1 72 THE SCIENTIFIC PAPERS OF 



equal to about 1 mercury unit, to which has to be added the 

 resistances of the leading wires, which are also made equal to each 

 other, and to about half a unit ; these resistances may therefore 

 both of them be expressed by y. 



We have, then v':v = C + y:X + y 

 or 



X-I(0 + T ) y 



V 



which is a convenient formula for calculating the unknown resist- 

 ance from the known quantities G and y, and the observed pro- 

 portion of v and v'. 



The constant of the instrument (y) is easily determined, from 

 time to time, by substituting a known resistance for X, and ob- 

 serving the volumes, v and v', after the current has been acting 

 during an arbitrary space of time, when in the above formula, y, 

 has to be separated as the unknown quantity, giving it the form 



, v' X - v C 



y = ~i~ . 



- v _ v' 



The condition of equality between the internal resistances of 

 both voltameters is ascertained by inserting equal known resist- 

 ances in both branch circuits, when v = v' should be the result. 

 Failing this, the balance is generally re-established by reversing 

 the poles of the battery, the reason being that hydrogen electrodes 

 are liable to accumulate metallic or other deposit upon their 

 surfaces, which is effectually removed by oxygen. 



Such reversals of current should be effected at frequent inter- 

 vals during the observation. Should this not suffice to establish a 

 balance of resistance, it will be necessary to push the electrodes 

 of the voltameter of greater resistance a little further into the 

 tube. 



The constant resistance of the instrument should, as nearly 

 as possible, represent a geometrical mean of the range of resist- 

 ances intended to be measured, because the greatest degree of accu- 

 racy is obviously obtained when the quantities, v and v', are nearly 

 alike. If the difference between v and v' is very great, the con- 

 stant y introduces an error into the result, because ,=. ^is not 



A + y 



