Online Encyclopedia
Search over 40,000 articles from the original, classic Encyclopedia Britannica, 11th Edition.
MODEL (0. Fr. modelle, mod. modele; I...
Online EncyclopediaEncyclopedia Home :: MIC-MOL
del.icio.us it!
|
See also:MODEL (0. Fr. modelle, mod. modele; It. modello, See also:pattern, See also:mould; from See also:Lat. modus, measure, See also:standard)
, a tangible See also:representation, whether the See also:size be equal, or greater, or smaller, of an See also:object which is either in actual existence, or has to be constructed in fact or in thought
.
More generally it denotes a thing, whether actually existing or only mentally conceived of, whose properties are to be copied
.
In foundries, the object of which a See also:cast is to be taken, whether it be for See also:engineering or See also:artistic purposes, is usually first formed of some easily workable material, generally See also:wood
.
The See also:form of this See also:model is then reproduced in See also:clay or See also:plaster, and into the See also:mould thus obtained the molten See also:metal is poured
.
The sculptor first makes a model of the object he wishes to See also:chisel in some plastic material such as See also:wax, ingenious and complicated contrivances being employed to See also:transfer this wax model, true to nature, to the See also: See also:Maxwell, H. v . See also:Helmholtz, E . See also:Mach, H . See also:Hertz and many others into intimate relation with the whole See also:body of mathematical and physical theory . On this view our thoughts stand to things in the same relation as models to the objects they represent . The essence of the process is the See also:attachment of one concept having a definite content to each thing, but without implying See also:complete similarity between thing and thought; for naturally we can know but little of the resemblance of our thoughts to the things to which we attach them . What resemblance there is lies principally in the nature of the connexion, the correlation being analogous to that which obtains between thought and See also:language, language and See also:writing, the notes on the stave and musical sounds, &c . Here, of course, the symbolization of the thing is the important point, though, where feasible, the utmost possible See also:correspondence is sought between the two—the musical scale, for example, being imitated by placing the notes higher or See also:lower . When, therefore, we endeavour to assist our conceptions of space by figures, by the methods of descriptive See also:geometry, and by various See also:thread and object models; our See also:topography by plans, charts and globes; and our mechanical and physical ideas by kinematic models—we are simply extending and continuing the principle by means of which we comprehend objects in thought and represent them in language or writing . In precisely the same way the micro-See also:scope or See also:telescope forms a continuation and multiplication of the lenses of the See also:eye; and the notebook represents an See also:external expansion of the same process which the memory brings about by purely internal means . There is also an obvious See also:parallelism with representation by means of models when we See also:express See also:longitude, mileage, temperature, &c., by See also:numbers, which should be looked upon as arithmetical analogies . Of a kindred See also:character is the representation of distances by straight lines, of the course of events in See also:time by curves, &c . Still, neither in this See also:case nor in that of maps, charts, musical notes, figures, &c., can we legitimately speak of models, for these always involve a See also:concrete spatial See also:analogy in three dimensions . So long as the See also:volume of See also:matter to be dealt with in See also:science was insignificant, the need for the employment of models was naturally less imperative; indeed, there are self-evident advantages in comprehending things without resort to complicated models, which are difficult to make, and cannot be altered and adapted to extremely varied conditions so readily as can the easily adjusted symbols of thought, conception and calculation . Yet as the facts of science increased in number, the greatest See also:economy of effort had to be observed in comprehending them and in conveying them to others; and the See also:firm See also:establishment of ocular demonstration was inevitable in view of its enormous superiority over purely abstract symbolism for the rapid and complete See also:exhibition of complicated relations . At the See also:present time it is desirable, on the one See also:hand, that the See also:power of deducing results from purely abstract premisses, without recourse to the aid of tangible models, should be more and more perfected, and on the other that purely abstract conceptions should be helped by See also:objective and comprehensive models in cases where the See also:mass of matter cannot be adequately dealt with directly . In pure See also:mathematics, especially geometry, models constructed of See also:papier-mache and plaster are chiefly employed to present to the senses the precise form of geometrical figures, surfaces and curves . Surfaces of the second See also:order, repre- Models in sented by equations of the second degree between Mathematics the rectangular co-ordinates of a point, are very and Physics. See also:simple to classify, and accordingly all their possible forms can easily be shown by a few models, which, however, become somewhat more intricate when lines of curvature, loxodromics and geodesic lines have to appear on their surfaces . On the other hand, the multiplicity of surfaces of the third order is enormous, and to convey their fundamental types it is necessary to employ numerous models of complicated, not to say hazardous, construction . In the case of more intricate surfaces it is sufficient to present those singularities which exhibit variation from the usual type of See also:surface with synclastic or anticlastic curvatures, such as, for example, a See also:sharp edge or point, or an intersection of the surface with itself; the elucidation of such singularities is of fundamental importance in See also:modern mathematics . In physical science, again, models that are of unchangeable form are largely employed . For example, the operation of the See also:refraction of See also:light in crystals can be pictured if we imagine a point in the centre of the crystal whence light is dispersed in all directions . The aggregate of the places at which the light arrives at any instant after it has started is called the See also:wave-front . This surface consists of two cups or sheets fitting closely and exactly one inside the other .
