The great error of the untrained mind of the primitive man was that he did not know the value of scientific evidence. He made wide leaps from observed phenomena to imagined causes, quite overlooking the proximal causes that were near to hand. The untrained observer of to-day makes the same mistake; hence the continued prevalence of those superst.i.tious misconceptions which primitive man foisted upon our race. But each new generation of to-day is coming upon the field better trained in at least the rudiments of scientific method than the preceding generation, and this is perhaps the most hopeful feature of present-day education. Some day every one will understand that there is no valid distinction between the natural and the supernatural; in fact, that no such thing as a supernatural phenomenon, in the present-day acceptance of the word, can conceivably exist.

All conceivable manifestations of nature are natural, nor can we doubt that all are reducible to law--that is to say, that they can be cla.s.sified and reduced to systems. But the scientific imagination, as already pointed out, must admit that any and every scientific law of our present epoch may be negatived in some future epoch. It is always possible, also, that a seeming law of to-day may be proved false to-morrow, which is another way of saying that man's cla.s.sification improves from generation to generation. For a "natural law," let it be repeated, is not nature's method, but man's interpretation of that method.

LOGICAL INDUCTION VERSUS HASTY GENERALIZATION

A great difficulty is found in the fact that men are forever making generalizations--that is, formulating laws too hastily. A few phenomena are observed and at once the hypothesis-constructing mind makes a guess as to the proximal causes of these phenomena. The guess, once formulated and accepted, has a certain influence in prejudicing the minds of future observers; indeed, where the phenomena involve obscure principles the true explanation of which is long deferred, a false generalization may impress itself upon mankind with such force as to remain a stumbling-block for an indefinite period. Thus the Ptolemaic conception of the universe dominated the thought of Europe for a thousand years, and could not be subst.i.tuted by the true theory without a fierce struggle; and, to cite an even more striking ill.u.s.tration, the early generalizations of primitive man which explain numberless phenomena of nature as due to an influence of unseen anthropomorphic beings remain to this day one of the most powerful influences that affect our race--an influence from which we shall never shake ourselves altogether free until the average man--and particularly the average woman--learns to be a good observer and a logical reasoner.

Something towards this end is being accomplished by the introduction of experimental research and scientific study in general in our schools and colleges. It is hoped that something towards the same end may be accomplished through study of the history of the development of science.

Scarcely anything is more illuminative than to observe critically the mistakes of our predecessors, noting how natural the mistakes were and how tenaciously they were held to, how strenuously defended. Most of all it would be of value to note that the false inductions which have everywhere hampered the progress of science have been, from the stand-point of the generation in which they originated, for the most part logical inductions. We have seen that the Ptolemaic scheme of the universe, false though it was in its very essentials, yet explained in what may be termed a thoroughly scientific fashion the observed phenomena. It is one way of expressing a fact to say that the sun moves across the heavens from the eastern to the western horizon; and for most practical purposes this a.s.sumption answers perfectly. It is only when we endeavor to extend the range of theoretical astronomy, and to gain a correct conception of the mechanism of the universe as a whole, that the essentially faulty character of the geocentric conception becomes apparent.

And so it is in many another field; the false generalizations and hasty inductions serve a temporary purpose. Our only quarrel with them is that they tend through a sort of inertia to go forever unchanged. It requires a powerful thrust to divert the aggregate mind of our race from a given course, nor is the effect of a new impulse immediately appreciable; that is why the ma.s.ses of the people always lag a generation or two behind the advanced thinkers. A few receptive minds, cognizant of new observations that refute an old generalization, accept new laws, and, from the vantage-ground thus gained, reach out after yet other truths.

But, for the most part, the new laws thus accepted by the leaders remain unknown to the people at large for at least one or two generations. It required about a century for the heliocentric doctrine of Copernicus to begin to make its way.

In this age of steam and electricity, progress is more rapid, and the greatest scientific conception of the nineteenth century, the Darwinian theory, may be said to have made something that approaches an absolute conquest within less than half a century. This seems a marvellously sudden conquest, but it must be understood that it is only the crude and more tangible bearings of the theory that have thus made their way. The remoter consequences of the theory are not even suspected by the great majority of those who call themselves Darwinians to-day. It will require at least another century for these ideas to produce their full effect.

Then, in all probability, it will appear that the nineteenth century was the most revolutionary epoch by far that the history of thought has known. And it owes this proud position to the fact that it was the epoch in all history most fully subject to the dominant influence of inductive science. Thanks to this influence, we of the new generation are able to start out on a course widely divergent from the path of our ancestors. Our leaders of thought have struggled free from the bogs of superst.i.tion, and are pressing forward calmly yet with exultation towards the heights.

