The earth arrives punctually every year at one end of this line in June, and at the other in December. The astronomical question is, When will Venus be there also at the same time? To answer requires a calculation which appalls. First, there is the planetary velocity proper of Venus, varying according as in the various parts of her elliptical orbit she is nearer to or further from the sun. Then there are the influences of planetary attraction—the earth and the other planets acting on Venus, accelerating or retarding her movements, and tending sometimes to draw her to one side of her orbit. Then there is or may be question of that nodal diameter shifting its position, and trying, as it were, to swing round the circle of the earth’s orbit. When all these calculations have been made, the diurnal movement of the earth must be taken into account, and the geography of her surface must be duly studied, to determine finally when the transit will take place, across what portion of the sun’s face the planet will be seen to travel, and from what portion of the earth’s surface that transit can be seen, and where in that portion stations for observing it can be placed with the greatest probability of success. It is a fearful sight even to look over a seemingly endless series of pages all bristling with serried columns of figures, broken every now and then by mysterious formulas of higher calculus, like a group of officers commanding a brigade. Mathematicians and astronomers may delight in them; we shall be satisfied to take the results. The transits of Venus go in pairs eight years apart. There can be only one pair to a century; some centuries will have none. The pairs occur alternately in June, as Venus descends from the upper to the lower half of her orbit, and in December, as she ascends again from it. Thus there were transits in December, 1631, and December, 1639. A second pair occurred in June, 1761, and June, 1769. A third pair is near at hand, in December, 1874, and December, 1882. The next century will have none. The fourth pair will appear in June, 2004, and June, 2012.