ON OHM^S LAW. 53 



Then A denoting tho dctcriuinant of the system of resistances (see Max- 

 well's ' Electricity,' vol. i. p. 399), we have rj denoting the current in the 

 galvanometer, 



5r='^{Z-2.i- + R/.FE=}. . (1) 



Prom (1) it follows at once that tho greater E, the further to the right the 

 balance will bo, provided /i is >0. 



Let us now, instead of keeping up an electromotive force E constantly, make 

 an alternation some hundred times a second between an electromotive force 

 E and an electromotive force i/E *; then supposing each to operate for an equal 

 time, tho whole current through tho galvanometer is given by 



o=i^W-^^^){^-\-y)'^+'^Fr-w{i+,f)} (2) 



if the electromotive force has in both cases the same direction, and by 



^=^i(^-2-^'Xl-2/)E + R^FE\l-y')} (3) 



if the directions are opposite. 



It appears, therefore, as was obvious without calculation, that the values 

 of X which give a balance are neither the same in the two cases (2) and (3), 

 nor equal to that in the case of either electromotive force acting continuously, 

 .In fact the balance is an apparent one if jeo be >0, due to the fact that we 

 are in case (2) as much under the balance for the larger electromotive force 

 {qua effect on the galvanometer) as we are over that for the smaller, so that 

 the needle is kicked equally this way and that so rapidly that it remains still. 

 Similar reasoning would show that the balance for case (3) lies most to the 

 right of all. In fact the values of x are : — 



Smaller electromotive force alone x = 4{Z+Ey.(P-?/^E-}, 



Case (2) x^ l{l+llf,VXl-y + 7f)W}, 



Larger electromotive force alone x = ^{Z+EyuP^E^}, 



Case (3) x = i{l+R^,ni+y-\-f)W}, 



which are evidently in ascending order if ?/ be < 1, 



Suppose now we find the balance for case (2) and then reverse our smaller 

 electromotive force ; the balance being thus disturbed, there will be a current 

 through the galvanometer ; and in order to experiment at the greatest advan- 

 tage this must be made a maximum. 



Substituting the second of the above values of x in formula (3), we get 



ff=lll^,V^W(y-f), (4) 



which is a maximum as far as y is concerned Avhen y=l-, the value off/ 

 being then 



«EP-E^ 

 ff=f^ 4A (^) 



The advantage of this method of experimenting is that it eliminates to a great 

 extent the temperature effect, which is similar to the eftect we arc lookiug 

 for, except that it depends on the time, which the other probably would not 



* N.B. In what follows ?/ is supposed < 1. 



