/ (;i:\f-R.iux.iii(>x oi- the Ki-.cirKoc.ii. theorem ,i<» 



Now if the surface Ix; taken as a sphere of radius R, centered at or 

 near the system, it is easily shown that if R is taken sutTicienth' large 



dn dR c ' 



and the surface integral \anishes. l"onse<|uenily we ha\e established 

 the generalized reciprocal theorem 



j\u' •F")dv =)"(,«" -F'jdv. 



The Reciprocal Theorem I has long been employed in electric 

 circuit theory, and has proveil extremely useful. As an example of 

 the practical utility of the generalized theorem II it may be remarked 

 that it enables us to deduce the transmitting properties of an antenna 

 system from its recei\ing properties. The latter may sometimes he 

 approximately deduced (|uite simply, as in the case of the wave 

 antenna, whereas a direct threoretical iletcrmination of the former 

 presents enormous difficulties. 