The two rays into which a single See also:ray is broken are always determined by the points of contact of certain tangent-planes See also:drawn to those sheets
.
With crystals possessing two axes these wave-surfaces display See also:peculiar singularities in the above sense of the See also:term, in that the inner See also:sheet has four protuberances, while the See also:outer has four See also:funnel-like depressions, the lowest point of each depression See also:meeting the highest point of each protuberance
.
At each of these funnels there is a tangent-See also:plane that touches not in a single point, but in a circle bounding the depression, so that the corresponding ray of light is refracted, not into two rays, but into a whole See also:cone of light —the so-called conical refraction theoretically predicted by See also:Sir W
.
R
.
See also: 
These include the thread models, in which threads are drawn tightly between movable bars, cords, wheels, rollers, &c . In See also:mechanics and engineering an endless variety of working models are employed to convey to the eye the working either of See also:machines as a whole, or of their component and subordinate parts . In theoretical mechanics models are often used to exhibit the physical See also:laws of motion in interesting or special cases—e.g. the motion of a falling body or of a See also:spinning-See also:top, the See also:movement of a pendulum on the rotating See also:earth, the vortical motions of fluids, &c . Akin to these are the models which execute more or less exactly the hypothetical motions by which it is sought to explain various physical phenomena—as, for instance, the complicated wave-machines which present the motion of the particles in waves of See also:sound (now ascertained with See also:fair accuracy), or the more hypothetical motion of the atoms of the See also:aether in waves of light . The varying importance which in recent times has been attached to models of this See also:kind is intimately connected with Theories of the changes which have taken See also:place in our See also:con-Naturie. ceptions of nature . The first method by which an See also:attempt was made to solve the problem of the universe was entirely under the See also:influence of See also:Newton's laws . In analogy to his laws of universal See also:gravitation, all bodies were conceived of as consisting of points of matter—atoms or molecules—to which was attributed a See also:direct See also:action at a distance . The circumstances of this action at a distance, however, were conceived as differing from those of the Newtonian See also:law of attrac-tion, in that they could explain the properties not only of solid elastic bodies, but also those of fluids, both liquids and gases . The phenomena of heat were explained by the motion of minute particles absolutely invisible to the eye, while to explain those of light it was assumed that an impalpable See also:medium, called luminiferous aether, permeated the whole universe; to this were attributed the same properties as were possessed by solid bodies, and it was also supposed to consist of atoms, although of a much finer See also:composition . To explain electric and magnetic phenomena the See also:assumption was made of a third See also:species of matter—electric fluids which were conceived of as being more of the nature of fluids, but still consisting of infinitesimal particles, also acting directly upon one another at a distance . This first phase of theoretical physics may be called the direct one, in that it took as its See also:principal object the investigation of the internal structure of matter as it actually exists . It is also known as the mechanical theory of nature, in that it seeks to trace back all natural phenomena to motions of infinitesimal particles, i.e. to purely mechanical phenomena . In explaining magnetic and See also:electrical phenomena it inevitably See also:fell into somewhat artificial and improbable hypotheses, and this induced J . Clerk Maxwell, adopting the ideas of See also:Michael See also:Faraday, to propound a theory of electric and magnetic phenomena which was not only new in substance, but also essentially different in form . If the molecules and atoms of the old theory were not to be conceived of as exact mathematical points in the abstract sense, then their true nature and form must be regarded as absolutely unknown, and their groupings and motions, required by theory, looked upon as simply a process having more or less resemblance to the workings of nature, and representing more or less exactly certain aspects incidental to them . With this in mind, Maxwell propounded certain physical theories which were purely mechanical so far as they proceeded from a conception of purely mechanical processes . But he explicitly stated that he did not believe in the existence in nature of mechanical agents so constituted, and that he regarded them merely as means by which phenomena could be reproduced, bearing a certain similarity to those actually existing, and which also served to include larger See also:groups of phenomena in a See also:uniform manner and to determine the relations that held in their case . The question no longer being one of ascertaining the actual internal structure of matter, many mechanical analogies or dynamical illustrations became avail-able, possessing different advantages; and as a matter of fact Maxwell at first employed special and intricate mechanical arrangements, though later these became more See also:general and indefinite . This theory, which is called that of mechanical analogies, leads to the construction of numerous mechanical models . Maxwell himself and his followers devised many kinematic models, designed to afford a representation of the mechanical construction of the See also:ether as a whole as well as of the See also:separate mechanisms at work in it: these resemble the old wave-machines, so far as they represent the movements of a purely hypothetical mechanism . But while it was formerly believed that it was allowable to assume with a See also:great show of See also:probability the actual existence of such mechanisms in nature, yet nowadays philosophers postulate no more than a partial resemblance between the phenomena visible in such mechanisms and those which appear in nature . Here again it is perfectly clear that these models of wood, metal and cardboard are really a continuation and