( 732 ) 



values of Q". We shall therefore put </i = —A, and tj^ = h,, so that 



art: 



<i.x'^=x — rrr;e I -^ e dz e I ^: e dzil) 



- I'l Ih 



§ 5. In etfeeting these integrations we have to distinguish whether 

 or no the point P, for which we intend to determine the state 

 of radiation, lies between the two just mentioned tangent planes. First 

 taking the latter case, the second integral of (7) is zero for positive 

 values of z', whereas in the first case we may take h, instead of 

 z' for the upper limit. Integration by parts gives 



fö''By 'tv,, /9^ÏP.' "tv/ .2jt rdiS,- 'tv-, 

 J dz" I ös' / TVJ dz' 



—hl — /ii —Al 



Now ö;« can only be represented by (1) if it is a continuous 

 function of the co-ordinates, but we may imagine nevertheless that 

 at the boundary of the space t, 5Ö and dB/öa' have arbitrarily 

 small values. These quantities may therefore be taken zero at the 

 boundary; as to 2P, this has already been done in the considerations 

 of the preceding paragraph. Hence the first term, given by the 

 integration by parts, vanishes; the second may again be integrated 

 by parts, so that finally 



The exponential factor under the sign of integration may be 



replaced by 1. Indeed, if a certain length /, of the same order of 



magnitude as the linear dimensions of the space t is very small in 



comparison with the wavelength >. of light, we may omit terms 



T I 



containing products of — and quantities of the order — , Now 



■fi- 



the integral taken over the portion of a plane z' = const, lying 

 within T. From this we infer 

 h, 

 C^^,.. dz' = fs-y dt 

 -h, 

 integrated over the volume t. We shall represent this integral by 



