QUADRANT ELECTROMETER. 187 



and their difference 



We have thus a means of at once determining the difference of 

 potential of the two quadrants and the potential of the needle. 



One remark must be made. If, in order to give the needle two 

 equal and opposite potentials, it is connected with one pole of an 

 element, the other pole of which is to earth, the preceding formulas 

 no longer hold strictly. The connection introduces in general an 

 electromotive force of contact, the sign of which does not change 

 with the pole of the battery, so that the needle does not take two 

 equal potentials of opposite signs. 



815. If the potential of the needle is so high that the ratio 



1 ' 2 may be neglected, formula (18) reduces to * \ (^ 



When the potential V of the needle is constant, the deflection is 

 simply proportional to the difference of potentials of the two 

 quadrants, and the capacity of the needle is then independent of 

 the deflection. The apparatus of Sir W. Thomson works under 

 these conditions. The gauge is usually adjusted upon the potential 

 of the Leyden jar, and hence that of the needle in connection with 

 it attains a value of 500 to 1000 volts, according to the degree of 

 sensitiveness which it is desired to obtain. 



The deflection is still expressed by the same formula (22) when 

 the quadrants are at constant equal potentials of opposite signs, and 

 the variable potential to be measured is that of the instrument. The 

 instrument is then perfectly symmetrical, and the needle, with the 

 exception indicated, deflects equally on either side when raised to 

 equal potentials of opposite signs. 



816. When the needle is connected with one pair of quadrants 

 that, for instance, whose potential was denoted by V 2 the formula 

 becomes 



In this case the deflection is proportional to the square of the 

 difference of the two potentials, and the needle sets towards the side 

 of that pair of quadrants with which it is not connected. 



