IN THE FIELD ROUND A THEORETICAL HERTZIAN OSCILLATol; 175 



Now, at r = r it is easy to see that the curve in which is plotted to r is 



still sloping towards the horizontal. For if = 77 and t ' = , its equation 



is approximately 



r.(r. + ) 



or, 77 decreases with increase off hyperlx)lically. 



Hence the minimum negative value sought must li<> lietween r and r a + qr,, say 

 at r + *?'/''! where 77 is less than unity but not necessarily very small. Thus \ve 

 must put w/r, = r)(j } where q is small, and endeavour to solve (xxxi). Sulwtitiiting, 

 we have 



-'Y V + <h 4 + -'/V + 4</Y + ^'y 7 ^? - v a = o, 



or, 



*N' + '/V + V + W + -''/'>? -1 = 0. 



Clearly, 17 must he of the form 170 + ^)\ ( f' + y$ 4 + w' + &c. Let us substitute 

 this value and equate the successive powers of q- as well as the constant term to zero. 

 We find 



47,J - I = 0, 



T?2 + $wl + 2ijl = 0, 



^, + >jj + 1277577, + 12770*7? + 877017, + 2770 = 0, 



jfo, + 20772771 + 477277, -|- 12^77, + 2477077,77, + 477? -f 877 77, -f 4771 + 277, = 0. 



(xxxii). 



These e< | nations give us 



r, = (ft s = -6299G 



77, = - f = - "375 

 770 = 

 77,= -0147C, 



Thus 



77 = -6299C, - -375^ + '01476^. 



We find at once that the re<iuirefl radius of the sphere at which the velocity of the 

 electric transverse wave takes a niinimum negative value 



(.gOQQfi \ 



+ -625 + -014767 4 ) ...... (xxxiii). 



The next term in the expression for the radius would involve </ c and may generally 

 be neglected. If the point of minimum velocity were half-way between the two 



