734 ZOOLOGY: M. M. METCALF PROC. N. A. S. 1867 Nov. X30 C. P. Olivier, "Meteors," 66-67, obsns. of Zezioli. H. A. Newton, Am. Jour. Sci. (3) 31, 424, 1886. Schiaparelli, "Sternschnuppen," 1871, 92, 100. 1872 Nov. 224 C. P. Olivier, "Meteors," 68. H. A. Newton, Am. Jour. Sci. (3) 31, 91, 1886. A. S. Herschel, Nature, 7,185-188,1873. This covers also Nov. 27th. 1872 Nov. 227 C. Meildrum, Nature, 7, 232-233, 1873. Marc-Dechevrens, C. R., 102, 307, 1885. 1885 Nov. 227 C. Meldrum, Nature, 33, 276, 1885. Schwerin, Nature, 34, 60, 1886. W. V. Denning, Nature, 33, 101-102, 1885. C. P. Olivier, "Meteors," 69. H. A. Newton, Am. Jour. Sci. (3) 31, 78-79, 1886. H. A. Newton, Am. Jour. Sci. (3) 31, 409-426, 1886. L. Cruls, C. R., 102, 406-407, 1886. W. Foerster, A. N., 114, 113-120, 1886. 1891 Nov. 2M5, 27 E. F. Sawyer, A. J., 11, 94-95, 1892. 1892 Nov. 223 -,Nature, 47, 257, 1893. J. G. Hagen, A. J., 12, 145, 1893. - W. J. Hussey, A. J., 12, 176, 1893. 1892 Nov.,23, 27 H. A. Newton, Am. Jour. Sci. (3) 45, 61-63, 1893. 1892 Nov. 233 J. K. Rees, A. J., 12, 145, 1892. B. F. Sawyer, A. J., 12, 146, 1892. C. A. Young, Nature, 47, 150, 1892. 1892 Nov. 227 C. P. Olivier, "Meteors," 39. H. A. Newton, Am. Jour. Sci. (3) 45, 63, 1892. 1899 Nov. 223-24 W. F. Denning, M. N. R. A. S., 60, 374, 1900. 1899 Nov. 224 C. P. Olivier, "Meteors," 69. 1900 Nov. 119, 22, 26, 27 I. von Benko, A. N., 155, 169-174, 1901. B. Hartwig, A. N., 155, 165-166, 1901. 1904 Nov. 21 K. Boblin, A. N., 167, 209, 1905. (The last three references were discovered too late for use in the paper.)

LARVAL STAGES IN A PROTOZOON By MAYNARD M. MZrCALr JoEms HOPKINS UNIVRSITY Read before the Academy April 28, 1925 This paper deals with the , a family of Infusorians, parasitic, or more properly commensal, in the recta of and toads. The family comprises two subfamilies, each of which has two genera. The subfamilies and genera are all very distinct and well defined. Ar- ranged in order of complexity and stages of evolutionary development, as I interpret the group, the classification is as follows: Downloaded by guest on September 25, 2021 VOrL. 12, 1926 ZOOLOGY: M. M. METCALF 735 CILIATA Protociliata Opalinidae Protoopalininae (2 nuclei) (cylindrical) 9 subgeneric groups Zelleriella (flat) Opalininae (4 to many nuclei) (cylindrical) 6 subgeneric groups (flat) Opalinae latae (broad, of oriental origin) Opalinae angustae (narrow, of occidental origin) Euciliata The most archaic genus, dating from the Triassic period, or earlier, is Protoopalina. This gave rise in the early Tertiary, in Sout1f America, to the genus Zelleriella. From Protoopalina came also, probably during the Jurassic Period in the Ceylon-Seychelles-Madagascar Land Mass, Cepedea,-by a process of multiplication of nuclei without division of the body. Cepedea gave rise to Opalina, probably in the Cretaceous period in southeastern Asia, by mere flattening of the body, giving us broad Opalinas, Opalinae latae. During the Pliocene, Hylas, coming from trop- ical America into North America, met there frogs and toads immigrant from Asia and bearing broad Opalinas of Asiatic origin. The Hylas adopted the broad Opalinas and changed them into the narrow forms, Opalinae angustae. This is stated here baldly-a mere summary of some of the taxonomic phases of a study occupying a couple of decades. Dr. Wenrich, of the University of Pennsylvania, and I have noticed that Opalinids in the tadpoles are different from those in the adult host. I first observed* that the tadpoles of the Green Frog, Rana clamitans, have very broad Opalinae, almost circular, but that the oldest tadpoles, ready for metamorphosis, I later found to show these Opalinoe as nar- row forms. The narrow Opalina passes through a broad stage recaling its ancestral condition, thus confirming, in part, my taxonomic hypothesis. But the chain of larval stages is longer than this. In tadpoles of Rana clamitans the very young Opalinids are elongated, cylindrical and have two nuclei. They are little Protoopalinas in appearance. They live and divide in this condition for several weeks. Later they increase the number of their nuclei by nuclear division unaccompanied by body division, becoming thus little Cepedeas. In this Cepedea condition they live and multiply for some weeks. Later they flatten to form very broad, circular Opalinas, the flattening beginning at the anterior end and progressing Downloaded by guest on September 25, 2021 736 ZOLOGYY: M. M. METCALF PROC. N. A. S. backward. Finally, after several weeks more, the broad forms change into true Opalinae angustae. This species of Opalina, found thus far only in tadpoles of Rana clamitans, I named provisionally Opalina larvarum, pointing out at the time indications that, in spite of its very broad form, it should be classed with the Opalinae angustae, though at that time the narrow, final