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Before the ink on his chart had barely dried, the Admiralty dispatched Halley on yet another mission. This one was not just for the sake of science. It involved the main artery of the English realm.

In the spring of 1701, Halley set out once again in the Paramore. He was to chart the tides and other vagaries of the English Channel, and in the furtive role of spy he was also to survey assets near French ports on the south side of the channel, which the French call “La Manche.”

Once again Halley had drawn up his own orders and leveraged the monarchy to support another scientific voyage:

What made tides ebb and flow had been pondered by such figures as Leonardo da Vinci. The 15th- and 16th-century Renaissance man realized that the tides were linked to the Moon but had no inkling as to how. A century later Galileo, too, would take a stab at the problem with no more success.

On the open sea, the effects of tides are negligible. But close to land, tides and currents are key for navigating or for winning naval engagements. By Halley’s day, so much shipping passed through the English Channel that any improvement in its navigation would have reaped big rewards.

Although many great philosophers of the day did not fail to recognize the Moon’s involvement, they, like da Vinci and Galileo before them, had little understanding of how or why. To find answers to this quandary, the leading minds sought to collect as much data as possible and then see what hypotheses might develop. Tides had been explained theoretically only shortly before Halley’s voyage with the publication of Newton’s Principia. Newton had solved the leading part of the mystery revealing how the Moon’s gravity was implicated. As Newton’s notions of gravity were yet to be widely applied, Halley significantly contributed to the dialogue on how the Moon influences tides as well as the Principia’s practical use.

Before the third voyage Halley had apparently once again subtly tried to ditch the Paramore for a better ship:

But his desire to complete the mission during the summer overtook such fancy. Three days later on April 26, 1701, Halley requested that he depart immediately “in order to get the Paramour Pink manned with such complement as their Lordships shall think fitting.” The Admiralty outfitted him with a pair of small boats, two extra cables, an additional anchor, and guns, as Halley specified, from the Tower of London, which housed the monarchy’s chief armory.

The Paramore wouldn’t sail until early June, however, because Halley had trouble manning his pink despite the favorable terms then offered by the Navy. Perhaps they could sense the danger of the spy component. Or it could have merely been the pay and labor. At the time of his third mission, the royal bounty for able seamen was 30 shillings and 25 shillings for ordinary seamen. Even combined with regular wages, this compensation wasn’t competitive with that of private merchants.

Richard Pinfold was the only crew member besides Halley who signed up and sailed on all three voyages. Pinfold was promoted from a captain’s servant to a captain’s clerke for the third trek, according to the wages book. They set sail without a full crew, short a few hands. On the way down the Thames from Deptford, Halley eventually procured four men from Rear Admiral Munden, whose 60-gun Plymouth was then in the Downs.

The tidal survey presented different challenges for Halley’s crew than his seagoing missions. The physical work was just as arduous but in different ways. Perpetually weighing and anchoring is extremely labor intensive, as is rowing a pinnace in circles to chase a tide. The ship still needed to be cleaned but not overhauled like at sea. Day-to-day dangers were not as great, as the shoreline was usually within sight. And they started exclusively on the friendly English side.

Daily, Halley recorded high and low water, the set and strength of

the flood and tides, and stages of the Moon. He noted in particular any anomalies in the flow, including half tides. He collected data on the “sand, shoals, depths of water, and anchorage” as well as the tidal flow and currents.

A month into the voyage, Halley once again crossed paths with Sir Clowdisley Shovell at Spithead, this time without incident. Shovell, who had overseen Halley’s court-martial proceeding in London and still sported his favorite emerald ring on his finger, was then captaining a flagship called the Triumph.

It was not long before Halley decided to attempt a foray on the French side of the channel. On July 11 the Paramore had reached Aldernay, one of the small channel islands off the coast of Britanny. His log of the third voyage details a typical day:

Everything went well. The next day back in Jersey on English soil Halley would acquire a 24th man, a pilot named Peter St. Croix. (He never filled the 25th spot authorized by the Lords.)

Like many a seaman, Halley harbored a long-standing interest in tides. In the summer of 1678, a Mr. Francis Davenport sent a letter to the secretary of the Royal Society. The letter detailed mysterious tides at the port of Batsha in the Gulf of Tonkin in southeastern China that ebbed and flowed typically only once a day.

Davenport observed the tides mainly to help large East Indiamen secure passage across the river at the bar. He surmised that the irregular tides might be attributed to a sandbank as well as assorted inlets in Tonkin bay. The tides were especially erratic during the monsoon season. He supposed that the combination of seasonal changes in the Moon’s motion and the monsoons caused the seeming randomness of the tides. He also enclosed a thorough data set of times, dates, and variation of the tides.

As a newly appointed Royal Society fellow, Halley jumped on the problem of the Tonkin tides. He identified a complex pattern behind the phenomenon and recognized that the daily high tide resulted from the rising Moon during the first half of the month and the setting Moon during the other half. He ruled out the monsoons as a factor and instead hypothesized that the bay of Tonkin’s tidal range was proportional to the position of the Moon with respect to where the Sun’s path crosses the celestial equator.

