Source: Histoire et Mémoires de l'Académie Royale, Année M. DC. XCIX.
Title: Moyen de se servir du feu pour faire mouvoir les machines.
Author: Pierre Varignon, French Mathematician
Page updated on Jan. 14th, 2018
The ancients had to do by force of arms, what we today do with extreme ease by different kinds of mills. They did not know, like we do, make water or air work in place of men and horses.
We still have one element to subjugate: the fire, similar in some way to those Indians whom the Spaniards have not yet been able to reduce to working in their mines.
Mr. Amontons does not despair that in the future we will get out of the fire as much service as from the air or from the water. He has imagined for this purpose a kind of mill, of which we shall endeavor to give some ideas.
The heat acts very powerfully and very quickly on the air. If air has complete freedom to expand, the fire only makes it rare and increases its volume. If it can not extend at all, it only increases the strength of its spring. If it can extend, but only to a certain extent, the force of its spring is all the less increased.
The cold, on the contrary, tightens the air and diminishes it spring.
The air, whose spring is increased by heat, can not sustain or raise a greater weight than that of 28 inches of mercury, or 32 feet of water which it usually carries.
On these principles, here is roughly the machine built by Mr. Amontons.
It consisted of a vertical wheel whose axis is horizontal and has two rows of concentric cells or buckets, in equal number, placed at its circumference. The cells of the outer row, which are much larger, are full of air. Those of the inner row, which are on one side and on the lower half of the wheel forming a quarter circle, are full of water. Since there is more weight on this side than on the other side, the wheel rotates until the water is evenly distributed on both sides of the vertical diameter.
In order to make the wheel running, it is necessary to make sure that the water which tends to fall, is supported by some force and pushed back up, so that it always occupies the same quadrant.
The greater weight of that side will always give motion to the wheel.
This is done the following way. The outer cells all pass, each in turn, on a fire disposed on one side of the wheel.
The air of the cell passing through it becomes scarce, but not with complete freedom, it goes through a communication pipe to press the water contained in the corresponding cell, and by increasing its spring, it pushes it up in a higher cell, whilst the cells themselves descend from that side by the movement of the wheel.
That of the outer cells which has passed on the fire to rarefy the air which it contained, and by increasing the spring, then passes into a reservoir full of water, so that its air by cooling quickly, reproduces its effect when passing again on the fire.
It's now only a matter of knowing:
How much time a cell has to spend in the fire to sufficiently rarefy the air it contains, which determines the time of an entire revolution of the wheel, because each cell will take the same time to take sufficient heat.
If the air of this heated cell will have time to find back its first volume during the rest of the revolution of the wheel, and if the water where it passes will hasten this effect sufficiently.
How much, taking into account the size of the spaces where the air will be able to extend, it will be less rarefied than it could have been rarefied, and consequently which increase of spring will remain to him, and what height of water will it be able to support and raise beyond the 32 feet that it supports naturally.
As it is advisable that the cells containing water hold about a quarter of the wheel, which makes a certain perpendicular height of water, it is this height which determines approximately the diameter of the wheel.
Monsieur Amontons has settled all these things by various experiments, some of which are new and curious, and all of which have assured him of the possibility of his machine.
He has found, for instance, that the heat of boiling water can only increase the volume of the air, or the force of its spring, by a little more than a third of what it is usually on surface of the earth ; that the water that is ready to evaporate is the one that cools and tightens the air the most.
After that, in order to judge the effect of this machine, and the force of resistance that it will be able to overcome, it is necessary to determine the quantity or the weight of water which will be put in the cells, and which will give the motion to the wheel, and take care to the time that the wheel will necessarily use to make a turn and the oblique direction of the weight of water relative to the circle, less advantageous than that of the resistant force which will act perpendicularly.
Everything calculated, Mr. Amontons finds that his machine will do at least the effect of 39 horses, and that as it should be expected that each horse maintained throughout the year for work, that however only goes on working days, amounts to 40 sols per day of work.
The profit of this machine will be all the greater, that the expense of the wood that will be burned in 24 hours, will be below 78 pounds. The same fire can still be used for other works; it is a power which ceases and resumes when one wishes, which is not subject to time and place.