CHAPTER NINE

Captains of Academe

DURING THE LAST DAYS of July 1914, in the final hours of peace, the European powers positioned themselves for the impending conflict. Germany prepared to march its army through the supposedly neutral country of Belgium. The French hurried to throw their military might between the advancing troops and Paris. The English, perceiving that they had interests on the Continent, organized an expeditionary force to send into the fray. Karl Pearson, the great admirer of German culture, found himself caught on the European side of the English Channel. He hurried home to London on the first day of the conflict and declared that the needs of his country were more important than his personal ambition or his love of science. “On August 3, 1914,” he wrote, “I at once put the whole Laboratory staff at the service of any [British] Government department that was in need of computing or statistical aid.”¹

In 1914, the Biometrics Laboratory employed a staff of ten computers, four men and six women. The military could have utilized all ten. They would have enlisted the men qualified for service and made them navigators and surveyors. The women, and those men who were unfit for military duty, would have been given jobs as clerks or engineering assistants. Pearson argued that the group should remain intact and under his control. “The Laboratory can do far better work nationally as a whole than scattered, as it is trained to work together.”²

At first, he was willing to accept relatively menial assignments for his computers. Beginning that fall, the Biometrics Laboratory “provided weekly some 500 or more graphs showing the state of unemployment of insured and of uninsured trade men and women.” The work required no advanced mathematics and was relatively straightforward, even though it kept the computers on a strict production schedule. “Six and sometimes eight series of these graphs were kept running and carried to date each week,” Pearson reported. The staff worked “without a break through all the vacations up to July [1915],” balancing the requirements of the statistical reports with the demands of Pearson’s biometrical research.³

When the laboratory staff returned from the summer vacation of 1915, Pearson learned that half of his workers were not satisfied with the role that they were playing in the war effort. The conflict still retained its heroic potential, its romantic promise of bold actions and daring deeds. On those days when the wind blew from the southeast, the more alert residents of London could hear the report of cannon and the muffled thud of exploding shells. Three of the male computers had tried to enlist in the army with the hope of serving on the front. All three were rejected by the recruiting office, but each had found a position in industries that were supplying the military. An equal number of female computers had also left the lab, one to serve in a hospital, one to teach, and one to rejoin her family.⁴ Pearson, conscious that he would have to train and recruit a new staff, decided to temporarily withdraw from war work.

On September 9, the war reached the Biometrics Laboratory. “We are all congratulating ourselves that we have seen a Zeppelin at last,” wrote one of the female computers. The Zeppelin had crossed the sea from Germany and followed railroad tracks into London. “I was coming home in a tram just before 11 PM,” she added, “when the driver called out that there was a Zep.” She got out of the tram and began walking home, keeping an eye on the big, hulking shape in the night sky. “Nobody obeyed the Instructions to seek shelter. We could see the flashes from the anti-aircraft guns but they all went very wide of the mark.” The airship was looking for the Charing Cross railroad station, which was situated on the river Thames, but it dropped a bomb near the university “and nearly every window is smashed and numerous shops were destroyed.” The computer reported that the population seemed to regard the event as an adventure rather than as a threat, claiming that the “whole of London is in a state of subdued excitement.”⁵

Pearson claimed that he was able to face the bombings with resolution. “I just went about my usual tasks,” he wrote after the war: “I made belief that it was nothing.”⁶ By December, he felt that his computers were ready to resume war work. This time they created shipping reports, “preparing graphs dealing with the tonnage required for various imports for the use of committees controlling these matters.”⁷ He reported that the work occupied all of the computers’ time, but at least one of his computers was still doing biometric computations. Pearson continued with his statistical research but spent increasing amounts of his time doing analyses for aircraft factories. The aviation industry was only a decade old, and its engineers had much to learn about structure, motion, lift, and drag. Most of the problems undertaken by Pearson involved the flexing of structural parts: propellers, wing struts, airframes. The mathematics of this analysis was somewhat tricky, but Pearson had studied the subject before he had become interested in mathematical statistics. The work brought him into direct contact with the military and introduced him to the big mathematical problem of the war: the calculation of bomb and shell trajectories, a subject known as mathematical ballistics.⁸

Mathematical ballistics lay behind the most brutal weapons of the war. It allowed artillery crews to aim their guns at distant targets, mortar crews to lob gas-filled shells from behind the protection of a hill, moving Zeppelins to bomb stationary structures, and defense gunners to destroy invading aircraft. It had a history as old and venerated as the history of mathematical astronomy, and it had a problem every bit as difficult as the three-body problem of Halley’s comet: the problem of modeling the atmospheric drag on the flying shell. This problem had been first encountered in the fifteenth-century cannonball experiments of Galileo Galilei (1564–1642). Galileo argued that the air had no effect upon the motion of the balls and concluded that trajectories were graceful parabolas through the sky.⁹ Newton placed Galileo’s analysis on a more formal foundation, but like his predecessor, he assumed that the cannonball was moving in vacuo. By the early eighteenth century, scientists had discovered that air resistance had a substantial impact upon ballistics trajectories, and they had also found it to be a complicated phenomenon. As a projectile neared the speed of sound, it created shock waves that dissipated energy and greatly increased the drag. For extremely high velocities, such as those achieved by projectiles as they left the barrel of a gun, the nature of the drag changed again. These variations thwarted any attempt to make a simple calculation of a trajectory. Scientists of the mid-nineteenth century could compute a trajectory only by using methods similar to those that had been used by Alexis Clairaut for Halley’s comet. They would track a projectile along an idealized path and adjust its position to account for the drag.¹⁰

