350 INDUCTION. 



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 

 upon which that science grounds its most important 

 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 obser- 

 vation : 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 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 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 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 new 

 induction, represented, in the aggregate of its results, 

 by a general proposition. 



Not only is the process by which an individual 



