# NEW TESTAMENT

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NEW TESTAMENT. (See Bible.) NEWTON, sir Isaac, the creator of natural philosophy, was born at Woolsthorpe, in Lincolnshire, Dec. 25,1642 (O. S.), and, at his birth, was so small and weak that his life was despaired of. On the death of his father, which took place while he was yet an infant, the manor of Wools thorpe became his heritage. His mother sent him, at an early age, to the village school, and, in his twelfth year, to the town of Grantham. While here, he displayed a decided taste for philosophical and mechanical inventions; and, avoiding the society of other children, provided himself with a collection of saws, hammers, and other instruments, with which he constructed models of many kinds of machinery. He also made hourglasses acting by the descent of water ; and, a new windmill, of a peculiar construction, having been erected in the town, he studied it until he succeeded in imitating it, and placed a mouse inside, which he called the miller. Some knowledge of drawing being necessary in these operations, he applied himself, without a master, to the study; and the walls of his room were covered with all sorts of designs. After a short period, however, his mother took him home, for the purpose of employing him on the farm, and about the affairs of the house, and sent him, several times, to market, at Grantham, with the produce of the farm. A trusty servant was sent with him, and the young philosopher left him to manage the business, while he himself employed his time in reading. A sundial which he constructed, on the wall of the house at Woolsthorpe, is still shown. This irresistible passion for study and science finally induced his mother to send him back to Grantham, where he remained till his eighteenth year, when he was entered at Trinity college, Cambridge (1660). A taste for mathematical studies had, for some time, prevailed there; the elements of algebra and geometry usually formed a part of the course, and Newton had the good fortune to find the celebrated doctor Barrow (q. v.) professor. In order to prepare himself for the lectures, Newton read the textbooks in advance : these were Sanderson's Logic and Kepler's Treatise on Optics ; the Geome try of Descartes (q. v.) was also one of the first books that he read at Cambridge. He next proceeded, at the age of about twentyone, to study the works of Wallis, and appears to have been particularly delighted with the celebrated treatise of that author entitled Arithmetica Infinitorum. Wallis had given the quadrature of curves whose ordinates are expressed by any integral and positive power of 1-x% and had observed that if, between the areas so calculated, we could interpolate the areas of other curves, the ordinates of which constituted, with the former ordinates, a geometrical progression, the area of the curve, whose ordinate was a mean proportional between 1 and 1-x2, would express a circular surface, in terms of the square of its radius. In order to effect this interpolation, Newton began to seek, empirically, the arithmetical law of the coefficients of the series already obtained ; and, having done this, he rendered it more general by expressing it algebraically. Perceiving that this interpolation gave him the expression, in series, of radical quantities, composed of several terms, he directly verified this induction by multiplying each series by itself the number of times required by the index of the root, and found, in fact, that this multiplication reproduced exactly the quantity from which it had been deduced. Having thus ascertained that this form of series really gave the developement of radical quantities, he was led to consider that they might be obtained still more directly, by applying to the proposed quantities the process used in arithmetic for extracting roots. This gave him, again, the same series, but made them depend on a much more general method, since it permitted him to express, analytically, any powers whatever of polynomials, their quotients and their roots, by considering and calculating these quantities as the developements of powers corresponding to integral negative, or fractional exponents. Indeed, in the generality and in the uniformity given to these developements the discovery of Newton really consists; for Wallis had remarked before him, with regard to monomial quantities, the analogy of quotients and roots with integral powers, expressed according to the notation of Descartes; and Pascal had given a rule for forming, directly, any term of the developement of binomial powers, the exponent being an integer. Thus was discovered the celebrated formula, known as Newton's Binomial Theorem, (q. v.) Newton further perceived, that there is hardly any ana lytical research, in which the use of it is not necessary, or at least possible, and immediately made a great number of the most important applications of it. Thus he obtained the quadrature of the hyperbola, and of many other curves, and also extended his formulae to the surfaces of solids, the determination of their contents, and the situation of their centres of gravity. Wallis, in his Ariihmet. In/in. (1665), had shown that the area of all curves may be found, whose ordinate is expressed by any integral power of the abscissa, and had given the expression for this area in terms of the ordinate. Newton, by reducing into series the more complicated functions of the abscissa, which