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As the degrees progressively diminished towards the south, but much more towards the middle than towards the extremities, the middle of the whole arc was taken; and, on comparing it with the degrees measured at Peru, between the years 1737 and 1741, the ellipticity of the earth was concluded to be 1/334 the mean degree, 57008 toises; and the METRE, which is the ten-millionth part of the quarter of the meridian, 443.296 lines of the old French toise which had been used at Peru.
So many took part in these singular experiments, which assumed rather the appearance of outdoor sports than of scientific demonstrations, that in a short time we had provided the asteroid with a very large number of little moons, or satellites, of gold, which revolved around it in orbits of various degrees of ellipticity, taking, on the average, about three-quarters of an hour to complete a circuit.
Q. Is there not a liability in the cylinder to become oval from the strain thrown on it by the piston? A. There is, no doubt, a tendency in oscillating engines for the cylinder and the stuffing box to become oval, but after a number of years' wear it is found that the amount of ellipticity is less than that which is found to exist in the cylinders of side lever engines after a similar trial.
The ellipticity of its companions was determined by Pickering and Douglass; indeed, that of No. 3 had long previously been noticed by Secchi. No. 3 also shows equatorial stripes, perceived in 1891 by Schaeberle and Campbell, and evident later to Pickering and Douglass; nor need we hesitate to admit as authentic their records of similar, though less conspicuous markings on the other satellites.
His first work, the "Mysterium Cosmographicum," is the record of a splendid blunder that cost him five years' toil, and he spent ten years of fruitless and baffled effort in the deduction of the laws of areas and orbital ellipticity. But this audacious diviner knew well the use of Hypothesis, and he applied it as an instrument of investigation as it had never been applied before.
The results of Clairaut's researches on the figure of the earth are mainly embodied in a remarkable theorem discovered by that geometer, and which may be enunciated thus: The sum of the fractions expressing the ellipticity and the increase of gravity at the pole is equal to two and a half times the fraction expressing the centrifugal force at the equator, the unit of force being represented by the force of gravity at the equator.
He found that the angular velocities of Mars at its nearest and farthest distances from the sun were in inverse proportion to the squares of the corresponding distances. This law, deduced, was the immediate path to the law of orbital ellipticity.
We mean that resulting from a certain slow astronomic rhythm, by which the northern and southern hemispheres are alternately subject to greater extremes of temperature. In consequence of the slight ellipticity of its orbit, the Earth's distance from the sun varies to the extent of some 3,000,000 of miles.
It must be borne in mind, however, that the ellipticity thus deduced from the movements of the moon, is not the ellipticity corresponding to such or such a country, the ellipticity observed in France, in England, in Italy, in Lapland, in North America, in India, or in the region of the Cape of Good Hope, for the earth's materials having undergone considerable upheavings at different times and in different places, the primitive regularity of its curvature has been sensibly disturbed by this cause.
These two inequalities of very different magnitudes connected with the cause which produces them by analytical combinations of totally different kinds have, however, both conducted to the same value of the ellipticity.
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