Page:EB1911 - Volume 18.djvu/670

 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 prime importance of description in the most general terms of the various spheres of phenomena, and holds that in each 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, electricity, &c.—by mechanical conceptions, this theory regards as mere ephemeral aids to perception, which are necessitated by 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 energetics (in the narrower sense), which looks upon the conception of energy, not that of matter, as the fundamental notion of all scientific investigation. It is in the main based on the similarities energy displays in its various spheres of action, but at the same time it takes its stand upon an interpretation or explanation of natural phenomena by analogies which, however, are not mechanical, but 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 present on a small scale a machine that is subsequently to be completed on a larger, so as to afford a trial of 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 weight varies as the cube of the linear dimensions, the surface of any single part and the phenomena that depend on such surfaces are proportionate to the square, while other effects—such as friction, expansion and 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 Isaac Newton, of the dependence of various effects on the linear dimensions, is treated in the article. 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 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 Washington Patent Office. Sometimes, again, other than purely mechanical forces are at work in models for purposes of investigation and instruction. It often happens that a 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 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 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 speed and accuracy, or apparatus for solving the higher equations, for determining the volume or area of geometrical figures, for carrying out integrations, and for developing a function in a Fourier’s series by mechanical means.

MODELS, ARTISTS’, the name given to persons who pose to artists as models for their work. The Greeks, who had the naked body constantly before them in the exercises of the gymnasium, had far less need of professional models than the moderns; but it is scarcely likely that they could have attained to the high level reached by their works without constant study from nature; and the story told of Zeuxis by Valerius Maximus, who had five of the most beautiful virgins of the city of Crotona offered him as models for his picture of Helen, proves their occasional use. The remark of Eupompus, quoted by Pliny, who advised Lysippus, “Let nature be your model, not an artist,” directing his attention to the crowd instead of to his own work, also suggests a use of models which the many portrait statues of Greek and Roman times show to have been not unknown. In Egypt, too, although the priesthood had control of both sculpture and painting as used for the decoration of temples and palaces, and imposed a strict conventionalism, there are several statues of the early periods which are so lifelike in their treatment as to make it certain that they must have been worked from life. At the period of the Renaissance, painters generally made use of their relations and friends as models, of which many examples might be quoted from Venice, Florence, Rome and other places, and the stories of Titian and the duchess of Ferrara, and Botticelli and Simonetta Vespucci, go to show that ladies of exalted rank were sometimes not averse from having their charms immortalized by the painter’s brush. But paid models were not unknown, as the story of the unfortunate contadino used by Sansovino as model for his statue of the little Bacchus will show. Artists’ models as a special class appear when the establishment of schools for the study of the human figure created a regular demand, and since that time the remuneration offered has ensured a continual supply. The prices and the hours of Work vary in different art centres. In England seven shillings is generally paid for a day of six hours, but models of exceptional beauty or talent frequently obtain more from successful artists or wealthy amateurs.

 MODEL-YACHTING, the pastime of building and racing model-yachts. It has always been customary for ship-builders to make a miniature model of the vessel under construction, which is in every respect a copy of the original on a small scale, whether steam-ship or sailing-vessel (there is a fine collection in the Victoria and Albert Museum, London). Many of these models are of exquisite workmanship, every rope, pulley or portion of the engine being faithfully reproduced. In the case of sailing yachts these models were often pitted against each other on small bodies of water, and hence arose the modern pastime. It was soon seen that elaborate fittings and complicated rigging were a detriment to rapid handling, and that, on account of the comparatively stronger winds in which models were sailed, they needed a greater draught. For these reasons modern model yachts, which usually have fin-keels, are of about 15% or 20% deeper draught than full-sized vessels, while rigging and fittings have been reduced to absolute simplicity. This applies to models built for racing and not to elaborate copies of steamers and ships, made only for show or for “toy cruising.”

Model-yacht clubs have existed for many years in Great Britain, Ireland and the United States, most of them holding a number of regattas during each season. The rules do not generally require the owner or skipper of a model to build his own craft, but among model-yachtsmen the designing and the construction of the boats constitute as important and interesting 