# The transit of Venus and the longitude problem – a brief(ish) history

The size of the solar system was one of the chief puzzles of 18th century science. Astronomers of the day knew that six planets – Mercury, Venus, Earth, Mars, Jupiter and Saturn – orbited the Sun (they had not yet discovered Uranus, Neptune and Pluto), and they knew the relative spacing of those planets. Jupiter, for instance, is five times further from the Sun than Earth. But how far is that in miles? The absolute distances were unknown.

Venus was the key. Edmond Halley realised this in 1716.

As seen from Earth, Venus crosses the face of the Sun in a pattern that repeats every 243 years. A pair of transits happens eight years apart, then again 121.5 years later, then 105.5 years later, 121.5 years later, 101.5 years later and so on.

So, in 1716, based on the work done by Johannes Kepler during the 1631 transit and by Jeremiah Horrocks and William Crabtree during the one that happened in 1639 (the first transit successfully observed), Halley knew he was unlikely to be around for the next pair, due in 1761 and 1769 (subsequent Venus transits took place in 1874, 1882, 2004 and the next is in 2012).

But, he reasoned, by using the principle of parallax, it would be possible to use the Venus transit as a means of calculating the distance between the Earth and Venus and, consequently, using trigonometry, the distance between the Earth and the Sun. The scale of the rest of the solar system would follow.

The easiest way to think about parallax is by holding your index finger up in front of your face and looking at it first with one eye closed and then with the other. Your finger will appear to shift but this is of course an effect created by the fact that you’re looking at the same object from two slightly different angles. Calculate those angles and the distance between your eyes (the parallax) and from these figures you can work out the distance of your finger from your face.

Before he died, Halley urged the scientific community to unite and apply this principle in observations of the upcoming Venus transits from different points around the globe.

His efforts resulted in 1761 in the largest international scientific undertaking the world had ever seen. Astronomers in over 100 locations observed the transit on June 6 that year, despite the fact the event took place in the midst of the Seven Year’s War.

Among those who set off from England to far-flung corners of the globe were Charles Mason and Jeremiah Dixon, whose names later became synonymous with the boundary they plotted between Pennsylvania and Maryland during a dispute between British colonies in North America. In years to come the Mason-Dixon Line became the symbolic and cultural divide between north and south, the different between freedom and slavery.

For the Venus transit, the Royal Society dispatched Mason and Dixon to Sumatra, though due to being attacked by a French warship, they only made it as far as the Cape of Good Hope in South Africa and conducted their observations from there.

The society also sent Nevil Maskelyne (right) to the island of St Helena, from which Halley had carried out the first complete observation of the transit of Mercury in 1677.

Despite all these efforts, observations of the 1761 transit were disappointing, in part due to poor weather conditions, in part to the persistent problem of accurately measuring longitude. If one cannot determine one’s precise coordinates on Earth, how is it possible to measure a precise distance to Venus, the Sun or indeed any other celestial body?

The Earth is divided into 360 degrees. Divide 360 by 24 – the number of hours the Earth takes to revolve each day – and you get 15 – the number of degrees the Earth revolves in one hour. Divide one hour or 60 minutes by 15 and you get 4 minutes – the number of minutes represented by a single degree.

But the distance represented by each degree varies from the Earth’s greatest girth, at the Equator, to its narrowest – the North or South Poles. One degree at the Equator is equal to 69 miles, whereas at the poles it is almost nothing.

If you were able to hover just above the Earth for 4 minutes, the land beneath your feet would move one degree. However, depending on your latitude, the distance of land that passed beneath you during that time would range from around 69 miles at the Equator (1,000 miles if you hovered for a full hour or 15 degrees) – whereas at the North or South Pole the Earth would still be revolving beneath your feet but you’d be hovering above the same piece of land.

While establishing latitude in the 18th century was a straightforward calculation based on the length of the day, the height of the sun or known stars above the horizon, longitude was a problem – especially at sea where navigators also had to take into account their speed in any calculations. The inability to establish accurate longitude ended up costing many sailors their lives.

Maskelyne’s attempts to observe Venus were ultimately frustrated by cloud but en route to St Helena he successfully used the combination of a quadrant made by John Hadley and Tobias Mayer‘s Lunar Tables to determine his position at sea. He also calculated St Helena’s precise longitude, which hadn’t been known previously.

His success in this respect secured him a commission from the Board of Longitude to continue testing the “lunar distance method” as the pre-eminent technique for determining one’s position at sea. The board had been established with the Longitude Act of 1714 and offered a prize of £20,000 to anyone who could solve the problem.

Maskelyne’s greatest rival was John Harrison (left), a self-educated clockmaker from Yorkshire, whose attempts to develop a marine chronometer that remained constant whatever the elements represented the biggest challenge to the lunar distance method. And yet, the board also entrusted Maskelyne to test out Harrison’s clocks on its behalf.

