Prof. A. Schuster's Electrical Notes, 177 



that the best galvanometer-resistance is that for which p=g, 

 and in that case 



*p _ 2B y (-2) 



— ; • • • • • • • . It-)) 



P lm 



With a given conductor and type of galvanometer, the smallest 

 change per unit-resistance which can be measured is given by 

 twice the ratio of the smallest current which can be detected by 

 means of a galvanometer having the same resistance as the one to 

 be measured to the greatest current which can be sent through the 

 galvanometer. 



For the smallest current which can be observed with a 

 galvanometer of given type we may write $ r y=a/(^g). 

 Inserting this in equation (3) and observing that the equation 

 holds only when p=g, we obtain 



& = _*=. U-) 



or: — 



The highest percentage accuracy ivith which a given resist' 

 ance can be measured is directly proportional to the square root 

 of the maximum electric work which can be done on it without 

 overheating. 



Sometimes the galvanometer-resistance is given but p may 

 be varied, as when we wish to design a bolometer or platinum 

 thermometer. Equation (2) shows that there will be an 

 advantage in taking p as large as possible provided we do 

 not thereby reduce the value of i m . This can be done by 

 increasing the length of the conductor without diminishing the 

 cross section. 



The case which most frequently occurs is the one in which 

 we have a certain, but not unlimited, choice of galvanometer. 

 Each laboratory will probably be provided with a low and a 

 high resistance galvanometer; but we cannot for each in- 

 dividual measurement construct one which has exactly the 

 right resistance. It is useful to realize, therefore, how much 

 we lose in sensitiveness by working with a galvanometer 

 which has not exactly the right resistance. 



Substituting again a/(^g) for Sy, the smallest observable 

 change of resistance 8p then becomes 



Phil. Mag. S, 5. Vol. 39. No. 237. Feb. 1895. N 



