The richest source of the Challenger material is the Radiolarian ooze of the central Pacific Ocean (Stations 265 to 274). This remarkable deep-sea mud consists for the greater part of well-preserved siliceous shells of Polycystina (SPUMELLARIA and NASSELLARIA). Not less important, however, especially for the study of the ACANTHARIA and PHÆODARIA, are the wonderful preparations stained with carmine and mounted in Canada balsam on the spot by Dr. John Murray. One such preparation (_e.g._, from Station 271) often contains twenty or thirty, sometimes even fifty new species. In many of these preparations the individual parts of the unicellular organism are so well preserved that they show clearly the characteristic peculiarities of the legions and orders. Since the material for these preparations was taken with the tow-net, not only from the surface of the sea but also from different bathymetrical zones, it furnishes valuable conclusions regarding the chorology, as well as the physiology and morphology of the group. For many new discoveries I am indebted to the study of such preparations, of which I have examined about a thousand from 168 different Stations (compare § 240). In addition to these about 100 bottles were handed to me, containing partly bottom-deposits, partly tow-net gatherings. Sir Wyville Thomson, who directed the investigations of the Challenger with so much devotion, and only partly saw its results, has laid me under a deep debt of obligation; not less is this the case, however, with his successor, Dr. John Murray. I am especially indebted to both gentlemen for the freedom they have allowed me in the carrying out of my work, and especially for the permission to include a description of all known Radiolaria in the Challenger Report, which has thus become a second edition many times enlarged of my Monograph published in 1862. Since all previous literature of the subject has been consulted and critically revised, it is hoped that this Report will form a useful foundation for future investigations. All names of sufficiently described Radiolaria published during the first half century of our knowledge of the class (from 1834 to 1884), are inserted in alphabetical order in the index at the end of this work.