Pythagoras. idleness, bodily exercises also made a considerable part Pythagoras. of his discipline. Soon after his appearance at these games, Pythagoras commenced his travels in quest of knowledge. He first visited Egypt, where, through the interest of Polycrates tyrant of Samos, he obtained the patronage of Amasis king of Egypt, by whose influence, combined with his own assiduity, patience, and perseverance, he at length gained the confidence of the priests; from whom he learned their sacred mysteries, theology, and the whole system of symbolical learning. In Egypt, too, he became acquainted with geometry and the true solar system; and, before he left that country, made himself master of all the learning for which it was so famed among the nations of antiquity. He afterwards visited Persia and Chaldea, where from the Magi he learnt divination, the interpreting of dreams, and astronomy. He is likewise said to have travelled into India, to have conversed with the Gymnosophists, and to have acquired from them a knowledge of the philosophy and literature of the east; and such was his ardour in the pursuit of science, that in quest of *De Fini- it, we are told by Cicero *, he crossed many seas, and bus, lib. iv. travelled on foot through many barbarous nations. $29. After Pythagoras had spent many years in gathering information on every subject, especially respecting the nature of the gods, the rites of religion, and the immortality of the human soul, he returned to his native island, and attempted to make his knowledge useful by instituting a school for the instruction of his countrymen. Failing of success in this laudable undertaking, he repaired to Delos, where he pretended to receive moral dogmas from the priestess of Apolio. He also visited Crete, where he was initiated into the most sacred mysteries of Greece. He went likewise to Sparta and Elis, and again assisted at the Olympic games; where in the public assembly he was saluted with the title of sophist or wise man, which he declined for one more humble. See PHILOLOGY, N° 1. and PHILOSOPHY, N° 1. He returned to Samos enriched with mythological learning and mysterious rites, and again instituted a school. His mysterious symbols and oracular precepts made this attempt more successful than the former had been; but meeting with some opposition, or being detected in some pious frauds, he suddenly left Samos, retired to Magna Grecia, and settled at Crotona. Here he founded the Italic sect (see PHILOSOPHY, N° 20.); and his mental and personal accomplishments, the fame of his distant travels, and his Olympic crown, soon procured him numerous pupils. His bold and manly eloquence and graceful delivery attracted the most dissolute, and produced a remarkable change in the morals of the people of Crotona. His influence was increased by the regularity of his own example, and its conformity to his precepts. He punctually attended the temples of the gods, and paid his devotions at an early hour; he lived upon the purest and most innocent food, clothed himself like the priests of Egypt, and by his continual purifications and regular offerings appeared to be superior in sanctity to the rest of mankind. He endeavoured to assuage the passions of his scholars with verses and numbers, and made a practice of composing his own mind every morning, by playing on his harp, and singing along with it the peans of Thales. To avoid the temptations of ease and the seductions of At Crotona he had a public school for the general benefit of the people, in which he taught them their duty, praising virtue and condemning vice; and parti cularly instructing them in the duties of social life. Besides this, he had a college in his own house, which he denominated xovßor, in which there were two classes of students, viz. iğwriginai, who were also called auscultantes, and original. The former of these were probationers, and were kept under a long examen. A silence of five years was imposed upon them; which Apuleius thinks was intended to teach them modesty and attention; but Clemens Alexandrinus thinks it was for the purpose of abstracting their minds from sensible objects, and inuring them to the pure contemplation of the Deity. The latter class of scholars were called genuini, perfecti, mathematici, and, by way of eminence, Pythagoreans. They alone were admitted to the knowledge of the arcana and depths of Pythagoric discipline, and were taught the use of ciphers and hieroglyphic writings. Clemens observes, that these orders corresponded very exactly to those among the Hebrews: for in the schools of the prophets, there were two classes, viz. the sons of the prophets, who were the scholars, and the doctors or masters, who were also called perfecti; and among the Levites, the novices or tyros, who had their quinquennial exercises, by way of preparation, Lastly, even among the proselytes there were two orders; exoterisci, or proselytes of the te; and intrinseci or perfecti, proselytes of the covenant. He adds, it is highly probable, that Pythagoras himself had been a proselyte of the gate, if not of the covenant. Gale endeavours to prove that Pythagoras borrowed his philosophy from that of the Jews; to this end producing the authorities of many of the fathers and ancient authors, and even pointing out the tracks and footsteps of Moses in several parts of Pythagoras's doctrine. But we