For the first two days of his seclusion J. T. Maston thought over the problem without touching the chalk. He read over certain works relative to the elements, the earth, its mass, its density, its volume, its form, its rotation on its axis, and translation round its orbit—elements which were to form the bases of his calculations. These are the principal, which it is as well the reader should have before him:— Form of the Earth: an ellipsoid of revolution, with a major diameter of 7926·6 miles, and a minor diameter of 7899·6 miles. The difference between the two, owing to the flattening of the spheroid at the Poles being 27 miles, or one two-hundred-and-ninety-third of its mean diameter. Circumference of the Earth at the Equator: 24,899 miles, the meridional circumference being 24,856 miles. Surface of the Earth: 197,000,000 square miles. Volume of the Earth: 260,000,000,000 cubic miles. Density of the Earth: five and a half times that of water, the mass being approximately 6,000,000,000,000,000,000,000 tons. Duration of the Earth’s journey round the Sun: 365 days and a quarter, constituting the solar year, or more exactly 365 days, 6 hours, 9 minutes, thus giving the spheroid an average velocity of 66,000 miles an hour. Rate of the Earth’s rotation at the Equator: 1037·4583 miles per hour. The following were the units of length, force, time, and inclination which J. T. Maston required for his calculations; the mile, the ton, the second, and the angle at the centre which cuts off in any circle an arc equal to the radius. It was on the 5th of October, at five o’clock in the afternoon—it is important to know the precise time in a work of such celebrity—that J. T. Maston, after much reflecting, began to write. And, to begin with, he attacked the problem at its base—that is, by the number representing the circumference of the Earth, and one of its great circles, viz. the Equator. The blackboard was placed in an angle of the room on an easel of polished oak, well in the light of one of the windows which opened on to the garden. Little sticks of chalk were placed on the shelf at the bottom of the board. A sponge to wipe out with was in the calculator’s left hand. His right hand, or rather his hook, was reserved for writing down the figures of his working. He began by describing the circumference of the terrestrial spheroid. At the Equator the curve of the globe was marked by a plain line representing the front part of the curve, and by a dotted line representing the back half of the curve. The axis was a perpendicular line cutting the Equator, and marked N.S. On the left-hand top corner of the board he wrote the number that used to represent the earth’s circumference in metrical measurement— 40,000,000.