The number of tracheæ in the body of an insect is very great. That patient anatomist, Lyonet, has proved this in his great work on the Goat-moth Caterpillar, _Cossus ligniperda_. Lyonet, who congratulated himself with having finished his long labours without having had to destroy more than eight or nine of the species he wished to describe, had the patience to count the different air-tubes in that caterpillar. He found that there were 256 longitudinal and 1,336 transverse branches; in short, that the body of this creature is traversed in all directions by 1,572 aeriferous tubes which are visible to the eye by the aid of a magnifying glass, without taking into account those which may be imperceptible. The complicated system of the breathing apparatus which we are describing is sometimes composed of an assemblage of tubes and membranous pouches, besides the elastic tubes which we have already mentioned. These pouches vary in size, and are very elastic, expanding when the air enters, and contracting when it leaves them, as they are altogether without the species of framework formed by the spiral thread of the tubular tracheæ, of which they are only enlargements. Fig. 13 is explanatory of these organs of respiration. The respiratory mechanism of an insect is easily understood. "The abdominal cavity," says M. Milne-Edwards, "in which is placed the greater part of the respiratory apparatus, is susceptible of being contracted and dilated alternately by the play of the different segments of which the skeleton is composed, and which are placed in such a manner that they can be drawn into each other to a greater or less extent. When the insect contracts its body, the tracheæ are compressed and the air driven out. But when, on the other hand, the visceral cavity assumes its normal size, or dilates, these channels become larger, and the air with which they are filled being rarefied by this expansion, is no longer in equilibrium with the outer air with which it is in communication through the medium of the spiracles. The exterior air is then impelled into the interior of the respiratory tubes, and the inspiration is effected." The respiratory movements can be accelerated or diminished, according to the wants of the animal; in general, there are from thirty to fifty to the minute. In a state of repose the spiracles are open, and all the tracheæ are free to receive air whenever the visceral cavity is dilated, but those orifices may be closed, and the insect thus possesses the faculty of stopping all communication between the respiratory apparatus and the surrounding atmosphere. Some insects live in the water; they are therefore obliged to come to the surface to take the air they are in need of, or else to possess themselves of the small amount contained in the water. Both these methods of respiration exist under different forms in aquatic insects.