784 PROF. W. H. MILLER ON THE CONSTRUCTION OF THE NEW STANDARD POUND. 
If^eight of Air. 
According to Ritter* the observations of Regnault'|“ show that in Paris, 
lat. 48° 50' 14", 60 metres above the level of the sea, a litre of dry atmospheric air at 
0°C., under the pressure of 760 millimetres of mercury, weighs 1'2932227 gramme. 
Assuming that atmospheric air contains on an average 0‘0004 of its volume of 
carbonic acid the density of which is 1'529 of that of atmospheric air, the weight of 
a litre of dry atmospheric air containing its average amount of carbonic acid, under 
the circumstances already stated, will be 1'2934963 gramme. It appears from the 
discussion of pendulum experiments by Mr. Baily:}:, that if we take G to denote the 
force of gravity at the mean level of the sea in lat. 45°, the force of gravity in lat. A, 
at the mean level of the sea, 
= 0(1—0-0025659 cos 2X). 
Poisson § has proved that the force of gravity in a given latitude at a place on the 
surface of the earth at the height 2 above the mean level of the sea 
ll 
rj 
X (force of gravity at the level of the sea in the same latitude). 
where r is the radius of the earth, its mean density, and the density of that part of 
the earth which is above the mean level of the sea. If, as is probable, 
3 p' 
2 — 2 p = 1’32 nearly, r=6366198 metres. 
Hence the weight in grammes of a litre of dry atmospheric air containing the average 
amount of carbonic acid, at 0°, and under the pressure of 760 millimetres of mercury 
at 0°, at the height s: above the mean level of the sea in lat. X, is 
1 -2930693 1 — 1 -32 jV 1 — 0-0025659 cos 2>.). 
Regnault found the expansion of air from 0° to 100°, under constant pressure, 
equal 0-36706 of its volume at 0°; also that, at 50°, the mercurial thermometer was 
a little in advance of the air thermometer |j. The difference between the mercurial 
and air thermometers, at 50°, amounts to about Hence, the expansion of air 
between 0° and 50°-2 is 0” 18353 of its volume at0°; or, between 0° and 50°, the ratio 
of the density of air at 0° to its density at is 1+0-003656#. The density of the 
vapour of water is 0-622 of that of air. Hence, if # be the temperature of the air, b 
the barometric pressure, v the pressure of the vapour present in the air, h and v being 
expressed in millimetres of mercury at 0°, at a place on the surface of the earth at a 
height z above the mean level of the sea, in lat. X, the weight in grammes of a litre 
*■ Memolres de la Societe de Physique et d’Histoire Naturelje de Genhve, t. xiii. p. 361. 
t Memoires de I’lnstitut, t. xxi. p. 157. J Memoirs of the Astronomical Society, vol. vii. p. 94. 
§ Traite de Mecanique, t. ii. p. 629. || Memoires de ITnstitut, tome xxi. pp. 91, 238. 
•[ Annales de Chimie, 3“® sdrie, tome v. p. 99. 
