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be said of the colours exhibited by thin plates and films. The rings and lines of colour will be nearly the same in character whatever may be the nature of the substance; nay, a void space, such as a crack in glass, would produce them even though the air were withdrawn by an air-pump. The conditions are simply the existence of two reflecting surfaces separated by a very small space, though it should be added that the refractive index of the intervening substance has some influence on the exact nature of the colour produced.

When a ray of light passes close to the edge of an opaque body, a portion of the light appears to be bent towards it, and produces coloured fringes within the shadow of the body. Newton attributed this inflexion of light to the attraction of the opaque body for the supposed particles of light, although he was aware that the nature of the surrounding medium, whether air or other pellucid substance, exercised no apparent influence on the phenomena. Gravesande proved, however, that the character of the fringes is exactly the same, whether the body be dense or rare, compound or elementary. A wire produces exactly the same fringes as a hair of the same thickness. Even the form of the obstructing edge was subsequently shown to be a matter of indifference by Fresnel, and the interference spectrum, or the spectrum seen when light passes through a fine grating, is absolutely the same whatever be the form or chemical nature of the bars making the grating. Thus it appears that the stoppage of a portion of a beam of light is the sole necessary condition for the diffraction or inflexion of light, and the phenomenon is shown to bear no analogy to the refraction of light, in which the form and nature of the substance are all impor

tant.

It is interesting to observe how carefully Newton, in his researches on the spectrum, ascertained the indifference of many circumstances by actual trial. He says:1 "Now the different magnitude of the hole in the window-shut, and different thickness of the prism where the rays passed through it, and different inclinations of the prism to the horizon, made no sensible changes in the length of the

1 Opticks, 3rd. ed. p. 25.

image. Neither did the different matter of the prisms make any for in a vessel made of polished plates of glass cemented together in the shape of a prism, and filled with water, there is the like success of the experiment according to the quantity of the refraction." But in the latter statement, as I shall afterwards remark (p. 432), Newton assumed an indifference which does not exist, and fell into an unfortunate mistake.

In the science of sound it is shown that the pitch of a sound depends solely upon the number of impulses in a second, and the material exciting those impulses is a matter of indifference. Whatever fluid, air or water, gas or liquid, be forced into the Siren, the sound produced is the same; and the material of which an organ-pipe is constructed does not at all affect the pitch of its sound. In the science of statical electricity it is an important principle that the nature of the interior of a conducting body is a matter of no importance. The electrical charge is confined to the conducting surface, and the interior remains in a neutral state. A hollow copper sphere takes exactly the same charge as a solid sphere of the same metal.

Some of Faraday's most elegant and successful researches were devoted to the exclusion of conditions which previous experimenters had thought essential for the production of electrical phenomena. Davy asserted that no known fluids, except such as contain water, could be made the medium of connexion between the poles of a battery; and some chemists believed that water was an essential agent in electro-chemical decomposition. Faraday gave abundant experiments to show that other fluids allowed of electrolysis, and he attributed the erroneous opinion to the very general use of water as a solvent, and its presence in most natural bodies.' It was, in fact, upon the weakest kind of negative evidence that the opinion had been founded.

Many experimenters attributed peculiar powers to the poles of a battery, likening them to magnets, which, by their attractive powers, tear apart the elements of a substance. By a beautiful series of experiments, Faraday proved conclusively that, on the contrary, the substance of

1 Experimental Researches in Electricity, vol. i. pp. 133, 134.
2 Ibid. vol. i. pp. 127, 162, &c.

the poles is of no importance, being merely the path through which the electric force reaches the liquid acted upon. Poles of water, charcoal, and many diverse substances, even air itself, produced similar results; if the chemical nature of the pole entered at all into the question, it was as a disturbing agent.

It is an essential part of the theory of gravitation that the proximity of other attracting particles is without effect upon the attraction existing between any two molecules. Two pound weights weigh as much together as they do separately. Every pair of molecules in the world have, as it were, a private communication, apart from their relations to all other molecules. Another undoubted result of experience pointed out by Newton is that the weight of a body does not in the least depend upon its form or texture. It may be added that the temperature, electric condition, pressure, state of motion, chemical qualities, and all other circumstances concerning matter, except its mass, are indifferent as regards its gravitating power.

