with the same velocity with which they met; that is, they will be equally distant, in equal times, both before and after their collision, although the absolute velocity of each may be changed. The circumstances attending this change of motion in the two bodies, using the above notation, are expressed in the two following formulæ : 2 bv + (B-b) ▼ B+b the velocity of B the velocity of b which needs no modification, when the motion of b is in the same direction with that of B. Sir Isaac Newton's theory of light and colours is deduced from clear and decisive experiments. 1st. That lights which differ in colour, differ also in degrees of refrangibility. ed. That the light of the sun, notwithstanding its uniform appearance, consists of rays differently refrangible. 3d. That those rays which are more refrangible than others, are also more reflexible. 4th. That as the rays of light differ in degrees of refrangibility and reflexibility, so they also dif fer in their disposition to exhibit this or that particular colour; and that colours are not qualifications of light derived from refractions or reflections of natural bodies, as was generally believed, but origiBnal and connate properties, which In the other case of b's motion, the general formulæ become -2bv+(B-b) V the velocity of are different in different rays, some brays being disposed to exhibit a red colour and no other, and some a green and no other, and so of the rest of the prismatic colours. B+b 2 BV — (B — b) v the velocity of B+b when b moves in a contrary direction to that of B, which arise from taking v negative. And (B—b) V B+b 2 BV B+b the velocity of B the velocity of b when b was at rest before impact, that is, when v=0. If a perfectly hard body impinge obliquely upon a perfectly hard and immoveable plane, it will, after collision, move along the plane. And its velocity before impact Is to the cosine of the angle of impact. But if the body be elastic it will rebound from the plane with the same velocity, and at the same angle with which it met it. 5th. That the light of the sun consists of violet-making, indigomaking, blue-making, green making, yellow-making, orange-making, and red-naking rays; and all of these are different in their degrees of refrangibility and reflexibility; for the rays which produce red colours are the least refrangible, and those that make the violet the most; and the rest are more or less refrangible as they approach either of these extremes, in the order already mentioned; that is, orange is least refrangible next to red, yellow next to orange, and so on; so that to the same degree of refrangibility there ever belongs the same colour, and to the same colour the same degree of refrangibility. COLOUR, in natural philosophy, 6th. Every homogeneal ray, conthat property of bodies which af sidered apart, is refracted accordfects the sight only; or that pro-ing to one and the same rule, so perty possessed by the elementary that its sine of incidence is to its rays of light, separated by any sine of refraction in a given ratio; means whatever, of exciting in us that is, every different coloured different sensations according to ray has a different ratio belonging their different refrangibility. Thus to it. colour may be considered in two 7th. The species of colour, and respects, as it regards bodies in ge- degree of refrangibility and reneral, and as it is produced by so-l'flexibility, proper to any particu lar light. all sorts of colours, when there is a due proportion in the mixture; so, on the contrary, blackness is produced by a suffocation and absorption of the incident light, which being stopped and suppress lar sort of rays, is not mutable by reflection or refraction from natural bodies, nor by any other cause that has been yet observed. When any one kind of rays has been separated from those of other kinds, it has obstinately retained its co-ed in the black body, is not relours, notwithstanding all endeavours to bring about a change. 8th. Yet seeming transmutations of colours may be made, where there is any mixture of divers sorts of rays; for, in such mixtures, the component colours appear not, but, by their mutually alloying each other, constitute an intermediate colour. fiected outward, but reflected and refracted within the body till it be stifled and lost. COLURES, in Astronomy and Geography, two great circles supposed to intersect each other, at right angles, in the pole, and to pass through the solstitial and equinoctial points of the ecliptic; that which passes through the former point being called solstitial colure, and the other the equinoc tial colure. COMBINATIONS, in Mathematics, denote the different colleetions that may be formed out of any given number of things, taken a certain number at a time, with out regard to the order in which they may be arranged; and are thus distinguished from permutations, or changes, which have reference to the order in which the several quantities may be disposed. 9th. There are, therefore, two sorts of colour, the one original and simple, the other compounded of these; and all the colours in the universe are either the colours of homogeneal, simple light, or compounded of these mixed together in certain proportions. The colours of simple light are, as we observed before, violet, indigo, blue, green, yellow, orange, and red, together with an indefinite variety of intermediate gradations. The colours of compounded light are differently compounded of these simple rays, mixed in various proportions: thus a mixture of yellow-making and blue-making rays exhibits a green colour, and a mixture of red and yellow makes an orange; and in any colour the same in specie with the primary ones may be produced by the composition of the two colours next adjacent in the series of colours generated by the prism, whereof the one is next more refrangible, and the other next less refrangible. But this is not the case with those which are situated at too great a (3) distance; orange and indigo do not produce the intermediate green, nor scarlet and green the intermediate yellow. 