a rule discovered by Mr Thomas Baker, whereby to find the center of a circle described to cut the parabola in as many points as an equation to be constructed hath real roots. Its principal use is in the construction of equations, and he hath applied it with good success as far as biquadratics.
The central rule is chiefly founded on this property of the parabola, that, if a line be inscribed in that curve perpendicular to any diameter, a rectangle formed of the segments of the inscript is equal to the rectangle of the intercepted diameter and parameter of the axis.
The central rule has the advantage over Cartes and De Latere's methods of constructing equations, in that both these are subject to the trouble of preparing the equation by taking away the second term. CENTRIFUGAL force, that force by which all bodies that move round any other body in a curve, endeavour to fly off from the axis of their motion in a tangent to the periphery of the curve, and that in every part of it. See Mechanics.
Centrifugal Machine, a very curious machine, invented by Mr Erskine, for raising water by means of a centrifugal force combined with the prelure of the atmosphere.
It consists of a large tube of copper, &c. in the form of a cross, which is placed perpendicular in the water, and rests at the bottom on a pivot. At the upper part of the tube is a horizontal cog-wheel, which touches the cogs of another in a vertical position; so that by the help of a double winch, the whole machine is moved round with very great velocity.
Near the bottom of the perpendicular part of the tube is a valve opening upwards; and near the two extremities, but on the contrary sides of the arms, or cross part of the tube, are two other valves opening outwards. These two valves are, by the affluence of springs, kept shut till the machine is put in motion, when the centrifugal velocity of the water forces them open, and discharges itself into a cistern or reservoir placed there for that purpose.
On the upper part of the arms are two holes, which are closed by pieces screwing into the metal of the tube. Before the machine can work, these holes must be opened, and water poured in through them, till the whole tube be full: by this means all the air will be forced out of the machine, and the water supported in the tube by means of the valve at the bottom.
The tube being thus filled with water, and the holes closed by their screw caps, it is turned round by means of the winch, when the water in the arms of the tube acquires a centrifugal force, opens the valves near the extremities of the arms, and flies out with a velocity nearly equal to that of the extremities of the said arms.
The above description will be very easily understood by the figure we have added on Plate LXXV., fig. 3, which is a perspective view of the centrifugal machine, erected on board a ship. ABC is the copper tube. D, a horizontal cog-wheel, furnished with twelve cogs. E, a vertical cog-wheel, furnished with thirty-six cogs. F, F, the double winch. a, the valve near the bottom of the tube. b, b, the two pivots on which the machine turns. c, one of the valves in the cross-piece; the other at d, cannot be seen in this figure, being on the other side of the tube; e, e, the two holes through which the water is poured into the machine. GH, the cistern, or reservoir. I, I, part of the ship's deck. The distance between the two valves c, d, is six feet. The diameter of these valves is about three inches; and that of the perpendicular tube about seven inches.
If we suppose the men who work the machines can turn the winch round in three seconds, the machine will move round its axis in one second; and consequently each extremity of the arms will move with a velocity of 18.8 feet in a second. Therefore a column of water of three inches diameter will issue through each of the valves with a velocity of 18.8 feet in a second: but the area of the aperture of each of the valves is 7.14 inches; which being multiplied Centripetal by the velocity in inches=225.6, gives 1610.784 cubic inches, the quantity of water discharged through one of the apertures in one second; so that the whole quantity discharged in that space of time through both the apertures is =3221.568 inches; or 193294.08 cubic inches in one minute. But 60812 cubic inches make a tun, beer-measure; consequently, if we suppose the centrifugal machine revolves round its axis in one second, it will raise nearly 3 tuns 44 gallons in one minute: but this velocity is certainly too great, at least to be held for any considerable time; so that, when this and other deficiencies in the machine are allowed for, two tuns is nearly the quantity that can be raised by it in one minute.
It will perhaps be unnecessary to observe, that as the water is forced up the perpendicular tube by the prelure of the atmosphere, this machine cannot raise water above 32 feet high.
An attempt was made to substitute this machine in place of the pumps commonly used on ship-board, but the labour of working was found to be so great as to render the machine inferior to the chain-pump. A considerable improvement, we apprehend, would be, to load with a weight of lead the ends of the tubes through which the water issues, which would make the machine turn with a great deal more ease, as the centrifugal force of the lead would in some measure act the part of a fly.
CENTRIPETAL force, that force by which a body is everywhere impelled, or anyhow tends, towards some point as a center. See Mechanics.
Centriscus in ichthyology, a genus of fishes belonging to the order of amphibia nantes. The head gradually ends in a narrow finout, the aperture is broad and flat; the belly is carinated; and the belly-fins united. There are two species, viz. 1. The scutatus has its back covered with a smooth bony shell, which ends in a sharp spine under which is the tail; but the back-fins are between the tail and the spine. It is a native of the East Indies. 2. The icolopax has a rough scabrous body, and a straight extended tail. It has two belly-fins, with four rays in each, and has no teeth. It is found in the Mediterranean.