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ed in every four hundred years, by reducing the leap year at the close of each century, for three successive centuries, to common years, and retaining the leap year at the close of each fourth century only.

This was at that time esteemed as exactly conformable to the true solar year, but it is found not to be strictly just, because that in four hundred years it gets one hour and twenty minutes, and consequently in 7200 years a whole day.

#he greatest part of Europe have long used the Gregorian style: but great Britain retained the Julian till the year 1752, when, by act of parliament, this style was adjusted to the Gregorian; since which time Sweden, Denmark, and other European states, who computed time by the Julian account, have followed this example.

GREGORY (JAMEs), professor of mathematics, first in the university of St. Andrews, and afterwards in that of Edinburgh, was one of the most eminent mathematicians of the seventeenth century. He was a son of the Rev. John Gregory, minister of Drumoak, in the county of Aberdeen, and was born at Aberdeen, in November 1638. His mother was a daughter of Mr. David Anderson, of Finzaugh, or Finshaugh , a gentleman who possessed a singular turn for mathematical and mechanical knowledge. This mathematical genius was hereditary in the family of the Andersons, and from them it seems to have been transmitted to their descendants of the names of Gregory, Reid, &c. Alexander Anderson, cousin german of the said David, was professor of mathematics at Paris in the beginning of the 17th century, and published there several valuable and ingenious works. The mother of James Gregory inherited the genius of her family; and observing in her son, while yet a child, a strong propensity to mathematics, she instructed him herself in the elements of that science. His education in the languages he received at the grammar-school of Aberdeen, and went through the usual course of academical studies in the Marischal college; but he was chiefly delighted with philosophical researches, into which a new door had lately been opened by the key of the mathematics.

Galileo, Kepler, Des Cartes, &c. were the great masters of this new method; their works therefore became the principal study of young Gregory, who soon

began to make improvements upon their discoveries in Optics. The first of these improvements was the invention of the reflecting telescope; the construction of which instrument he published in his “Optica Promota,” in 1663, at twentyfour years of age. This discovery soon attracted the attention of the mathematicians, both of our own and of foreign countries, who immediately perceived its great importance to the sciences of optics and astronomy. But the manner of placing the two specula upon the same axis appearing to Newton to be attended with the disadvantage of losing the central rays ef the larger speculum, he proFo an improvement on the instrument, y giving an oblique position to the smaller speculum, and placing the eye-glass in the side of the tube. It is observable, however, that the Newtonian construction of that instrument was long abandoned for the original, or Gregorian, which is now always used when the instrument is of a moderate size; though Herschell has preferred the Newtonian form for the construction of those immense telescopes, which he has of late so successfully employed in observing the heavens. About the year 1664, or 1665, o; to London, he became acquainted wi Mr. John Collins, who recommended him to the best optic glass-grinders there, to have his telescope executed. But as this could not be done, for want of skill in the artist to grind a plate of metal for the object speculum into a true parabolic concave, which the design required, he was much discouraged with the disappointment,and,after a few imperfect trials made with an ill-polished spherical one, which did not succeed to his wish, he dropped the pursuit, and resolved to make the tour of Italy, then the mart of mathematical learning, that he might prosecute his favourite study with greater advantage. And the University of Padua being at that time in high reputation for mathematical studies, Mr. Gregory fixed his residence there for some years. Here it was that he published, in 1667, “Vera Circuli et Hyperbolae Quadratura,” in which he propounded another discovery of his own, the invention of an infinitely converging series for the areas of the circle and hyperbola. He sent home a copy of this work to his friend Mr. Collins, who communicated it to the Royal Society, where it met with the commendations of Lord Brounker and Dr. Wallis. He reprinted it at Venice the following year, to which he added a new work, entitled

