cerning the relative approach or recession of many stars as regards the earth.

Tides are vast waves, and were the earth's surface entirely covered by an ocean of uniform depth, they would admit of very exact theoretical investigation. The wholly irregular form of the several seas introduces unknown. quantities and complexities 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 Lowestoft and Brill on the coast of Holland, in latitude 52° 27′ N, and longitude 3 h. 14 m. E, no tides would be found to exist. At that point the two waves would be of exactly the same amount, but in opposite phases, so as to neutralise each other. This assertion was verified by a surveying vessel of the British navy y.

Prediction in other Sciences.

Generations, or even centuries, will probably elapse before mankind are in possession of a mathematical theory of the constitution of matter as complete and satisfactory as the theory of gravitation. Nevertheless, mathematical physicists have in recent years acquired a fair hold of some of the simple relations of the physical forces to matter, and the proof is found in some remarkable 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

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

afterwards verified almost exactly 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 pressure of 1300 atmospheres, water did not freeze until cooled down to -18° Cent. 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, by bending it, must cause a cooling effect. Although the amount of effect to be expected in a certain apparatus was only about four-thousandths of a degree Centigrade, Dr. Joulea succeeded in detecting and measuring the effect to the extent of three-thousandths of a degree, such is the delicacy of modern methods of measurement. 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 Thompson completely verified. The mathematical investigation of the thermo-elastic qualities of metals has enabled my illustrious friend to

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

a Philosophical Transactions,' 1858, vol. cxlviii. p. 127.

b Ibid. p. 130.

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 occupied 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 by Siemens and Latimer Clark, 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 1838o.

The joint relations of heat and electricity to the metals constitute almost a new science of thermo-electricity. Sir W. Thompson was enabled by theory 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.

C

Tyndall's 'Faraday,' pp. 73, 74; 'Life of Faraday,' vol. ii. pp. 82, 83. d Tait's Thermodynamics,' p. 77.

Chemistry, although to a great extent an empirical science, has not been without prophetical 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 almost a necessary inference, and theory has not been found at fault. 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 been multiplied almost indefinitely. The theoretical chemist by the classification of his specimens and the manipulation of his formulæ can plan out as it were the creation of whole series of unknown oils, acids, alcohols, and such like products, just as a designer might draw out a multitude of patterns. 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 selenium, and even oxides of ammonium, which it remains for the future to verifye.

Prediction by Inversion of Cause and Effect.

There is one process of experiment which has so often led to important discoveries as to deserve separate description and illustration-I mean the inversion of Cause and Effect. Thus if A and B in one experiment produce C as a consequent, then antecedents of the nature of B

e Hofmann's 'Introduction to Chemistry,' pp. 224, 225.

and C may usually be made to produce a consequent of the nature of A inverted in direction. When we apply heat to a gas it tends to expand; hence if we allow the gas to expand by its own elastic force, cold is the result; that is B (air) and C (expansion) produce the negative of A (heat). Or again, B (air) and compression, the negative of C, produce A (heat). Similar results may be ex

It is a most familiar law

pected in a multitude of cases. that heat expands iron and nearly all solid bodies. What may be expected, then, if instead of increasing the length of an iron bar by heat we use mechanical force and stretch the bar? Having the bar and the former consequent, expansion, we should expect the negative of the former antecedent, namely cold. The truth of this inference was proved by Dr. Joule, who investigated the amount of the effect with his usual skillf.

This inversion of cause and effect in the case of heat may be itself again inverted in a highly curious manner. It happens that there are a few substances which are unexplained exceptions to the general law of expansion by heat. India-rubber especially is remarkable for contracting when heated. Since, then, iron and india-rubber are oppositely related to heat, we may expect that as distension of the iron produced cold, distension of the india-rubber will produce heat. This is actually found to be the case, and any one may detect the effect by suddenly stretching an india-rubber band while the middle part is in the mouth. Whenever stretched it will be found to grow slightly warm, and when relaxed cold.

The reader will readily see that many of the scientific predictions mentioned in preceding sections were due to the principle of inversion; for instance, Professor Thompson's speculations on the relation of pressure and the melting-point. But many other illustrations could be

f Philosophical Transactions,' (1855) vol. cxlv. pp. 100, &c.