1891.] Application to Periodic Electric Currents. 211 



Also i-i + = (a + &) =i(ai + &i)+i*(a + &) ---- (20). 



2(o 1 +ta a ) ( 



^ (ai + &i) (0261 + 0162) 0*2 + 62) (ai 61 0262) XO-IN 



' 



It may be well to examine, first, the consequences of (19), in the 

 case of simple resistances. Here 



! = 2o 1 6 1 /(o 1 + 6 1 ), s 2 = (23). 



.n accordance with the plan proposed, we are to make e^ = 0, 

 = ;* ei = r, fi = Si. Our equation then becomes 



I 



/ 2 



Here ai is still at disposal, and we see that according to (24) it 

 ought to be diminished without limit. This conclusion does not 

 harmonize with one obtained by Mr. Heaviside.f It must be ob- 

 served, however, that ai = is unpractical, involving, as it does, 

 ' *i = 0, /! = 0. Even according to (24) there is little to be gained by 

 diminishing a^ below, say, \ l>\. In this case 



|6i, / l = 5 1 = |6 1 ---- (25). 



uch an arrangement as (25) may be recommended for practical 

 use. 



When bi is large, there may be advantage in taking a^ relatively 

 smaller than in the above example. In such cases we approach the 

 limiting condition of things, and have approximately 



fi = s t = 2! ............ (26), 



T5T ................. (27) ' 



And the smallness of /i in comparison with bi may sometimes be a 

 convenience. 



* These conditions require no attention in galvanometric testing with steady 

 currents, being satisfied by p = 0, independently of the nature of the instrument. 



t Loc. cit., p. 120, " In conclusion, if, to measure a certain resistance, the best 

 resistances for the galvanometer, battery, and the three sides, a, 5, c, were required, 

 then we should have to make a = b = c = d = e =f." 



