But the lengthening of the reproductive period alone may result in a marked increase in the length of life, as is proved by the queen-bee. In all these cases it is easy to imagine the operation of natural selection in producing such alterations in the duration of life, and indeed we might accurately calculate the amount of increase which would be produced in any given case if the necessary data were available, viz. the physiological strength of the body, and its relations to the external world, such as, for instance, the power of obtaining food at various periods of life, the expenditure of energy necessary for this end, and the statistics of destruction, that is, the probabilities in favour of the accidental death of a single individual at any given time. These statistics must be known both for the imagos, larvae, and eggs; for the lower they are for the imagos, and the higher for the larvae and eggs, the more advantageous will it be, _ceteris paribus_, for the number of eggs produced by the imago to be increased, and the more probable it would therefore be that a long reproductive period, involving a lengthening of the life of the imago, would be introduced. But we are still far from being able to apply mathematics to the phenomena of life; the factors are too numerous, and no attempt has been made as yet to determine them with accuracy. But we must at least admit the principle that both the lengthening and shortening of life are possible by means of natural selection, and that this process is alone able to render intelligible the exact adaptation of the length of life to the conditions of existence. A shortening of the normal duration of life is also possible; this is shown in every case of sudden death, after the deposition of the whole of the eggs at a single time. This occurs among certain insects, while nearly allied forms of which the oviposition lasts over many days therefore possess a correspondingly long imago-life. The _Ephemeridae_ and Lepidoptera afford many examples of this, and in an earlier work I have collected some of them[92]. The humming-bird hawk-moth flies about for weeks laying an egg here and there, and, like the allied poplar hawk-moth and lime hawk-moth, probably dies when it has deposited all the eggs which can be matured with the amount of nutriment at its disposal. Many other Lepidoptera, such as the majority of butterflies, fly about for weeks depositing their eggs, but others, such as the emperor-moths and lappet-moths, lay their eggs one after another and then die. The eggs of the parthenogenetic _Psychidae_ are laid directly after the imago has left the cocoon, and death ensues immediately, so that the whole life of the imago only lasts for a few hours. No one could look upon this brief life as a primitive arrangement among Lepidoptera, any more than we do upon the absence of wings in the female _Psychidae_; shortening of life here is therefore clearly explicable.