THE STORY OF TRANSITS 429 



It is not difficult to see that if the planets are exactly at M 

 and P, or at N and Q, then Venus will appear to travel right 

 across the centre of the solar disc along a diameter, a very rare 

 event indeed. In such a case the transit would occupy about 

 eight hours. More frequently, however, the path is displaced 

 towards the edge of the sun, the " limb," as it is called techni- 

 cally, and the duration of the phenomenon is correspondingly 

 reduced. We see, therefore, that a transit can occur only when 

 the earth is near P or Q, and only then if Venus happens to be 

 near M or N at the same time. 



A calculation will show that the earth is at P on June 5, 

 and at Q on December 7, so that whenever a transit of Venus 

 occurs at all, it must take place on or about those dates. 



One of the most interesting questions in connection with 

 transits is the frequency with which they occur. Venus goes 

 round the sun once in about 224I of our days, whilst our own 

 year contains about 36s J on the average. Now, thirteen times 



224I is 2,92 1 1 days and eight times 365 1 is 2,922, results which 

 show that thirteen Venusian years are very nearly equivalent 

 to eight of our own. There have been many occasions when the 

 earth has been near P and Venus near M on the same day. A 

 transit may have taken place. Twelve months later the earth 

 is back at P, but Venus is not at M, for it passed that point 140 

 days previously. In two years' time the earth comes back to 

 P again, but again Venus is not at M. This goes on for seven 

 years, but when the earth comes back to P in the eighth year, 

 it finds that Venus has made thirteen revolutions and has now 

 come close to M ; it is not quite in the same place as it was eight 

 years before, owing to the small inequality discussed above. A 

 transit is observed. By the time the next eight years come 

 round the effect of this inequality has been magnified sufficiently 

 to prevent another taking place. It is, indeed, impossible to 

 have more than two successive transits in these short eight -year 

 periods, for, whilst two may be separated by such an interval, 

 yet under no circumstances can three take place in sixteen years. 

 Even two do not always come. If Venus is almost exactly 



