seems to fail at several points. If past time be infinite, why may not matter have been created infinite also? It would be most reasonable, again, to suppose the matter destroyed in any time to be proportional to the matter then remaining, and not to the original quantity; under this hypothesis even a finite quantity of original matter could never wholly disappear from the universe. For like reasons we cannot hold that the doctrine of the Conservation of Energy is really proved, or can ever be proved to be absolutely true, however probable it may be regarded on many grounds.

Tendency to Hasty Generalization.

In spite of all the powers and advantages of generalization, men require no incitement to generalize; they are too apt to draw hasty and ill-considered inferences. As Francis Bacon said, our intellects want not wings, but rather weights of lead to moderate their course. The process is inevitable to the human mind; it begins with childhood and lasts through the second childhood. The child that has once been hurt fears the like result on all similar occasions, and can with difficulty be made to distinguish between case and case. It is caution and discrimination in the adoption of general conclusions that we chiefly have to learn, and the whole experience of life is one continued lesson to this effect. Baden Powell has excellently described this strong natural propensity to hasty inference, and the fondness of the human mind for tracing resemblances real or fanciful. Our first inductions,' he saysk, 'are always imperfect and inconclusive; we advance towards real evidence by successive approximations and accordingly we find false generalization the

i Novum Organum,' bk. I. Aphorism 104.

k The Unity of Worlds and of Nature,' 2nd edit. p. 16.

besetting error of most first attempts at scientific research. The faculty to generalize accurately and philosophically requires large caution and long training; and is not fully attained, especially in reference to more general views, even by some who may properly claim the title of very accurate scientific observers in a more limited field. It is an intellectual habit which acquires immense and accumulating force from the contemplation of wider analogies.'

Hasty and superficial generalizations have always been the bane of science, and there would be no difficulty in finding endless illustrations. Between things which are the same in number there is a certain resemblance, namely in number, but in the infancy of science men could not be persuaded that there was not a deeper resemblance implied in that of number. Pythagoras was not the inventor of a mystical science of number. In the ancient Oriental religions the seven metals were connected with the seven planets, and in the seven days of the week we still have, and probably always shall have, a relic of the septiform system ascribed by Dio Cassius to the ancient Egyptians. The disciples of Pythagoras carried the doctrine of the number seven into great detail. Seven days are mentioned in Genesis; infants acquire their teeth at the end of seven months; they change them at the end of seven years; seven feet was the limit of man's height; every seventh year was a climacteric or critical year, at which a change of disposition took place. Then again there were the seven sages of Greece, the seven wonders of the world, the seven rites of the Grecian games, the seven gates of Thebes, and the seven generals destined to conquer that city.

In natural science there were not only the seven planets, and the seven metals, but also the seven primitive colours, and the seven tones of music. So deep a

hold did this doctrine take that we still have its results in many customs, not only in the seven days of the week, but the seven years' apprenticeship, puberty at fourteen years, the second climacteric, and legal majority at twentyone years, the third climacteric. The system was reproduced in the seven sacraments of the Roman Catholic Church, and the seven year periods of Comte's grotesque system of domestic worship. Even in scientific matters the loftiest intellects have occasionally yielded, as when Newton was misled by the analogy between the seven tones of music and the seven colours of his spectrum. Other numerical analogies, though rejected by Galileo, held Kepler in thraldom; no small part of Kepler's labours during seventeen years was spent upon numerical and geometrical analogies of the most baseless character; and he gravely held that there could not be more than six planets, because there were not more than five regular solids. Even the acute genius of Huyghens did not prevent him from inferring that but one satellite could belong to Saturn, because, with those of Jupiter and the Earth, it completed the perfect number of six. A whole series of other superstitions and fallacies attach to the numbers six and ninel.

It is by false generalization, again, that the laws of nature have been supposed always to possess that simplicity and perfection which we attribute to particular forms and relations. The heavenly bodies, it was held, must move in circles, for the circle was the perfect figure. Even Newton seemed to adopt the questionable axiom that nature must always proceed in the simplest way; in stating his first rule of philosophizing, he addsm: To this purpose the philosophers say, that nature does nothing in

1 Baring-Gould, 'On the Fatalities of Number,' in 'Curious Myths of the Middle Ages' (1866), p. 209.

vain, when less will serve; for Nature is pleased with simplicity, and affects not the pomp of superfluous causes.' Keill, again, lays down" as an axiom that 'The causes of natural things are such, as are the most simple, and are sufficient to explain the phenomena: for nature always proceeds in the simplest and most expeditious method; because by this manner of operating the Divine Wisdom displays itself the more.' If this axiom had any clear grounds of truth, it would not apply to proximate laws; for even when the ultimate law may appear simple the results may be infinitely diverse, as in the various elliptic, hyperbolic, parabolic, or circular orbits of the heavenly bodies. Simplicity is naturally agreeable to a mind of very finite powers, but to an Infinite Mind everything is simple.

Every great advance in science consists in a great generalization, pointing out deep and subtle resemblances. The Copernican system was a generalization, in that it classed the earth among the planets; it was, as Bishop Wilkins expressed it, 'the discovery of a new planet,' but it was opposed by a more shallow generalization. Those who argued from the condition of things upon the earth's surface, thought that every object must be attached to and rest upon something else. Shall the earth, they said, alone be free? Accustomed to certain special results of gravity they could not conceive its action under widely different circumstances. No hasty thinker could seize the deep analogy pointed out by Horrocks between a pendulum and a planet, true in substance though mistaken in some details. All the advances of modern science rise from the conception of Galileo, that in the heavenly bodies, however apparently different their condition, we

n Keill, Introduction to Natural Philosophy,' p. 89.
o Jeremiæ Horroccii Opera Posthuma' (1673), pp. 26, 27.

shall ultimately recognise the same fundamental principles of mechanical science which are true on earth.

Generalization is the great prerogative of the intellect, but it is a power only to be exercised safely with much caution and after long training. Every mind must generalize, but there are the widest differences in the depth of the resemblances discovered and the care with which the discovery is verified. There seems to be an innate power of insight which a few men have possessed pre-eminently, and which enabled them, with no exemption indeed from labour or temporary error, to discover the one in the many. Minds of excessive acuteness may exist, which have yet only the powers of minute discrimination, and of storing up, in the treasure-house of memory, vast accumulations of words and incidents. But the power of discovery belongs to a more restricted class of minds. Laplace said that, of all inventors who had contributed the most to the advancement of human knowledge, Newton and Lagrange appeared to possess in the highest degree the happy tact of distinguishing general principles among a multitude of objects enveloping them, and this tact he conceived to be the true characteristic of scientific genius.