The structure of the tracheae is remarkable: they are elastic and consist of an outer cellular, and an inner chitinous layer; this latter is strengthened by a peculiar spiral fibre, which gives {129}to the tubes, when examined with the microscope, a transversely, closely striated appearance. Packard considers[46] that in some tracheae this fibre is not really spiral, but consists of a large number of closely placed rings. Such a condition has not, however, been recorded by any other observer. The spiral fibre is absent in the fine capillary twigs of the tracheal system, as well as from the expanded sacs. The mode of termination of the capillary branches is not clear. Some have supposed that the finest twigs anastomose with others; on the other hand it has been said that they terminate by penetrating cells, or that they simply come to an end with either open or closed extremities. Wistinghausen[47] states that in the silk-glands the tracheal twigs anastomose, and he is of opinion that the fine terminal portions contain fluid. However this may be, it is certain that all the organs are abundantly supplied with a capillary tracheal network, or arboreal ramification, and that in some cases the tubes enter the substance of tissues. Near their terminations they are said to be 1/30 to 1/60 millimetre in diameter. [Illustration: FIG. 71.—Portion of the abdominal part of tracheal system of a Locust (_Oedipoda_): _a_, spiracular orifices; _b_, tracheal tubes; _c_, vesicular dilatations; _d_, tracheal twigs or capillaries. (After Dufour.)]