In his paper, which was published in 1684 and formally established the Moon’s influence with an equation, Halley modestly commented on how little the world knew of tides, including those off British shores “of which we have had so long experience.” But the completion of Newton’s Principia would change such perspectives. Newton had realized that to strengthen his masterpiece he needed to add a general theory of the Moon’s motion, which would contribute to explaining the mystery of the tides.

Flamsteed, who viewed himself as the authority on tidal prediction, was displeased with Halley and Newton’s endeavors on the subject, but he gave Newton his data on lunar motion albeit grudgingly. Many believe it was Flamsteed and Halley’s discourse over tides that led to the rift between the two astronomers.

Flamsteed had published charts on the tides at London. The then royal astronomer wrote that “there is every where about England, the same difference betwixt the spring [high] and neap [low] tides that is here observed in the river Thames.” However, he was wrong. And

Halley was quick to note that. The tides in a river are not necessarily related to tides at coastal ports, he asserted. “But it is hence found that the said tables are not applicable to sea ports, where there is not the same reason for anticipation of the neap tides upon the quarter moons.” Not to mention that in the big picture, tides in shallow seas and estuaries are more complicated than those in the open ocean.

Deftly sidestepping Flamsteed’s jealousy, Halley went ahead and summarized tidal theory as explained by Newton’s laws and presented the work to King James II, who was also known for his seamanship, along with a copy of Newton’s Principia. Halley’s explanation was intended for readers curious about tidal phenomena but not up to the task of understanding the high-level math entailed in Newton’s treatise. Halley’s contribution was soon added to the key manuals used to teach the art of navigation to seamen.

In Book III, the final book, of his Principia, Newton explained the anomalous tides in the port of Batsha in the Gulf of Tonkin, a feat Halley had previously believed impossible. “The whole appearance of these strange Tides, is without any forcing naturally deduced from these Principles, and is a great Argument of the certainty of the whole Theory,” Halley exclaimed. It was Newton’s attention to the tides that expedited the general acceptance of his theory of universal gravitation, most scholars contend.

Exposing his talent for science exposition, Halley wrote: “… being sensible of the little leisure which care of the Public leaves to Princes, I believed it necessary to present with the Book a short Extract of Solution of the Cause of the Tides in the Ocean. A thing frequently attempted but till now without success. Whereby Your Majesty may judge of the rest of the Performances of the Author.” In this way it was Halley, who after Newton was the person most familiar with his Principia, who made the work directly accessible to those who weren’t up to speed with Newton’s mathematics.

In his letter presenting the polished Principia to James II, Halley summarized Newton’s concept of gravity and how it regulated the motion of planets, comets, and the Moon. According to Halley,

Newton attributed the tides to the “decrease of gravity from the contrary attraction of the Sun and Moon, whereby the water being less pressed rises where they are vertical, and subsides when they are in the horizon.”

In simpler terms, the way the Moon pulls various portions of the Earth differs. If Earth is viewed as a crust completely covered by water, the Moon pulls on the layer of water as it orbits Earth. The Moon pulls on the oceans on the side of Earth facing it more strongly than the remainder of the planet, because they are closest to it, causing the water to bulge toward the Moon—or a high tide. Meanwhile on the opposite side of Earth, the crust is closer to the Moon than the ocean. The Moon pulls the crust away from the deep oceans also inducing a high tide on the far side. As Earth rotates on its axis, each location on Earth will experience both tidal bulges. The areas of high water levels are high tides, and the areas of low levels are low tides.

But the dynamics are further complicated by the Sun. While the Moon orbits Earth, the duo, together, also orbit the Sun. When the Sun and the Moon line up, their gravitational forces combine to cause very high and very low tides, which are called spring tides. When the Sun and the Moon are out of kilter, the gravitational forces cancel each other out, causing neap tides, which are not as markedly high and low. Newton’s Principia went on to elucidate why tides vary from day to day as well as place to place with latitude, as gravitational effects shift with the constantly changing interactions between Earth, the Moon, and the Sun.

Halley also explained to the king in greater detail Newton’s explanation of the strange tides at Tonkin, where only one tide occurs each day. The second tide is effectively cancelled because two tidal streams run from the South China Sea into the Gulf of Tonkin. They are out of phase with each other by six hours due to geographical obstacles in one of the streams.

Newton properly credited Flamsteed with supplying the lunar observations that made the later edition of the Principia possible: “All the world knows that I make no observations myself,” he wrote in a

February 1695 letter thanking Flamsteed. Apparently Newton was in Halley’s camp on the issue of sharing scientific data.

Before Halley’s sea adventures, Newton also helped him develop his theory of the secular acceleration of the Moon, which said that the satellite actually increases its velocity with respect to Earth. According to the Royal Society Journal Book, Newton had surmised “that the bulk of the Earth did grow and increase … by the perpetual accession of new particles attracted out of the ether by its gravitating power,” and Halley proposed that “this increase of the moles of the Earth would occasion an acceleration of the Moon’s motion, she being at this time attracted by a stronger [centripetal force] than in remote ages.” Halley demonstrated this phenomenon by matching up predicted times of ancient eclipses of the Moon with recorded ones.

