When Computers Were Human (6 page)

In February 1765, the British Admiralty approved Maskelyne's plan for an almanac, gave him a staff of five computers, and told him to begin work on celestial tables for 1767. To all involved with the project, including Maskelyne and the members of the Admiralty, this assignment must have seemed quite reasonable. Under normal circumstances, the almanac staff would have to produce a new publication every year. Maskelyne had fully twenty-two months before the start of 1767, almost twice
the time he should have needed, but the process of recruiting and training his computing staff proved to be more challenging than he had anticipated. He organized the computing staff as a cottage industry, a form of production that was still common in England, even though it was starting to be eclipsed by the factory. In cottage production, the workers labored in their own homes. Their materials, instructions, and often their tools were provided by the company or individual for whom they worked. In the clothing industry, cottage workers might receive carded wool and spin it into yarn. For the
Nautical Almanac
computers, Maskelyne provided paper, ink, and instructions that were called “computing plans.” Maskelyne wrote these plans on one side of a heavy sheet of folded stationery. The instructions, scrawled in a slightly disheveled hand, summarized each step of the calculation. Occasionally, he would illustrate the computations with a hasty sketch of an astronomical triangle. On the other side of the paper he drew a blank table, ready for the computer to complete.
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The computers produced tables that tracked the motion of a planet or the sun, tables that were called ephemerides in the plural (or an ephemeris in the singular). Most of these ephemerides were double-computed, prepared by two independent computers working from the same plan. Each computer would send Maskelyne a version of the ephemeris. Maskelyne would forward the two ephemerides to a third computer, who had the title of comparator. The comparator would search the two ephemerides for discrepancies and correct the mistakes. The only tables that were not double-computed were those of lunar motion. These tables were divided in half. One computer would calculate the moon's position at noon. The other would compute the position at midnight. The comparator would merge the two tables and make sure that the two sets of calculations were consistent.
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Initially, Maskelyne assigned two computers to prepare the 1767 volume of the almanac. A third acted as the comparator, and the remaining two were put to work on the 1768 volume. From what we know of his staff, all of them came from the second tier of astronomical talent. Most commonly, they had demonstrated some skill at astronomy but lacked the resources or the connections to acquire one of the prestigious scientific appointments at Cambridge or Oxford. The first computer of the 1767 volume, William Wales (1734–1798), came from a poor family in the north of England. The second computer, Israel Lyons (1739–1775), was a Jew and was unwilling to make the profession of belief that might gain him a place at the church-centered universities. The comparator, Richard Dunthorne (1711–1775), had shown the greatest ability to advance himself as a scientist. He, too, was born to a lower-class family but had demonstrated his mathematical prowess by analyzing the motion of
the moon. This work had given him a minor reputation as an astronomer and had connected him to a wealthy patron who provided Dunthorne with a regular income.
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4a. Computing sheet of Nevil Maskelyne

Whenever possible, Maskelyne attempted to reduce the amount of calculation by borrowing tables from other sources, such as the
Connaissance des Temps
. He also simplified some of the calculations by employing the method of interpolation. Interpolation expands a table by estimating
intermediate values rather than by calculating these numbers from the original equations. It is a mathematical means of connecting the dots. The computers would link the moon's position at noon to its location at midnight using a polynomial, a mathematical expression that is the sum of terms such as x, x
²
, and x
³
. With this polynomial, the computers estimated the moon's location at three-hour intervals without having to calculate new values from Mayer's tables.
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4b. Computing instructions prepared by Nevil Maskelyne

Even with Maskelyne's attempts to minimize the workload, the 1767
almanac fell behind schedule. Wales and Lyons needed time to learn the new computing procedures and develop the skill that would get the work done most efficiently. By the spring of 1766, Maskelyne recognized that his two computers would not be able to finish their computations in time for publication the following fall. Both were engaged in at least one other job and could not devote extra time to completing the calculations. Lyons worked as a surveyor and did other work for the British Admiralty, while Wales was involved in a number of astronomical projects. Fortunately, Maskelyne had a reserve pool of labor, the two computers who were preparing the second issue of the almanac. He told this pair to put aside their calculations and assist Wales, Lyons, and Dunthorne with the first issue. Together, the five computers finished the tables in late fall. The 1767 issue of the almanac appeared only six days after the start of the year.
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As the computers moved to the second and third almanacs, they were able to claim the first benefit that Smith had ascribed to divided labor, the increase in dexterity and speed. After three years of calculations, the almanac staff had completed all of the almanacs through the 1773 volume and were beginning the calculations for 1774. By 1780, they were creating tables six years in advance, and Maskelyne was able to reduce the number of computers from five to four.
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The division of labor for Maskelyne's first
Nautical Almanac
offered no innovation beyond the methods commonly applied in English commerce. The only difference between the computers and the carders and weavers of the cloth industry was the fact that the computers' product, the ephemerides, could be folded into a neat packet and sent through the mails. A more radical approach to the division of labor was found at the French Bureau du Cadastre. The bureau, a civil mapping agency, was a product of the French Revolution and hence embraced notions about labor and organization that were far more radical than those employed by Maskelyne at the British
Nautical Almanac
. The bureau prepared maps for governance, taxation, and land transactions. Initially, it had no computing division beyond a few assistant surveyors. It assembled a staff of almost one hundred computers when it became involved with the standardization of weights and measures that produced the metric system.

