property, that if a circle rolls on the inside of another of twice its diameter, the epicycloid described is a right line. In practice, the piston rod, or other reciprocating part, may be attached to any point on the circumference of the wheel c.

m

m'

B

6. Double Rack and Pinion.-This is a contrivance for an alternating motion with a gradual change. A B is a double rack, with circular ends, fixed to a beam that is capable of moving in the direction of its length. The rack is driven by a pinion P, which is susceptible of moving up and down in a groove m m', cut in the cross piece. When the pinion has moved the rack and beam until the end в is reached, the projecting a meets the spring s, and the rack is pressed against the pinion. Then the pinion, working in the circular end of the rack, will be forced down the groove m m' until it works in the lower side of the rack, and moves the beam back in the opposite direction; and thus the motion is continued. The motion of the pinion in the groove will be diminished, if, instead of a double rack, there be used a single row of pins which are parallel to the axis of the pinion: this plan is sometimes adopted in the machines called mangles.

7. The Universal Lever.-This is a French invention, and is often, from the name of the inventor, called lever de la Garousse. It consists of a bar a b, moving upon a centre c, and having a moveable catch, or hook, hh' attached to each side, and acting upon the oblique teeth of a double rack; so that, as b and a alternately rise and fall in the reciprocal motion, the hooks h and h' successively lay hold of the teeth of the beam A B, and draw it up in the direction в A.

8. The Tachometer.-This is a very ingenious contrivance, which we owe to Mr. Donkin, for the purpose of measuring small variations in velocity. The contrivance is, in fact, hydrodynamical, but we mention it here, and the simplicity of its principle will render it easy of comprehension.

If a cup with any fluid, as mercury, be placed upon a spindle, so that the brim of the cup shall revolve horizonally round its centre, then the mercury in the cup will

assume a concave form, that is, the mercury will rise on the sides of the cup, and be depressed in the middle; and the more rapid the rotation of the cup, the more will the surface of the mercury be depressed in the middle and rise at the sides; the figures being those of hollow paraboloids. Now, if the mouth of this cup be closed, and a tube inserted into it, terminated in the cup by a ball-shaped end, and half filled with some coloured liquid, as coloured spirits of wine; then it is evident that the more the surface of the mercury is depressed the more the fluid in the tube will fall, and vice versa. Consequently, the velocity of rotation of the cup, and of the spindle to which it is attached, will be indicated by the height of the liquid in the tube; and, indeed, absolutely measured by it, when the apparatus has been subjected to the adequate preparatory experiments.

For a more minute description, see Trans. Soc. of Arts, vol. xxvi., or the article Tachometer in the PANTOLOGIA.

Two plates, exhibiting a great variety of contrivances for converting rotatory, reciprocating, and other motions, one into the other, and thus facilitating the construction of machinery, are given in my Treatise of Mechanics.

A large and valuable plate of the same kind, exhibiting 178 useful elementary mechanical combinations, has been lately published at Manchester, and is sold in London by Ackerman. I scarcely know a more interesting present than this would be to a young mechanic.

CHAPTER XI.

HYDROSTATICS.

1. Hydrostatics comprises the doctrine of the pressure and the equilibrium of non-elastic fluids, as water, mercury, &c. and that of the weight and pressure of solids immersed in them.

2. DEF. A fluid is a body whose parts are very minute, yield to any force impressed upon it (however small), and by so yielding are easily moved among themselves.

Some attempt to give mechanical ideas of a fluid body by comparing it to a heap of sand: but the impossibility of giving fluidity by any kind of mechanical comminution will appear by considering two of the circumstances necessary to constitute a fluid body 1. That the parts, notwithstanding any compression, may be moved in relation to each other, with the smallest conceivable force, or will give no sensible resistance to motion within the mass in any direction. 2. That the parts shall gravitate to each other, whereby there is a constant tendency to arrange themselves about a common centre, and form a spherical body; which, as the parts do not resist motion, is easily executed in small bodies. Hence the appearance of drops always takes place when a fluid is in proper circumstances. It is obvious that a body of sand can by no means conform to these circumstances.

