Origin of Eight-Year Generating Cycle 93 



'* Since the interval between isach conjunction is 

 about a year and three-fifths, the whole time occupied 

 before the position SV5E5 is reached by the conjunc- 

 tion-line will be five times 1| years, or 8 years, 

 less the short interval corresponding to the Earth's 

 motion over the arc E5E. We see, then, how it comes 

 to pass that an interval of eight years brings round 

 nearly the same circumstances as at the beginning of 

 the interval, and why, therefore, when a transit has 

 occurred, another may occur eight years later. . . . 



" And now let us consider the effect of the inclina- 

 tion of the orbit of Venus to that of the Earth, still, 

 for the sake of simplicity, lea\'ing out of account the 

 slight eccentricity of the orbits. 



"If EE', VV (Figure 25), represent the two orbits, ^ 

 and M be the place of the Earth at the autumnal 

 equinox, then the line EE' represents the intersection 

 of the two orbit-planes; and if, as before, we regard 

 the plane of the paper as containing the orbit EE', 

 then the part V'vV of the path of Venus is to be 

 regarded as slightly above, the part Vv'V as slightly 

 below, the plane of the paper. Accordingly the end 

 of the pointer which we have supposed Venus to 

 carry round the Sun, passes above the semi- circle 

 E'eE and below the semi-circle Ee'E'. And suppos- 

 ing this pointer to be of the length SE, so that its 

 end appreciably travels round Ee'E'e (except for 

 the displacement below and above the plane of this 



* In the description of Figure 25 I have altered slightly Proctor's 

 lettering so as to correspond with the use I shall make of the reasoning 

 later on. Proctor starts with the transit of 1631 while I begin with that 

 of 1761. 



