Collective Experiments. There is an interesting class of experiments which enable us to observe a number of quantitative results in one act. Generally speaking, each experiment yields us but one number, and before we can approach the real processes of reasoning we must laboriously repeat measurement after measurement, until we can lay out a curve of the variation of one quantity as depending on another. We can sometimes abbreviate this labour, by making a quantity vary in different parts of the same apparatus through every required amount. In observing the height to which water rises by the capillary attraction of a glass vessel, we may take a series of glass tubes of different bore, and measure the height through which it rises in each. But if we take two glass plates, and place them vertically in water, so as to be in contact at one vertical side, and slightly separated at the other side, the interval between the plates varies through every intermediate width, and the water rises to a corresponding height, producing at its upper surface a hyperbolic curve. The absorption of light in passing through a coloured liquid may be beautifully shown by enclosing the liquid in a wedge-shaped glass, so that we have at a single glance an infinite variety of thicknesses in view. As Newton himself remarked, a red liquid viewed in this manner is found to have a pale yellow colour at the thinnest part, and it passes through orange into red, which gradually becomes of a deeper and darker tint. The effect may be noticed in a conical wine-glass. The prismatic analysis of light from such a wedge-shaped vessel discloses the reason, by exhibiting the progressive absorption of different rays of the spectrum as investigated by Dr. J. H. Gladstone.2 A moving body inay sometimes be made to mark out. its own course, like a shooting star which leaves a tail behind it. Thus an inclined jet of water exhibits in the clearest manner the parabolic path of a projectile. In Wheatstone's Kaleidophone the curves produced by the combination of vibrations of different ratios are shown by 1 Opticks, 3rd edit. p. 159. 2 Watts, Dictionary of Chemistry, vol. iii. p. 637. placing bright reflective buttons on the tops of wires of various forms. The motions are performed so quickly that the eye receives the impression of the path as a complete whole, just as a burning stick whirled round produces a continuous circle. The laws of electric induction are beautifully shown when iron filings are brought under the influence of a magnet, and fall into curves corresponding to what Faraday called the Lines of Magnetic Force. When Faraday tried to define what he meant by his lines of force, he was obliged to refer to the filings. "By magnetic curves," he says,1 "I mean lines of magnetic forces which would be depicted by iron filings." Robison had previously produced similar curves by the action of frictional electricity, and from a mathematical investigation of the forms of such curves we may infer that magnetic and electric attractions obey the general law of emanation, that of the inverse square of the distance. In the electric brush we have a similar exhibition of the laws of electric attraction. There are several branches of science in which collective experiments have been used with great advantage. Lichtenberg's electric figures, produced by scattering electrified powder on an electrified resin cake, so as to show the condition of the latter, suggested to Chladni the notion of discovering the state of vibration of plates by strewing sand upon them. The sand collects at the points where the motion is least, and we gain at a glance a comprehension of the undulations of the plate. To this method of experiment we owe the beautiful observations of Savart. The exquisite coloured figures exhibited by plates of crystal, when examined by polarised light, afford a more complicated example of the same kind of investigation. They led Brewster and Fresnel to an explanation of the properties of the optic axes of crystals. The unequal conduction of heat in crystalline substances has also been shown in a similar manner, by spreading a thin layer of wax over the plate of crystal, and applying heat to a single point. The wax then melts in a circular or elliptic area according as the rate of conduction is uniform or not. Nor should we forget that Newton's rings were an early and most impor 1 Faraday's Life, by Bence Jones, vol. ii. p. 5. tant instance of investigations of the same kind, showing the effects of interference of light undulations of all magnitudes at a single view. Herschel gave to all such opportunities of observing directly the results of a general law, the name of Collective Instances, and I propose to adopt the name Collective Experiments. 