it is then ( — j , or less than v „~ n „\ In other 



56 Notices respecting New Books. 



succession being thrown upon the solar spectrum, the probability of 

 falling on a dark space, producing coincidence, is in each separate 

 case one-half. The probability that all the 60 lines will fall in coin- 

 cidence is found by multiplying together all the separate probabilities; 

 ,60 i 



1,152,930,000,000,000,000* 



words, the odds are more than 1,000,000,000,000,000,000 to 1 

 against all the 60 bright lines having fallen into coincidence with 

 dark lines of the solar spectrum, had chance alone governed the dis- 

 tribution. We cannot but believe, then, that there was something 

 more than chance in the matter. 



Otherwise stated, there are more than a trillion of modes in which 

 the 60 bright lines might be distributed among the dark lines, as 

 regards coincidence and non-coincidence. Of these the very mode 

 which occurs, that of perfect coincidence, is that which would occur 

 were there iron in the sun's atmosphere. The conclusion is irre- 

 sistible that there is iron in the sun's atmosphere. It is proved, as 

 Kirchhoff says, " with as great a degree of certainty as we can attain 

 in any question of physical science." 



In this calculation we have indeed supposed the dark solar lines 

 to be placed at equal intervals ; but all the probabilities remain 

 exactly the same, however irregular their distribution, provided the 

 dark spaces act', bV , cc', &c. are equal to half the whole spectrum ; 

 that is to say, provided no two of the lines A, B, C, &c. approach 

 within less than one millimetre of each other. As, however, many 

 lines do approach nearer than this, the probability of mere casual 

 coincidences is even less than we escimated. If we add the fact that 

 the lines are observed to correspond not only in position, but also in 

 relative brightness, the problem becomes vastly more complex, but 

 the conclusion immensely more certain. Finally, as the prismatic 

 apparatus is improved, the apparent breadth of the lines will be di- 

 minished, their number greatly increased. The coincidences will 

 therefore become both greatly more numerous, and each coincidence 

 will have a higher value in the elimination of chance ; the proof 

 attains an indefinite degree of certainty limited only by truth itself. 



If the reader object that these coincidences are only apparent, and 

 that we can never know whether or not the infinitely thin lines 

 A, B, C, M, N, &c. coincide, he is not wrong, but possibly forgets 

 that all inductive truths rest upon mere appearance, and involve a 

 margin of error or mistake in observation. This problem of the iron 

 lines in the solar spectrum we look upon as an epitome of the induc- 

 tive method of science, identically the same, indeed, as any other 

 inductive problem in principle, but beautifully simple and luminous 

 in its procedure. And thus Kirchhoff's memoir seems to us not 

 only a very interesting, but also a most improving subject of study. 



The occurrence of iron in the sun's atmosphere having been thus 

 rendered practically certain, the Professor proceeds to prove the un- 

 doubted presence or apparent absence of many other elements in the 

 sun's atmosphere. Nothing can be more gratifying than the first 

 acquisition of such a far-reaching mode of investigation and proof as 



