xii.] THE INDUCTIVE OR INVERSE METHOD. 



ing from the incandescent vapour of iron, it became appa- 

 rent that at least sixty bright lines in the spectrum of iron 

 coincided with dark lines in the sun's spectrum. Such coin- 

 cidences could never be observed with certainty, because, 

 even if the lines only closely approached, the instrumental 

 imperfections of the spectroscope would make them appa- 

 rently coincident, and if one line came within half a milli- 

 metre of another, on the map of the spectra, they could not 

 be pronounced distinct. Now the average distance of the 

 solar lines on KirchhofFs 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 5 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 

 ^ 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 I 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 ^. Coinci- 

 dence 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 (^) 60 or less than I in a trillion. The 

 odds, in short, are more than a million million millions 

 to unity against such casual coincidence. 1 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. 



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 onH 



1 Kirchhoff's Researches on the Solar Spectrum. Fiist part, trans- 

 lated by Roscoe, pp. 18, 19. 



