In the process of division, the continual formation of new valves, enclosed in the older girdle bands, will naturally cause a reduction in the size of the frustule. While this reduction, owing to the elasticity of the girdle, does not always occur, I believe, yet, in most cases, the diameter is so reduced that a rejuvenescence of growth is required. This is caused by the production of auxospores which may appear without conjugation. In this process, the beginning of which, in certain species, may be noticed by the increase in the size of the girdle as in reduplication, the two valves separate and within is formed a more or less spherical mass about twice the size of the original frustule and which forms on its circumference two large and often shapeless valves. These valves form others which assume the appearance of the original valves, but larger, and proceed to grow in the usual way. The reduction in size of the frustule seldom proceeds further than about half the size of the type form, so that, as a general rule, it may be stated that diatoms are not often smaller than half the larger size. REPRODUCTION The process of reproduction has been observed in many cases, but the conclusions reached are somewhat at variance with each other. The auxospore formation is simply a {11}method of rejuvenescence. When, however, the auxospores are thrown off from filamentous diatoms, it is probable that two may conjugate, their contents dividing each into two daughter cells which unite into two zygospores. The usual method is the union of two frustules, which, throwing off the old valves, coalesce into a single mass of protoplasm which produces an auxospore, sometimes called a sporangial frustule. It is stated that in some cases two frustules coalesce and produce two auxospores. The existence of spores in diatoms is a much-disputed point. While they have never been seen, the inference that they exist is very great, as otherwise it becomes difficult to understand the sudden growth of species in localities and under conditions that seem to preclude the actual presence of the living frustule. It is a matter of common observation that, in examining collections of living forms, minute frustules or brownish globules appear to resemble larger diatoms. In gatherings of Gomphonema, when many specimens are sessile on the same object, numerous intermediate sizes, varying from minute globules to the type, are seen, yet not positively demonstrable as the same.