It may be noticed that the difficulties of Bouguer and De la Condamine included troubles with untrustworthy instruments; but during the following half-century, while geodetic work proceeded apace in France, and was also carried on by measurements in South Africa, North America, and Italy, instruments making for greater precision were being designed. [Illustration: Fig. 15.--Ramsden’s Theodolite.] The instruments and data available during the sixteenth and seventeenth centuries had been fairly effective in skilled hands for the observation of latitude, but observations for longitude remained very difficult. Regiomontanus had prepared ephemerides for 1474–1506, and Columbus used them; Peter Apianus made a series for 1521–70, but the results continued to be far from accurate till the appearance of Kepler’s Rudolphine Tables in 1526. Harrison’s work on the chronometer had been anticipated as early as 1530 by Gemma Frisius, who indicated the possibility of using a clock in determining longitude; but even Huygens’s clock was not found effective for this purpose. In 1735, however, John Harrison’s first chronometer appeared, and afforded the accurate measurement of time under varying conditions which is essential to the calculation of longitude. About 1737 Jonathan Sission produced a theodolite, and later in the century Ramsden’s greatly improved theodolite (actually a pioneer instrument, greatly though its type was afterwards modified in detail) was constructed and brought into use in the trigonometrical survey of England and Wales, which was begun in 1784. [Illustration: Fig. 16.--Modern five-inch transit Theodolite.]