ERRATA. First Paper, read February 1, 1904. Page 185, line 8 from foot, for “£ = read “c = _^0.” dx dx ,, 196, ,, 16 from top, for “ dcf ” read “ d-rf.” ,, ,, ,, ,, ,, for “instead of 0” read, “ instead of Third Paper, January 23, 1905. Page 564, line 2 from foot, after “ speed” insert “ and smoothness.” Fourth Paper, read July 17, 1905. Page 1067, line 28, delete “whole.” ,, ,, ,, ,, for “ the whole ” read “ a considerable part of the/ ,, 1078, ,, 12 from foot, for “(115) ” read “(116).” PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. s~d>c. y/ PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. VOL. XXV. {IN TWO PARTS.) PART II. (Containing pages 593-1259.) MARCH to JULY 1905. EDINBURGH: PRINTED BY NEILL AND COMPANY, LIMITED. MDCCCCVI. CONTENTS. Sur les Sarcodines du Loch Ness. Note de M. le Dr E. Penard, presentee par Sir John Murray, K.C.B. Issued separately May 4, 1905, . . . . . . . . The Rhizopods and Heliozoa of Loch Ness. By James Murray. Communicated by Sir John Murray, K.C.B. Issued separately May 10, 1905, Note on the Rainfall on the Drainage Area of the Talla Reservoir. By B. Hall Blyth and W. A. Tait. (With a Map.) Issued separately May 10, 1905, ...... Remarks on the Rainfall Records in the Talla Drainage Area during the years 1896 to 1902. By P. D. Donald, A.M.Inst.C.E. Communicated by W. A. Tait, M.Inst.C.E. Issued separately May 10, 1905, ....... Some further Results in the Mathematical Theory of Seiches. By Professor Chrystal. Issued separately May 11, 1905, The Theory of Continuants in the Historical Order of Develop- ment up to 1880. By Thomas Muir, LL.D. Issued separately May 17, 1905, ....... Suggestions towards a Theory of Electricity based on the Bubble Atom. By John Eraser, late Ordnance Survey, Edinburgh. Communicated by Dr W. Peddie. Issued separately May 18, 1905, Variant Forms of Vanishing Aggregates of Minors of Axi- symmetric Determinants. By Professor W. H. Metzler. Issued separately May 20, 1905, ...... The Constitution of Complex Salts. — I. Derivatives of the Sesqui- oxides. By Alexander T. Cameron, M.A. Communicated by Dr Hugh Marshall, F.R.S. Issued separately May 25, 1905, . A Report on the Medusae found in the Firth of Clyde (1901- 1902). By Edward T. Browne, B.A., Zoological Research . Laboratory, University College, London. Communicated by Sir John Murray, K.C.B., F.R.S. Issued separately July 5, 1905, Notes on the Pelagic Fauna of the Firth of Clyde (1901-1902). By Edward T. Browne, B.A., Zoological Research Laboratory, University College, London. Communicated by Sir John Murray, K.C.B., F.R.S. Issued separately July 6, 1905, A Report on the Free-Swimming Crustacea found in the Firth of Clyde, 1901 to 1902. By Thomas Scott, LL.D., F.L.S., etc. Communicated by Sir John Murray, K.C.B., F.R.S. Issued separately July 7, 1905, . . . PAGE 593 609 616 630 637 648 680 717 722 738 779 792 Contents. I’AGE vi Certain Mathematical Instruments for Graphically Indicating the Direction of Refracted and Reflected Light Rays. By J. R. Milne, B.Sc., Carnegie Scholar in Physics. Issued separately July 7, 1905, ...... Ankylostomiasis, or the Miners’ Worm Disease. By Thomas Oliver, M.A., M.D., LL.D., F.R.C.P., Physician to the Royal Infirmary, and Professor of Physiology, University of Durham, College of Medicine, Newcastle-upon-Tyne. (With Two Plates.) Issued separately July 10, 1905, ..... A Form of Bolometer adapted for Physiological Investigation. By Walter Colquhoun, M.A., M.B., Physiological Laboratory, University of Glasgow. Issued separately July 10, 1905, A New Method of Preparing Esters. By W. W. Taylor. Com- municated by Professor Crum Brown, F.R.S. Issued separately August 29, 1905, ....... On the Action of Radium Bromide on the Electromotive Phenomena of the Eyeball of the Frog. By John G. M‘Kendrick, M.D., F.R.S., and Walter Colquhoun, M.A., M.B. Issued separately August 29, 1905, Cape Hunting Dogs ( Lycaon pict us) in the Gardens of the Royal Zoological Society of Ireland. By D. J. Cunningham, F.R.S., Professor of Anatomy, University of Edinburgh. (With Two Plates.) Issued separately August 29, 1905, Note on Some of the Magnetic Pmperties of Demagnetised and Annealed Iron. By James Russell. Issued separately August 29, 1905, ....... Vanishing Aggregates of Determinant Minors. By Professor W. H. Metzler. Issued separately August 29, 1905, Les Concretions phosphatees de 1’ Agulhas Bank (Cape of Good Hope). Par Dr Leon W. Collet, Mem. de la Soc. Geol. Suisse, assistant de Sir John Murray, K.C.B. Avec une note sur la Glauconie qu’elles contiennent, par Gabriel W. Lee, B.Sc. Communique par Sir John Murray, K.C.B. (With Four Plates.) Issued separately September 6, 1905, . Evaporation of Musk and other Odorous Substances. By John Aitken, LL.D., F.R.S. Issued separately September 30, 1905, . On the Opacity of Aluminium Foil to Ions from a Flame. By George A. Carse, M.A., B.Sc., 1851 Exhibition Science Research Scholar of Edinburgh University ; Emmanuel College, Cambridge. Issued separately September 30, 1905, . The Theory of General Determinants in the Historical Order of Development up to 1852. By Thomas Muir, LL.D. Issued separately September 30, 1905, ..... Note on some generally accepted Views regarding Vision. By Dr W. Peddie. Issued separately October 23, 1905, Note on the Boiling Points of Aqueous Solutions. By the Rev. S. M. Johnston, B.A. Communicated by Professor J. G. MacGregor, F.R.S. Issued separately November 4, 1905, 806 813 827 831 835 843 849 853 862 894 903 908 948 952 Contents. PAGE A Comparative Study of the dominant Phanerogamic and Higher Cryptogamic Flora of Aquatic Habit, in Three Lake Areas of Scotland. By George West. (With Fifty-five Plates.) Issued separately November 11, 1905, ..... 967 Magnetic Quality in a Boscovichian Assemblage of Molecular Magnets. By Dr W. Peddie. Issued separately November 20, 1905, . . . . . . . 1025 Deep Sea Ship-Waves. ( Continued from Proc. B.S.E., January 23, 1905.) By Lord Kelvin. Issued separately December 1 1 , 1905, ........ 1060 Complete Heart-block, with Dissociation of the Action of the Auricles and Ventricles. By W. T. Ritchie, M.D., F.R.C.P.E. Communicated by Dr George A. Gibson. Issued separately December 14, 1905, ...... 1085 A Regular Fortnightly Exploration of the Plankton of the two Icelandic Lakes, Thingvallavatn and Myvatn. By C. H. Ostenfeld, Inspector of the Botanical Museum, Copenhagen, and Dr C. Wesenberg-Lund. Communicated by Sir John Murray, K.C.B., F.R.S. (With Three Plates.) Issued separ- ately January 5, 1906, ...... 1092 Meetings of the Royal Society — Sessions 1903-1905, . . 1168 Donations to the Library, . . . . . .1194 Obituary Notices, ...... 1228 Abstract of Accounts for Session 1904-1905, . . . 1241 Index, ........ 1252; 1904-5.] Sur les Sarcodines du Loch Ness. 59: Snr les Sarcodines du Loch Ness. Note de M. le Dr E. Penard, presentee par Sir John Murray, K.C.B. (MS. received February 17, 1905. Read March 6, 1905.) Au mois d’Aout dernier, Mr Scourfield eut l’obligeance de me remettre a Berne, lors dn congres de Zoologie, trois petits flacons, dont deux contenaient du detritus pris au fond du Loch Ness, et le troisieme du plankton provenant du meme lac ; ces diverses recoltes dataient de 1903, et etaient conservees a l’alcool. Plus tard, en Novembre, Mr Scourfield m’adressa egalement trois tubes provenant de la meme localite, et dont le contenu, recolte le 7 du meme mois, etait encore dans son eau d’origine, de sorte que beaucoup des organismes s’y trouvaient vivants et souvent en bonne sante. Dans diverses publications, oil j’avais attire l’attention sur l’existence au fond des lacs suisses de toute une serie de Sarco- dines speciaux, j’avais exprime l’opinion que cette faune caracte- ristique pourrait bien se retrouver dans les grands lacs du reste de l’Europe ; il m’etait en effet difficile d’imaginer que la Suisse fut seule privilegiee sous ce rapport. Les flacons de Mr Scourfield ont done ete les bien venus, et je me suis livre a un examen serieux de leur contenu. Les resultats de ces investigations, bien que peu concluants encore, ne sont pas sans presenter quelque interet, et peut-etre vaut-il des maintenant la peine de les signaler. Yoici d’abord quels ont ete les Sarcodines trouves : — No. 1. 7th August 1903. Mud from bottom of Loch Ness , off Doe Burn. Depth 27 2 feet. Alcool. Arcella hemisphcerica , Perty . Arcella vulgaris , Ehrenberg . Assulina minor , Penard Campascus minutus, Penard . Bare. Bare. 1 exemplaire. 3 exemplaires. PEOC. ROY. SOC. EDIN. — VOL. XXV. 38 594 Proceedings of Royal Society of Edinburgh, [sess. Centropyxis aculeata, Stein . Clathrulina elegans , Cienkowsky . Gorythion dubium, Taranek . Cyph oder ia ampulla (Ehrenb.) Dijjlugia acuminata , Ehrenb., var. infflata, Penard .... Difflugia constricta , Ehrenb. ? Dijjlugia globulosa, Dujardin* .? Difflugia pristis , Penard Difflugia pyriformis, Perty . Difflugia pyr if or mis, var. lacustris, Penard . Euglypha alveolata , Dujardin Euglyplia brachiata, Leidy (forma jlexuosa, Penard) Euglyplia ciliata (Ehrenb.) . ? Gromia nigricans, Penard E deopera petricola, Leidy Hyalosphenia papilio , Leidy . Lecquereusia modesta , Rhumbler . Lecquereusia spiralis (Ehrenb.) Nebela bur sella, Yejdovsky . Nebela collar is, Leidy . Nebela lageniformis , Penard . Nebela tubulosa, Penard % Nebela vitrcea, Penard . Pare. Rare ; sans tige. Tres-rare. Abondante. Assez commune. Commune sous differentes formes. Rare. Commune. Tres-rare dans sa forme typique, mais on trouve beaucoup de petites formes que Ton peut rap- porter a cette espece. Assez commune. Plutot rare. Pas tres-rare. Pas commune. 4 exemplaires. Rare. 1 exemplaire. Assez rare. Pas commune. Pas tres-rare. Diverses formes, revetant surtout l’apparence de la Nebela bohemica de Taranek. 2 exemplaires. 1 exemplaire. Pas tres-rare. * Ces recoltes ayant ete conservees dans 1’alccol, il n’a pas ete possible de determiner les rhizopodes autrement que par leur coquille, et dans certains cas la determination est restee quelque peu incertaine ; c’est ce qui explique les points d’interrogation que l’on trouvera quelquefois. .1904-5.] Sur les Sarcodin4s du Loch Ness. 595 Paidinella chromatophora, Lauter- born ..... Placocysta lens , var , Penard Pontigulasia bigibbosa, Penard Quadrula symmetrica , F. E. Schulze Quadrula symmetrica , var. irregu- laris, Penard .... Rphenoderia dentata , Penard . Sphenoderia lenta , Schlumberger . Trinema enchelys (Ehrenb.) . Trinema linear e, Penard 1 exemplaire. Rare. Pas tres-rare. Assez commune. Plutot rare. 1 exemplaire. Rare. Abondante, surtout dans sa grande et belle forme. Rare. No. 2. 8th August 1903. Mud from bottom of Loch Ness, near Foyers. Depth 680 feet. Alcool. Centropyxis aculeala , Stein . Difflugia constricta , Ehrenb. . Diffluyia pyrif or mis, Perty . Euglypha compressa, Carter . Pontigulasia bigibbosa, Penard Quadrula symmetrica, F. E. Schulze Rare. Rare. Rare. Rare. Pas tres-rare. Rare. No. 3. 30 th August 1903. Plankton Collection. Loch Ness {south end). Alcool . Clatlirulina elegans , Cienkowsky . Sans tige. Raphidiophrys coyiglobata (Greeff) Commune. Raphidiophrys pallida, F. E. Schulze ..... 1 exemplaire. En outre quelques Difflugia pyriformis et D. constricta, de faible taille. No. 4. Itli November 1904. Loch Ness, 300-400 feet. Eau. (Le signe * indique que l’animal a ete trouve vivant.) * Amoeba granulosa, Gruber . . Tres-abondante. *Acanthocystis myriospina, Penard . Rare. 596 Proceedings of Royal Society of Edinburgh. D *Arcella hemisphcerica, Perty . Arcella vulgaris , Ehrenb. Assulina minor , Penard Assulina seminulum, Leidy , * Campascus minutus, Penard . Clathrulina elegans , Cienkowsky . * Cochliopodium bilimibosum (Auer- bach) ..... *Cyphoderia ampulla (Ehrenb.) *Diflugia acuminata , Ehrenb. * Difflugia acuminata , var. infata, Penard ..... Diflugia constricta , Ehrenb. . Difflugia curvicaulis, Penard * Diflugia gramen, Penard * Diflugia lanceolata , Penard . ^Difflugia pyriformis, Perty, var. lacustris, Penard Diflugia ? spec. nova ..... Euglypha alveolata , Dujardin Euglypha ciliata (Ehrenb.) . Euglypha brachiata, Leidy (forma flexuosa, Penard) *Gromia nigricans , Penard Heleopera petricola , Leidy Lecquereusia modesta, Rhumbler . Nebela collaris , Leidy . Nebela bur sella, Vejdovsky . Nebela crenulata , Penard Nebela lageniformis, Penard . Nebela americana, Taranek . Nebela militaris, Penard 1 Nebela vitrcea, Penard . * Pompholyxophrys exigua (Hertwig et Lesser) ..... * Pseudodifflugia horrida, Penard Abondante. Commune. Tres-rare. Tres-rare. 2 individus. Rare ; sans tige. Commune. Tres-commune. Diverses varietes. Commune. Diverses varietes. 