Currents l>y means of the "Pliaseograph" 979 



The equation (18) is then simplified to 



i 2 4- e 2 — 2ei cos </> = i 2 sin 2 <£. . . . (21) 



This equation represents ellipses inscribed in a quadrangle. 

 Its axes are consequently the lines 



e=±i , m) 



If e is eliminated between the equations (21) and (22) we 

 obtain 



2i 2 + 2/ 2 cos</) = ; 2 sin 2 (/> (23) 



The two z-values obtained from this formula are the coordi- 

 nates of A and B. They can be exchanged for the semiaxes 

 a, b, 



a = i lx /2 ; b = i 2X /2 ; 



a 2 = 2i 2 ; b* = 2i 2 2 ; 



a 2 (l — cos (f)) = ? 2 sin 2 cj) ; 

 b 2 (l + cos (j> = i 2 sin 2 <p. 



By division is obtained 



a 2 — a 2 cos (p = b 2 + b 2 cos ^> ; 



C0S *=^+i;s ( 24 ) 



We have consequently only to measure the axes of the 

 ellipse to find phase-difference and from this self-induction 

 and capacity. 



There remains to be mentioned a third way in which the 

 apparatus can be worked, i. e. by the use of an auxiliary 

 current in one measuring wire. In the first place we can 

 then think of the use of a constantly decreasing or increasing 

 current which gives to the luminous point a lateral deviation 

 with constant rapidity, at the same time as the other mea- 

 suring-wire registers the desired current-curve. Here belong 

 also the methods of registering the characteristics of electric 

 machines. In another place we will deal more fully with 

 this subject. There remains to be considered some appli- 

 cations of the above-mentioned methods. 



VII. Alternate Currents. 



Under this heading I will bring together some registerings 

 of the relations between current and voltage with self-induc- 

 tions, capacities, transformers, &c. 



Figs. 9 and 10 (PL XIX.) show some current-voltage 



