ME. W. CEOOKES ON THE ATOMIC WEIGHT OF THALLIUM. 
317 
ill being now included, and from the data thus obtained its true weight is calculated. 
There have thus been obtained : — 
a. The weight of the glass + thallium. 
(3. The weight of the glass-}- nitrate of thallium, 
y. The weight of the glass alone. 
From these data the atomic weight of thallium can be calculated by the formulae 
given in the next section. 
Section V.— CALCULATION OF THE EESULTS. 
The succeeding results must not be regarded as embodying all the attempts to 
determine the atomic weight ; for, as stated in the preceding section, many of the appa- 
ratus were broken at various stages of the operation. The calculations, however, serve 
to illustrate the weighings which came to a successful issue. 
For the accurate determination of the weighings, it will be seen that it is necessary to 
ascertain the density of the ordinary atmosphere at the place where the weighings are 
made. Ritter has deduced from Kegnault’s observations that in Paris, lat. 48° 50' 14", 
at 60 metres above the level of the sea, a litre of dry atmospheric air at 0° C. and 760 
millims. pressure weighs P2932227 gramme. It is well established that if G repre- 
sents the force of gravity at the mean level of the sea in lat. 45°, the force of gravity in 
lat. X at the mean level of the sea=G(l — 0-0025659 cos 2x). 
The force of gravity in a given latitude at a place on the surface of the earth at a 
height ^ above the mean level of the sea 
multiplied by the force of gravity at the level of the sea in the same latitude, r being 
the radius of the earth = 63966198 metres, its mean density, and $' the density of that 
part of the earth which is above the mean level of the sea ; and if the ratio s' : g be 
taken as 5 : 11, then 
2 — ^( = 1-32 nearly. 
Continuing the reasoning, Professor Miller has shown that a litre of dry atmospheric 
air, containing the average amount of carbonic acid, at 0° and 760 millims. pressure, at 
i the height z above the mean level of the sea in lat. X, weighs in grammes 
! 1-2930693 (1-1-32 (1-0-0025659 cos 2x). 
It has been shown by Regnault and others that, between 0° and 50°, the ratio of the 
density of air at 0° to its density at C is 1 + 0-003656^, and that the density of the 
vapour of water is 0 - 622 of that of air. Therefore the weight in grammes of a litre of 
air will be 
1-2930693 
1 + 0 - 003656 ^ 
- — (l — 1-32 0 (1-0-0025659 cos 2x), 
MDCCCLXXIII. 
2 
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