﻿206 Mr. A. Russell on the Dead Points of a 



find, by multiplying both sides of equation (1) by dt and 

 integrating, that 



M&Cl=p,Gtq cos 6 + 7 sin O cos 6> |? 2 /(2KR) - W/R}, (2) 



very approximately, where Q, is the initial angular velocity of 

 the needle. Thus II will be zero if the right-hand side of 

 equation (2) vanishes. In general the heat generated by 

 eddy currents in the needle is negligibly small, and so W may 

 be put equal to zero when 12 is zero. Hence, in this case 



2fiG cos o + 7 sin O cos o {q o /{KR)} = O, 



and therefore 



S ia0 o =_2^.5 (3) 



where V, the initial P.D. between the terminals of the 

 condenser, may be positive or negative. 



At the points determined by equation (3) there will be no 

 throw produced on charge and discharge respectively. These 

 points, which the author calls dead-points, can be determined 

 rapidly and accurately with low-resistance galvanometers. 



If we vary the resistance x between the terminals of the 

 condenser and find the position y of the dead-point corre- 

 sponding to charge, then plot a curve of y and x, we get a 

 straight line. This line, however, does not pass through the 

 origin. We have to suppose, therefore, that the " effective 

 internal resistance" of the condenser is R : and that R in 

 formula (3) is given by R=^ + R, 1 . 



Drawing a line through the point ( — R 1? 0), making the 

 same angle with the axis of X as the line-locus of the dead- 

 points for charge, but on the opposite side from it, we get the 

 locus of the dead-points for discharge. The distances of the 

 dead-points also from the centre of the scale were found 

 experimentally to be inversely proportional to the applied 

 voltages and all the lines passed approximately through the 

 point ( — Ri, 0). In these experiments, a standard 1-micro- 

 farad condenser by a well-known maker was used, and its 

 effective internal resistance was 4 ohms. The resistance of a 

 0'05-microfarad condenser was found to be 32 ohms, and of 

 a 3-microfarad condenser for alternating-current work 1*6 

 ohms. 



In practice the energy given to the needle is negligibly 

 small compared with that expended in heating the path of 

 the electric current. We may consider therefore that the 

 internal resistance R x of the condenser is defined by the 



