Notwithstanding what we said about the universality of this force, and how it affects all forms of matter, it may still appear as if the air were an exception.  But it is not so; the air also gravitates.  The fact that it gravitates is proved in various ways.  First, if it did not, it would not accompany the earth in its movements round the sun; the earth would sweep along into space, and leave it behind it.  Secondly, if we place a bottle from which the air is exhausted in a balance and exactly poise it with a counter-weight, and then open it and let in the air, it will show at once that the air has weight or gravitates by immediately descending.  Thirdly, if we extend a piece of india-rubber over the end of a vessel and begin to withdraw the air from it, we shall see the india-rubber sink in, under the pressure of the air outside, to fill up the space left vacant by the removal of the included air.  The fact that air gravitates we have already taken for granted in explaining the ascent of a balloon; and the proofs now given are enough to show that the cause assumed is a real one.  The lighter gas rises and the heavier sinks by law of gravitation.

Gravitation and Cohesion.—­Unlike the attraction of aggregation, or cohesion, which acts only between particles separated from each other by spaces that are imperceptible, gravitation takes effect at distances which transcend conception, but it diminishes in force as the distance increases.  The law according to which it does so is expressed thus; its intensity decreases with the square of the distance; that is to say, at twice the original distance it is 1-4th; at thrice, 1-9th; at four times, 1-16th, for 4, 9, 16 are the squares respectively of 2, 3, and 4.  To take an instance, a ball which weighs 144 lb. at the surface of the earth will weigh 1-4th of that, or 36 lb., when it is twice as far from the centre as it is at the surface; and 1-9th, or 16 lb. when it is thrice as far; and 1-16th, or 9 lb. when it is four times as far.  The attraction of cohesion, on the other hand, as we say, acts only when the particles seem almost in contact, and it ceases altogether when once, by mechanical or other means, the bond is broken, in consequence of the particles being forced too near, or sundered too far from, one another.

One distinguishing difference between the attraction of gravitation and that of cohesion is, that whereas the former is uniform, the latter is variable; that is, under gravitation the attraction of any one particle to any other is the same, but under cohesion, some sets of particles are more forcibly drawn together than others.  For instance, a particle of iron and a particle of cork gravitate equally, but particles of iron and particles of cork among themselves do not cohere equally.  And it is just because those of the former cohere more than those of the latter, that a piece of iron feels harder and weighs heavier than a piece of cork.