1895.] On the Calibration of the Capillary Electrometer. 19 



upon this slit, so that the movements of the meniscus are recorded 

 in a polar curve in which time is measured by the angular displace- 

 ment, and the position of the mercury by the radius vector. 



In such a curve, the total indicated E.M.F. is made up of two 

 parts, viz. : — 



(A) A. part indicated by the distance the meniscus has moved 

 from its zero position. This corresponds to the scale readings of the 

 instrument, as used for measuring a steady difference of potential. 



(B) A part indicated by the velocity with which the meniscus is 

 moving. This is proportional to the polar sub-normal to the curve, 

 which can be easily measured. 



The algebraic sum of these two parts represents the total P.D. of 

 the source at that instant. By repeating the process for a number 

 of points on the curve, a derived curve can be drawn showing the 

 actual variations of the E.M.F. during the passage of the plate. 



Considered as a practical means of measuring electromotive 

 changes of short duration, the method set forth in my paper is open 

 to one grave objection.* It assumes that the time relations of the 

 apparatus employed correspond to the formula 



r = ae~ c9 - 



To expect the maker of the electrometer to guarantee this would 

 greatly enhance the cost of an instrument necessarily fragile, and it 

 would be equally fatal to the general adoption of the method if the 

 experimenter had to go through a tedious series of measurements 

 with each new capillary. 



The process of calibration which I am about to describe is a 

 general one, applicable to all kinds of dead-beat instruments of 

 which the excursions can be recorded in polar curves, and by an 

 obvious modification applicable also to curves with rectangular 

 co-ordinates. It takes into account all "errors" except over- 

 shooting, and this, in the case of the capillary electrometer, can be 

 got rid of by inserting a sufficient external resistance. A point of great 

 practical importance is that no special care is needed in photograph- 

 ing the three " Normal Excursions " required for the purpose. 



The principle of the method, so far as it relates to the calibration 

 of the sub-normal, which is the only difficult part, is as follows : — 



Assuming that the resistance in circuit is such as to render the 

 electrometer perfectly dead-beat, we may extend the law of the 

 time-relations of the movement to include all forms of capillary, 

 thus : — 



The ratio of the velocity of the meniscus to the difference between 

 the E.M.F. of the source, and that of the charge contained in the 

 electrometer, is constant for any given part of the capillary, but may 

 * ' Phil. Trans.,' vol. 183, A, p. 101. 



C 2 



