SIR,-Some years ago, I joined two small Watch-Glasses, of the same diameter, in a bason of water, by pressing their edges together with my finger and thumb, so as to fill them completely. When taken out, I was then in possession of a single microscope, whose focal length being 3-16ths of the distance of distinct vision, magnified the surface of an object 25 times. It then occurred to me, that two such glasses cemented together, leaving a small aperture to fill them up with pure spirit, and cased in a small frame similar to the drawing, would form an instrument simple in construction, and excellent as a pocket companion, for the examination of minute objeets, such as plants, insects, &c. For the purpose of holding objects to be examined, I place a brass pin, turning on a hinge, in the manner represented, on one side of the frame, and a forceps, with screw, on the other, both of such a length as to set exactly to the focus of the lens. There is a groove on each side of the frame to receive the pin and forceps when not used. One principal object ought to be, to make the frame sufficiently thick to protect the convexity of the glass-a small shagreen case would secure the whole. ( 394 ) WORK OF STEAM-ENGINES IN CORNWALL. From a Return of the Work performed by Fifty-nine Steam-Engines employed in the Cornish Mines, for July, 1825, it appears that six of them accomplished as follows : SIR,-Having observed a letter in a late Number of your Publication, requiring information relative to the advantage of applying Steam on Woolf's principle, and calling on any of the first engineers" for assistance, allow me, through the same medium, to attempt a reply. Although I by no means lay claim to the above rank, "mine being the last of all the families of Benjamin, and I the youngest in my father's house," I contemplate little difficulty in convincing our friend F. J-k-n, that an absolute advantage is derived by such application, which may be clearly demonstrated by practice or theory, mechanics or mathematics. Let us proceed, and suppose, without entering into minute detail, that we have a single (or double) engine on Woolf's principle, the relative capacities of the cylinders being as 1 to 5 (which cylinders we will designate by a and b); we raise the steam in the boiler to the pressure of 50lb. per square inch; let us blow through, and then apply it to the top of a, whilst, at the same time, the valves at the bottom of a, and top of b, are opened; the steam which was below the piston of a rushes into the space above the piston of b, and expanding itself into five times the space it previously occupied, is, of course, reduced to 10lb. per square inch, which acts with equal force on the top of b and bottom of a; therefore the effective force of the steam on the pistons may be stated at 50-10lb = 40lb. on a, and 10lb. on 6, by which it is very evident, that a great addition of power is derived from raising steam to a high temperature in the boiler, and employing it in that state before reducing it to a common pressure. NEW IMPERIAL MEASURE. Whatever may be said of the principle, facts are stubborn things; by facts it may be, and is, clearly demonstrated in almost every case in which this plan has been adopted, and I feel assured this engine only requires to be fully known for its more general adoption; reflecting, as it does, infinite credit on the inventor, who, with mighty strides, has trod the paths of science, admirably improved this invaluable assistant, and given to the world the efforts of his genius. SIR,-In your instructive Magazine, Number 100, a Correspondent requests information relative to Woolf and Edwards's Steam Engines. The writer asks how the steam, after leaving the high pressure cylinder, gains its power to act on the low pressure one? "and further," Will not the steam serving the high pressure cylinder have as much power to resist the return of the high pressure piston, as it will to give action to the low pressure piston? I answer, if the two cylinders were of the same diameter, the fact 395 piston, on account of its having 90 square inches more to act upon. I believe these engines work with steam, first, upon the high pressure piston, at a pressure of about 50lbs. upon the square inch; and the first action of the steam upon the low pressure piston will be nearly of the same impetus-I say, the first action, because the pressure will vary as room is made for it to expand, by the ascent or descent of the low pressure piston. When it has expanded into the whole length of the large cylinder, it is by that means brought down to an ordinary pressure, say five or six pounds, upon the square inch (a proper temperature for condensation), which next takes place, and a vacuum produced, on the same principle as in a Watt's engine, by which a further gain of 10lbs. upon every square inch of the low pressure piston is effected, by working the steam over again. If you think the above will have any tendency to settle the controversy between your Westminsterbridge-road Correspondent and his fellow-workmen, your giving it a place in your useful miscellany will oblige, Your obedient servant, EDMUND FEARNLEY. NEW IMPERIAL MEASURE. .D would undoubtedly be as it has al- Shipley, near Bradford, Yorkshire. Let us, for example, suppose two cylinders; the high pressure one 10 inches area, and the low pressure one 100 inches area; the steam leaving the high pressure cylinder of 10 inches, is made to act upon the low pressure piston of 100 inches; and though there is the same resistance against the former as there is action upon the latter, yet it is evident, on well-known principles, there will be a gain of power upon the low pressure SIR, I beg to offer a shorter solution of T. H.'s problem than your Correspondent, Mr. Lake. Let s = solid required, Rr, the greater and less radii of = 0. = a, and DGE Now y=x. tau. is equation to generating line GD; but, by Differential Calculus, any solid of revolution = 396 μ) xphs u STEAM-ENGINE RULES. = circumference of circle). By substitution, solid=π. tan. O sx dx, integrating between s ca and sc = a+h. Respected Friend,-I have been much gratified by the perusal of your useful publication, but have received greater pleasure from no circumstance