chord, the Sages of Thebes, and the Gates of Thebes, but it does not extend beyond the fact that they were all seven in number. Between the most discrete notions, as, for instance, those of time and space, analogy may exist, arising from the fact that the mathematical conditions of the lapse of time and of motion along a line are similar. There is no identity of nature between a word and the thing it signifies; the substance iron is a heavy solid, the word iron is either a momentary disturbance of the air, or a film of black pigment on white paper; but there is analogy between words and their significates. The substance iron is to the substance iron-carbonate, as the name iron is to the name iron-carbonate, when these names are used according to their correct scientific definitions. The whole structure of language and the whole utility of signs, marks, symbols, pictures, and representations of various kinds, rest upon analogy. I may, perhaps, hope to enter fully upon this important subject at some future que, and to attempt to show how the invention of signs ables us to express, guide, and register our thoughts. w" be sufficient to observe here that the use of words sently involves analogies of a subtle kind; we should be at a loss how to describe a notion, were we not y to employ in a metaphorical sense the name of suficiently resembling it. There would be no or the sweetness of a melody, or the brilliance ge, unless it were furnished by the taste of e brightness of a torch.

y examination of the cases in which we e word analogy, shows that it includes all Mance or similarity. The analogy may

arity of number or ratio; or in like Peace. It may also consist in more etween physical properties. We the word inconsistently with custom,

if we said that there was an analogy between iron, nickel, and cobalt, manifested in the strength of their magnetic powers. There is a still more perfect analogy between iodine and chlorine; not that every property of iodine is identical with the corresponding property of chlorine; for then they would be one and the same kind of substance, and not two substances; but every property of iodine resembles in all but degree some property of chlorine. For almost every substance in which iodine forms a component, a corresponding substance may be discovered containing chlorine, so that we may confidently infer from the compounds of the one to the compounds of the other substance. Potassium iodide crystallizes in cubes; therefore it is to be expected that potassium chloride will also crystallize in cubes. The science of chemistry, as now developed, rests almost entirely upon a careful and most extensive comparison of the properties of substances, bringing to light deep-lying analogies. When any apparently exceptional or new substance is encountered, the chemist is guided in his treatment of it entirely by the analogies which it seems to present with previously known substances.

In this chapter I cannot hope to illustrate the allpervading influence of analogy in human thought and science. All science, it has been said, at the outset, arises from the discovery of identity, and analogy is but one name by which we denote the deeper-lying cases of resemblance. I shall only try to point out at present how analogy between apparently diverse classes of phenomena often serves as an all-important guide in discovery. We thus commonly gain the first insight into the nature of an apparently unique object, and we thus, in the progress of a science, often discover that we are treating over again, in a new form, phenomena which were well known to us in another form.

Analogy as a Guide in Discovery.

There can be no doubt that discovery is most frequently accomplished by following up hints received from analogy, as Jeremy Bentham remarked. Whenever a phenomenon is perceived, the first impulse of the mind is to connect it with the most nearly similar phenomenon. If we could ever meet a thing wholly sui generis, presenting no analogy to anything else, we should be incapable of investigating its nature, except by purely haphazard trial. The probability of success by such a process is so slight, that it is preferable to follow up the slightest clue. As I have pointed out already (vol. ii. p. 24), the possible modifications of condition in experiments are usually infinite in number, and infinitely numerous also are the hypotheses upon which we may proceed. Now it is selfevident that, however slightly superior the probability of success by one course of procedure may be over another, the most probable one should always be adopted first.

The chemist having discovered what he believes to be a new element, will have an infinite variety of modes of wing and investigating it. If in any one of its qualities De stance displays a resemblance to an alkaline metal, cance, he will naturally proceed to try whether it ssss other properties common to the alkaline metals. ea de apparently simplest phenomenon presents so y for notice that we have a choice at each Pamong many hypotheses.

cult to find a more instructive instance which the mind is guided by analogy than ps by Sir John Herschel of the course of we was led to anticipate in theory one experimental discoveries. Sir John

Works,' vol. viii. p. 276.

Herschel noticed that in three physical phenomena, a screw-like form, technically called helicoidal dissymmetry, was presented, namely in electrical helices, plagihedral quartz crystals, and the rotation of the plane of polarization of light. As he himself has said b, I reasoned thus: Here are three phenomena agreeing in a very strange peculiarity. Probably, this peculiarity is a connecting link, physically speaking, among them. Now, in the case of the crystals and the light, this probability has been turned into certainty by my own experiments. Therefore, induction led me to conclude that a similar connexion exists, and must turn up, somehow or other, between the electric current and polarized light, and that the plane of polarization would be deflected by magneto-electricity.' By this course of analogical thought Sir John Herschel had actually been led to anticipate Faraday's great discovery of the influence of magnetic strain upon polarized light. He had tried as long ago as 1822-25 to discover the influence of electricity on light, by sending a ray of polarized light through a helix, or near a long wire conveying an electric current. Such a course of inquiry, followed up with the persistency of Faraday, and with his experimental resources, would doubtless have effected the strange discovery. Herschel also suggests that the plagihedral form of quartz crystals must be due to a screw-like strain during the progress of crystallization; but the notion, although probable, remains unverified by experiment to the present day.

If ever men approach the investigation of the mechanism of thought, they must be guided by analogy. Already many philosophers have drawn analogies between nerve influence and the transmission of vibrations. Dr. Briggs, Newton in his 24th Query, and Hartley, have vaguely speculated concerning such vibrations, and some b Life of Faraday,' by Bence Jones, vol. ii. p. 206.

countenance is now given to the notion by the somewhat similar rate of propagation of nerve pulses and soundwaves in soft bodies. But the phenomena of memory are far more difficult to reduce to any material mechanism, and I know of no material analogy but the interesting one suggested by Hooke, who likens memory to those bells or vases which Vitruvius mentions to be placed in the ancient theatre, which did receive and return the sound more vigorous and strong; or like the unisontoned strings, bells, or glasses, which receive impressions from sounds without, and retain the impressions for some time, answering the tone by the same tone of their own.'

Analogy in the Mathematical Sciences.

Whoever wishes to acquire a deep acquaintance with the constitution of Nature must observe that there are deep analogies which connect whole branches of science in a parallel manner, and enable us to infer of one class of phenomena what we know of the other. It has thus happened on several occasions that the discovery of * unsuspected analogy between two hitherto distinct branches of knowledge has been the starting-point for a rapid course of discovery. The truths readily observed in the one may be of a different character from those which present themselves in the other. The analogy, when once pointed out, leads us easily to discover regions of one science yet undeveloped, but to which the key is furnished by the corresponding truths in the other science. An interchange of aid most wonderful in its results may thus take place, and at the same time the wind rises to a higher generalization, and a more comprehensive view of mind and nature.

ePosthumous Works,' p. 141.