3rd. Upon the degree of compression to which this fluid, supposed to be perfectly elastic, is subjected, upon which will depend the rapidity with which it will close in and fill the space behind the body in motion. ~The resistance of a fluid to a body as the squares of the velocities.~ Firstly, with regard to the velocity of the body. It is evident that a plane moving through a fluid in a direction perpendicular to its surface, must impart to the particles of the fluid with which it comes in contact, a velocity equal to its own; and, consequently, from this cause alone, the resistances would be as the velocities; but the number of particles struck in a certain time being also as the velocities, from these two causes combined, the resistance of a fluid to a body in motion, arising from the inertia of the particles of the fluid, will be as the square of the velocity. ~Cohesion of the particles of a fluid, and friction.~ Secondly, a body moving in a fluid must overcome the force of cohesion of those parts which are separated, and the friction, both which are independent of the velocity. The total resistance then, from cohesion, friction, and inertia, will be partly constant and partly as the square of the velocity. ~Result.~ The resistances therefore are as the squares of the velocities in the same fluid, and as the squares of the velocities multiplied by the densities in different fluids. Hitherto, however, we have imagined a fluid which does not exist in nature; that is to say, a _discontinued_ fluid, or one which has its particles separated and _unconnected_, and also perfectly non-elastic. ~Atmosphere, and its properties bearing on the question of its resistance.~ Now, in the atmosphere, no one particle that is contiguous to the body can be moved without moving a great number of others, some of which will be distant from it. If the fluid be much compressed, and the velocity of the moving body much less than that with which the particles of the fluid will rush into vacuum in consequence of the compression, it is clear that the space left by the moving body will be almost instantaneously filled up, (plate 23, fig. 2); and the resistance of such a medium would be less the greater the compression, provided the density were the same, because the velocity of rushing into a vacuum will be greater the greater the compression. Also, in a greatly compressed fluid, the form of the fore part of the body influences the amount of the retarding force but very slightly, while in a non-compressed fluid this force would be considerably affected by the peculiar shape which might be given to the projectile. ~Resistance increased when the body moves so fast that a vacuum is formed behind it.~