believe the learned author was misled by the Christian Platonists. The authority of Pythagoras among his pupils was so great, that it was even deemed a crime to dispute his word; and their arguments were considered as infallibly convincing, if they could enforce them by adding, that "the master said so;" an expression which af terwards became proverbial in jurare in verba magistri. This influence over his school was soon extended to the world, and even his pupils themselves divided the applause and approbation of the people with their master; and the rulers and legislators of all the principal towns of Greece, Sicily, and Italy, boasted of being the disciples of Pythagoras. To give more weight to his exhortations, as some writers mention, Pythagoras retired into a subterraneous cave, where his mother sent him intelligence of every thing which happened during his absence. After a certain number of months he again re-appeared on the earth with a grim and ghastly countenance, and declared in the assembly of the people that he was returned from hell. From similar exaggerations it has been asserted that he appeared at the Olympic games with a golden thigh, and that he could write in letters of blood whatever he pleased on a looking-glass; and that by setting it opposite to the moon, when full, all the characters which were on the glass became ச agoras became legible on the moon's disc. They also relate, —— that by some magical words he tamed a bear, stopped the flight of an eagle, and appeared on the same day and at the same instant in the cities of Crotona and Metapontum, &c. At length his singular doctrines, and perhaps his strenuously asserting the rights of the people against their tyrannical governors, excited a spirit of jealousy, and raised a powerful party against him; which soon became so outrageous as to oblige him to fly for his life. His friends fled to Rhegium; and he himself, after being refused protection by the Locrians, fled to Metapontum, where he was obliged to take refuge in the temple of the muses, and where it is said he died of hunger about 497 years before Christ. Respecting the the time, place, and manner of his death, however, there are various opinions, and many think it uncertain when, where, or in what manner he ended his days. After his death his followers paid the same respect to him as was paid to the immortal gods; they erected statues in honour of him, converted his house at Crotona into a temple to Ceres, appealed to him as a deity, and swore by his name. Pythagoras married Theano of Crotona, or, according to others, of Crete, by whom he had two sons, Telauges and Mnesarchus, who, after his death, took care of his school. He is said also to have had a daughter called Dumo. Whether he left any writings behind him is disputed. It seems probable, however, that he left none, and that such as went under his name were written by some of his followers. The golden verses which Hierocles illustrated with a commentary, have been ascribed to Epicharmus or Empedocles, and contain a brief summary of his popular doctrines. From this circumstance, and from the mysterious secrecy with which he taught, our information concerning his doctrine and philosophy is very uncertain, and cannot always be depended on. The purpose of philosophy, according to the system of Pythagoras, is to free the mind from incumbrances, and to raise it to the contemplation of immutable truth and the knowledge of divine and spiritual objects. To bring the mind to this state of perfection is a work of some difficulty, and requires a variety of intermediate steps. Mathematical science was with him the first step to wisdom, because it inures the mind to contemplation, and takes a middle course between corporeal and incorporeal beings. The whole science he divided into two parts, numbers and magnitude; and each of these he subdivided into two others, the former into arithmetic and music, and the latter into magnitude at rest and in motion; the former of which comprehends geometry, and the latter astronomy. Arithmetic he considered as the noblest science, and an acquaintance with numbers as the highest good. He considered numbers as the principles of every thing; and divided them into scientific and intelligible. Scientific number is the production of the powers involved in unity, and its return to the same; number is not infinite, but is the source of that infinite divisibility into equal parts which is the property of all bodies. Intelligible numbers are those which existed in the divine mind before all things. They are the model or archetype of the world, and the cause of the essence of beings. Of the Monad, Duad, Triad, Tetrad, and Decad, various explanations have been given by Pythagoras various authors; but nothing certain or important is known of them. In all probability, numbers were used by Pythagoras as symbolical representations of the first principles and forms of nature, and especially of those eternal and immutable essences which Plato denominated ideas; and in this case the Monad was the simple root from which he conceived numbers to proceed, and as such, analogous to the simple essence of deity; from whence, according to his system, the various properties of nature proceed. * *History Music followed numbers, and was useful in raising the mind above the dominion of the passions. Pythagoras considered