184 M. E. Edlund en the Nature of Electricity. 



opposite to that of the inducing current,, cos ^' will be ='-45":> 



which also changes sign with x^. Introducing these values of 

 r, of cos 6, and cos 6^ into the induction-formula (18), we obtain 



It follows from this that the induction of the element ds is 

 the same in both the halves into which the induced circuit is 

 divided by the plane of yz, and that the induced currents go in the 

 direction inverse to that of the inducing current on the same side. 



Eut it is evident that each element of the inducing circle has 

 the same inducing action as the element ^5 above considered. 

 Therefore the total induction of the inducing circle upon an ele- 

 ment of the induced circle will be 



values and that of r, and (after taking the integral between the 

 limits ?/j= +11 and ?/j = — H) multiply the latter by 2, we obtain 

 as expression of the total induction^ after replacing y^ by E,zi 

 and consequently dy-^ by Rj^w : — 



Isow ds = / J2l_^,o } ^^^^ '^'i = ^"i~!/i- If we introduce these 



1 _ (E^ + R^^ + 2RRiZ. + .^?-)^^' 



+ ^^^oi\ .p. ,;J,ot.t;!, ..^. ■ • (19) 



Felici has experimentally demonstrated the following ])rin- 



ciple. Let two circular current-circuits A and B, of equal radius 



E, be placed parallel at the distance z the one from the other, 



so that the Ime uniting their centres makes a right angle with 



the planes of the circuits ; two other circular circuits C and J), 



each having the radius Ej, are placed in the same manner, but at 



z ^ 

 a distance z^ from each other such that ^=~. If now through 



ill XV I 



each of the circles A and C an inducing current of the same in- 

 tensity be passed, the induced current of B will be to that of D 

 as the radius E is to the radius E^ 



"With the aid of this principle the function F(r) can be deter- 

 mined. If, in the above integral formula, E be made =rEj and 

 F (r) =hr = h v^ 2E2 + ^^hi -f- z\ in which Z> is a constant, we 

 obtain 



+ 477^/5fE [ 



+ 1 Vl-v^du 



^---(2 + 2. + |jy' 