“Geometriae Pars Universalis, inserviens Quantitatum Curvarum, Transmutationi et Mensurae,” in which he is allowed to have shewn, for the first time, a method for the transmutation of curves. These works engaged the notice, and procured the author the correspondence, of the greatest mathematicians of the age, Newton, Huygens, Wallis, and others. An account of this piece was also read before the Royal Society, of which Mr. Gregory, being returned from his travels, was chosen a member the same year, and communicated to them an account of the controversy in Italy about the motion of the earth, which was denied by Riccioli, and his followers. Through this channel, in particular, he carried on a dispute with M. Huygens, on the occasion of his treatise on the quadrature of the circle and hyperbola, to which that great man had started some objections; in the course of which our . produced some improvements of his series. But in this dispute it happened, as it generally does on such occasions, that the antagonists, though setting out with temper enough, yet grew too warm in the combat. This was the case here, especially on the side of Gregory, whose defence was, at his own request, inserted in the Philosophical Transactions. It is unnecessary to enter into particulars: suffice it therefore to say, that, in the opinion of Leibnitz, who allows Mr. Gregory the highest merit for his genius and discoveries, M. Huygens has pointed out, though not errors, some considerable deficiencies in the treatise above-mentioned, and shown a much simpler method of attaining the same end. In 1688, our author published at London another work, entitled “Exercitationes Geometricæ,” which contributed still much further to extend his reputation. About this time he was elected Professor of Mathematics in the University of St. Andrews, an office which he held for six years. During his residence there he married, in 1669, Mary, the daughter of George Jameson, the celebrated painter, whom Mr. Walpole has termed the Vandyke of Scotland, and who was fellow-disciple with that great artist in the school of Rubens, at Antwerp. In 1672, he published “The great and new Art of weighing Vanity: or a Disoovery of the Ignorance and Arrogance of the great and new Artist, in the pseudo-philosophical Writings. By M. Patrick **** Archbedal to the UniverVOL. VI.

sity of St. Andrews. To which are on: nexed some Tentamina de Motu Penduli et Projectorum.” Under this assumed name, our author wrote this little piece, to expose the ignorance of Mr. Sinclare, professor at Glasgow, in his hydrostatical writings, and in return for some ill usage of that author to a colleague of Mr. Gregory’s. The same year Newton, on his wonderful discoveries in the nature of light, having contrived a new reflecting telescope, and made several objections to Mr. Gregory’s, this gave birth to a dispute between those two philosophers, which was carried on during this and the following year, in the most amicable manner, on both sides; Mr. Gregory defending his own construction, so far as to give his antagonist the whole honour of having made the catoptric telescopes preferable to the dioptric, and showing that the imperfections in these instruments were not so much owing to a defect in the object speculum, as to the different refrangibility of the rays of light. In the course of this dispute our author described a burning concave mirror, which was approved by Newton, and is still in good esteem. Several letters that passed inthis dispute are printed by Dr. Desaguliers, in an appendix to the English edition of Dr. David Gregory’s “Elements of Catoptrics amd Dioptrics.”

In 1674, Mr. Gregory was called to Edinburgh, to fill the chair of mathematics in that university. This place he had held but little more than a year, when, in October 1675, being employed in shewing the satellites of Jupiter through a telescope to some of his pupils, he was suddenly struck with total blindness, and died a few days after, to the great loss of the mathematical world, at only 37 years of age.

. to his character, Mr. James Gregory was a man of very acute and penetrating genius. His temper seems to have been warm, as appears from his conduct in the dispute with Huygens: and, conscious perhaps of his own merits as a discoverer, he seems to have been jealous of losing any portion of his reputation by the improvements of others upon his inventions. He possessed one of the most amiable characters of a true philosoper, that of being content with his fortune in his situation. But the most brilliant part of his character is that of his mathematical genius as an inventor, which was of the first order; as will appear by the following list of his inventions and discoveries. Among many others may be reck