connected with it, than from that noble disinterestedness with which men of the same profession communicate their knowledge to each other. No sooner does a mechanic make known his ignorance of any particular subject, and express his desire to be informed, than generally there are several of his brother mechanics willing, and often eager, to give him the information which he requests. I should question if another instance could be found of men so ready to possess their goods in common, losing sight of all emolument and fame, and influenced by the pure motive of bencfitting those who are but too often considered and treated as rivals in trade. In my youth I took great delight in mechanical and mathematical studies; and although I have, for many years, ceased to be a mechanic by profession, I well remember the pleasure with which I imparted whatever I had met with in books, acquired by study, or struck out by my own invention, to all who showed themselves desirous of being made partakers of what I considered a treasure. In those days I contrived many simple and easy rules, either for my own convenience or that of my friends, by which the labour of calculations, often recurring, was greatly abridged, or the operation put within the reach of such as were but little accustomed to apply mathematical investigations to mechanical principles. Some of these, which I have often found useful, and which at present recur to my remembrance, I shall subjoin, that, if you think them of sufficient importance to deserve a place in your Magazine, they may, through that medium, be transmitted to your very numerous class of readers. 1st. To find an equivalent for the power of a steam-engine, expressed in horse power. Let a horse power be equal to 200 pounds, raised at the rate of 2 miles per hour, as laid down by writers on that subject. Let a low-pressure engine, with a load of 10 pounds to the inch, work at the rate of 11 strokes per minute, 8 feet stroke. Then multiply the diameter of the piston by its circumference, and cut off two figures from the right hand of the product, we have the number of horses' power exactly. Example.-Let the diameter of the cylinder be 28 inches, then will the circumference be 28 inches nearly, and 28 x 88 = 2464; whence the engine equals 24 horses' power. If the engine be supposed to move with the load of 10 pounds to the inch, at the rate of 200 feet per minute, find the power, as before, and increase it by 1-7th part of itself; thus, 21.64 + 24.64 28.16, equal 28 horses' power. 7 = 4 30.7, equal 304 horses' power nearly. 2nd. To find the load, on the square inch, of an engine employed iu pumping water. Divide 5 times the diameter of the pump by 4 times the diameter of the multiply by 5, and divide by 3 (or cylinder; square the quotient, and the pounds avoirdupois on each square annex a cipher, and divide by 6), gives inch of the piston for every fathom deep, exactly. Example.-Let a 40-inch cylinder draw a 10-inch bucket 50 fathoms deep. ON THE FRICTION OF CORDS. which, being multiplied by the depth, 17.5 gives 8.138, &c. pounds to the inch. 3rd. To estimate the power of an engine working expansively. Add 1 to the hyperbolic logarithm of the number of times to which the steam is expanded; multiply by the force of the steam, and divide by the number of times to which the steam is expanded, gives an equivalent force, which, acting uniformly throughout the whole stroke, will produce the same effect. Example 1.-Let the force of the steam first admitted be 17 pounds to the inch, and be shut out at the middle of the stroke. Then 1+6931472 × 2 = 397 14.815, &c. a constant equivavalent force. Example 2.-Let the steam in a high(say 75 pounds to the inch); length of pressure engine equal 5 atmospheres stroke 5 feet; steam shut out after the piston had moved 8 inches. Here 60÷8 = 7.5. 75 And 1+ 2.0149 × =30.149 pounds, 7.5 or a constant force of two atmospheres. N.B. If the steam be let off without condensation, there must be 15 pounds to the inch deducted from the equivalent constant force, for the resistance of the atmospheres. Hyperbolic Logarithms. No. 1.25 .2231435 34 1.1786549 5 1.6582280 74 1.9810014 24 2금 22222 23 N.B. The sum of any two or more logarithms is equal to the logarithm of the product or rectangle of their respective numbers, thus, 6931472+ 1.7047481=2.3978953, which is the logarithm of twice 5, or 11. 4th. To find the weight of a hollow cast-iron cylinder. To the inside diameter, in inches, add the thickness of metal in inches; multiply by the thickness of metal in inches, and by nine times the length in feet, or three quarters the length in inches; the product (cutting off two. figures from the right hand) will be the weight in cwts., reckoning the specific gravity of cast iron to be 7.4. The same rule will also serve for a circular plate, considering it has a cylinder whose inside diameter is 0, and length the thickness of the plate. Example 1.-Required the weight of a pump 11 inches diameter within, thickness of an inch, length 8 feet. Here 11+.75 x 75 x 8 x 9 = 634.5; whence the weight = 6.345 cwt. Example 2.-Required the weight of a cast-iron circular plate, 6 feet diameter, and 5 inches thick. Here, internal diameter ness of metal = 36 inches, length inches. Then (+36 × 36 × 5 × the weight 48.6 cwts. These rules I have, very many times, found useful, and to know that they were rendered equally serviceable to others, would confer a pleasure on your friend, J-L-. Ichthyotrophia, 9th Month, 1825. ON THE FRICTION OF CORDS. SIR, Professor Leslie, of Edinburgh, in his work entitled Elements of Natural Philosophy, page 212, on the Friction of Cords, says, "If the weight balanced a traction of 4 lbs. at the end of a semicircumference, it would balance 16 lbs. at a complete circumvolution. At the end of two turns.. 256 lbs. four do. 65536 lbs. &:"" These conclusions are drawn from theoretical investigation, it is to be presumed; but, as no theory is entitled to full credit until it has stood the test of experiment, I shall take the liberty of stating the results of some experiments on this subject, for the purpose of correcting the conclusions above quoted, and to prevent practical mechanics from being misled by such high authority. |