INDUCTION IN GENERAL. 



t87 



selves must be decided by other rules, 

 and these it is now our purpose to in- 

 vestigate. If this thira part of the 

 operation be, in many of the ques- 

 tions of practical life, not the most, 

 but the least arduous portion of it, 

 we have seen that this is also the case 

 in some great departments of the field 

 of science ; in all those which are 

 principally deductive, and most of all 

 in mathematics, where the inductions 

 themselves are few in number, and so 

 obvious and elementary that they seem 

 to stand in no need of the evidence of 

 experience, while to combine them so 

 OS to prove a given theorem or solve 

 a problem may call for the utmost 

 powers of invention and contrivance 

 with which our species is gifted. 



If the identity of the logical pro- 

 cesses which prove particular facts 

 and those which establish general 

 scientific truths required any addi- 

 tional confirmation, it would be suf- 

 ficient to consider that in many 

 branches of science single facts have 

 to be proved, as well as principles ; 

 facts as completely individual as any 

 that are debated in a court of justice, 

 but which are proved in the same 

 manner as the other truths of the 

 science, and without disturbing in 

 any degree the homogeneity of its 

 method. A remarkable example of 

 this is afforded by astronomy. The 

 individual facts on which that science 

 grounds its most important deduc- 

 tions, such facts as the magnitudes 

 of the bodies of the solar system, 

 their distances from one another, the 

 figure of the earth, and its rotation, 

 are scarcely any of them accessible to 

 our means of direct observation : they 

 are proved indirectly by the aid of in- 

 ductione founded on other facts which 

 we can more easily reach. For ex- 

 ample, 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 supplements ; and since the angle 

 at the earth's centre subtended by the 

 distance between the two places of ob- 

 servation 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 quadrilateral being radii of the 

 earth ; the two remaining sides and 

 the diagonal, or in other words, the 

 moon's distance from the two places 

 of observation, and from the centre 

 of the earth, could be a.scertained, at 

 least in terms of the earth's radius, 

 from elementary theorems of geo- 

 metry. At each step in this demon- 

 stration a new induction is taken in, 

 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 also 

 (as we have shown to be the case in 

 all legitimate reasoning) a general 

 proposition might have been con- 

 cluded instead of a single fact In 

 strictness, indeed, the result of the 

 reasoning is a general proposition ; a 

 theorem respecting the distance, not 

 of the moon in particular, but of any 

 inaccessible object ; showing in what 

 relation that distance stands to cer- 

 tain other quantities. And although 

 the moon is almost the only heavenly 

 body the distance of which from the 

 earth can really be thus ascertained, 

 this is merely owing to the accidental 

 circumstances of the other heavenly 

 bodies, which render them incapable 

 of affording such data as the applica- 

 tion of the theorem requires ; for the 

 theorem itself is as true of them as it 

 is of the moon.* 



• Dr. Whewell thinks it improper to 

 apply the term Induction to any operation 

 not terminating in the establishment of a 



