NOTES AND ADDITIONS. 311 



not altered by the deflection. Then, in the case of this ap- 

 paratus also, the strength of the currents may be regarded 

 as proportionate to the tangent of the angle of deflection. 

 A glance at fig. 19, on p. 57, shows that the displacement 

 of the scale is equal to the tangent of the double angle of 

 deflection. For so small an angle we may put 



tc, (2 ) = 2ty , 



that is to say, the tangent of the double angle is equal to 

 double the tangent of the single angle. And from this it 

 follows that the strength of the currents is proportionate to 

 the displacement of the scale directly observed. 



10. TENSIONS IN CONDUCTORS (p. 133). 



To determine the absolute amount of tension at any 

 point in a conductor, it would be necessary electrically to 

 isolate the conductor, and to connect the point in question 

 with a sensitive electrometer. But if any point of the iso- 

 lated conductor is brought into conducting connection with 

 the surface of the earth, this point would assume a tension 

 equal toO, without any alteration in the differences of tension 

 at the various points. Other points of the conductor may 

 now be brought successively into connection with the earth, 

 thus altering the absolute values of the tensions at the 

 separate points, though the difference between the tensions at 

 the various points remains the same. From this it follows 

 that these differences are alone of importance for us. In our 

 later explanations we have therefore represented the matter 

 as though certain points (the boundaries between the longi- 

 tudinal and cross section) had a tension =0 ; that is, we always 

 thought of them as connected with the earth. All tensions 

 that are greater than this we call positive, all that are less 

 negative. 