1 Such experiments will in many subjects only give the first hint of the nature of the law in question, but will not admit of any exact measurements. The parabolic form of a jet of water may well have suggested to Galileo his views concerning the path of a projectile; but it would not serve now for the exact investigation of the laws of gravity. It is unlikely that capillary attraction could be exactly measured by the use of inclined plates of glass, and tubes would probably be better for precise investigation. As a general rule, these collective experiments would be most useful for popular illustration. But when the curves are of a precise and permanent character, as in the coloured figures produced by crystalline plates, they may admit of exact measurement. Newton's rings and diffraction fringes allow of very accurate measurements. Under collective experiments we may perhaps place those in which we render visible the motions of gas or liquid by diffusing some opaque substance in it. The behaviour of a body of air may often be studied in a beautiful way by the use of smoke, as in the production of smoke rings and jets. In the case of liquids lycopodium powder is sometimes employed. To detect the mixture of currents or strata of liquid, I employed very dilute solutions of common salt and silver nitrate, which produce a visible cloud wherever they come into contact.2 Atmospheric clouds often reveal to us the movements of great volumes of air which would otherwise be quite unapparent. Periodic Variations. A large class of investigations is concerned with Periodic Variations. We may define a periodic phenomenon as one which, with the uniform change of the variable, returns 1 Preliminary Discourse, &c., p. 185. 2 Philosophical Magazine, July, 1857, 4th Series, vol. xiv. p. 24. time after time to the same value. If we strike a pendulum it presently returns to the point from which we disturbed it, and while time, the variable, progresses uniformly, it goes on making excursions and returning, until stopped by the dissipation of its energy. If one body in space approaches by gravity towards another, they will revolve round each other in elliptic orbits, and return for an indefinite number of times to the same relative positions. On the other hand a single body projected into empty space, free from the action of any extraneous force, would go on moving for ever in a straight line, according to the first law of motion. In the latter case the variation is called secular, because it proceeds during ages in a similar manner, and suffers no Tepíodos or going round. It may be doubted whether there really is any motion in the universe which is not periodic. Mr. Herbert Spencer long since adopted the doctrine that all motion is ultimately rhythmical, and abundance of evidence may be adduced in favour of his view. The so-called secular acceleration of the moon's motion is certainly periodic, and as, so far as we can tell, no body is beyond the attractive power of other bodies, rectilinear motion becomes purely hypothetical, or at least infinitely improbable. All the motions of all the stars must tend to become periodic. Though certain disturbances in the planetary system seem to be uniformly progressive, Laplace is considered to have proved that they really have their limits, so that after an immense time, all the planetary bodies might return to the same places, and the stability of the system be established. Such a theory of periodic stability is really hypothetical, and does not take into account phenomena resulting in the dissipation of energy, which may be a really secular process. For our present purposes we need not attempt to form an opinion on such questions. Any change which does not present the appearance of a periodic character will be empirically regarded as a secular change, so that there will be plenty of non-periodic variations. The variations which we produce experimentally will often be non-periodic. When we communicate heat to a 1 First Principles, 3rd edit. chap. x. p. 253. gas it increases in bulk or pressure, and as far as we can go the higher the temperature the higher the pressure. Our experiments are of course restricted in temperature both above and below, but there is every reason to believe that the bulk being the same, the pressure would never return to the same point at any two different temperatures. We may of course repeatedly raise and lower the temperature at regular or irregular intervals entirely at our will, and the pressure of the gas will vary in like manner and exactly at the same intervals, but such an arbitrary series. of changes would not constitute Periodic Variation. It would constitute a succession of distinct experiments, which would place beyond reasonable doubt the connexion of cause and effect. Whenever a phenomenon recurs at equal or nearly equal intervals, there is, according to the theory of probability, considerable evidence of connexion, because if the recurrences were entirely casual it is unlikely that they would happen at equal intervals. The fact that a brilliant. comet had appeared in the years 1301, 1378, 1456, 1531, 1607, and 1682 gave considerable presumption in favour of the identity of the body, apart from similarity of the orbit. There is nothing which so fascinates the attention of men as the recurrence time after time of some unusual event. Things and appearances which remain ever the same, like mountains and valleys, fail to excite the curiosity of a primitive people. It has been remarked by Laplace that even in his day the rising of Venus in its brightest phase never failed to excite surprise and interest. So there is little doubt that the first germ of science arose in the attention given by Eastern people to the changes of the moon and the motions of the planets. Perhaps the earliest astronomical discovery consisted in proving the identity of the morning and evening stars, on the grounds of their similarity of aspect and invariable alternation.1 Periodical changes of a somewhat complicated kind must have been understood by the Chaldeans, because they were aware of the cycle of 6585 days or 19 years which brings round the new and full moon upon the same days, hours, and even minutes of the year. The earliest efforts of Laplace, System of the World, vol. i. pp. 50, 54, &c. G G |