[Illustration: Figure 16.--HEADSTOCK OF A GERMAN INSTRUMENT-MAKER'S LATHE, typical of the mid-19th century, showing the traverse spindle, interchangeable lead screws, and semicircumferential nut containing several leads. The nut may be brought into engagement by the lever at top rear of the headstock. This releases the end thrust control on the spindle simultaneously with engagement of the nut. (Smithsonian photo 49839.)] [Illustration: Figure 17.--DAVID WILKINSON'S SCREW-CUTTING LATHE, patented in the United States in 1798. Note the ready facility with which the lead screw may be exchanged for another and the same means of supporting and driving as in figure 15. (U.S. National Archives photo.)] An attack on this problem, which interestingly reverts to the fundamental principle of motion derived from a master screw without the intervention of other mechanism (fig. 19), is covered by a patent[5] issued to Charles Vander Woerd, one-time superintendent of the Waltham Watch Company. The problem is well stated in the patent: This invention relates to the manufacture of leading screws to be used for purposes requiring the highest attainable degree of correctness in the cutting of the screw-threads of said screw ... as, for example, in machines for ruling lines in glass plates to produce refraction [sic] gratings for the resolution of the lines of the solar spectrum, such machines being required to rule many thousands of lines on an inch of space by a marking device which is reciprocated over the glass plate and is fed by the action of a leading screw after the formation of each line. Great difficulty has been experienced in constructing a leading screw for this and other purposes, in which the thread is so nearly correct as to produce no perceptible variation in the microscopic spaces between the ruled lines or gratings.... Various causes prevent the formation of a thread on the rod or blank, which is absolutely uniform and accurate from end to end of the rod. Among other causes are the variations of temperature from time to time, the imperfections of the operating leading screw, the springing of the leading screw and of the rod that is being threaded, and other unavoidable causes, all of which, although apparently trivial and producing only slight variations in the thread at different parts of the rod or blank, are of sufficient moment to be seriously considered when a screw of absolute accuracy is desired. [Illustration: Figure 18.--NASON'S LATHE, patented in 1854, showing a master lead screw driven at less than work speed so that the master could be of a coarser and more durable pitch than the work. U.S. patent 10383.]