12 ART. 15. — H. NAGAOKA: NOTE ON THE POTENTIAL 



we can conveniently write 



^ =4;r^^(l + £) (24) 



4:7r^ax 



Since e is a very small quantity, we can, with tolerable accuracy, 

 put 



Expressing (19) by means of ^,, 



ATz^Jax 2(1-2 (7i + 2 gi*-2 <7i7 L -^^gi/l ^^ ^' ^' ^' 



+ 6^i^-4g/ + 8^i«-l3 5;+ )}-4] (26) 



The above expression is useful when the coils are very near each 

 other. In such cases, q.^ is a very small quantity, so that by putting 



32 (7i'^-40 gi* + 48 gi^-32 5i«=£i 



T^= on /-U9 ,,., r%(-){^ + 8gi(l-gi) + s.}-4l (27) 



For r>70°, where -s/n r=^^"' ^i"* is negligibly small, and 

 M 



-2(ïiè^[%(|;){i+«''.+n}-*] 



(28) 



4;r-y/aic 



where ^(—- ^q\-\-H 

 Finally (22) gives 

 -j^= 192 ;r^^ ^ ^ (1 + 20 g'^ + 225(7* +1840 7*^+ 12120 g«+ ) (29) 



It will not be altogether out of place to digress on the practical 

 utility of the several formulae above obtained. 



In the iirst place, there is no need of finding r from A; or A;', 



