All other predictions in optical science are, however, thrown into the shade by the theoretical discovery of conical refraction by the late Sir W. R. Hamilton, of Dublin. In investigating the passage of light through certain crystals, Hamilton found that Fresnel had slightly misinterpreted his own formulae, and that, when rightly understood, they indicated a phenomenon of a kind never witnessed. A small ray of light sent into a crystal of arragonite in a particular direction, becomes spread out into an infinite number of rays, which form a hollow cone within the crystal, and a hollow cylinder when emerging from the opposite side. In another case, a different, but equally strange, effect is produced, a ray of light being spread out into a hollow cone at the point where it quits the crystal. These phenomena are peculiarly interesting, because cones and cylinders of light are not produced in any other cases. They are opposed to all analogy, and constitute singular exceptions, of a kind which we shall afterwards consider more fully. Their strangeness rendered them peculiarly fitted to test the truth of the theory by which they were discovered; and when Professor Lloyd, at Hamilton's request, succeeded, after considerable difficulty, in witnessing the new appearances, no further doubt could remain of the validity of the wave theory which we owe to Huyghens, Young, and Fresnel.1

Predictions from the Theory of Undulations.

It is curious that the undulations of light, although inconceivably rapid and small, admit of more accurate measurement than waves of any other kind. But so far as we can carry out exact experiments on other kinds of waves, we find the phenomena of interference repeated, and analogy gives considerable power of prediction. Herschel was perhaps the first to suggest that two sounds might be made to destroy each other by interference. For if onehalf of a wave travelling through a tube could be sepa

1 Lloyd's Wave Theory, Part ii. pp. 52–58. Babbage, Ninth Bridgewater Treatise, p. 104, quoting Lloyd, Transactions of the Royal Irish Academy, vol. xvii. Clifton, Quarterly Journal of Pure and Applied Mathematics, January 1860.

2 Encyclopædia Metropolitana, art. Sound, p. 753.

rated, and conducted by a longer passage, so as, on rejoining the other half, to be one-quarter of a vibration behindhand, the two portions would exactly neutralise each other. This experiment has been performed with success. The interference arising between the waves from the two prongs of a tuning-fork was also predicted by theory, and proved to exist by Weber; indeed it may be observed by merely holding a vibrating fork close to the ear and turning it round.1

It is a result of the theory of sound that, if we move rapidly towards a sounding body, or if it move rapidly towards us, the pitch of the sound will be a little more acute; and, vice versa, when the relative motion is in the opposite direction, the pitch will be more grave. This arises from the less or greater intervals of time elapsing between the successive strokes of waves upon the auditory nerve, according as the ear moves towards or from the source of sound relatively speaking. This effect was predicted by theory, and afterwards verified by the experiments of Buys Ballot, on Dutch railways, and of Scott Russell, in England. Whenever one railway train passes another, on the locomotive of which the whistle is being sounded, the drop in the acuteness of the sound may be noticed at the moment of passing. This change gives the sound a peculiar howling character, which many persons must have noticed. I have calculated that with two trains travelling thirty miles an hour, the effect would amount to rather more than half a tone, and with some express trains it would amount to a tone. A corresponding effect is produced in the case of light undulations, when the eye and the luminous body approach or recede from each other. It is shown by a slight change in the refrangibility of the rays of light, and a consequent change in the place of the lines of the spectrum, which has been made to give important and unexpected information concerning the relative approach or recession of stars.

Tides are vast waves, and were the earth's surface entirely covered by an ocean of uniform depth, they would admit of exact theoretical investigation. The irregular form of the seas introduces unknown quantities and com

1 Tyndall's Sound, pp. 261, 273.

plexities with which theory cannot cope. Nevertheless, Whewell, observing that the tides of the German Ocean consist of interfering waves, which arrive partly round the North of Scotland and partly through the British Channel, was enabled to predict that at a point about midway between Brill on the coast of Holland, and Lowestoft no tides would be found to exist. At that point the two waves would be of the same amount, but in opposite phases, so as to neutralise each other. This prediction was verified by a surveying vessel of the British navy.1

Prediction in other Sciences.

