dv} nearly. Hence .63,315= .63/252/ Q, E, D. decimal to a fraction, subtract the Hence, to reduce a circulating terminate figures from the whole; and place for denominator of the remainder as many 9's as there are circulating figures, with as many 9's as there are terminate ones. CIRCUMFERENCE, in a general sense, denotes the line, or lines, bounding any figure. 6. Area = v(dv-3 v2) nearly. CIRCUMFERENTOR, an instruThe area of circular zones is ment used by surveyors in taking found by finding the difference of angles; it consists of a brass circle the two segments. And the area and index, in one piece, common. of circular rings, by finding the ly about seven inches in diameter, difference of the areas of the two and index about fourteen inches circles. Or by making D and dlong, and one and a half inches the diameters. CIRCULATING Decimals, consist of a repetition of a number of digits, as 646464, &c. 4127127127, &c.; in fact, every decimal that is not finite, is a circulating decimal, or is such, that if continued far enough the same figures will again broad. On the circle is a card or compass, divided into 360 degrees; the meridian line of which an swers to the middle of the breadth of the index. There is also soldered on the circumference a brass ring, on which screws another ring with a flat glass in it, so as to form a kind of box for the needle, sus. pended on the needle in the centre of the circle. There are also two sights to screw on, and slide up and down the index, as also a ball and socket screwed on the under side of the circle, to receive the leg of the three-legged staff. CIRCUMSCRIBED Figure, is that which is drawn about another fourth proportional 144. 2. Divide the altitude of the vessel into 144 equal parts here the last will fall to the last hour; the three next above to the last part but one; the five next to the tenth hour; lastly, the twenty-three last to the first hour. For since the times increase figure so as to touch all its angles, evacuated each hour. 1. As the or to touch it by every side. part of time 1 is to the whole time CISSOID, in the higher Geome-12, so is the same time 12 to a try, is a curve line of the second order, invented by Diocles, a Greek geometrician, for the purpose of finding two continued mean proportionals between two other given lines. The generation of this curve is as follows; at the extremity of the diameter of a circle draw a tangent, and from the opposite ex-in the series of the natural numtremity of the diameter draw any number of lines meeting the tangent. Set off upon these from the tangent, the same distances that are within the circle; and the curve drawn through these points is the Cissoid. The cissoid has the following properties: 1. The curve has two infinite legs, meeting in a cusp, and tending continually towards the indefinite line, which is their common asymptote. 2. The curve bisects each semi-circle. 3. Letting fall perpendiculars from any corresponding points, the portions at each extremity of the diameter, and also of the line meeting the tangent, are equal to each other. 4. If the diameter bea, the absciss, and the ordinate = y; then is aa-x=: y2: x2, or as y2. (ax), which is the equation of the curve. 5. The whole infinitely long cissoidal space, contained between the infinite asymptote, and the curves of the cissoid, is equal to triple the generating circle. 6. All cissoids are similar figures. CLEPSYDRA, an instrument or machine serving to measure time by the fall of a certain quantity of water. The use of clepsydræ is very ancient; they were invented in Egypt, under the Ptolemies; as were also sun-dials. Their use was chiefly in the winter, as the sundials served in the summer: but they had two great defects; the one, that the water ran out with a greater or less facility, as the air was more or less dense; the other, that the water ran more readily at the beginning than towards the conclusion. Suppose a cylindrical vessel, whose charge of water flows out in twelve hours, were required to be divided into two parts, to be bers 1, 2, 3, 4, 5, &c. and the altitudes, if the numeration be in a retrograde order from the twelfth hour, increase in the series of the unequal numbers 1, 3, 5, 7, 9, &c. the altitudes computed from the twelfth hour will be as the squares of the times, 1, 4, 9, 16, 25, &c. Therefore the squares of the whole time, 144, comprehend all the parts of the altitude of the vessel to be evacuated. But a third proportional to 1 and 12 is the square of 12, and consequently it is the num ber of equal parts into which the altitude is to be divided, to be distributed according to the series of the unequal numbers, through the equal interval of hours. There were many kinds of clepsydra among the ancients; but they all had this in common, that the water ran generally through a narrow passage, from one vessel to ano ther, and in the lower was a piece of cork, or light wood, which as the vessel filled, rose up by degrees, and showed the hour. CLIMATE, or CLIME, in the ancient Geography, a part of the surface of the earth, or zone, bounded by two lesser circles parallel to