10th. The most surprising and wonderful composition of light is that of whiteness; there is no one sort of rays which can alone exhibit that colour: it is ever compounded, and to its composition all the aforesaid primary colours are requisite. 11th. As whiteness is produced by a copious reflection of rays of In order to find the number of combinations that a given number of things will admit of, let us take the continued product of the factors, (x + a) (x + b) (x + c) (x + d,) &c. viz. a + a x + b (1) x2 + a (2)+c a 3 + a x + ab + d x2 + a as ub 23 Now it is obvious, that in each of these formulæ the coefficient of the second term is equal to the sum of all the quantities a, b, c, &c. that enter into the expression; the third is the sum of all the pos sible combinations of every two sort, n of another sort, p of another sort, &c., by taking 1 at a time, 2 at a time, 3 at a time, &c. to any given number of things at a time. Rule. Place in one horizontal row m + 1 units, annexing ciphers on the right hand, tiil the whole number of units and ciphers exceeds the greatest number of things to be taken at a time by unity Under each of these terms write the sum of n + 1, left-hand terms, including that as one of them under which the number is placed; and under each of these, the p + 1 left-hand terms of the last line; then the g + 1 terms of this, and so on through all the number of different things, and the last line will be the answer. The theory of combinations is of the greatest use in the doctrine of chances and probabilities, for the probability of an event happening or failing depends generally upon the number of combinations that may be formed, or that may take place amongst the circumstances on which the event ultimately depends. COMBUSTIBLE Bodies, are those bodies which when once set on tire will continue to burn without the farther accession of fuel. The above formulæ leads us also to the method of finding the whole possible number of combinations that may be formed out of a given COMET, in Astronomy, a heanumber of things n, by taking 1,2, venly body, appearing at uncertain 3, 4, &c. at a time, to n, at a time; periods, and which, during the for this it is obvious will be equal time of its appearance, has a mo. to the sum of all the coefficients tion in some respects similar to of the expanded binomial (+1,) those of the planets. The orbits wanting the first term. But the of the comets however differ from sum of all these coefficients is those of the planets, in their being equal to 2", therefore the number more eccentric, and being inclined of possible combinations of n things to the plane of the ecliptics in anis equal to 2n-1. The single quan- gles of various magnitudes, the tities a, b, c, &c. being classed un-plane of some of them being nearly der the general term combination, for the sake of analogy, if these be excluded the formulæ will be 2n (n.+ 1.) Thus the number of all the combinations that may be formed out of the five letters a, b, c, d, e = 25-1 = 31, or excluding the single terms, the number of combinations is 25-6 26. To determine the number of combinations that may be formed out of a given number of things, in which there are m things of oue coincident, and others nearly perpendicular to the plane of the ecliptic. The motions of comets are also some of them direct, and others retrograde, whereas those of the planets are all direct. Comets are popularly divided into three distinct classes, viz. bearded, tailed, and hairy comets; though this distinction relates rather to the circumstance under which they are seen, than to any difference of the bodies them. selves. Thus, when the comet is eastward of the sun, and moves from it, it is said to be bearded; when the comet is westward of the sun, and sets after it, it is said to be tailed; and when the sun and the comet are in opposition, the train is hid behind the body of the comet, excepting a little which appears round it in the form of a border of hair, hence it is called hairy, and hence the name of comet is derived. upper extremity than near the centre of the comet. 6. Their tails are always transparent, and the smallest stars are seen through them without any sensible diminution of their light, and without those effects of refraction which might be expected from viewing them through a visible medium, which circumstance seems to indicate that the tails are composed of extremely rare and attenuated matter; but with regard to their The estimates that have been formation we may be said to be given of the magnitudes of comets, totally ignorant, notwithstanding are not sufficiently accurate to be the numerous hypotheses that depended upon; for it does not have been advanced on this subappear that they distinguish be-ject. The tail of the comet of 1811, tween the nucleus and the sur- when at its maximum, subtended rounding atmosphere. Some co- an angle of at least 16 degrees, and mets, from the apparent magnitude was computed to be at least 23 and distance compared, have been million miles in length. judged to be much larger than the The comet of 1759 is known to moon, and even equal to some of perform its revolution in 76 years, the primary planets. The diame- nearly, whence it appears that its ter of that of 1744, when at the mean distance is about 18 times distance of the sun from us, mea- that of the earth, or a little less sured about 1, and therefore its than the mean distance of Uranus; diameter must be about three times but, in consequence of the great ecthe diameter of the