continuator (kontinuator)

[F. con tinuateur Sp. Pg. continua dor = It. continua tore, The purely chronological or annalistic method [of history), though pursued by the learned Bar on i us and his continuators, is now generally abandoned. Schaff , Hist. Christ. Church, I. § 4. continue (kon-tin'u), v.; pret. and pp. continued, ppr. continuing. [ continuous. The use of the navel is to continue the infant unto the mother. Sir T. Browne , Vulg. Err., v. 5. 2. To extend from one point to another; produce or draw out in length: as, continue the line from A to B; let the line be continued to the boundary.-3. To protract or carry on; not to cease from or terminate. Ser, if it please your goodne e for to hire [hear], With yow I haue contynued my seruice In pese and rest. Generydes (E. E. T. S.), 1. 577. O continue thy loving kindne unto them that know thee. Ps. xxxvi. 10. IMG:content-1175.png:[blocks in formation] You know how to make yourself happy, by only continu ing such a life as you have been long accustomed to lead. Pope . 5. To carry on from the point of suspension; resume the course of; extend in the same course: as, to continue a line of railroad from its present terminus; the story will be contin ued next week. - 6. To suffer or cause to remain as before; retain: as, to continue judges in their posts. Disturbances in the celestial regions; though so regulated and moderated by the power of the Sun, prevailing over the heavenly bodies, as to continue the world in its Bacon , Physical Fables, i., Expl. state. IMG:content-1176.png:[blocks in formation] IMG:content-1177.png:[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small] where a, b, c, d, e, etc., and a, β, γ, δ, etc., are usually taken to represent whole numbers. A proper continued fraction is one in which a = β = γ = δ = etc. = 1. An improper continued fraction is one in which these quantities are all -1. The quantities a, b, c, d, e, etc., are termed the quotients or incomplete quotients. A term in at ing continued fraction is one having a finite number of one in which the quotients constitute a finite series recurring over and over again without ceasing. - Continued or continual proportionals, a series of three or more quantities compared together, so that the ratio is the same between every two adjacent terms, viz., between the first and second, the second and third, the third and fourth, etc.: as, 1, 2, 4, 8, 16, etc., where the terms con tinually increase in a double ratio. Such quantities are also said to be in continued proportion, and a series of continued proportionals is otherwise called a geometrical continuous To this habit of continuity of attention, tracing the first simple idea to its remoter consequences, the philosophical genius owes many of its discoveries. I. D'Israeli, Lit. Char., p. 178. To break the continuity of the land, and afford the easier and readier intercourse of water conveyance. D. Webster , Speech, June 5, 1828. Fire will live in it [vapor of the grotto del Cani] no longer than in water, because it wraps itself about the flame, and by its continuity hinders. air and nitre from coming to its succour. Add is on, Italy. 2. In math . and philos . , a connection of points (or other elements) as intimate as that of the instants or points of an interval of time: thus, the continuity of space consists in this, that a point can move from any one position to any other so that at each instant it shall have a definite and distinct position in space. This statement is not, however, a proper definition of continuity , but only an exemplification drawn from time. The old definitions - the fact that adjacent parts have their limits in common (Aristotle), infinite divisibility (Kant), the fact that between any two points there is a third (which is true of the system of rational numbers) - are inadequate. The le unsatisfactory definition is that of G. Cantor, that continuity is the perfect concatenation of a system of points - words which must be understood in special senses. Cantor calls a system of points concatenated when any two of them being given, and also any finite distance, however small, it is always po ible to find a finite number of other points of the system through which by succe ive steps, each le than the given distance, it would be po ible to proceed from one of the given points to the other. Не terms a system of points perfect when, whatever point not belonging to the system be given, it is po ible to find a finite distance so small that there are not an infinite number of points of the system within that distance of the given point. As examples of a concatenated system not perfect, Cantor gives the rational and also the irrational numbers in any interval. As an example of a perfect system not concatenated, he gives all the numbers whose expre ion in decimals, however far carried out, would contain no figures except 0 and 9. The simplest of the Concrete Sciences, Astronomy and Geology, yield the idea of continuity with great distinctne . I do not mean continuity of existence merely; I mean continuity of causation: the unceasing production of effect the never-ending work of every force. H. Spencer , Study of Sociol., p. 322. The motion of a material particle which has continuous existence in time and space is the type and exemplar of every form of continuity . Clerk Maxwell , Matter and Motion, Art. xxv. 3. In zoöl. and an at., that part of a thing which lies between the two ends, as the shaft of a long bone, or its diaphysis, as distinguished from its condyles or epiphyses, or the middle portion of the bill of a bird, as distinguished from the base and apex. [Chiefly an anatomical term, and especially a surgical one: as, the fracture of a bone in its continuity.)- Continuity of forms, in the Kantian philos., the doctrine that if A and Bare two concepts such that A includes the whole content of B and more, there will always be a third con cept C, such that A includes the whole content of C and progre ion. Continued voyage, or continuous voy--Equation of continuity, in hydrodynamics, the equa age, a voyage prosecuted to completion. In the law of prizes, a voyage of a ve el carrying contraband of war, or carrying goods intended for a blockaded port, although in fact ended by stopping short of the unlawful destination and making a transhipment in order to evade the law, is treated by some courts as if continued, thus bringing upon the ve el and cargo the same liability as if it had continued the voyage and effected the unlawful purpose. continuedly (kon-tin'ud-li), adv. Without interruption; without ceasing. By perseverance, I do not understand a continuedly uniform, equal course of obedience, and such as is not inter rupted with the least act of sin. Norris. IMG:content-1178.png:[blocks in formation] 2. One who carries forward anything that had been begun, or takes up a course that had been pursued, by another or others; a continuator: as, the continuer of a history. Mr. Winthrop is a distinguished continuer of the mem orable line of occasional orators in which Ma achusetts has been. so fruitful. New York Evening Post , Oct. 30, 1886. continuing (kon-tin'u-ing), p . a . [Ppr. of continue, v.] Remaining fixed or permanent; abiding; lasting; enduring; persevering. Here have we no continuing city. Continuing guaranty. See guaranty . Heb. xiii. 14. more, while C includes the whole content of B and more. tion which expre es that any change in the quantity of fluid within any closed surface is, in the absence of sources or sinks within the surface, due to the flow of fluid through the surface. In its differential form the equation is IMG:content-1179.png:[blocks in formation] where t is the time, p the density, x, y, z the rectangular coördinates, and u, v, w the corresponding components of the velocity. - Law of continuity, the doctrine that continuous changes in conditions will be accompanied by continuous changes in the results. This law was first set forth by Leibnitz in 1687, and employed to show that the properties of the parabola may be deduced from those of the ellipse, the laws of rest from those of motion, etc. Later he declared it applicable to such questions as whether there is an uninterrupted series of species from the highest to the lowest. The doctrine has often been understood as implying that there are no abrupt variations in nature. From the knowledge of the complete state at any instant of a thing whose motion obeys the law of continuity , we can calculate where it was at any past time, and where it will be at any future time. W. K. Clifford, Lectures, I. 122. Solution of continuity, rupture; separation of parts intimately connected. = Syn. Continuance , etc. See con tinuation .