So likewise, if we take two loose pulleys, (which will not add much to the complication of the Machine) and make the third term 1 inch, the fourth will become 4⁄3, shewing the ratio of the progression to be 1⁄3, so that the series of 12 terms will stand thus:
| Terms, | 1 | — | 2 | — | 3 | — | 4 | — | 5 | — | 6 | — | 7 | — | 8 | — | 9 | — | 10 | — | 11 | — | 12 | |
| loose; | loose; | 1; | 4⁄3; | 5⁄3; | 6⁄3; | 7⁄3; | 8⁄3; | 9⁄3; | 10⁄3; | 11⁄3; | 12⁄3; | or, |
four inches for the largest groove in the concentric part of the System.
Now we saw before, that the first and last pulley were in diameter to each other, as 1 to 12; whereas, here, with only two loose pulleys, these extremes are but as 1 to 4: dimensions much more convenient and manageable. The 5th. figure of the Plate 7, is intended to shew graphically, the effect of this modification of the principle. In that figure, if the line a, be the diameter of the first pulley, that of the sixth pulley will be shewn by the line b c; but if the same line a be made the second pulley, the diameter of the sixth will be shewn by the line e d; only 2⁄3 of the former. And in fine, if the same a, be the third pulley, the sixth will have it’s diameter reduced to the line f g, only one half of what it was in the first case. In a word, the more loose pulleys are put before the fixed ones begin, the nearer to cylindrical will the general form become; and the more conveniently may pulleys be used for general purposes. I might even assert, that if one, or at most two loose pulleys had been used in the above-mentioned experiments, the result would have been as favourable to the System, with respect to the weight of the tackle and stress on the ropes, as it was in respect of power; where it’s advantages were important and undeniable.
OF
A POWER-WHEEL,
Turned by heated Air, Gas, &c.
This Wheel (see Plate 8, fig. 1,) is technically called a Bucket-wheel. It is plunged almost entirely in water, oil, mercury (or other heavy fluid) contained in the vessel A B. It’s axis carries a waved wheel a b, on which rolls a friction-pulley p, running on a pin in the mortice of the bar c d. This bar works the pump f; which by the descent of it’s loaded Piston, drives cold air (or gas) into the tube g, communicating with several collateral ones placed across the vessel, so as to convey the air to h, below and beyond the centre of the wheel. A fire being made at F under this vessel, the water (or other fluid) is brought to a proper heat; and if then the pump f, be made to give a stroke or two, air will be forced from the tubes at h, which having been heated in the passage, will bubble up into the buckets h, i, k, &c. and turn the wheel so as to perpetuate it’s own supplies from the Pump, and furnish a surplus of power for other purposes. This results from the fact, that air (for example) in rising to the temperature of boiling water, expands, under the pressure of the atmosphere, to about three times the volume it occupied at the mean temperature: so that it resists the entrance into the vessel as unity, and acts (when heated) as 3: leaving a power of two, in the form of a rotatory motion.
It will occur to many readers, that azotic gas or nitrogen, might be used with advantage to turn this wheel: only adding to the Machine a long returning tube, leading from the top of the vessel, through air or water, to the suction valve of the pump f; and that in order to bring down the temperature of the gas from the heat it had acquired in the vessel, to the mean temperature; at which this gas is said to occupy only 1⁄7 of the space it fills when at the heat of boiling water.
I have now to observe that this invention was executed in 1794, of which abundant proof remains. Since then, it has been proposed by other persons, and is I think, patentized either in France or England: but a different method is employed of introducing the cold air, namely an inverted screw of Archimedes, whose manner of working I do not entirely recollect. What I here wish to observe is, that this concurrence of idea between others and myself, gives me no pain; since it would be more strange if it did not happen, while so many active minds are ransacking nature for the very purpose of unveiling her secrets. Only I think it incumbent upon me to use every method, consistent with truth and honour, to avoid being thought unjust enough to purloin other people’s ideas, and call them my own.
OF
AN EQUABLE PUMP,
Or Machine for raising Water without interruption or concussion.
This Machine is represented in Plate 8, fig. 2 and 3. It is composed of two barrels A B, both of them forming part of the column of water to be raised; connected together by a crooked tube C, of equal diameter, out of which the lower Piston-rod passes through a stuffing box into the air: as does the upper Piston-rod at D, where the column leaves the Pump to pass upward. The two Pistons fixed to the rods E and F, are of the bucket kind; made as thin and light as possible; their valves opening upwards and their motions being such, generally, that when one of them is drawn up, the water rises through the other, then descending: But here lies both the novelty and utility of this Machine; these upward and downward motions are not reciprocal: Both Pistons fall faster