THERMAL CONDUCTIVITIES OP SOME ELECTRICAL INSULATORS. 443 



Therefore 



IT ..1 n 



1 1 2 ' I 



^r--~ 2 - 



JTTA IT *. i n 



MIT nirx 



jr /nwa 



* \ 2* 



v Inita, 



K M-oT 



where p = N/c'+r* 2<r cos 6. 

 When n is large, the term 



[-WF5 



T 



1(1 



/*wa 



t /r 



' \ 2/ 



Incomes equal to 



(GRAY and MATHEWS, p. 68). The series in square brucketa is therefore convergent. 

 If the term within square brackets be written , n satisfies the equation 



3?-* """ ? 3r T r" 30* \ '2l . 

 The mean value of u taken along any circle of radius j> in a plane perpendicular to 

 the x axis and enclosing no singularities is therefore equal to I ( j/- ) " where u, 

 is the value of at the centre of the circle.* Hence the mean value of u taken over 



* II. WEIIKK, Muth. Ann.,' vol. 1, p. 9 (1869). 

 3 L 2 



