The former would see Venus as at A, fig. 48, the other would see her as at B; and the distance between the two lines _a a´_ and _b b´_ along which her centre is travelling, as watched by these two observers, is known quite certainly to be 18,000 miles, if the observers' stations are 7,000 miles apart in a north-and-south direction (measured in a straight line). Thence the diameter S S´ of the sun is determined, because it is observed that the known distance _a b_ is such and such a part of it. And the real diameter in miles being known, the distance must be 107 times as great, because the sun looks as large as any globe would look which is removed to a distance exceeding its own diameter (great or small) 107 times. But unfortunately it is no easy matter to get the distance _a b_, fig. 48, determined in this simple manner. The distance 18,000 miles is known; but the difficulty is to determine what proportion the distance bears to the diameter of the sun S S´. All that we have heard about Halley's method and Delisle's method relates only to the contrivances devised by astronomers to get over this difficulty. It is manifest that the difficulty is very great. [Illustration: Fig. 49.] For, first, the observers would be several thousand miles apart. How then are they to ensure that their observations shall be made simultaneously? Again, the distance _a b_ is really a very minute quantity, and a very slight mistake in observation would cause a very great mistake in the measurement of the sun's distance. Accordingly, Halley devised a plan by which one observer in the north (or as at A, fig. 47) would watch Venus as she traversed the sun's face along a lower path, as _a a´_ fig. 49; while another in the south (or as at B, fig. 47) would watch her as she traversed a higher path, as _b b´_ fig. 49. By timing her they could tell how long these paths were, and therefore how placed on the sun's face, as in fig. 49; that is, how far apart, which is the same thing as determining _b a_, fig. 48. This was Halley's plan, and as it requires that the duration of the transit should be timed, it is called the method of durations. Delisle proposed another method--viz., that one observer should time the exact moment when Venus, seen from one station, _began_ to traverse the path _a a´_, while another should time the exact moment when she _began_ to traverse the path _b b´_; this would show how much _b_ is in advance of _a_, and thence the position of the two paths can be determined. _Or_ two observers might note the _end_ of the transit, thus finding how much _a´_ is in advance of _b´_ This is Delisle's method, and it has this advantage over Halley's--that an observer is only required to see _either_ the beginning or the end of the transit, not _both_.