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Nathaniel Bowditch The Practical Navigator

July 2024
28min read

Salem’s irascible little “arithmetic sailor” made seamanship a science and left all mariners in his debt

Three items were often listed ax essential in the sea bag of every youngster who heeded the rail of blue-water ships and wandered down the long road to the nearest port: a knowledge of the Gospel, a pair of woolen socks knitted by his mother, and a book— The New American Practical Navigator . The ascending order of importance was never questioned. The Gospel might in time of peril provide confusing answers, and the socks develop holes, but the book would never fail. It would lead him anywhere on earth and bring him home safely and surely across the trackless ocean.

This was not always so.

Around the end of the eighteenth century, something like an uneasy truce existed between the townspeople of Salem, Massachusetts, and an irascible young man named Nathaniel Bowditch. He had a way with figures the like of which nobody in Salem had ever seen, and if he had stuck to his sums in the ship chandlery where he worked, he and Salem might have gotten along quite nicely. Bowditch, however, was not a man to hide his talents. He was eager, almost before anyone asked, to demonstrate his mathematical skill—often by proving how he had discovered an error in Sir Isaac Newton’s Principia Mathematica —and if the listener couldn’t follow the calculus, he was likely to be called a stupid dolt. This attitude made Bowditch few friends, but it wasn’t until he set himself squarely against the maritime dogma of the times and challenged the authority of practical men that he stirred up real opposition. Hut he also proved that he had the finest mathematical mind in America, if not the entire world. What he bequeathed to succeeding generations—his New American Practical Navigator —is proof of his genius.

Bowditch insisted that mathematics does not lie. He said that if two and two made four on land, it was equally true on a ship a thousand miles at sea. He committed the heresy of proclaiming that mariners should navigate their ships precisely by mathematics and celestial observation instead of trusting to practical experience and luck, ff they would only put their faith in the unvarying stars, so this land-bound book-keeper said, ships would reach their destinations more swiftly and safely.

The problem of determining exactly a position on the surface of the globe was one that had long baffled seafaring men. There was nothing new in Bowditch’s idea of celestial navigation. Steering by the stars had been practiced for countless centuries, but there was a vast difference between this and using them to calculate a precise position. By the late 1700’s, rough instruments and calculations had been worked out for finding one’s position on land, but it was a lengthy and laborious process, requiring a great deal of astronomy and mathematics as well as a means of knowing the exact time. Furthermore, the final results were not truly accurate.

In navigating a ship certain things were possible, ot course. Distances run could be determined by dead reckoning—that is, by measuring the miles traveled through the water and then applying this figure to known compass headings. In beating into the wind, however, where the vessel sideslipped through the water, or in sailing through unknown currents and tides, dead reckoning was liable to grave errors.

A ship’s latitude could be determined by celestial observations if the mariner was up on his mathematics and had good instruments on board. Taking altitudes on the sun and moon, and sometimes on such stars as Polaris, Sirius, or Vega, had enabled generations of pre-nineteenth century sailors to establish distances north or south of the equator.

Navigation in those days was actually a pretty rough and ready business. Such refinements as were known for establishing “fixes” were far too complicated lor the rugged seamen who walked the poop decks of merchant and navy ships of the period. Captains took their vessels out and—it they were lucky—brought them home by “seaman’s eye” and “seaman’s feel”: the smell and feel of the wind, the look of the sky, the color of the water, the characteristics of the ocean floor far beneath them. Experienced navigators could take sights on the sun and moon and, by following the selected latitude across the ocean, make a reasonably accurate landfall. Bad weather or contrary winds could complicate the navigator’s task, however, and he still had no reliable method for determining a position in longitude—his distance east or west of the prime meridian at Greenwich, England.

By 1800, the need lor more accurate navigation had become acute. The navies of the world were dividing the earth into far-reaching political and commercial empires; demands for raw materials were soaring; industry was producing surplus goods that commanded enormous profits abroad. Shipbuilders were turning out larger vessels capable of safely carrying heavier and more valuable cargoes. Time was money and power—fortunes awaited the ships that got there first with the most.

Everything was ready and waiting, except that men still did not know how to navigate properly. Voyages that should have been accomplished in weeks took months, and those that should have been completed in months sometimes took years.

In the face of this need, mariners still held to the old ways of doing things. They took the ships out on seamanship alone. Book learning and mathematics were simply not to be trusted. Many an “arithmetic sailor” in hopes of a quick passage had put his faith in paper and pencil instead of his own good sea-sense and had come to grief. Little wonder that people derided Bowditch and his talk of the infallibility of numbers.

