174 A Short History of Astronomy [CH. VI. 



observer from A, where he sees the moon rising, to B, where 

 he sees it setting. When he is at c, on the line joining the 

 centres of the earth and moon, the point o appears to be in 

 the centre of the moon's disc, and the portion CQ c' is visible, 

 c R c invisible. But when the observer is at A, the point P, 

 on the right of o, appears in the centre, and the portion 

 a P a is visible, so that c' a' is now visible and a c invisible. 

 In the same way, when the observer is at B, he can see the 

 portion c b, while b' c 1 is invisible and Q appears to be in 

 the centre of the disc. Thus in the course of the day 

 the portion a Q b' (dotted in the figure) is constantly visible 

 and b R a' (also dotted) constantly invisible, while a c b 

 and a' c b' alternately come into view and disappear. In 

 other words, when the moon is rising we see a little 

 more of the side which is the then uppermost, and when 

 she is setting we see a little more of the other side which is 

 uppermost in this position. A similar explanation applies 

 when the observer is not on the earth's equator, but the 

 geometry is slightly more complicated. In the same way, as 

 the moon passes from south to north of the equator and back 

 as she revolves round the earth, we see alternately more and 

 less of the northern and southern half of the moon. This 

 set of changes the simplest of several somewhat similar 

 ones which are now known as librations of the moon being 

 thus thought of as likely to occur, Galilei set to work to test 

 their existence by observing certain markings of the moon 

 usually visible near the edge, and at once detected altera- 

 tions in their distance from the edge, which were in general 

 accordance with- his theoretical anticipations. A more 

 precise inquiry was however interrupted by failing sight, 

 culminating (at the end of 1636) in total blindness. 



But the most important work of these years was the 

 completion of the great book, in which he summed up 

 and completed his discoveries in mechanics, Mathe- 

 matical Discourses and Demonstrations concerning Two 

 New Sciences, relating to Mechanics and to Local Motion. 

 It was written in the form of a dialogue between the same 

 three speakers who figured in the Dialogue on the Systems, 

 but is distinctly inferior in literary merit to the earlier 

 work. We have here no concern with a large part of 

 the book, which deals with the conditions under which 