Generations, or even centuries, may elapse before mankind are in possession of a mathematical theory of the constitution of matter as complete as the theory of gravitation. Nevertheless, mathematical physicists have in recent years acquired a hold of some of the relations of the physical forces, and the proof is found in anticipations of curious phenomena which had never been observed. Professor James Thomson deduced from Carnot's theory of heat that the application of pressure would lower the melting-point of ice. He even ventured to assign the amount of this effect, and his statement was afterwards verified by Sir W. Thomson. "In this very remarkable speculation, an entirely novel physical phenomenon was predicted, in anticipation of any direct experiments on the subject; and the actual observation of the phenomenon was pointed out as a highly interesting object for experimental research." Just as liquids which expand in solidifying will have the temperature of solidification lowered by pressure, so liquids which contract in solidifying will exhibit the reverse effect. They will be assisted in solidifying, as it were, by pressure, so as to become solid at a higher temperature, as the pressure is greater. This latter result was verified by Bunsen and Hopkins, in the case of paraffin, spermaceti, wax, and stearin. The effect upon water has more recently been carried to such an extent by Mousson, that under the vast

1 Whewell's History of the Inductive Sciences, vol. ii. p. 471. Herschel's Physical Geography, § 77.

2 Maxwell's Theory of Heat, p. 174. Philosophical Magazine, August 1850. Third Series, vol. xxxvii. p. 123.

pressure of 1300 atmospheres, water did not freeze until cooled down to -18° C. Another remarkable prediction of Professor Thomson was to the effect that, if a metallic spring be weakened by a rise of temperature, work done against the spring in bending it will cause a cooling effect. Although the effect to be expected in a certain apparatus was only about four-thousandths of a degree Centigrade, Dr. Joule1 succeeded in measuring it to the extent of threethousandths of a degree, such is the delicacy of modern heat measurements. I cannot refrain from quoting Dr. Joule's reflections upon this fact. "Thus even in the above delicate case," he says, "is the formula of Professor Thomson completely verified. The mathematical investigation of the thermo-elastic qualities of metals has enabled my illustrious friend to predict with certainty a whole class of highly interesting phenomena. To him especially do we owe the important advance which has been recently made to a new era in the history of science, when the famous philosophical system of Bacon will be to a great extent superseded, and when, instead of arriving at discovery by induction from experiment, we shall obtain our largest accessions of new facts by reasoning deductively from fundamental principles."

The theory of electricity is a necessary part of the general theory of matter, and is rapidly acquiring the power of prevision. As soon as Wheatstone had proved experimentally that the conduction of electricity occupies time, Faraday remarked in 1838, with wonderful sagacity, that if the conducting wires were connected with the coatings of a large Leyden jar, the rapidity of conduction would be lessened. This prediction remained unverified for sixteen years, until the submarine cable was laid beneath the Channel. A considerable retardation of the electric spark was then detected, and Faraday at once pointed out that the wire surrounded by water resembles a Leyden jar on a large scale, so that each message sent through the cable verified his remark of 1838.2

The joint relations of heat and electricity to the metals constitute a new science of thermo-electricity by which

1 Philosophical Transactions, 1858, vol. cxlviii. p. 127.

• Tyndall's Faraday, pp. 73, 74; Life of Faraday, vol. ii. pp. 82, 83.

Sir W. Thomson was enabled to anticipate the following curious effect, namely, that an electric current passing in an iron bar from a hot to a cold part produces a cooling effect, but in a copper bar the effect is exactly opposite in character, that is, the bar becomes heated. The action of crystals with regard to heat and electricity was partly foreseen on the grounds of theory by Poisson.

Chemistry, although to a great extent an empirical science, has not been without prophetic triumphs. The existence of the metals potassium and sodium was foreseen by Lavoisier, and their elimination by Davy was one of the chief experimenta crucis which established Lavoisier's system. The existence of many other metals which eye had never seen was a natural inference, and theory has not been at fault. In the above cases the compounds of the metal were well known, and it was the result of decomposition that was foretold. The discovery in 1876 of the metal gallium is peculiarly interesting because the existence of this metal, previously wholly unknown, had been inferred from theoretical considerations by M. Mendelief, and some of its properties had been correctly predicted. No sooner, too, had a theory of organic compounds been conceived by Professor A. W. Williamson than he foretold the formation of a complex substance consisting of water in which both atoms of hydrogen are replaced by atoms of acetyle. This substance, known as the acetic anhydride, was afterwards produced by Gerhardt. In the subsequent progress of organic chemistry occurrences of this kind have become The theoretical chemist by the classification of his specimens and the manipulation of his formulæ can plan out whole series of unknown oils, acids, and alcohols, just as a designer might draw out a multitude of patterns. Professor Cayley has even calculated for certain cases the possible numbers of chemical compounds.2 The formation of many such substances is a matter of course; but there is an interesting prediction given by Hofmann, concerning the possible existence of new compounds of sulphur and

common.

1 Tait's Thermodynamics, p. 77.

2 On the Analytical Forms called Trees, with Application to the Theory of Chemical Combinations. Report of the British Association, 1875, p. 257.