Nathaniel Bowditch began life respectably enough. He was born in Salem in 1773, into a family whose men followed the two professions of so many New Englanders—farming and seafaring. By the time little Nat arrived, the luck of the family seemed to have run out. His mother, Mary Bowditch, was dying, and the child knew more of cold and hunger than anything else.

During the long periods that his father, Habakkuk Bowclitch, spent at sea, the boy did what he could to nurse his mother, and to keep her and his small brothers and sisters from freezing to death in the Massachusetts winters. Between voyages, when the unlucky and ineffectual father was home, things were better. Unfortunately these periods always ended too soon, owing to Habakkuk’s habit of seeking the solace of rum to help him forget the “awfule Sights he Hadde seen at sea.” When the binges were over, Habakkuk took ship again, leaving his nearly penniless family behind to shift as best it could.

Mary Bowditch died one bitter, snowy night when Nat was ten. He was apprenticed to a ship chandlerindentured until he reached twenty-one years of age—and his brothers and sisters were distributed among various relations and neighbors. Though the Bowditch men were noted for brawn, this lonely little boy simply did not grow. He remained weak, short, and spindly—and he stayed that way throughout his life. But his mental capacity made up for what he lacked in physical prowess. His temperament seems to have been choleric, but his mind was clear and, in argument, deadly as a trap. He was phenomenally impatient with his brawnier but less gifted contemporaries if he found them guilty of illogic or overstatement.

Bowditch’s first love and passion was mathematics, and his skill became apparent at a very early age. When he was fourteen somebody gave him an algebra text, and he stayed up night after night with it, completely enthralled by the beauty of its unassailable logic. Books of all kinds were available, even in the Salem of those days, and for the most part they were of very high caliber. For example, the entire library of the great Irish philosopher and scientist, Richard Kirwan, had been captured off the coast of England and brought home to nearby Beverly by a privateer. There were books in French, Latin, and Spanish, and Bowditch devoured them all, mastering each language that stood between him and the information he coveted. By 1796, when Bowditch was twenty-three, he possessed one of the most thoroughly educated minds in America.

But what was he to do in Salem, and what was Salem to do with him? One small commission came his way. The Commonwealth of Massachusetts hired him to survey his home town. This he did with great dispatch and accuracy; we read that those who were associated with him in the project admitted he was “powerful in calculation.”

Once this surveying job was finished, however, Salem seemed to hold little promise for the budding young mathematician and astronomer. Bowditch continued to work in the chandlery. At one end of the long counter he set up a kind of workshop with models of spheres, the heavens, triangles, and other tools of his “useless” profession. When he was not keeping books or arguing with the ship captains who came to buy everything from marling needles to anchor chain, he figured and calculated endlessly.

In the Salem of those days glory, romance, money, and security all came from the sea. Youngsters who could, manned the ships. Those with the knack of command and a quick Yankee eye for profits rose to be captains, often in their teens, and made fortunes for themselves and their owners. The weaklings, like Bowditch, stayed home and did the chores. They kept the books, made out the endless manifests, calculated the profits and losses.

To compound the hopelessness of his position and to make his misery even more acute, Bowditch had fallen in love—with a Salem girl named Elizabeth Boardman, the daughter of a shipmaster who had been lost at sea. She not only returned his love but seems also to have understood him completely. She believed in him and stood up for him and his “nonsense” in the face of the entire seafaring community. Unfortunately, then as now, marriage required money, and Nat could scarcely support himself. The sea—the only source of income that he knew of—was denied him.

At this bleak moment there appeared an old boyhood friend, Captain Henry Prince. Slightly older than Bowditch, he had gone to sea at an early age and had been a shipmaster lor many years. Prince seems to have been a very good friend, and what was more important, was inclined to believe in the possibility of accurate navigation by the stars. He had sense enough to know that il what Bowditch said was true, then passages could be accomplished in half or onethird the usual times with a corresponding increase in profits. Known as one of Salem’s shrewdest, most daring and capable captains, Prince was already moderately wealthy, had his eye on a fine white house in Salem, and looked forward to retirement.

He had just been given command of the Henry , owned by Elias Hasket Derby [ see “To the Farthest Port of the Rich East,” AMERICAN HERITAGE , February 1955], wno engaged Prince to take her on a coffee trading voyage to the isle of Bourbon (now Réunion), in the Indian Ocean. Bowditch persuaded Prince to sign him as second mate and clerk and also to let him take along a lew pairs of shoes lor profitable trade on his own account—an “adventure” it was called in those days.