the equator; and of such a breadth, as that the longest day in the parallel nearer the pole exceeds the longest day in that next the equa tor, by some certain space, as half an hour, or an hour. Vulgarly, the term climate is bestowed on any country or region differing from another, either in respect of the seasons, the quality of the soil, or even the manners of the inhabitants, without any re, gard to the length of the longest day ČLOCK, a well-known instrument for measuring time; it is regulated by means of a Pendulum, the laws of which will be found under that article. CLOUD, a visible aggregate of minute drops of water suspended in the atmosphere. It is concluded, from numerous observations, that the particles of which a cloud consists, are always more or less electrified; and this fluid has hence been considered as the cause of the formation of all clouds whatever, whether of thunder, hail, rain, or snow. two. The co-efficient of the fourth term is equal to the sum of all the product, taken three and three together, with their signs changed, and so on; and, finally, the abso lute term is equal to the product of all the roots, with their signs changed, if the number of terms be even; but without being changed, if the number of terms be odd; this term being here supposed to stand on the left-hand side of the equation. Ɑ=1 −(p + q +r) b= Pq + pr+ gr c =- pqr and the same for every order of equations. The hypotheses which assumes Thus, for example, in the cubic the existence of vesicular vapour, equation, x2 + ax2 + bx + c = 0; and makes the particles of clouds supposing the roots to be p, q, and to be hollow spheres, which uniter, we shall have and descend in rain when ruptured, however sanctioned by the authority of several eminent philosophers, does not seem necessary to the science of meteorology in its present state; it being evident The sum of all the co-efficients that the buoyancy of the particles of the binomial (a + an) = 2n, and is not more perfect than it ought of (a-x)n = on = 0; that is, the to be, if we regard them as mere sun of the positive co-efficients is drops of water. In fact, they al-equal to the sum of the negative ways descend, and the water is ones; and consequently their sum elevated again only by being con- is equal to zero. See Binomial verted into invisible vapour. Theorem. CO-EFFICIENTS, in Algebra, COFFER Dam, a term applied are numbers or letters prefixed to by engineers to denote the enclo other letters, or unknown quanti-sures formed for laying the founties, into which they are supposed to be multiplied; and with such letters, or the quantities, making a product, or co-efficient product. dation of piers and other works in water, to exclude the surrounding fluid, and thus forming a protection both to the work and workmen. COHESION, that species of attraction which, uniting particle to particle, retains together the com When a quantity stands alone, without being preceded by any number or letter, it is always supposed to have unity for its co-effi-ponent parts of the same mass; cients. In equations the absolute term is sometimes classed under the general term co-efficient, in which it is supposed to be prefixed to r° or y, &c. all such quantities being equal to unity: thus, in the formula x3 + ux2+cx+d, the co-efficients are 1, a, c, and d; the first 1 being understood, and the last being supposed to precede 2° = 1. In equations we have the following remarkable property of the co-efficients; viz. 1. The co-efficient of the second is equal to the sum of the roots of the equation with their signs changed. 2. The co-efficient of the third term is equal to the sum of all the product, taken two and being thus distinguished from adhesion, or that species of attraction which takes place between the surfaces of similar or dissimilar bodies. The following table shows the weights necessary to tear asunder rods of different substances, whose bases were each a square inch, the weights being applied in the direction of their length. lbs. Avoirdupoise. 135000 74000 .... Copper, cast ..... 2900 inches; the weight which broke it 2600 Other experiments have been made to ascertain the strength of cohesion in bodies, when placed horizontally, and loaded with weights in different parts. The weights, and their distances from the point of support, are shown in the following table: Woods Dist. in Inch. Wt. in oz. In the above table the rods were rectangular parallelopipedons, and the side of their square section .26 of an inch. Coulomb found the lateral cohesion of brick and stone only more than the direct cohesion, which, for stone, was 215lb. for a square inch; for good brick, from 280 to 300. For farther information on this subject, the reader may consult Ritter on Cohesion, Gilbert's Journal, iv. 1; Benzenberg on Cohesion, Gilbert, xvi. 76; Fontana on Solidity and Fluidity, Soc. Ital. i, 89; and Dr. T. Young on the Cohesion of Fluids, in the Phil. Trans. for 1805, or in the second volume of his "Natural Philosophy." COLD, in cominou language, denotes the sensation which is felt, or the effect which is produced, by the abstraction of