Since his day, gravity has been discovered to be the bond which binds the solar system together, and its laws have been studied out. The differential and integral calculus, also discovered and perfected since his day, has enabled the scholar to grapple with intricate questions of higher mathematics, which, without its aid, would have remained insoluble. Availing themselves of the laws of gravity and of the aid of the calculus, astronomers have been able to give us a mathematical demonstration of Kepler’s laws, which, from being mere isolated facts or numerical coincidences, have passed into the realm of scientific truths. Now, we know the length of our own year—365.2422414 days; we know also the length of the year of Venus—224.70048625 days. If we divide the former by the latter, square the quotient, and then extract the cube root of this quotient, we shall obtain the number which indicates the proportion between the two mean distances. Applying this, we learn that if the distance of the earth from the sun be taken as 100,000,000 miles, the mean distance of Venus will be 72,333,240 miles. And consequently, when they are in the same direction from the sun, and supposing both to be at their mean distances from that luminary, the distance between them must be, according to the same proportion, 27,666,760 miles. It is obviously enough to know the actual value of either of those three distances to learn very easily the other two. The observations of the transit are intended to ascertain the last and smaller one. How this is done, and what difficulties are to be surmounted in doing it, we shall see further on. Just now we will remark that supposing the observer to have ascertained to the very furlong this distance, during the transit, between the planets, he must still do much before he can apply his proportion. That holds good only for the mean distances. There are only two points in the orbit or ellipse of each planet around the sun which are at the mean distance from that focus. Were those points for both planets to be found on the lines of the nodes, the matter would be easy. But it is not so. In June, the earth is approaching her greatest distance; in December, she is nearing her smallest distance from the sun. A similar embarrassment exists for the orbit of Venus. But the astronomer can bravely grapple with this double difficulty. He has learned the eccentricity and consequent shape of each ellipse, and he can calculate how far, proportionately, the actual distance of either planet, at any given point of its orbit, exceeds or falls short of the true mean distance. Such calculations have to be made for the earth and for Venus as they will stand on the 8th of next December. When this is done, the astronomer is at liberty to make use of the actual distance learned by observation, and to apply the Keplerian formula.