A clearer understanding of air resistance began to emerge in the 1860s, as military engineers began to amass a large collection of data. The first of this data came from pendulum tests. Gunnery crews would fire a shell at a large pendulum and measure the displacement of the bob. From these measurements, the engineers could determine the velocity of the shells and, ultimately, the atmospheric drag. By 1870, the armies of Prussia, Great Britain, France, Russia, and Italy had all estimated the nature of drag. These estimates took the form of graphs rather than mathematical expressions. No simple expression described the relationship between the velocity of a shell and the drag. The French estimate, usually called the Gâvre function, after the French proving ground, was generally considered to be the most reliable of the time. It was used by an Italian professor, Francesco Siacci (1839–1907), to create a simple means of computing trajectories.

Siacci was a teacher at the Turin Military Academy and had served briefly as an artillery commander with the army during a brief conflict with Austria.¹¹ Rather than calculating the entire flight of a shell, he concentrated on four factors: the range of the trajectory, the time of flight, the maximum height of the shell, and the velocity at impact. Each of these quantities could be used by an artillery officer to plan and direct artillery. The time of flight was used for setting fuses so that the shells would explode over the heads of enemy troops rather than in the ground. The maximum height was used for mortar fire over hills and tall buildings. The terminal velocity gave the amount of energy in a shell and suggested the extent of damage it could produce. Rather than compute these values for all guns and all shells, Siacci chose a strategy that resembled Nevil Maskelyne’s approach to the lunar distance method of navigation. He prepared a set of mathematical tables that described idealized trajectories and then gave rules for transforming values from these tables into the motion of a real shell. The final results were only approximations of the real trajectory, but they were sufficiently accurate for the cannon of the day, including the old smoothbore cannon that had been used in the American Civil War and the new rifled steel barrels that were being produced by Krupp Industries in Prussia.¹² Siacci’s ballistics tables were quickly adopted by the armies of the industrialized countries. American officers translated Siacci’s original paper into English less than a year after it appeared in Italian.¹³

Had the First World War been only a duel of large guns across the fields of Flanders, then Siacci’s method would have sufficed for most of the ballistics calculations. This method had its flaws, but most of them could be fixed with only a little effort. The biggest corrections would have included a refinement of the atmosphere drag function and the introduction of more detail into the mathematical equations. Ballistics officers were now able to measure the velocity of shells with electrical instruments. Their experiments had shown the need to incorporate new factors into the equations, including the density of the atmosphere and the direction of high-level winds. These changes could be handled without a large, permanent computing staff.¹⁴ Computers were needed to help with artillery problems that came from the growing use of aircraft. Since Siacci’s tables presented only a few points of the trajectory, they could not be used for antiaircraft artillery, for bombing, or for aerial combat. Anti-aircraft defense, a problem that became increasingly important during the war, was like duck hunting. The gunnery crew would fire an explosive shell into the air, hoping that it would explode near an oncoming plane. To place that shot close to the plane, the gunners needed to know how fast a shell travels along the upward slope of its trajectory, information that was not easily gleaned from Siacci’s theory.¹⁵

The British army first turned to a Cambridge professor, John Littlewood (1885–1977), for help with ballistics analyses. They gave him a lieutenant’s commission and assigned him to work at the Woolwich Arsenal, a military facility located to the east of Greenwich.¹⁶ Littlewood was an expert with differential equations and could quickly produce rough approximations of “vertical fire,” the term used by the army for antiaircraft trajectories. When he needed more detailed calculations, he asked for assistance from the faculty and students at Cambridge. Often, he turned to Karl Pearson’s former computer Frances Cave-Browne-Cave at Girton College. Professor Cave-Browne-Cave gladly offered to do calculations for Littlewood, but she had many responsibilities and occasionally needed help herself. “We had to ask my Girton sister to come home before she had finished her work on guns,” reported her sister Beatrice, “so I have been checking some of the most urgent of her work for her.”¹⁷

The calculations for antiaircraft and anti-Zeppelin fire were substantially more complicated than those of the old Siacci theory. Computers needed to produce a complete trajectory, not just the endpoint and the time of flight. They calculated these trajectories using the method of mechanical quadratures, the same method that Andrew Crommelin had used to prepare the ephemeris of Halley’s comet. They called their version of this technique “the method of small arcs,” for it divided the full trajectory of a shell into a series of tiny, curved steps. At each step of the calculation, they would advance the shell, estimate how much it had slowed in that interval, and recompute the drag. The process was simpler than computing the orbit of a comet, as the shell was influenced only by air resistance and earth’s gravity rather than by the conflicting pulls of the planets. Even with this relative simplicity, the computation of a single trajectory by the method of small arcs still required at least a full day of effort.