it as a science to be reduced to mathematical principles and proportions, and is said to have discovered the musical chords from the circumstance of several men successively striking with hammers a piece of heated iron upon an anvil. This story Dr Burney discredits; but allows, from the uniform testimony of of Music, writers ancient and modern, that he invented the har- vol. i. monical canon or monochord, (see MONOCHORD). The P. 441. music of the spheres, of which every one has heard, was a most fanciful doctrine of Pythagoras. It was produced, he imagined, by the planets striking on the ether through which in their motion they passed; and he considered their musical proportions as exact, and their harmony perfect. Pythagoras, as we have already seen, learned geometry in Egypt; but by investigating many new theorems, and by digesting its principles, he reduced it to a more regular science. A geometrical point, which he defines to be a monad, or unity with position, he says corresponds to unity in arithmetic, a line to two, a superficies to three, and a solid to four. He discovered several of the propositions of Euclid; and on discovering the 47th of book 1st, he is said to have offered a hecatomb to the gods; but as he was averse to animal sacrifices, this assertion is surely false. His great progress in astronomical science has been mentioned elsewhere. See ASTRONOMY, No 11, 22. and PHILOSOPHY, N° 15, 16. Wisdom, according to Pythagoras, is conversant with those objects which are naturally immutable, eternal, and incorruptible; and its end is to assimilate the human mind to the divine, and to qualify us to join the assembly of the gods. Active and moral philosophy prescribes rules and precepts for the conduct of life, and leads us to the practice of public and private virtue.— On these heads many of his precepts were excellent, and some of them were whimsical and useless. Theoretical philosophy treats of nature and its origin, and is, according to Pythagoras, the highest object of study. It included all the profound mysteries which he taught, of which but little is now known. God be considers as the universal mind, diffused through all things, and the self-moving principle of all things (avTouatioμos Tây a), and of whom every human soul is a portion * * Cicero de Senect. It is very probable, that he conceived of the Deity as a 27. subtle fire, eternal, active, and intelligent; which is not inconsistent with the idea of incorporeality, as the ancients understood that term. This Deity was primarily combined with the chaotic mass of passive matter, but he had the power of separating himself, and since the separation he has remained distinct. The learned Cud worth argu Pythagoras, worth contends, that Pythagoras maintained a trinity of hypostases in the divine nature, similar to the Platonic triad (see PLATONISM). We cannot say that his ments appear to have much force; but we think the conclusion which he wishes to establish extremely probable, as Plato certainly drew his doctrine from some of the countries which Pythagoras had visited before him. Subordinate to the Deity there were in the Pythagorean creed three orders of intelligences, gods, demons, and heroes, of different degrees of excellence and dignity. These, together with the human soul, were considered as emanations from the Deity, the particles of subtle ether assuming a grosser clothing the farther they receded from the fountain. Hierocles defines a hero to be a rational mind united with a luminous body. God himself was represented under the notion of monad, and the subordinate intelligences as numbers derived from and included in unity. Man is considered as consisting of an elementary nature and a divine or rational soul. His soul, a self moving principle, is composed of two parts; the rational, seated in the brain; and the irrational, including the passions, in the heart. In both these respects he participates with the brutes, whom the temperament of their body, &c. allows not to act rationally. The sensitive soul perishes; the other assumes an ethereal vehicle, and passes to the region of the dead, till sent back to the earth to inhabit some other body, brutal or human. See METEMPSYCHOSIS. It was unquestionably this notion which led Pythagoras and his followers to deny themselves the use of flesh, and to be so peculiarly merciful to animals of every description. Some authors, however, say, that flesh and beans, the use of which he also forbade, were prohibited, because he supposed them to have been produced from the same putrified matter, from which, at the creation of the world, man was formed. 