constant differences in the four legions, which have given rise to the names--PERIPYLEA, ACTIPYLEA, MONOPYLEA, CANNOPYLEA. The capsule-membrane was first indicated as the most important and absolutely constant component of all Radiolaria, and as the differential character of the class, in my Monograph (1862, pp. 69-71). The careful investigations of R. Hertwig have confirmed this view and at the same time have yielded the most important conclusions regarding the nature and systematic significance of the openings in the capsule (_op. cit._, 1879, pp. 105-107). On the contrary, Karl Brandt has recently propounded the theory that the capsule-membrane is by no means a constant part of the Radiolarian organism, but is lacking in certain species of _Collozoum_ and _Sphærozoum_ (1881, p. 392). This contradiction is explained by the fact that in some #Collodaria# and #Acanthometra# the formation of the central capsule takes place much later than in the other Radiolaria, in some {xxix}species indeed only just prior to the development of the swarm spores. I have recognised the presence of it in all species which I have investigated (more than a thousand), and even in those in which Brandt denies its existence. It is often very delicate and may easily be overlooked, especially when the contents of the capsule are colourless, but in all cases by the prudent application of staining fluids and other reagents its presence may be demonstrated. Even in those cases in which the contour of the capsule was not visible, and its contents appeared to pass without definite boundary into the matrix of the extracapsulum, it was possible by the use of appropriate stains or reagents, which would not penetrate the capsule, or of those solvents which were capable of dissolving its contents and of causing it to swell up like a distended bladder, to recognise the existence of the membrane. Those Radiolaria in which it is truly absent are young animals of species in which the membrane is only formed immediately before sporification, and persists but for a short time (_e.g._, species of _Collozoum_, _Sphærozoum_, _Acanthometra_, _Acanthochiasma_, &c.). 57. _The Capsule-Openings of the Peripylea (or Spumellaria)._--The capsule-membrane of the PERIPYLEA is generally perforated by extremely fine and numerous pores, which are distributed at equal distances over the whole surface, and are precisely alike in all parts of the capsule. Hence the SPUMELLARIA may be called "Holotrypasta" or "Porulosa"; they agree with the ACTIPYLEA in being devoid of an osculum or operculum; they are distinguished from the latter group mainly in that their pores are equally distributed over the whole surface of the capsule, whilst in the ACTIPYLEA the pores are disposed in definite groups or lines, separated by large imporous areas.