There were two approaches to the problem of measuring the AU. Halley’s method required observers to see both the ingress and the egress of Venus on the solar disc and accurately time the interval between them. Typically it takes Venus between five and six hours to cross the solar disc. The difference in transit times between northern and southern observers is about twenty minutes or so, if the lines of transit stay well away from the centre of the solar disc. It is this difference that needs to be timed to ± 2 seconds if Halley’s “500^th part at least” is to be attained. Joseph-Nicholas Delisle (1688 – 1768), professor of astronomy at the College de France, Paris proposed the second approach. Here observers needed to time either the ingress or the egress (and not both). The difference between ingress (or egress) times for eastern and western observers is about seven minutes or so. An accuracy of ± 1 second is required to reach Halley’s limit.

Both methods required collaborations. Each needed two successful observers, at widely separated, cloud-free sites. Single observations were useless. Because of the vagaries of the weather, success could only be guaranteed if many astronomers travelled to observe the event from different places. Both methods required the largest possible base-line. Halley’s had to be north-south, so astronomers chose cool, high latitudes in both the northern and southern hemisphere. Delisle’s method works best with a long east-west base-line (although it is possible to use a variant using a North-South baseline), so observers mainly travelled towards the sweltering, humid equator to spots as far apart in longitude as possible. Accurate maps were drawn indicating the exact segments of the Earth from which (for Halley’s) both ingress and egress could be seen (typically about 25% of the Earth’s surface), or (for Delisle’s) either ingress or egress (typically about 50% of the Earth’s surface in each case) could be seen. Delisle published such a chart in August 1760, less than a year before the 1761 transit. Weather records were scrutinised; the distribution of suitable continents, islands, cities and political affiliations were noted; ease of access was considered. Places where the Sun was too low in the sky (altitudes less than about 10°) were usually ruled out. The friendliness of the natives and the freedom from disease were borne in mind.

The observers needed to do two things. First they had to establish where they were. Today, with satellite navigation, this can be done to an accuracy of a few metres, in a minute or so. In those days it required many days of detailed solar and stellar observations taken using delicate transit instruments, coupled with accurate timings and the use of well-regulated state-of-the-art clocks. Even so accuracies of ± 100s of metres was the best that could be hoped for.Secondly the transit had to be timed. Consider ingress. There is an instant (t₁) when the disc of Venus first touches the disc of the Sun. This is difficult to time because you have to predict the exact place on the edge of the solar disc where this happens and point a well aligned, high magnification telescope at that spot so as to capture the moment of contact. Venus then appears to slowly move onto the solar disc, and there is a second instance (t₂) when it is just ‘on-board’, and the two discs are again just touching. The interval (t₂ – t₁) is about 1200 seconds.

The Halley and Delisle methods both required instants like t₂ to be timed to an accuracy of about one second. This proved to be completely impossible. The Sun is a huge sphere of hot gas, and its circular edge seems to be ‘boiling’ when observed through a telescope, especially after the sunlight has passed through the Earth’s turbulent atmosphere. The transiting disc of Venus is jet black. There is a huge difference between the intensity of the solar luminosity and the darkness of the disc of Venus and this contrast produces an irradiance which the eye finds great difficulty in dealing with. Venus does not break away cleanly from the solar rim. Venus appears pear-shaped, the neck lingeringly attached to the edge of the Sun. When the neck finally breaks Venus has seemingly jumped well onto the disc. Good, trained non-communicating observers, at the same site, found that their timings of the t₂ moment differed by as much as 30 to 40 seconds. This so-called black-drop effect was first noticed in 1761. James Ferguson (1710 – 1776) the Scottish astronomer, horologist and artist concluded that some of the timing error was due to using different sizes of telescopes with different magnifications (the larger the magnification the earlier t₂ was recorded.) It was also very clear that all eyes were not “equally quick and good.” Unfortunately the error was not diminished when photography was introduced in the nineteenth century. Instead of Halley’s hoped for “500^th part at least”, his method had plummeted to “a 15^th”, and Delisle’s was nearly a factor of two worse.