LETTER XVI.

THE SAME SUBJECT CONTINUED.

LET us now quit the researches of Newton, and see how far his mathematical deductions have been confirmed by experience. This is the true test of all hypothetical reasoning, and is what he himself lays down as the basis of every philosophical enquiry. The great utility and importance of this interesting subject was far from being unknown to the ancients. We are assured from the testimony of Herodotus, and other early historians, that attempts had been made to discover the true figure of the earth, by many of the most celebrated mathematicians of antiquity: Ptolemy, in his Almagest, has preserved the measures of Hipparchus, Eratosthenes and Posidonius, who all lived before the time of Christ; and from what M. Bailly has advanced in his Histoire de l'Astronomie Moderne, it appears highly probable, that this singular enterprise had been undertaken in the still more remote ages of the world.

But as all the determinations of the ancients are uncertain, on account of our being unacquainted with the length of their stadium, or principal measure, I shall pass over the peculiar methods and operations they employed, and proceed to those of the moderns, which are far more accurate and scientific. Riccioli attempted to measure the earth according to a method mentioned by Kepler. It

was known from observation, that heavy bodies, in falling, tend towards the centre of the earth. And as the distance of any two places upon the surface of the earth may be considered as the base of a triangle, whose vertex is at the centre, he measured a large base of this kind, in the most accurate manner possible, and found the angles which it made with a plumb line at each of its extremities. The sum of these angles, by a property in geometry, being taken from a hundred and eighty degrees, gave him the angle at the vertex; and as he had now obtained the measure of an angle at the centre of the earth, and the length of a corresponding arc upon its surface, it was easy, by the rule of proportion, to find the length of the whole circumference. For, by the property of the circle, as the degrees in this angle are to three hundred and sixty degrees, so is the length of the base to the circumference required.

This method of Riccioli, however, is more ingenious than accurate; he wanted to measure the earth, without having recourse to celestial observations; but the independence to which he aspired was not to be obtained. Order and regularity are only to be found in the heavens; and it is to them we are indebted for almost all we know of the earth. We are deceived by every thing around us; even our senses mislead us; and what we think ourselves the best acquainted with, frequently proves to be an illusion. Objects seen at a distance never appear in their true places; they are always more or less elevated, according to the

season, and the hour of the day; and on this account, it is not easy to determine either their true height, their direction, or the angle at the centre, which depends upon this direction. By not attending to these particulars, Riccioli was mistaken near six thousand toises in the length of a degree.

The next who attempted to determine the circumference of the earth was Snellius, a German. He measured the distance between Alcmaer and Bergen-op-zoom; and by taking the celestial arc, which corresponds to this distance, with proper instruments, he found the length of a degree to be fifty-five thousand and twenty-one toises. But the person who engaged in this enterprise with the most success, was our countryman Mr. Richard Norwood. In the year 1635, he took the sun's altitude, when it was in the summer solstice, both at London and York, with a sextant of five feet radius, and by that means found the difference of latitude between these two cities to be two degrees and twenty-eight minutes. He then measured their distance, in the usual manner; and having taken into the account all the turnings and windings in the road, with the ascents and descents, he reduced it to an arc of the meridian, and found it to contain twelve thousand eight hundred and forty-nine chains; which distance, being compared with the difference of latitude, gave him five thousand two hundred and nine chains to a degree, or about sixty-five English miles.

This method will want no explanation, if the two places be considered as lying under the same

meridian, which indeed is nearly the case; for then the terrestrial and celestial arcs will exactly correspond with each other, and the relation of either of them to the whole circumference will be readily found. The same thing may also be easily performed, by trigonometry, when the two places lie under different meridians; for if we measure the distance of any two objects, and take the angles which each of them make with a third, the triangle, formed by the three objects, will become known; so that the other two sides may be as accurately determined by calculation, as if they had been actually measured in the same manner as the first. And by making either of these sides the base of a new triangle, the distances of other objects may be found by trigonometry as before; and thus, by a series of triangles, connected together at their bases, we might measure the whole circumference of the earth. But this would be an enterprise as useless as it is laborious: for since we know the relation which any part of a circle bears to the entire circumference, the measure of a few degrees, or even of one single degree, will be sufficient to give the measure of the whole.

All the measures, however, that had been hitherto taken were subject to many inaccuracies, on account of the little attention that was then paid to the niceties of instrumental observations. The means of precision, which have since been found so necessary to an exact investigation of this delicate subject, were then wanting; and without them, it was impossible for either genius or indus

try to avoid considerable errors. By applying the telescope to the quadrant, and furnishing it with a micrometer, we are able to direct it with more certainty to the object, and to find the measures of angles with far greater exactness than could have been done by those who were unacquainted Iwith these admirable inventions.

The Academy of Sciences at Paris, perceiving, from these considerations, the necessity of a new measure of the earth, represented the execution of it as a matter of national honour and importance. All the states of Europe were now enjoying the blessings of a profound peace; and in this interval of happiness and repose, when the voice of genius could be heard, and the talents of individuals united, and directed to one object, the Academy, with a zeal not always to be found in large bodies of men, were unanimously disposed to encourage and assist in the undertaking. This was a moment favourable to the sciences; both the king and his ministers were men of liberal and enlarged minds; improvements were constantly made in every branch of useful knowledge, and genius had something more than empty praise, as a reward for its labour.

M. Picard was the person employed to perform this important business. He began by measuring the distance between Villejuif and Juvisy; (Pl. 1x. fig. 3.) and this base, which he found to be five thousand six hundred and sixtythree toises, was the one to which he referred all his calculations. He next placed himself at Juvisy,