As natural science progresses, physicists gain a kind of insight and tact in judging what qualities of a substance are likely to be concerned in any class of phenomena. The physical astronomer treats matter in one point of view, the chemist in another, and the students of physical optics, sound, mechanics, electricity, &c., make a fair division of the qualities among them. But errors will arise if too much confidence be placed in this independence of various kinds of phenomena, so that it is desirable from time to time, especially when any unexplained discrepancies come into notice, to question the indifference which is assumed to exist, and to test its real existence by appropriate experiments.

Simplification of Experiments.

One of the most requisite precautions in experimentation is to vary only one circumstance at a time, and to maintain all other circumstances rigidly unchanged. There are two distinct reasons for this rule, the first and most obvious being that if we vary two conditions at a time, and

1 Principia, bk. iii. Prop. vi. Corollary i.

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find some effect, we cannot tell whether the effect is due to one or the other condition, or to both jointly. A second reason is that if no effect ensues we cannot safely conclude that either of them is indifferent; for the one may have neutralised the effect of the other. In our symbolic logic AB Ab was shown to be identical with A (p. 97), so that B denotes a circumstance which is indifferently present or absent. But if B always go together with another antecedent C, we cannot show the same independence, for ABC Abe is not identical with A and none of our logical processes enables us to reduce it to A.

If we want to prove that oxygen is necessary to life, we must not put a rabbit into a vessel from which the oxygen has been exhausted by a burning candle. We should then have not only an absence of oxygen, but an addition of carbonic acid, which may have been the destructive agent. For a similar reason Lavoisier avoided the use of atmospheric air in experiments on combustion, because air was not a simple substance, and the presence of nitrogen might impede or even alter the effect of oxygen. As Lavoisier remarks,1 "In performing experiments, it is a necessary principle, which ought never to be deviated from, that they be simplified as much as possible, and that every circumstance capable of rendering their results complicated be carefully removed." It has also been well said by Cuvier that the method of physical inquiry consists in isolating bodies, reducing them to their utmost simplicity, and bringing each of their properties separately into action, either mentally or by experiment.

2

The electro-magnet has been of the utmost service in the investigation of the magnetic properties of matter, by allowing of the production or removal of a most powerful magnetic force without disturbing any of the other arrangements of the experiment. Many of Faraday's most valuable experiments would have been impossible had it been necessary to introduce a heavy permanent magnet, which could not be suddenly moved without shaking the whole apparatus, disturbing the air, producing currents by changes of temperature, &c. The electro-magnet is

1 Lavoisier's Chemistry, translated by Kerr, p. 103.
Cuvier's Animal Kingdom, introduction, pp 1, 2.

perfectly under control, and its influence can be brought into action, reversed, or stopped by merely touching a button. Thus Faraday was enabled to prove the rotation of the plane of circularly polarised light by the fact that certain light ceased to be visible when the electric current of the magnet was cut off, and re-appeared when the current was made. "These phenomena," he says, "could be reversed at pleasure, and at any instant of time, and upon any occasion, showing a perfect dependence of cause and effect." 1

It was Newton's omission to obtain the solar spectrum under the simplest conditions which prevented him from discovering the dark lines. Using a broad beam of light which had passed through a round hole or a triangular slit, he obtained a brilliant spectrum, but one in which many different coloured rays overlapped each other. In the recent history of the science of the spectrum, one main difficulty has consisted in the mixture of the lines of several different substances, which are usually to be found in the light of any flame or spark. It is seldom possible to obtain the light of any element in a perfectly simple manner. Angström greatly advanced this branch of science by examining the light of the electric spark when formed between poles of various metals, and in the presence of various gases. By varying the pole alone, or the gaseous medium alone, he was able to discriminate correctly between the lines due to the metal and those due to the surrounding gas.2

Failure in the Simplification of Experiments.

In some cases it seems to be impossible to carry out the rule of varying one circumstance at a time. When we attempt to obtain two instances or two forms of experi ment in which a single circumstance shall be present in one case and absent in another, it may be found that this single circumstance entails others. Benjamin Franklin's experiment concerning the comparative absorbing powers of different colours is well known. "I took," he says, "a

1 Experimental Researches in Electricity, vol. iii. p. 4.
2 Philosophical Magazine, 4th Series, vol. ix. p. 327.

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