174 IXDUCTIOX. 



aid of inductions founded on other facts v.hicli we can more easily 

 reach. For example, the distance of the moon from the earth was 

 determined by a very circuitous process. The share which direct 

 observation had in the work consisted in ascertaining, at one and the 

 same instant, the zenith distances of the moon, as seen from two 

 points very remote from one another on the earth's surface. The 

 ascertainment of these angular distances ascertained their supple- 

 ments ; and since the angle at the earth's centre subtended by the 

 distance between the two places of observation was deducible by 

 spherical trigonometry from the latitude and longitude of those places, 

 the angle at the moon subtended by the same line became the fourth 

 angle of a quadrilateral of which the other three angles were known. 

 The four angles being thus ascertained, and two sides of the quadri- 

 lateral being radii of the earth ; the two remaining sides and the diag- 

 onal, or in other words, the moon's distance from the two places of 

 observation and from the centre of the eaith, could be ascertained, at 

 least in terms of the earth's radius, fi'om elementary theorems of geom- 

 etry. At each step in this demonsti'ation we take in a new induction, 

 represented, in the aggregate of its results, by a general proposition. 



Not only is the process by which an individual astronomical fact 

 was thus ascertained, exactly similar to those by which the same 

 science establishes its general truths, but moreover (as we have shown 

 to be the case in all legitimate reasoning) a general proposition might 

 have been concluded instead of a single fact. In strictness, indeed, 

 the result of the reasoning is a general proposition ; a theorem re- 

 specting the distance, not of the moon in particular, but of ani/ inac- 

 •cessible object ; showing in what relation that distance stands to certain 

 other quantities. And although the moon is almost the only heavenly 

 body the distance of which from the earth can really be thus ascer- 

 tained, this is merely owing to the accidental circumstances of the 

 other heavenly bodies, which render them incapable of affording such 

 data as the application of the theorem requires ; for the theorem itself 

 is as true of them as it is of the moon. 



We shall fall into no error, then, if in treating of Induction, we limit 

 our attention to the establishment of general propositions. The prin- 

 ciples and rules of Induction, as directed to this end, are the principles 

 and rules of all Induction; and the logic of Science is the universal 

 Logic, applicable to all inquiries in which man can engage, and the 

 test of all the conclusions at which he can anive by inference. 



CHAPTER II. 



OF INDUCTIONS I>tPROPERLY SO CALLED. 



§ 1. Induction, then, is that operation of the mind, by which v^e in- 

 fer that what we know to be true in a particular case or cases, ^\all be 

 ?,rue in all cases which resemble the former in certain assignable 

 respects. In other words. Induction is the process by which we con- 

 dude that what is tiiie of certain individuals of a class is tnie of the 