represent the ordinates, changed them into a series of monomial terms, to each of which he was able to apply the rule of Wallis. He thus obtained as many portions of the whole area as there were terms, and, by their addition, obtained the total. But the far more extensive, and, in some respects, unlimited applications that Newton made of this rule, depended on a general principle, which he had made out, and which consisted in determining, from the manner in which quantities gradually increase, what are the values to which they ultimately arrive. To effect this, Newton regards them, not as aggregates of small homogeneous parts, but as the results of continued motion, lines being considered as described by the movement of points, surfaces by that of lines, solids by that of surfaces, and angles by the rotation of their sides. Again, considering that the quantities so formed are greater or smaller, in equal times, according as the velocity with which they are developed is more or less rapid, he endeavors to determine their ultimate values from the expression for these velocities, which he calls fluxions, naming the quantities themselves fluents. In fact, when any given curve, surface or solid, is generated in this manner, the different elements which either compose or belong to it, such as the ordinates, the abscissas, the lengths of the arcs, the solid contents, the inclinations of the tangent planes, and of the tangents, all vary, differently and unequally indeed, but nevertheless according to a regular law, depending on the equation of the curve, surface or solid under consideration. Hence Newton was able to deduce from this equation the fluxions of all these elements, in terms of any one of the variables, and of the fluxion of this variable, considered as indeterminate; then, by expanding into series, he transformed the Wallis's rule became applicable ; thus, by applying it successively to each, and taking the sum of the results, he obtained the ultimate value, that is, the fluent of the element, which he had been considering. In this consists the method of fluxions, of which Newton, from that time, laid the foundation, and which, eleven years later, Leibnitz again discovered, and presented to the world in a different form,that of the differential calculus. Newton made these important discoveries before completing his twentythird year, and collected them in a manuscript, entitled Analysis per Mquationes JS/umero Terminorum i?ifinitas, but did not communicate them to any one. About this time (1665), being obliged to quit Cambridge on account of the plague, he retired to Woolsthorpe, and now turned his attention more closely to subjects of natural philosophy. As he was one day sitting under an appletree, the fall of an apple led him to reflect on the nature of that remarkable principle which urges all bodies towards t he centre of the earth. " Why," he asked himself, "may not this power extend to the moon ? and, if so, what more would be necessary to retain her in her orbit about the earth?" He considered that if the moon was retained about the earth . by terrestrial gravity, the planets, which move round the sun, ought, similarly, to be retained in their orbits by their gravity towards that body. Setting out with the law of Kepler (q. v.), that the squares of the times of revolution of the different planets are proportional to the cubes of their distances from the sun, Newton found, by calculation, that the force of solar gravity decreases proportionally to the square of the distance; and having thus determined the law of the gravity of the planets towards thfe sun, he endeavored to apply it to the moon; that is, to determine the velocity of her motion round the earth by means of her distance, as settled by astronomers, and of the intensity of gravity, as shown by the fall of bodies at the earth's surface. To make this calculation, it is necessary to know exactly the distance from the surface to the centre of the earth, expressed in parts of the same measure that is used in marking the spaces described, in a given time, by falling bodies at the earth's surface ; for their velocity is the first term of comparison that determines the intensity of gravity at this distance from the centre, which we apply afterwards at the moon's VOL. ix. 23 mains only to be seen if gravity, when thus diminished, has precisely the degree of energy necessary to counteract the centrifugal force of the moon, caused by her observed motion in her orbit. Unfortunately, at that time, there existed no correct measure of the earth's dimensions. (See Degrees, Measurement of.) Newton was obliged to employ the imperfect measures then in use, and found that they gave for the force which retains the moon in her orbit, a value greater by one sixth than that which results from her observed circular velocity. This small difference seemed, to his cautious mind, a strong proof against his bold conjecture. He imagined that some unknown cause modified, in the case of the moon, the general law of gravity indicated by the motion of the planets. Yet he did not abandon his leading notion, but determined to wait till study and reflection should reveal to him this supposed unknown cause. In 1666, he returned to Cambridge, was chosen fellow of his college (Trinity college) in 1667, and, the next year, was admitted A. M.; but he did not disclose his secrets even to his instructer, doctor Barrow. In 1668, however, Mercator (q. v.) published his Logarithmoteclmia, in which he had obtained the area of the hyperbola referred to its asymptotes, by expanding its ordinate into an infinite series, which was the main secret of Newton^s method. Barrow showed this work to Newton, who immediately gave him his own treatise (the Analysis, &c), but did not yet publish it. In the course of 1666, his attention had been accidentally drawn to the phenomena of the refraction of light through prisms. His experiments led him to conclude that light, as it emanates from the radiating bodies, is not a simple and homogeneous substance, but that it is composed of a number of rays, endowed with unequal refrangibility, and possessing different coloring properties. More than two years elapsed before he returned to his researches on this subject; but, in 1669, being appointed professor of mathematics, and preparing to lecture on optics, he endeavored to mature his first results, and composed a complete treatise, in which the fundamental properties of light were unfolded, established and arranged by means of experiments alone, without any mixture of hypothesisa novelty at that time almost as surprising as these proper* ties themselves. Thus it appears, that the three great discoveries which form the glory of his life,the Method of Fluxions, the Theory of Universal Gravitation, and the Decomposition of Light,were conceived before the completion of his 24th year. In 1672, Newton was chosen a fellow of the royal society, to which he communicated a description of a new arrangement for reflectingtelescopes, which rendered them more convenient by diminishing their length without weakening their magnifying powers, and, soon after, the first part of his labors on the analysis of light. When the first feelings of surprise and admiration, excited by this noble work, had subsided, the society appointed three members to study it fully, and report upon it. Hooke, a man of extensive acquirements and an original turn of thought, but of excessive desire of renown, being one of the members, undertook to draw up the report. Instead of discussing the new facts, as presented by the experiments of Newton, he examined them merely in relation to a hypothesis of his ownthat light is simply the effect of vibrations excited and propagated in an elastic mediumand concluded by allowing whatever appeared reconcilable with his own hypothesis, and by advising Newton not to seek any other explanation of the facts. Newton in reply (Phil. Trans., vii), after exposing some errors of Hooke, adduces new experiments confirming his former results, and refutes the objections to the production of whiteness by the mixture of all the rays. To several other attacks (particularly one by Huygens), which appeared in the Philosophical Transactions, and which were conducted on similar principles, he was obliged to reply. In vain did he declare that he neither advanced nor admitted any hypothesis whatever, and that his sole object was to establish and connect facts by means of the laws of nature. This severe and abstract methodof reasoning was little understood, and it is hardly conceivable into what minuteness of detail he was obliged to enter. So much was he disgusted with these difficulties, that he gave up his intention of printing his lectures on Optics with his treatise on Series. Before quitting the lists, however, he addressed another paper (1675) to the royal society, completing the account of his results, and of his views on the nature of light. This treatise, united with his first paper on the analysis of light, afterwards served as the base of the great work Treatise on Optics (1704), in which, however, the experimental investigation of the phenomena is more extensive, and more strictly separated from all hypothesis. The new experiments with which it was enriched, relate principally to the colors observed in thick plates of all bodies, when they are presented, in a proper manner, to the incident ray. Newton reduced them to the same laws as those of the phenomena in thin plates; and then, considering these law* as established facts, equally certain with the particular experiments from which they are deduced, yet far more universal, he unites them all in one general property of light, each peculiarity of which is characterized with such exactness as to make the general property a pure expression for all the observed laws. The essence of this property is, that each particle of light, from the instant when it quits the radiating body whence it emanates, is subject, periodically, and at equidistant intervals, to a continual alternation of dispositions, to be reflected from, or transmitted through, the surfaces of the diaphanous bodies which it meets with ; so that, for instance, if such a surface presents itself to the luminous particle during one of the alternations, when the tendency to reflection, which Newton called the "fit of easy reflection," is in force, this tendency makes it yi^kl more easily to the reflecting power of i:he surface; while, on the other hand, it yields with more difficulty when it is in the contrary phase, which he termed the "fit of easy transmission." (See Light, and Optics.) In his paper of 1675, after excusing himself for proposing a conjecture as to the nature of light, and declaring that it had no connexion with the facts which he had discovered, he goes on to give one which he should l3e inclined to consider most probable, if he were obliged to