By the spring of 1916, the computers of the Biometrics Laboratory, including Beatrice Cave-Browne-Cave, were accepting requests for trajectory calculations directly from the Ministry of Munitions. At first, they gave low priority to the ballistics work. “These [trajectories] you told me to leave till the last as you might not have them done,” Beatrice Cave-Browne-Cave wrote to Pearson; “shall I go on to this now?”¹⁸ Pearson approved this request, but he was still trying to devote as much time as possible to his statistical research. He asked the computers to clean and measure a collection of skulls that spring, a task that uncovered an infestation of insects.¹⁹ He also kept at least one of the computers away from the ballistics calculations. This computer, a Norwegian student, did most of her work outside of the Biometrics Laboratory.²⁰

As spring moved to summer, the Ministry of Munitions expanded its requests for ballistics calculations from Pearson and his staff. Though the computers faced an increasingly rigid production schedule, Pearson attempted to sustain the same egalitarian air that he had shown during the days of experiments at Hampden Farm. When he received a packet of printed materials from the Ministry of Munitions, he found that he, rather than his staff, was being credited with producing the calculations. “Please do not place my initials on the charts and tables,” he replied to the ministry. “It would have the appearance of arrogating to myself work due to a number of people of whom I am only one.” He had come to refer to his combined laboratories as the Galton Laboratory, and he requested, “If a mark of this kind is needful will you please place GL upon them, which will be quite as distinctive as KP and cover the whole staff of the Galton Laboratory.”²¹

Though the war demanded self-sacrifice, it also offered new opportunities to the computers and encouraged them to look beyond the walls of University College, London. In August 1916, Beatrice Cave-Browne-Cave announced that she would leave the laboratory to take a better-paying position with the Ministry of Munitions. Pearson had not anticipated this news and was not pleased to be losing so experienced a computer. “I may be quite wrong,” he wrote Cave-Browne-Cave, “but frankly I do not consider you have ‘played the game.’” In part, he was distressed because Cave-Browne-Cave was abandoning a recently signed contract with the college, but he also felt that the computers should be motivated by something beyond money or position. “I should never attempt to hold an assistant, who wishes to leave,” he explained, “because it is evidence to me that their heart is not in their work and that they have not full loyalty to the ideas of our Founder, [Francis Galton].” He ended their collaboration by stating that “under the circumstances I should prefer, as it would save friction which is not compatible with the pressure of present work, if you did not return at all to the Laboratory.”²²

By the end of the year, ballistics computations dominated all the work of the laboratory. In one request, an assistant at the Ministry of Munitions apologized for the demands it was making upon the Biometrics Laboratory staff. “Your people, being trained to work together, could probably get results out very much more quickly than we, being amateurs at computation.” To emphasize the demands placed upon the ministry, he added, “we have large amounts of work we could take on, if only there was a possibility of getting them finished.”²³ By that time, Pearson was finding it difficult to replace the men who had gone to war and the women who had found more profitable employment in the war industries. Increasingly, Pearson recruited young boys to be his computers. Unlike the boy computers of George Airy’s observatory, these computers were students at prestigious public schools and were serving for three or six months before they were called into the army.²⁴

As the conflict moved into its third year, the pressures of the war began to weary Pearson. The demands for ballistics calculation had only increased. The Ministry of Munitions needed more tables, more detailed computations, and more extensive analyses. They had increased the upper limits for antiaircraft trajectories, which had originally been set at an altitude of 15,000 feet, to 17,000 feet, then to 20,000 feet, next to 25,000 feet, and finally to 30,000 feet.²⁵ Attacks on London only increased the demands upon the laboratory. Following a damaging attack in September 1917, a distressed ministry official wrote to Pearson, “From the experience of last night it is evident that the work of the Anti-aircraft Experimental section will have to be tackled with even greater energy than at present if we are to make any impression on the Huns.”²⁶ However, Pearson had little energy left. He was tired of recruiting and training new computers, saw no end to the ballistics calculations, and was frustrated that his research had stagnated. Just one week later, when he received a review of recent calculations, he gave full vent to his frustration and fatigue. The review was a gentle note in a neutral language with no obvious evidence of personal rancor. It stated there must be “some mistake in the sign of correcting terms—small things added instead of subtracted.” The writer, an official with the Munitions Ministry, stated that there was “nothing to be done except to call your attention to the matter” and ended with the “hope it will prove to be possible to set matters right without imposing new calculations.”²⁷