1 coquille vide. Commune ; de forme peu speciale. Tres-abondante. Commune. 4 exemplaires. Rare. Rare. Assez commune. 2 exemplaires. Rare. Pas tres-rare. Rare. Tres-rare. Tres-rare. Tres-rare. 3 individus. Tres-rare. Rare. 1 individu. Commune. 1904-5.] Sur les Sarcodinds du Loch Ness. 59 1 Quadrula symmetrica , F. E. Schulze, var. irregularis , Penard * Sphenoderia lenta , Schlumberger . Trinema enchelys (Ehrenb.) . Cyphoderia ? spec, nova 1 individu. Plutot rare. Pare. 2 coquilles vides. No. 5. 7 th November 1904. Loch Ness. Fine net. 400-500 feet. Eau. Centropyxis aculeata , Stein. Cyphoderia ampulla (Ehrenb.). Difflugia acuminata , Ehr., var. inflata , Penard. Difflugia constricta, Ehrenb. * Difflugia lanceolata , Penard. Difflugia pyriformis, Perty, var. lacustris, Penard. Euglypha hrachiata , Leidy (forma Jlexuosa, Penard). Heleopera rosea, Penard. Lecquereusia modesta, Rhumbler. Nebela collaris, Leidy. Quadrula symmetrica, F. E. Schulze. Sphenoderia lenta , Schlumberger. Toutes ces especes etaient fort rares, et presque toujours repre- sentees par des coquilles vides. No. 6. 7 th November 1904. Loch Ness. Coarse net. 300-400 feet. Cette recolte, bien que renfermant quelques rbizopodes, etait tres-pauvre, et n’a pas ete etudiee. Les listes que Ton vient de lire ne montrent qu’une analogie tres-lointaine avec la faune des Sarcodines des lacs suisses ; a part une demi-douzaine d’especes, sur lesquelles nous reviendrons bientdt, nous avons la la faune habituelle de la plaine, et surtout celle des tourbieres. Mais il fallait s’y attendre : tous les lacs possedent dans une certaine mesure, outre les formes qui peuvent leur etre propres, la faune generale de la contree avoisinante ; et dans le Loch Ness surtout, entoure de tourbieres, extremement btroit dans toute sa longueur, et qui jusqu’a un certain point pourrait etre compare a une riviere ou a un canal, c’est cette 598 Proceedings of Royal Society of Edinburgh. [sess. faune generale qu’on doit y rencontrer la mieux representee. Les rivieres Oich, TarfF, etc., deversent sans doute dans le lac une masse considerable de debris, et de fait les recoltes de Mr Scourfield con- sistaient pour une bonne part en debris organiques de toute sorte, fibres vegetales, fragments de feuilles de sphagnum et de mousses, etc.,* et comme ces vegetaux hdbergent constamment une quantite immense de rhizopodes, il est impossible que ces derniers ne se trouvent pas forcement meles aux debris, tantot a l’etat de coquilles vides, tantot parfaitement vivants et en apparence acclimates dans leurs nouvelles conditions d’existence. En tout cas les resultats de ces recherches ne sont pas depourvus d’un certain interet, et sous ce rapport je voudrais considerer un peu plus au long quelques-uns des organismes qui viennent d’etre cites. Ce sont les suivants : — Amoeba granulosa , Gruber. f Cette amibe, remarquable surtout par les corpuscules eristallises et en general bicuspides dont elle est constamment remplie, se montrait en assez grande abondance, et en parfaite sante, dans la recolte du 7 ISTovembre. On la rencontrait alors sous deux formes, soit pourvue de deux gros noyaux, soit multinucleee, et alors les noyaux, au nombre de 15, 20, 30 et plus, etaient ou bien globuleux ou bien ellipsoidaux, mais dans la regie tous de meme forme dans un meme individu , il est probable que la forme ellipsoidale etait l’indice d’une division commencante du noyau. En 1902, j’avais egalement trouve V Amoeba granulosa tantot pourvue de nombreux noyaux tres-petits, tantot munie d’un seul noyau tres-gros ; il est probable que dans le Loch Ness les individus uninuclees devaient aussi exister, et si je n’en ai pas trouve de tels c’est qu’ils y etaient sans doute rares ; mais en tout cas le fait de ^existence de ces nombreux individus a deux noyaux est en lui-meme assez curieux a noter. * J’ai meme rencontre, dans la recolte du 7 Aout 1903, un exemplaire d’un curieux rotifere, appartenant suivant toute apparence au genre Callidina, protege par une enveloppe speciale en forme de bouteille, et que dans differentes occasions j’ai trouve dans les mousses et le sphagnum de la Suisse. Cette espece interessante est, si je ne me trompe, actuellement a l’etude en Ecosse, et nous ne tarderons sans doute pas a en avoir la description. t Zeitsch. fur wiss. Zool., vol. xli., 1885. 1904-5.] Sur les Sarcodines du Loch Ness. 599 Dijfflugia pyriformis, Perty. Cette espece n’etait pas rare dans la plupart des recoltes, et se montrait sous differentes formes, generalement petites ; mais la mieux representee etait la variete lacustris, Penard, caracteristique des lacs profonds, a coquille etroite, sub-cylindrique, peu renflee en arriere, souvent pourvue a sa partie anterieure d’une sorte de collier de pierres plus grosses que celles du reste de l’enveloppe. Difflugia acuminata , Ehrenberg. Cette difflugie se rencontrait dans le Loch Ness en assez grande quantite, sous differentes formes, mais le plus souvent representee par la variete inflata , Penard, que Ton trouve communement dans les grands lacs ; mais ici la coquille, tres-renflee et bien caracteris- tique comme forme, etait moins volumineuse que dans le lac de Geneve (140 a 175 /x; a Geneve 200 p, en general). Difflugia , spec, nova? Dans -la recolte du 7 Novembre, j’ai trouve a quatre reprises differentes un organisme dont on pourrait donner la description suivante : — Coquille en forme de flacon aplati, ovale-quadrangulaire Fig. 1. — Difflugia 1 , coquille vue par son cote large ; 2, vue par son cote etroit ; 3, vue d’en haut. sur sa face large, rectangulaire-allongee sur sa face etroite, a parois irr4gulieres, bosselees, plus ou moins onduleuses, renflees par places et sur d’autres points repoussees en dedans. La section transversale donne la figure d’un rectangle allonge. Ouverture buccale terminale, petite, depourvue de rebord ou de collerette, 600 Proceedings of Boyal Society of Edinburgh. [sess. ovale dans son contour Cette coquille se compose d’une membrane ou pellicule chitinoide incolore, transparente, sur laquelle reposent des fragments silicenx aplatis, irreguliers, souvent tres-grands et entremeles de plus petits. Longueur 154 g, largeur 110 g, epaisseur 40 g. Les quatre coquilles rencontrees, identiques les unes aux autres, semblaient bien indiquer un rhizopode, et en particulier une difflugie, qui ne rappellerait alors aucune espece jusqu’ici d^crite ; mais c’etaient la des enveloppes vides, et en l’absence de toute indication plus precise, il faut attendre de nouveaux renseignements pour songer a appliquer a cet organisme une denomination quel- conque. Pontigulasia bigibbosa, Penard.* Cette espece, qui jusqu’ici s’est montree specialement lacustre, etait dans quelques-unes des recoltes representee par des exemplaires assez nombreux et typiques, cependant d’une largeur relative inferieure a celle qu’elle atteint dans le lac de Geneve, et en meme temps d’un volume plus faible. Nebela vitrcea , Penard.f La Nebela vitrcea n’a. ete rencontree jusqu’ici que dans le lac de Geneve, a 20, 30, 40 metres et plus de profondeur ; elle semble etre derivee de la Nebela crenulata , Penard, laquelle habite les tourbieres a sphagnum ; mais elle se distingue de cette derniere espece par une taille beaucoup plus forte (170 a 200 g en moyenne, au lieu de 65 a 90 g), par une forme moins reguliere, plus etroite, bosselee, par ses grandes ecailles plates et non plus rondes, par un noyau d’une structure un peu differente. Dans le Loch Ness on trouvait par ci par la des coquilles vides que l’on ne pouvait se refuser a assimiler a la Nebela vitrcea , mais plus petites (140 g), et plus regulieres de contour que dans la forme typique. Comme d’autre part la Nebela crenulata , provenant sans doute des tourbieres avoisinantes, se trouvait representee dans les memes recoltes, il etait parfois difficile de distinguer entre les deux especes ; la Nebela vitrcea du Loch Ness n’etait plus tout-a-fait celle du lac de * Faune rhizopodique, 1902, p. 322. t Revue suisse de Zool., t. vii., 1899, p. 43. 1904-5.] Sur les Sarcodinds du Loch Ness. 601 Geneve, mais semblait servir de terme de passage entre les deux especes typiques, vitrcea et crenulata. Quadrula symmetrica, F. E. Schulze, var. irregularis , Penard.* Cette variete, beaucoup plus grande que l’espece type, d’une forme et d’une apparence nettement distinctes de cette derniere, a ete decrite en 1891 comme provenant des Montagnes Eocheuses (sphagnum a Caribou, Colorado, 10,000 pieds d’altitude), et n’a jamais ete retrouvee en Europe ; aussi est-il interessant de constater sa presence dans le Loch JSTess, ou elle se montrait bien typique, mais sous la forme de coquilles vides et provenant sans doute des tourbieres du voisinage. Traitees par l’acide sulfurique bouillant, les coquilles laissaient subsister un petit tas de plaques carrees, que la flamme du chalumeau n’arrivait pas k faire disparaitre ; ces plaques sont done ici siliceuses.f Lagerheim, confirme plus tard par moi-meme, a recemment montre que, dans sa Quadrula subglobosa {Quad, irregularis, Archer ; Quad, globulosa, Penard), les plaques etaient formees d’une combinaison de calcium ; quant a la Quadrula symmetrica de F. E. Schulze, les plaques passent pour y etre siliceuses, mais en realite, la preuve en est encore a faire. Les resultats obtenus sur cette variete irregularis ne sont alors pas depourvus d’un certain int6ret, en donnant une probabilite en faveur de l’opinion qui veut que dans l’espece type les plaques soient siliceuses en effet. Campascus minutus, Penard. I Ce petit rhizopode, qui jusqu’ici ne s’etait rencontre que dans quelques lacs suisses, se montrait dans le Loch Ness parfaitement typique. En general on le trouve, dans le lac de Geneve, associe au Campascus triqueter, Penard, mais dans les recoltes de Mr Scourfield, il se montrait seul. II n’est pas tout-a-fait impossible, par contre, que le Campascus cornutus de Leidy se soit trouve dans le Loch Ness; Mr Scourfield * American Naturalist, December 1891, p. 1073. t Comme du reste je l’ai d6ja montre ailleurs ( Archiv fur ProtistenTcunde , vol. ii., 1903, p. 262). t Revue suisse de Zool., t. vii. , 1899, p. 59. 602 Proceedings of Royal Society of Edinburgh. [sess. m’a en effet remis un croquis d’une coquille vide rapportee de ce lac. et qui rappelle le C. cornutus ; mais comme le seul exemplaire obtenu etait represente par une coquille vide, faite d’ecailles plus grandes que dans Forganisme decrit par Leidy, et muni en arriere de deux cornes plus longues, et comme la forme de cette coquille ne paraissait guere etre celle d’un Campascus vrai, il n’est pas possible de se prononcer ; peut-etre le corps mou, avec ses pseudo- podes deployes, aurait-il montre, comme Mr Scourfield le pensait lui-meme, qu’il y avait plutot la une Nebela , peut-etre meme la Neb. caudata de Leidy. Cyphoderia ampulla (Ehrenberg). Cette espece se rencontrait assez abondamment dans plusieurs- des recoltes, et sous di verses formes, mais presque toujours trapue, robuste, et remarquable par la tendance qu’avaient les petits disques qui forment la coquille a s’agrandir (atteignant 2f et 3 /x, au lieu de 2 p dans la Cyphoderia type), a devenir bi-convexes et a, imbriquer les unes sur les autres. II y avait la un type special, qu’on ne trouve pas aux environs de Geneve. Beaucoup d’individus semblaient egalement passer peu a peu a une forme plus grande (130 a 155 /x), qui aurait pu facilement etre assimilee a la var. major, Penard, caracteristique des lacs profonds; mais la var. major typique est de plus forte taille encore (200 a 220 /x), et les disques qui en composent la coquille se touchent les uns les autres sans imbrication. ? Cyphoderia Dans la recolte du 7 Hovembre, j’ai trouve deux coquilles vides, absolument identiques Tune a l’autre, et qui paraissaient devoir etre rapportees soit au genre Campascus , soit plutbt au genre Cyphoderia , mais dont les caracteres etaient trop incertains pour que l’on put songer a donner de l’espece une diagnose quelconque. La coquille, allongee, de 140 /x de longueur, presque droite, pointue en arriere, montrait une section trail sversale a peu pres triangulaire, et on pouvait y distinguer une face dorsale renflee et parcourue sur toute sa longueur d’une arete mediane, puis une face ventrale aplatie. Cette coquille etait tout entiere composee 1904-5.] Sur les Ear codings du Loch Ness. 603 de disques minces, ronds, inegaux entre eux mais toujours beaucoup plus grands que dans les genres Campascus ou Cyplioderia , se recouvrant tres-legerement par leurs bords a la maniere des ecailles des Euglypha. A la par tie anterieure ces ecailles s’arretaient brusquement et en desordre, pour laisser largement ouvert un orifice arrondi, horde d’ecailles dont plusieurs faisaient saillie au dehors, comme s’il y avait eu la un col qui plus tard aurait ete casse. Dans le cas ou la coquille serait a l’etat normal pourvue d’un col .veritable, orne d’une collerette hyaline, ce serait la un Campascus ; sinon il y faudrait voir une Cyplioderia , que Ton Fig. 2. — ? Cyplioderia. 