integration of our process of thought; for, according to the view in question, physical theory is merely a See also:mental construction of mechanical models, the working of which we make See also:plain to ourselves by the analogy of mechanisms we hold in our hands, and which have so much in See also:common with natural phenomena as to help our comprehension of the latter . Although Maxwell gave up the See also:idea of making a precise investigation into the final structure of matter as it actually is, yet in See also:Germany his work, under G . R . See also:Kirchhoff's See also:lead, was carried still further . Kirchhoff defined his own aim as being to describe, not to explain, the See also:world of phenomena; but as he leaves the means of description open his theory differs little from Maxwell's, so soon as recourse is had to description by means of mechanical models and analogies . Now the resources of pure mathematics being particularly suited for the exact description of relations of quantity, Kirchhoff's school laid great stress on description by mathematical expressions and formulae, and the aim of physical theory came to be regarded as mainly the construction of formulae by which phenomena in the various branches of physics should be determined with the greatest approximation to the reality . This view of the nature of physical theory is known as mathematical phenomenology; it is a presentation of phenomena by analogies, though only by such as may be called mathematical . Another phenomenology in the widest sense of the term, maintained especially by E . Mach, gives less prominence to mathematics, but considers the view that the phenomena of motion are essentially more fundamental than all the others to have been too hastily taken . It rather emphasizes the See also:prime importance of description in the most general terms of the various See also:spheres of phenomena, and holds that in each See also:sphere its own fundamental law and the notions derived from this must be employed . Analogies and elucidations of one sphere by another —e.g. heat, See also:electricity, &c.—by mechanical conceptions, this theory regards as See also:mere ephemeral aids to See also:perception, which are necessitated by See also:historical development, but which in course of time either give place to others or entirely vanish from the domain of science . All these theories are opposed by one called See also:energetics (in the narrower sense), which looks upon the conception of See also:energy, not that of matter, as the fundamental notion of all scientific investigation . It is in the See also:main based on the similarities energy displays in its various spheres of action, but at the same time it takes its stand upon an See also:interpretation or explanation of natural phenomena by analogies which, however, are not mechanical, but See also:deal with the behaviour of energy in its various modes of manifestation . A distinction must be observed between the models which have been described and those experimental models which pre- Baperi- sent on a small scale a See also:machine that is subsequently mental to be completed on a larger, so as to afford a trial of Models. its capabilities . Here it must be noted that a mere alteration in dimensions is often sufficient to cause a material alteration in the action, since the various capabilities depend in various ways on the linear dimensions . Thus the See also:weight varies as the See also:cube of the linear dimensions, the surface of any single See also:part and the phenomena that depend on such surfaces are proportionate to the square, while other effects—such as See also:friction, expansion and See also:conduction of heat, &c., vary according to other laws . Hence a flying-machine, which when made on a small scale is able to support its own weight, loses its power when its dimensions are increased . The theory, initiated by Sir See also:Isaac Newton, of the dependence of various effects on the linear dimensions, is treated in the See also:article See also:UNITS, DIMENSIONS OF . Under simple conditions it may often be affirmed that in comparison with a large machine a small one has the same capacity, with reference to a See also:standard of time which must be diminished in a certain ratio . Of course experimental models are not only those in which purely mechanical forces are employed, but also include models of thermal, electro-magnetic and other engines—e.g. dynamos and telegraphic machines . The largest collection of such models is to be found in the museum of the See also:Washington Patent See also:Office . Sometimes, again, other than purely mechanical forces are at work in models for purposes of investigation and instruction . It often happens that a See also:series of natural processes—such as motion in liquids, internal friction of gases, and the conduction of heat and electricity in metals—may be expressed by the same See also:differential equations; and it is frequently possible to follow by means of measurements one of the processes in question—e.g. the conduction of electricity just mentioned . If then there be shown in a model a particular case of electrical conduction in which the same conditions at the boundary hold as in a problem of the internal friction of gases, we are able by measuring the electrical conduction in the model to determine at once the MODEL-See also:YACHTING numerical data which obtain for the analogous case of internal friction, and which could only be ascertained otherwise by intricate calculations . Intricate calculations, moreover, can very often be dispensed with by the aid of mechanical devices, such as the ingenious calculating machines which perform additions and subtractions and very elaborate multiplications and divisions with surprising See also:speed and accuracy, or apparatus for solving the higher equations, for determining the volume or See also:area of geometrical figures, for carrying out integrations, and for developing a See also:function in a See also:Fourier's series by mechanical means . (L . |
|
|
[back] MOCK |
[next] MODELS |
Additional information and Comments
There are no comments yet for this article.
Highlight the code below, right click and select "copy." Paste it into a website, email, or other HTML document.
Do not copy, download, transfer, or otherwise replicate the site content in whole or in part.
Links to articles and home page are encouraged.
