Newcomb faced a second labor conflict that was resolved only after a hearing by the secretary of the navy. In this incident, Newcomb accused a senior staff member of being “incapacitated for effective work,” a phrase that probably implied that the worker arrived at the office drunk, and of taking “one week to do what a skilled computer should do in one or two days.” The staff member defended himself by claiming that Newcomb had showed favoritism to incompetent computers, that he was only concerned with “advancing his personal reputation,” and that he had “diverted practically three-fourths of the appropriation made for the support of the Almanac Office for years past to a purpose for which it was not intended.”61 The hearing was reported in embarrassing detail by the local papers, but the issue was ultimately resolved in Newcomb’s favor.62 However, the departure of the troublesome employee provoked the secretary of the navy to impose a little more control over almanac operations. “To avoid further trouble,” he wrote, he would “remove the almanac office from the Navy Department Building to the Naval Observatory, where it naturally belongs.”63
18. Simon Newcomb
Simon Newcomb was an astronomer, but like Pearson, he had a wide range of interests. He met Pearson during a trip to Europe in 1899.64 There was probably no way the two could have been friends, as their political values seemed to have little in common. Pearson, who was just starting the Hampden Farm experiments, seems to have treated Newcomb with respect, but there is no evidence that the two men corresponded after Newcomb’s visit. The two came into contact again only after four years had passed and Newcomb had become the director of the Congresses that were planned for the 1904 World’s Fair in St. Louis. Newcomb wrote to Pearson and asked if he would come to the United States to discuss the methods of statistics at one of the Congresses. Pearson had no interest in such an event and brusquely declined, stating that “I see no possibility of my being able to afford a visit to America from either standpoint of time or money”65
By then, Newcomb had retired from the Nautical Almanac Office and had turned to promoting the use of mathematics in “other branches of science than astronomy,” especially in the “examinations and discussions of social phenomena.”66 As this concept seemed to be related to the goals of Pearson, Newcomb wrote to the English statistician and asked him to help found an “Institute for the Exact Sciences.” “The nineteenth century has been industriously piling up a vast mass of astronomical, meteorological, magnetical, and sociological observations and data,” he explained to Pearson. “This accumulation is going on without end, and at great expense, in every civilized country.” His proposed institute would collect and process this data. One division of the organization would concentrate on data from experiments. A second group would assemble data that had been collected by observing social phenomena. The third division of the institute would be a large computing laboratory. The computers would process the data gathered by the other two divisions and would develop new mathematical methods that could be applied “to the great mass of existing observations.”67
The new institute would be expensive to organize and to operate, but Newcomb believed that he could find funds at the Carnegie Institution of Washington, a philanthropy founded by U.S. Steel president Andrew Carnegie (1835–1919). As it operated in 1904, the Carnegie Institution was a granting agency that provided small amounts of money to researchers scattered across the country. Newcomb believed that this strategy was misguided. “We find that centralization is the rule of the day in every department of human activity,” he argued. “Two men anywhere will do more when working together than they will when working singly.”68 He argued that a transformed Carnegie Institution, one that followed his model for an institute of exact sciences, would make better use of Carnegie’s money and would be “in the true spirit and intent of its founder.”69
Pearson showed no enthusiasm for Newcomb’s plan. Unlike Newcomb, who had spent all of his career working for a military agency, Pearson knew what it was like to ask for research funds with cap in hand and suspected that it would be difficult to extract money from the Carnegie Institution and nearly impossible to transform the organization, as Newcomb envisioned. He also may have felt threatened by the proposed organization, as the proposed Institute for the Exact Sciences would do work similar to that done at the Biometrics Laboratory. Newcomb was not easily dissuaded by Pearson’s objections, and he pushed the statistician to support the idea.70 It was a simple plan, he told Pearson, and it was important to avoid “thinking that I have in view something more comprehensive than I really have.”71 However, Pearson would not be moved and replied through a secretary that “Professor Karl Pearson is very much obliged for your letter re: Carnegie Institution proposals. He still considers the matter extremely difficult of execution.”72
By 1906, Pearson’s Biometrics Laboratory could handle most of the tasks that Newcomb outlined for his Institute for the Exact Sciences. To be sure, it was smaller than Newcomb’s proposed institute, and its mathematical methods had taken a circuitous route from the observatory and almanac before they reached the problems of evolution and human behavior. With each passing year, the computing staff was gaining skill and experience with different forms of calculation. By 1906, Pearson could report that the group had mastered the art of mathematical table making. He had set his staff to work evaluating the functions that described the average behavior of random quantities. A typical function was the bell curve, sometimes called the normal curve. This curve described how certain quantities, such as the heights of people or the width of a crab’s body, clustered around a central average value. Statisticians need to know the area underneath the bell curve, a value that is tedious and time-consuming to compute. Pearson had his computers tabulate these values as a service to the general scientific community. “It is needless to say that no anticipation of profit was ever made,” wrote Pearson; the computers “worked for the sake of science, and the aim was to provide what was possible at the lowest rate we could.” When he published a book of these tables, he apologized for having to set a price on the work but claimed “That to pay its way with our existing public, double or treble the present price would not have availed.”73
