1895.] on the Absolute Measurement of Electrical 'Resistance. 615 



In measuring a resistance we have to determine what I have 

 called the equilibrium rate of rotation corresponding to that resist- 

 ance, i. e. the rate of rotation such that, on reversing the direction of 

 the current through coil and resistance by the commutator, the 

 reading of the galvanometer is unchanged. 



Now, it is not very easy to hit this exactly without making a 

 great many trials, and, fortunately, it is not necessary for us to do so. 

 The current produced in the galvanometer circuit by the difference 

 of the electromotive-forces at the disc and at the resistance is pro- 

 portional to that difference, and, if the current is small, it is propor- 

 tional to the scale deflection on reversal. We shall commit no 

 appreciable error, therefore, if we are near the equilibrium rate, in 

 assuming that the difference between the equilibrium rate and the 

 actual rate is proportional to the scale deflection on reversal, or, 

 what comes to the same thing, that the difference R — M n is pro- 

 portional to the scale deflection on reversal. 



If we take four or five rates of rotation near the equilibrium rate, 

 and determine t j.e deflections on reversal corresponding to each, we 

 can by interpolation determine the rate of rotation that would cor- 

 respond to no deflection, i. e. the equilibrium rate. If, say, we take 

 five such rates, some on one side and some on the other of the 

 equilibrium rate, we get five equations as follows : — 



where l lt l 2 , l 3 , Z 4 , l 5 are the deflections corresponding to rates of 

 rotation n 19 n 2 , w 3 , n±, n 5 , and C is a constant. 



Combining these by the method of least squares, we may readily 

 obtain the most probable values of R and C. 



If the greatest accuracy is not required, we may content ourselves 

 with two observations, one on one side of the equilibrium rate, and 

 the other on the other side. 



The elementary observation in the determination of a resistance 

 with any given apparatus is, then, the determination of scale deflection 

 on current reversal corresponding to a rate of rotation simultaneously 

 measured. 



To obtain this scale deflection accurately we must obtain it as a 

 mean of the values given for it by a number of successive reversals 

 succeeding one another as quickly as possible, in order to eliminate 

 slight variations in the position of the galvanometer needle due to 

 the slight remaining variations in the thermo-electric force at the 

 external brush contact, and the slight variations of speed that the 

 observer at the tuning-fork has to correct. It is therefore best not 

 to wait for the needle to come even approximately to rest after the 



2 t 2 