adopt any. He then admits the existence of an imperceptible fluid (which he calls (Ether), extending every where in space, and penetrating all bodies with different degrees of density. This fluid he considers as highly elastic, and, consequently, pressing against itself and the material parts of other bodies, with an energy proportional to its actual density. If this aether be disturbed or agitated, in any one point, by any cause which produces a vibratory motion, this motion must transmit itself, by undulations, through all the rest of the medium ; and if these undulations encounter, in their passage, the material particles forming the substance of any body, they will agitate them with considerable force. Now, light, he admits, consists of a peculiar substance, different from the aether, but composed of great velocity, agitate the aether in their passage, and excite undulations. He does not attempt to determine the essence of these particles. From this time till 1679, Newton communicated nothing to the royal society, and in this interval appears to have been occupied with astronomical observations. In that year he had occasion to write to Hooke about a system of physical astronomy, on which the royal society had asked his opinion. In his letter he proposed, as a matter deserving attention, to verify the motion of the earth by direct experiment, viz. by letting bodies fall from a considerable height, and observing if they follow exactly a vertical direction; for if the earth turns, since the rotary velocity at the point of departure must be greater than at the foot of the vertical, they will be found to deviate from this line towards the east, instead of following it exactly, as they would do if the earth did not move. Hooke replied, that wherever the direction of gravity is oblique to the axis of the earth, bodies in falling change parallels, and approach the equator. This led Newton to consider whether the elliptical motion of the planets could result from a force varying inversely as the square of the distance, and, if so, under what circumstances such a result would ensue. In proposing his experiment to the society, he had considered the motion of the heavy body as determined by a force of constant intensity, and had concluded the trajectory to be a spiral, doubtless because he imagined the body to fall in a resisting medium, such sis the air. Hooke replied, that it should not be a spiral, but that in a vacuum it would be an eccentric ellipse, which, in a resisting medium, would change into an eccentric ovoidal curve; and he represented the eccentric ellipse as the consequence of a force inversely proportional to the squares of the distances from the earth's centre. Newton, having examined this result by mathematical calculations, found that an attractive force, emanating from a centre, and acting inversely as the squares of the distances, would produce motions exactly resembling the planetary motions, both in regard to the form of the orbit and the velocity of the body at each point. This was the secret of the system of the world; but it still remained to account for the discordance of the moon's motion, which had before (1665) embarrassed Newton. But, in 1682, having learned the results of the new measure Jb'mdmg, as he advanced, the manifest tendency of these numbers to produce the longdesired results, he became so much agitated as to be unable to go on with his calculation, and requested one of his friends to finish it. Two years were spent in penetrating the consequences of this discovery, and preparing his immortal work, Philosophies Naturalis Principia Mathematica, during which time he lived only to calculate. He would sometimes rise, and, suddenly arrested by some new conception, would sit on his bedside for hours together, and would forget his meals, unless reminded of the necessity of taking nourishment. It was not till 1686, that he finally concluded to present his work to the society, at the expense of which it was printed, in 1687. Not more than two or three of his contemporaries were capable of understanding it, and more than fifty years elapsed before the great physical truth which it contained was thoroughly understood by the generality of scientific men. In 1687, Newton was one of the delegates sent by the university of Cambridge, to maintain its rights before the high commission court, when they were attacked by James II, and, in 1688, was elected, by the university, to the convention parliament, but never distinguished himself in that body. He had always taken great interest in chemistry, and occupied himself occasionally with experiments in that science. He had constructed a small laboratory for prosecuting his investigations, and seems, after the publication of the Principia, to have devoted almost his whole time to them. One morning (1692), he had accidentally shut up his little pet dog Diamond in his room, and, on returning, found that the animal, by upsetting a candle on his desk, had destroyed the labors of several years. On perceiving his loss, he only exclaimed, " Oh, Diamond ! Diamond! you little know the mischief you have done." But the grief caused by this circumstance injured his health, and, M.Biot endeavors to show, for some time impaired his understanding. This fact of a derangement of his intellect, according to Biot, explains why Newton, though only fortyfive years old when the Principia was published, never after gave to the world a new work