There probably has never been a more maladroit seaman than the clerk of the Henry . To cap his lack of experience and natural ineptitude, he was also inclined to seasickness, a blow to his dignity. He knew that few captains, even old friends, could afford a hand who did nothing but keep books, and pride drove him very hard, it is recorded that lie finally became a sort of “assistant” to the helmsman!

There was, however, one consolation: Prince encouraged Bowditch to experiment as much as he liked with pencil and slate. We can imagine the excitement and joy he must have had at this opportunity to verify his theories. Near shore or in dangerous waters, the Henry no doubt was navigated by the usual methods, for in spite of Prince’s desire to know if there really was anything to this business of mathematical navigation, he was too fine a seaman to take undue risks with his ship. But in the long reaches of the open sea, Bowditch had his chance. As far as he was concerned, the trip was a complete success, and Prince could not help but agree. The Henry made a phenomenally fast voyage and the reason was apparent: she had been sailed across the ocean in a straight line .

In Bowditch’s struggle to perfect his methods, the big obstacle was the determination of longitude when out of sight of land. This, in somewhat oversimplified terms, is arrived at today by calculations relying on the difference between the observed local time at the ship’s meridian and the known time at the same moment at the prime meridian in Greenwich. By expressing these degrees of arc, or time difference, in nautical miles, the ship’s exact position east or west of the prime meridian is established.

For centuries, accurate determination of a position in longitude was so vital that many maritime countries, starting with Spain in 1598 and including Portugal, Venice, France, and England, offered very substantial rewards for a solution.

It seems simple enough. You build a good watch, set it to Greenwich time when you leave port, and thus carry the time of the prime meridian with you wherever you go. The trouble was that none of the clocks or watches available in Bowditch’s day could come anywhere near the accuracy demanded; in a tossing ship at sea they could not be depended upon at all.

Great Britain had long since established a permanent Board of Longitude to examine all solutions advanced, and for decades had offered the sum of £20,000—an astounding reward for those days—to the man who could invent a reliable clock. It finally went, in 1773, to Joseph Harrison, before Bowditch. But it wasn’t very practical for many years to come.

Work continued toward developing a practical and dependable chronometer, but meanwhile eminent astronomers and experimenters devoted much effort to finding a way of telling Greenwich time at sea independent of mechanical timepieces. These ranged all the way from the outright use of black magic to improbable schemes involving the orbits of the satellites of Jupiter, or the occultation by the earth’s moon of certain stars. None of them worked.

Bowditch, however, turned the trick on the voyage of the Henry . The high point for him is very simply recorded in his journal: “… Thursday thought of a method of making a lunar observation.” And indeed he had. By means of three simultaneous observations on the moon and a fixed star (or the sun) he was able to calculate the angular distance between them and from this look up the Greenwich time in the Nautical Almanac , a work published annually by the Commissioners of Longitude in London.

Bowditch himself modestly writes in the preface to the first edition of the New American Practical Navigator : “A new method of working a Lunar Observation is given in this work … it was invented by the author … and taught by him to a number of persons in 1796 … he not having seen any method possessing the peculiar advantages of uniformity in applying the corrections …” It was a major achievement. For the first time in history men could accurately establish positions east or west of the prime meridian.•

… In passing it should be mentioned that around 1800 a reliable ship’s chronometer was finally developed. It was a fantastically expensive and complicated mechanism, however, and many years were to pass before it came into general use at sea. The determination of longitude by lunar sights is no longer used, as modern chronometers and more advanced concepts do the job better, but at the time Bowditch’s discovery was of enormous importance.

The Henry returned to Salem on January 11, 1796, exactly one year after she had sailed. Bowditch was to have three months ashore.

At this period, the start of the nineteenth century, Salem was engaged in a deadly struggle with Boston to become the queen city of American shipping. The Far East—the Philippines, the Indies, the whole vast Orient—was the prize, richer than any man’s imagination could conceive. Daily the ships sailed down the channel from Salem harbor, reaching farther and farther, to return one, sometimes two, sometimes three years later, deeply laden and fat with profits that in a single voyage might run as high as seven hundred per cent. The little New England town was rich in spices, silks, rare goods from the whole world. It rang at night to the boisterous shouts of celebrating seamen. The great shipowners—Elias Derby, the Crowninshield family, and others—exercised a feudal lordship over the whole village and its people.

Old Elias Derby—the same who owned the Henry —conceived a bold plan. The route of the Boston ships to the Orient was south to Cape Horn, then north and west across the Pacific. Salem ships took to the east across the Atlantic, doubled the Cape of Good Hope, and then headed north and east again into the Indies. Derby decided that he would send a ship where no ship from Salem following this route had ever gone before—clear to Manila, the fabled pearl, the trading post of the whole Orient.

