8 Messrs. Richardson, Nicol, and Parnell on the 
hydrogen at 0° C.and 76 cms. of mercury. Let p, v,and P, V 
be the average pressures and volumes of the gas in the 
portions of the apparatus to the left and right of the stop- 
cock A (fig. 1) respectively. Let h, and hz be the initial and 
final readings of the. right-hand side of the sulphuric-acid 
gauge, o its internal sectional area, and p the ratio of the 
density of sulphuric acid to that of mercury. Then the total 
quantity of gas which has diffused out during an experiment 
is given by 
] 1 
—dm=— R d(pv)= — R (pov + vdp), 
where dv=(hj—hy)o and dp=2p(hi—hy) +5P, SP being 
the increase of the pressure on the left-hand side of the gauge 
produced by the motion of the liquid. 
Hence 6P = —a(hg—h,) a 
. Substituting we get 
1 
—dm == R (hy— hy) Ez + op(1 + 7H 5 
since p=P very nearly. As the effect varies very rapidly 
with the temperature of the tube, something has to be allowed 
for the cooling of the platinum tube near the leads. This 
was done by neglecting one centimetre at each end; thus 
the tube, which was really 10 cms. from lead to lead, was 
assumed to have the same effect as a tube 8 cms. long 
uniformly heated to the temperature of the middle point of 
the actual tube. This gave 4°52 sq. cms. as the effective 
superficial area of the hot tube. Putting in this value and 
values found for p, a, and V, we obtain the reduction formula 
hy>—h, 
© ~ ; = mo 4 0, Vv 
(Q)= 2°544 x 10 ( : )l 272v + 0844p (1+ =) |. 
The area of cross-section o was determined by cutting 
down the gauge and weighing a column of mercury in it of 
known length. It was important to determine the volume v, 
of the apparatus to the right of the gauge when the mereury 
was at the zero mark in the burette C,; with some accuracy. 
This was done by cutting down the gauge at the point N in 
the diagram, replacing the sulphuric acid in it by mercury, 
shutting off the tap A and altering the volume of air in the 
‘burette by moving the mercury reservoir. The end N being 
open to the atmosphere, corresponding readings of the pres- 
sure (on the gauge) and of increase of volume, v—v,, (on 
the burette) were taken. These on reduction gave v,=46°3 c.c. 
