RESISTANCE BY A METHOD BASED ON THAT OF LORENZ. 
31 
voltmeter placed across either resistance. The voltage across the resistance R is 
balanced (by the help of a tuned vibration galvanometer) against the voltage induced 
in the secondary circuit of the mutual inductance. The value of the variable mutual 
inductance is found by comparison with a fixed mutual inductance whose value is 
calculated from its dimensions, and the resistance R is determined in terms of this 
inductance and the frequency of the alternating current. 
Table I. gives the principal results, the values given in columns 5, 6, and 7 being 
those given by the experimenters. It will be seen that in some cases mercury 
standards of resistance were available, and in other cases the results are given in 
terms of the British Association unit (B.A. unit) or the Siemens unit. When 
mercury standards of resistance were available, the results (previous to 1892) state 
the length at 0° C. of a column of mercury having a uniform cross-section of 
1 sq. mm. and a resistance of 1 ohm. The Siemens unit of resistance is the resistance 
at 0° C. of a column of mercury 100 cm. in length and 1 sq. mm. in cross-section; 
results which give the absolute value of the Siemens unit may therefore be reduced 
to give the length representing 1 ohm by taking the reciprocal of the absolute value 
and multiplying by 100. 
In 1892, and again in 1908, the international ohm was defined as the resistance of 
a specified column of mercury. In 1892 Dr. von Helmholtz pointed out that a 
difficulty arose in determining the cross-section of a column of mercury owing to 
there being some doubt as to the correct value for its density. He suggested that 
the difficulty should be avoided by stating the mass of a mercury column of a given 
length which has a resistance of 1 ohm. This was agreed to and the international 
ohm was defined as the resistance at 0° C. of a column of mercury 14‘4521 gr. in 
mass and having a length of 106'3 cm. The number 14'4521 is the product of 1'063 
and 13'5956, the latter number representing at that time the mean of the best 
determinations of the density of mercury at 0° C. The cross-section of the specified 
column is therefore equal to 1 sq. mm. or nearly so. The ratio of the international 
ohm to the Siemens unit may therefore be taken as 1'063. 
The B.A. unit is so much referred to in the earlier determinations that it may be 
useful to state clearly what is meant by the unit. In 1864 Messrs. Matthiessen and 
Hockin constructed a number of coils of various materials to represent at certain 
specified temperatures resistances of 10 9 cm./sec. units of resistance as determined by 
the 1862-3 British Association Committee on Electrical Standards. The resistances 
of these coils did not keep absolutely constant, and in after years the B.A. unit was 
taken as the mean of the values of six of these coils at the temperature at which they 
were stated by Hockin to be correct. The B.A. unit of one period is not, therefore, 
necessarily the same as that of another period. Every precaution was, of course, 
taken to ensure constancy, but with wire standards of resistance great difficulty is 
experienced. In after years* it proved possible to trace the changes in these coils 
* ‘B.A. Elec. Stands. Committee Report/ 1908. 