stage, in very old tadpoles, had not been seen. The name should now be made permanent, instead of provisional. In its life subsequent to conjugation Opalina larvarum passes through, as noted, a well-defined series of larval stages, each stage corresponding to an ancestral genus or subgenus, being in order of development-first Protoopalina, then Cepedea, then an Opalina lata and ultimately reaching its definitive Opalina angusta condition. In the tadpole of Rana catesbeiana, our northern Bull Frog, a different course is taken. The young forms of this still unnamed Opalinid are Protoopalina-like. These flatten to become Zelleriellas, and later increase the number of their nuclei, becoming Opalinas, first of the broad form, then of the narrow. This all tends to confirm my interpretation of the phyletic - the several genera and subgenera probably having evolved in the order shown in the taxonomic chart, from Protoopalinae to Opalinae angustae. The phylogeny and taxonomy were postulated as in the chart years before this recent confirmation was found in the development of the Opalinae in Green Frog and Bull Frog tadpoles. These progressive stages in development, each retained for a period of some weeks, may properly be called larval stages. The fact that division, asexual reproduction, is occurring in each of these stages makes them no less larvae. Of course the recapitulative nature of these larval stages is of especial interest, helping us interpret the phyletic history of this the most archaic family of Ciliate Infusorians. The several larval stages in the life history of Opalina are not due to divergent adaptation to special environmental conditions, but are purely phyletic, repetitive of the an- cestral history. Few, if any, finer examples of a series of developmental stages repetitive of ancestral history are found among or , either metazoan or protozoan. Larval stages are far from unknown among . One of the most striking examples is seen in the Suctoria, a group of Ciliata lying at the other end of the class from the archaic Opalinidae. The Suctoria, in the course of their development, have a true Ciliate stage, indicating that they have arisen from true . This would hardly have been suspected without knowledge of the character of their larvae. There are a number of implications in the life cycle of the higher Opal- inidae, interesting to follow out, but these will be left for a fuller paper. The whole subject could be discussed in terms of the interworking of at Downloaded by guest on September 25, 2021 VOL. 12, 1926 MA THEMA TICS: S. LEFSCHETZ 737 least four inherent trends in mutation present in the family (tendencies (a) to postponing the division of the body after nuclear division, (b) to delay in completing mitotic division of the nucleus when once begun, (c) to flatten- ing of the body, (d) to elongation of the body). By their conjunction or disjunction in inheritance these four trends give rise to the several sub- families and genera and to some of the subgenera mentioned in the taxo- nomic chart. But this treatment of a phylogeny as a shuffling of trends is too unfamiliar for condensed discussion. * Metcalf-The Opalinid Ciliate Infusorians, Bulletin 120, United States National Museum, pp. 244-246.

TRANSFORMATIONS OF MANIFOLDS WITH A BOUNDARY By S. LE1VSCHrTZ DEPARTMUNT OP MATHEIATICS, PRINCETON UNIVGRSITY Communicated October 22, 1926 1. The object of this note is to outline the extension of the coincidence and fixed point formulas which I have already obtained for transforma- tions of manifolds without boundary.' The notations will be those of the papers just quoted. By means of matrices we shall first greatly simplify the formulas already given. Any matrix of elements ai, or ajj will be denoted by a (i.e., like the elements with positional indices dropped), its transverse by a' and if it is square the sum of the main diagonal elements will be called the trace. We also set C;, = ||(v^.Ys*,/) 11 where the y's are cycles of fundamental sets for the operation ,, C,, is square of order R,, and its determinant -- 1 (Veblen). Then the first formula, p. 43, of the Transactions paper gives at once: (- 1)+ CIAEn_=a,A ; e-;, = ( 1)(+)C, a (1) By applying (53.3), loc. cit., to the first formula on p. 47, replacing the d's by the y's, then making use of (1) and of the fact that transposed matrices have equal traces we find: (rn .r") = 2(-1)u trace C.. ., C,,71a}, (2) whose form is as advantageous as it is condensed. 2. We now consider a manifold Mn with a boundary F,,n1 It is found necessary to demand that F,,1 be itself a manifold and that if M. is a copy of M,, when we match the corresponding boundary points then Vn = Mn- M,, is also a manifold (without boundary, of course). It amounts to certain homogeneity requirements along F-,,. Downloaded by guest on September 25, 2021