He owned a big vessel called the Astrea —too large and slow for the normal trade routes, but perhaps just the thing for the long and difficult voyage to the Philippines. Derby poured money into her outfitting. Unusually heavy and lofty masts, stout rigging, spars, sails—everything was added to make the Astrea fit for the dangerous trip.

As captain, Derby selected Henry Prince, possibly because of the very fast and profitable voyage Prince had just turned in on the Henry . In any case, Derby knew that in Prince he had an exceptionally fine seaman who could be trusted to drive a ship to the very limits of her capacity and at the same time keep a sharp eye on those all-important profits.

Now, no matter what explanation Derby or anyone else might have had for the Henry ’s fast voyage, Prince knew that she had been navigated . Accordingly, he convinced Derby that Bowditch should go along on the trip to Manila, and the little mathematician was signed as supercargo. The Astrea cleared Salem on a stormy day in March, 1796.

The first leg of the voyage took them to Lisbon for water and a cargo of wine, then south for the long reach to the tip of Africa, then north to the isle of Bourbon, a last water stop for Salem ships outbound to the Indies.

With the aid of a favorable monsoon—and Bowditch’s navigation, no doubt—the ship worked her way across the Indian Ocean, through the islands, into the China Sea, and thence to Manila. By the time she had disposed of her cargo and reloaded, the monsoon wind, which shifts direction twice yearly, had changed, and was now blowing from the north. With this fair wind behind her, the Astrea cleared Manila for Salem again and after an uneventful trip arrived safely in May, 1797, having been gone about fourteen months.

During this first voyage of the Astrea to Manila, Bowditch found time to improve and simplify his method of determining longitude until he was fully satisfied that it was reliable. The problem of these lunar sights solved, one further block remained, and it was perhaps the more vexing.

The mathematics of navigation (really applied astronomy)—calculus and spherical trigonometry—were beyond the abilities of most mariners. In addition, they took much too long. If a fix were to be of any practical value to a ship, it would have to be simply and accurately made and it would have to be available soon after the sights had been taken. In spite of his impatience with minds less gifted than his own, Bowditch was fully aware of these problems. How could involved mathematical concepts be made easy?

Attempts had already been made—notably by the famous English mathematician, John Hamilton Moore—to deal with the difficulty by formulating tables for each possible reading of the altitudes above the horizon of the various navigators’ stars. This set of figures was then applied to the problem of the moment, and by means of simple formulas, plus plain addition and subtraction, the fix could be made. Once these tables were assembled, the correct solution to any problem in navigation would be available to any seaman, no matter how unlettered, as long as he could read a sextant properly and remember his sums.

In the period after the first voyage of the Astrea , Bowditch made the acquaintance of an enterprising young man named Edmund M. Blunt. Blunt was a Newburyport book publisher who had pirated and printed in America a set of Moore’s tables, which he called Moore’s Navigator . Though this book was the best thing available at the time, it was rudimentary, and from it no small part of the sailor’s mistrust for mathematical seamanship was derived.

Blunt had heard of Bowditch’s genius and begged him to find out what was wrong with the Navigator . Bowditch agreed to do what he could. To begin with, he found that Moore’s method for establishing longitude was not fully reliable. Secondly, the calculations in the tables had been done so carelessly that the book was literally a mass of errors. We read in Bowditch’s journal: “Another error in Moore’s … Eight errors in Moore’s today … Five more errors in Moore …” And so on. Eventually, Bowditch was to note the incredible total of over eight thousand mistakes. Even to revise these existing tables to the point where they could be trusted, Bowditch needed a great deal of time, another long sea voyage if possible. The opportunity was to come sooner than he anticipated.

Another necessity dictated his return to the sea. During the period ashore he had married Elizabeth Boardman. He continued to work on the Moore revisions, but he quickly found the world does not pay for effort alone. There was only one way of obtaining another financial stake, and so in August of 1798, five months after his marriage, he again sailed with Captain Prince in the Astrea , this time for Spain.

Bowditch must have kissed his bride good-by with a heavy heart and deep forebodings. Elizabeth was seriously ill with consumption. In Alicante his worst fears were realized. He received word indirectly that she had died. Bowditch had never been popular in Salem, and a plaintive entry in his journal is indicative of the humble status of this heartsick and lonely man: “… none of my friends in Salem have seen fit to notify me or give me any details of the death of my beloved wife.”