56. Sat. iii. Of the symbols of Pythagoras little is known. They have been religiously concealed; and though they have awakened much curiosity, and occasioned many ingenious conjectures, they still appear to us dark and trifling. As a specimen we give the following: "Adore the sound of the whispering wind. Stir not the fire with a sword. Turn aside from an edged tool. Pass not over a balance. Setting out on a journey, turn not back, for the furies will return with you. Breed nothing that hath crooked talous. Receive not a swallow into your house. Look not in a mirror by the light of a candle. At a sacrifice pare not your nails. Eat not the heart or brain. Taste not that which hath fallen from the table. Break not bread. Sleep not at noon. When it thunders touch the earth. Pluck not a crow. Roast not that which has been boiled. not on the ground. Plant not a palm. Breed a cock, but do not sacrifice it, for it is sacred to the sun and moon. Plant mallows in thy garden, but eat them not. Abstain from beans." Sail The following precepts are more important: "Discourse not of Pythagorean doctrines without light. Above all things govern your tongue. Engrave not the image of God in a ring. Quit not your station with out the command of your general. Remember that the paths of virtue and of vice resemble the letter Y. To this symbol Persius refers *, when he says, Pythagoras sics. Python. Et tibi quæ Samios diduxit litera ramos, Surgentem dextro monstravit limite collem. There has the Samian Y's instructive make Pointed the road thy doubtful foot should take; There warn'd thy raw and yet unpractis'd youth, To tread the rising right-hand path of truth. The scantiness and uncertainty of our information respecting Pythagoras, renders a regular and complete account of his life and doctrines impossible. A modern author of profound erudition, pronounces him Ancient to have been unquestionably the wisest man that ever caphylived, if his masters the Egyptian priests must not be excepted. This is saying a great deal too much; but that he was one of the most distinguished philosophers of antiquity, or, as Cicero expresses it, vir præstanti sapientia, appears very evident; and his moral character has never been impeached. The mysterious air which he threw over his doctrines, and the apparent inanity of some of his symbols, have indeed subjected him to the charge of imposture, and perhaps the charge is not wholly groundless; but when we consider the age in which he lived, and the nature of the people with whom he had to deal, who would in all probability have resisted more open innovations, even this will not appear so blameable as at first sight we are apt to think it; and it is worthy of notice, that the worst stories of this kind have come down to us in a very questionable shape, and with much probability appear to be false. PYTHAGOREANS, a sect of ancient philosophers, so called from being the followers of Pythagoras. the preceding article. See PYTHIA, the priestess of Apollo at Delphi, by whom he delivered oracles. She was so called from Pythius, a name of that god, which is said to have been given him on account of his victory over the serpent Python. The Pythia was at first required to be a young girl, but in latter times she was a woman of 50 years of age. The first and most famous Pythia was Phemonöe. Oracles were at first delivered by her in hexameter verse. All the pythias were to be pure virgins, and all of them delivered their oracles with great enthusiasm and violent agitations. See ORACLE and DELPHI. PYTHIAN GAMES, in Grecian antiquity, sports instituted near Delphos in honour of Apolio, on account of his slaying the serpent Python. See APOLLO.These games, at their first institution, were celebrated only once in nine years; but afterwards every fifth year, from the number of the Parnassian nymphis who came to congratulate Apollo, and to make him presents on his victory. The victor was crowned with garlands. PYTHON, in fabulous history, a monstrous serpent, produced by the earth after Deucalion's deluge. Juno being exasperated at Latona, who was beloved by Jupiter, commanded this serpent to destroy her; but flying from the pursuit of the monster, she escaped to Delos, where she was delivered of Diana and Apollo; the latter of whom at length destroyed Python with his arrows, in memory of which victory the Pythian games were instituted. See APOLLO. Q. Q, Q. or q, the 16th letter and 12th consonant of our alphabet; but is not to be found either in Quadi. the Greek, old Latin, or Saxon alphabets; and indeed some would entirely exclude it, pretending that k ought to be used wherever this occurs. However, as it is formed in the voice in a different manner, it is undoubtedly a distinct letter: for, in expressing this sound, the cheeks are contracted, and the lips, particularly the under one, are put into a canular form, for the passage of the breath. Marcgrave's Hut, Brasil. The q is never sounded alone, but in conjunction with u, as in quality, question, quite, quote, &c. and never ends any English word. As a numeral, Q stands for 500; and with a dash over it, thus, for 500,000. Used as an abbreviature q signifies quantity, or quantum. Thus, among physicians, q. pl. is quantum placet, i. e." as much as you please" of a thing; and q. s. is quantum sufficit, i.e. "as much as is necessary." Q. E. D. among mathematicians, is quod erat demonstrandum, i. e. "which was to be demonstrated:" and Q. E. F. is quod erat faciendum, i. e. “which was to be done." " as if Q. D. among grammarians is quasi dictum, i. it were said ;" or, as who should say." In the notes of the ancients, Q stands for Quintus, or Quintius; Q. B. V. for quod bene vertat; Q. S. S. S. for quæ supra scripta sunt ; Q. M. for Quintus Mutius, or quomodo; Quint. for Quintilius; and Quæs. for quæstor. 