At last some new observations permitted him to establish beyond all doubt the connection of these facts, in appearance so contradictory. He discovered that, during the whole of the fine season, the plant-lice are solitary and viviparous, but that towards the autumn these creatures return to the ordinary course of things, and are propagated by eggs, whose development requires the co-operation of a male and female individual. These eggs are hatched in Spring, and produce only viviparous plant-lice. In the autumn the males and females show themselves, and from that moment ovipositing recommences. These curious facts, seen and published more than a century ago, have been verified many times since. In 1866 M. Balbiani asserted that the plant-lice are hermaphrodite, or of both sexes at the same time, which would explain the facts observed by Charles Bonnet. But the anatomical proofs appealed to by Balbiani in support of this idea are far from establishing the existence of this arrangement of sexes among them. The observations of Charles Bonnet produced profound astonishment among naturalists, and, in this respect, 1743 may be considered as a memorable year. The simple statement of the few experiments which he made, and which we have cited, has sufficed to show how rapid is the multiplication of aphides. A single female produced generally 90 young ones; at the second generation these 90 produce 8,100; these give a third generation, which amounts to 729,000 insects; these, in their turn, become 65,610,000; the fifth generation, consisting of 590,490,000, will yield a progeny of 53,142,100,000; at the seventh, we shall thus have 4,782,789,000,000; and the eighth will give 441,461,010,000,000. This immense number increases immeasurably when there are eleven generations in the space of a year. Fortunately a great many carnivorous insects wage fierce war against the plant-lice, and destroy immense numbers of them. Thus they are kept in check, and prevented from multiplying inordinately. To show with what prodigious abundance the reproduction of these little but formidable parasites must go on, we will relate a fact which was made known to us by M. Morren, Professor in the University of Liége.