The Astrea returned to Salem in April, 1799. Bowditch turned his corrections of Moore over to Blunt, and the book was copyrighted in May of the same year. In spite of his lack of personal acceptance in Salem, and in spite of his grief over the death of his wife, there was for Bowditch one ray of light. In certain circles his genius as a mathematician was beginning to be recognized. He was elected to the American Academy of Arts and Sciences. Yet in September of 1799, when his revised edition of Moore’s Navigator appeared, the title page didn’t even mention Bowditch’s name.

While the book was on the press—in July—Bowditch again sailed with Captain Prince in the Astrea , and again for Manila. Anticipating a third edition of Moore’s , Blunt had asked Bowditch to continue his corrections, but the day before the Astrea left port, Blunt appeared on board with another idea. The moment seemed right, he said, for a whole new book on navigation. Instead of continuing to revise Moore during the voyage that lay ahead, Blunt suggested that Bowditch do a book that would be truly his own—one that would have everything in it that Moore’s lacked and that would, above all, be accurate.

Bowditch immediately agreed. He abhorred the blustering, and to him stupid, men who went to sea. Their inefficiency (by his standards), their heavy-handed intolerance and slavish acceptance of dogma enraged him. On the other hand, he loved the sea deeply and was profoundly moved by the stately grace of the great square-riggers. He was fascinated at the thought of writing a book that could guide them safely about the world by means of careful, accurate mathematics. He was delighted at the idea that something of his could enable the great ships to fulfill their inherent functional loveliness and the precise, marvelous logic that had gone into their construction.

Yet Bowditch knew that, except for the vast miscellany of information he had collected in his journals, a book of his own meant starting completely from scratch. It would take years to finish, but as the coast of America dropped astern of the Astrea , he summoned up all his enthusiasm and set to work.

Ordinarily, American ships outbound to the Orient waited for the shift in the monsoon and then headed north into the Indies with a fair wind. In steady airs, with the wind from the stern, a ship would not have to tack exceedingly, and positions could be determined accurately enough to give her a reasonable chance for survival in the maze of islands that lay ahead.

Following this procedure—waiting for favorable winds—a vessel might take as long as three years to make the round trip between Salem and Manila. But Prince and Bowditch determined to sail the Astrea by the stars alone and have her home in a year or less. Prince was well aware of the chances he was taking; nevertheless, he entrusted the navigation of his ship to the little “arithmetic sailor.” When he reached the Indian Ocean, he piled on the canvas and at once headed north into the teeth of the monsoon.

Nowadays it is almost impossible to estimate the very real dangers of such a voyage. During the Astrea ’s first trip to Manila the wind had been dead astern, blowing the ship swiftly and surely to its destination. This time it was dead ahead; tacking back and forth, the ship had to fight her way mile by mile toward Manila.

Such a voyage meant long watches when the entire crew was on deck. Time after time the anchor was let fly on the run to save them from a submerged reef or to assist them in clawing off a lee shore. On the ship struggled through unknown waters, past cannibal islands, relying on charts that were so incomplete and so filled with error as to be nearly useless. And all this in the face of the monsoon—the captain disdaining to wait for the fair wind the Good Lord himself had provided to bring simple and devout mariners safely to their destinations.

For the sailors the worst uncertainty of all, of course, was that of the ship’s position, known only to scrawny Nathaniel Bowditch, the supercargo, who could scarcely be trusted to stand a proper watch. Deeper and deeper the Astrea worked her way into the tortuous waters of the Indies. Time after time the ship was saved by the superb seamanship of Captain Prince and his crew. Nevertheless, as islands, channels, and capes kept appearing out of the mists exactly when and where Bowditch said they would, even the crew began to be impressed.

Bowditch was not content merely to navigate the ship himself. He knew that if his methods—and the book he was writing—were to be truly useful, they would have to be within the grasp of the most untutored seaman. Accordingly he undertook to teach every man in the Astrea to navigate, holding classes and drawing diagrams in chalk on the holystoned decks. The charts were explained to the men. He taught them how to use a sextant. Daily positions were worked out. He refined, sharpened, and clarified his explanations until finally every man aboard, from the cabin boy up, could establish the daily fix. Only then was Bowditch satisfied. He had already known that celestial navigation was trustworthy—he now knew that the involved astronomical concepts could be made simple enough for anyone to use, quickly and accurately.