1, coquille vide ; 2, ecailles qui forment la coquille. pourrait rapprocher de Cyph. calceolus , Penard; mais par ces grandes ecailles, cette espece se distinguerait en realite de toutes celles que l’on connait dans l’un et l’autre de ces deux genres. Euglypha alveolata, Dujardin. Parmi les exemplaires examines, il s’en est rencontre un, de taille relativement tres-forte (115 /x longueur, 64 /x largeur), que Fon aurait ete tente d’assimiler a F Euglypha aspera , Penard, caracteristique des lacs suisses, si les ecailles en avaient possede le petit aiguillon caracteristique ; mais ici les ecailles etaient lisses. Placocysta lens , Penard.* Cette espece, particuliere jusqu’ici au lac de Geneve, s’est montree representee dans le Loch bless par quelques individus, * Faune rhizopodique , 1902, p. 514. 604 Proceedings of Royal Society of Edinburgh. [sess. tous un peu differents du type normal, a coquille relativement etroite, ovale, et a ecailles particulierement fortes et bien marquees. Paulinella chromatophora, Lauterborn.* Cet elegant petit organisme, un des plus curieux sans doute parmi tous les rhizopodes d’eau douce, decouvert en 1895 par Lauterborn dans les gazons a diatomees du Rhin pres de Ludwigshafen dans le Palatinat, et que j’ai moi-meme retrouve en assez grande abondance dans le lac aux environs de Geneve, s’est montre dans le Loch Ness represente par une seule coquille vide, parfaitement typique. Pseudodifflugia horrida, Penard.f Cet organisme s’est rencontre en grande abondance dans la peche du 7 Novembre 1904, et la plupart des individus se montraient bien vivants. La forme, trapue, souvent presque spherique, s’ecartait quelque peu de celle qui est normale pour l’espece ; l’enveloppe, formee d’une pellicule mince, chitineuse, sur laquelle reposait un feutrage de particules fines de toute sorte, incolores, ou bien jaunes ou brunes, differait egalement quelque peu de celle que l’on a indiquee dans cette espece ; mais le plasma se montrait absolument typique, ainsi que son noyau. Je voudrais alors a cet egard signaler deux particularity, qui ne manquent ni l’une ni l’autre d’interet : — En 1902 deja, j’attirais l’attention sur le fait que, dans les environs de Geneve, tous les individus sans exception renfermaient dans leur plasma un nombre considerable de batonnets, bacteries ou filaments parasites, tres- minces, de 20 /x environ de longueur, analogues mais non identiques a ceux que Ton trouve normalement dans le genre Pelomgxa; or dans le Loch Ness, tous les individus egalement possedaient ces bacteries, parfaitement identiques a celles de Geneve ; mais elles se trouvaient ici en nombre si considerable que Tanimal en paraissait malade, ne deployant que tres-rarement ses pseudopodes ; il semblait y avoir plutot une . epidemie qu’un phenomene de symbiose normale. * Zeitscli. fur wiss. Zool., vol. lix., p. 538, 1895. + Faune rhizopodique , 1902, p. 452. 1904-5.] Sur les Sar codings du Loch Ness. 605 Un second fait, pins curieux encore, concerne egalement un para- site : — Apres avoir ecrase un grand nombre d’individus, j’ai pu m’assurer que, dans les trois quarts environ de ces animaux, on trouvait, dans l’interieur du plasma, un organisme de 15 a 20 /x de longueur, incolore, pyriforme-aplati, renfle et legerement acumine en arriere, plus etroit en avant, revetu d’une cuticule extraordinairement fine, lisse. Cet organisine, depourvu de cils comme de flagellum, etait creuse sur sa face ventrale d’une gouttiere mediane longitudinale, plus profonde en avant ou elle s’elargissait en figurant une tache claire et arrondie. Dans l’interieur du corps on voyait des grains brillants tres-petits, avec quelques-uns de plus Fig. 3. — Parasite dans la Pseudodifflugia horrida. 1, le parasite vu par sa face ventrale ; 2, vu de trois quarts ; 3, vu de c6te. gros, puis une grande vesicule contractile qui fonctionnait d’une maniere tres-paresseuse, grossissant et diminuant lentement et sans montrer de systole vraie. L’organisme restait immobile, ou bien se voyait agite d’un tremblement qui semblait provenir de causes externes (rencontre de microorganism es, etc.). Ce curieux parasite, qu’a premiere vue on aurait pu prendre pour un flagellate et en particulier pour un Peranema , doit en realite representer autre chose, et rappelle de tres-pres cet infusoire bien plus grand (40 /x) qu’en 1904 je decrivais comme parasite dans l’interieur d’un heliozoaire (. Raphidiophrys viridis )* Mais ce n’est pas le meme ; il y a la deux organismes, analogues mais distincts, deux especes pouvant appartenir au meme genre ; mais ce genre quel est-il ? Comme l’annee derniere je me le demande encore. En tout cas le fait de la presence d’une seconde espece * Heliozoaires d'eau douce , Geneve, 1904, p. 65 et 167. 606 Proceedings of Royal Society of Edinburgh. [sess. dans un second Sarcodine serai t de nature a nous faire croire a T existence d’un genre special, modifie par et pour le parasitisme, mais sur la connaissance duquel nous n’avons jusqu’ici que des renseignements tres-insuffisants, et qui meriterait d’etre mieux connu. Raphidiophrys pallida , F. E. Schulze. Ce bel heliozoaire, partout rare et que Ton ne rencontre guere que dans les lacs et les rivieres, s’est montre dans le Loch Ness represente par un seul individu, parfaitement caracteristique, dans la peche pelagique du 8 Aout 1903. Raphidiophrys conglobata (Greeff). Dans ma monographie des Heliozoaires d’eau douce, a la pag. 330, j’emettais l’avis que le Sphcerastrum conglobatum de Greeff* pourrait bien n’etre apres tout qu’une Raphidiophrys , et peut-etre meme representerait la Raphidiophrys elegans de Hertwig et Lesser. Or dans la peche pelagique du 8 Aout on trouvait en assez grande abondance un heliozoaire colonial, que l’on pouvait assimiler sans hesitation au Sphcerastrum de Greeff. Examine a sec, et apres Taction sur le squelette de l’acide sulfurique bouillant, cet heliozoaire s’est alors revele comine une Raphidiophrys nette- ment typique ; mais ce n’etait pas la Raphidiophrys elegans ; les spicules, qui dans cette derniere espece sont presque ronds, c’est-a- dire d’un ovale dont le grand axe est a peine different du petit, etaient ici elliptiques-allonges, de 10 ju de longueur sur 5 /x de largeur, et arques en ogive a leurs deux extremites. La forme de ces spicules, toujours la meme sur tous les individus examines, montre la certainement un organisme special ; ce n’est plus un Sphcerastrum , puisque Ton ne saurait distinguer ce genre des Raphidiophrys , mais c’est une espece autonome, qui me semble alors devoir prendre le nom de Raphidiophrys conglobata. A propos de cette espece, il me reste a relever un detail assez curieux : on sait que dans beaucoup d’heliozoaires le noyau, gene par les fils axiaux qui, venant du grain central, le pressent au passage, est frequemment et pour ainsi dire normalement * Archiv fur mikr. Anat., vol. xi., 1875, p. 29. 1904-5.] Sur les Sarcodinds du Loch Ness. 607 defigure, prenant une forme conique avec pointe dirigee vers le centre de l’animal, ou bien, comme cela a ete surtout observe dans Acanthocystis turfacea , dechiquete de dentelures ou pro- fondement ere use. Or je n’ai jamais vu dans aucun heliozoaire des deformations aussi profondes et aussi caracteristiques que dans la Raphidiophrys conglobata-, si Ton examine, par exemple dans une preparation au baume et apres coloration au carmin, une colonie se rapportant a cette espece, on y trouve la plupart des individus possesseurs de noyaux lobes ou creuses, et souvent les lobes, au nombre de 2, 3, 4 ou 5, sont assez profondement £L i ... c Fig. 4. — Deux individus d’une colonie de Raphidiophrys conglobata, apres preparation au baume et coloration au carmin. A gauche, on voit le noyau de c6te ; a droite, on le voit d’en haut ; a , ectoplasme ; b, endoplasme ; ,c, noyau: decoupes pour qu’il semble y avoir plusieurs noyaux appliques les uns contre les autres. La figure 1, par exemple, montre la forme acquise par le noyau sur un individu ou ce noyau se voit de cbtej la figure 2 montre le noyau d’un autre individu, mais vu de face, c’est-a-dire en plongeant, de maniere a ce que la pointe du noyau se trouve au milieu de la figure. Comme nous Favons pu precedemment, les recoltes envoyees par Mr Scourfield avaient pour moi un interet quelque peu special, et cet interet consistait surtout dans la recherche des Sarcodines caracteristiques jusqu’ici des lacs profonds de la Suisse. Les resultats aujourd’hui obtenus ne permettent, il faut le dire, encore aucune conclusion serieuse. Ils sont loin cependant d’etre nuls ; en effet, parmi les especes rencontrees, il en est quelques-unes au 608 Proceedings of Royal Society of Edinburgh. [sess. moins qui sont interessantes sous ce rapport special : le Campascus minutus d’abord, qui jusqu’ici n’a jamais ete vu que dans les lacs suisses ; puis la Pontigulasia bigibbosa , la Difflugia pyriformis var. lacustris, la Difflugia acuminata var. inflata , qui semblent egalement etre particulieres aux lacs ; la Nebela vitroca , qui malheureusement dans le Loch Ness ne se presente pas sous une forme assez caracteristique pour qu’on puisse l’identifier a celle du Leman ; la Placocysta lens , qui semble ici representer une variete speciale ; enfin la Cyplioderia ampulla , toujours abondante dans les lacs et qui dans le Loch Ness revetait une structure un peu particuliere. Si l’on songe que les recherches faites aux environs de Geneve ont permis de constater l’existence de 48 especes ou varietes bien nettes,* speciales aux lacs suisses et qui partout manquent a la plaine, on sera porte a douter de Tidentite possible de la faune sarcodinienne des grands lacs en general. Mais il ne faut pas oublier que le Loch Ness n’est probablement pas tres-bien qualifie pour des etudes de ce genre ; qu’il n’y a ete opere qu’un petit nombre de recoltes ; enfin que l’Ecosse a bien d’autres lacs, et que ces lacs sont maintenant l’objet d’ etudes systematiques qui ne pourront guere manquer de nous fournir des resultats plus precis. Geneve, 26 Janvier 1905. * Les Sarcodines des Grands Lacs, Geneve, 1905, Kiindig editeur. ( Issued separately May 4, 1905.) 