in any branch of science, and merely published some which had been previously composed. Doctoi Brewster, however, refutes tins notion In 1696, he was appointed warden of the mint* a general recoinage having then been undertaken. In this office, he rendered essential service, and, in 1699, was made master of the mint. In 1701, he was again returned to parliament by his university; in 1703, he was chosen president of the royal society ; and, in 1705, was knighted by queen Anne. In 1704, he gave to the world bis Optics (in English ; translated hi to Latin by doctor S. Clarke), which contains all his researches on light. The whole merit of this extraordinary work has not been fully appreciated till within a few years. Other works, published about this time, were his Aritkmetica Universalis (1707; more complete, 1712); Mdhodus Differentialis (1711); and his Analysis per Equationes Nmnero Terminorum infiniias (1711). We have already given an account of the celebrated dispute between Newton and Leibnitz (1712), in the article Leibnitz. (See the Commercium Epistolicum, or Collection of Letters, published by the Royal Society in 1712). The princess of Wales (daughterinlaw of George I), a woman of a cultivated mind, had received Newton with great kindness, and was fond of conversing with him. Newton having one day explained to her a system of chronology which he had composed for his amusement, she requested a copy for her own use. A copy was also given to abb6 Conti, who immediately published it without Newton's knowledge ; and it therefore became necessary to prepare a more correct edition, which appeared in 1728, under the title Chronology of Ancient Kingdoms amended. His Observations upon the Prophecies of Holy Writ (1733) is an attempt to show the fulfilment of the prophecies. In his Historical Account of two notable Corruptions of the Scriptures, he discusses the two passages in the Epistles of St. John and St. Paul, relating to the Trinity, which he supposes to have been altered, by copyists. At this period of his life, the reading of religious works, with the conversation of his friends, formed almost his only amusement, after performing the duties of his office. He had almost ceased to think of science; and, during the last ten years of his life, when consulted about any passage in his works, he would reply, " Ask Mr. De Moivre; he knows better than I do." When his friends expressed their admiration of his discoveries, he said, " To myself I seem to have been as a child playing on the seashore, while the immense ocean of truth lay unexplored before me." His countenance was rather calm than expressive ; his manner, rather languid ; his health was good until his eightieth year, when he suffered from a calculous disorder, which occasioned his death March 20,1726-7. His corpse lay in state, in Jerusalem chamber, Westminster, and, on the 28th, was interred in Westminster abbey. A monument was erected to his memory, by his family, with an inscription ending with these words, applicable to Newton only : Sibi gratulentur mortales tale tantumque exstitisse humani generis.* His statue, by Roubiliac, stands in his college, at Cambridge. Horsley's edition of his Works (5 vols., 4to.,177985), with the Opuscula, collected by Castillon (3 vols., 4to., Lausanne, 1744), and his letters, inserted in the Biographia Biitannica, contains nearly all his printed works.f Pemberton's View of Newton's Philosophy (1728), and Maclaurin's Account of Newton's Discoveries, are valuable works. See, also, Birch's History of the Royal Society (vol. 3d). The b3st edition of the Principia is that of Leuueur and Jacquier (4 vols., 4to., Geneva, 173942 ; 4 vols., 8vo., Glasgow, 1822). A Life of Newton, by doctor Brewster, appeared in 1831. The article JYeivton, in the Biographit Universelle^ by M. Biot, is very complete. The Collections for the History of Grantham, with authentic Memoirs of Sir Isaac Newton, contains much important matter.* Pope's epitaph on Newton is weJl known:¦ Isaacus Newton hicjacet, Quern immortalem cadi, natura, Tempus ostendunt, Mortalem hoc marmor fatetur. Nature and all her works lay hid in night, God said; Let Newton be,and all was light.f The manuscripts, letters., and other papers of Newton, have been preserved in different collections. His correspondence with Cotes, relative to the second edition of the Principia, and amounting to between 60 and 100 letters, a considerable portion of the manuscript of that work, and two or three letters to doctor Keill, on the Leibnitzian controversy, are preserved in the library of Trinity college, Cambridge. Newton's letters to Flamstead, about 34 in number, are deposited in the library of Corpus Christi college, Oxford. Several letters of Newton, and, we believe,,the original specimen which he drew up of the Principia, exist among the papers of Mr. William Jones (the father of sir William Jones), which are preserved at Shirburn castle, in the library of lord Macclesfield. But the great mass of Newton's papers came into the possession of the Portsmouth family, through his niece, lady Lymington, and have been safely preserved by that noble family. There is reason to believe that they contain nothing which could be peculiarly interesting to science 3 but as the correspondence of Newton with contemporary philosophers must throw considerable light on his personal history, we trast that it will, ere long, be given to the public. (Brewster's Life cf Newt on J)