Surveying the Transit of Venus
Theatrum Orbis Terrarum, by Abraham Ortelius, Typus Orbis Terrarum, 1572.
Human history has been shaped by colonialism, and one wave of colonialism resulted in the founding of the United States. In fact, most countries were colonized by European powers from the late fifteenth century until just after World War II. At its height, the British Empire controlled nearly a quarter of the world’s nations.
How did Britian and the other European countries do it? Each country invested in a national effort that focused its existing internal structures on colonizing other countries. The military, religious, governmental, aristocratic, business, technological and cultural establishments were all leveraged to locate and extract valuable resources from lands near and far.[1]
A wealth of information and knowledge
The wealth from early colonization also brought a wealth of new information and knowledge to the imperial powers. In Britian in 1660, a new society was founded to ‘transform knowledge, profit, and health and the conveniences of life’ – the Royal Society. Its members (fellows) would “observe the natural world, conduct experiments, discuss their outcomes, and eventually publish the results.” [2]
The street facade of the Piccadilly wing of Burlington House in London, England. Illustrated London News, 1873.
Royal Society
Early on, the Royal Society held weekly meetings where lawyers, merchants, physicians, aristocrats and landowners would get together to see weekly presentations on new discoveries followed by lively discussions. It wasn’t long before the Society began publishing those presentations, theses and experiments in a journal. Scientists across Europe were eager to participate, and early members included John Locke and Isaac Newton who published his ground-breaking work Principia Mathematica under the Royal Society’s imprimatur.
The Royal Society also welcomed members from other countries, including Antoni van Leeuwenhoek, Benjamin Franklin and William Penn.
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Thomas Penn, 1752. By Arthur Devis - Philadelphia Museum of Art, Public Domain,
Before long, the Royal Society had members in all parts of the globe, making it possible to achieve coordinated research that had never been done before. For example, back in the 1760s, no one knew how far the Earth is from the Sun – and without that measurement, astronomers also could not calculate the size of the solar system and how far stars are from the earth. There was no standard measure for that type of distance. Back in 1716 Edmond Halley, a Royal Society Fellow, “. . . alerted the scientific community to be ready for the 1761 and 1769 transits of Venus. He noted that if Venus was observed from multiple spots as it crossed the disc of the sun, you could . . . get the much sought sun-Earth distance.” [3] “Halley's idea was to observe and measure the transits from separate points, as far apart as possible, giving a wide base-line from which to use basic trigonometry to calculate the distance between Venus and the earth.”
The Royal Society took up Halley’s challenge and began an international effort to establish points throughout the Empire to take measurements of the transit of Venus. Even countries who were at war agreed to participate.[4] French astronomer Jean-Baptiste Chappe d’Auteroche undertook a grueling 3,300 trip to Siberia to take measurements there; Captain Cook sailed to Tahiti; and Charles Mason and Jeremiah Dixon were commissioned by the Royal Society in 1760 to go to the Cape of Good Hope to observe the 1761 transit from that location. In all, measurements were attempted from 120 locations around the world. Not every location could report data because observations relied on a clear day, and a cloudy sky would render all preparations futile. Additionally, there were problems with poor equipment and inexperienced observers. So another effort was planned for the 1769 transit.
This time an improvement in equipment was available. Thomas Penn, the Chief Proprietor of colonial Pennsylvania (also one of William Penn’s 17 children) purchased a transit designed by the famous London instrument maker, John Bird.
Bird, had previously developed and produced the first sextant, the device that made global ocean navigation possible. He was commissioned by the Royal Society to design a transit that was portable and accurate enough to be used as an equal altitude instrument to establish true north by timing the passage of selected stars crossing the meridian[5]. This capability also made it an extremely accurate instrument for surveying.
According to Karie Diethorn, Chief Curator, Independence National Historical Park, “You had to have a clear sky whether it is night or day”. Unfortunately, on June 3rd, 1769, it was cloudy in the Europe and UK, so the observations made with Thomas Penn’s transit meant that “the only accurate information collected in 1769 was collected by Philadelphians. . . . it really brought those scientists here in America up to the notice of the rest of the Western world.”
Interestingly, the same transit used in Philadelphia to track the transit of Venus was later used by Mason and Dixon. Thomas Penn, who had been granted the province of West Jersey (now Pennsylvania) by the King, and Charles Calvert, Baron Baltimore, proprietor of Maryland, hired Mason and Dixon to plot out the border between Maryland and Pennsylvania, now known as the Mason - Dixon line. In the scramble to profit from royal land grants, it had become essential to establish accurate borders between provinces to avoid conflict. The Mason-Dixon line is noted for it’s accuracy and for the hardiness of the surveyors who lugged it across 233 miles of wilderness.
Thank you!
Berntsen would like to thank Karie Diethorn, Chief Curator, Independence National Historical Park, Al Cavalari, a NPS Volunteer and Chris Lantelme, Surveyor, for making this blog possible. Their suggestions and insights really brought history to life.