66 e. QUAB, in Ichthyology, the name of a Russian fish, which is said to be at first a tadpole, then a frog, and at last a fish. Dr Mounsey, who made many inquiries concerning these pretended changes, considers them all as fabulous. He had opportunity of seeing the fish itself, and found that they spawned like other fishes, and grew in size, without any appearances to justify the report. He adds, that they delight in very clear water, in rivers with sandy or stony bottoms, and are never found in standing lakes, or in rivers passing through marshes or mossy grounds, where frogs choose most to be. QUABES, are a free people of Africa, inhabiting the southern banks of the river Sestos, and between that and Sierra Leona. They are under the protection of the emperor of Manow. QUACHA, or QUAGGA. See EQUUS, MAMMALIA Index. QUACHILTO, in Ornithology, is the name of a very beautiful Brasilian bird, called also yacazintli and porphyrio Americanus. It is of a fine blackish purple colour, variegated with white; its beak is white while young, but becomes red as it grows older, and has naked space at its basis, resembling in some sort the coot; its legs are of a yellowish green; it lives about the waters, and feeds on fish, yet is a very well tasted bird. It imitates the crowing of a common cock, and makes its music early in the morning. QUACK, among physicians, the same with empiric. See EMPIRIC. QUADI, (Tacitus); a people of Germany, situated to the south-east of the mountains of Bohemia, on the Quadi banks of the Danube, and extending as far as the river A Quadrant. Marus, or March, running by Moravia, which country they occupied. QUADRAGESIMA, a denomination given to lent, from its consisting of 40 days. See LENT. QUADRANGLE, in Geometry, the same with a quadrilateral figure, or one consisting of four sides and four angles. QUADRANS, the quarter or fourth part of any thing, particularly the as, or pound. QUADRANS, in English money, the fourth part of a penny. Before the reign of Edward I. the smallest coin was a sterling, or penny, marked with a cross; by the guidance of which a penny might be cut into halves for a halfpenny, or into quarters or four parts for farthings; till, to avoid the fraud of unequal cuttings, that king coined halfpence and farthings in distinct round pieces. QUADRANT, in Geometry, the arch of a circle, containing 90°, or the fourth part of the entire periphery. Sometimes also the space or area, included between this arch and two radii drawn from the centre to each extremity thereof, is called a quadrant, or, more properly, a quadrantal space, as being a quarter of an entire circle. QUADRANT, also denotes a mathematical instrument, of great use in astronomy and navigation, for taking the altitudes of the sun and stars, as also for taking angles in surveying, &c. This instrument is variously contrived, and furnished with different apparatus, according to the various uses it is intended for; but they all have this in common, that they consist of a quarter of a circle, whose limb is divided into 90°. Some have a plummet suspended from the centre, and are furnished with sights to look through. The principal and most useful quadrants are the common surveying quadrant, astronomical quadrant, Adams's quadrant, Cole's quadrant, Gunter's quadrant, Hadley's quadrant, horodictical quadrant, Sutton's or Collins's quadrant, and the sinical quadrant, &c. Of each of which in order. 1. The common surveying quadrant, is made of brass, wood, or any other solid substance; the limb of which is divided into 90°, and each of these farther divided into as many equal parts as the space will allow, either diagonally or otherwise. On one of the semidiameters are fitted two moveable sights; and to the centre is sometimes also fixed a label, or moveable index, bearing two other sights; but in lieu of these last sights there is sometimes fitted a telescope: also from the centre there is hung a thread with a plummet; and on the under side or face of the instrument is fitted a ball and socket, by means of which it may be put into any position. The general use of it is for taking angles in a vertical plane, comprehended under right lines going from Quadrant. from the centre of the instrument, one of which is horizontal, and the other is directed to some visible point. But besides the parts already described, there is frequently added to the face, near the centre, a kind of compartment, called the quadrat, or geometrical square. See QUADRAT. Plate CCCCLVIII. fig. t. This quadrant may be used in different situations: for observing heights or depths, its plane must be disposed perpendicularly to the horizon; but to take horizontal distances, its plane is disposed parallel thereto. Again, heights and distances may be taken two ways, viz. by means of the fixed sights and plummet, or by the label: As to which, and the manner of measuring angles, see GEOMETRY and MENSURATION. 2. The astronomical quadrant is a large one, usually made of brass, or wooden bars faced with iron plates; having its limb nicely divided, either diagonally or otherwise, into degrees, minutes, and seconds; and furnished with two telescopes, one fixed on the side of the quadrant, and the other moveable about the centre, by means of the screw. There are also dented wheels which serve to direct the instrument to any object or phenomenon. The use of this curious instrument, in taking observations of the sun, planets, and fixed stars, is obvious; for being turned horizontally upon its axis, by means of the telescope, till the object is seen through the moveable telescope, then the degrees, &c. cut by the index give the altitude required. See ASTRONOMY Index. 