discoveries made by algebra are wholly to be imputed to that symbolical language made use of in it: for by this means we are enabled to represent things in the form of equations and by variously proceeding with these equations, to trace out, step by step, the several particulars we want to know. Add to all this, that by such a notation, the eyes and imagination are also made subservient to the discovery of truth; for the thoughts of the mind rise up and disappear, according as we set ourselves to call them into view; and, therefore, with out some particular method of fixing and ascertaining them as they occur, the retrieving them when out of sight would be no less painful, than the very first exercise of deducing them one from another. As, therefore, we have frequent occasion to look back upon the discoveries already made, could these be no otherwise brought into view, than by the same course of thinking in which they were first traced, so many different attentions at once must needs greatly distract the mind, and be attended with infinite trouble and fatigue. But now, the method of fixing and ascertaining our thoughts by a happy and well chosen notation, entirely removes all those obstacles; for thus, when we have occasion to turn to any former discovery, as care is taken all along to delineate them in proper characters, we need only cast our eye on that part of the process where they stand expressed, which will lay them at once open to the mind in their true and genuine form. By this means we can take, at any time, a quick and ready survey of our progress, and running over the several conclusions already gained, see more distinctly what helps they furnish towards obtaining those others we are still in pursuit of. Nay, further, as the amount of every step of the investigation lies before us, by comparing them variously among themselves, and adjusting them one to another, we come at length to discern the result of the whole, and are enabled to form our several discoveries into an uniform and well-connected system of truths, which is the end and aim of all our inquiries. NOTES, in music, characters which mark the sounds; i. e. the elevations and fallings of the voice, and the swiftness and slowness of its motions. In general, under notes are comprehended all the signs or characters used in music, though in propriety the word only implies the marks VOL. V. which denote the degrees of gravity and acuteness to be given to each sound. NOTONECTA, in natural history, boatfly, a genus of insects of the order Hemip. tera. Snout inflected; antennæ shorter than the thorax; four wings folded cross-wise, coriaceous on the upper half; hind-legs hairy, formed for swimming. There are seventeen species in two divisions, viz. A. Lip elongated, conic. B. Conic, spinous at the sides. Mr. Donovan in his English insects has described N. clauea: upper wings yellow-brown, the anterior margin brightbrown dotted with black, the tip bifid. It is found in Europe. NOTOXUS, in natural history, a genus of insects of the order Coleoptera. Antennæ filiform; four feelers, hatchet-shaped; jaw one-toothed; thorax a little narrowed behind. There are about thirteen species. N. moneceros, described in Donovan's insects, has a thorax projecting like a horn over the head; shells pale, with a black band and dot. It inhabits Europe on umbelliferous plants. NOVEL, in the civil law, a term used for the constitutions of several emperors, as of Justin, Tiberius, Leo, and more particularly of those of Justinian. The constitu tions of Justinian were called novels, either from their producing a great alteration in the face of the ancient law, or because they were made on new cases, and, after the revisal of the ancient code, compiled by order of that emperor. Thus the constitutions of the emperors Theodosius, Valentinian, Marcian, &c. were also called novels, on account of their being published after the Theodosian code. NOVEL assignment, or new assignment, a term in law pleadings which it is difficult to explain to those unacquainted with prac tical pleading. It occurs in actions of trespass, where the form of the declaration being very general, the defendant pleads in bar a common justification; to which the plaintiff replies by stating, that he brought his action as well for a certain other trespass which he states with more particularity, as for that which is justified. This is called a new assignment. NOVEMBER, in chronology, the 11th month of the Julian year, consisting only of thirty days: it got the name of November, as being the ninth month of Romulus's year, which began with March. NOUN, in