heat. Thus the climate of Great Britain is a cold climate, in comparison with that of the West India islands; and a hot climate in comparison with that of Siberia. If a man warms one of his hands near a fire, whilst he cools his other hand by means of ice; and if afterwards he plunges both his hands in a bason of wa ter of the common temperature of the atmosphere, that water will feel cold to the hand that has been heated, and hot to the other hand. From this, it appears that cold is not any thing real, but merely a privation of heat; so that instead of saying that a body has been cooled to a certain degree, it may with equal truth and propriety be said that the body has been depriv ed of heat to that certain degree. Notwithstanding the simplicity of this theory, and the conviction which seems to accompany it, phi losophers have often entertained doubts concerning it; and they have endeavoured to inquire into the real state of the matter, by deCount Rumford found the cohe- vising experiments capable of desive strength of a cylinder of iron, monstrating whether the cause of an inch in diameter, 63466, or heat was any thing real, and that 631731b.; the mean 63320; which of cold only a privation or dimiis only more than Emerson's re-nution of the former; or, vice versa, whether the cause of cold was any sult. Sickingen makes the compara- thing real, and that of heat a ditive cohesive strength of gold, minution; or, lastly, whether the 150955; of silver, 195771; of plati-production of heat, and the prona, 262361; of copper, 304696; of soft iron, 362927; of hard iron, 559830. Guyton makes platina a little stronger. In Buffon's experiments, b, d, and I, being the breadth, depth, and length of a beam of oak, in duction of cold, were not owing to 1 1 fects, viz. enlargement of the bulk of bodies, the separation of their parts, &c. are such as must be produced by the introduction of something real; and the abstraction of this principle may naturally produce the effects of cold, such as contraction of the buik of bodies, agglutination, &c.; whereas it would be unnatural to suppose that a body contracts its bulk, as its parts come into closer contact, because something else has been introduced amongst them. With respect to the last supposition, viz. whether the effects of heat and those of cold be not owing to two distinct principles, a few arguments, and the equivocal result of a few experiments, have, at tinies, been adduced in support of it. But the general and prevailing opinion among philosophers is, that a single element, called caloric, produces heat, or the effects of expanding bodies separating their parts, &c.; and that cold is only a relative expression; that is, meaning only the decrement of heat; so that real or absolute cold consists only in the total abstraction of caloric; and, that such a point, viz. the zero of heat may be determined, has been shown by the experiments, the discoveries, and the calculations of some late eminent philosophers, viz. Irvine, Black, Crawford, and others. COLLIMATIOŃ, Line of, in a telescope, is a line passing through the intersection of those wires that are fixed in the focus, and the centre of the object glass. when the two bodies meet each other; for, in that case, the sum of the motions after the impact is equal to the difference of their motions before it, not to their sum. If the impact of two perfectly hard bodies be direct, they will, after impact, either remain at rest, or move on uniformly together with different velocities, according to the circumstances under which they met. Let B and b represent two per fectly hard bodies, and let the ve locity of B he represented by V, and that of b by v, which may be taken either positive or negative, according as 6 moves in the same direction as B, or contrary to that direction, and it will be zero when b is at rest. This notation being understood, all the circumstance of the motion of the two bodies, after collision, will be expressed by the formula, velocity = BV+bv B+b velocity BV when the body b was at rest. In COLLISION, in Mechanics and Physics, is the meeting and mutual striking of two or more bodies, one of which, at least, is in mo- These formula arise from the sup tion. The most simple of the prob- position of the bodies being perlems relating to collision, is that of fectly hard, and consequently that a body proceeding to strike against the two after impact move on unianother at rest, or moving before formly together as one mass. it with less velocity, or approach-cases of perfectly elastic bodies, ing towards it. Des Cartes sup- other formulæ have place which posing that the same quantity of express the motion of each body absolute motion always exists in separately, as in the following prothe world, concluded that the sum position. of the motions after the impact If the impact of two perfectly was equal to the sum of the mo-elastic bodies be direct, their relations before it. But the propositive velocities will be the same tion is true only in the first and both before and after impact, or second of these cases; it is false they will recede from each other |