1904-5. ] The Rhizopods and Heliozoa of Loch Ness. 609 The Rhizopods and Heliozoa of Loch Ness. By James Murray. Communicated by Sir John Murray, K.C.B. (MS. received February 24, 1905. Read March 6, 1905.) Dr Penard has examined and reported upon the Rhizopods and Heliozoa collected in Loch Ness at depths exceeding 250 feet. No littoral samples were sent to him, as his object was to investi- gate the sarcodine fauna peculiar to deep lakes. The majority of the species found in the deep collections were recognised as belonging to the fauna of the littoral region, or of the adjacent moors, only some half a dozen species or varieties being regarded as peculiar to the abyssal region. In order to complete the list of the Sarcodina of Loch Ness, in so far as this can be done from the observations made by the Lake Survey, I now add the names of several species which were not detected in any of the collections sent to Dr Penard. Nearly all are common bog species. List of Species. Amoeba, radiosa, Ehr. Arcella discoides, Ehr. „ artocrea, Leidy. Difflugia lobostoma , Leidy. Hyalosphenia elegans , Leidy. ,, cuneata , Stein. N ebela flabellulum, Leidy. , , carinata , Archer. Placocysta spinosa, Carter. Actinophrys sol, Muller. Actinospherium eichhorni Nebela barbata, Leidy. * ,, bipes (Carter). Acanthocystis chcetophora, Schrank. (Ehr.). Mr D. J. Scourfield also observed : — Difflugia urceolata, Carter. Nebela caudata , Leidy. * Named by Dr Penard from drawing sent to him. PROC. ROY. SOC. EDIN. — YOL. XXV. 39 610 Proceedings of Royal Society of Edinburgh. [sess. Dr Penard enumerates about fifty species, five of which are Heliozoa, and the rest Rhizopods, one species only of the latter belonging to the Foraminifera, Adding the sixteen species observed by members of the Lake Survey, we have a total of sixty-six species of Sarcodina in Loch Ness. This is not a very formidable list, when we bear in mind that Penard has discovered in the lakes of Switzerland close on fifty species and varieties which are peculiar to these lakes, in addition to the many common species also found there. When Rhizopods are dredged from the bottom of Loch Ness the great majority of the examples found are usually empty shells ; those which contain sarcode are generally quiescent, and it is only by the exercise of great patience that one can witness the pro- trusion of the pseudopodia, and thus ascertain that the sarcode is really that of the Rhizopod, and not of some intruder. All the collections, however, were not in this condition ; on several occasions there was brought up from considerable depths (250 to 300 feet) material in which Rhizopods were numerous, of large size, and were actively and voraciously feeding when examined immediately after the collections were made. Such nests were apparently small, and I was never able to get similar results by dredging again at the same spots. The Rhizopods found on these occasions all belonged to a few common species, the only peculiarities being their large size and great activity. These collections also included large numbers of Entomostraca, Rotifera, Infusoria, and larvae of Insects. These limited areas must apparently be well situated for the reception of numbers of un- witting migrants from the shore ; the large size of the Rhizopods seems to indicate that they are also favourable for the maintenance of animal life, probably by offering a plentiful supply of food. On 16th November 1903 the following species were found, all about twice as large as the average of littoral specimens : — Difflugia globulosa, D. pyriformis , D. acuminata , D. spiralis , Nebela collaris . and Quadrula symmetrica. Species of other groups than Rhizopods were not unusually large, which brings into prominence the greater variability of the Sarcodina. Origin of abyssal Rhizopod fauna. — Dr Penard has shown that there are in Loch Ness some species and varieties of Rhizopods 1904-5.] The Rhizopods and Heliozoa of Loch Ness. 611 which he believes to be confined to the abyssal region of great lakes; into the question of their origin in»Loch Ness he does not enter. The problem of the origin of abyssal species is one of great interest ; that of their dissemination from lake to lake one of great difficulty. If it be the case that the fifty Rhizopods peculiar to Swiss lakes are all good species, or varieties of some degree of permanence, there is nothing surprising in the fact ; it fits in with the other biological phenomena. Geneva possesses in the abyssal region large numbers of peculiar species, belonging to many diverse groups, — Worms, Molluscs, Entomostraca, etc., etc. Everything indicates a long-continued isolation, and relatively great antiquity of the Lake of Geneva. When we turn to Loch Ness we find that the biological phenomena are utterly different. The lake is altogether poorer in species ; the abyssal region especially is very poor. Hundreds of dredgings have been taken by many experienced workers, with the most varied apparatus, and the total result (Rhizopods apart) is something less than a score of species, every one of which is a common littoral form. Everything, in short, indicates that the loch, as a biological entity, is of the most recent origin ; there has not even been time for it to get very fully stocked with such organisms as might easily migrate into it from adjacent countries. If, then, there were in Loch Ness Rhizopods peculiar to itself, the fact would be an isolated one, without parallel among other groups of organisms ; we would be compelled to suppose that these animals were capable of more rapid modification than others. If, however, we are told that there are in Loch Ness Sarcodina peculiar to the abyssal region of the lake, but identical with abyssal species of the lake of Geneva, we are confronted with a very difficult problem — viz. to account for the transmission from one lake to another of heavy animals, living on the bottom at depths of hundreds of feet, and which have no means of propagation by minute reproductive elements which might float to the surface and so subserve the dissemination of the species. Dr Penard recognises that in Loch Ness there is very little to support his theory that there is a peculiar Rhizopod fauna of deep 612 Proceedings o f Royal Society of Edinburgh. [sess. lakes, just some half a dozen Rhizopods, and most of these merely varieties, closely related to well-known species. If a simple explanation of the origin of these abyssal Rhizopods could be offered which would not require us to postulate some unknown means whereby the peculiar species might be transferred from lake to lake, it would be worthy of consideration. I think we have such a simple explanation in the suggestion that the few peculiar abyssal Rhizopods found in Loch Hess are probably not really good species or varieties of any degree of permanence, but merely modifications of common littoral species, directly produced by the influence of the abyssal conditions on each individual during its period of growth. It will be observed that the majority of Dr Penard’s abyssal Rhizopods are varieties, and that in one instance it was doubtful to which of two related species — one littoral, the other abyssal — the variety found in Loch Hess should be referred. The term variety is used by different authors in such diverse senses — by some being employed as though equivalent to species, by others as denoting a sub-species, a race or a strain, while still others apply it to mere states or conditions — that in an investigation of this sort it is desirable to indicate what is implied by the term. It seems to me important to restrict the term to those forms which we believe to be stable, though not of specific value, and that it should not be applied to mere peculiar modifications which have no permanence. If this distinction is not made between stable and temporary modifications, and we are content to name as distinct varieties, or even as species, every peculiarity of form observed, the physiological significance of variation is liable to be obscured. This is well illustrated in the case of the hyaline Daphnia so common in lakes. This animal is exceedingly variable, and the extremes of form are very different in appearance from one another. So long as these various shapes of Daphnia were re- garded as distinct species no progress was made towards an understanding of the causes of the variation, — we had a number of species, that was all. When, however, it came to be recognised that they were all due to changes of form of one species, attention was devoted to discovering the causes of the variation, and now, 1904-5.] The Rhizopods and Heliozoa of Loch Ness. 613 by the researches of Wesenberg-Lund and others, the problem is well on the way towards solution, the relation of the changes of form to the temperature and specific gravity of the water being almost demonstrated. The abyssal Rhizopods are unicellular animals of the simplest group of the Protozoa, extremely plastic, being simply Amoebse with shells, and are known to be extraordinarily variable, so much so that Leidy considered that different species, even species assigned to distinct genera, passed by insensible gradation one into another. In such animals it would not be surprising if the peculiar abyssal conditions as to light, temperature, pressure, etc., were to produce decided modification of form in individuals which grew up under these conditions. A dwarfing or increase of size, coupled with a relatively greater or less development of the chitinous plates of which the tests of most species are composed, might result in the production of very different-looking indi- viduals. The chitinous plates, according as they merely meet at the edges or overlap in greater or less degree, give rise to great differences of appearance, and some change of this kind might account for the difficulty Dr Penard found in deciding whether a Loch Hess Nebela should be assigned to N. Crenulata or to N. vitroea. The abyssal conditions being approximately similar in all deep lakes, the changes of form might always take definite directions, and this parallel modification might explain the occurrence of peculiar abyssal “ species,” apparently identical, in widely separated lakes. Further researches may modify our conclusions as to the abyssal fauna of our Scottish lakes ; it may prove that the abyssal Rhizopods are good species and varieties ; some means of dis- semination of abyssal species may be discovered, difficult though it is to imagine such ; the work of specialists may show that other groups than Rhizopods have abyssal species ; but, in the present state of our knowledge, it is easier to derive the abyssal fauna of our lakes from the shores of the lakes themselves, and from the surrounding country, than from those distant lakes in which alone similar abyssal conditions will be found. 014 Proceedings of Royal Society of Edinburgh. [sess. Complete List of Sarcodina observed in the Lake Survey Collections from Loch Ness. Class SARCODINA. Sub-class LOBOSA. Order Amcebcea. Amoeba granulosa , Grub. | Amoeba radiosa , Ehr. Order Testacea. Cochliopodium bilimbosum (Auerbach). Difflugia acuminata , Ehr. ,, ,, var .inflata, Penard . ,, curvicaulis , Penard. „ pyriformis, Perty. ,, „ var. lacustris, Penard ,, lanceolata , Penard. ,, globulosa , Duj. gramen , Penard. ,, pristis, Penard. ,, constrida , Ehr. ,, urceolata , Carter. ,, lobostoma, Leidy. „ spec, nova, Penard. Gentropyxis aculeata , Stein. Pontigulasia bigibbosa, Penard. Lecquereusia modesta, Rhumbler. ,, spiralis (Ehr.). Heleopera petri cola , Leidy. ,, msea , Penard. Hyalosphenia papilio, Leidy. Hyalosphenia cuneata, Stein. ,, elegans, Leidy. Nebela collaris. Leidy. ,, flabellulum , Leidy. „ americana , Taranck. ,, lageniformis , Penard. ,, tubulosa, Penard. „ bur sella, Vejdovsky. „ milit or is, Penard. ,, crenulata , Penard. ,, vitrcea, Penard. ,, bipes (Carter). ,, carinata, Archer. ,, caudata, Leidy. „ borbata, Leidy. Quadrula symmetrica, F. E. Schulze. ,, ,, var. irregu- laris, Penard. Arcella hemisphcerica, Perty. ,, vulgaris, Ehr. ,, discoides, Ehr. ,, artocrea, Leidy. 1 904-5.] The Rhizopods and Heliozoa of Loch Ness. 615 Sub-class FILOSA. Order Monostomina. Cyphoderia ampulla (Ehr.). ,, „ var. major , Penard. „ spec, nova? Penard. Campascus minutus, Penard. Assulina seminulum, Leidy. „ minor , Penard. Corythion dubium, Taranck. Euglypha alveolata, Duj. „ brachiata, Leidy. ,, ciliata (Ehr.). Euglypha compressa , Carter. Placocysta spinosa, Carter. „ lens , Penard. Paulinella chromatophora , Lauterborn. Pseudodifflugia horrida, Penard. /S' phenoderia lenta, Scblumberger. „ dentata, Penard. Trinema enchelys (Ehr.). ,, linear e, Penard. Sub-class RETICULOSA. Order Foraminifera. Gromia nigricans , Penard. Sub-class HELIOZOA.' Order Aphrothoraca. Actinophrys sol, Ehr. | Actinospherium eichhorni (Ehr.). Order Chalarothoraca. Acanthocystis chcetophora, Schrank. , , myriospina , P en ard . Pomphalyxophrys exigua (Hert. et Less.). Raphidiophrys pallida, F. E. Schulze. „ conglobata (GreefF). Order Desmothoraca. Clathrulina elegans, Cienkowsky. ( Issued separately May 105 1905.) 616 "Proceedings of Royal Society of Edinburgh. [suss. Note on the Rainfall on the Drainage Area of the Talla Reservoir. By B. Hall Blyth and W. A. Tait. (With a Map.) (MS. received January 28, 1905. Read May 1, 1905.) In 1895 the Edinburgh and District Water Trustees obtained an Act of Parliament for the introduction of a new water supply to the city of Edinburgh drawn from the Talla Water, one of the upper tributaries of the river Tweed. The Bill as originally introduced contained provisions for giving off 4,000,000 gallons a day as compensation to the stream, and for appropriating the remainder of the water. The Tweed Salmon Fisheries Commissioners and other pro- prietors interested were advised that the proposed amount of com- pensation was too small, and after various negotiations a clause was ultimately adjusted providing that rain gaugings should be taken over the drainage area for a period of seven years from the 1st Janu- ary 1 896 by the authors of this note (Mr Tait having been appointed in lieu of his predecessor), and that thereafter they should fix — tak- ing all the circumstances into consideration — what was the avail- able annual rainfall of the district. One-third of this ascertained quantity was then to be given as compensation to the stream, the remaining two-thirds being appropriated for the supply of the city. To carry out these provisions, seven gauges were placed on the drainage area at varying altitudes. The drainage area and the positions of these gauges are shown on the accompanying Ordnance Map, and the heights above Ordnance datum are as under — The top water level of the reservoir is 950 feet above Ordnance datum. Monthly readings were taken at all the gauges for seven years from January 1896, and in addition, at the three last-named stations, which were easily accessible, daily readings were taken from independent gauges. The results of these are given in the following table : — 1496*05 feet. 2627-34 „ 2258-28 „ 1859-92 „ No. 5 . „ 6 . 