grammar, a part of speech, which signifies things without any relation C NUM NUM to time; as a man, a house, sweet, bitter, express the quantity of units, as 1, 2, 5, 4, &c. See GRAMMAR. NOURISHMENT. See PHYSIOLOGY. NUDE contract, nudum pactum, a bare promise without any consideration, and not authenticated by deed, which is therefore 'void in law. NUISANCE, signifies generally any thing that does hurt, inconvenience, or damage to the property or person of another. Nuisances are of two kinds, public and private, and either affect the public or the individual. The remedy for a private nuisance is by action on the case for damages, and for a public nuisance by indictment. Amongst the nuisances which most commonly occur are the erecting of noxious manufactures in towns, and in the vicinity of ancient houses; such as the erecting a vitriol manufactory, to the annoyance of Disorderly the neighbours in general. houses, bawdy houses, stage booths, lotteries, and common scolds, are also public nuisances. Where the injury is merely to an individual, and not to the public, the individual only has an action, but not in the case of a public nuisance, where the private injury is merged, or lost, in that of the public, but where an individual receives a particular injury by a public nuisance. And any one aggrieved may abate, that is, pull down and remove a nuisance, after which he can have no action: but this is a dangerous attempt to take the law into one's own hands. It must be done without riot, if at all. Every continuance of a nuisance is a fresh nuisance, and a fresh action will lie. NUL tiel record, no such record in law, is the replication which the plaintiff makes to the defendant when the latter pleads a matter of record in bar to the action, and it is necessary to deny the existence of such record, and to join issue on that fact. NUMBER, a collection of several units, NUMBERS, kinds and distinctions of. Ma- &c.; whereas ordinal numbers, are those rable with unity; as a number, incommensurable with unity, is termed irrational or a surd. See SURD. In the same manner a rational whole number is that whereof unity is an aliquot part; a rational broken number, that equal to some aliquot part of unity; and a rational mixed number, that consisting of a whole number and a broken one. Even number, that which may be divided into two equal parts without any fraction, as 6, 12, &c. The sum, difference, and product of any number of even numbers, is al ways an even number. An evenly even number, is that which may be measured, or divided, without any remainder, by another even number, as 4 by 2. An unevenly even number, when a number may be equally divided by an uneven number, as 20 by 5. Uneven number, that which exceeds an even number, at least by unity, or which cannot be divided into two equal parts, as 3, 5, &c. The sum or difference of two uneven numbers make an even number; but the factum of two uneven ones make an uneven number. If an even number be added to an uneven one, or if the one be subtracted from the other, in the former case the sum, in the latter the difference, is an uneven number; but the factum of an even and uneven number is even. The sum of any even number of uneven numbers is an even number; and the sum of any uneven number of uneven numbers is an uneven number. Primitive, or prime numbers, are those only divisible by unity, as 5, 7, &c. And prime numbers among them selves, are those which have no common measure besides unity, as 12 and 19. Perfect number, that whose aliquot parts added together make the whole number, as 6, 28; the aliquot parts of 6 being 3, 2, and 1,= 6; and those of 28 being 14, 7, 4, 2, 1, 28. Imperfect numbers, those whose aliquot parts, added together, make either more or less than the whole. And these are March. distinguished into abundant and defective; an instance in the former case is 12, whose aliquot parts 6, 4, 5, 2, 1, make 16; and in the latter case 16, whose aliquot parts 8, 4, 2, and 1, make but 15. Plain number, that arising from the multiplication of two numbers, as 6, which is the product of 3 by 2; and these numbers are called the sides of the plane. Square number, is the product of any number multiplied by itself: thus 4, which the factum of 2 by 2, is a square number. Every square number added to its root makes an even number. Polygonal, or polygonous numbers, the sums of arithmetical progressions beginning with unity: these, where the common difference is 1, are called triangular numbers; where 2, square numbers; where 3, pentagonal numbers; where 4, hexagonal numbers; where 5, heptagonal numbers, &c. See