Shortly thereafter, in 1697, Halley lectured the Royal Society on the propagation of tides near the British Isles. And he published his later tidal paper in the Philosophical Transactions.

At the time of this third voyage, tensions with Spain were mounting. The part of Halley’s mission that entailed intelligence collection on the English Channel was a well-guarded secret. Martin Folkes, who would assume the presidency of the Royal Society in 1741, for one, asserted that Halley’s channel survey was merely a cover for his clandestine mission. Halley was dispatched to gather intelligence about the defensive strength of the French near channel ports.

What’s more, to Halley’s original instructions the Admiralty added the following warning about taking liberties in publishing any data he gathered while on the mission: “And in case during your being employed on the Service, any other Matters may Occur unto you the observing and Publishing whereof may tend towards the Security of the Navigation of the Subjects of his Majesty or other Princes trading into the Channel you are to be very careful in taking notice thereof.”

Unlike Newton, Halley had few reservations about applying sci-

ence to improve military capabilities. In fact, Halley had become an expert in many aspects of weaponry and combat.

Another early practical application of Newton’s gravity work was determining the variable rainbow arc of a cannonball or other projectile to make it more deadly accurate. In 1686 Halley coauthored a paper on gunnery. It was titled “A Discourse Concerning Gravity, and Its Properties, Wherein the Descent of Heavy Bodies, and the Motions of Projects [projectiles] Is Briefly, but Fully Handled; Together with the Solution of a Problem of Great Use in Gunnery.”

The trajectory problem was a long-standing one that required Newton’s calculus to be properly solved. Halley calculated how a projectile should travel through the air under Newton’s new theory of gravity. He demonstrated how to set up a mortar to hit a given target no matter its starting point by fiddling with its elevation. Halley also recognized the value of developing standard mortars, ejectable bombs, and gunpowder charges to increase targeting accuracy.

Five years later he also authored an unpublished paper on how high bullets should be shot to reach their intended targets. In some of his other papers he wrote on such practical topics as how to balance the weight of guns on a ship’s deck to minimize strain on the hull.

As Halley continued the channel survey, whenever he went into port whether for provisions or due to inclement weather, he and his crew would hear rumors that war was indeed on the horizon. But he refused to let stormy skies of either persuasion interfere with his mission. Halley’s third voyage may have been short on exotic glamour compared to his first and second voyages, but it would bear practical fruits for channel travelers.

In a letter dated September 13, Halley wrote to Burchett reporting the success of his mission. He knew the Admiralty would be pleased with his coastal survey and his tidal observations. What is more, he mentioned that he may have discovered some general principles along with his useful findings.

On Halley’s return to London in mid-October, the Paramore was

laid up at Deptford and her wages paid off. Halley’s surgeon William Erles received about 24 pounds and his boatswain Richard Price roughly half that or 12 pounds. Able men were paid six pounds apiece for more than a five-month-long mission. Payment of the bulk of Halley’s 142-pound salary ($143,000 in U.S. currency today) was deferred. He received a mere three shillings at the payoff.

In wages the total amount doled out for all three of Halley’s voyages barely exceeded 1,000 pounds ($1 million in 2005). The figure includes compensation of all three crews—roughly 100 men—for their respective duty periods.

By now Halley had become something of a celebrity, an English darling with his popularity soaring. Queen Anne, perhaps impressed by his poem to her, gave him a bonus of 200 pounds on top of his wages “for his extraordinary pains and care he lately took” in surveying the tides and the channel. His resulting chart, “A New and Correct Chart of the Channel Between England and France … with the Flowing of the Tides and the Setting of the Current,” represented another precedent. It is considered the first true tidal chart.

Once again, Halley was thinking ahead of his time. No one would conduct a similar survey for a century or publish a tidal chart for another large body of water for 150 years. His chart would be widely used by mariners throughout the 18th century. Along with detailing the shoals, anchorages, depths, and coastlines like other maps of the day, Halley’s map offered two key improvements.

The first was a formula for estimating the height of water in the channel at specific sites according to the Moon’s position. They are demarked by Roman numerals on the map. The second was a new method for surveying the coast (see Appendix). Called the resection method, it relied on fixing horizontal angles by the Sun to achieve greater accuracy than the conventional practice of using a magnetic compass. “This is a very easy and expeditious way for putting down the soundings in Sea Charts in their proper places, and may be practiced in a ship under sail,” Halley advised.

Nothing is known of the results of the spy mission. No records survive. Either Halley failed to collect anything of value or he succeeded brilliantly in keeping all of it secret.

Halley was due to get his land legs back and return to the ranks of civilian life. He set about publishing the comet work, which he had undertaken a decade earlier, before more important matters with the Paramore interrupted him.