Page:Popular Astronomy - Airy - 1881.djvu/168

154 accurately. The diameter of the earth is nearly eight thousand miles, and from the knowledge of that we shall be able to determine all the others. It must then be carefully borne in mind that the diameter of the earth AB, in Figure 43, is the same as the diameter of the earth A'B', in Figure 44.

Suppose, then, that there is to occur a transit of Venus: that is to say a conjunction of the sun and Venus is about to take place, when Venus is near the node of her orbit, in which case Venus is seen to pass across the sun's face. We will suppose that the observation is to be made at two Observatories, one of which is near the North Pole of the earth, and the other near the South Pole of the earth. From the relation of the motions of different planets expressed in Kepler's third law (that the squares of the periodic times are proportional to the cubes of the distances), it follows that the periodic times increase in a greater proportion than the distances from the sun, and that the actual motions of the more distant planets in their orbits are slower. Thus, suppose one planet is 4 times as far from the sun as another; then its periodic time is 8 times as great (since the square of 8 is equal to the cube of 4); but the orbit which it describes is only 4 times as large; and thus it moves with only half the speed in that orbit. In like manner the motion of the earth in its orbit is slower than the motion of Venus in her orbit. Therefore, as the earth is moving in the direction from AB towards a, and Venus is moving with greater speed in the direction from V towards v, the inhabitants of the earth will see Venus moving apparently across the sun in the direction from E towards F, or from C towards D, (or in a retrograde direction). Now, first, let us examine in Figure 43 what will be the