POLYGO NAL. Pyramidal numbers: the sums of polygonous numbers, collected after the same manner as the polygons themselves, and not gathered out of arithmetical progressions, are called first pyramidal numbers: the sums of the first pyramidals are called second pyramidals, &c. If they arise out of triangular numbers, they are called triangular pyramidal numbers; if out of pentagons, first pentagonal pyramidals. From the manner of summing up polygonal numbers, it is easy to conceive how the prime pyramidal numbers are found, viz. (a− 2) n3 + 3 n2 — (a—5) n 6 the prime pyramidals expresses all NUMBER of direction, in chronology, some one of the 35 numbers between the Easter limits, or between the earliest and latest day on which it can fall; i. e. between the 22d of March and the 25th of April. Thus, if Easter Sunday fall as in the first line be low, the number of direction will be as on the lower line. Easter-day........... 22, 23, 24, 25, 26, 27, 28, 29, 30, 31. and so on till the number of direction and April. 1, 2, 3, &c. 11, 12, 13, &c. ing table with the dominical letter on the left hand, and the golden number at top; then where the columns meet is the number of direction for that year. C 2 Thus, for the present year, 1808, the dominical letter being B, and the golden number 4, we find the number of direction 27, to which add 21, and the sum is 48 from the 1st of March; deduct 31 for the number of days in March, and the remainder gives the day of April for Easter Sunday. NUMBER, golden, in chronology. See GOLDEN number. NUMBER, in grammar, a modification of nouns, verbs, &c. to accommodate them to the varieties in their objects, considered with regard to number. See GRAMMAR. NUMBERS, in poetry, oratory, music, &c. are certain measures, proportions, or cadences, which render a verse, period, or song, agreeable to the ear. NUMERAL letters, those letters of the alphabet which are generally used for figures, as I, V, X, L, C, D, M. NUMERATION, or notation, the art of expressing in characters any number proposed in words; or of expressing in words any number proposed in characters. ARITHMETIC; NOTATION. See NUMERICAL, or NUMERAL, something belonging to numbers; as numerical algebra is that which makes use of numbers instead of letters of the alphabet. Also, numerical difference is the difference whereby one individual is distinguished from another. Hence a thing is said to be numerically the same, when it is so in the strictest sense of the word. NUMIDIA, the PINTADO, or guineahen, in natural history, a genus of birds of the order Gallinæ. Generic character: bill strong and short, with a carunculate cere at the base, in which the nostrils are lodged; head horned with a compressed coloured callus; wattles hanging from the cheeks; tail short, and pointing downwards; body speckled. There are four species. N. meleagris, is of the size of a very large fowl, and is the meleagris of the ancients, who used to prize it as a high delicacy. Its native territory is Africa, and particularly, perhaps, Nubia. It is gregarious, having been often seen in very numerous flocks. It is now extremely common in this country. The female lays many eggs, and, secreting her nest, sometimes will suddenly appear with a family of twenty young ones. It is a bird of harsh sound, and almost perpetually uttering it. The flesh of the young birds is valued, and its eggs are thought preferable to those of the common hen. See Aves, Plate X. fig. 5. NUNEZ (PERO) in biography, one of the ablest mathematicians of his time, born at Alcaza do Sal, in Portugal. He taught publicly in the university of Coimbra, and instructed the Infante de Luis so well, that it is said he fitted him for a professor. Pero Nunez is well known in the history of science, as the person who made the first improvement in the method of reading an observed angle, and the scale which he invented for this purpose, though it has received some improvements, is still called the Nonius, his latinized name. His works are numerous. NUT-galls are excrescences formed on leaves of the oak by the puncture of an insect which deposits an egg on them. The best are known by the name of Aleppogalls, imported very largely into this country for the use of dyers, calico printers, &c. These are hard like wood, of a blueish colour, and of a disagreeable taste. They are partly soluble in water, and what remains is tasteless and possesses the properties of the fibre of wood. By experiments Mr. Davy found that 500 grains of Aleppo-galls formed with water a solution which yielded by slow evaporation 185 grains of matter, which was compos ed of