entrance and departure of Venus on the sun's face at both places, and therefore ascertaining the whole duration of the passage at both places, and consequently the difference of durations; if that difference bears the same proportion to the whole time as what we have computed on the assumption of Figure 43, then the assumption of distance in Figure 43 is a true one; if the proportion of the difference to the whole time is the same as that computed in Figure 44, then the assumption of distance in Figure 44 is true; if neither of these agree, another assumption may be made which will come near the truth.
I then pointed out that the difference of durations (on any supposition of distance) may be much increased by choosing two stations, one as at A (Figure 45), such that it has nearly turned to the shady side of the earth when the transit is commencing, (or in other words, such that the transit begins shortly before sunset,) and has just turned to the illuminated side when the transit is ending, (or in other words, such that the transit ends shortly after sunrise,) as the former circumstance makes the beginning of the transit earlier, and the latter makes the end of it later, and therefore, the time occupied by the apparent passage along CD, which is the longer, is still more increased; and by choosing another station B, such that the transit begins in the morning and ends in the afternoon, in which case the time occupied by the passage along EF, and which is already the shorter, is still more diminished. And thus, upon any supposition of the sun's distance, the difference of the durations of the transit is increased, and therefore, in comparing the observed difference of durations with the computed difference, a small error of observed durations will be a smaller proportional part of the
