Origin of Eight-Year Generating Cycle 95 



By means of this theorem Proctor computes that the 

 length of the transit regions pp', qq' is about 3° 28'. 



Figure 26 will facilitate the discussion of the eight- 

 year cycle of Venus in its relation to the Earth and the 

 Sun. In 1761 and in 1769 there were June transits of 

 Venus and in 1874 and 1882 there were December 

 transits. Let us assume that at the 1761 transit the 

 Earth and Venus stood in their orbits at the points E 

 and V. Then according to the reasoning which has 

 just been traversed the next inferior conjunctions of 

 Venus and the Earth were at EiVi, E2V2, E3V3, E4V4, 

 E0V5. The conjunction at E5V5 was just 2° 22' behind 

 the point at which Venus and the Earth stood eight years 

 before, and as E5 fell within the transit region there 

 was a June transit in 1769. Now just as the fifth 

 conjunction E5 was 2° 22' behind E, so the sixth 

 conjunction occurred 2° 22' behind Ei; the seventh, 

 2° 22' behind E2; the eighth, 2° 22' behind E3; the 

 ninth, 2° 22' behind E4; and the tenth, 2° 22' behind E5. 

 In case of all five of the conjunction regions, there were 

 inferior conjunctions 2° 22' behind the points of con- 

 junction which occurred eight years previously. The 

 sequence is followed out in Figure 26 to the 81st 

 conjunction. 



If now we consider the two transit regions pp', qq', 

 we observe that the recession of the conjunction lines 

 at the rate of 2° 22' in eight years caused the conjunc- 

 tions in the region VE to recede from the transit 

 region pp', and those in the region ViEi to approach the 

 transit region qq'. The distance of Ei from E is about 

 215^° and the distance of the transit region qq' from 

 the transit region pp' is 180°. As the transit region is 



