314 THE ELECTRIC TELEGRAPH. 



and 



C.tan.0' = 



+ r + r" ^ 



of which x is the resistance of the element, r that of the 

 galvanometer and connections, and r that added to reduce 

 the deflection. 



By combining these two equations, C and E are eliminated, 

 and the resistance x of the element obtained in the same 

 measure as that in which r and r are expressed in 



_ r tan. (/ -f r") tan. 0' 

 tan. 0' tan. 



If we use the galvanometer as a sine instrument, instead 

 of reading off the angles of deflection < and $', the coils 

 being turned through the angles a and a ', the formula 

 becomes 



_ r' sin. a (r + r") sin. a' 

 sin. a' sin. a 



When neither a sine nor tangent galvanometer, but only" 

 a galvanoscope, the functions of whose needle- deflections are 

 unknown, is at the command of the operator, he can deter- 

 mine exactly the resistance of the element in the following 

 way: 



The element to be measured is connected in the circuit of 

 a rheostat or other wire, whose length is adjustable, and that 

 of the coil of the galvanoscope. 



If the resistance of the galvanoscope coil be g, that of the 

 rheostat wire r, and that of the element x 9 the needle being 

 deflected, say a degrees from the magnetic meridian, the 

 intensity, according to Ohm, is 



- 



E being the electro-motive force, as before, F the unknown 

 function of the angle, and therefore F (a ) the intensity. 

 A resistance equal to r + g being connected between the 

 poles of the element, the current will be split into two equal 

 parts, one part going through the galvanometer and rheostat, 



