320 
ME. W. CKOOKES ON THE ATOMIC WEIGHT OF THALLIUM. 
from data given by two weighings, one at ordinary and one at a greatly diminished air- 
pressure, is as follows : — 
Let LI denote the substance to be weighed, and 
h its true weight (in vacuo ) in grains. 
First Weighing in Air of Ordinary Density. 
Let W denote the material weight which balances H, 
w „ „ true weight of W observed in air, 
x ,, „ weight of air displaced by W, 
t „ „ temperature, 
P ,, „ pressure, in height of mercury, reduced to 32° F., 
1) ,, ,, bulk of W in grs. of water at max. density, 
k „ „ weight of air displaced by H : 
iv, x, t, p, h being given, required to find Jc, 
h—k=w—x. 
V 
z 
V 
f' 
55 
35 
55 
55 
55 
55 
35 
Second Weighing in a Rare Atmosphere. 
Let y denote the weights which balance H, 
true weight of y in air of ordinary density, 
,, weight of air displaced by y, 
temperature, 
,, pressure, in height of mercury, reduced to 32° F., 
„ bulk of y in grains of water at max. density, 
l denote the weight of air displaced by H : 
y, t', p', V being given, to find l and z, 
h — l=y — z ; 
hence k-l=y—w-\-x—z. 
By Tables A and B, 
V= y -b 
w 
density rare air 
0-001293893 
max. den. water F ^ ° ^ 3 v t) + l°g j + d-003656 ’ 760 ’ 
, 7 » , density rare air , 
.-. log A+Iog v t nr: lo2f Z, 
° & max. density water ° 5 
l density rare air 
I: density common air 11 ( su PP ost )- 
Let m=y — w-\-x—z m , then k—l—m, j=n. 
Hence l=nk , k—nk=m , k= m 7 mn 
m 
1 —n 
1 — n 
or li—y — 
, 1 = 
1 — n 
mn 
Hence h=w~x - f 
1 —n 