In addition to navigating the vessel, teaching the crew, and standing his regular watch, he continued doggedly at work on the book. Besides the tables and the rest of the navigational material, he also began compiling a huge mass of related figures and information. He amended the ship’s charts. He developed and put down in precise and simple language methods for taking bearings, calculating distances, speeds, and other data vital to mariners working their vessels close to the land. He formulated exact terms and nomenclature for the construction, outfitting, and handling of ships. In short, he slowly began to compile a bible that would include everything men knew about ships and the sea.

The outward passage was finally completed. The dangerous complex of the Indies was again behind, the run up the China Sea was done, and the final “Land-ho!” rang from the masthead. The Philippines loomed dark and low on the horizon, precisely when Bowditch expected them to. Prince swiftly worked his way down the coast and a few days later quite non-chalantly let fly the anchor in the pale green waters of Manila Bay. The Astrea had completed the voyage in astounding time: six months, twenty-three days.

Her presence was unbelievable to the people of Manila. The ship claimed the impossible—a run through the Indies against the monsoon—but there was no disputing the facts as the evidence lay tranquilly swinging on her anchor in the harbor. Soon her crew, and Bowditch in particular, were local sensations—the pride of the handful of Americans living in the city. It was conceded that there was “more knowledge of navigation on board that ship than there ever was on all the vessels that ever floated in Manila Bay.” Captain Prince took pleasure in boasting that every man jack could take a lunar sight and work up a position “as well as Sir Isaac Newton himself, were he alive.””

“Captain Prince found a ready market for the goods in his floating warehouse, and soon trading was completed. The Astrea lay deep in the water, laden with sugar, pepper, indigo, and hides—commodities that would command high prices back in New England. The astonished Manilans were now due for another shock. The monsoon would shortly make its semiannual shift and would then blow steadily out of the southwest—the direction of the Astrea ’s homeward route. Any ordinary ship would have settled down to wait six months for the next shift and the necessary fair wind. But the Astrea was no ordinary ship. One fine morning the scholarly crew of mathematicians loosed the sails and weighed anchor. Disdaining the threat of the monsoon, they laid their course for Salem and home.

The return passage also was accomplished by celestial navigation and was made in record time, despite a bad leak that kept the men pumping for months on end. The vessel made her landfall on the Massachusetts coast in September, 1800, and sailed up the channel to an incredulous Salem approximately fourteen months after she had left.

If he had expected to be welcomed in triumph, Bowditch was disappointed. No triumph awaited him. Fortunately, however, he had returned from the sea with enough money to see his way clear to finishing the book, and once ashore, he kept at it. This was long before the days of mechanical calculators, and there were thousands upon thousands of complicated computations to be made for the tables. Since Bowditch was determined that his work could be trusted, he worked each set of figures three times.

Captain Prince had also retired from seafaring (at the venerable age of thirty-five). He had his fine white house in Salem, which he kept well stocked with good wines, Havana cigars, and mementos from past voyages. Relations between him and Bowditch seem to have been somewhat strained at this time; Bowditch found few reasons to visit his old friend.

In spite of the fact that this must have been one of the most trying periods of his life, it was not all lonely work. In October of 1800 he married again, this time his cousin, Mary Ingersoll, a strapping, handsome country girl who loved the solitary little mathematician with all her heart. The marriage was extremely happy, and no doubt the affection of this devoted wife helped Bowditch finish the enormous task he had set himself. Mary wanted nothing more than to see that her husband had the chance to finish his book; like poor Elizabeth before her, she had complete faith in him and in what he was trying to do.

At last the final calculation had been made and meticulously checked. The manuscript, which Bowditch called The New American Practical Navigator , was delivered to Blunt, who instantly recognized the value of what he held in his hands. Rather than try to publish it immediately in America, he took it to London—to, of all places, the publishers of Moore’s New Practical Navigator , which he had previously pirated! These people were understandably cool to Mr. Blunt and his manuscript from America, but after a careful examination of the work they also recognized its value and undertook to bring it out. The New American Practical Navigator appeared in Boston in June, 1802, simultaneously with the English edition. It offered to the unsuspecting world more accurate and useful information on ships, the sea, and all things maritime than had ever been seen before.

As much as, if not more than, Matthew Fontaine Maury, the great American chart maker and oceanographer, Nathaniel Bowditch placed all future navigators in his debt. For the first time, men could measure the heavens and in perfect faith entrust their destinies to the paths of the stars. The New American Practical Navigator was not just another navigation book. It was a tool—as important as sextant or compass.

It is impossible to examine a first edition of this book and not feel, even over this great distance of time, a thrill of pride in what Nathaniel Bowditch accomplished. Even in appearance the book is impressive. The approximately six hundred pages are beautifully bound; the text, printed on excellent paper, is still clear and legible. The copperplates and sketches are painstakingly executed, exquisite in detail. The prose is simple, precise, and to the point.

