34 M. W. Siemens on a new reproducible Standard 
temperature of the ice-water varied between 0° and 2° C., and 
that of the standard between 19° and 22° C.; and as the con- 
ductibility of copper is diminished about 0°4 per cent. for every 
degree Centigrade, the differences in the above measurements, 
which are all under 1 per cent., are thereby fully accounted for ; 
and there can be no doubt that in this way standard measures 
of resistances can be reproduced of any degree of accuracy. 
The observed resistances in Table IV. ought strictly to have 
been diminished by the resistance of the mercury in the glass 
vessel to the spreading of the current, that is, by the resistance 
encountered by the current in passing from the orifice of the 
tube to the amalgamated copper conductors. This resistance 
may, without any considerable error, be taken as the resistance 
of a hemispherical shell, whose lesser radius is equal to the inner 
radius of the tube, and whose greater radius, on account of its 
comparative magnitude, may be taken as infinite. Now the 
resistance of a hemispherical shell of radius x and thickness dz 
being called dW, we have 
dx 
whence 
(ee) 
re { dx 1 r 
20° Qra Orta 
The resistance to the spreading of the current in the mercury at 
both ends of the tube is therefore equal to the resistance of a 
portion of the tube whose length is half its diameter. This 
resistance ought to be still further increased, because the surface 
of the mercury in the tube is flat and not hemispherical, as is 
assumed in the above calculation ; but these two sources of error 
are each of them so trifling, that their jomt effect may be 
neglected. 
The straight tubes used in the experiments hitherto described 
cannot be very conveniently employed as standards; I therefore 
got M. Giessler of Berlin to make me some spiral glass tubes, 
having their extremities turned up and provided with small ves- 
sels in which to receive the conducting wires. ‘These glass spirals 
were fastened, as shown in fig. 4, into the wooden cover of a 
broad glass vessel filled with water. The temperature of the water 
in the vessel was observed by means of a thermometer introduced 
through an opening in the cover. The glass spirals were easily 
filled with mercury, so as to be free from air-bubbles, in the follow- 
ing manner :—The orifice of the tube in one of the glass vessels 
was first stopped by means of a suitably shaped cork; the other 
vessel was then filled with mercury, the air being suffered to 
escape gradually by the cork at the other end, which was only 