The comment angered Pearson, in a way that few things ever did. He had faced scientific criticism before and had accepted it as part of the scientific process. To him, this event seemed to be an unwarranted interference, a challenge to his authority. He took it as a personal affront and demanded an apology. The official, surprised by Pearson’s reaction, stated that he had intended no offense, but this was not enough to placate the statistician.²⁸ Surprised by the extent of the controversy, a friend of Pearson tried to intervene, but he, too, was rebuffed. “I cannot understand why you should not believe my statement,” he told Pearson, “that I, at any rate, have neither heard nor seen nor made any statement other than one of respect for your work.”²⁹ It took nearly six weeks for the ministry officials to restore a working relationship with Pearson. The chief of ordnance research offered a full apology and acknowledged “how much we were asking of you in wishing you to accept dogmatic rules without explanations or reasons.”³⁰ For his part, Pearson agreed that there were errors in the calculations, which had been created when one of his computers misread an intermediate value.³¹

Pearson returned to work in December 1917, but he no longer seemed to be fully engaged in war calculations. When he wrote the ministry that “I don’t think our people are likely to stick it out so long as [the Germans] will,”³² he was speaking as much for himself as for the British people. Three months later, just as the Germans launched a threatening offensive, Pearson announced that he wished to withdraw from war work and return to his statistical research. This time, no one in the Ministry of Munitions attempted to change his mind. They transferred most of the Biometrics Laboratory computers to a government building and assigned a military officer to oversee them.³³ Pearson was sanguine about the change. “I have promised to disappear,” he wrote to one computer, in order “to gain room for spring cleaning during the first week of April.” If the weather was good, he might go hiking; “otherwise I suppose to go on steadily with the work at some place in the neighborhood.”³⁴

The American computers were not in the war long enough to follow the path set by Karl Pearson, but all had to weigh the claims of patriotism, personal glory, and scientific accomplishment. Unlike the staff of the Biometrics Laboratory, most of the American computers were promising graduate students or young mathematics faculty. As a whole, the computers were part of a generation that ardently supported American intervention in the European war. Long before President Woodrow Wilson declared war on Germany, college students formed campus battalions, practiced formations in gymnasiums, and spent the summer at special army training camps. “The muster rolls at [the camps],” observed one historian, “sounded like Who’s Who and The Social Register combined.”³⁵ The most adventurous of the college men joined Canadian regiments or, like the young Ernest Hemingway, volunteered to drive ambulances for the Red Cross. For Hemingway, the Red Cross was not a humanitarian service but the chance “to die in all the happy period of undisillusioned youth, to go out in a blaze of light.”³⁶ Harvard, Columbia, and Yale sent large proportions of their student body to the war. Princeton University, where President Wilson had once taught political science, was home to the most active recruiting station in the nation.³⁷

In their part of the preparation for combat, scientists formed a civilian research organization within the National Academy of Sciences. The organization, called the National Research Council, was intended “to bring into cooperation governmental, educational, industrial and other research organizations.” The group was endorsed by President Wilson but was never fully embraced by either the army or the navy. On the eve of the war, the army assumed control over the National Research Council, placed it under the authority of the Signal Corps, and gave its members commissions in the army reserve. Most of war’s scientific research was done under the close supervision of military officers.³⁸

Ballistics research, including trajectory computation, was overseen by the Army Ordnance Department. The leader of the computing activity was the Princeton mathematician Oswald Veblen (1880–1960), nephew of the economist Thorstein Veblen. While the elder Veblen is usually associated with the liberal strains of American thought, Oswald Veblen was conservative and an advocate of American intervention in the European conflict. He began looking for a position in the military before Woodrow Wilson asked for a declaration of war. After an initial rebuff, the Department of Ordnance offered him a captain’s commission and placed him in charge of experimental ballistics.³⁹ He spent the first summer of American involvement in the war, the summer of 1917, waiting to be called for duty. During the intervening months, he read ballistics treatises and corresponded with mathematicians interested in working for the war.⁴⁰ He was inducted on August 30, given basic training on November 20, and ordered to report to the army’s new Aberdeen, Maryland, Proving Ground on January 18, 1918.⁴¹

The Aberdeen Proving Ground was the largest military project of the war, the Manhattan Project of its age. The army spent $73 million to build the facility.⁴² They acquired 35,000 acres of Chesapeake Bay shoreline and evicted 11,000 residents, including the owners of thirty farms and the entire population of a substantial country town.⁴³ The Aberdeen Proving Ground replaced an older testing facility at Sandy Hook, New Jersey, a spit of land that stuck into New York Harbor. The army chose the Aberdeen site because it lay on the rail line between Baltimore and Philadelphia. It would be the last stop in a manufacturing process that would begin at factories in Pennsylvania, Maryland, New York, and Ohio. The factories would ship guns, shells, and charges to Aberdeen, where ordnance officers would test, or “proof,” these devices before deploying them to army arsenals.