It is a vast store of information for the mariner. We find chapters on winds, currents, the obligations of an owner, the duties of a master, a dictionary of sea terms, an explanation of all possible maneuvers of square-riggers at sea and the appropriate commands for their accomplishment. There are even sections on marine insurance, bills of lading, and bills of exchange.

Mathematically the book is a treasure house. Starting with simple fractions, Bowditch takes the reader calmly and logically through decimals, geometry, algebra, logarithms, on up into the more involved trigonometry and calculus of navigation, with numerous side excursions into geography, astronomy, mensuration, gauging, surveying, and the like. There is even a section devoted to “questions to exercise the learner.”

As far as the mechanics of navigation were concerned, nothing like this work had ever been seen. It corrected existing tables and made them trustworthy once and for all. There are twenty-nine tables, and Bowditch carefully listed how each was derived. He so much improved the standard method of calculating latitude that it might be said he devised a completely new one.

In addition to hit, new method, the only truly workable one at the time, of computing longitude by lunar measurements, the book also included other procedures that were entirely Bowditch’s. His sections on coasting, piloting, and marine surveying incorporated original tables and systems relating to the distance of visibility of objects at sea, and are still in use.

Except for some interest in British naval and shipping circles, however, the book caused hardly a ripple in the maritime world. But in the realm of scholars and mathematicians, the genius of its author was recognized instantly. Bowditch was made a fellow of several scientific societies in Great Britain. At home, Harvard University offered him a degree, which he accepted, and a chair in mathematics, which he refused. But more than honors, more than degrees, more than teaching jobs, Bowditch wanted vindication and approval; he wanted his book, his methods, to be used by those for whom they were intended—the men who took ships to sea, and particularly Salem men. Yet among seafarers, old customs and ways die hard. There is nothing in the record to indicate that the New American Practical Navigator was welcomed enthusiastically by the mariners of Salem or anywhere else. What should have been for Bowditch a time of joy and satisfaction, again must have been a time of bitterness. He appears, during this period immediately after the publishing of his book, to have had no intimates, except for his family. He stayed at home in Salem, doggedly hoping against hope for a change of some kind.

During the approximately two years that elapsed between his return on the last voyage of the Astrea and the time of the appearance of the New American Practical Navigator in 1802, we know little of his financial status. He had, of course, returned from Manila with some money. Once back in Salem, he invested in a trading schooner and is thought to have profited. He also invested in a sealing expedition and is said to have lost heavily. Since he had remarried and had a family to support, it is probably safe to conclude that now, in addition to his other problems, he was again faced with the perennial need for money. A way out of all these difficulties, and one which was to change his life completely, offered itself in the fall of 1802, shortly after the book was out.

At this time Salem was rapidly becoming the pepper capital of the world. Salem pepper ships bought directly from the natives on East Indian islands, many of them completely unknown, then transshipped tens of thousands of pounds of the precious commodity to markets in Europe and America. The trade was extremely dangerous. More than a few Salem vessels ended their days on some lonely beach or reef, captured by pirates, their crews murdered, eaten, or sold into slavery by the fierce natives. The profits were so fantastic, however, that many were willing to take the risks.

For this trade, a syndicate of Salem merchants purchased a three-masted square-rigger called the Putnam —small, but nearly new, fast, and in excellent condition—and selected Nathaniel Bowditch to take her out as master, with a share of the profits. It is not known if Bowditch actually bought into the company, or if his “share” was merely that usually given the captain. In any case, it is interesting to speculate about why he was chosen to command the vessel. Certainly the relatively inexperienced and slight statured mathematician was not the man one might normally expect to find in such a position. The Putnam was bound for one of the most dangerous areas in the world. (Only three years later, she was, in fact, lost to the natives and seven of her company were massacred.) She was armed heavily; she was expected to defend herself. If she were to return home safely she would need the most capable and resolute men possible. Perhaps the syndicate desperately needed a fast voyage to catch a certain market, or to meet certain obligations. At any rate, Bowditch commanded the Putnam when she cleared Salem for Sumatra in November of 1802.

The ship was lucky. Trading was good, the fast proas of the native head-hunters were eluded, and very quickly she was on her way home with a rich cargo of wild pepper.

The Putnam approached the New England coast late in December of 1803, during the height of a terrible storm. For days the whole eastern seaboard had been snowbound by the worst blizzard anyone could remember. A prudent master who found his ship in these waters at such a time kept well offshore, hoping he wouldn’t be dismasted or that the seams of his vessel wouldn’t open under the pounding of the seas.

