File:Manège aérodynamique, whirling arm, de Robins, 1805.png

I think it incumbent on me to describe the machines and methods made use of on this occasion, together with an account of the nature and events of the trials thus exhibited. For I conceive a narration of this kind, corroborated by the recollection of those gentlemen who were then present, will be a much, stronger confirmation of the principles, I advance, than the result of any experiments, which depended merely on my own relation. For my single evidence might perhaps be considered as precarious; as I might at least be suspected of being biassed, towards those novel doctrines, of which I profess myself in some degree the inventor. To begin then with this narration, it is necessary to mention, that, in the first paper delivered to the society, I asserted the two following propositions :
First, “ That the resistance of the air to a 12 lb. iron bullet, moving with a velocity of 25 feet in a second, is not less than half an ounce avoirdupois.”
Secondly, “ That the resistance of the air, within certain limits, is nearly in the duplicate proportion of the velocity of the resisted body."

These propositions are in themselves neither unknown nor doubtful; but yet, as they are the basis of some other assertions, which have been hitherto constantly contested and denied; I thought it requisite to evince their veracity by more unquestioned and simpler methods, than have been hitherto practised; for, this purpose, I therefore caused a machine to be made of the form represented in the annexed drawing (Plate II. Fig. I), which was most excellently executed under the direction of Mr Ellicot, and was completely fitted for the use intended by many contrivances, some of them not contained in the drawing, nor necessary to be particularized in this place. For it is sufficient for the purpose of the following experiments, to destribe its general fabric, by observing that BCDE is a brass barrel moveable on its axis, and so adjusted by means of friction wheels, which are not represented in the drawing, as to have no friction worth attending to. The frame, in which this barrel is fixed, is so placed, that its axis may he perpendicular to the horizon. The axis itself is continued above the upper plate of the frame, and has fastened it a light hollow cone AFG; from the lower part of this cone there is extended a long arm of wood GH, which is very thin, and cut feather-edged, and at its extremity there is a contrivance for fixing on the body, whose resistance is to be investigated (as here the globe P) and, to prevent the arm GH from swaying out of its horizontal position by the weight of the annexed body P, there is a brace AH of fine wire fastened to the top of the cone, which supports the end of the arm. Round the barrel BCDE there is wound a fine silk line, the turns of which appear in the figure, and after this line hath taken a sufficient number of turns, it is conducted nearly horizontally to the pully L, over which it is passed, and then a proper weight M is hung to its extremity. If this weight be left at libertv, it is obvious, that it will descend by its own gravity, and will by its descent turn round the barrel BCDE, together with the arm GH and the body P fastened to it. And whilst the resistance on the arm GH aiid oh the body P is less than the weight M, that weight will accelerate its motion, and thereby ; the motion of GH and P will increase, and consequently their resistance will increase, till at last this resistance and the weight M become nearly equal to each other. The motion with which M descends, and with which the body P revolves, will hot sensibly differ from an equable one. Whence it is not difficult to conceive, that by proper observations made with this machine. The resistance of the body P may be determined, the most natural method of proceeding in this investigation is as follows. Let the machine have first acquired its equable motion (which, as will hereafter appear, will be usually attained in five or six turns from the beginning) and then let it be observed, by counting a number of turns, what time is taken up by one revolution of the body P; then taking off the body P and the weight M, let it be examined, what smaller weight will make the arm GH revolve in the same time, as when P was fixed to it; this smaller weight being taken from M, the remainder is obviously equal in effort to the resistance of the revolving body P; and this remainder being reduced in the ratio of the length of the arm to the semidiameter of the barrel, will then become equal to the absolute quantity of the resistance. And as the time of one revolution is known, and consequently the velocity of the revolving body; there is thereby discovered, the absolute quantity of the resistance to the given body P, moving with a given degree of celerity. And note, that to avoid all exceptions, I have generally chose, when the body P was removed, to fix in its stead a thin piece of lead of the same weight, placed horizontally; so that the weight, which was to turn round the arm GH without the body P, did also carry round this piece of lead. This I did, lest it should be objected, that the body P retarded the weight M by its quantity of matter, as well as by its resistance. But mathematicians will easily allow, that there was no necessity for this precaution.