ON THE SPECIFIC RESISTANCE OF MERCUR5T. 353 



should have changed by exactly the same amount during the last twenty-one years, it 

 is inferred that no change has taken place in them, and the B.A. unit is defined as 

 the mean of the values of the six coils at the temperatures at which they were said 

 by HOCKIN (B.A. Report, 1867) to be correct. It was used in this sense by Loi-d 

 I! \vi.i:n;ii in his electrical papers (' Phil. Trans.,' 1881, &c.), and this is the meaning 

 attached to it in the various reports of the Electrical Standards Committee since the 

 year 1882. 



The method employed in making the observations differed but little from that given in 

 Lord RAYLEIGH'S paper. The resistance at Cent, of the column of mercury filling the 

 tube is determined, in B.A. units ; the length, L, of the column of mercury is measured ; 

 its mean cross section is found by measuring at a known temperature the length, I, of a 

 column nearly filling the tube, and then finding the mass of mercury in the column. 

 The mean cross section thus found needs correction for irregularities in the tube, and 

 these are obtained by the ordinary process of calibration. The formula, as given in 

 MAXWELL'S 'Electricity and Magnetism' (vol. 1, 362), requires a small correction, 

 for the fact that the length of the column used to determine the cross section does not 

 quite fill the tube. 



Let * be the cross section at a distance x from one end. Let X be the length of a 

 thread of mercury, which is passed along the tube, when its middle point is at 

 a distance x from one end. Then, assuming the cross section to be constant over 

 the length X, we have s = C/X, where C is the constant volume occupied by the 

 thread ; hence, if n be the number of points at whioh X is measured and p the density 

 of mercury in grammes per c.c., 



Again, let ^ be the average cross section of the tube over the portion (L I) at the 

 end which is not occupied by the mercury used to find the average cross section, and 

 let s be the average cross section of the rest of the tube. 



Then, 



,.;=_' : : . ; :;;-.?*; ...... < 



and, if r be the resistance of a column of mercury 1 metre long, 1 square mm. in 

 section, at Cent., R the measured resistance of the tube, 



therefore, 



MDCCCLXXXVIH. A. 2 Z 



