The difference of durations was about 22 minutes. We may perhaps say, that 7 minutes of this was caused by Wardhoe being north of the earth's centre, 5 minutes by Otaheite being south of the earth's centre, and 10 minutes by the circumstance that at Wardhoe the transit began near sunset, while at Otaheite it began near sunrise.
On computing, from the known dimensions of the earth, the distances of the points A,a,B,b, in miles, and finding (by the proportion which I have mentioned before) how distant in miles were the lines CD, EF, how much they differed in length, and how much they appeared to differ when respect was had to the different positions of the two stations at the beginning and end of the transit; and finding what must be the actual diameter of the sun in miles, in order that the difference between these lines CD, EF, thus altered for the changes of positions of the two stations, might bear to their whole length the same proportion which the difference of observed durations of transit bore to the whole duration of transit, and computing from this diameter of the sun in miles what his distance in miles must be to make his apparent angular diameter what we know it to be; it was found that the mean distance of the sun is 95,300,000 miles. If the distance of the sun had been only 47,650,000 miles, the difference of durations of transit at Wardhoe and Otaheite would have been 44 minutes.
The method of determining the sun's distance, which I have thus attempted to illustrate, is one of the most difficult subjects for a public lecture that I know; and if I have given you a few notions of it I shall be perfectly satisfied. I shall make some further remarks on this subject in the next lecture.