3. Cole's quadrant is a very useful instrument invented by Mr Benjamin Cole. It consists of six parts, viz. the staff AB (fig. 1.); the quadrantal arch DE; three vanes A, B, C; and the vernier FG. The staff is a bar of wood about two feet long, an inch and a quarter broad, and of a sufficient thickness to prevent it from bending or warping. The quadrantal arch is also of wood; and is divided into degrees, and third-parts of a degree, to a radius of about nine inches; to its extremities are fitted two radii, which meet in the centre of the quadrant by a pin, round which it easily moves. The sight-vane A is a thin piece of brass, almost two inches in height and one broad, placed perpendicularly on the end of the staff A, by the help of two screws passing through its foot. Through the middle of this vane is drilled a small hole, through which the coincidence or meeting of the horizon and solar spot is to be viewed. The horizon vane B is about an inch broad, and two inches and a half high, having a slit cut through it of near an inch long and a quarter of an inch broad; this vane is fixed in the centre-pin of the instrument, in a perpendicular position, by the help of two screws passing through its foot, whereby its position with respect to the sight-vane is always the same, their angles of inclination being equal to 45 degrees. The shade-vane C is composed of two brass plates. The one, which serves as an arm, is about four inches and a half long, and three quarters of an inch broad, being pinned at one end to the upper limb of the quadrant by a screw, about which it has a small motion; the other end lies in the arch, and the lower edge of the arm is directed to the middle of the centre pin: the other plate, which is properly the vane, is about two inches long, being fixed perpendicularly to the other plate, at about half an inch distance from that end next the arch; this vane may be used either by its shade or by the solar spot cast by a convex lens placed therein. And, because the Quedant wood-work is often apt to warp or twist, therefore this vane may be rectified by the help of a screw, so that the warping of the instrument may occasion no error in the observation, which is performed in the following manner: Set the line G on a vernier against a degree on the upper limb of the quadrant, and turn a screw on the backside of the limb forward or backward, till the hole in the sight-vane, the centre of the glass, and the sunk spot in the horizon-vane, lie in a right line. To find the sun's altitude by this instrument: Turn your back to the sun, holding the instrument by the staff with your right hand, so that it be in a vertical plane passing through the sun; apply your eye to the sight-vane, looking through that and the horizon-vane till you see the horizon; with the left hand slide the quadrantal arch upwards, until the solar spot or shade, cast by the shade-vane, fall directly on the spot or slit in the horizon-vane; then will that part of the quadrantal arch, which is raised above G or S (according as the observation respected either the solar spot or shade) show the altitude of the sun at that time. But if the meridian altitude be required, the observation must be continued; and as the sun approaches the meridian, the sea will appear through the horizon-vane, and then is the observation finished; and the degrees and minutes, counted as before, will give the sun's meridian altitude: or the degrees counted from the lower limb upwards will give the zenith-distance. 4. Adams's quadrant differs only from Cole's quadrant in having an horizontal vane, with the upper part of the limb lengthened; so that the glass, which casts the solar spot on the horizon-vane, is at the same distance from the horizon-vane as the sight-vane at the end of the index. 5. Gunter's quadrant, so called from its inventor Edmund Gunter, besides the usual apparatus of other quadrants, has a stereographical projection of the sphere on the plane of the equinoctial. It has also a kalendar of the months, next to the divisions of the limb. Use of Gunter's quadrant. 1. To find the sun's meridian altitude for any given day, or the day of the month for any given meridian altitude. Lay the thread to the day of the month in the scale next the limb; and the degree it cuts in the limb is the sun's meridian altitude. Thus the thread, being laid on the 15th of May, cuts 59° 30', the altitude sought; and, contrarily, the thread, being set to the meridian altitude, showe the day of the month., 2. To find the hour of the day. Having put the bead, which slides on the thread, to the sun's place in the ecliptic, observe the sun's altitude by the quadrant; then, if the thread be laid over the same in the limb, the bead will fall upon the hour required. Thus suppose on the 10th of April, the sun being then in the beginning of Taurus, I observe the sun's altitude by the quadrant to be 36°; I place the bead to the beginning of Taurus in the ecliptic, and lay the thread over 36° of the limb; and find the bead to fall on the bour-line marked three and nine; accordingly the hour is either nine in the morning or three in the afternoon. Again, laying the bead on the hour given, having first rectified or put it to the sun's place, the degree cut by the thread on the limb gives the altitude. Note, the bead may be rectified otherwise, by bringing |