176 Prof. .A. Schuster's Electrical Notes. 



which is the greatest that can with safety be used. In 

 ordinary laboratory practice our battery-power is generally 

 sufficient, so that it is the heating of the conductors which 

 puts the limit to a measurement of resistance ; and I propose 

 to discuss the question from this point of view. It may be 

 answered in a very simple maimer. Imagine any network 

 of conductors, and let i be the current which passes through 

 the resistance to be measured (p). Consider a small change 

 of resistance Bp. This change will alter the currents, and, 

 amongst others, that passing through the galvanometer which 

 forms the measuring; instrument. The change in the currents 

 is the same as if an electromotive force numerically equal to 

 i$p was introduced into the branch of which p forms part. 

 In order that this electromotive force should affect the galva- 

 nometer, which we take to have a resistance g, there must be 

 some one mesh of the network of conductors which contains 

 both p and g. If there should be no other resistances in that 

 mesh, and if/? does not form part of any other mesh, the current 

 By in the galvanometer produced by the change of resistance 

 Bp will be given by 



8y=^P- (1) 



P+g 



If the above conditions are not satisfied, and they never can 

 be completely, the current through the galvanometer will be 

 smaller than the value given. It w r ill be shown that we may 

 make such experimental arrangements as will render equa- 

 tion (1) approximately correct ; at any rate, that equation will 

 give us a lower limit for the change of resistance 8p which 

 produces an appreciable effect, if for i we substitute the 

 maximum current which can pass the resistance. If this is 

 denoted by i m and if By stands for the smallest current the 

 galvanometer can detect, we obtain 



Bp _ By 

 p+g" *»" 



(2) 



This represents a somewhat important proposition : — 

 With a given resistance and galvanometer, the ratio of the 

 smallest change of resistance which can be detected to the sum of 

 the given and galvanometer resistance is equal to the ratio of the 

 smallest current which can be detected by the galvanometer to 

 the maximum current which can be sent through the resistances. 

 If we have a choice of galvanometers and take account of 

 the fact that for the same type of instrument the deflexion 

 varies as the square root of the resistance, equation (2) shows 



