Let us suppose an apparatus to be constructed of the description represented in the annexed engraving: _a_ is a water cistern, whence water is to be raised by the pump _b_, to supply the cistern; _c d_ is a small pipe with a stop-cock at _e_, which lets the water from cistern _c_ into a strong water-tight bellows _f_. The bellows have no valve, but a cock _g_ to let out the water into cistern _a_; _h_ is a weight, and _i_ a rack on the top of the bellows which works in the cogs on the axle of the large cog-wheel _j_; _j_ turns the little cog-wheel _k_, that gives motion to the arm _l_, and works the pump-handle _m_; _n_ is an upright rod on the end of the lever _o_, which rod has a turn at _p_ and _q_ for the top of the bellows to press against in ascending and descending. The water being let into the bellows from the pipe _d_, will cause the top of the bellows, with the weight and rack, to ascend till the former reaches and presses _p_, which will move the lever _o_ and the arm or rod _r_; by which means the stop-cock _e_ of the pipe will be shut, and the cock _g_ opened, and the water let in from the bellows into the cistern _a_. The top of the bellows will now descend till it comes down and presses the turn _q_, which will again shut the cock _g_ and open _e_, on which the water will again flow from the pipe into the bellows, and cause the top with the rack to ascend. [Illustration] Now it is generally known that the power of an hydrostatic bellows is thus calculated:-- As the area of the orifice or section of the pipe, To the area of the bellows: The weight of water in the pipe is, To the weight the bellows will sustain on the top-board. We will suppose, therefore, the pipe _d_ to be 10 feet high, with a bore equal to 1 square inch, which would give 120 cubic inches, and about 4¼ lbs. of water. Let us suppose, also, the boards of the bellows to be 20 inches square, which gives 400 square inches. When the water is let from the pipe into the bellows, there will be a pressure of 4¼ lbs. on every square inch, which on the whole will amount to 1,700 lbs. Now take half of this force and place it on the top of the bellows; there will then be a working power of 850 lbs. up and down, and allowing the bellows to raise one foot, it will contain about 20 gallons of water. Now the question is, will not the machinery, with a moving power of 2 feet and 850 lbs., raise 20 gallons of water 10 feet, which would, of course, cause the motion to be perpetual?--JOHN SIMS. Pwllheli, North Wales, Dec. 11, 1829. The foregoing device brought from another correspondent the following: Had Mr. Sims gained the power exerted by the descending weight on his bellows, he would have been fortunate indeed; but it unfortunately happens that its returning power (or an equivalent) was expended in raising it.