by subtracting unity from each of the epacts belonging to those new moons, they might be made to serve for the subsequent century. And as there are only thirty possible series of these numbers, it was sufficient to show by a table, what series belonged to every century; by which the times of the new moons might be readily discovered.

This is a concise account of the Gregorian reformation; and if you are desirous of further information, I must refer you to works written expressly upon the subject; for to have given a minute detail of every particular, would have required a large volume. If what has been said, however, be properly attended to, it will enable you to form a general idea of this intricate business; which, as the matter is now fully settled, is all that is requisite. It only remains just to mention, what reception this alteration of the style met with, from the different states of Europe.

Pope Gregory ordered all the ecclesiastics under his jurisdiction to conform to this new method of reckoning, and exhorted the Christian princes to adopt it in their dominions. But the protes

tant states, at that time, refused it; the reformed religion being in its infancy, the zeal of its professors was violent, and their opposition to the pope unbounded: whatever bore the appearance of his authority, was rejected as an unwarrantable encroachment upon their newly-acquired liberties; and though the propriety of the alteration was ac

knowledged, it was condemned on account of its orginating with a party so extremely obnoxious to

them.

But the difference between the old and new style, as the Julian and Gregorian accounts are generally called, occasioned great confusion in the commercial affairs of the different states of Europe. In England, particularly, this inconvenience was considerably felt, and several attempts were accordingly made to introduce the reformed calendar; but popular prejudices were too strong to be easily overcome. The mathematicians, indeed, more influenced by scientific considerations than cavils about points of religion, were continually urging the necessity of some correction, and proposed several methods of obtaining it, which might be adopted without inflaming the minds of the multitude.

One of the most simple and ingenious of these, I shall just mention; which was, that an act should be passed, declaring that there should be no leap-year for forty years to come; by which means, the ten days, that had been gained by the old account, would have been imperceptibly lost, and the old style reduced to the new, without any sensible variation in the fixed time of feasts, and other observances. A proposal of this kind was sent to Dr. Wallis, then professor of Geometry at Oxford, for his opinion: but the doctor, with a narrowness of sentiment, which could scarcely have been expected from a man of his extensive erudition, observed, that the proposal was specious enough in appearance, but that the hand of Joab

might be perceived in it. He imagined it to have originated with the papists; and though he acknowledged its propriety, was yet afraid of its being adopted, lest it should open the door to further encroachments.

But though all proposals were at that time rejected, yet those who wished for a reformation, still continued their applications; and in 1752, an act of parliament, after much debate, was obtained for this purpose. And as a hundred and seventy years had elapsed since the Gregorian alteration took place, the old style had consequently gained above a day more upon the course of the sun than it had at that time; it was therefore enacted, that instead of cancelling ten days, as had been done by the Pope, eleven days should be left out of the month of September; and, accordingly, on the second of that month, the old style ceased, and the next day, instead of being the third, was called the fourteenth.

It may be observed, however, that the Gregorian reformation met with many opponents from men of science; Mastlin, Scaliger, Vieta, and other mathematicians, attacked it with great violence, and proposed methods of their own, which they considered as less exceptionable. But Clavius, to whom the care of this business was assigned, after the death of Luilius, composed a large work in its vindication, and victoriously combated all his adversaries. Some defects, however, it must be acknowledged, are to be found in this method; but the task of reformation was

difficult; the reformers had to choose among a number of inconveniences, and they appear to have preferred the least considerable; we ought, therefore, to applaud them for their skill, rather than censure them for defects which no human abilities could have wholly avoided.

LETTER XV.

OF THE MENSURATION OF THE EARTH.

To measure the earth, and thence to determine its magnitude and figure, is one of the most astonishing enterprises, that ever was undertaken by man. Confined to a particular spot, without any other scale or model than his own proper dimensions, how is he to find the distances of places which he can never visit, and to embrace the vast circumference of the globe? The space he has passed through, may be estimated by the number of steps he has taken, and this will furnish him with some of the most simple measures, the foot and the yard; the cubit is also the length of his arm, from the elbow to the end of the middle finger; and the fathom, or toise, is the distance he can reach with his two arms extended; but what are these small measures in comparison to the perimeter of the earth? They are but as a grain of sand to the largest mountain. Difficulties, however, serve but as incitements to action; and man, instead of being confounded by the inadequacy of his natural powers, finds a resource in his intelligence which supplies their defect: he multiplies small measures, till he arrives at the greatest, and forms to himself an unit, to which he refers all the parts of the universe.

By means of chains and cords, which are certain multiples of the toise, or the yard, he obtains