1537-59 feet. 966-03 „ 1196-48 „ TABLE No. I. — Edinburgh and District Waterworks — Talla Scheme. Rainfall in 1896 to 1902. 1904-5.] Rainfall on Drainage Area of Talla Reservoir. 617 Duplicate Gauges— Monthly Readings. No. 7. At Quarter Hill. 1196-48 ft. o “OSMOMO^OOiaHOJlO 00 1 CO J "5 No. 6. At Talla Linns Foot Farm. 966-03 ft. d “OSOOOJCOOOOOOOiOHOOVO P^iO-^COCO^OSCiCOCMOO'p »(NMtD(NO>OlO(NNN!NOO 56’24 6 At Gameshope Farm. 1537-59 ft. ^CQlONOON'JlOiaiMCHQ flMiom®NocoHOoo99 al^^N(NO(DN^O®mH C T-l i-H 68-04 h x2s <3 w < d «^6^HIQN^0HN®K) roCOCOCOCMOVOCOCOOOVOCMOO a CM CO VO Daily Readings. £ i At Quarter Hill. 1196-48 ft. s QOJOlffiOOOOONOOOffiiO vniQOiNOJpiNiNpyH g(NNlQHOCOifllMi£3>OH® 42*99 ei CD o & At Talla Linns Foot Farm. 966 03 ft. d »mooaoo^i©(NTHO(NcoiQ 1 H^9999«C3 00 hoot)iio 1 HOU3iONN®INOO c OO CO lO No. 5a. At Games- hope Farm. 1537-59 ft. d ^^VOOSJ^OVOvOOirHOiVOaO SO)M!MiOt>,9999®9N K^^NIMOffiN^OCCOO 66-97 o' |Z3 s <3 5 w 6 o No. 4. At Games- hope Loch. o Cb 1 a 1 d Smnowwoomooion® HoOCOfNOOlOS^WOSHt^tN ioCO'C<0)!NOWN^a?0(j]0 CJ * vO 1

si(N®OH)iminHtio^^iOH)( CO CC , I aiO) © 05 lO M »C Tfrl l£5 CO & 12 fl«s©io©H05©foinvaHoo .OOIONMMHIOOSOH (M H CHm©M(Nl0M©^M^05 ci ?J3 r <4-1 +i~ P o c CO 'tfO'tfvo4iH©.l S3 S 9 92 t: . ® £ ® 6 a J3 © 1-Q gj P ►»5d«.5 ► S S3 r^1 “U s © Note.—* The gauges at Lochcraighead and at Ravenscraig were found frozen at the end of January, and were not emptied till the end of February. The gauge at Locheraighead was again found frozen at the end of March, and was not emptied till the JAMES WILSON, end of April. In dividing the total amounts collected in these gauges for the two months, the average of the remaining gauges B. HALL BL Y TH. on each month was taken, and the total amounts collected for the two months were divided proportionally. 1898. 1904-5.] Rainfall on Drainage Area of Talla Reservoir. 619 (NOlONHOfNMiOOOm KrltlOiaMOONH^poOH j ^COh^PKNHiotXOION 48 09 * 1 sS OOCICOMOOCOOIOCONO •^(^OMOlOCT^OOr-'M Ip 1 o VO ©OCOOCOO'OCOVOOOCO ®(Nioioooy NomcoH 60-05 02^ OOOO'QCO'ilNiMraHNOOtM M^ONMnOMiOfflCOCl ©©>©vO'>* I— 1 J s a c g»^3 °1 an NCON®>Oin'^(M®®lOM OO OOOMaThMHOl»®fflO) '#T)<-'®(N®rJ«010NNO} 61-62 te a $ 8) | e3 CO (N r- i«0 1^C?®®05N®N oocoosojvot— i©'tf.t''.?oa5 ®®lQi0^tNl0CnC5iO(M>flo 3 2 CJ ®H(MiaiOOMiON(MOOCl »rfl^CnC5Cl©H©COH® vo^^-^Mi^cocqvo4ji©oON(N (MNH^OOONlMlOCO'MH Si t-»C5W.t^OmO(N®>©iOC0 79-10 ^ nS 00‘C5 0J>-t— 1 O © (M © © ^®®Nooco®i«ooiioN 1 Ol CM Is ts “ ° G-C ® s to OB o g g ^ f-l (U © « > OONCKNOONNOOCTNfN NN®®iojqi)8iO®lNlM 70-72 * * M®iQINNn®NO)®oiO W®NOOOOMNNMOON vo 00 © u 05 ^ o © fiG-S * * NOlOIMnNONOrtf]® ^t^r-~iC5oo»Oi^-^^ti©ir^co O >OCOH®(NiOHC1®NQOH r-H o g | G§ *• r^4rio»"o^ v— ^ ' — * r-H 00 so * * * ■^NCOCOHNOQOOOONO cpcO^Ot— icooom^i — 81-89 <3 cs § A5 > M)S^ Lg © © a ©| o c«oft %s^ ++ OGiOrtOO^H^N^OlO 'O M O NN H M OO H O ^ t^COtO^^(M©(N©«OC®CN 6879 nocooooinci^kohjico 00 -*3 © © ^ lls-g WOHClCOWHffiCXMOO© Mp®^ooi>ffiowKioro CO *D icocicNt— i® ia ® ® iq (N vo g o ©.S VO©-^^COi^4*CiO 1 3 T— * ;o 00 No. 5. At Gamesliope Farm. O ^oiQooiamCMao(Na®o | MOOOOtiO‘P9'lWO CO (N ‘P 1 mOOMH^OOOOiOONOOOO^J j CO N OO Average. d ®ocfflooioioo^ioa®a M © M O KKO K ^ «D Vft N (O 1 P i— 1 72-70 . GO o No. 7a. At Quarter Hill. 1196-48 ft. d CD QON^OOr-i005NH05^05 ^NMNhnOOOOIiNh giaNOMiQ-iKNia^iaoo 55-49 1 § 3 Ph fcH ►J ◄ 03 CO 6 £ At Talla Linns Foot Farm. 966 03 ft. d ^loooooaoMN^^noM HcO!N05lQlM(NOO©^NH9 1 oi©lOO'^io©CO©*)'©N(N j 1 os o eS iO o At Games- hope Farm. 1537-59 ft. 1 d ^iNlOOOMKNCOaHffiH HMfflONOTfKNNffiOHH 1 i»XCOHt)<000010©©OOCON G r-H 86 77 Monthly Readings. No. 4. At Games- hope Loch. 1859-92 ft. d* 1 ®OOOOONOOOOlQO(NMN I HOoocQMoOiQINmNNHip i tc©OOM©OOiC©©NNiO © r-i 00 1 SO No. 3. At Ravens- craig. 00 1 ©■ 1 I 00 O f>1 CO S * ++ coo QtOifNaOOlQOWWMl' ! m1Q-1!N(NffiOO>ONNOOiO© u CO 0° No. 1. At Meggat Head (Talla Moss). 1496-05 ft. d *iQNMflOOO(NOCNOON 1 QT)H'^kOip^9C'lOH>00C5TH j KlOC-IOI>lfflO^>QiCo4tl»CO<0'‘tf‘0 kO O OJlOCOOINMmOOONiQO HCD!MCOC5050COCONCCCE ■^CO^NHlOINOOOlN'^CQ kOkococooi-H-'^os©’-^1-1^1 TUCOOCNNOffioolONOa mcNmotNOHCDNCo^^ W(^CDC00005INCQ1005NN N®«OOV<»COi7iHC!i^>CO (NH«iiHWHCOT)<^WU5 -'tfl CO m P* KlcJ WS SH pq'^' 0000'ctfC5C5COmNM-^ Tj(MTi(NH»GH®ffiN'^kO COCMCMUOCOOi— lOOOSt^CO'^f C®N®®®®KO®00® ®roWCOC5N.OSMiO®COH CO(N(N-^(NW3HOO®'^'Q O O — 1 I^WMWCMNMW ®(NCI«Nl^CONCOiOHin mciwrarac; hn®n^>o 00 00 o co CO kO COCMCMOCO'^OOkO'^OdOOOO OS OJCNOMl'kOONOOHM.I CMCMC-l^CMCOrH'ctCkOCOCOCO © • • • § a i~> £ s V £ g «, - 3 3 3 © ° l2 ^ £ C t- O SrO S NOiaoNN®ON>Q'<)('# XONOMNO^pOCON COOCMCOCMr— ICMCNCO CO ''f CO 36*35 kOOOl^kOkOkOCMOOCOCOCM NCO^I^m^OOHCOCO® kOCMCO^COT-HCOCM^COCOOS 1 • OO kO COCMkOt--.kaoOOCOCOCOCMOO HMOMHNOHiOrlOOtO t^.CMkO-^CO^H'^rti'stCkOCOO 59 19 o>OTj((McoMi>. I CO 1 03 1 1 o s i 8 I OS 1 iQCONCONHkOMOlCOOCO NO)^NnlQT)l®HCDXX) k£3 (M 00 CO t — I CO P--!)0«I t'-.CM-'+i'^flCOT— 1 rtl Tjc Tfi lO CO O I— 1 lOkOWHOQCiWat.N^ C5©Cp^f®i>^OJ50®®l'. 1 iCOrtlCMr-CCOCO'cji^COt'- ■ CO 1 o kO MMOOhOONNNOO'# BaOOOWNOOHOip COHT)C'^(MH^'^^kONW 50'11 54 "59 O kO 1.0 O O 00 • O r— 1 •^rioioot^oicocooocooooo (N ^ Cl r- iT^CO'^f'^tCOlO COCOOOOOCOkOOSl-^OOkO O N 05 CO M N 9 Cl CO k£i 1 COr— iCOCOCMi— iCMCOCOkOkOOO J os »o 1902. January .... February .... March .... April .... May ..... June . July August .... September .... October . . Novembei . . December .... Total. HALL BLYTH. A. TAIT. TABLE I. — continued. — “ — f IS * H’ S' 1 * Average. ---Hi ♦ 1 W I'tl 2*56 6-10 5-22 478 4-87 5 98 11-42 wi iS 1 2 73 8-45 573 7-35 1% 572 iJS 1 3-29 6-25 s If' 0-30 3-38 6- 87 5-28 iS 7- 13 15-57 In8.3r 3-97 1 05 if 5-22 I'll 8-01 17 11 5- 28 !g 6- 23 3 '87 6 64 673 7- 10 1203 W 277 0-34 378 5-11 470 5 07 4- 01 5- 79 5-24 10-19 Ins. Dec. 6-45 775 470 6-34 5-95 7 19 14-09 ir 1-08 475 8 05 8-50 1 17-50 m-8Dr 530 1 0-96 4 58 6- 23 4-03 G-64 4-45 7- 18 277 4 76 4-15 iS 4-75 Total. 63-61 81-82 75*61 74-68 8677 70-94 55-49 7270 87-35 | 71-38 5187 KOm-j SrtfiA'S?-. foujen.. sappe emptied out. I I I •s, I ! ! 5 t t 6 I I § 622 Proceedings of Royal Society of Edinburgh. [sess. The net result of the gaugings shows that the average annual rainfall on the drainage area during the period of seven years was 62*51 inches. Of course, seven years was much too short a period from which to fix the average annual rainfall for all time, and recourse was then had to the observations from all the adjoining districts, which had been kept for a long period, including the seven years in question. The result of comparing these, showed that the average annual rainfall during the seven years was about 4 per cent, less than the average during periods varying from fifty to sixty years at the places where the records had been kept, and consequently this proportion was added to the amount of rainfall obtained from the actual gaugings on the drainage area, thus bringing the average annual rainfall as over a long period up to 65 inches. To arrive at the available annual rainfall, there was then deducted from this quantity 12 inches — as fixed by Mr Mansergh, F.R.S., after a reference to him — to reduce the quantity to the average of the three driest consecutive years, and a further quantity of 15 inches, which had been agreed on by the authors as the amount represented by evaporation and absorp- tion, leaving 38 inches as the average amount of the available annual rainfall. The extent of the drainage area is 6180 acres, and this gives a daily amount of 14,598,000 gallons, one-third of which has to be given off as compensation, and the remainder being appropriated for the purposes of supply. The following points may be noted in connection with the gaugings : — At the three stations where both daily and monthly readings have been kept the two sets of readings agree very closely indeed. The average annual rainfall at stations 5a, 6a, and 7a, where daily readings were recorded, was 6 TOO inches, while the corresponding amount from the monthly readings was 6T01 inches. The number of days on which no rain fell was — at 5a, 1036, or 40*53 per cent. ; at 6a, 1095, or 42*84 per cent. ; and at 7a, 1118, or 43*74 per cent. The days on which less than TlF of an inch fell were respec- 1904-5.] Rainfall on Drainage Area of Talla Reservoir. 623 tively, 1508, or 59*00 per cent.; 1582, or 61*89 per cent.; and 1718, or 67*21 per cent. ; while the days on which over an inch fell were 118, or 4*61 per cent. ; 70, or 2*74 per cent. ; and 34, or 1*38 per cent. There were 36 records of more than 2 inches in one day, and of these 25 were at 5a, 8 at 6a, and 3 at 7a. There were three readings of over 3 inches, all at gauge 5a, and the highest recorded reading on any one day was on 1st November 1898, when 3*57 inches of rain fell at that point. The heaviest continuous rainfall was from 26th to 30th Decem- ber 1897 inclusive — 5 days in all — when 9*99 inches were recorded at gauge 5a, 8*23 at 6a, aud 5*02 at 7a. The longest period of practically continuous rainfall was from 11th September to 11th October 1896 inclusive, 31 days in all, at gauge 5a, when 13*89 inches were recorded. During this time, 11 days and 3 days were recorded at 6a and 7a respectively as having no rain. The extreme variation between the rainfall of two consecutive days occurred on October 31st and November 1st, 1898, when the readings were : — With regard to the monthly readings, these show that on the average of the seven stations, there were 2 months on which less than 1 inch fell, 39 months on which the fall was between 1 inch and 5 inches, 39 months on which the fall was 5 inches and under 10 inches, and 4 months on which the fall was 10 inches or over. The wettest station was 5a, which had only 1 month under 1 inch, 33 months between 1 and 5 inches, 42 months between 5 and 10 inches, and 8 months over 10 inches; while the driest station was 7a, which had 3 months with a fall under 1 inch, 55 months between 1 and 5 inches, 24 months between 5 and 10 inches, and 2 months with a fall over 10 inches. The greatest rainfall in any one month was in December 1900, when the average at the seven stations was 14*09 inches, ranging Oct. 31st Nov. 1st Oct. 31st Nov. 1st at 5 a. at 6a. 624 Proceedings of Royal Society of Edinburgh. [sess. from 10*19 at 7a to 17*11 inches at 5a, the latter being the heaviest monthly rainfall recorded in the period under review. The rainfall in the different months is shown in the appended tables Nos. 2 and 3. Table No. 2 is made up by selecting respectively the highest and lowest individual readings ob- tained. Table No. 3 is made up on the basis of the average of all the gauges. The average under : — annual rainfall at the different gauges is No. 1 56*23 No. 5a 73*92 „ 2 . 65*53 „ 6a . 61 43 „ 3 . 66*02 5, 7a 47-66 „ 4 . 66*81 The highest rainfall in any one year recorded at a particular gauge was 89*88 in 1897 at gauge No. 5a, and the lowest was 36*37 in 1902 at gauge 7a. The only fact which seems to be established as the result of the gaugings is that station 5a is the wettest from every point of view. It had the heaviest daily, monthly, and annual rainfall, and the largest total rainfall, and station 7a is the driest station. It would seem therefore that the ordinary rule that prevails, viz., that rainfall increases by 2 or 2J per cent, for each 100 feet of ascent, can only be accepted with considerable modifications, and that a great deal must depend on the direction and nature of the prevailing winds, and on the exposure of the gauges. The lowest gauge is No. 6a, which is at a height of 966 feet, and shows an average rainfall of 61*43, while the highest gauge, No. 2, at a height of 2627 feet, has an average annual rainfall of 65*53, or an increase of only 0*41 per cent, per hundred feet of rise, and gauge No. 5a, with a height of 1537 feet, has an average rainfall of 73*92, equal to an increase of 3*56 per cent, per hundred feet of rise. The annexed diagram shows by circles the average annual rainfall recorded at each of the gauges, and by dotted line the rainfall that might have been expected at each of the gauges, taking the rainfall at the lowest gauge as a basis, and adding 2J per cent, per hundred feet of rise to the others. 