Introductory Definitions and Remarks I. On the Pressure of Non-elastic Fluids III. On the Equilibrium, Stability, and Oscillations of Floating- Bodies IV. On the Phenomena of Attraction in Capillary Tubes BOOK IV. HYDRODYNAMICS. 1. On the Discharge of Fluids through Apertures in the Bottom I. Equilibrium of Elastic Fluids II. On the Admeasurement of Altitudes with the Barometer III. On the Motion of Air when the Equilibrium of Pressure is IV. On the Theory of Air-pumps, and Fumps for raising Water 523 MECHANICS. Remarks on Machinery in General. 1. MECHANICS, according to the original import of the word, treats of the energy of Machines: and these machines are nothing more than organa, or tools, interposed between the workman, or natural agent, and the task to be accomplished, in order to render that work capable of being performed, which under the limits and circumstances proposed would have been difficult, if not impossible, without the intervention of some of these contrivances. Machines are interposed, as was remarked (art. $79. vol. I.), chiefly for three reasons. 1. To accommodate the direction of the moving force, to that of the resistance which is to be overcome. 2. To render a power which has a fixed and certain velocity efficacious in performing work with a different velocity. 3. To enable a natural power, having a certain determinate intensity, to balance or to overcome another power or obstacle, whose intensity or resistance is greater. Each of these purposes may be accomplished in different ways: i.e. either by machines which have a motion round some fixed and supported point, as the lever, the pulley, and the wheel and axle; or by those which, instead of being supported by a fixed point, about which they move, furnish to the resistance, or body to be moved, a solid path, along which it is impelled, as the inclined plane, the wedge, and the screw. Compound machines are peculiar combinations of these six, of which we have treated individually in the first book of our first volume: some remarks likewise upon their combination have been given in Book I. Chap. IV. art. 161. and Book II. Chap. VI. And we have treated of the strength of the materials of which machines may be composed, in Book I. Chap. V. Such farther observations as appear necessary to complete a theoretical and practical knowledge of Machinery in general, previous to our alphabetical description of particular machines, will now be presented to the student. VOL. II. B 2. Simplicity in the construction of machines cannot be too warmly recommended to the young engineer: for multiplicity of parts and of motions increases the expence of erection, augments the friction, and multiplies the danger of failure by the bending or by the inaccurate adjustment of the parts. In consequence of the effects of friction (of which we shall speak more fully, art. 24, &c.), it is well known to all engaged in the practice of mechanics, that by no combination of wheels, or levers, or other powers, can one weight be made to move another with a greater or even an equal momentum: and by the multiplication of wheels, levers, &c. the effect of the machine, instead of being increased, is diminished in proportion to the augmented friction of the moving parts. Hence it follows that in practice, effect is lost by mechanical combination, but gained by simplification; and that the most perfect machine is that which operates by the fewest moving parts. In order to contrive a simple machine to be theoretically equivalent in power to a complex one, the following rule may be observed: Construct the various parts of the simpler machine so that the velocity of the impelled point (art. 365.) shall be to that of the working point, in the same ratio as they are in the compound machine; then will the effects of these two machines be the same, so far as depends upon pure theory: but in practice the simpler will be the more efficacious, in consequence of the diminution of friction. 3. For an example, suppose the compound machine, fig. 1. pl. II. were to be proposed, in order that a more simple one might be constructed to perform the same work. Let CA, the lever to which the power is applied, be 10 feet, DE 5 feet in diameter, EF2 feet, HI3 feet, GH=5 feet, and KL I foot, the latter being the cylinder on which the rope raising the weight w folds. Now the diameter of the circle described by the power at A is 20 feet: and to find the diameter of the circle whose circumference is equal to the space passed over by w in one revolution of the lever CA, reduce the following fraction, viz. X DE 2AC GH X KL £0 × 1 × ÷ = 1 of 2AC; conse quently the velocity of the weight is of that of the power. And hence, if upon the vertical axis CM (fig. 2. pl. II.) a wheel be fixed, the diameter kl of which is equal to 4 feet (that is, of 2AC), the weight w will be raised the same height by the simple as by the compound machine, at every revolution of the power A. So that, the simple machine ACмkl, will be at least equal in effect to the compound one ACMDEFGHIKL, and the wheels DE, EF, GH, HI, and KL, are extraneous, and probably prejudicial. 