Much of the 18th century was characterized by a split between astronomers, as represented by Maskelyne, and “mechanics” such as Harrison.

Maskelyne was appointed Astronomer Royal in 1765 and in doing so won himself a seat on the Board of Longitude, putting him in a position whereby he was both competing for the Longitude Prize and at the same time able to have a say in who was declared winner. He set about producing his own tables, detailing the positions of the moon, the planets and 57 stars every hour of every year in relation to the Earth’s surface.

Building on the work of Mayer (and predecessors such as the first Astronomer Royal, John Flamsteed – who established the Observatory at Greenwich and toiled for more than forty years to catalogue almost 3,000 celestial bodies – plus Tycho Brahe and Halley) Maskelyne’s first Nautical Almanac came out in 1767, ready for use the following year. It was subsequently published annually.

But Harrison and his fellow clockmakers still claimed the marine chronometer technique could deliver greater accuracy, and so, when Captain James Cook was dispatched in 1768 to Tahiti to observe the 1769 transit of Venus, the longitude problem hadn’t yet been resolved.

Due to the disappointments of the 1761 transit observations, Cook’s ship, the Endeavour, was laden with instruments designed to insure more accurate measurements than had ever been made before.

While at sea, Cook used the finest available Hadley sextant (courtesy of Jesse Ramsden), allowing him to determine the elevation of celestial objects with respect to the horizon. Cook could calculate his latitude as long as the position of the objects in the sky (using the Nautical Almanac) and the time of the observation (using noon) were known.

On land, a quadrant measures the altitudes of celestial objects to obtain the latitude and to check the clocks, and the one supplied to the Endeavour for the purpose of observing the Venus transit was made by John Bird.

To observe the transit itself, a telescope fitted with a micrometer and a good pendulum clock were needed.

Cook was an accomplished astronomer himself but the official position aboard the Endeavour went to Charles Green, who had been involved in the Royal Observatory’s 1761 transit of Venus activities but found himself out of a job when Maskelyne took over and hired his own assistant.

Green was armed with two reflecting telescopes made by the Scottish instrument maker James Short, one of which was fitted with an object-glass micrometer made by Peter Dollond. The Navy also supplied Cook with a Gregorian telescope he had used on a previous expedition, but before the Endeavour set sail he too had it fitted with a micrometer.

Four clocks were provided for the voyage, three by John Shelton and one by George Graham.

The clocks were there to provide a local time service during shore-based stopovers; the quadrant and sextant allowed observations vital in the determination of latitude and longitude, and maintaining a local time-service; and the telescopes were primarily supplied for the all-important transit observations.

Cook and Green were both well versed in alternative methods of calculating time, including that put forward in 1610 by Galileo Galilei. As the first man to turn a telescope to the skies, he encountered an embarrassment of riches, including the discovery of four moons orbiting Jupiter. He named these Cosimo, Francesco, Carlo and Lorenzo after the sons of Cosimo II de’ Medici, the Grand Duke of Tuscany, in the hope of securing his patronage. The “Medician stars”, which Simon Marius claimed to have discovered at the same time, giving them the names by which we know them today – Io, Europa, Ganymede and Callisto – experienced eclipses so predictably that Galileo claimed one could set a watch by them. He had found “the clock of heaven”.

All these things came into play when on June 3, 1769, Cook, Green and Daniel Solander (the Swedish naturalist brought along by the Royal Society’s designate Joseph Banks) watched Venus pass in front of the Sun. Two other groups of men from the Endeavour spread out across Tahiti and neighbouring Moorea to observe the event – the last opportunity anyone alive at that time would have to do so. Despite the superiority of their equipment and knowledge and a glorious, cloudless day, the accuracy of their data also disappointed due to the black drop effect.

This meant that while the measurements of the Sun’s distance from Earth subsequently determined were an improvement on those calculated by Horrocks, it was another 105.5 years before further observations were possible and the distance could be refined. These days we can bounce radio waves of Venus and indeed any other planet to calculate their distance from Earth (the Sun is about 150 million kilometres or 93 million miles away).

Meanwhile, Harrison finally received at least a portion of the Longitude Prize in 1773 – just three years before he died. But due to the high cost of his marine chronometers, Maskelyne’s lunar distance method predominated well into the 19th century and only finally died out with the advent of wireless telegraph time signals in the 20th century.

Maskelyne’s impact was such that the Royal Observatory, Greenwich became the pinpoint through which the Prime Meridian was established in 1884 – a line drawn from North to South pole via London, dividing East and West, the point at which longitude and Greenwich Mean Time are still decided to this day.

The main sources for this article were: Dava Sobel’s Longitude; Wayne Orchiston’s paper James Cook’s 1769 transit of Venus expedition to Tahiti (use a Google search to locate the PDF); The Telescopes and Astronomical Instruments of Captain James Cook by Larry Brown; Maskelyne, Mason and Dixon, 1761 by John Grimshaw; and NASA.