The statistical tables were only a small part of the computations at the Biometrics Laboratory. The bulk of the computations summarized large sets of data and were difficult to undertake without an adding machine or other calculating device. Indeed, Pearson often referred to the work of calculation as “cranking a Brunsviga,” a phrase that understated the role of computation at the Biometrics Laboratory. Through the first decades of the twentieth century, every member of the laboratory undertook at least a little calculation each day. In 1908, one visitor complained “that preoccupation with mastery of details of calculation and technique obscured, to some extent, the full meaning and scope of the new science.”74
This new science, the science of mathematical statistics, offered a new way of studying a vast range of human problems, including those found in medicine, anthropology, economics, sociology, and even psychology, a field that was not quite separated from the discipline of philosophy. However, in the first decade of the twentieth century, Pearson’s new science was still linked, at least partially, to the study of human inheritance, a field that had acquired the name of eugenics. Francis Galton had been an early proponent of eugenics and had established a laboratory that collected family trees and looked for patterns of human inheritance. In his eighty-eighth year, Galton proposed to donate his laboratory and his fortune to University College London. The money would be used to support a professor of eugenics, a position that was given to Karl Pearson. Pearson’s interest in eugenics is well documented and has been the subject of several scholarly studies. “When it came to biometry, eugenics, and statistics,” wrote historian Daniel Kevles, “[Pearson] was the besieged defender of an emotionally charged faith.”75 Grateful for the financial support, Pearson accepted the position, which put him in charge of two laboratories. “There is undoubtedly work enough f
or two professors,” he wrote, “but it is an ideal of a distant future.”76
CHAPTER EIGHT
Breaking from the Ellipse: Halley’s Comet 1910
Once more the west was retreating, once again the orderly stars were dotting the eastern sky. There is certainly no rest for us on the earth.
E. M. Forster, Howards End (1910)
“BEFORE THE 1835 RETURN [of Halley’s Comet] there were at least five independent computations of the orbit,” complained the English astronomer Andrew Claude de la Cherois Crommelin (1865–1939), “and it is difficult to understand why an equal amount of interest is not shown in the approaching return.”1 As Crommelin well knew, astronomers had no pressing questions that would be answered by calculating the comet’s orbit. Newton’s analysis of the solar system had been accepted by astronomers as the laws of celestial motions. The contradictions to these laws, which were being explored by Albert Einstein, offered no idea that might be tested by the return of a comet. In 1909, less than a year before the expected return, there could be found only two calculations of the date of perihelion. The first had been done by Pontécoulant, the computer of the 1835 return. Pontécoulant had cycled his 1835 equations through one more orbit, though he had added data to his analysis and included new terms to account for the gravity of Neptune. As no new planets had been discovered since 1846, many scientists felt that there was nothing to add to the calculation, but Andrew Crommelin disagreed. “Doubtless [Pontécoulant] regarded it as certain that there would be numerous investigations when the time drew nearer,” he argued. “This is borne out by the fact that there are certainly some slips or misprints” in the computations.2
During the late nineteenth century, some astronomers had experimented with nontraditional ways of computing cometary orbits. The Swedish astronomer Anders Jonas Ångström (1814–1874) had adopted a statistical approach. Making no effort to address the physics of the orbit, he confined his attention to the dates of the comet’s returns. From his analysis, he discovered that the average time between perihelions was 76.93 years and found that this period varied in a cyclical manner. With this information, he constructed a simple equation to predict the date of the perihelion. Applying this equation to all of the known sightings of the comet, he computed the date of every return. In most cases, the equation missed the actual date by only a few months. Though these values did not approach the accuracy of Pontécoulant’s 1835 calculation or even Alexis Clairaut’s 1758 work, they were far more accurate than the equation’s prediction of the 1910 return. Ångström’s equation suggested that the first return of the twentieth century would not occur until 1913, three years after the generally accepted prediction. Crommelin was not impressed with this work. “We have here a curve which admirably fits 25 successive passages,” he wrote, “and yet the first time it is used to predict a return it breaks down utterly, the error being almost 3 years or three times the largest previous error.”3
In spite of his French name, Crommelin was a British subject and an assistant astronomer at the Greenwich Observatory. He reported to George Airy’s successor and oversaw the observatory’s program of data reduction. The computing staff included ten full-time adult computers and twenty-six occasional workers, who reduced observations or prepared ephemerides when the research demanded it. They occupied a new facility behind the original observatory building which was equipped with calculating machines, slide rules, mathematical tables, and other computing aids.4 This office structure, which combined the central computing room of William Stratford with the part-time workers of Nevil Maskelyne, could also be found in business offices of the time. Increasingly, office managers were forming a single pool of secretaries and stenographers to handle normal correspondence and were relying on outside workers for the extra demand of peak seasons. The United States Navy had also adopted this model for their computers, combining the calculating staffs of the Naval Observatory and the American Nautical Almanac into a single staff of eight, and relying on the contributions of twenty part-time computers at key times of the year, such as during the final preparation of the almanac.5
