446 On the two great powers, [Srpr. 
enlarged) has to support a column of air, the base of which is four 
particles, two being shown in the side view. Hence the atmospheric 
force tending to compress any two gaseous particles must increase as 
they recede from each other; and even very considerably, for aerial 
fluids expand much from small increments of temperature*. 
The experiments of Mr. Dauton, Dr Luc, and others, made chiefly 
between the freezing and boiling points of water, lead to the conclusion 
that gases expand zo (of their bulk at 32°) with each accession of 
temperature of one degree (Farh.) in a simple arithmetical progression ; 
and it appears assumed that this is the law of their expansion by heat. 
Hence air at 32° by an advance of 480 degrees, i. e. to 512°, would 
have its bulk doubled. Let us suppose two cubical pints of air to be 
taken; and let one of them be expanded to double its bulk, i. e. to a 
quart. Since the distance of the atoms increases as the cube root of 
the bulk; the bulk of one of these portions of air having become 2 to 
the other as 1; the distance of the atoms will have increased in the 
former in the ratio of the cube root of 2 to the cube root of I, i. e. as 
1.26 to 1 nearly ; and since the number of atoms under a given surface 
of the gas expanded to a quart will be 100, while there are 158 under 
the same surface in the pint, and the pressure being constant on a 
given surface, 100 atoms of the former will have to support as much 
as 158 of the latter. Let the pressure be called 158. It is plain each 
particle of the quart will be pressed on by a force 1.58, while each of 
the pint will have to bear only a pressure of 1. 
Again, since, as was shown by Newron, the mutual elasticity of 
the particles of air (and the same is assumed with regard to all gases), 
varies inversely as their distance, i. e. decreases in the direct proportion 
of their separation; and since the pressure increases as the square of 
their distance; the total absolute force expanding a gas must be in- 
* The reader will not, it is hoped, think that the following error is here com- 
mitted of supposing that by increasing the surface of a volume of gas the compres- 
sion of its parts is increased; as for instance, that the compression of the parts 
of a spherical pint of gas (in which form the surface is the least possible) would 
be increased by moulding the volume into any other form, as that of a long cylin- 
der, where the surface would be greatly increased. So long as the number of par- 
ticles in a given volume is constant, the pressure and mutual re-action of the atoms 
will of course not vary, whatever may be the extent of surface exposed to the at- 
mosphere or to any vessel it is contained in. But directly the number of particles 
in a given bulk, ceases to be constant owing to expansion, the pressure on each 
particle, of necessity must increase, whether it be a superficial particle contiguous 
to the air, or inside of the vessel, or a central one receiving the pressure from the 
other particles and re-acting against it. 