4. For another example take the following. In the common wheel and axle, the advantage gained is in the ratio of the radius of the winch to that of the barrel: so that when it is proposed to increase that advantage, either the handle must be lengthened, or the diameter of the axle diminished; neither of which, however, is practicable beyond certain limits, because the handle might be too long for convenient management, or the axle too slender to support the load: in such cases it is usual to annex another wheel and pinion, or a tackle of pulleys. But the following construction is greatly preferable. In fig. 7. pl. I. the part A of the barrel is larger than the part B, and the rope which passes under the pulley c and sustains the weight D is wound upon each in contrary directions. Whenever, therefore, the handle EF is turned, so as to gather the rope upon the larger cylinder, it will be given off by the smaller: and for every turn of the larger, or its correspondent portion of rope wound up, there will be given off a portion of rope answering to the circumference of the smaller. Consequently, the quantity of unwound rope will be less after such a turn, by a portion equal to the difference between the circumferences of the two cylinders; and the weight D will be raised through half that space. Whence, since the radii of circles are as their circumferences, we may use this analogy: As the radius of the winch, To half the difference of the radii of the cylinders; To the power balancing it. In fig. 8. is exhibited a simple capstan in which the same contrivance is adopted. Here, if the upper barrel A were 17 inches diameter, and the lower B 16 inches, the pulley c being also 16 inches diameter; it will be obvious that this simple capstan will be equivalent to an ordinary capstan of the same length of bar EF, and diameter of barrel B, combined with a 16-fold tackle of pulleys; and at the same time free from the great loss by friction and bending of ropes, which would absorb at least a third of the power of a 16-fold tackle. One peculiar advantage of this engine is, that the half difference of the radii of A and B may be diminished ad libitum, without weakening the cylinder, increasing the friction, or requiring any rapid curvature of the rope. This windlass has likewise the peculiar property of holding the weight at any part of its rise or fall without needing a rachet wheel and catch. Its only practical disadvantage is, that a great quantity of rope must be used to produce a moderate change in the position of the weight; but the quantity of rope will be much less than what is requisite for an equivalent tackle of pulleys. This ingenious contrivance is generally ascribed to the celebrated George Eckhardt; and he probably invented it without knowing that it had been used elsewhere: but we have seen a figure, from which our figure 8 is merely a copy, in some Chinese drawings of nearly a century old. 5. The methods of communicating motion from one thing to another, or from one point to another, are almost infinitely diversified so that it will not be expected that they should all be described here. It is manifest that the communication of motion will in different circumstances be better effected by means of one simple machine (or, as they are usually called, mechanical power), than by another; and much of the skill of the engineer consists in choosing the instrument most proper for the purpose proposed: and the same will be the case with regard to more complex machines. In some instances a simple lever, or a simple unbent cord, will answer better than any combination: in others it may be highly advantageous to use a combination of levers acting upon each other, by means of so many fulcra; and by these the direction may be changed at pleasure: in others, as when motion is communicated to a series of wheels and axles in succession, it may be effected by a rope running in grooves round one wheel and the succeeding axle; or by what was described in vol. I. art. 246. under the name of tooth and pinion work in others again, by a barrel and winch with an endless screw. And many other contrivances will readily suggest themselves to an ingenious artist. 6. But such simple methods cannot always be adopted. Thus when it is required by means of a rotatory motion to produce a reciprocating one, as the alternate motion of the pistons of pumps, for example; one of the following contrivances may be used. To a vertical shaft as AP (fig. 6. pl. 11.) fix a large horizontal wheel MOIL, the lower part of which is indented in waves MSO, O91, &c. of which the constituent arches are either circular or parabolic. On a convenient point D of an upright post as a centre of motion, let a lever EDC move; one end of it carrying the moveable vertical wheel CR, in size properly adjusted to the waves of the horizontal wheel; the other EF being a circular arc to which is applied the chain EG of the pump. Then whilst the great wheel is turned by the lever NA from o towards 1, the wave a presses down the wheel OR, and raises the end E of the lever, and thus draws up the water in the pump G. But when the deepest part o of the wave is past the highest part of the wheel CR, the wheel rises up into the hollow s, and so the chain EG descends till the next wave raises it again. Thus the passage of every wave by the wheel CR causes a stroke of the pump. If the number of waves be odd, and another pump wheel and lever be placed diametrically |