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means of reflection, though the instruments themselves are small and portable. Circular instruments may be considered as improvements of Hadley’s octant, and the marine sexant, which are for the same purpose; viz. for observing the altitudes, distances, &c. of the heavenly bodies, extremely useful for navigators in finding the moon’s distance, and other nautical purposes. The best instruments of this kind, are those of Mayer, Borda, and Rios. C1R cular Parts (Napier's), are the legs, the complement of the hypothen use, and the complements of the two oblique angles of a right angled spherical triangle. Napier’s general rule is this: the rectangle, under the radius and the sine of the middle part, is equal to the rectangle under the tangents of the adjacent parts, and to the rectangle under the cosines of the opposite parts. The right angle or quadrantal side being neglected, the two sides and the complements of the other three natural parts are called the circular parts; as they follow each other, as it were, in a circular order. Of these, any one being fixed
| upon as the middle part, those
next it are the adjacent, and those farthest from it the opposite parts. This rule contains all the particular rules for the solution of rightangled spherical triangles.
C1Rcular Sailing, the method of navigating a ship upon a great circle of the globe.
CIRcular Sectors, are the areas bounded by any arc of a circle and two radii; the measure of which is found as follows:
Let & represent the length of the arc of the sector, and m its measure, in degrees, minutes, &c.; then
1. Area of sector = | ri
Circular Segment is the space bounded by o, arc and its chord; the area of which may be found by the following formula:
If Al represent the area of the circular sector, and C the chord of the arc, then
The area of circular zones is found by finding the difference of the two segments. And the area of circular rings, by finding the difference of the areas of the two circles. Or by making D and d 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 reclar. When the figures recur from the beginning the decimal is called pure ; and when there are some figures before the circulation, it is called mired. The denominator of every pure circulating decima. ...o.sists of as many 9’s as there are figures in the
Hence, to reduce a circulating decimal to a fraction, subtract the 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 terminale Olles. CIRCUMFERENCE, in a general sense, denotes the line, or lines, bounding any figure. CIRCUMFERENTOR, an instrument used by surveyors in taking angles; it consists of a brass circle and index, in one piece, commonly about seven inches in diameter, and index about fourteen inches long, and one and a half inches broad. On the circle is a card or compass, divided into 360 degrees; the meridian line of which answers 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, suspended 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
figure so as to touch all its angles, or to touch it by every side. CISSOID, in the higher Geometry, 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 iines. The generation of this curve is as follows; at the extremity of the diameter of a circle draw a tangent, and from the opposite extremity 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 langent, are equal to each other. 4. If the diameter be = a, the absciss = x, and the ordinate = y; then is a : a - a = : y : a*, or a 3 = 3/2. (a — a 3, 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 clepsydrae 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 liad 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 Moded into two parts, to be 04
evacuated each hour. 1. As the part of time 1 is to the whole time 12, so is the same time 12 to a 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 in the series of the natural numbers 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 number 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 clepsydrae among the ancients; but they all had this in common, that the waterran generally through a marrow passage, from one vessel to another, 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 equator, 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 regard to the length of the longest
&Lock, a well-known insurument for measuring time; it is regulated by means of a Pendulum, the laws of which will be found under that articie. CLOUD, a visible aggregate of minute drops of water suspended in the atmosphere. It is concluded, from numerous ebservations, 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. The hypotheses which assumes the existence of vesicular vapour, and makes the particles of clouds to be hollow spheres, which unite 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 that the buoyancy of the particles is not more perfect than it ought to be, if we regard them as mere drops of water. In fact, they always descend, and the water is elevated again only by being converted into invisible vapour. CO-EFFICIENTS, in Algebra, are numbers or letters prefixed to other letters, or unknown quantities, into which they are supposed to be multiplied; and with such letters, or the quantities, making a product, or co-efficient product. When a quantity stands alone, without being preceded by any number or letter, it is always supposed to have unity for its co-efficients. 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 utlity: thus, in the formula ro + ar” + cz + d, the co-efficients are 1, a, c, and d , the first 1 being understood, and the last being supposed to precede a' = 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 *: product, taken two and 95.
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. Thus, for example, in the cubic equation, a 3 + are + ba + c = 0; supposing the roots to be p, q, and r, we shall have a = — (p + q + r.) b = pa -H pr–H qr - =—pgr and the same for every order of equations. The sum of all the co-efficients of the binomial (a + an) = 2n, and of (a —a)n = 0n = 0; that is, the sum of the positive co-efficients is equal to the sum of the megative ones; and consequently their sum is equal to zero. See Binomial Theorem. COFFER. Dam, a term applied by engineers to denote the enclosures formed for laying the foundation of piers and other works in water, to exclude the surrounding fluid, and thus forming a protection both to the work and workmen. COHES10N, that species of attraction which, uniting particle to particle, retains together the component parts of the same mass ; 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. Avoir
METALs. dupoise. Steel . . . . . . . . . 135000 Iron bar . . . . . . . 74000 Cast iron - - - - - - - 50100 Copper, cast - * * * * 28600 Silver, ditto - - - - - - 41500 Gold, ditto . . . . . . 22000 Tin, ditto - - - - - - 4000
Bismuth - - - - - - - 2900 Zinc - - - - - - - - - 2600 Antinuomy • - - - - - - 1000 Lead, cast - - - - - - 860
woods. dupoise. Beech, Oak - - - - - - 17300 . Alder • - - - - - - - - 13900 Elin - - - - - - - - - - 13200 Mulberry . . . . . . . 12500 Willow - - - - - - - - 12300 Ash - - - - - - - - - - 2000 Plum - - - - - - - - - I 1800 Elder • - - - - - - - - 10000 Firs. . . . . . . . . . . 8330 Walnut - - - - - - - - 8130 Pitch, Pine . . . . . . 7656 Cypress - - - - - - - - 6000 Poplar - - - - - - - - - 5500 Cedar - - - - - - - - - 4380
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 :
rectangular parallelopipedons, and the side of their square section .26 Qf an inch. Coulomb found the lateral cohesion of brick and stone only # more than the direct cohesion, which, for stone, was 215 lb. for a square inch ; for good brick, from 280 to 300. Count Rumford found the cohesive strength of a cylinder of iron, an inch in diameter, 6.3466, or 631731). ; the mean 633.20; which is only 3, more than Emerson's reSult. Sickingen makes the comparative cohesive strength of gold, 150955; of silver, 19771; of plati. na, 202361 ; of copper, 304696; of soft iron, 362927; of inard iron, 559830. Guyton makes platina a little stronger. In 13ution's experiments, b, d, and l, being the breadth, depth, and length of a beam of oak, in
For farther information on this subject, the reader may consult Ritter on Cohesion, Gilbert's Jourmal, 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 commou language, denotes the sensation which is felt, or the effect which is produced, by the abstraction of heat. Thus the clinnate 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 water of the conimen 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 deprived of heat to that certain degree.
Notwithstanding the simplicity of this theory, and the conviction which seems to accompany it, philosophers have often entertained doubts concerning it; and they have endeavoured to inquire into the real state of the matter, by devising experiments capable of demonstrating whether the cause of heat was any thing real, and that of cold only a privation or dimimution of the former; or, vice versa, whether the cause of cold was any thing real, and that of heat a diminution ; or, lastly, whether the production of heat, and the production of cold, were not owing to two distinct principles or elements. On the supposition that the cause of one of those effects only is real, it is much more natural to suppose that the cause of heat is the real principle or clement, since its ef