Berntsen is proud to have served surveyors for more than 50 years. We provide durable equipment and excellent customer service focused on supporting surveyors as they continue to build this great country.
Below is some information for those who are interested in delving into the math of the Transit of Venus.
Parallax method as described by Dr. Sten Odenwald (NASA / ADNET) in his blog post
Technology Through Time: Issue #75 The Mathematics of the Transit of Venus
Figure 1. The four contacts for a transit of Venus. From left to right are contacts I, II, III and IV
“The idea proposed by Scottish astronomer James Gregory in 1663 was to use the next transit of Venus to measure the distance to Venus, and then perform just this simple calculation. In 1691, following a transit of Mercury, Sir Edmund Halley showed in great detail just how this could be done for Venus, and so began the quest for the distance to Venus using the transits. But just how would this be done?
According to 'Halleys Method', first you needed observers located at great distances from one another on the part of Earth facing the sun at the exact time of the transit. Each party would carefully measure the time that the disk of Venus 'touched' the sun on one edge of the sun disk, and exited the sun on the opposite limb of the sun. This pair of events was actually four separate events called contacts. Each of these had to be timed to split-second accuracy between these far-flung stations on Earth. [Figure 1]
Once the exact contact times were determined, an elaborate mathematical calculation was performed to determine the path of Venus across the sun on specific chords, and the shift between these chords that would indicate a parallax shift. Because the stations were located at different geographic coordinates (longitude and latitude), corrections had to be made for the slight difference in contact times due to the East-West station differences in longitude.
The three most difficult challenges required that the observers had to coordinate their clocks across many different time zones, have clear enough weather to observe the whole transit from their location, and to be able to see exactly when the disk of Venus made its four Contacts even though the atmosphere was unstable, and even Venus had a fuzzy appearance with its own atmospheric distortions. Errors in any of these measurements or corrections would easily add up to thousands of miles of error in determining the distance to Venus and so the distance from Earth to the sun.
Time
Figure 2. Structure of a parallel chord: parallel chords on a circle. These could represent two paths for Venus across the sun along path AB and PQ, representing oversavtion made at two different locations on Earth.
It was entirely no good to use the local times at the different observatories to 'time' an astronomical event. Instead, everyone agreed to convert their local times to 'Greenwich Mean Time' (GMT or 'Zulu Time'). This was the official, scientific time that a clock at the Greenwich Observatory in England kept. It was also the time used by Mariners to navigate across the longitudes. (We now call it Coordinated Universal Time or UTC because it is based on an atomic clock, not the old-style pendulum clock!)
Today, with all the air traveling we do, most of us are familiar with 'time zones', and how to adjust your watches so that you are keeping the right time in the places you are visiting. Astronomers do this backwards. They take the local time of their observatory (say 3:00 p.m. Eastern Standard Time), and convert it to 'GMT' by adding the appropriate number of hours (3:00 p.m EST is 8:00 p.m. GMT or 20:00 Universal Time)
The transit of Venus has four 'Contact' times that accurately defined the particular chord that the planet takes across the disk of the sun. You only actually need two points to define the chord, but four measurements along the chord improve your accuracy in placing the path taken by Venus exactly on the right chord!
Once you have accurately measured what chord was observed by a single station, you then have to compare this with all the other chords, and partial chords, measured by other astronomers, allowing for many geometric changes in perspective and timing.
Generally, observers that are located at the same longitude on Earth but at different latitudes will mostly see a shift in the path of Venus across the sun that is perpendicular to each transit chord. One observer would see a chord, say AB, and the other would see the chord CD, with AB parallel to CD but shifted slightly along the perpendicular line between both chords. How do we interpret the different transit chords? For this we need to understand how parallax works!
Parallax
Figure 3. The basic geometry of triangulation.
In ordinary land surveying, the disk of Venus in the above sketch might actually be a distant mountain peak and two observers are located at 'A' and 'B' separated by a few miles. The base angles at A and B will be measured with a theodolite, and knowing the base distance from A to B, the distance to the peak can be worked out with a simple scaled drawing or with trigonometry. To find the distance to a planet or other astronomical object, instead of measuring the base angles A and B, you measure the vertex angle instead. For the transit of Venus, observers on the Earth at A and B will be separated by thousands of miles. The disk of Venus projected onto the disk of the sun will appear at slightly different locations. By measuring the angle shift between the two spots on the sun, you can determine the vertex angle, and from the baseline distance A to B, determine the distance to Venus. In practice, however, this is an extremely difficult measurement to make because the disk of Venus is so small (1/60 of a degree) and the parallax angles are very difficult to measure directly (1/120 of a degree!). This is why astronomers have used the entire path of Venus across the disk of the sun as a better means of determining the parallax angle.
To see the whole blog post by Dr. Sten Odenwald go to: Transit of Venus Articles