Waiting for Veblen at the Aberdeen post office was a letter from a professor who had taught him at the University of Chicago. It praised the young mathematician as being “High in Academic and in Military Life!!”⁴⁴ They were flattering sentiments, but they must have seemed far removed from the physical reality of the proving ground. The military base was little more than a construction site. There were a few wooden buildings, lots of tents, and miles of dirt roads. The winter was desperately cold, the worst on record. Water froze on the Chesapeake, and the wind raced unhindered through the army tents. Veblen was not able to start an experimental program until early February. He described his first efforts as “more picturesque than satisfactory.” The test ranges were not finished, so Veblen gathered data by firing a cannon across an open field. After a series of rounds, he would “go down the range on horseback while the firing was suspended for meals, identify the shell holes and place distinctive marks in them to enable them to be identified by the surveyors.” The bitter weather slowed the work, though Veblen noted that the winter storms deposited fresh sheets of snow, which erased the craters from earlier trials and provided an unblemished surface for a new round of shots.⁴⁵

20. Captain Oswald Veblen before departing for the Aberdeen Proving Ground

His computational problems began after he completed the range work. His computing staff consisted of three army officers who worked at Sandy Hook. They remained at the old facility in order to teach trigonometry and surveying to new recruits. On top of their teaching duties, they were expected to analyze Veblen’s data and compute the trajectories for a range table, a table that artillery officers would use to prepare their campaigns. Their first job was to reduce the data, a task similar to reducing astronomical data. They had to adjust the data so that all the values indicated how the gun would perform under what artillery officers called “standard conditions.” Under standard conditions, the air is still, with a temperature of fifteen degrees centigrade and a density of .075126 pounds per cubic foot.⁴⁶ Veblen had given them formulas to do the reductions, including ways of correcting for crosswinds and “jumps” or motion of the gun barrel during firing.

From the start, the computations went badly. The “difficulties in long range correspondence about the many technical details were very great,” Veblen observed.⁴⁷ The computers had not observed the firings and did not understand all of the data. Some of the shots seemed anomalous and the results contradictory. The ballistics formulas were confusing, and Veblen’s instructions were incomplete. In early March, the computers asked Veblen to come to Sandy Hook and help them with the calculations. After he returned to Aberdeen, they requested a second visit. Ten days later, with the tables still incomplete, they asked for one more session. On this last trip, Veblen worked with the computers until the calculations were done. The four of them finished checking the results a few hours before dawn on the morning of March 26. Veblen’s diary for the day contained the single line “3:00 A.M. Finished tables.”⁴⁸

This first project was an opportunity for Veblen to experience every step that was needed to gather ballistics data and create range tables, an opportunity to learn the problems of ballistics calculation. He seemed to have learned his lessons well, for his new computing staff at Aberdeen never had this kind of frustrating experience. He transferred the three Sandy Hook computers to the new proving ground in order to form the core of the new group. Their efforts were augmented by three Princeton graduate students. To oversee this group, he recruited Joseph Ritt (1893–1951) and gave him the title “Master Computer.” Ritt was a professor of mathematics at Columbia University and Veblen’s link to the old, traditional computing labs.⁴⁹ In 1911, Ritt had spent a year as a member of the Coast and Geodetic Survey computing floor. The group had a new name, the Department of Longitude, but its methods and procedures were little changed. Myrrick Doolittle, who had become the grand old man of scientific calculation, arrived in his office every day to adjust triangulation surveys, as he had thirty years before.⁵⁰ From the Coast Survey, Ritt moved to the combined Computing Division of the Naval Observatory. At the observatory, he spent one year reducing data for the astronomers and a second year preparing ephemerides for the Nautical Almanac Office.

Though he chose a Master Computer who had been trained at conventional computing offices, Veblen did not follow the traditional model for computing floors. He placed computers on the firing ranges of Aberdeen and put them “under the direct observation of the firing officers.”⁵¹ The first facility to include a computing staff was called the “water range” because the shells overflew an island and landed in the Chesapeake Bay. The range was not completely finished when it began testing guns in April 1918. Veblen remembered: “It was necessary to haul ammunition and guns over roads which were often two feet deep in mud. The only conveyance which was able to get through was a six-mule team. Even the Ford was powerless.”⁵² One computer would hike or ride a horse to the gun mount. Two or three others would take a small boat to observation towers on the far side of the bay. These computers had a telephone connection to the range officers, who notified them of each firing so that they could time the length of flight.⁵³ From measurements of the splash made by the shell, they would compute the length of the shot and its deviation to the left or right.

