ON THE SPECIFIC RESISTANCE OF MERCURY. 
175 
of section cannot be neglected, the actual resistance is greater than the formula would 
lead us to suppose, as is evident if we imagine the section to become at one place very 
small. 
In general we must regard s as a function of the position ( x ) along the tube at 
which it is taken. For the purposes of the present paper we may assume with 
sufficient approximation (see Lord Rayleigh’s £ Theory of Sound,’ § 308) 
v 
The necessary data with respect to s are obtained by a calibration of the tube. “ If 
a small quantity of mercury is introduced into the tube and occupies a length X of the 
tube, the middle point of which is distant x from one end of the tube, then the area s 
of the section near this point will be s= C/A., where C is some constant. The weight 
of mercury which fills the whole tube is 
where n is the number of points at equal distances along the tube, where X has been 
measured, and p is the mass of unit of volume. 
“ The resistance of the whole tube is 
“ Hence 
and 
R= f«fc r L 
J s C ' ' n 
WR=, p2W s(i)F 
WE 
r— pL 2 
gives the specific resistance of unit of volume” (Maxwell’s ‘Electricity,’ § 362). 
In the sequel 
is denoted by /x ; it is a numerical quantity a little greater than unity. 
Another correction is required in our method of working to take account of the 
resistance offered by that part of the mercury in the terminal cups, which is situated 
just beyond the ends of the tube. The question is identical with that of the correc¬ 
tion necessary in calculations of pitch for the open ends of organ pipes (see ‘ Theory of 
Sound,’ § 307, and Appendix A), and it scarcely admits of absolutely definite solution. 
We cannot, however, be far wrong in adding to the actual length of the tube ‘82 of 
its diameter, which corresponds to the supposition that the diameter of the mercury 
column suddenly becomes infinite. Since, in our experiments, the whole correction 
