The Reasons of Motive Forces

First Book,

THEOREM IX.

Some men have greatly deceived themselves in the construction of several machines, which, after being built, did not succeed nor produce the effect they intended, because they were ignorant of the principles of motive forces. Such was the case with those who translated Hero Refers to Hero of Alexandria, a mathematician and engineer from the 1st century AD whose work Pneumatica was a foundational text for Renaissance engineers., who made many of their figures incorrectly. I shall recount one on this subject to show that air passes through water; the fifty-fifth problem is illustrated in this manner:

A technical diagram illustrates a hydraulic experiment. A large cylindrical vessel (marked A and B) sits on a base (K, L, M, N). Inside, an inverted U-shaped siphon (D) has an inlet (C) and an outlet (E) exiting through the bottom. Three short, wide tubes (F, G, H) at the base of the vessel surround the bottom of the siphon legs. Dotted vertical lines (marked O) indicate a specific height above tube H. A vertical support frame with a handle is labeled J.

Let there be a vessel marked A. B. on the base L. K. M. N., in which there are three siphons A tube used to convey liquid upwards from a reservoir and then down to a lower level. as the figure demonstrates, and at each of these, there is a small short pipe marked F. G. H. These are larger than the siphons so that the water from the said siphons can pass between the two. Thus, when pouring water into the vessel A. B., when it reaches the top of siphon E., the said siphon will empty all the water that had been put into the vessel, and then the small pipe H. will remain full of water. Afterward, when water is put back into the vessel (says the translator), the said water will rise to the surface C. without flowing through the siphon E., because (he says) the water being in pipe H. will prevent the air from leaving the siphon, and consequently prevent its flow. This cannot be so, for the said pipe H. being short as it is pictured, the air will bubble through the water as soon as the water exceeds the surface E. by the height of the pipe H. And so, to prevent this accident, it would be necessary for the said pipe H. to be as high as the hidden lines O. original: "lignes occultes." In architectural and technical drawing of this period, "occult" or "hidden" lines refer to what we now call dotted or dashed lines., and to do the same for the other pipes F. G. It is certain that water measures itself by its length A reference to the principle of hydrostatic head or vertical height., and if the distance between the surface of the siphon and the surface of the water in Vessel A. B. is longer than the pipes F. G. H., the air will pass or bubble through the water as has been said. The experience of this is also seen in a lead or copper pipe, for if one puts one of the ends in water (provided it is not too deep) and blows through the other end, the air, as has been said, will bubble right through the water. A similar occurrence of the same nature also happens to simple pumps when one wishes to force water to rise higher than the nature of the machine allows; air will enter through the water, as will be shown hereafter regarding machines designed for raising water with pumps.

THEOREM X.

To provide knowledge of moving forces by means of a counterweight, we shall begin with the scale, otherwise called the Roman balance Also known as a steelyard; a weighing device with asymmetrical arms that uses a sliding weight to find the mass of an object.. Let there be a balance beam marked A. B., whose point of gravity Here, De Caus refers to the pivot or fulcrum. is marked C., and let the said beam be graduated into eight equal parts—namely, four on each side of the point of gravity. Thus, if a weight of 12 pounds original: "liures." The French livre was a unit of weight roughly equivalent to a modern pound. is hung at point I., it will be equally balanced by a similar weight hung at point D. And if a weight [of]