Following the shots, the observing computers would phone these numbers to the computer at the gun mount. The computer reduced the data to standard conditions using the air temperature, gun temperature, humidity, jump of the barrel, direction of the wind, and other factors. Under this system, Veblen reported, “it is possible to know the results of any firing for range [distance] within a few minutes after the last shot was fired.” At the end of the day, after the boat picked up the observers, the range computer would take the day’s calculations back to the central computing lab, where the staff would complete the work. Veblen confessed that the lab was really nothing more than a “small shack” that was “ordered for this section [the computing group] on Friday morning and the section moved in on Saturday afternoon.”⁵⁴

Veblen implemented this plan on all of the Aberdeen ranges, though some of the facilities lacked proper equipment. On one of the antiaircraft fire ranges, before the computers acquired range finders, they resorted to techniques that might have been borrowed from Francis Galton or a scientist of Laputa. They would fire the shells vertically into the night sky and photograph the bursts against the background of the fixed stars. After the photographs were developed, the computers would measure the distance between the shell burst and the stars. With this data, they would use the tables of the nautical almanac to compute the altitude of the burst.⁵⁵

Aberdeen had no residences for women and hence had no female computers. The only women who worked at the base were a pair of secretaries, who were forbidden to spend the night at the proving ground.⁵⁶ The army began hiring female computers only when it opened an office of experimental ballistics in Washington, D.C. This office was directed by Major Forest Ray Moulton (1872–1952), who was a professor of astronomy at the University of Chicago before he accepted a reserve commission. Moulton took the job of preparing ballistics materials for ordnance officers. In the spring of 1918, he was given an office in a temporary building on the Washington Mall and told to hire a staff. As other officers had already discovered, Moulton found it difficult to hire enough men, so he offered positions to women.

The young women of 1918 could not attend the special training summer camps, volunteer for a Canadian regiment, or even fire a 12-inch gun at the Aberdeen Proving Ground. Though they were generally enthusiastic about the war, their feelings were checked by the roles that they were offered in the conflict. The first year of the war was also the year of women’s suffrage, the year that a corps of committed women moved to Washington, D.C., in order to win the right to vote. While the men were preparing to fight in France, women were picketing the White House, lobbying the members of Congress, and marching up and down Pennsylvania Avenue. One congressional aide recalled seeing “cultured, intellectual women arrested and dragged off to prison because of their method of giving publicity to what they believed to be the truth.”⁵⁷

The suffrage movement surrounded the world of Elizabeth Webb Wilson (1896–1980). Wilson was the daughter of a Washington physician, a flaxen-haired, dimple-cheeked member of the capital’s wealthy classes. She studied mathematics at George Washington University, a school just a few blocks west of the White House. Her daily trolley ride took her past the lobbyists, the pickets, and the marches. Like herself, many of the suffrage leaders were the daughters of physicians. As far as we know, she took no part in the effort that ultimately caused President Wilson to endorse the suffrage amendment, Congress to approve the measure, and the states, one by one, to give their consent. Yet, in the spring of 1918, she took her own small stand for women’s equality. When she heard that the federal government would employ women in war offices, she applied for a job that would “release a man for the front.” It was the “patriotic thing to do,” she recalled. But when she was offered a position, she refused it on the ground that it was “insufficiently mathematical.” She had been the top mathematics student in her graduating class, the first woman to win the school’s mathematics prize. Though her college peers had judged her a quiet and timid woman, she stood her ground and stated that she would only take a war job where her mathematical talents “could be utilized to the fullest.”⁵⁸ The personnel office offered her a second position, which she also declined, and then a third. In all, she rejected nine jobs before accepting an appointment as Moulton’s chief computer.

21. Elizabeth Webb Wilson in the spring of 1917

Elizabeth Wilson’s persistence was a small victory for feminism. Washington had already established itself as a city of opportunity for single women. The novelist John Dos Passos described contemporary stenography offices in the capital, where “the typewriters would trill and jingle and all the girls’ fingers would go like mad typing briefs, manuscripts of undelivered speeches by lobbyists, occasionally overflow from a newspaperman or a scientist.”⁵⁹ A woman could earn seventeen or twenty dollars a week, enough to pay the rent on her own apartment, send some money to her family, and have enough left to occasionally purchase clothes from one of the finer department stores. The Washington office of experimental ballistics employed both men and women and put them in situations where they had to work together. The computing staff had sixteen workers and was split equally between female and male. Like Wilson, the other seven women were the offspring of prosperous homes and graduates of coeducational schools with strong mathematics programs. Two of the women had studied at the University of Chicago, two at Brown University, and one each at Cornell University, Northwestern University, and Columbia University.⁶⁰

The staff of the Washington ballistics office stood midway between the mathematicians and engineers of Aberdeen and the officers in the army’s artillery corps. Using data from the Aberdeen ranges, they prepared tables and documents for those who would actually command the guns in battle. The work was often sensitive or political in nature, requiring Moulton to negotiate among different branches of the military to establish standard operating procedures. “As a consequence of the various interests involved,” he wrote about one problem, the work “had to be taken up somewhat formally.”⁶¹ In this environment, the mathematicians worked closely with the computers to prepare material that was both accurate and appropriate for the situation. During Wilson’s first weeks in the office, she and Moulton had to prepare a range table for a French gun firing American ammunition. Wilson demonstrated “both personal mastery of the technical operations involved,” wrote one of the mathematicians in the office, “and skill in supervising and checking the work of others.”⁶²

