In many cases of scientific induction we may apply the principle of the inverse method in a simple manner. If only two, or at the most a few hypotheses, may be made as to the origin of certain phenomena, we may sometimes easily calculate the respective probabilities. It was thus that Bunsen and Kirchhoff established, with a probability little short of certainty, that iron exists in the sun. On comparing the spectra of sunlight and of the light proceeding from the incandescent vapour of iron, it became apparent that at least sixty bright lines in the spectrum of iron coincided with dark 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 millimetre 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 mm., 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 1/2 mm. 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 1/2 mm., 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 1 mm. 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 1/2. 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 (1/2)^{60} or less than 1 in a trillion. The odds, in short, are more than a million million millions to unity against such casual coincidence.[153] 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 be observed if iron existed in the sun, than that they should arise from chance. Hence by our principle it is immensely probable that iron does exist in the sun. [153] Kirchhoff’s *Researches on the Solar Spectrum*. First part, translated by Roscoe, pp. 18, 19. All the other interesting results, given by the comparison of spectra, rest upon the same principle of probability. 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.