EXLEY’S PROPOSITIONS. 
661 
€o>\ When electric atoms are in the ves- 
sel, they also will retain small atmospherules 
el' ethercdl matter, which, although lessdense 
than those of iiie leiiacious atoms, vvill have 
considerable densitj, if the spheres of repul- 
sion of the electiic atoms he very small, which 
is probable. It is also manifest, that the at- 
mospherules of both the tenacious and elec- 
tric atoms will be more dense, when tlie ethe- 
real atoms are more compressed or ciowded 
together. 
Prop. 2. Things being as in prop. 1, the 
actions of any two atoms on each other, com- 
bined with the mutual actions of the whole 
mass on each of the two, will be a repelling 
force between them, inversely proportional to 
their distance. 
Let sbe the centre of the vessel in which ethe- 
real atoms of one sort are compressed by a 
consideratiie force : then, since the absolute 
force of the ethereal atoms is very small, the 
distance between their centres vvill also be ex- 
ceedingly small, constituting points in a sphere 
such as in Newton’s 73rd Prop. B. I. Prin., 
and by that proposition any corpuscle or 
atom r?, placed at any point of this sphere, 
will, by tlie mutual actions of the whole mass 
be attracted by a force proportional to its 
distance from the centre s; hence, if the 
atom a were left to the action of lliis resultant, 
undisturbed by any other influence or obstacle, 
it would move to the centie by a velocity 
determined by this law. The same reason- 
ing applies to any other atom h, in the sphere ; 
therefore, both would, in the absence of all 
obstacle, or other force on eachother, approach, 
and at the same time meet in the centre, and 
always their distances from each other would 
be ptoportional to that of either from the 
centre: but this measures their accelerating 
force, which is, therefore, as tlieir distance. 
But, besides the mutual actions, which 
alone would produce the above motions, the 
atoms a and h act independently, and directly 
on each other, by an accelerating force, 
inversely, proportional to the square of their 
distance, (1st prin.); this must, therefore, 
be compounded with the former ; thus, the 
force between them varies as the distance, 
directly, and as the square of the distance, 
inversely ; that is, as the distance inversely. 
Again, since one of the centres of every 
two contiguous atoms is within the sphere of 
repulsion of the other; riie force, here in- 
vestigated is a repelling force ; which also ap- 
pears from this, that if the compressing force 
were removed, f^the atoms would separates 
hence, the proposition is true when the ethereal 
atoms are of one kind. But, it any number 
of these be removed, and ilieir places supplied 
by other atoms, in such manner, that exactly 
the same equilibrium may be maintained, we 
shall still have the same conclusion. 
Prop, 3. If the absolute forces or spheres 
of repulsion of ilie tenacious atoms be in- 
creased or diminished, the resultant repelling 
force, as determined in the last proposition, 
will not be altered : provided that none of the 
atmospherules of tenacious atoms are pene- 
trated by the centres of others, so as to dis- 
place the atmospherules on the contiguous 
sides ; that is, on the parts between the two 
tenacious atoms. 
For their tendency to separate depends, 
not on their absolute forces, or spiieies of 
repulsion, as is evident from the last proposi- 
tion ; but on tiie law of force, and the given 
pressure, and these remaining, the repelling 
force between the atoms a and b v/i!l also 
remain unaltered. 
Or thus ; let one of the atoms be mcreased 
in its absolute force in any ratio; then the 
force between it and every other atom in the 
vessel is increased in the same ratio; but the 
repulsion between it and contiguous atoms, 
and, consequently, between all contiguous 
atoms, is increased in that ratio : therefore, the 
equilibrium continues ; that is, a variation 
in the absolute force produces no change of 
equilibrium, and their tendency to separate 
remains as before. The truth of the proposi- 
tion is manifest, when the sphere of repulsion 
only is changed. 
Def. 1. A single group of atoms is a collec- 
tion of tvvo or more tenacious atoms, such, 
that all tlieir centres are within the sphere of 
repulsion of some one of them, as in fig. 4. 
Def. 2. A double group of atoms is two 
tenacious atoms or two single groups, or one 
atom or single group connected by a third 
atom or single group, such that the connect- 
ing atom or group displaces the greatest part 
of the ethereal and electric atoms between 
the two atoms or groups which it connects, 
and the parts of their atmospherules on the 
contiguous sides, as in fig. 5 and 6. 
Cor. 1. Considering a single group as one 
atom, there will be always in equal volumes 
of different gases an equal number of atoms, 
the pressuie being given. 
For, 1st, when the tenacious atoms are 
distinct, and separate, and of the same kind; 
this follows from the 2nd and present pro- 
positions ; since, being in the’ gaseous form, 
they are kept apart by intervening ethereal 
mailer; and, since they are of the same kind, 
they will be uniformly arranged in the vessel ; 
therefore, on the other hand, if two gases of 
two given sorts occupy equal, volumes, and 
contain an equal number of tenacious atoms, 
the centres will be equi-distant ; therefore, 
the separating forces (by this and the pre* 
ceding proposition) will be equal ; and 
hence, they will sustain the same pressure; 
tlierefore when the pressure is given, the num- 
ber of atoms is equal. 
2nd. It is manifest from the same propo- 
sitions, that a single group will occupy a 
volume equal to that occupied by a single 
tenacious atom; for, since the centres of all 
the atoms in the group are within the sphere 
of repulsion of one of them, the centre of 
gravity of the group may be considered as the 
centre of a single atom, and the contour of the 
spheres of repulsion as a surface of repulsion 
of greater magnitude ; hence, it will have a 
single distinct aimospherule, and will act as a 