1904-5.] Rainfall on Drainage Area of Talla Reservoir. If 4 A p I a — 01 ( * V VT 1 - \ \ _ «\ \ T~ J \ IT) \ On $ V; q; l \ ? N. \ — a; )\ | < | S>1 "o 'V ft £ V ? I % V. V I a • 5 \ ft 3 ft 'J & c. S \ 1 V QJ __a ! __ ~V* * ^■VSJ t- 1 ^ .« ! 0 1 1', m n, Qd' -e~ \ \ \ | \ ~T i A If It ? J : § § s i 3 5 PROC. ROY. SOC. EDIN. — VOL. XXV. 40 626 Proceedings of Royal Society of Edinburgh. [sess. During the period of gauging, three of the gauges were tampered with — No, 3 in May 1896, No. 7 in April 1899, No. 2 in June 1899 — and in these cases the average of the remaining gauges for the month was assumed. No. 2 gauge was frozen in January and March 1897, in February 1898, in January 1899, and in January, February, and March 1900. No. 3 was frozen in January 1897, in February 1898, in January 1899, and in January, February, and March 1900; No. 4 in January 1900. In dividing the total amounts collected in these gauges during the frozen period, the average of the remaining gauges during each month was taken, and the total amount frozen was divided proportionally. At the outset, it was arranged that the various gauges should be so placed that their readings should give a proper representation of the rainfall over the drainage area to the Talla Reservoir. The daily gauges Nos. 5, 6, and 7 were so placed that they might be very easily and regularly reached by persons living or engaged in the neighbourhood. For instance, the Tweedsmuir school- master attended to No. 7, and the farmers or shepherds attended to Nos. 5 and 6, which were placed close to the farmhouses of Gameshope and Talla Linns. The daily and monthly readings were used to check one another. The whole of the monthly gauges were regularly visited and read on the first day of each month by two assistant engineers who represented the two arbiters. The authors have much pleasure in recording their high appreciation of the faithful manner in which their assistants performed their duty, notwith- standing the particularly inclement weather conditions on many occasions. The reading of the monthly gauges involved a pretty hard day’s work even in ordinary weather. The section accom- panying the paper gives an indication of the ground that had to be traversed and the hills that had to be ascended by the observers between the times that they left their carriage on the road and returned to it again. It will readily be understood that in foggy weather it was a matter of no small difficulty to find some of the outlying gauges, especially at places where there were neither fences nor running water. On the other hand, on account of deep snow and drifts, the observers’ work at times was still harder. It 1904-5.] Rainfall on Drainage Area of Talla Reservoir. 627 628 Proceedings of Royal Society of Edinburgh. [sess. is worthy of mention that at one particular place which had to be passed on about six different occasions during the time of deep snow, the observers were able to walk along the top of a fence wall over three miles in length, and so saved tramping through the snow, which was level with the cope of the wall. The monthly rain gauges used were 8-inch copper “mountain rain gauges,” graduated to read 16 inches of rainfall, and made by Casella of London. The total depth of the outer case of the gauges is 4 feet inches, and when fixed in position, were sunk in the ground about 3 feet, and protected from sheep by a stob and wire fence forming an area of about 20 feet square. The authors are strongly of opinion that when rain gauge read- ings have to be taken over a period of years, the period should commence and terminate at some other period than the last day of December, as at such a time many of the gauges may be found to be frozen. The authors are glad to be able to state that, upon their recom- mendation, the Water Trust have agreed to continue the recording of the rainfall at all the seven stations, and they are satisfied that the information so obtained will be of great benefit, not only to the Trustees themselves, in the event of their afterwards extending their area of supply, but also to other local authorities, engineers, and others interested in the determination of the many problems connected with rainfall which have to be considered in connection with questions regarding water supply. [Vol. XXV. 1904-5.] Rainfall on Drainage Area of Talla Reservoir. 629 TABLE No. 2. Month. Average. Maximum. Year. Gauge. Minimum. Year. Gauge. January . 459 8-31 1900 5a 1-85 1897 7a February . 3*99 8-21 1897 5a 0-80 1900 4 March . 4*45 11-45 1897 i 5ci 0-30 1900 4 April . . 4-59 7 70 1898 4 1-98 1898 7a May 3-37 803 1900 5 a 0-54 1896 6a June 4-45 10-00 1900 1 1-16 1902 7a July . . 4-01 7-45 1896 3 1-08 1901 1 August 5-80 13-54 1897 4 2-06 1899 1 September 6-04 10-50 1901 3 319 1902 7a October . 6*02 8 93 1898 5a 3-05 1902 7a November 6-44 15-65 1899 5a 1-69 1896 7a December . 8-76 17-11 1900 5a 2-40 1899 2 TABLE No. 3. Month. Average. Maximum. Y ear. Minimum. Y ear. January 4-59 6-83 1899 2-51 1897 February 3-99 6-32 1899 1 95 1902 March . 4-45 9-12 1897 079 1900 April 4-59 6-39 1898 2-31 1896 May . . . 3-37 6-45 1900 075 1896 June 4-45 7-75 1900 1-63 1902 July . 4-01 6-74 1896 1-64 1901 August . 5-80 11-^9 1897 2-46 1899 September . 6-04 8-31 1896 4-14 1902 October. 6-02 7-46 1898 4 49 1902 November . 6-44 12-66 1899 2*46 1896 December . 8-76 14-09 1900 2-97 1899 ( Issued separately May 10, 1905.) 630 Proceedings of Royal Society of Edinburgh. [sess. Remarks on the Rainfall Records in the Talla Drainage Area during the years 1896 to 1902. By P. D. Donald, A.M.Inst.C.E. Communicated by W. A. Tait, M.Inst.C.E. (MS. received February 10, 1905. Read May 1, 1905.) i A striking feature of the results obtained at the seven gauges in the drainage area is the divergence from the commonly accepted rela- tion between rainfall and height above sea-level. The following table shows the “theoretical” amounts of rainfall, averaging 62-51 inches, that might have been expected at the several gauges, on the assumption that there was a uniform increase of 3 per cent, for every 100 feet of rise ; and in comparison with these, the amounts actually recorded, also averaging 62 '51 inches. Comparison of Actual Rainfall Records with Rainfall INCREASING UNIFORMLY 3 PER CENT. FOR EVERY 100 FEET OF RISE. G-aiige No. Height above Sea-Level. | “ Theoretical ” Annual Rainfall Average Annual Rainfall recorded. Difference in Inches. Percentage Divergence from “Theo- retical ” Rainfall. feet. inches. inches. + + 1. 1496-05 59-40 56-22 j 3-18 5-4 2. 2627*34 76-30 65-53 10'77 14*1 3. 2258*28 70-90 66-02 4-88 6-9 4. 1859*92 64-80 66-82 2-02 3-1 5a. 1537-59 60-00 73-92 13-92 23-2 6a. 966-03 51-30 61-43 10-13 19-8 7a. 1196-48 54-90 47-66 7-24 13-2 Average 62-51 1 62-51 1904-5.] Rainfall Records in the Talla Drainage Area. 631 If the position and exposure of the gauges are taken into con- sideration in the comparison of the records, the result very strongly corroborates the conclusion that has been drawn from the results of similar gaugings elsewhere, that in high -lying districts the greatest rainfall is to he expected, not on the summits of the hills, hut in the valleys between. Gauges Nos. 5a and 6a, which have the highest records of rainfall, and show the greatest divergence from the 3 per cent, rule, both on the side of excess, are situated in valleys with steep sides, rising to 500 feet above the gauge level in the case of No. 5a, and 900 feet in the case of No. 6a. Gauges Nos. 2 and 3 are on the summits of the highest hills in the drainage area, and No. 7a, which, with the exception of one year, has, by a considerable amount, the lowest record of all the gauges, is situated on the summit of a ridge on the watershed. Dividing the gauges, therefore, into three groups, a comparison may be made of the records obtained at similarly situated gauges, as in the following table. Increase on Lowest Percentage Increase per 100 feet of Rise. Gauge No. Height. Average Annual Gauge. Rainfall. Inches. Per cent A. Gauges near Watershed, but in Depression between Watershed Summits. 1. 1496-05 56-22 4. 1859*92 66-82 10-60 1*8*9 5-25 B. Gauges on Watershed Summits. 2. 2627-34 65*53 17-87 37-3 2-6 3. 2258-28 66-02 18-36 38-4 3-6 7a. 1196-48 47*66 C. Gauges in Valley s at foot of steep slopes. 1 5a. 1537-59 73-92 12'49 20-4 3*6 6a. 966*03 61*43 As may be seen in the table next following, the records at gauge No. 1 show almost twice as much total variation, in relation to the 632 Proceedings of Royal Society of Edinburgh. [sess. average rainfall over the whole area, as is shown by any of the other gauges ; and therefore, in this case particularly, a comparison with other gauges based on the short period of seven years is not unlikely to yield an anomalous result. The higher average records at No. 3 gauge than at No. 2, although the former is at a lower level, may have some reference to the position of No. 3, between the adjoining higher ground of White Coomb and Hart Fell, on the E.N.E. and W.S.W. respectively, outside the drainage area. The annual rainfall at each gauge, dealt with in the above tables, is the average of the amounts recorded during the seven years. In order to see whether the records at the several gauges bear ap- proximately the same proportion throughout the period under review, the records of each year are analysed and compared with the average in the table following. Gauge No. 5a record is, with one exception, the highest in each year, and its practically uniform proportion throughout to the average of the seven gauges is worthy of note. The other gauges exhibit considerably more variation, and this is most marked in the case of No. 1. 1904-5.] Rainfall Records in the Talla Drainage Area. 633 Ph Minimum per cent, under average per cent. SO so SO Hi © SO CC sO SO Maximum per cent, over average per cent. j SO so SO SO sp SO r—l 1>» OS OS 03 SO 1 1 1 1 1 Average of 7 years. Per cent, of average. SO _ sp O so sO 00 OO «o OS O O O i— l OS © © rH Inches. 1 00 CO 03 03 • i— 1 i— 1 i— i i— 1 i— 1 © © Inches. 45-49 50-11 54-59 50- 46 59-25 51- 07 36-37 Cl © OS HI 1901 Per cent, of average for year. 1 sp ^ sp sp . SO 1 so SO OS CO O SO rH 1 !>. © © © 03 © OO j— 1 rH i— 1 i— 1 i— 1 © © rH Inches. 40-19 56-46 58*18 55-24 64-32 56*36 43-45 CO o o o Per cent, of average for year. j so p> _ so SO 03 H< CO © i>- © 00 rH o © rH OS rH rH i— 1 rH 1 . © I 2 © Inches. 63-61 81*82 75-61 74-68 86-77 70 94 55-49 1 © 03 1 ^ 1899 Per cent, of average for year. so sp SO so OO H< GO OO © © © OO © © © <03 OS l>- rH rH j-H r—l © © Inches. 57-63 68-79 68-07 70-72 79-10 63-15 51-86 Cl © SO © 1898 Per cent, of average for year. sO so SO so SO - © 3>» SO | Ci © © os 00 rH i Per cent, of average for year. p so »0 so OC Hi C © © rH ® 2 ® H H ® N o © 1 Inches. 74- 91 79-82 76-97 83-76 89-88 75- 90 54*13 co 1896 Per cent, of average for year. so so »p so rH rH © © SO Cl HI © © © rH rH © |^ © © Inches. rH 00 © sO H< © OS SO 00 ©OS 00 © 00 CO 1^- !