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. [Illustration] 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. --- 252 buckets filled per minute. 40 the weight of water in each bucket. ----- 10080 lbs. expended per minute. 10 feet height of wheel. ------ 11) 100800 momentum, dividing by 11 feet as the height of reservoir. ------ 3) 9163.636 divided by 3. -------- 3054.545 multiplying by 2. 2 -------- 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. CHAPTER IV PNEUMATIC, SIPHON AND HYDRO-PNEUMATIC DEVICES The Hydrostatical Paradox Next to the wheel with levers and weights, we believe this simple Hydrostatical Paradox has more frequently occurred to mechanical and scientific tyros as a means whereby it was hoped to attain Perpetual Motion. There is no record that we know of of the name of anyone who has ever attempted it, and, yet, the instances are doubtless myriads. The author believes he has heard dozens of young persons mention it as a means of obtaining a continuous flow of water. In 1828, Niel Arnott, M. D., published the third edition of his "Elements of Physics, or Natural Philosophy." At page 141 under the subject of "Mechanics" he comments generally on the subject of Perpetual Motion, and says: