The learned geometrician of Basle summarises his idea as follows: “I believe that there can exist in nature other animals who are in size as far above us and ordinary animals as we and our animals are above microscopic animalculæ, and who observe us in our world with their microscopes as we observe that infinite multitude of animalculæ with ours. I go further and maintain that there might be beings incomparably larger again, and I suppose as many degrees upward as are found in going downwards, for I do not see why we should constitute the highest degree.” Leibnitz replied to Bernoulli: “I am not afraid of advancing the opinion that there are in the universe animals that are as much our superiors in size as we are above the animalculæ which we only discover by means of a microscope, for nature knows no limits. On the other hand, it may be and it must be that there are in the small grains of dust and in the smallest atoms worlds which are not inferior to ours in beauty and variety.” The exceedingly small microscopic organisms discovered and studied by Ehrenberg at the beginning of the nineteenth century seemed to place this population in evidence. Pascal had written, as early as 1660, or perhaps even in 1654, in his _Pensées_: “What is man in the infinite? Let a flesh-worm offer him in the smallness of its body parts which are yet smaller. Legs with joints, veins in those legs, blood in those veins, humours in that blood, drops in those humours, vapours in those drops. Suppose that in dividing up these last things he should spend his forces of imagination and that the last object at which he could arrive be the subject of our present discussion. He will perhaps think that that is the extreme of smallness in Nature. But I shall open for him a new abyss. I shall not only paint for him the visible universe but the immensity of nature which one can conceive within the range of this small atom. Let him see in it an infinity of worlds, every one with its firmament, its planets, its earths, in the same proportion as the visible world, on that earth animals and finally flesh-worms in which he will find again what the first flesh-worms presented to him. Let him go on finding the same thing without end and without rest. Let him lose himself in those marvels as astonishing in their smallness as the others are in their size, for who would not be astonished that our body, hardly perceptible in the universe which itself would be imperceptible in the grand totality, should now be a colossus, a world or rather a universe in comparison with the nothingness which we can never arrive at.