Different fluids have different degrees of fluidity, according to the facility with which the particles may be moved amongst each other. Water and mercury are classed among the most perfect fluids. Many fluids have a very sensible degree of tenacity, and are therefore called viscous or imperfect fluids.

3. DEF. Fluids may be divided into compressible and incompressible, or elastic and non-elastic fluids. A compressible or elastic fluid is one whose apparent magnitude is diminished as the pressure upon it is increased, and increased by a diminution of pressure. Such is air, and the different vapours. An incompressible or non-elastic fluid is one whose dimensions are not, at least as to sense, affected by any augmentation of pressure. Water, mercury, wine, &c. are generally ranged un

der this class.

It has been of late years proposed to limit the application of the term fluids to those which are elastic, and to apply the

word liquid to such as are non-elastic. But it is an unnecessary refinement.

4. DEF. The specific gravity of any solid or fluid body is the absolute weight of a known volume of that substance, namely, of that which we take for unity in measuring the capacities of bodies.

Comparing this definition with that of density (DYNAMICS, Def. 2), it will appear that the two terms express the same thing under different aspects.

SECTION I.-Pressure of Non-elastic Fluids.

1. Fluids press equally in all directions, upwards, downwards, aslant, or laterally.

This constitutes one essential difference between fluids and solids, solids pressing only downwards, or in the direction of gravity.

2. The upper surface of a gravitating fluid at rest is horizontal.

3. The pressure of a fluid on every particle of the vessel containing it, or of any other surface, real or imaginary, in contact with it, is equal to the weight of a column of the fluid, whose base is equal to that particle, and whose height is equal to its depth below the upper surface of the fluid.

4. If, therefore, any portion of the upper part of a fluid be replaced by a part of the vessel, the pressure against this from below will be the same which before supported the weight of the fluid removed, and every part remaining in equilibrium, the pressure on the bottom will be the same as it would if the vessel were a prism or a cylinder.

5. Hence, the smallest given quantity of a fluid may be made to produce a pressure capable of sustaining any proposed weight, I either by diminishing the diameter of the column and increasing its height, or by increasing the surface which supports the weight.

6. The pressure of a fluid on any surface, whether vertical, oblique, or horizontal, is equal to the weight of a column of the fluid whose base is equal to the surface pressed, and height equal to the distance of the centre of gravity of that surface below the upper horizontal surface of the fluid.

7. Fluids of different specific gravities that do not mix, will counterbalance each other in a bent tube, when their heights above the surface of iunction are inversely as their specific gravities.

A portion of fluid will be quiescent in a bent tube, when

the upper surface in both branches of the tube is in the same horizontal plane, or is equidistant from the earth's centre. And water poured down one branch of such a tube (whether it be of uniform bore throughout, or not) will rise to its own level in the other branch.

Thus water may be conveyed by pipes from a spring on the side of a hill, to a reservoir of equal height on another

hill.

8. The ascent of a body in a fluid of greater specific gravity than itself, arises from the pressure of the fluid upwards against the under surface of the body.

9. DEF. The centre of pressure is that point of a surface against which any fluid presses, to which if a force equal to the whole pressure were applied it would keep the surface at rest, or balance its tendency to turn or move in any direction.

10. If a plane surface which is pressed by a fluid be produced to the horizontal surface of it, and their common intersection be regarded as the axis of suspension, the centres of percussion and of pressure will be at the same distance from the axis.

11. The centre of pressure of a parallelogram, whose upper side is in the plane of the horizontal level of the liquid, is at of the line (measuring downwards) that joins the middles of the two horizontal sides of the parallelogram.

12. If the base of a triangular plane coincides with the upper surface of the water, then the centre of pressure is at the middle of the line drawn from the middle of the base to the vertex of the triangle. But, if the vertex of the triangle be in the upper surface of the water, while its base is horizontal, the centre of pressure is at 3 of the line drawn from the vertex to bisect the base.

Illustrations and Applications.

1. If several glass tubes of different shapes and sizes be put into a larger glass vessel containing water, the tubes being all open at top; then the water will be seen to rise to the same height in each of them, as is marked by the upper surface a c, of the liquid in the larger vessel.

2. If three vessels of equal bases, one cylindrical, the