22 HEYL & BRIGGS— THE EARTH INDUCTOR COMPASS. 



The approximate first quadrant roots of (4) are 17° 24' and 

 72° 36' instead of the mid-points of the octants 22° 30' and 67° 30'. 

 At these roots the value of (f> — is nearly 4°, as shown in the fol- 

 lowing table. 



If cfi lies in the second quadrant (Fig. 6), we have 



/0 - 90°\ / 180° - (/>\ 



Potential at P = — | 5 — I sin — I ^ — I cos 6, 



V 90 / \ 90 / 



/</) - 90°\ /i8o° - ct)\ 

 Potential at = I 5 — I sin + I 5 — I cos d. 



V 90 / V 90 / 



If these are equal, we have 



180° - (f) 



tan 6 — — — a 



</> - 90° 



TT 2 — tan 6 TT 2 cos 6 — sin d , ^ 



2 I - tan 2 cos - sm ^^^ 



The maximum and minimum values of ^ — ^ in this quadrant are 

 approximately at ^=: 107° 24' and 162° 36'. The values of (f> — ^ at 

 these points are 4° 4' as in the first quadrant. 



We may now obtain by computation from (2) and (5) the values 

 of ^ previously indicated by symmetrical considerations. 



If, as in Fig. 2, cos ^ = and <j) is in the first or second quad- 

 rant, both formulas give <^ = 7r/2. 



If, as in Fig. 3, sin 8 = — (V2/2), cos 0=\'2/2 and <f> is in the 

 second quadrant, formula (5) gives 



To avoid in practical construction the non-uniform distribution of 

 resistance around a circle which would be necessary to give a uni- 



