THE MEASUREMENT OF RESISTANCE 



161 



determined. Let the connections be as shown in Fig. 88. The 

 resistances of the various circuits are indicated on the diagrams; 

 2 5 and i& are the galvanometer currents, i B the battery current. 

 Let Si be the resistance between 3 and 4; with the connections 

 shown in the diagram, it is the parallel resistance of S and N 

 (Fig 87). 



i(rs + a + X) - i B (X + a) + i s a = 0. 



; 5 (r 5 + + &)- ia(a + Si) + i* = 0. 



I'efre + Si + a') - ^(Si + or') + i\a' = 0. 



i' 5 (r 6 + Z + aO - *V* + ') + *' / = 0. 



Position TI 



FIG. 88. Mesh diagram for Kohlrausch method. 



Solving for the desired currents and letting 



?_ 

 M 



<*(r b + r 6 + Si + X) + (r 5 + &)(* + X) 



M' = 



is = 



(r 5 



-f 



i'e = Jlf'a'frs + Si) + 5 

 z' 6 = M'la'fre + X) 



Now let the deflection per ampere due to the coil carrying i& 

 be A and that for the coil carrying i' 6 be 5. Then, as the two coils 

 oppose each other and their effects are very nearly equal, the 

 resultant deflection will be 



For position 7, 

 Dj = M[A{ a (r & +Si)+Si(r & +X)}-B{a(r b +X)+X(r,+ Si)}]. 



For position II, 

 D II = M'(A{a'(r 6 +X)+X(rs+S l )}-B{a'(r b +Si)+Si(r b +X)}]. 



Conditions for Balance. Suppose that by adjusting the resist- 

 ances the deflection is made nil for both positions of the rocker; 

 that is, 



Dj = Dn = 0. 



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