POTENTIAL AND CAPACITY 89 



is at positive potential the needle will tend to set under the 

 earth-connected pair of quadrants, while if the outside body is at 

 negative potential the needle will tend to set under the pair of 

 quadrants connected to it. If the torsion couple introduced by 

 the displacement is so great that the displacement is always small, 

 then the angle of displacement is, as we shall show below, nearly 

 proportional to the difference of potential between the pairs of 

 quadrants. It is also, for a certain range, nearly proportional to 

 the potential of the needle, so that the sensitiveness of the instru- 

 ment may be adjusted by altering the charge in the jar. It is usual 

 to calibrate the scale of the electrometer by putting on known 

 differences of potential from the terminals of cells of known voltage. 



Dolazalek electrometer. A modification of the instrument 

 introduced by Dolazalek, which is more sensitive than the original 

 type, is much used. In this the quadrants are smaller and are 

 mounted often on amber pillars. The needle is made of silvered 

 paper and so is lighter, ana it is preferably suspended by a quartz 

 fibre made conducting or by a very fine metallic wire. The Leyden 

 jar can then be dispensed with and the needle can be charged 

 directly from a battery of, say, 100 volts. There is a potential 

 of maximum sensitiveness, however, which can be found by trial 

 for the particular instrument used. The instrument is contained 

 in a brass case with a window for the beam of light to pass to and 

 from the mirror. 



Elementary theory of the quadrant electrometer. 

 We shall take the case in which the two pairs of quadrants, which 

 we denote respectively by 1, 1' and 2, 2', are maintained at 

 constant potentials \\ V 2 . The needle is connected to the jar, 

 which has very great capacity compared with its own. The 

 potential of both jar and needle therefore remains sensibly constant 

 even if the charge on the needle varies. We denote this potential 

 by V n . If V 4 is greater than Vj the needle tends to move towards 

 1, 1', and it will only be in equilibrium when the electrical couple 

 is balanced by the torsional couple. Now had the quadrants and 

 needle, after charging, been insulated, the motion of the needle 

 would have diminished the electrical energy of the system, the 

 differences of potential of the fixed charges decreasing, and the 

 position of equilibrium would have been that in which the decrease 

 in electrical energy on small displacement would have just supplied 

 the work necessary for the increase in torsion. But the potentials 

 remaining constant, there is an actual increase in the energy of the 

 system. The area of the needle under 1,1', where the difference of 

 potential i> greatest, increases, and therefore its charge increases 

 and consequently the electrical energy increases. The energy is 

 -upplied by the sources which maintain the constant potentials, the 

 supply being sufficient both for the increase in electrical energy 

 and for that used in in<Tea>ing the torsion of the wire. We shall 

 make use of the following important theorem : 