The metric system grew out of an attempt by the National Assembly to gain control of the French economy. In March of 1790, barely eight months after the storming of the Bastille prison, the National Assembly debated a proposal to discard “the incalculable variety in our weights and measures and their bizarre names” and adopt a unified measurement system based upon scientific principles.
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At that time, each region was free to establish its own set of measures. Local officials easily manipulated
these measures to their own advantage in a number of ways. Commonly, they could keep a large measure to collect taxes of grain and produce but reserve smaller measures for the payment of their own debts.
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The Académie des Sciences agreed to create the new system of weights and measures. They quickly stipulated several basic principles for the new system. They agreed that the standards of weight and length should be beyond the control of any political organization and that the units for area, volume, and even weight should be related to the unit for length. In one of their final discussions, the Académie stated that the new measures should form a decimal system. All units should be related through multiples of ten. For example, the meter, the standard measure of length, would be divided by ten to produce the decimeter, which in turn could be divided to produce the centimeter, the millimeter, and the micrometer. The liter, the gram, and the dyne, the standard units of volume, mass, and force, could also be divided or expanded in decimal multiples. The members of the Académie argued that this same principle should govern all standard units, including those that measured angles. Under their proposal, a right angle would no longer have 90 degrees. Instead, it would be split into one hundred new units called grades.
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The proposal for the decimal measurement of angles produced a major computational problem that led to the creation of a computing office at the Bureau du Cadastre. The principal users of angle measure, navigators and surveyors, did their work with sines, cosines, and other trigonometric functions. Without trigonometric tables prepared for the decimal grades, the new standard for angle measure would be unused. No surveyor or navigator, even one ardently committed to the revolutionary cause, would measure angles in grades if he had to convert his numbers into degrees in order to use a sine table. Openly or surreptitiously, they would measure their angles in degrees and use the trigonometric tables of the ancien régime to calculate their position on the globe or the area of a piece of land.

The director of the Bureau du Cadastre was Gaspard Clair François Marie Riche de Prony (1755–1839), a civil engineer with the country's elite Corps des Ponts et Chaussées, the Corps of Bridges and Highways. De Prony came from a family of “modest but ancient title” in the province of Beaujolais. His mathematical skill had brought him to the attention of the corps and gained him entrance to the corps's preparatory school in Paris. He graduated at the top of his class from the school and proudly accepted the uniform of a corps officer, which came with royal fleur-de-lys buttons.
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Following his graduation, de Prony had hoped to live in the capital and pursue scientific research, but the conventional assignment for young engineers was a term of service in the field. He fulfilled his duty and found
a way back to Paris by taking an appointment as an inspector, an officer who critiqued the mathematical analyses of other engineers and verified calculations. Though the assignment involved no independent work, he found it a pleasing activity, reporting that “happy circumstances then put me in contact, with the most distinguished savants of the capital.” It also brought him into contact with foreign savants, including Nevil Maskelyne. De Prony met Maskelyne when the corps decided that it needed to remeasure the difference in longitude between Paris and London. Beyond the intellectual challenge of this work, an accurate measurement of the difference would allow French surveyors to use the British
Nautical Almanac
in their work and enable the Académie des Sciences computers to compare their tables with the output of Maskelyne's computers. As part of the effort to measure the difference between the two capitals, de Prony traveled to Greenwich, met Maskelyne, and inspected the work of the almanac computers.
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De Prony had become leader of the Bureau du Cadastre because of a cautious and uneasy relationship between the corps engineers and revolutionaries. The revolutionaries were wary of the corps, their uniforms, and their fleur-de-lys buttons, yet they needed the services of corps officers and could not easily dismember the group. In an attempt to weaken the authority of the corps, the revolutionary government tried to disperse the officers, most of whom resided in Paris, and have them take positions in the countryside.
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In early 1791, the government ordered de Prony to move to southwest France but found that he was unwilling to take the assignment. “I have received your letter, informing me that I am appointed engineer-in-chief for the departement of the Pyrenees,” he wrote to his superintendent. “In these circumstances, I beg you to permit me to remain in Paris.” He argued that he was working on two reference books that would be difficult to complete without the resources found in the capital. Claiming that the research had “already cost me many sleepless nights,” he stated that he was willing to forgo a formal assignment so long as he could stay in Paris and continue with his research. After a brief confrontation, a senior officer intervened and gave de Prony the job at the Bureau du Cadastre.
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