NUTATION, in astronomy, a kind of tremulous motion of the axis of the earth, whereby, in each annual revolution it is twice inclined to the ecliptic, and as often returns to its former position. Sir Isaac Newton observes, that the moon has the like motion, only very small, and scarcely sensible. NUTMEG, in natural history, the kernel of a large fruit, not unlike the peach, the produce of a tree called by botanists MyRISTICA, which see. The nutmeg is separated from its investient coat, the mace, before it is sent over to us; except that the whole fruit is sometimes imported in preserve, by way of sweetmeat, or as a curiosity. See MACE. The nutmeg, as we receive it, is of a roundish or oval figure, of a tolerably compact and firm texture, but easily cut with a knife, and falling to pieces on a smart blow. Its surface is not smooth, but furrowed with a number of wrinkles, running in various directions, though principally longitudinally. It is of a greyish brown colour on the outside, and of a beautiful variegated hue within, being marbled with brown and yellow variegations, running in perfect irregularity through its whole substance. It is very unctuons and fatty to the touch, when powdered, and is of an extremely agreeable smell, and of an aromatic taste, without the heat that attends that kind of flavour in most of the other species, There are two kinds of nutmeg in the shops, the one called by authors the male, and the other the female. The female is the kind in common use, and is of the shape of an olive: the male is long and cylindric, and has less of the fine aromatic flavour than the other, so that it is much less esteemed, and people who trade largely in nutmegs will seldom buy it. Besides this oblong kind of nutmegs, we sometimes meet with others of perfectly irregular figures, but mere lusus naturæ, not owing to a different species of the tree. The longer male nutmeg, as we term it, is call ed by the Dutch the wild nutmeg. It is always distinguishable from the others, as well by its want of fragrancy, as by its shape: it is very subject to be worm-eaten, and is strictly forbid, by the Dutch, to be packed up among the other, because it will give occasion to their being worm-eaten by the insects getting from it into them, and breeding in all parts of the parcel. The largest, heaviest, and most unctuous of the nutmegs are to be chosen, such as are the shape of an olive, and of the most fragrant smell. NUTRITION. See PHYSIOLOGY. NYCTANTHES, in botany, a genus of the Diandria Monogynia class and order. Natural order of Sepiariæ. Jasmineæ, Jussien. Essential character: corolla, salver shaped, with truncated segments; capsule, two-celled, margined; seeds solitary. There are seven species, of which N. undulata, wave-leaved Nyctanthes, is a shrub about six feet in height, the young shoots are hairy; leaves of a shining green, smooth, in pairs from the joints, bitter, without any smell; flowers white; calycine segments six; of the corolla six, seven or eight, narrow, much waved on the edge; fruit superior, resembling a black cherry, containing a round hairy seed. It is a native of the East Indies, where it is much cultivated on account of the sweetness of the flowers, which are worn by the ladies in their hair. NYMPH, among naturalists, that state of winged-insects between their living in the form of a worm, and their appearing in the winged or most perfect state. The eggs of insects are first hatched into a kind of worms, or maggots; which afterwards pass into the nymph-state, surrounded with shells or cases of their own skins; so that, in reality, these nymphs are only the embryo-insects, wrapped up in this covering; from whence they at last get loose, though not without great difficulty. NYMPHÆ. See ANATOMY. NYMPHÆA, in botany, water-lily, a genus of the Polyandria Monogynia class and order. Natural order of Succulentæ. Hydrocharides, Jussieu. Essential character, calyx four, five, or six leaved; corolla many petalled; berry many celled, truncated. There are six species, of which N. alba, white water-lily, has a tuberous root, creeping far and wide in the mud; the whole plant is larger than the yellow water-lily; petioles and peduncles round, within full of pores; flowers large and very handsome, petals white, from sixteen to twenty in number; stamens sixty-eight, or seventy; germ roundish; style none; stigma rayed; according to Linnæus, the flower raises itself out of the water and expands about seven o'clock in the morning, closing again, and reposing upon the surface of the water soon after four in the evening. The roots have an astringent bitter taste; |