With the Greenwich computing staff at his disposal, Crommelin could have been tempted to improve Pontécoulant’s calculations simply by devoting all of his resources to the task. He could have divided the calculation into smaller steps and assigned all of his computing staff to the problem. Instead, he returned to the original analysis of the comet’s motion and removed a key element that had been the basis for all cometary calculations, the elliptical orbit. Beginning with Edmund Halley’s work in 1695, astronomers had assumed that the comet followed the idealized orbit of an ellipse and computed how the planets stretched and altered this path. As a calculation stepped the comet around the sun, it would eventually place the object so far from its original orbit that astronomers would have to recalculate the ellipse. This adjustment was a time-consuming task, but it was essential in order to maintain the accuracy of the work. It “is a frequently troublesome process and does away with much of the advantage that there is in assuming that the comet is moving in an ellipse,” wrote Crommelin.6
Rather than attempting to improve Ångström’s work or correcting the equations of Pontécoulant, Crommelin argued that he would get the best results by “discarding the elliptical hypothesis altogether and proceeding by mechanical quadratures.”7 Mechanical quadratures is a method for solving differential equations, the basic mathematical expressions that model the motion of bodies in space. Differential equations describe relationships between the position of an object, its velocity, and the forces acting upon it. Newton solved a differential equation when he analyzed the way in which one body moves around another under the influence of gravity. He had used the techniques of calculus to solve this equation and discovered that one of the possible results was an ellipse. Mechanical quadratures, a technique now called “numerical integration,” was an alternative to Newton’s calculus. It solves a differential equation solely by numerical methods, with no reference to the original ellipse or any other curve.
Crommelin, with the assistance of an observatory colleague, Phil Crowell (1879–1949), identified the basic differential equations that described the path of the comet and created a computing plan for the Greenwich Observatory computing staff. The computing plan had certain similarities to the plan that Clairaut had used in 1757. It located all the key objects in space and described the forces acting between them. At each step of the calculation, the computers advanced the comet, Saturn, Jupiter, and the other planets forward by a small distance. They did not worry about elliptical orbits but instead followed the direction of the forces. Once they had moved the objects, they had to recalculate all the forces. It was a slow and methodical process, one that required much grinding of Brunsvigas and other calculating machines. Without adding machines, only the most dedicated computers would attempt to use mechanical quadratures to compute the orbit of Halley’s comet. Even though Crommelin and Crowell had the assistance of the Greenwich Observatory computing staff, they found that the work took longer than they had anticipated. “Owing to the pressure of time it has not been possible to do the whole of the work in duplication,”8 they confessed. They were able only to confirm that there were no gross errors in the result, which suggested that the perihelion would occur on April 17.
When Halley’s comet appeared as a faint speck in September 1909, the two astronomers returned to their calculations in order to get an exact date for the perihelion. Rather than recalculate the entire orbit using mechanical quadratures, they simply employed the traditional formula for an elliptical orbit. “This assumption is amply sufficient to give the date of perihelion,” they wrote.9 This calculation gave a date of April 20, and though this result was of some interest to astronomers, it proved to be of limited importance to the larger public in both Europe and the United States. Those outside of the scientific community looked for some larger meaning in the comet, something beyond the periodic cycling around the sun of a material lump. The author
Mark Twain saw it as the grand end of his era. “I came in with Halley’s Comet in 1835,” he wrote. “It will be the greatest disappointment of my life if I don’t go out with Halley’s Comet.”10
19. Path predicted for Halley’s comet in 1910 as seen from London
“We had the sky up there, all speckled with stars,” Twain had written in his novel The Adventures of Huckleberry Finn, “and we used to lay on our backs and look up at them, and discuss about whether they was made or only just happened.” Twain’s protagonist could not believe that anyone or anything could have created the stars because “it would have took too long to make so many,” but he conceded that they might have been laid, like the eggs of a frog. In the years that had passed since Twain wrote this novel, astronomers had developed some tools that could gather information on the constitution and origin of the comets. By dividing the reflected light of the comet into its individual colors, they were able to identify some of the substances to be found in its head and tail. Such information was of interest to an age that was anxious about the fact that the Earth would pass through the tail of the comet. A French astronomer was quoted in the New York Times as stating that the comet “would impregnate the atmosphere [of the Earth] and possibly snuff out all life on the planet.”11 Of all the predictions, both good and ill, that circulated in the spring and winter of 1910 concerning the comet, only Twain’s prediction of his own demise proved to be accurate. Twain died on April 20, 1910, just as the comet was passing through its perihelion and was starting on its outbound course.
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