Department of
Science & Technology Studies
University College London

Nicholas Kollerstrom's
Horrocks and the
Dawn of British Astronomy  

A written tradition of British astronomy began with a specific person: Jeremiah Horrocks -- even though he lived for a mere 22 years (1618-1641). He lived in a village near present-day Liverpool, and his colleague William Crabtree lived near Manchester. The latter subsequently was killed in the Civil War. The group that formed around them were Britain's first Keplarians, 'nos Keplari' as they called themselves, and were distinguished as being the first people to gain a realistic notion of the solar system's size.

Crabtree witnessing the Transit of Venus, 1639

Venus Transits the Sun

Horrocks witnessed the first-ever-seen transit of Venus across the Sun in 1639,  whereby he concluded that the 'solar parallax' was 14 arcseconds. Thereby, a huge size of the solar system was implied. Kepler had put this as one arcminute, while the true value is 10". Solar parallax is the angle which the radius of the Earth makes, as seen from the Sun. When in 1662 the Dutch astronomer Helvetius published some material by Horrocks (Venus in Sole Visa), he scaled up this solar-parallax figure to 40", as he could not credit the scale of the solar system implied by Horrocks's figure.

At the Venus-transit, Venus was 1' 3" in diameter (Kollerstrom 1991), exactly what William Crabtree found it to be. Horrocks measured it at 1' 24". Horrocks described his friend Crabtree as 'a man who has few superiors in mathematical learning' and described how awestruck Crabtree had been on perceiving the little disc of Venus moving against the face of the Sun: 'rapt in contemplation he stood, motionless, scarce trusting his senses through excess of joy.'

Figure 1Size of the Solar System

Kepler's solar system was about seven times too small, though his lunar distance was more or less correct. His third law concerned the proportional distances of the planets, not their actual distances. The north-country group of astronomers came to appreciate the real dimensions of the solar system. Horrocks put the Sun at 15,000 earth-radii (60,000 miles) away, from his solar-parallax value, arguing that the solar system was ten times larger than traditionally believed (Venus in Sole Visa, p.202).

After his death, Horrock's books on astronomy in his library were found to be all from abroad, as there were no British books on the subject. In his volume of Lansberg's Tabulae Motuum which Horrocks autographed in 1635, he listed twenty-four European astronomical authors whose works he had read, with no English authors except for the mediaeval Anglo-Irish Sacrobosco. Details of his life are indeed scant, but Chapman has conjectured that Horrocks may have been a schoolmaster, who intended to become ordained when old enough. The year of his birth is uncertain, but Chapman has inferred it to be 1619, from the statement made by the mathematician John Wallis, who published his works, that Horrocks died at twenty-two years of age (Chapman, 1990).

A New Lunar Theory
The lunar theory evolved by Horrocks was viewed by John Flamsteed as, '...questionless the finest of his monuments.'. He developed it between January 1637 and December 1638, when Horrocks was just twenty years old, in which period he was studying at Emmanuel college, Cambridge. The diagram (figure 1) depicts its eight-stage sequence. This extends over thirteen months, the period the Sun takes to go around the ecliptic with respect to the lunar apse. The vertical line in the diagram has the Sun conjunct the apse line, at maximum eccentricity of the lunar orbit and zero displacement of the apse line from its mean value. The apse line revolves once per nine years or forty degrees per annum which motion is not shown on this diagram, its movements being with respect to an immobile mean-apse. The eccentricity E, a variable distance, has been inscribed, not upon the mean apse but upon the equated apse line AP.

Newton's TMM of 1702 'embodies a developed version of Jeremiah Horrocks' lunar theory, what one might call Newton's interpretation of Halley's variation of Flamsteed's version of Crabtree's account of Horrock's lunar theory'. (Kollerstrom 1995, see bibliography) The theory was first coherently formulated in a letter of William Crabtree of 1642. The historian Eric Forbes wrote that:  'Horrox had left no description of the theory itself, but Crabtree was helped in his reconstruction by rough diagrams drawn on loose papers.' (Forbes, 1975, p.63). This is incorrect, as there is at Cambridge University Library a 'Philosophical notebook' used by Horrocks, whose last few pages describe that theory. Curtis Wilson is the only historian of science to have noted this, indicating the rather minimal interest in the subject. The main bulk of this notebook is concerned to find the date (and time) when the world began. (He believed that the planets would then all have been at their apogee positions.) From 1636, Horrocks and Crabtree regularly measured the solar diameter and noted its seasonal changes, to provide evidence supporting Kepler's first law. The Yorkshire astronomer William Gascoigne invented a telescopic eyepiece, around 1640. Flamsteed grew up in Derby ( a similar latitude to Grantham where Newton grew up) and then brought South the Horroxian manuscripts.

See Betty M.Davis, 'The Astronomical work of Jeremiah Horrocks' UCL MSc thesis, 1967.

For a recent study, see

The contents of this page remain the copyrighted, intellectual property of Nicholas Kollerstrom.  Details. rev: May 1998