lines in the sun's spectrum. Such coincidences could never be observed with certainty, because, even if the lines only closely approached, the instrumental imperfections of the spectroscope would make them apparently coincident, and if one line came within half a millemetre of another, on the map of the spectra, they could not be pronounced distinct. Now the average distance of the solar lines on Kirchhoff's map is 2 millemetres, and if we throw down a line, as it were, by pure chance on such a map, the probability is about one-half that the new line will fall within millemetre on one side or the other of some one of the solar lines. To put it in another way, we may suppose that each solar line, either on account of its real breadth or the defects of the instrument, possesses a breadth of millemetre, and that each line in the iron spectrum has a like breadth. The probability then is just one-half that the centre of each iron line will come by chance within I millemetre of the centre of a solar line, so as to appear to coincide with it. The probability of casual coincidence of each iron line with a solar line is in like manner. Coincidence in the case of each of the sixty iron lines is a very unlikely event if it arises casually, for it would have a probability of only (1) or less than 1 in a trillion. The odds, in short, are more than a million million millions to unity against such casual coincidenced. But on the other hypothesis, that iron exists in the sun, it is highly probable that such coincidences would be observed; it is immensely more probable that sixty coincidences would e observed if iron existed in the sun, than that they ld arise from chance. Hence by our principle it is mensely probable that iron does exist in the sun. All the other interesting results given by the comon of spectra, rest upon the same principle of proba Researches on the Solar Spectrum.' First part, trans- bility. The almost complete coincidence between the spectra of solar, lunar, and planetary light renders it practically certain that the light is all of solar origin, and is reflected from the surfaces of the moon and planets, suffering only slight alteration from the atmospheres of some of the planets. A fresh confirmation of the truth of the Copernican theory is thus furnished. A vast probability may be shown to exist that the heat, light, and chemical effects of the sun are due to the same rays, and are so many different manifestations of the same undulations. For a photograph of the spectrum corresponds exactly with what the eye observes, allowance being made for the great differences of chemical activity in dif ferent parts of the spectrum; and delicate experiments with the thermopile also show that, where there is a dark line, there also the heat of the rays is absent. Sir J. Herschel proved the connexion between the direction of the oblique faces of symmetrical quartz crystals, and the direction in which the same crystals rotate the plane of the polarisation of light. For if it is found in a second crystal that the relation is the same as in the first, the probability of this happening by chance is; the probability that in another crystal also the direction would be the same is, and so on. The probability that in n + 1 crystals there would be casual agreement of direction is the nth power of Thus, if in examining fourteen of. crystals the same relation of the two phenomena is discovered in each, the probability that it proceeds from uniform conditions is more than 8000 to 1". Now, since the first observations on this subject were made in 1820, no exceptions have been observed, so that the probability of invariable connexion is incalculably great. е e Edinburgh Review,' No. 185, vol. xcii. July 1850, p. 32; Herschel's 'Essays,' p. 421; Transactions of the Cambridge Philosophical Society," vol. i. p. 43. A good instance of this method is furnished by the agreement of numerical statements with the truth. Thus, ina manuscript of Diodorus Siculus, as Dr. Young states 5, the ceremony of an ancient Egyptian funeral is described as requiring the presence of forty-two persons sitting in judgment on the merits of the deceased, and in many ancient papyrus rolls the same number of persons are found delineated. The probability is but slight that Diodorus, if inventing his statements or writing without proper information, would have chosen such a number as forty-two, and though there are not the data for an exact calculation, Dr. Young considers that the probability in favour of the correctness of the manuscript and the veracity of the writer on this ground alone, is at least 100 to I. It is exceedingly probable that the ancient Egyptians had exactly recorded the eclipses occurring during long periods of time, for Diogenes Laertius mentions that 373 solar and 832 lunar eclipses had been observed, and the ratio between these numbers exactly expresses that which would hold true of the eclipses of any long period, of say 1200 or 1300 years, as estimated on astronomical grounds h It is evident that an agreement between small numbers, or customary numbers, such as seven, one hundred, a myriad, &c., is much more likely to happen from chance, and therefore gives much less presumption of dependence. If two ancient writers spoke of the sacrifice of oxen, they would in all probability describe it as a hecatomb, and there would be nothing remarkable in the coincidence. On similar grounds, we must inevitably believe in the human origin of the flint flakes so copiously discovered of late years. For though the accidental stroke of one stone 8 Young's 'Works,' vol. ii. pp. 18, 19. h History of Astronomy,' Library of Useful Knowledge, p. 14. against another may often produce flakes, such as are occasionally found on the sea-shore, yet when several flakes are found in close company, and each one bears evidence, not of a single blow only, but of several successive blows, all conducing to form a symmetrical knifelike form, the probability of a natural and accidental origin becomes incredibly small, and the contrary supposition, that they are the work of intelligent beings, approximately certain i. An interesting calculation concerning the probable connexion of languages, in which several or many words are similar in sound and meaning, was made by Dr. Young k. Application of the Theory of Probabilities in The science of astronomy, occupied with the simple relations of distance, magnitude, and motion of the heavenly bodies, admits more easily than almost any other science of interesting conclusions founded on the theory of probability. More than a century ago, in 1767, Michell showed the extreme probability of bonds connecting together systems of stars. He was struck by the unexpected number of fixed stars which have companions close to them. Such a conjunction might happen casually by one star, although possibly at a great distance from the other, happening to lie on the same straight line passing near the earth. But the probabilities are so greatly against such an optical union happening often in the expanse of the heavens, that Michell asserted the existence of a bond between most of i Evans' 'Ancient Stone Implements of Great Britain.' London, 1872 (Longmans). k Philosophical Transactions,' 1819; Young's 'Works,' vol. ii. pp. 15-18. the double stars. It has since been estimated by Struve, that the odds are 9570 to 1 against any two stars of not less than the seventh magnitude falling within the apparent distance of four seconds of each other by chance, and yet ninety-one such cases were known when the estimation was made, and many more cases have since been discovered. There were also four known triple stars, and yet the odds against the appearance of any one such conjunction are 173,524 to 11. The conclusions of Michell have been entirely verified by the discovery that many double stars are in connexion under the law of gravitation. Michell also investigated the probability that the six brightest stars in the Pleiades should have come by accident into such striking proximity. proximity. Estimating the number of stars of equal or greater brightness at 1500, he found the odds to be nearly 500,000 to I against casual conjunction. Extending the same kind of argument to other clusters, such as that of Præsepe, the nebula in the hilt of Perseus' sword, he saysm: 'We may with the highest probability conclude, the odds against the contrary opinion being many million millions to one, that the stars are really collected together in clusters in some places, where they form a kind of system, while in others there are either few or none of them, to whatever cause this may be owing, whether to their mutual gravitation, or to some other law or appointment of the Creator.' The calculations of Michell have been called in question by the late James D. Forbes", and Mr. Todhunter vaguely 1 Herschel, 'Outlines of Astronomy,' 1849, p. 565; but Todhunter, in his History of the Theory of Probability,' p. 335, states that the calculations do not agree with those published by Struve. Philosophical Transactions,' 1767, vol. lvii. p. 431. Philosophical Magazine,' 3rd Series, vol. xxxvii. p. 401, December, aiso August. 1849. |