oned his reflecting telescope; burning concave mirror; quadrature of the circle and hyperbola, by an infinite converging series; his method for the transformation of curves; a geometrical demonstration of Lord Brounker's series for squaring the hyperbola; his demonstration that the meridian line is analogous to a scale of logarithmic tangents of the half.complements of the latitude : he also invented, and demonstrated geometrically, by help of the hyperbola, a very simple converging series for making the logarithms: he sent to Mr. Collins the solution of the famous Keplerian problem by an infinite series ; he discovered a method of drawing tangents to curves geometrically, without any previous calculations; a rule for the direct and inverse method of tangents, which stands upon the same principle (of exhaustions) with that of fluxions, and differs not much from it in the manner and application; a series for the length of the arc of a circle, from the tangent, and vice versa. These, with others for measuring the length of the elliptic and hyperbolic curves, were sent to Mr. Collins, in return for some received from him of Newton’s, in which he followed the elegant example of this author, in delivering his series in simple terms, independently of each other.— These, and other writings of our author, are mostly contained in the following works, viz.: 1. Optica Promota; 4to. London, 1663. 2. Vera Circuli et Hyperbolae Quadratura, 4to. Padua, 1667 and 1668. 3. Geometriae Pars Universalis, 4to. Padua, 1668. 4. Exercitationes Geometricae, 4to. London, 1668. 5. The great and new Art of weighing Vanity, 8vo. Glasgow, 1672. The rest of his inventions make the subject of several letters and papers, printed either in the Philos. Trans. vol. iii., the Commerc. Epistol. Joh. Collins, et aliorum, 8vo. 1715, in the appendix to the English edition of Dr. David Gregory's Elements of Optics, 8vo. 1735, by Dr. Desaguliers, and some series in the Exercitatio Geometrica of the same author, 4to, 1684, Edinburgh; as well as in his little piece on Practical Geometry. GREgony (DR. Davin), Savilian professor of astronomy, at Oxford, was nephew of the above-mentioned Mr. James Gregory, being the eldest son of his brother, Mr. David Gregory of Kinardie, a gentleman who had the singular fortune to see three of his sons all professors of mathematics, at the same time, in three of the British universities, viz. our author

David at Oxford, the second son James at Fdinburgh, and the -third son Charles at St. Andrew's. Our author David, the eldest son, was born at Aberdeen, in 1661, where he received the early parts of his education, but completed his studies at Edinburgh; and, being possessed of the mathematical papers of his uncle, soon distinguished himself likewise as the heir of his genius. . In the 23d year of his age he was elected professor of mathematics in the University of Edinburgh : and in the same year he published “Exercitatio Geometrica de Dimensione Figurarum, sive Specimen Methodi generalis dimetiendi quasvis Figuras,” Edinb. 1684, 4to. He very soon perceived the excellence of the Newtonian philosophy, and had the merit of being the first that introduced it into the schools, by his public lectures at Edinburgh. “He had (says Mr. Whitson, in the Memoirs of his own life, i. 32.) already caused several of his scholars to keep acts, as we call them, upon several branches of the Newtonian philosophy; while we, at Cambridge, poor wretches, were ignominiously studying the fictitious hypothesis of the Cartesian.” In 1691, on the report of Dr. Bernard's intention of resigning the Savilian professorship of astronomy at Oxford, our author went to London; and being patronised by Newton, and warmly befriended by Mr. Flamstead, the astronomer royal, he obtained the vacant professorship, though Dr. Halley was a competitor. This rivalship, however, instead of animosity, laid the foundation of friendship between these eminent men; and Halley soon after became the colleague of Gregory, by obtaining the Professor. ship of Geometry in the same university. Soon after his arrival in London, Mr. Gregory had been elected a Fellow of the Royal Society ; and, previously to his election into the Savilian Professor. ship, had the degree of Doctor of Physic conferred on him by the University of Oxford. In 1693, he published in the Philos. Trans. a solution of the Florentine problem, “De Testudine veliformi quadrabili; ” and he continued to communicate to the public, from time to time, many ingenious mathematical papers by the same channel. 1695, he printed at Oxford, “ Catoptricae et Dioptrica: Sphaerica. Elementa,” a work, which, we are informed, in the preface, contains the substance of some of his public lectures read at Edinburgh eleven years before. This valuable treatise was republished in English first with additions by Dr. William Brown, with the recommendation of Mr. Jones and Dr. Desaguliers; and afterwards by the latter of these gentlemen, with an appendix, containing an account of the Gregorian and Newtonian telescopes, together with Mr. Hadley's tables for the construction of both those instruments. It is not unworthy of remark, that, in the conclusion of this treatise, there is an observation, which shows that the construction of achromatic telescopes, which Mr Dolland has carried to such great perfection, had occurred to the mind of i)avid Gregory, from reflecting on the admirable contrivance of nature in combining the different humours of the eye. The passage is as follows: “Perhaps it would be of service to make the object lens of a different medium, as we see done in the fabric of the eye; where the crystalline humour (whose power of refracting the rays of light differs very little from that of glass) is by nature, who never does any thing in vain, joined with the aqueous and vitreous humours (not differing from water as to their power of refraction) in order that the image may be painted as distinct as possible upon the bottom of the eye.”. In 1702, our author published at Oxford, in folio, “Astronomiae Physicae et Geometrica: Elementa,” a work which is accounted his master-piece. It is founded on the Newtonian doctrines, and was esteemed by Newton himself as a most excellent explanation and defence of his philosophy. In the following year he gave to the world an edition, in folio, of the works of Euclid in Greek and Latin; being done in a prosecution of a design of his predecessor, Dr. Bernard, of printing the works of all the ancient mathematicians. In this work, which contains all the treatises that have been attributed to Euclid, Dr. Gregory has been careful to point out such as he found reason, from internal evidence, to believe to be the productions of some inferior geometrician.” In prosecution of the same plan, Dr. Gregory engaged soon after, with his colleague Dr. Halley, in the publication of the conics of Apollonius; but he had proceeded only a little way in the undertaking, when he died at Maidenhead in Berkshire, in 1710, being the 49th year of his age. Besides those works published in our author’s life-time, as mentioned above, he had several papers inserted in the

