Astronomy. [Lecture I 



must have something relative here to serve as 

 the basis of our operation. The horizontal pa- 

 rallax, as it is called, has therefore been a com- 

 mon basis employed for measuring the distances 

 of the heavenly bodies from the earth. With 

 respect to the moon, this method answers with 

 great accuracy, but with respect to the sun it is 

 liable to great error, for reasons which I shall 

 afterwards state, and as to the fixed stars, it is 

 altogether inapplicable. Indeed, from their great 

 distance they can have no parallax of this kind. 

 To explain what I have now remarked, I 

 must refer to the diagram (PL XXVI. fig. 118.) 

 .where BAG represents one half of the earth, 

 A C its semidiameter, S the sun, supposed at an 

 immense distance, m the moon, and E K O L a 

 part of the moon r s orbit. C R S is a line repre- 

 senting the rational horizon of an observer at A 

 extended to the sun ; H A O his sensible horizon 

 extended to the moon's orbit. A L C is the 

 angle under which the earth's semi-diameter AC 

 is seen from the moon at L. AS C is the angle 

 under which it is seen from the sun at S. Now 

 it is evident that the angle A L C is equal to the 

 angle O A L, and the angle A S C to the angle 

 O A,/*; and consequently, as the angle O Ay is 

 much less than O A L, the earth's semidiameter 

 appears much greater as seen from the moon at 

 L than from the sun at S, and therefore the earth 

 is at a much greater distance from the sun than 

 from the moon. 