>. © CO 03 SO so so © © SO H< Cl OO SO Gauge No. j g3 I 1 (M CO ^ m W j V be e8 5 t> < 634 Proceedings of Royal Society of EdAnburgii. [mm. Considering the question of the maximum range of variation of rainfall in selected periods, and taking the average of the seven gauges, it is seen that in the period under review the maximum annual rainfall was 76 '47 inches and the minimum 49*62 inches, or, respectively, a variation of 22*4 per cent, above and 20 '6 per cent, below the mean of the seven years, namely, 62*51 inches; or 17*6 per cent, above and 23*6 per cent, below the calculated mean annual rainfall over a long period, namely, 65 inches. If the shorter period of one month is taken, the range of varia- tion is, naturally, found to be very much greater, as is shown in the table below, in which the figures for each month of the year are given. The comparative regularity of the amount of rainfall during the month of October is noticeable, and also the great range of variation in the rainfall for March. Average of 7 Gauges. Maximum Minimum Per- centage Per- centage Month. Average Rainfall of 7 years. Maximum Rainfall recorded. Minimum Rainfall recorded. Rainfall above Average. Rainfall below Average. above Average. Maximum. below Average. Minimum. Inches. Inches. Inches. Inches. Inches. Per cent. Per cent. Jany. 4*59 6-83 2-51 2-24 2-08 49 45 Feb. 3*99 6*32 1-95 2-33 2-04 58 51 March 4*45 9-12 0-79 4-67 3-66 105 82 April 4*58 6-39 2-31 1-81 2-27 40 50 May 3-38 6-45 0-75 3-07 2-63 91 78 June 4-45 7*75 1-63 3-30 2-82 74 63 July 4-01 674 1-64 2-73 2-37 68 59 Augt. 5*80 11-29 2-46 5-49 3-34 95 58 Sept. 6-04 8-31 4*14 2*27 1-90 38 31 Oct. 6*02 7*46 4-49 1-44 1-53 24 25 Nov. 6*44 12-66 2-46 6-22 3*98 97 62 Dec. 8 76 62*51 14-09 2-97 5-33 5-79 61 66 This suggests the investigation of the monthly distribution of rainfall throughout the year, and in the following table the result is given for each year and for the average of the seven years. The rainfall for each month in any year is stated as hundredth parts of the total rainfall for that year, still taking the average of the seven gauges. This table also brings out the comparative regularity of the rainfall of October in relation to that of the whole year. 1904-5.] Rainfall Records in the Talla Drainage Area. 635 Monthly Distribution of Rainfall. Rainfall stated as hundredth parts of total Rainfall in particular Year. 1896 1897 1898 1899 1900 1901 1902 Average of 7 years. Maximum above Average Minimum below Average. Jan. 6-1 3-3 6-8 10-4 8-8 6-5 10-5 7-4 3-1 4-1 Feb. 6‘7 8*3 6-7 9-6 4-1 4-4 3-9 6-4 3-2 2-5 Mar. 11-4 11-9 3-1 9-0 1-1 5‘7 7-5 7-1 4-8 6-0 Apr. 4-0 6-6 10-4 8-0 4-9 9-8 8-5 7-3 3-1 3-3 May 1-3 4-7 4-6 7'0 8-9 5*1 5-6 5*4 3-5 4*1 June 9-4 6-8 6-4 3-2 10-6 9*4 3-3 7-1 3-5 3-9 July 11 *6 5-8 2-9 7-7 6*5 3’1 7-4 6-4 5-2 3-5 Aug. 6*2 14-8 10-7 3-8 8-7 12-7 7-1 9-3 5-5 5*5 Sept. 14-3 6-4 9-1 8-8 8-2 14-1 8-3 9-7 4-6 3-3 Oct. 9*8 6-5 12-1 8-7 9-9 12-5 9-1 9-6 2-9 3-1 Nov. 4*2 7-8 11-8 19-3 8-9 7-5 12-6 10-3 9-0 6-1 Dec. 15-0 17-1 15-4 4-5 19-4 9-2 16-2 14-0 5-4 9-5 100-0 100-0 100-0 100-0 100-0 100-0 100-0 100-0 The question of the monthly distribution of the rainfall is of practical importance in the determination of the reservoir storage required to be provided in order that a uniform daily supply of water, based on a figure of annual rainfall, may he regularly maintained. In the present case, the minimum daily yield of the drainage area having been based upon an annual rainfall (as recorded in rain-gauges) of 53 inches, a minimum monthly rainfall of 4*42 inches and a daily rainfall of *145 inches is required in order that this yield may be obtained without the provision of reservoir storage, assuming for the moment that the rate of loss by evaporation, etc. remains constant throughout the year. The total annual requirement of 53 inches of rainfall was ex- ceeded in 6 years out of the 7 under review ; hut of these 6 years, there were 3 in which for 6 months the monthly requirement of 4*42 inches was not obtained ; 2 years in which there was a shortage during 3 months ; and in the year with the maximum rainfall of 76*47 inches, the rainfall was less than 4 '42 636 Proceedings of Royal Society of Edinburgh. [sess. inches during 1 month. In the year with the minimum rainfall of 49 ‘62 inches there were no fewer than 8 months during which the rainfall did not reach 4*42 inches per mensem. If account he taken of the varying rate of evaporation, etc., which is at a maximum during summer, when there is also the least rainfall, and if the daily records he examined in place of the monthly records, the inequality of varying supply and regular demand is more marked, and the greater necessity shown for the provision of reservoir storage. (Issued separately May 10, 1905.) 1904-5.] Prof. Chrystal on Mathematical Theory of Seiches. 637 Some further Results in the Mathematical Theory of Seiches. By Professor Chrystal. (MS. received March 20. 1905. Read same date.) § 1. In the practical calculation of the periods and nodes of the lakes we have hitherto examined it has been found that the use of the Seiche Functions gives the best results. Indeed, as will appear from details presently to he submitted to the Society by Mr E. M. Wedderburn and myself, the agreement between theory and observation, so far as we have gone, is beyond what might reasonably have been expected. Also the phenomena of concave lakes, i.e. such as have no shallows or points of minimum depth, are easily deducihle from the formulae given in an abstract ( Proc . R.S.E. , vol. xxv. p. 328, 6th Oct. 1904) which I communicated to the Society on 18th July 1904. On the other hand, the theory of convex lakes is less easy of manipulation, chiefly owing to the difficulty in calculating the roots of the equations (£(c , 1 ) = 0 , 1) = 0. S 2. It seems, therefore, to he worth while to work out the theory for another class of cases, where all the solutions can be expressed by means of elementary transcendents. The normal or o- - v - curve in these cases is a simple quartic curve ; viz. : — o- = 7?-(l - v2/a2)2 for concave lakes; o- = h{\ + v2/a2)2 for convex lakes. § 3. My starting-point was a slightly generalised form of an equation used by Stokes in 1849, in his well-known paper on the Breaking of Railway Bridges (Collected Works, vol. ii. § 7, p. 186), viz. (fty (z - a)2(z - b )2-~ + cy = 0 , . . . ( 1 ) the general solution of which is y = A (z - a)m(z - b)n + B (z - a)n{z - b)m, . . ( 2 ) where m and n are the roots of the quadratic p2 - p + c/(a- b)2 = 0. (3) 638 Proceedings of Royal Society of Edinburgh. [sess. § 4. Since our object at present is general explanation, nothing will be lost by supposing the lake to be of uniform breadth and rectangular cross-section. In that case, using the notation of the abstract above referred to, we shall have h(x)£ — u = P sin nt ; du £ = " Tx’ • (*) (5) where £ and £ are the horizontal and vertical displacements of the seiche ; and h(x) = h(a 2 + x 2)2 is the depth at a distance x from the origin.* The differential equation for P is now

(!2) Hence the period of the v-nodal seiche is given by = 27 rlly J{gd(±vV/k* - 1)} ; . . (33) where When the lake is symmetrical, q= —p, r = s ; and (34) and (35) take the simpler forms 1904-5.] Prof. Chrystal on Mathematical Theory of Seiches. 643 § 10. For a truly convex lake h cannot vanish, and we have $2 _ // 4^-2/*2 - 1 \ _ 1 //1-A2/4t2\ Sj v V167T2/*a - 1/ 2 v \l-/£2/167rV’ • • • (36) which is the characteristic property of convex lakes. §11. The particular case where p= — q = a is of some interest. We then have k = ir and y = 2. Therefore %, = Kit J{gd(w- 1)}, = ttI/ J{gd(2v-l)(2v + l); . . (37) so that the periods are inversely proportional to the square roots of integers as in the case of concave parabolic lakes. For the present special case we have ^2/^1= x/(U/3.5) = J5/5 = *447 . . (38) If we put q= —p and r = d we return to the formula for a flat lake, as in § 8. § 12. There is no difficulty in calculating the position of the nodes of the various seiches by means of the formula (5). But, as numerical results are not in immediate view, the length of the calculations is too great to justify their insertion in the present paper. Comparison with the Period Formula of Du Boys. § 13. If we denote the period of the v-nodal seiche, as calculated by the formula of Du Boys,* by dTv , we have for a purely concave quartic lake fT„ = dx v f(gh)J qa2-x2 vaj(yh) log j a +p ia + q \ ( a -pi a - 2f Hence T dxv _ T ~ x V k va Jigh ) • (39) • (40) and, in particular, (41) “ Essai theorique sur les Seiches Arch. Geneve , xxv. 628, 1891. 644 Proceedings of Royal Society of Edinburgh. [suss. It follows that Du Boys’ rule should give for the uninodal period of a concave lake a value which is too large. This we have found to he the case in Loch Earn and Loch Treig, the two concave lakes whose periods we have as yet examined. It is perhaps worthy of note that, if we denote the ratio T2/Tx by r, then it follows from (24) and (41) that § 14. For the periods of a purely convex quartic lake the formula of Du Boys gives C&v 2 fp dx J q (ft + £ v J(gh)J qa2 + x va J(gh) k ya J (gh) tan a tan a (43) Hence and, in particular, k2 \ 4^vy; (44) *1 -A1-*)- ■ - ■ <"» Hence Du Boys’ formula gives too small a period for the uninodal seiche in a purely convex lake. If XJ%1 = r , we get, as in the last paragraph, ’d3* ■ T. : - y(i^) (46) § 1 5. The results of the last two paragraphs explain a matter that at first puzzled me considerably. The fact that, in order to get good results with Du Boys’ rule (Tj = 2 jdl/ J{gli) ) , we must integrate along the line of greatest depth, and pay no attention to the area or breadth of the section, makes it very difficult to believe that the formula can have any definite physical meaning. Indeed, from his point of view, the formula ought rather to be Tx = 2 j dljifijag) , where b is the surface breadth and a the area of a cross-section. This last formula, however, gives less satisfactory results where we have tried it than Du Boys’ own. 1904-5.] Prof. Chrystal on Mathematical Theory of Seiches. 645 The truth, however, is that the lakes, such as Ness and Geneva, where Du Boys’ rule gives the best results, have normal () = irl/ J(gh), whereas Tj = irlj J(2gh) by the theory I have developed. Hence dTj/Tj = = 1*414. Nevertheless, Du Boys’ rule is valuable as an empirical formula, easy of application, and giving in many cases a good first approximation, which is better the larger the number of nodes. It must also retain a historical interest as one of the first successful attempts to submit the very complicated phenomena of seiches to calculation. Anomalous Seiche in a Concave Quartic Lake. § 16. We now return to consider the solution of the differential equation (8) for which 0 = 0, and therefore c = a 2. The roots of the quadratic (10) are then equal; and the process of § (5) gives only one independent fundamental integral, viz. : — y = (a1 - x 2)“. The solution can, however, he completed by a well-known use of this particular integral. We thus get P = (a2-x2)‘ when x = p ; . . (51) and i = hf^)isinnt’ when*=g> • • (52> where A, and /x are not both zero. This solution is, in fact, £h(a2 - x 2)2 = ^ X(~ 0i)5 fel , 02 3 • < • 3 0») = (01 > 02 » • • • I 0i) (0i+ 1 > • • • 0«) + (01 , 02 > • • • ) 0<-l) fe+2 3 • • • 3 0*) , Smith therefrom deduces that and (01 3 02 5 • * • j 0i— 1 > 0t J 0i+l 5 • • • 3 0l) ~ (01 3 02 3 • • • 3 0i-l) j 0], 3 • • • 3 0i) + (01 ) • • • 5 0i-2) noting in regard to the former that the two numbers squared on the right are mutually prime. He then makes application to the theorem referred to in the title of his paper. 1904-5.] Dr Muir on the Theory of Continuants. 649 Studnicka, F. J. (1872, March). [Ueber eine besondere Art yon symmetralen Determinanten und deren Yerwendung in der Theorie der Kettenbriiche. Sitz- ungsb bohm. Ges. d. Wiss. (Prag), Jahrg. 1872, pp. 74-78.] The determinant referred to in the title is a1 - 1 . 1 a2 - 1 1 a3 an and the fact of its skewness is what Studnicka utilises in finding the ordinary expansion of it. Using the general theorem which gives an expression for any determinant in the form of an aggre- gate of terms each consisting of two parts, viz., (1) a product of diagonal elements, and (2) the cofactor of this product in the determinant, he notes that the said cofactors are either zero-axial skew determinants of odd order and therefore vanish, or are of even order and have sometimes the value 0 and sometimes the value 1. This last statement, though correct so far as it goes, is not in any way attempted to he justified. In illustration of it and of the inappositeness of the procedure We may take the case of the 4th order, viz. a1 - 1 1 a2 -1 1 % - 1 1 a4 for which would be obtained + a1a2\ . - 1 + ax a3 1 1 • + aYa4\ . - 1 | + a2 a3 1 . 1 + a2a4 5 . • + a3 a4\ . -1 ■ J 1 . 650 Proceedings of Royal Society of Edinburgh. [sess. . -1 . . -1 . + oq 1 . - 1 . 1 . + a2 . . -1 . 1 . + a3 1 + 1 -1 1 and thence ultimately oq a2 a3 a4 4- a1a2 + aY a4 + 6 F Ps + ^ Ps ~ UyiPi + Pq 1904-5.] Dr Muir on the Theory of Continuants. 651 and his problem is to obtain for any one of the said series an expression involving no others of the series except the first two, the multipliers uY , u2 , . ... y and the addends tt1 , 7t3 , . . . . He does not draw attention, as he might well have done, to the fact that if the 7r’s had been absent, the equations would have been of the familiar type which gives rise to continued fractions. Taking the case of seven equations he says the result of solution is 1 u 2 1 -1 . “a - 1 • 1 »4 - 1 . 