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INDUCTION. 



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 processes which prove parti- 

 cular facts and those which establish general scientific truths, 

 required any additional confirmation, it would be sufficient 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 im- 

 portant deductions, 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 inductions founded on other facts which 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 as- 

 certainment 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 dedu- 

 cible 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 ascertained, at least 

 in terms of the earth's radius, from elementary theorems of 

 geometry. At each step in this demonstration we take in a 



