Free The Dawn of Innovation by Charles R. Morris Page A

divisions by geometric methods, using a compass and square edge, but beyond fairly crude resolutions, any method of marking by hand was apt to be greatly inaccurate. The solution was leverage. Releasing a pin could drop a trip-hammer: a small motion was converted into a much larger one. But leverage could be reversed, and a gross movement converted into a much finer one. And that was the path of truth. 14
    The illustrations on pages 52–53 show various methods of achieving greater precision from imprecise measuring tools, most commonly by exploiting the leverage gained from screws and gears. Assume a tool or workpiece held by a chuck that is moved by a screw with twenty threads to the inch. Rotate the screw one full rotation, and the chuck advances by a twentieth of an inch. A gear train with a net twenty-to-one gear-tooth ratio would accomplish the same result. Such solutions are easy to envision, but they just relocate the problem—from making accurate measurements
to making accurate screw threads and gear teeth. Clockmakers had small machines for cutting gear teeth early in the eighteenth century, but they weren’t especially precise. Individual prodigies like John Harrison could work marvels of precision by hand, but that was not a solution either. The challenge was to embed the required level of precision in machinery that could make other machines, so those machines could pass on their precision to generations of new tools and instruments. That took the better part of a hundred years.
    Why did it take so long? Because as a practical matter, it is not possible to make an accurate screw thread without an accurate screw-cutting lathe, which is impossible to make without tools with accurate screw threads. In other words, accuracy could be achieved only by a process of successive approximation. And that is a tedious path, with many byways, involving better metals, better bearings, even better magnifying lenses. The work took place primarily in England because naval and other high-end engineering applications had created a market for high-precision scientific instruments for astronomy, surveying, and a host of industrial uses. Brilliant scientists in other countries were not as successful. For example, a French nobleman, the Duc de Chaulnes, made several important advances in gear-cutting machinery, but he was working with his own money and lacked the thick network of machine users, designers, and craftsmen that existed in England.
    Jesse Ramsden usually gets credit for inventing the first industrial-scale dividing engine. It didn’t cut the gear teeth but marked their placement, which was the essential task. “Inventing,” in this context, is not quite the right word, for all such machines were developments of others’ work. Several important features of the Ramsden dividing engine, like screw-based motion controls, were inspired by predecessors like de Chaulnes, as Ramsden freely acknowledged. One of his best-known instruments representing “the best design of the time” 15 (from the late 1780s) was a large theodolite, or surveying telescope, which fixes locations by taking the intersection of horizontal and vertical circles. Measurements were read from verniers (see illustration) and viewed through microscopes. Ramsden built two of the instruments, which were used for a complete survey of Great Britain. At a distance of ten miles, the instrument was accurate to one arc second, or about three inches.

    Â 

    A. Astronomer Tycho Brahe (1546–1601) popularizes the use of linear transversals to achieve greater precision. If the marks on the two axes at the limits of the day’s technlogy for acurate gradiation, simply making the grid and drawing the transversals as shown improves the accuracy by a factor of ten. The heavy vertical line intersects at the. 04horizontal mark. B. By yhe eighteenth century astronomers learned to improve astral measurements with are transversals. The