314 COMPARISON OF RESISTANCES. 



Suppose we divide the tube into a series of equal lengths by the 



divisions a, b, c /, m, except the last which is arbitrary, and the 



corrections of which are a, /?, y, A, /* ; putting 



we get an approximate value for the resistance of the tube between 

 the divisions a and m, by the expression 



R _ ^C 2 F I i 1 e 2 (m- 



v 



and this value is more exact as the total number of divisions is 

 greater. 



In order to ascertain if the subdivision is sufficient, a series of 

 analogous calculations is repeated by giving C values which gradually 

 decrease, and we stop when the differences of the successive results 

 become inappreciable. 



If the extreme divisions a and m are chosen, so that the ratio 



- given by this expression is equal to , the resistance of the 



'/> (o'l)* 



column of mercury comprised between them at the temperature of 

 zero will be exactly an ohm. 



In comparative experiments it is necessary that the ends termi- 

 nate in vessels of large diameter, also containing mercuryv Theory 

 and experiment show that to the special resistance of the tube must 

 be added that of the portions of mercury which are near its ends in 

 the vessels, and that the correction for this double communication is 

 obtained with sufficient accuracy if we add to the length of the tube 

 a fraction of its diameter equal to 0-82. After- having calculated 

 the length of the tube^ which corresponds to an ohm, 0*82 of the 

 diameter is subtracted, and it is cut off to this new length. 



In this way M. Benoit produced four standards, the difference of 

 whose resistance did not exceed crooo2.* 



924. A straight mercurial standard is inconvenient. Copies may 

 be constructed by means of a narrow tube of any given form, con- 

 taining mercury, and whose ends are connected with reservoirs of 

 large diameter. Fig. 177 represents a standard, the tube of which, 

 twisted in the form of a double spiral, has been filled with mercury 

 in vacuum, and is connected with external reservoirs by platinum 



* BENOIT. Comptes rendus y Vol. xcix., p. 864. 1884. 



