An arc was measured and the length of the degree calculated in England by Richard Norwood in 1633–37. Important improvements in instruments appear about this time. Thus François Vernier introduced in 1630 the microscopic attachment named after him the vernier, through which close and accurate reading of scales may be made. In 1643 appeared Torricelli’s barometer, and in 1648 Pascal, in France, applied the principle of the difference of atmospheric pressure at different elevations to the measurement of height above sea-level. A little later follows the application of the telescope to surveying instruments. In 1669 Jean Picard, measuring an arc in France, used a quadrant fitted with a telescope in which crossed wires were inserted, providing lines and a point (the intersection of the wires) in the field of observation, for the purpose of ensuring accuracy. Meanwhile, in 1657, Christian Huygens, a Dutch scientist, introduced (if he did not actually invent) the pendulum clock; and Jean Richer, using one in the course of astronomical work undertaken in South America for the French Academy of Sciences, found that the pendulum regulated to beat seconds in Paris failed to do so in Cayenne. This opened up the problem of the deviation of the earth’s figure from the true sphere; Sir Isaac Newton had argued such deviation to exist from mathematical theory associated with the rotation of the earth, and Huygens himself also investigated the question. Their conclusions, and that to be drawn from Richer’s pendulum observation, represented the earth as an oblate spheroid, or (in simpler expression) as somewhat flattened at the poles, the polar diameter being shorter than the equatorial. On this showing, a degree measured, let us say, in the north should be longer than one measured nearer the equator; but J. and D. Cassini, in the course of an extensive triangulation in France in 1684–1718, obtained an opposite result. Their measurements were subsequently proved inaccurate, but not before much controversy had arisen as to whether the earth is a prolate spheroid (as their results would go to prove), or oblate, as held by Newton and Huygens; and the French Academy had despatched expeditions to Peru and to Lappland, there to measure arcs for comparison. The Peruvian arc was measured by Pierre Bouguer and Charles de la Condamine in 1735–45, in the face of difficulties sufficiently reflected by the length of time occupied and by the fact that they fell out over the work and published separate accounts of it; the Lappland arc was worked out by P. L. M. de Maupertuis and his party in 1736–37. [Illustration: Fig. 13.--Davis’s Back-staff.] [Illustration: Fig. 14.--Pretonius’s Plane-table.]