412 THE MATHEMATICAL PRINCIPLES [BOOK III the excesses of the length of the pendulum at Paris above the lengths of the isochronal pendulums observed in those latitudes are a little greater than by the table of the lengths of the pendulum before computed. And therefore the earth is a little higher under the equator than by the prece ding calculus, and a little denser at the centre than in mines near the sur face, unless, perhaps, the heats of the torrid zone have a little extended the length of the pendulums. For M. Picart has observed, that a rod of iron, which in frosty weather in the winter season was one foot long, when heated by lire, was lengthened into one foot and -]- line. Afterward M. de la Hire found that a rod of iron, which in the like winter season was 6 feet long, when exposed to the heat of the summer sun, was extended into 6 feet and f line. In the former case the heat was greater than in the latter ; but in the latter it was greater than the heat of the external parts of a human body ; for metals exposed to the summer sun acquire a very considerable degree of heat. But the rod of a pendulum clock is never exposed to the heat of the summer sun, nor ever acquires a heat equal to that of the external parts of a human body ; and, therefore, though the 3 feet rod of a pendulum clock will indeed be a little longer in the summer than in the winter season, yet the difference will scarcely amount to \ line. Therefore the total difference of the lengths of isochronal pendulums in different climates cannot be ascribed to the differ ence of heat ; nor indeed to the mistakes of the French astronomers. For although there is not a perfect agreement betwixt their observations, yet the errors are so small that they may be neglected ; and in this they all agree, that isochronal pendulums are shorter under the equator than at the Royal Observatory of Paris, by a difference not less than 1{ line, nor greater than 2