26 M. W. Siemens on a new reproducible Standard 
especially which any one could reproduce with ease and with suf- 
ficient accuracy, seemed to me to be to adopt the resistance of. 
mercury as the unit. Mercury can easily be procured or ren- 
dered of sufficient, almost indeed of perfect purity. As long 
as it is fluid, it has no different molecular states affecting its 
conducting power; its resistance is more independent of tempe- 
rature than that of any other simple metal ; and finally, its specific 
resistance 1s very considerable, so that numerical comparisons 
founded on it as a standard are small and convenient. 
I therefore determined to try if it were possible, by means of 
the ordinary glass tubes of commerce and purified mercury, to 
obtain by suitable methods fixed standard measures of resistance 
of sufficient accuracy. The great difficulty seemed to be the 
impossibility of obtaining glass tubes of a form exactly cylin- 
drical. The diameter of the internal cavity of ordinary glass 
tubes generally varies irregularly. By gauging them, however, 
with a thread of mercury, some pieces of about 1 metre long 
may be selected out of a great number, the diameters of which 
vary almost uniformly. Such tubes as these may be regarded 
as truncated cones, the resistance of which ean be calculated. 
The volume of the cone filled with mercury can be determined 
with great ease and accuracy by weighing the metal contained. 
Let ABCD, Plate II. fig. 1, be such a truncated cone, rand 
R being the radu of its upper and lower circular extremities, and 
Zits length. Let MN be a section parallel to the flame AB, 
and at the distance # from it; let dx be the thickness of this 
section, and zits radius. Then,if W be the resistance of the 
cone in the direction of its axis, and dW the resistance of the 
element MN in the same direction, 
nh plac 2s 
Tz 
But m2 
o— Cer: a “fs 
i 
Therefore, differentiating with respect to 2, 
dz. dae 
a eS, 
whence 
a usp dz ; 
and by substituting this value of da in the first equation, we get 
De. te 
iy =e es 
(R—r)7 z 