There are many tales, most of them no doubt apocryphal, about exactly what happened next. The facts themselves are sufficiently fascinating without embellishment.

Late on Christmas Day, a rumor spread through the murk and gloom that enveloped Salem. It was said that Nathaniel Bowditch had been seen in town! Some claimed it was his ghost. Others said that it was truly Bowditch in the flesh; that he had driven the Putnam ashore and had somehow managed to make his way to the village. In any event the news was not good. Ghost or no ghost, if Bowditch was in Salem it could mean only that the ship was lost. The port had of course been tightly closed by the winter blizzard.

The syndicate that owned the Putnam must have experienced some horrifying moments before Bowditch finally showed up in dripping oilskins, thin as a rail, and convinced them that he was neither a ghost nor a miserable castaway. The ship? She was tied up safely at Derby wharf!

Bowditch had done the impossible. He had brought the Putnam safely to her berth in the midst of the storm. He admitted that two days before, he had had the good fortune to speak another vessel which had helped him establish his position. And on December 24, when the snow had turned to “thick rainy weather, latter part moderate to foggy,” he had managed during a lull in the storm to take two good shots of the sun. This definite establishment of the ship’s position, plus an excellent compass and a fleeting glimpse of the “Eastern Point of Cape Ann” through the fog as they worked their way up the channel, had been sufficient. Otherwise, all he had done was to apply some “simple arithmetic”!

This was a feat that could not be ignored. Bowditch and his arithmetic had done what no shipmaster in Salem—or ‘anywhere in the world—could have done, bluster as he might. Bowditch was an overnight hero.

From then on his methods were not only put to immediate use but were taught and avidly studied. As the years passed, any man who had sailed with Bowditch proudly considered that he had sat at the feet of the master. Nor was he wrong. For the first time in history, men could venture forth on the ocean and know exactly where they were. To a large extent Bowditch made possible the great age of American shipping. The tall clippers standing out from Canton to New England made their marvelous voyages because they were manned and navigated by men who had studied their New American Practical Navigator .

And what has happened to the book over the years? Published continuously since 1802 and now in about its seventieth edition, it has been one of the great best sellers of all time. Bowditch, and after his death his family, carefully amended and republished it until 1868, when the work was taken over by the Hydrographic Office of the Bureau of Navigation, United States Navy. Known familiarly as H.O. No. 9, it is truly a national monument. Until the period after World War I and the advent of newer methods, coupled with the increasing use of various electronic aids spurred on by World War II—loran, radar, gyrocompasses, inertial guidance systems, to mention a few—“the Bowditch” was the navigator’s bible. The book is still going strong as the basic working and reference text on celestial navigation—in the air and on the sea.

Bowditch never again sailed after the voyage of the Putnam . As the years passed, he emerged from his shell of loneliness. He took an active, and vociferous, part in community affairs—politics, school elections, and the like; he reared a large and very notable family; he helped establish the first maritime insurance company in America.

In 1823 he moved to Boston with his family, where he continued to prosper. His “commentaries” on Pierre Simon Laplace’s Mécanique Céleste ran to over four thousand pages, twice the size of the original, and made this notable work by “the Newton of France” available to the English-speaking world. Bowditch bore the publishing expense himself—it cost him $12,000, a third of his life’s savings. He also brought out many other works—on comets, meteors, and solar eclipses—but his greatest work remains H.O. No. 9, “the Bowditch.”

Honors were heaped upon him. He was made a Fellow of the Royal Society of London and Edinburgh, the Royal Academy of Palermo and Berlin, the Royal Irish Society, the Royal Astronomical Society of London, and many others. He was elected secretary of the East India Marine Society of Salem and offered various chairs in mathematics and natural philosophy—at Harvard, at the University of Virginia, and at West Point. He was elected president of the American Academy of Arts and Sciences. In 1810 he was elected an overseer at Harvard and in 1826 was made a member of its governing corporation. When he died in 1838, ships of all nations in ports throughout the world flew their flags at half-mast as the news spread, and cadets at the United States Naval School wore mourning badges. It was as though mariners everywhere recognized not only the loss of a great scientific and mathematical genius, but of a very good and trustworthy friend, whose work guided them safely across dark and unknown oceans.

But possibly the greatest honor, the one that would have pleased Bowditch most, was the inscription on the commemorative statue erected in Salem by the Marine Society: “… As long as ships shall sail, the needle point to the North, and stars go through their wonted courses in the heavens, the name of Doctor Bowditch will be revered.”

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