earth: at ano-centricity of its orbit, its aphelion ther time the diameter of its nu- point, or greatest distance from cleus was nearly equal to that of the sun, is nearly double that of the Jupiter. Hence it has been con-above planet. The perihelion disjectured, that some of the solar tance of this comet is about 6 of eclipses recorded in history, that cannot be verified by calculation from tables of the sun and moon, have been occasioned by the interposition of comets between the sun and the earth. The principal phenomena which have been observed with respect to the tails of comets are: 1. Their tails appear the largest and brightest immediately after the passage through their perihelion, or nearest approach to the sun. 2. The tail of a comet always declines from a just opposition to the sun, towards those parts which the body or nucleus pass over, in its progress through its orbit. 3. This declination is the smallest when the head or nucleus approaches nearest the sun, and is still less near the neucleus of the comet, than towards the extremity of the tail. 4. The tails are somewhat brighter and more distinctly defined in their convex than in their concave part. 5. They are also broader at the the mean distance of the earth, which being taken from 36, the mean transverse axis of its orbit, leaves 354 for its aphelion distance, which is nearly double the greatest distance of Uranus, and about four times that of Saturn. It is extremely difficult to determine, from computation, the elliptic orbit of a comet, to any degree of accuracy: for when the orbit is very eccentric, a very small error in the observation will change the computed orbit into a parabola, or hyperbola. Now, from the thickness and inequality of the atmosphere with which the comet is surrounded, it is impossible to determine, with any precision, when either the limb or centre of the comet pass the wire at the time of observation. And this uncertainty in the observations will subject the computed orbit to a great error. The only safe way to get the period of comets, is to compare the elements of all those which it transfers its motion to another body. which have been computed, and where you find they agree very well, you may conclude that they COMMUTATION, in Astronomy. are elements of the same comet, it Angle of commutation is the disbeing so extremely improbable tance between the sun's true place that the orbits of two different seen from the earth, and the place comets should have the same incli- of a planet reduced to the ecliptic; nation, the same perihelion dis- and is, therefore, found by subtance, and the places of the peri-tracting the same longitude from helion and node the same. Thus, the heliocentric longitude of the knowing the periodic time, we get planet. the major axis of the ellipse; and the perihelion distance being known, the minor axis will be known. When the elements of the orbits agree, the comets may be the same, although the periodic time should vary a little; as that may arise from the attraction of the bodies in our system, and which may also alter all the other elements in a small degree. COMETARIUM, a machine for conveying an idea of the revolution of a comet about the sun. It is contrived in such a manner, as by elliptical wheels to show the unequal motion of a comet in every part of its orbit. COMMENSURABLE, among geometricians, au appellation given to such quantities as are measured by one and the same common measure. COMMENSURABLE Numbers, whether integers, surds, or fractions, are such as can be measured or divided by some other number without any remainder; such are 12, and 18, as being measured by 6 and 3: also 2 √2, and 3 √2, being measured by 2. COMMENSURABLE in Power, is said of right lines, when their squares are measured by one and the same space or superficies. COMMENSURABLE Surds, those that being reduced to their least terms, become true figurative quantities of their kind; and are therefore as a rational quantity to a rational one. COMPASS, or Mariner's Compass, an instrument used at sea by mariners, to direct and ascertain the course of their ship. The invention of this instrument is commonly ascribed to Flavio Gioia, or Flavio, of Malphi, about the year 1302. The common construction of the mariner's compass is extremely simple. It consists of a circular brass box, which contains a paper card; on which is drawn the 32 points of the compass; and this card is fixed on a magnetic needle, which always turns to the north, except a small deviation which is variable at different places, and at the same place at different times. Azimuth CoMPASS. This differs from the common sea compass only in this, that the circumfer ence of the card or box is divided into degrees; also to the box is fitted an index with two sights, which are upright pieces of brass placed diametrically opposite to each other, having a slit down the middle of them, through which the sun or star is to be viewed at the time of observation. The use of this instrument is to take the bearing of any celestial object, when it is in or above the horizon, in order to find from the magnetical azimuth, or amplitude, the variation of the needle. These are the thirty-two principal points of divisions drawn on the compass card; and are otherCOMMON Measure or Divisor, wise called Rhumbs; each of which in Arithmetic, is that number has a particular denomination exwhich will divide two other num-pressed by means of the initials of bers without leaving a remainder; the four first points, North, East, and the greatest of such divisors South, West. is called the greatest common measure, or greatest common divisor. COMMUNICATION of Motion, that act of a moving body by Each point contains 11° 15', andis divided into points, containing 2° 48' 5". COMPASSES, or Pair of Com |