CHAP, vi.] ELECTRICITY AND MAGNETISM. 317 



Such an instrument was known as a Rheostat, but it is 

 now superseded by the resistance coils explained below. 



(b) The method explained above can be used with 

 any galvanometer of sufficient sensitiveness, but if a 



"tangent galvanometer is available the process may be 

 shortened by calculation. Suppose the tangent galvano- 

 meter and an unknown resistance R to be included in 

 the circuit, as in Fig. 128, and that the current is strong 

 enough to produce a deflection of d degrees : Now sub- 

 stitute for R any known resistance R', which will alter the 

 deflection to d' ; then (provided the other resistances of 

 the circuit be negligibly small) it is clear that since the 

 strengths of the currents are proportional to tan d and 

 tan d' respectively, the resistance R can be calculated by 

 the inverse proportion. 



tan d : tan d' = R' : R. 



(c) With a differential galvanometer (Art. 203), and a 

 set of standard resistance coils, it is easy to measure the 

 resistance of a conductor. Let the circuit divide into two 

 branches, so that part of the current flows through the 

 unknown resistance and round one set of coils of the 

 galvanometer, the other part of the current being made 

 to flow through the known resistances and then round 

 the other set of coils in the opposing direction. When 

 we have succeeded in matching the unknown resistance 

 by one equal to it from amongst the known resistances, 

 the currents in the two branches will be equal, and the 

 needle of the differential galvanometer will show no 

 deflection. With an accurate instrument this null method 

 is very reliable. \ 



(d) The best of all the ways of measuring resistances 

 is, however, with a set of standard resistance coils and 

 the important instrument known as Wheatstone's Bridge, 

 described below in Art. 344. 



(e) To measure very high resistances the plan may be 

 adopted of charging a condenser from a standard battery 

 for a definite period through the resistance, and then 



