Source: Treatise on the Motion of Rockets
Author: William Moore, of the Royal Military Academy, Woolwich.
Date: 1813
Appendix B
On the combustion of the composition of a rocket, an elastic fluid is generated, the full force of which is exerted in the first instant alike in all directions, whether there be any other substance for it to act against or not. Hence, if, in a vacuum, the combustion took place as freely as in common air, the force of a laminum of the composition in its transformed state (equal to the initial strength of the same into the rocket's base), would be that which constantly acted upon the rocket during the time of its burning; for it is only the first force of the gas in this case that has effect upon the body to move it, it being the very next succeeding instant so greatly diminished from the extreme velocity with which it rushes into the vacuum, that it affords, comparatively speaking, no resistance what ever to the fluid next generated, whereby more motion to the rocket would be communicated.
Supposing the elastic force of the gas from the rocket composition to be 1000 times as great as the elastic force of the atmosphere at the earth's surface, it will be found by accurate computation that the velocity with which it would rush into a vacuum is nearly at the rate of 8 miles per second!
Each laminum of gas, as it is produced, acts upon and fires at the same time the following laminum of composition; when the produce of this exerts its force upon, and converts into fluid, in the same manner, the next contiguous laminum of matter, which acts upon and fires the next, and so on continually, till the whole body of the rocket is consumed. If the rocket burns in a medium, then, as there is a body reacting against the fluid that rushes from the rocket, there is not so instantaneous a dissipation of the force of the latter the moment after it is generated, but a time of its action upon the rocket, which is greater or less according as the surrounding medium is more or less dense and elastic.
In this case, therefore, more motion is communicated to the body than in the former, and, but for the resistance to the forepart of the rocket, it would move farther in a medium than in a vacuum. A gun recoils farther when fired with powder and ball than when it is charged only with powder, from the same cause of a longer action of the fluid against the breech of it.