238 LECTURES TO SCIENCE TEACHERS. 



of quadrants), and one (the needle) movable about an axis, 

 the arrangements being of the symmetrical kind that I 

 have described, and the movable body is maintained at a 

 constant high potential. The potentials of the two fixed 

 conductors are different, and it is this difference which we 

 wish to measure. Let Y denote the potential of the needle, 

 let Yj and Y 2 be the potentials of the two fixed conductors ; 

 let be the angle of deflection of the needle from the posi- 

 tion which it would occupy were V x and V 2 equal, then it 

 can be shown that if Y x be greater than Y 2 , 



= 0(V 1 -.V 3 )[V -J(V 1 + V 9 )] . . (A) 



where C is a constant. Now if Y be very great in com- 

 parison with Y x and Y 2 , the second term, ^ (Yj + Y 2 ), of the 

 last factor may be omitted in this expression, and we obtain 



In the use of the quadrant electrometer this is practically 

 the state of affairs ; for, as I have just said, Y is the 

 potential of the Leyden jar with which the needle of the 

 electrometer is connected, and the potential of the jar is 

 always maintained very great indeed in comparison with 

 that of any electrification that this delicate instrument is 

 employed to measure. 



Taking now the formula (B) we see in the first place 

 that 6, the angle of deflection, is in simple proportion to the 

 difference of potentials Y x - Y 2 of the quadrants, that is, of 

 the two bodies tested, Y being kept constant. Secondly, 

 we see that as is proportional to Y , V 1 Y 2 being 

 constant, the deflection for any given difference of poten- 

 tials is greater the greater Y . Thus the sensibility of 

 the instrument is proportional to the potential of the 

 needle. By altering the charge of the Leyden jar, therefore, 

 we may alter the sensibility of the electrometer. 



To keep the charge of the Leyden jar constant, which 

 you see is essential in carrying out any set of measure- 

 ments which are to be immediately comparable, there is 

 a " gauge " connected with the electrometer, as well as 

 a minute electric machine within the glass jar, and supported 

 from the main cover, by means of which the charge can be 

 increased or diminished. The gauge is really an electro- 

 meter, precisely similar in construction to one that I shall 



