Needle of a Quadrant Electrometer. 447 



Considering the case of the electrometer with which the 

 author is at present working, for which 7 = 14*2 seconds and 

 X = 1*J1, We find that tire error attains its first and subse- 

 quent maxima at k 304 T, 1*304 T, 2-304 T, ... &c. respec- 

 tively. The error at its first maximum amounts to about 

 45 per ceiit., at the second maximum 8 per cent., and indeed, 

 if we measure times and the positions of the needle from the 

 time and position occupied by the needle when the quadrant 

 was released from its earth connexion, even though we allow 

 such a time ^ to elapse that the exponential term has 

 practically died down to zero, we shall make an error of 



100\T 

 T~. — 2 , >,2 \ P er cent. Thus suppose, for example, in the case 



of the instrument here considered the quadrant were released, 

 and an observation were taken 60 seconds later. The ex- 

 ponential term would have died down to a very small amount 

 by this time, but there would still remain an error of 2*4 

 per cent. In fact, though the needle ultimately moves with 

 uniform velocity, the straight line representing its motion, 

 when produced back, does not pass through the origin, a 

 certain amount of time having been as it were lost in creating 

 motion in the needle. As observations arc frequently 

 measured from the instant of releasing the quadrant, the 

 error here discussed is worthy of serious consideration. 



The error may be completely avoided by taking successive 

 observations when the periodic term is zero. All readings 

 measured from the position of rest of the needle will then 

 be wrong, but they will be wrong by a constant amount, so 

 that if the reading corresponding to the position of rest is 

 omitted, the others will serve to determine accurately the 

 ideal motion of the needle. Thus the first reading should be 



T 

 taken at t= ~- <y, and the succeeding readings at intervals 



of a period. For example, in the case of the instrument 

 above referred to, the first observation should be taken at 

 £ = 1*5 seconds, the second at £ = 15*7, and so on. 



If the period of the needle is not an exact number of half 

 seconds, the method may appear rather troublesome, if one 

 is using a chronometer beating half seconds, but in practice 

 no difficulty occurs, for it is sufficient for the purpose in 

 hand to take the period as corresponding to the nearest whole 

 number of half seconds. Although the error thereby intro- 

 duced into the periodic term is cumulative in the successive 

 observations, the whole term itself soon dies out owing to 

 the exponential factor. 



