492 M. H. Weber on the Heat-conducting Power 



In order to determine the quantity p in accordance with equa- 

 tions {6), when the rod had assumed the state of periodic limits 

 the conduction to H and I was connected with the galvanometer. 

 A motion of the needle then commenced^ variable with the time 6. 

 The forces on which this motion depends are (1) the horizontal 

 component of the earth^s magnetism, (2) the deadening force, 

 (3) the force exerted by the thermo-current upon the needle. 

 The torsion-moment which the first two forces exert upon the 

 needle with a deflection (f> are 



^ w at 



T being the horizontal component of the earth^s magnetism, m 

 the magnetic moment of the needle, and w the resistance of the 

 circuit. In order to determine also the torsion-moment of the 

 third force, we must consider that the intensity of the thermo- 

 current is a quantity which varies with the time, whereby an 

 induction of the current upon itself is occasioned, and the con- 

 sequence is a diminution of the intensity. For, let i be the in- 

 tensity of the thermo-current which is actually passing through 

 the circuit at the time 6, 2j the intensity which would be ob- 

 served if the current remained constant, then is 



where y is a constant depending on the resistance and the form 

 of the circuit. According to equations (6), however, in an even 

 period 



. _ a(M-Ng-^^) 

 *i 



in an odd period 



2i = 



w 



a(-M^-fNe-^g) 

 w 



Prom this it follows that the intensity i actually present in 



the circuit at the time 6 can be represented by an expression of 



the form 



. a(A + Be-P^) 



l=~ -, 



w 



where A and B are constants. Hence the torsion-moment of 

 the third force becomes 



and we obtain for the equation of motion of the needle of the 

 galvanometer, if k denotes the moment of inertia of the needle 



