Isaac Newton: The Last Sorcerer. Michael White

gravitation, at this stage (1666) merely illustrate his contention that planets experience a receding force from the Sun governed by an inverse square relationship. It was only later that Newton was able to equate this receding force with a force pulling planets towards the Sun and to realise that this pulling force is also governed by the same inverse square law.

      Yet the thought that there existed an equal and opposite force which countered the receding force could not have been far from his thoughts – not least because of the familiar example of the stone on a string. And indeed, later in life, Newton dated his realisation of a force of gravity (the force pulling a planet towards the Sun) also acting by the inverse square law to the same time as he had conceived how the receding force could be calculated.

      Just before he died, Newton wrote of the dawning of the idea in a letter to the Huguenot scholar Pierre Des Maizeaux:

      I began to think of gravity extending to the orb of the Moon & having found out how to estimate the force with which a globe revolving within a sphere presses the surface of the sphere from Kepler’s rule of the periodical times of the planets being in sesquialterate [3:2] proportion of their distances from the centres of their orbs, I deduced the forces which keep the planets in their orbs must be reciprocally as the squares of their distances from the centres about which they revolve.¹⁷

      It is implicit here that the notion of an inward pulling force was in place at the time when he elucidated the magnitude of the receding force, but there is some debate about when this step really was made. There was a series of calculations made both on the lease document and in other documents written in Latin and almost certainly composed no earlier than 1667. (We know this because Newton never wrote in Latin before his return to Cambridge in 1667.) Together, these documents show a step-by-step development of the idea of both forces operating by the inverse square law. What is certain is that it was sometime before 1667 when Newton applied his method of determining the receding force to the case of the Moon’s passage around the Earth.

      The calculation was actually a very simple one. In order to work out the strength of the receding force of the Moon by his newly devised method, Newton needed to know the period of one revolution of the satellite. This was readily available from the work of contemporary astronomers: 27 days 8 hours. He also needed to know the distance between the Moon and the Earth, and the best estimate for this at the time was that the distance to the Moon was sixty times the Earth’s radius. Unfortunately, however, the best figure then known for the radius of the Earth, based upon a figure calculated by Galileo, was inaccurate – 3,500 miles (over 400 miles too small). Consequently, the figure Newton obtained for the receding force experienced by the Moon was incorrect and did not demonstrate the inverse square relationship accurately.

      Disheartened and exhausted by the effort, Newton abandoned the idea for several years, concluding that he had oversimplified the matter and that there must be some other force, perhaps related to Descartes’s vortex theory, that could explain planetary dynamics – something he had overlooked. It was not until 1685, when he was preparing the Principia, that he finally used a more accurate figure for the Earth’s radius (found by a Frenchman, Jean Picard, some years earlier) and consequently found that the inverse square relationship worked perfectly.

      It is clear from this succession of calculations alone that Newton did not realise the entire theory of gravity in one flash of inspiration. The Woolsthorpe years provided a foundation, both conceptual and mathematical, upon which during the following twenty years he constructed a detailed theory based on both alchemical knowledge and experimental verification. (See Chapters 7 and 9.) All of these elements were essential. If the mathematics had not been developed during the 1660s, Newton’s intuitive grasp of the nature of planetary motion would have remained little more than a good idea. Without his in-depth knowledge of alchemy (which he practised during the 1670s and ’80s), he would almost certainly never have expanded the limited notion of planetary motion as he saw it in 1665/6 into the grand concepts of universal gravitation, of attraction and repulsion, and of action at a distance. Finally, if the experimental evidence had not been gathered, then Newton’s theories, even if substantiated by mathematics, would not have carried the weight they did in his Principia, nor would they have so readily inspired the practical application of mechanics and the laws of motion which led, a century later, to the Industrial Revolution.

      In March 1666 Newton returned to Cambridge briefly, but by June the plague again threatened and he was forced to return to Woolsthorpe. During the summer of that year he decided the time was right for him to claim officially his right to gentleman status, and he attended the Herald’s visitation at Grantham, making the process legal. For the first time he wrote, ‘Isaack Newton of Wolstropp. Gentleman, age 23.’¹⁸

      Although this may have seemed premature, Newton’s credentials were quite sound. Certainly, his father could not have taken the title of gentleman, but Isaac junior was not only related to the lower gentry, via the Ayscoughs on his mother’s side, he was also in line for a substantial inheritance upon Hannah’s death. Above all, he was a scholar – a graduate of Trinity College, Cambridge.

      Little is known of this second period in Woolsthorpe, between June 1666 and March the following year. He probably divided his time between studying at home and visiting Babington (who lived close by) and the Clarks in Grantham. It would be fair to assume that Hannah still harboured hopes that his stay would be permanent. But, though Newton could still work efficiently in Woolsthorpe, the rural lifestyle had never suited him and he would have had no intention of remaining away from the university any longer than caution dictated. And by the summer of 1666 one of the factors enabling his return to Cambridge was about to make its mark on history. More than 100 miles away, in London, the Great Fire was about to eradicate the last vestiges of the plague from the capital, and the disease soon began to recede elsewhere.

      The university reopened in early 1667 and Newton was able to return to Cambridge and to begin the struggle to obtain both his Master of Arts degree and a guarantee for a future at Trinity – the all-important fellowship.

      If fellowships were awarded according to merit, then by any measure Newton would have been worthy of one; but they were not. Indeed, his scientific achievements, even if known to the college authorities, would have had little influence. His success depended more upon available vacancies within the hierarchy and knowing the right people.

      The acquisition of a fellowship was of the utmost importance to Newton. Without it, he would have been unable to continue at Cambridge and would perhaps have been forced into obscurity as a farmer or encouraged to accept a rectorship in some isolated rural spot. He had not shone academically, and had not been ‘a face’ around college; nor was he very wealthy. His tutor, Benjamin Pulleyn, had been helpful in securing the first stage of his pupil’s academic ascent and had probably introduced him to Barrow; but, although the Lucasian Professor proved imperative to Newton’s later success, he could provide little help in 1667. Again Newton made use of his association with Humphrey Babington, who in 1667 had been promoted to senior fellow – one of eight men who answered directly to the Master and selected new fellows and minor fellows. But, even with Babington’s help, Newton might still have foundered if it had not been for a series of serendipitous events. Because of the plague, there had been no fellowship elections during 1665 and 1666. Even so, when Newton returned to Trinity in early 1667 there were only nine positions to be filled from a total complement of some sixty academics.

      By chance, that year the number of vacancies had been inflated by several retirements and a death occasioned by events which vividly convey the atmosphere of Restoration Trinity. A senior fellow had been recently removed on the grounds of ‘mental aberration’ of some unknown variety, and two other fellows had been forced to retire through injuries sustained after falling down the staircase leading to their rooms while in a drunken stupor. A fourth, the poet Abraham Cowley, had died after catching a fever brought on by a night spent sleeping in a field after a bout of heavy drinking. Luckily for Newton, this created a lengthy enough list to give him an opening.

      After