Transformer Indicator Diagrams. 471 



so that if 7 be the galvanometer deflexion for a given 

 position of the eommutating brushes when Ci is flowing in 

 px and C 2 , correctly directed, in p 2 , the ordinate of the wave 

 which is the vector sum of %Ci and ?i 2 C 2 at the instant of 

 commutation is the product of 7 by Xt\T/4M. 



The same principle can obviously be extended to the 

 determination of the vector sum of any number of equi- 

 periodic currents each affected by an independent numerical 

 multiplier. 



In the paper already quoted it is also shown that if a coil 

 of v turns of wire is looped on a magnetic circuit in which a 

 periodic magnetic flux of period T is pulsating, and if the 

 ends of the coil are connected through the synchronous 

 commutator that changes twice per period to a high resist- 

 ance r, and thence to a galvanometer as before, the ordinate 

 F of the flux-wave and the corresponding galvanometer 

 deflexion f3 for any position of the eommutating brushes are 

 connected by the relation 



Hence any desired set of ordinates of a flux-wave can be 

 obtained. 



3. From what precedes it is obvious that in order to obtain 

 practically the vector sum of nfii and n 2 C 2 , where n Y and n 2 

 are numbers and Cx and C 2 currents of equal period, it is 

 necessary to have a triad p ± , p 2 . and s of coils such that the 

 mutual inductance of p x and .* is to that of p 2 and s as n x is 

 to n 2 . These can be wound in three grooves turned out of a 

 circular disk of seasoned wood that has been well baked and 

 then soaked in melted paraffin. A rough approximation to 

 the required ratio of 31 v to M 2 can be obtained by attention 

 to the relative numbers of turns, and a preliminary adjust- 

 ment can most quickly be made by the wave-tracer as 

 follows : — Send a periodic current of suitable value through 

 the common secondary s. Join together one end from each 

 •of pi and p 2 and connect the junction to one fixed brush of 

 the commutator. Brino- the other ends of two terminals of a 

 two-way key. from whose moving tongue a connexion is 

 made, to the other fixed brush. Join the two movable 

 brushes of the commutator through a suitable resistance r to 

 the galvanometer. Thus, when a current is flowing in s, 

 either p x or p 2 can be put in circuit with the galvanometer, 

 and the deflexions y r and y 2 due to jh and p 2 respectively for 

 every position of the moving brushes are in the ratio of M x 

 to it,, since X ,, T ^ 



