282 THE PRINCIPLES OF SCIENCE. 



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 

 KirchhofFs map is 2 millemetres, and if we throw down 

 a line, as it were, by pure chance on such a map, the pro- 

 bability 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 

 T 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 (l) 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 01 . 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 com- 

 parison of spectra, rest upon the same principle of proba- 



d KirchhofTs 'Researches on the Solar Spectrum.' First part, trans- 

 lated by Professor Roscoe, pp. 18, 19. 