Philos. Trans, vol. xviii, xix., xxi, xxiv, and xxv, particularly a paper on the Catenarian curve, first considered by our author. He left also, in manuscript, a short Treatise of the Nature and Arithmetic of Logarithms, which is printed at the end of Keill’s translatiens of Commandine's Euclid ; and a treatise of Practical Geometry, which was afterwards translated, and published in 1745, by Mr. Maclaurin. Dr. David Gregory married, in 1695, Elizabeth, the daughter of Mr. Oliphant, of Langtown in Scotland. By this lady he had four sons, of whom, the eldest, David, was appointed Regius Professor of modern history, at Oxford, by King George the First, and died at an advanced age in 1767, after enjoying, for many years, the dignity of Dean of Christ Church in that University. When David Gregory quitted Edinburgh, he was succeeded in the Professorship of that University by his brother James, likewise an eminent mathematician, who held that office for thirty-three years, and retiring in 1725, was succeeded by the celebrated Maclaurin. A daughter of this Professor James Gregory, a young lady of great beauty and accomplishments, was the victim of an unfortunate attachment, that furnished the subject of Mallet’s well-known ballad of William and Margaret. Another brother, Charles, was created Professor of Mathematics at St. Andrews, by Queen Anne, in 1707. This office he held with reputation and ability for thirtytwo years; and resigning, in 1739, was succeeded by his son, who eminently inherited the talents of his family, and died in 1763. GRENADE, or GnRNApo, in o affairs, a kind of small bomb or shell, being furnished with a touch-hole and fuse, and is thrown by hand from the tops, hence they are frequently styled hand-grenades. The best way to secure one’s-self from the effects of a grenade is to lie flat down on the ground before it. bursts. The grenades are of much later invention and use than the bomb. They are usually about three inches in diameter, and weigh near three pounds. The metal may be one quarter or three-eighths of an inch thick, and the hole about onesixth. GREWIA, in botany, so named in honour of Nehemiah Grew, M. D. F. R. S. the famous author of the “Anatomy of vegetables,” a genus of the Gynandria Polyandria class and order. Natural order of Columniferae. Tiliaceae, Jussieu. Essential character: calyx five-leaved; etals five, with a nectareous scale at the É. of each ; berry four-celled. There are thirteen species. GRIAS, in botany, a genus of the Polyandria Monogynia class and order. Natural order of Guttiferae, Jussieu. Essential character: corolla four-petalled ; calyx four-cleft; stigma sessile, crossshaped ; drupe with an eight-furrowed nucleus. There is but one species, viz. G. cauliflora, anchovy-pear. This tree is about fifty feet in height, branching at the top; leaves on short petioles, pendulous, two or three feet long ; flowers from the stem, on short, scaly, manyflowered peduncles. The uprightness of the growth, and the size of the leaves, give this tree a very elegant appearance. The fruit is nearly as large as an alligator's egg, resembling it very much in shape, but of a brown colour; they pickle the fruit, and eat it in the same manner with the East Indian mango, which it resembles in flavour. This beautiful tree is common in many parts of Jamaica, growing generally in low moist places. GRIELUM, in botany, a genus of the Decandria Pentagynia class and order. Natural order of Gruinales. Essential character: calyx five-cleft: petals five, filament permanent ; pericarpium five, with one seed in each. There is only one species, viz. G. tenuifolium, a native of the Cape of Good Hope. GRIFFON, in heraldry, an imaginary animal, feigned by the ancients to be half eagle and half lion ; by this form they intended to give an idea of strength and swiftness joined together, with an extraordinary vigilance in guarding the things intrusted to its care. Thus the heathen naturalists persuaded the ignorant, that gold mines were guarded by these creatures with incredible watchfulness and resolution. GRINDERS. See ANATOMY. GRINDING, the reducing hard substances to fine powders, either by the mortar, or by way of levigation upon a marble. GRIPE, in the sea-language, is a piece of timber fayed against the lower piece of the stern, from the fore-most end of the keel, joining with the knee of the head: its use is to defend the lower part of the stern from any injury; but it is often

