The Coccididæ, like all Homoptera, produce great numbers of young; but their increase does not appear to be as rapid as that of some other families. The numbers of some Aphididæ or Aleurodidæ produced from a single female in the course of a single year have been calculated at hundreds of thousands, if not millions; and as many as eleven generations have been produced in little over half a year. Coccids, however, as a rule, do not propagate at this alarming rate. Many, if not the great majority of them, produce in this country but one generation in the year, e.g., _Mytilaspis pomorum_, _Cœlostoma zælandicum_, &c. Others, such as _Icerya purchasi_, breed more often; and probably climate has a good deal to do with the frequency, for Mr. Comstock says that in the United States _Mytilaspis pomorum_ breeds once a year in the North and twice in the South. In point of fact, it does not seem possible to lay down any rule on the subject. Unfortunately, _Icerya_ is not only a frequent breeder, but also the most destructive insect of the family in New Zealand. The number of young produced by each female seems also to vary. The author has counted from 30 to 80 eggs in the puparium of _Mytilaspis pomorum_; as many as 350 in the ovisac of _Icerya purchasi_, and about the same number of _Cœlostoma zælandicum_: and a female of _Lecanium hesperidum_ examined in spring contained 93 embryos. These figures do not denote any remarkable fertility; but, as in the majority of cases males are but seldom met with, sometimes even entirely unknown (e.g., _Lecanium hesperidum_), it follows that nearly every insect is capable of propagation, and the increase in numbers is therefore more rapid than might be anticipated otherwise. How the females in the species apparently destitute of males are enabled to produce young is perhaps one of the most mysterious things in Nature. The male of _Mytilaspis pomorum_ has never been found in New Zealand or Europe, and doubtfully in America. _Lecanium hesperidum_ has been known and studied for nearly two hundred years without any male, pupa or adult, being discovered. Yet both of these species go on increasing regularly and in great numbers, and show no signs of extinction.