Reflecting on the experience, Moulton saw an unusual camaraderie between the mathematicians and the computers. “The unfailing courtesy and the evidence of mutual helpfulness which were manifested in numerous ways,” he wrote, “were inspired not alone by military customs and the proprieties of the situation, but much more by sincere mutual respect and personal regard.” Wilson, the only member of the office staff from Washington, acquired the role of chief computer and social leader. She hosted a dinner for the office staff at her parents’ home and a party at her father’s club.⁶³

When the ballistics computers recalled their service in the First World War, they would remember the summer of 1918. “It would be difficult to gather in any way an equal number of individuals who would have more in common and whose relations would have been more harmonious,” wrote Moulton.⁶⁴ The number of firings at Aberdeen increased each day, and the data flowed from the gun mounts to the proving ground’s computing building and from there to the experimental ballistics office in Washington. Veblen spent much of the summer traveling in search of new computers, but whenever possible, he would catch an early train back to Aberdeen so that he could join the artillery crews on the range. He would fire the guns until the dimming light made further observations impossible.⁶⁵ He recruited mathematical talent from universities, from industry, and even from the offices of the Encyclopedia Americana. “The demand was immediate,” remembered one computer, so “[I] terminated my [job]. I took the next train to New York, where I changed for Aberdeen.”⁶⁶ In less than two months, Veblen added twenty-three graduate students or new PhDs to his staff, bringing the total number of computers at Aberdeen to thirty. Twice that summer, the army engineers had to double the size of the computing building.⁶⁷

During those months, the computers gathered range data for naval guns mounted on railroad cars, tested new designs of streamlined shells, and uncovered a major design flaw in existing shells, a problem that Moulton judged to be “so great that the guns were of little value.”⁶⁸ Yet the problem that most interested them was a major revision of Siacci’s ballistics theory. “Upon entering the army,” wrote Moulton, “a hasty examination of the classical ballistic methods showed … that they were wholly inadequate for current demands.” He argued that Siacci’s analysis “contained defects of reasoning, some quite erroneous conclusions, and the results were arrived at by singularly awkward methods.”⁶⁹ His criticisms were unduly harsh, as the First World War armies were using the theory for problems that Siacci had not foreseen. Siacci had not planned for the problems of high-altitude fire, antiaircraft guns, and long-range artillery, nor had he anticipated that an army might have at its disposal a staff of forty-six human computers.

By all accounts, Siacci’s theory continued to work fairly well for short- and intermediate-range artillery, but events in the first years of the war had shown that it failed dramatically in long-range artillery and high-angle mortar attacks, in addition to its shortcomings for antiaircraft fire, bombing, and fire from aircraft. While the staff would be able to correct some of these deficiencies, Moulton concluded that he should develop a new, comprehensive ballistics theory that could be used to analyze any circumstance. The work engaged the computing staffs in both Aberdeen and Washington and challenged them to use the most sophisticated mathematical concepts at their disposal. Moulton created the central outline of the theory. Other mathematicians handled specific problems with the theory, such as adjustments for altitude, the spinning of the projectile, or the rotation of the earth. Elizabeth Webb Wilson, who helped prepare the tables for the theory, recalled discovering that “the Germans had the advantage because the earth turned toward the east, therefore as they were shooting toward the west, their bullets carried further into the allies’ lines.”⁷⁰

The computers were mathematicians, not ordnance engineers, and were most interested in the mathematics of Moulton’s ballistics theory. One computer, ignoring the advantages to the gunnery crew, recalled how the work “made a brilliant use of the new theory of functionals,”⁷¹ a concept that was then on the frontier of mathematical research. Isolated from friends and family, separated by an ocean from the dangers of war, the computing staff at Aberdeen lived the life of extended adolescence. They hiked through the countryside and conducted unauthorized, and probably unscientific, experiments with TNT and smokeless powder. From the collected scraps and rubble of ordnance experiments, they invented surreal versions of checkers and chess. At night they would gather in the computing shack, play cards, and do the things that young men do when they are at war, though perhaps they were unique in calculating their winnings and loses on adding machines which by day computed the trajectories of shells. After the cards were dealt, the conversations would wane as the players computed the probabilities that their opponents held winning hands. When they spoke, they talked not of lost opportunities or of distant family members, but of the mathematics that they loved and the theorems that they would prove.⁷² One computer wrote that the experience “furnished a certain equivalent to that cloistered but enthusiastic intellectual life which I had previously experienced at the English Cambridge.”⁷³