made the larger, to make the ship keep a good wind. Gnipe is also a sea-term, for a ship's

“turning her head more to the wind than

she should ; this is caused either by overloading her a-head, the weight of which presses her down, so that she will not readily fall off from the wind; or by staying or setting her masts too much aft; which is always a fault in short ships that draw much water, since it causes them to be continually running into the wind: though in floating ships, if the masts be not stayed very far aft, they will never keep a good wind. GRISLEA, in botany, a genus of the Octandria Monogynia class and order. Natural order of Calycanthemae. Salicariae, Jussieu. Essential character: calyx four-cleft ; petals four, from the incisures of the calyx; filaments, very long, ascending ; capsule globular, superior, onecelled, containing many seeds. There are two species, viz. G. secunda and G. tomentosa, the latter is a beautiful flowering shrub, a native of the hills and valleys through the northern provinces of the Carnatic in...the East Indies.

GRIT, a genus of argillaceous earths, with a texture more briless porous, equable, and rough to the touch. It neither gives fire with steel, nor effervesces with acids. When fresh and breathed on, it exhales an earthy smell. Its specific gravity varies from 2.0 to 2.6, and is used for mill stones and whet-stones, and sometimes for filtering-stones and buildIng. GROMETS, in the sea-language, small rings formerly fastened with staples to the yards, to make fast the gaskets, but now never used.

GRONOVIA, in botany, a genus of the Pentandria Monogynia class and order. Natural order of Cucurbitaceae. Essential character: petals five, together with the stamens inserted into the bell-shaped corolla; berry dry, inferior, containing one seed. . There is but one species, viz. G. scandens, climbing gronovia, an annual plant; sending out many trailing branches like those of the cucumber, closely set with broad leaves, which have a strong smell. Peduncles many flowered, axillary.

GROSS, in law-books, signifies absolute, or independent of another: thus, an advowson in gross, is one distinct and separate from the manor.

Ghoss BEAK, the English name of

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