Next to wheels and weights, the use of liquids in a hydraulic, hydrostatic, or hydro-mechanical manner have been sought to be utilized by Perpetual Motion seekers as a means of obtaining energy from the machine not supplied to the machine. The foregoing are only a few of the many devices of that kind, but they are the most simple of those that have been brought to light, and consequently better illustrate the manner in which it has been sought to utilize the interesting properties of liquid pressure and mobility in the solution of the problem.
An examination of the preceding devices discloses that in each case the inventor sought by the energy of the descent of a liquid to elevate through the same distance of ascent the same or a greater quantity of the same liquid, or in some cases to obtain from the pressure of a liquid a greater force than is required to expand a bag, bellows or vessel, submerged the same distance below the level.
The impossibility of all of these schemes is apparent from the same reasoning that is applied to illustrate and show the impossibility of obtaining Perpetual Motion by the use of wheels, weights, levers and the force of gravity.
In each case the basic idea and error was in supposing that by some possibility the descent of a liquid through a given distance could be made to deliver more energy than would be required to elevate the same quantity of liquid the same distance. As a matter of fact, the descent of a liquid, the same as any other weight, through a given distance represents exactly the amount of energy necessary to elevate the same weight of liquid through the same distance measured vertically. Some loss by friction of the liquid in the containing tubes is inevitable as well as from friction in the working parts of the mechanism. Therefore, as this loss continues, some outside energy must be supplied. If all friction could be eliminated (which is an impossibility) and if the liquid were started in motion, the motion would be constant, but no energy could be taken from it for running other machinery without reducing the motion.
There have been many arguments on this subject. We select one which was elicited by the publication in "Mechanics' Magazine" of an account of the device of the author of the "Voice of Reason." This argument was published in "Mechanics' Magazine" in 1831, and is as follows:
I am induced to make an attempt to demonstrate the utter impossibility, under any circumstances, of making a water-wheel that will supply itself instead of having any surplus power.
The accompanying drawing represents part of an overshot wheel in section, the buckets only part filled, by which the whole of the water expended continues to act through a greater portion of the circumference than it otherwise would do. The area of the vertical section of the complement of water to each bucket is made 40 inches; and taking the breadth of the wheel at, say 28 2/3 inches, gives 40 lbs. as the weight of water in each bucket; therefore, as there are 12 buckets containing 40 lbs. each, No. 13 30 lbs., and No. 14 only 20 lbs., altogether making a total of 530 lbs. acting on the wheel at the same time;—to show clearly all the effect that can be expected from this, I have divided the horizontal radius into a scale of 40 equals parts (there being 40 lbs. in each bucket); and from the gravitating centre of the fluid contained in each is drawn a perpendicular to the scale, where the effective force, or weight in each bucket, may be read off as on the arm of a common steelyard. The weights will be found as follows, viz:—
No. Lbs. 1 21½ 2 26¼ 3 30½ 4 33¾ 5 36¾ 6 38¾ 7 39¾ 8 40 9 39½ 10 38 11 35¾ 12 32½ 13 21 14 12 It is therefore quite evident that, although we have 530 lbs. acting on one side of the wheel, a column of water weighing 446 lbs. reacting at the same distance from the centre, on the opposite side, will exactly balance the whole 530 lbs. contained in the buckets; so that about a sixth of the expenditure rests on the axis without producing any useful effect, and the wheel so loaded must remain in a state of rest. Now, in spite of friction and the vis inertia of matter, if we suppose the wheel at work, it can raise only 446 lbs. at the expense of 530 lbs.; but even if it could raise the whole 530 lbs., we should then be but little nearer the mark, for we must remember that the gravitating centre of our power falls through a space of only 8 ft. 11 in., while the water must be raised at least 11 ft. before it could be laid on and delivered clear of the wheel.
As a further means of coming at the end I had in view at the commencement of this letter, I will conclude with a simple rule for calculating the quantity of water a wheel of this kind will raise:—Multiply the number of pounds expended in a minute by the height or diameter of the wheel in feet, divide the product by the height (also in feet) of the reservoir to be filled, and two-thirds of the quotient will be the answer required. Example, for the wheel above described, making six revolutions per minute:—
42 buckets on wheel.
6 revolutions per minute.
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252 buckets filled per minute.
40 the weight of water in each bucket.
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10080 lbs. expended per minute.
10 feet height of wheel.
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11) 100800 momentum, dividing by 11 feet as
the height of reservoir.
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3) 9163.636 divided by 3.
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3054.545 multiplying by 2.
2
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6109.09 answer in lbs.So that for every 1008 gallons expended on the wheel, we only gain sufficient power to supply 611 nearly.
See also Chap. XV, Bishop Wilkin's Work, appearing at page 297 et seq. supra.
| No. | Lbs. |
| 1 | 21½ |
| 2 | 26¼ |
| 3 | 30½ |
| 4 | 33¾ |
| 5 | 36¾ |
| 6 | 38¾ |
| 7 | 39¾ |
| 8 | 40 |
| 9 | 39½ |
| 10 | 38 |
| 11 | 35¾ |
| 12 | 32½ |
| 13 | 21 |
| 14 | 12 |