetic field to> 

 be simply periodic with respect to z and t and write them in. 

 the form 



EW=AW<? n ^ a * + P\ Ef = 0, El 1} = 0, (1) 



H^O, Ry = ^J^-«-~+ri, Hi 1} = 0. (2) 



Here p and A (1) are constants; n represents as before the- 

 frequency of transmitted vibrations. In what follows we 

 propose to give, to the disturbance defined by (1) and. (2), 

 the name of incident or primary wave. 



According to the present view, the primary wave is con- 

 ceived to get undisturbed across the aggregation of molecular 

 vibrators ; its progress continues in fact over indefinite depths- 

 in the medium without any mitigation or attenuation what- 

 ever. The only effect of the medium is to superimpose, on- 

 the field propagated with the incident wave, a secondary field 

 arising under the joint operation of the vibrators. From 

 each vibrator that is struck by waves travelling along in the- 

 medium, an infinite sequence of secondary waves is pro- 

 ceeding : when all these combine, a resultant tumultuous- 

 secondary radiation becomes established. The steady state- 

 is regarded as that which will not be further disturbed 

 owing to adjustment and readjustment of the primary wave 



