ELECTROMOTIVE FORCES OP THE ELECTRIC ARC. 313 



lower frequencies a small percentage of the alternating current flowed round the 

 battery side of the circuit ; but this did not affect the accuracy of the results, as the 

 expressions for the impedance and power- factor are independent of the current, so 

 that it is only necessary to maintain the testing current constant during each test. 



The circuit for measuring the alternating part of the P.D. arc lamp V A , the P.D. 

 between the terminals of K, V B , and the P.D. total. V, consisted of : 



M, a thermo-galvanometer, whose deflections were practically proportional to the 

 mean squared value of the current through it, and which, though practically 

 non-inductive, gave a deflection of about 500 scale divisions for 1 milliampere 

 of alternating current. The deflections of this instrument were read on the 

 same scale as those of T, so that both could be observed at one time ; 



p 4 , an ordinary resistance box, 



k, a key, 



S 1( a switch, consisting of mercury cups in a wax block, 



G, a condenser which allowed a current due to the alternating part of the P.D. to 

 flow through M, but prevented any current due to the direct P. I.), from 

 flowing through it, 



4 and 5, mercury cups by means of which the measuring circuit could be connected 

 to either the points 1 and 2 ; 2 and 3 ; or 1 and 3 ; to measure V A . V R , and V 

 respectively. 



The impedance of the measuring circuit, which consists of the thermo-galvanometer 

 M, the resistance p t , and the .condenser G, need not be accurately known, as it is only 

 the relative values of V A , V a , and V which are required to a high degree of accuracy 

 and not their absolute values. As the frequency in each experiment was kept 

 constant to well within 1 per cent., the impedance of the measuring circuit need not 

 be quite independent of the frequency. 



In all arcs neither the direct P.D. nor the current keep quite steady, owing to the 

 necessity of feeding the carbons together, and to the impurities, cracks, &c., existing 

 in them, so that the comparatively slow variations produced must be prevented from 

 sending any appreciable currents through M ; for this reason the capacity of G was 

 made as small as compatible with the impedance of the measuring circuit, not 

 depending too much on the frequency. A standard j mf. condenser was used for G 

 for all frequencies from 120,000 to 10,000 -- per second inclusivs ; down to 3,000 

 1 mf. was employed, and for all lower frequencies 5 mf. Even under these conditions 

 it was absolutely essential that the battery B should not be in use for any other 

 experiments, or spurious currents were obtained through M, and such a thing as the 

 arc giving a small hiss sent the spot off the scale. 



The key k was so arranged that in its up position the condenser G was always kept 

 charged to the correct. P. D., so that on depressing it G was neither suddenly charged 

 nor discharged through M, for owing to the delicate nature of the latter any 



VOL. com. A. 2 s 



