Astronomy as a physical science will receive consideration in the next number; here only the mathematical elements are noticed, and they are everywhere manifest. The same general laws control all material bodies, those near to us, and those seen at a distance. So the science of the stars is not now mere theory, but has all the elements of mathematical certainty. When dealing with such vast numbers and magnitudes as engage the astronomer’s attention, with a few known principles or laws, and abundant recorded telescopic observations for the basis of their work, men can calculate even more accurately than they can count or measure. Having once prepared their theorem, aided by the logarithms of Napier[1] that simplify and shorten the more difficult arithmetical calculations, they can readily determine the distance, magnitude and motions of a planet, and know that it is done with sufficient exactness. The distances of the heavenly bodies are generally determined by their parallax, that is the difference between the directions of the bodies as seen from two different points. The inclination of the lines thus drawn is the angle of parallax. By supposing the lines prolonged to the sun, and other lines drawn through the points selected to the center of the earth a quadrangle is formed, all the angles and sides of which are easily found. In measuring very minute parallaxes it may not be possible to determine the exact position of the body as projected on the celestial sphere, but in that case recourse can be had to relative parallax, or the difference between the parallaxes of two bodies lying nearly in the same direction. The best opportunity for this is afforded by the transit of Venus, and on this account great interest is felt in that phenomenon, and extensive preparations are made for taking accurate observations. The figure, size and density of the celestial bodies have all been calculated with approximate certainty. The orbits, through which they pass in their revolutions, described, and their velocities ascertained. There is a solar system of which the sun is the center, and in its relation to the planets stationary, though really moving on through infinite space; the orbits through which planets move are not circles, but more or less elliptic, having the sun at one focus of the ellipse. That planets move in ellipses was announced by Kepler[2] as the first law governing their motions, and a second deduced from this and confirmed by observations, is that they do not move with equal velocity in all parts of their orbits; and that _a line drawn from the center of the earth to the center of the sun passes over equal spaces in equal times_. He also found as a third law that _the squares of the times of the revolutions of the planets are proportional to the cubes of their mean distances from the sun_.