considered in connexion with the Dynamical Theory. 5 



manent change of their molecular state may be neglected. From 

 the value X the current gradually increases or diminishes to that 

 determined according to Ohm's law, by the resistance of the 

 combined circuit. It may be seen from the expression just found 

 that the resistance of the branch may be varied without affect- 

 ing the spark, provided always that it is not so great in relation 

 to the self-induction as to make the time-constant compa- 

 rable in magnitude with the duration of the spark. The spark 

 depends only on the comparative self-induction of the branch 

 circuit, being small when this is small, and when this is great 

 approximating to its full value jLx 2 . 



These results are easily illustrated experimentally. I have 

 two coils of thick wire belonging to an electromagnet, which for 

 convenience I will call A and 13. Each consists of two wires of 

 equal length, which are coiled together. These may be called 

 Aj A 2 , Bj B 2 . When A x A 2 are joined consecutively, so that 

 the direction of the current is the same in the two wires, we have 

 a circuit whose self-induction is four times that of either wire 

 taken singly. But if, on the contrary, the current flows oppo- 

 site ways in the two wires, the self-induction of the circuit be- 

 comes quite insensible. 



The main circuit may be composed of the wire A l (A 2 remain- 

 ing open) into which the current from a single Daniell cell is 

 led, and which can be opened or closed at a mercury cup. One 

 end of the branch circuit dips into the mercury while the other 

 communicates with the wire whose entrance or withdrawal from 

 the cup closes or opens the main circuit. In this way the coils 

 of the branch may be said to be thrown in at the break. 



If the branch is open, we obtain at break the full spark, 

 whose value is §L# 2 . If the wire B 2 be thrown in, the spark 

 is still considerable, having approximately the value |L<r 2 for 

 N = L. And if 6^3 are thrown in, so that the currents are 

 parallel, the spark is still greater and is measured by ^L^ 2 x ^. 

 But if the currents are opposed, the spark disappears, because 

 now N = 0; so that the addition of the wire B 2 , whereby the 

 resistance of the branch is doubled, diminishes the spark. It 

 is true that to this last case our calculation is not properly 

 applicable, inasmuch as the time-constant of the branch is so 

 exceedingly small. But it is not difficult to see that in such a 

 case (where the self-induction of the branch may be neglected) 

 the tension at the breaking-points, or more accurately the dif- 

 ference of potential between them, cannot exceed that of the 

 battery more than in the proportion of the resistances of the 

 branch and main circuits, so that it could not here give rise to 

 any sensible spark. Soft iron wires may be introduced into the 

 coils in order to exalt the effects ; but solid iron cores would 