APPENDIX

(p. 95). J. J. Thompson, D.Sc., LL.D., Ph.D., F.R.S.,etc., Electricity and Matter, p. 75 ff., New York, 1904. The Silli-man Lectures, delivered at Yale University, May, 1903.

(p. 96). Ibid., pp. 88, 89. 3 (p- 97)- Ibid., p. 89.

(p. 97). Ibid., p. 87.

(p. 102). George F. Kunz, "Radium and its Wonders," in the Review of Reviews for November, 1903, p. 589.

(p. 105). E. Rutherford, Radio-Activity, p. 330, Cambridge, 1904.

(p. 106). Ibid., p. 330.

(p. 106). Compte Rendu, pp. 136, 673, Paris, 1903.

(p. 106). Revue Scientifique, April 13, 1901. 10 (p. 106). Compte Rendu, p. 136, Paris, 1903.

(p. 108). J. J. Thompson, Electricity and Matter, p. 162, New York, 1904.

(p. --). E. Rutherford, Radio-Activity, p. 340, Cambridge, 1904.

(p. 185). Dr. Duclaux, who was one of Pasteur's chief a.s.sistants, and who succeeded him in the directorship of the Inst.i.tute, died in 1903. He held a professorship in the University of Paris during the later years of his life, and his special studies had to do largely with the chemical side of bacteriology.

(p. 217). Lord Kelvin's estimate as quoted was expressed to the writer verbally. I do not know whether he has anywhere given a similar written verdict.

A LIST OF SOURCES

I.--PERIOD COVERED BY VOLUME I.

An ax agoras. See vol. i., p. 240.

Archimedes. See vol. i., p. 196.

Many of the works of Archimedes are lost, but the following have come down to us: (1) On the Sphere and Cylinder; (2) The Measure of the Circle; (3) Conoids and Spheroids; (4) On Spirals; (5) Equiponderants and Centres of Gravity; (6) The Quadrature of the Parabola; (7) On Bodies Floating in Liquids; (8) The Psammites; (9) A Collection of Lemmas.

Aristarchus. See vol. i., p. 212.

Magnitudes and Distances of the Sun and Moon is the only surviving work.

In the Armarius of Archimedes another work of Aristarchus is quoted--the one in which he antic.i.p.ates the discovery of Copernicus. Delambre, in his Histoire de Vastronomie ancienne, treats fully the discoveries of Aristarchus.

Aristotle. See vol. i., p. 82.

An edition of Aristotle was published by Aldus, Venice, 1495-1498, 5 vols. During the following eighty years seven editions of the Greek text of the entire works were published, and many Latin translations.

Berosus. See vol. i., p. 58.

The fragments of Berosus have been trans, by I. P. Cory, and included in his Ancient Fragments of Phoenician, Chaldean, Egyptian, and Other Writers, London, 1826; second edition, 1832.

Democritus. See vol. i., p. 161.

Fragments only of the numerous works ascribed to Democritus have been preserved. Democriii Abdereo operum fragmenta, Berlin, 1843, edited by F. G. A. Mullach. Diodorus Siculus. See vol. i., p. 77.

The Historical Library. Perhaps the best available editions of Diodorus are Wesseling's, 2 vols.; Amstel, 1745; and Dindorf's, 5 vols., Leipzig, 1828-1831. English trans, by Booth, London, 1700. Diogenes Laertius. See vol. i., p. 121.

The Lives and Opinions of Eminent Philosophers (trans. by C. D. Yonge), London, 1853.

Eratosthenes. See vol. i., p. 225.

The fragments of his philosophical works were published at Berlin, 1822, under the t.i.tle Eratosthenica. His poetical works were published at Leipzig, 1872. Euclid. See vol. i., p. 193.

His Elements of Geometry is still available as an English school text-book.

Galen (Claudius Galenus). See vol. i., p. 272.

Galen's preserved works are exceedingly bulky. The best-known edition is that of C. G. Kuhn, in 21 volumes.

Hero. See vol. i., p. 242.

The Pneumatics of Hero of Alexandria, from the original Greek. Trans, by B. Woodcroft, London, 1851. Herodotus. See vol. i.t p. 103.

History. English trans, by Beloe, 1791 and 1806. Trans, by Canon Rawlinson, London, 1858-1860. Hipparchus. See vol. i., p. 233.