Let us further suppose a creature (resembling, say, a ladybird in shape) having length and breadth, but no thickness, to crawl along this meridian. Although it has no thickness, we shall imagine it to have one property of a solid body, that of being opaque, so that it can throw a shadow if properly illuminated. We assume the globe itself to be transparent. At the North Pole we suppose a very strong point-source of light, a little electric lamp, that sends out rays freely in all directions. The insect begins its journey at the South Pole and sets out along the meridian to reach the North Pole. It is illuminated by the lamp all the way, so that it continually throws a shadow on the white table. The shadow moves along the table farther and farther from the South Pole, in proportion as the insect moves up the meridian, with the difference that while the insect is describing an arc of a circle, its shadow moves along a straight line. The position of the shadow can be determined at any moment by drawing the straight line connecting the lamp to the insect, and producing it to meet the white surface of the table; the point of intersection is the projection of the insect on the plane. At the beginning of the excursion the shadow is exactly as large as the flat insect itself, if we assume that its dimensions are negligible compared with the surface of the sphere, for it will then coincide with its own shadow. But when the insect crawls upwards, its shadow will increase, because of the shortened distance between the insect and the lamp, and because the points of projection on the table separate more and more as their distances from their corresponding points on the sphere become greater. There is thus a twofold increase. The shadows move away more and more rapidly, and at the same time increase in size. When the insect gets very near the North Pole, its shadow, now of enormous dimensions, has moved to a very great distance; and when finally it reaches the Pole, its shadow becomes infinitely great and thus stretches to infinity. But let the insect wander on along the meridian, past the North Pole, down towards the South. At the moment when it passes the upper Pole its shadow jumps from the right side to the left. Its shadow now emerges from an infinite distance to the left, and, instead of being infinite size, again becomes finite in dimensions as it approaches. It contracts as it approaches, and, in short, the same process as occurred during the first half of the journey now occurs in the reverse order.