The trenches in France had their own intellectual life, at least for the English troops. “The efficiency of the postal service made books as common at the front as parcels from Fortnum and Mason’s,” wrote critic Paul Fussell, “and the prevailing boredom of the static tactical situation … assured that they were read as in no other war.”⁷⁴ For the scientists at the front, there were opportunities to observe and speculate. The English meteorologist Lewis Fry Richardson (1881–1953) found that many of his days were uninterrupted by combat or even by rumors of combat. The battles most often occurred at sunrise or sunset, when one side or the other was shielded by the glare from the low-lying sun. He served as an ambulance driver and had little responsibility beyond the work of caring for his vehicle. During the quiet hours, he worked at his science, theorizing about the movement of the winds, the distribution of humidity, the impact of the light from the sun. “My office was a heap of hay in a cold rest billet,” he recalled. His approach to the problem was not a statistical method, like that used by the U.S. Weather Service in the 1870s, but a differential equation model that had much in common with the mathematics of astronomy and ballistics.⁷⁵

Richardson described his analysis of the weather as “a scheme of weather prediction, which resembles the process by which the Nautical Almanac is produced.”⁷⁶ He derived a series of differential equations that described how the weather changed moment by moment. These equations tracked seven basic properties of the atmosphere: its movement (in three dimensions), density, pressure, humidity, and temperature. The computing plan for these equations divided the globe into “a special pattern like that of a chessboard,” a grid of longitude and latitude lines that marked 2,000 points where the weather would be computed in increments of three hours. “It took me the best part of six weeks to draw up the computing forms,” he recorded, and when he attempted the calculations, he discovered that he required an equal amount of time to calculate a single advance of the weather at one of the points. His duties at the front had prevented him from fully concentrating on the arithmetic, and at one point, he had misplaced his manuscript. “During the battle of Champagne in April 1917,” he recalled, “the working copy was sent to the rear, where it became lost, to be re-discovered some months later under a heap of coal.”⁷⁷ When he finished the calculations, he concluded that “with practice, the work of an average computer might go, perhaps, ten times faster.” From this one exercise, his little respite from the war, he concluded that it would require 32 computers to keep pace with the weather at one grid point, 32 computers to complete a single three-hour prediction in exactly three hours. As there were 2,000 points in his scheme, he would require total of 64,000 human computers to track the weather for the entire globe.⁷⁸

“After so much hard reasoning,” Richardson asked, “may one play with a fantasy?” He had not come to France in search of glory. He was a Quaker and a conscientious objector to war. Rather than serve in the military, he had chosen to drive an ambulance. His fantasy was a world where the soldiers massed on the Western Front were put to work reproducing the earth’s weather in numbers. He would take 64,000 soldiers from the front lines and make them computers in a giant spherical computing room, a room that would have been larger than any sports stadium of Richardson’s day. The internal “walls of this chamber are painted to form a map of the globe,” he wrote. The North Pole would be on the ceiling, while Antarctica would be marked on the floor. England would be found three-quarters of the way toward the top, its shape nearly hidden by one of the many balconies that ringed the inside of the room. Upon these balconies, Richardson imagined, “a myriad computers are at work upon the weather of the part of the map where each sits.” He suggested that the computers might work on large sheets of paper and then display their results on “numerous little night signs” so that others could read them.⁷⁹

The calculations would be directed by a senior computer, a scientist who had worked through every step of the mathematics. This computer would stand on the top of a tall and slender column that rose from the floor like the column for Admiral Nelson in Trafalgar Square or a tall skyscraper in a city of lesser office buildings. “Surrounded by several assistants and messengers,” the senior computer would “maintain a uniform speed of progress in all parts of the globe.” Richardson suggested that this computer “is like the conductor of an orchestra, in which the instruments are slide-rules and calculating machines.” In his scheme, the conductor’s baton was replaced by a pair of colored spotlights. The computer would turn “a beam of rosy light upon any region that is running ahead of the rest, and a beam of blue light upon those who are behindhand.” Outside of the computing room, the computer oversaw a scientific compound, which included a radio station to transmit the weather predictions, a secure storeroom to hold old computing sheets, and a building that held “all the usual financial, correspondence and administrative offices.” Next to the sphere was a training room and a research lab, as “there is much experimenting on a small scale before any change is made in the complex routine of the computing theatre.” Richardson’s weather compound ended at the border of Arcadia, the land where numbers stood for things of nature, rather than the flight of artillery shells, the output of a factory, or the commerce of men. “Outside are playing fields, houses, mountains and lakes,” wrote Richardson at the end of his fantasy, “for it was thought that those who compute the weather should breathe of it freely.”⁸⁰

The fantasy of a giant computing laboratory was, perhaps, not so unrealistic to those who served on the battlefields or carried the wounded to safety. During his three years with the ambulance corps, Richardson saw hundreds of miles of trenches that were filled with thousands and thousands of soldiers. All he had imagined was the simple act of winding those trenches into a ball and using their occupants for the peaceful end of computing the weather. However, in 1918, weather did not represent the same kind of threat as the German army, so that no government had any interest in building a laboratory for 64,000 computers, 6,400 computers, or even 640 computers. Only one facility approached Richardson’s vision of a computing compound with houses and lakes and trees. It employed but forty-two computers and was located in a Maryland town named Aberdeen.