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 tr
aditional 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
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