1 u5 -1 . 1 u6 - 1 1 U>] uifii + A) -£l + *l ^3 and viewing the last column as the sum of the three columns u\Pi Po ~ Pi • 7r1 ^5 he thence readily obtains ui 1 P8~ - 1 u2 1 -1 . Uo - 1 1 - 1 . 1 1*5-1 . • . 1 -1 1 Uyj Pi U2 1 1 Uo ~ 1 . • 1 f*4 - l . . . 1 -1 1 UQ 1 ^1 Uh -1 . . M, - 1 . i «4 -i . . 1 2*5 - 1 1 u6 - 1 1 u7 652 Proceedings of Royal Society of Edinburgh. [sess. where on the right, as desired, no /T s occur except the first two.* Immediately on this he formulates the general result, distin- guishing, of course, the case of /3.2r from that of /32r+ 1- A more noteworthy fact, however, hut unnoticed by Casorati, is that a preferable form of result is obtainable by expressing the last determinant in terms of the 7r’s and their cofactors. Writing , w2 , . . . , ufj for the determinant which is the cofactor of , and not confining ourselves to the special case where 7r2 , 7r4 , 7r6 , . . . all vanish, we should then have /^8 “ ( U1 > Uc2 ? • ’ • > Utl) fil + {u2 j u3 > • • • J Ut) Po ~ (U3 5 ui j • • • 5 Ul)7rl (“4 > ' * * ’ (u1)TTb 77 & and, further, the consideration of two cases, viz., where the suffix of /3 is even and where it is odd, would not then be necessary. Bauer, G. (1872). [Yon einem Kettenbruche Euler’s und einem Theorem von Wallis. Abhandl. d. k. bayer. Acad. d. Wiss. (Munchen) II. Cl. xi. (2), pp. 99-116.] The continued fraction referred to is n m + , WtI ™+1+^r2 + and the theorem is that announced by Wallis in connection with the identity 32 2 +52 2 + * It may be well to note in passing that if 7t2 , 7r4 , 7r6 , . . . had occurred in the 3rd, 5th, 7th, ... of the set of equations, respectively, the solution would have been equally simple, the only difference then being that the first column of the last determinant would have had these quantities in the 2nd, 4th, 6th, . . . places. 1904-5.] Dr Muir on the Theory of Continuants. of Brouncker, viz., that the product of 653 2(a - 1 + 32 and a + 1 + is a2. The two things are linked together in the title because the main feature of the paper is the establishment of a relation between a continued fraction of Euler’s type and a continued fraction of the very different type which appears in Wallis’ theorem. If we denote by S the continued fraction n + a9 + -2 a3 + + n + ar_ i which includes Euler’s, and by T the fraction the relation in question is w(S + l) S + n ~ or as Bauer puts it, «(Pr+Qr) Pr + nQr ’ where Qr — a, 1 a. l3 1 - n - ar_x a, 654 Proceedings of Royal Society of Edinburgh. [sess. and Pr is n times the complementary minor of the element in the place (1,1) of Qr. In the latter form it is a relation between continued-fraction determinants, and as such claims our attention. By way of proof Bauer increases each row by all the rows following it, and thereafter diminishes each column except the last by the columns immediately preceding it, and thus obtains — n 1 ar + 1 — n — a l al 1 OLr -f- 1 -n- a2 a2 ar + 1 ar_! ar + 1 — —n — ar_x a,. and therefore = — TzDj + (n + cq) • | D2 — (ar + 1) * II | , if Dj be put for the determinant got by deleting the first row and first column of Qr , D2 for the determinant got by deleting the first two rows and first two columns, and II for ( n + a2) (w + a8) . . . (n + ar-1). Similarly, of course, P r = n -n 1 . . a,. + 1 — n — a2 a2 1 . ar + 1 a-r-i ar + 1 . . . — n — o.r_ i cir j and thus by altering the (1,1) element into a1 — (n + cq) there is obtained Pr = - n(n + a1)J)2; so that on the elimination first of Dx and then of D2 from these expressions for Qr and Pr there results Pr+Q,-(» + a1)| (l-»)Ds-(2-b1 + d + b , S + d-b i consequently d b1 + L b. 2 d S + d-b1 d + bi h2 + d + i2_h^ 2'S + d + \ 2 + bi + d + b -b + ^ *= - . — Z a + °2 °i + d + bz-b2+ 2 S + d-\ and therefore finally i t ft+_v | 2 °l + h 2 U2 d+b\ bi+ d + b"i-bs+ > 1 - + 1 + *L b 3 1 PEOC. EOY. SOC. EDIN. — VOL. XXV. 'd\* 9/ . 42 658 Proceedings of Royal Society of Edinburgh. [sess. Nachreiner, V. (1872, Dec.). [Beziehungen zwischen Determinanten und Kettenbrtichen. (Dissert.) 24 pp. Miinchen.] The starting-point here is Spottiswoode’s short statement given on p. 374 of the 51st volume of Crelle’s Journal. This having been quoted, pains are then taken to establish a so-called “generalisation,” viz. where - ur+l 7, ar-\- . °r+ ^ OL . 1 H + ar br+ 1 -1 ar+ 1 br+2 -1 ar+ 2 «»- 1 bn -1 an but unfortunately the left-hand side of the identity is not given as here, ar + being incorrectly put * instead of its reciprocal. ar+ 1 + • • • The identity <*i bi ■ c1 a2 b2 C2 a3 aY 1 V 1 a2 1 • ^2^2 a3 is next demonstrated, the procedure involving the division of the 2nd, 3rd, 4th, .... columns by bx , bYb2 , bfbfb*, respectively, and thereafter the multiplication of the corresponding rows by the same. This is used to deduce some variants of the above “generalisation,” and then the results thus far obtained are * This oversight runs through Sect. I., and should be corrected in the results marked (3), (4), (6), (7), (8). 1904-5.] Dr Muir on the Theory of Continuants. 659 employed in dealing with known properties of continued frac- tions. The third section opens with the identity «o 1 A a-. 1 % 1 1 A4 1 11 bn a„ 1 A0 • 2 2 • -2 an- 1 1 A n—l 1 bn an 1 K where A-^c^-— , and generally a °i a b2 K-a2 . A3=a3 61&3 A r—ar- br_1br_fr_i . . . . t)f)r_cfr_^ . . . . This is reached by a rather curious process, of which only the first two steps need be indicated.* They are, in the case of the fifth order, — «0 1 . . a0 1 \ a1 1 t— H to tP b2 a2 1 h «3 1 b3 az 1 at 1 «4 h ao 1 ... 11 “0 1 b± a1 1 . &4 a4 1 b2 a2 1 &2 a.2 1 1 1 1 a3 1 h Jh 1 a4 1 “A 63 &4 1 * The transformation is probably most readily effected by dividing the 2nd, 3rd, 4th, .... rows by \ , b2 , b-J) 3 , &2&4 , bxb 3&5 , &2&4&6 , > respectively, and multiplying the 3rd, 4th, 5th, .... columns by the same, the most instructive order of performing these operations being that in which each division is immediately followed by the corresponding multiplication. As the number of the divisions is necessarily one more than the number of multi- plications, the reason for the outside factor bn bn- 2 4 .... on the left mem- ber of the identity is also thus made apparent. 660 Proceedings of Royal Society of Edinburgh. [sess. The rest of the paper (pp. 13-24) is occupied mainly with con- tinued fractions, and contains nothing new in regard to the related determinants. Possibly the nearest approach to a fresh result is the use of the known identity 1 + %~ai + „ + to suggest (p. 16) that &0 - «i - 1 axaz a2 - as = axa2 . . . an_j j aQ -a1+a2 . i Gunther, S. (1873). [Darstellung der Naherungswerthe von Kettenbriichen in inde- pendenten Form, iv + 128 pp. Erlangen.] When we come to Gunther we have reached the first formal treatise on our subject. His booklet consists of three chapters, the second of which, with the title “ Darstellung der Zahler und Henner jedes Naherungsbruches in Determinanten-Form,” is that which mainly concerns us. The first chapter (pp. 1-30) is of the nature of a historical review of the various modes proposed for the calculation of convergents, and the third is professedly an applica- tion of the results of the second chapter to “ Analysis, Algebra, und Physik.” That portion (§ 6) of chapter i. which deals with the introduc- tion of determinants into the treatment of continued fractions attributes the first idea of the existence of the relation to Ramus (1855) ; notes that Heine (1859) discovered it independently; and nevertheless represents Heine as having used a result of Painvin’s. All this, of course, stood at the time * in need of serious modifica- tion, which unfortunately was not forthcoming, with the result * For Heine’s repudiation see his Handbuch der Kug elf unction, i. (1878), pp. 261-262. 1904-5.] Dr Muir on the Theory of Continuants. 661 that some of the inaccuracies continue to he propagated in text- books to the present day. In the second and third chapters neither pains nor space is spared to furnish an exposition of known results, with careful citation of the titles of all writings made use of, whether important or unimportant.* Throughout the two chapters, however, only one new and noteworthy property in regard to continued-fraction determinants is brought to light, the source of it being an identity attributed to Heilermann,f viz. x + i t)n , = x + bA - 4--^ bo Vv ^3^4 * + T+ *+h+h-x±li+bb_ where the number of b’s appearing on both sides is n. Clearly the numerator of each convergent on the left must have an intimate relation with the numerator of one of the convergents on the right, and this Gunther doubtless sought to discover. The result which he established is X 1 -1 b2 -1 X h ... -1 i .... as.-' b.2n_ - 1 1 x + b1 - \b 2 — 1 X + &2 + ^3 — ^3^4 . — 1 x + b4 + b5 where the order-number of the determinant on the right is half that of the determinant on the left. The demonstration occupies as many as five pages (pp. 70-74) ; probably the character of it will be sufficiently understood from seeing it applied without comment to the case where n = 2. The steps are — * The total number of footnote references in the book is 116. t Zeitschrift f. Math. u. Phys., v. (1860), pp. 362-363. 662 Proceedings of Royal Society of Edinburgh. [f H 1 a = (-)4-‘ X — 1 = x - 1 \ 1 - 1 . b2 x — 1 x b2 - 1 b2 x -1 \ 1 - 1 . 6X -1 1 ■ • i, 1 . . \ 1 • h • 1 x+ &x -1 = Z+&3 \ - i >1 -1 1 . *3 1 = - 1 ■c + b2 + b2 K bib2 &3&4 b2 = x + \ -1 x + \ - 1 X + &2 "t" ^3 ^2 - bYb2 x + b2 + bz bA • ^2^4 J x + bY - 1 — bf 2 # + b<2 + 63 &A 6364 &3&4 a; + - 1 - b1b2 x + b2 + b2 bA \\ : bfff)^ , -5- bihAh> b1b2 = | x+b1 - 1 | - bf 2 a; + b2 + b2 x + b-L - 1 ~\b2 x + b2 + b2 !. bA -5- Whh^ The case where the original determinant is of odd order is not referred to. Similarly, the continued fraction 1 + 1 — b1 + hi 1-^2 + 1904-5.] Dr Muir on the Theory of Continuants. suggests the finding (pp. 80, 81) of the results 663 i b, -ii \ ■ -i i-\ n+ 1 1, and 1-&! \ = “1 i — ^2 ^3 "I 1-&3 | n ) 1 — &]_ + ^1^2 — ^1^2 ^3 d* • • • • the latter of which may be compared with a result obtained by Nachreiner when under the same influence. In an appendix there appears as a “ personliche Mittheilung von Hrn Professor Dr Stem ” the statement that “ auch Sylvester sich der Kettenbruch-determinanten bedient hat.’5 Gunther, S. (1873, March). [Ueber die allgemeine Auflosung von Gleichungen durch Ketten- briiche. Math. Annalen , vii. pp. 262-268.] The starting-point here is a result of Furstenaii’s,* viz., that the smallest root of the equation xn + an_ 1 x W_1 + . . . . + a2x2 + axx + aQ = 0 is]P/R, where E, is the persymmetric determinant % an- 1 i Uq a j a 2 an_2 an_ ^ 1 . $0 cq an_ 3 ^n— 2 Q"n-\ 1 • • a0 an- 4 an- 3 ®n- 2 ®n-\ of infinite order, and P is the determinant got from it by altering a1 , a0 in the first column into — a0 , 0 . All that is of interest in * Furstenau, E. Darstellung der reellen Wurzeln algebraisclier Gleich- ungen durch Determinanten der Koefficienten. 35 pp., Marburg, 1860. A short but clear account of the essential parts of this pamphlet will be found in the Zeitschrift f. Math. u. Phys., vi. Liter. Zeitung, pp. 9-11. 664 Proceedings of Royal Society of Edinburgh. [sess. the paper from our present point of view is the fact that P and R, are changed so as to have the zero elements on the under side of the main diagonal matched by like elements in the corresponding places on the upper side, with a view to expressing the root of the equation in the form of an interminate continued fraction. The procedure need not be described at length ; it will be understood at once by applying it in the case of the determinant al a2 a3 1 CL~y $2 $3 % a1 a2 ao ? — -a course which also enables us to test the accuracy of the illus- trative example given later in the paper. In the first place, the element in the place (1, 4) is changed, the result being a2 a3 ai a2 af - ao a1 a3a2 - a a0 d^CL-^ -a. secondly, the element in the place (1, 3) is changed, the result being a2 a0 ai af CL^Ci^ aQ a2aY - a3a{ a2a0 Ct-^ CIqCL^ CSq . a3a2 ; and lastly, the element in the place (2, 4), with the result ax a2 a0 a1 af - a3aY a0 a2aY - a3a0 ( a2 2 - a3a^) (a3a2 — cq) - (a2ai ~ a3ao) (a2 ~ a%) a2aQ ( a2 2 — ay^) (a36q — a0) - a2afaf - a2) a3a2 ( a2 2 - a3oq) It is thus seen that if the equation for solution be the quartic a*4 + a3x3 + a2x2 + aYx + a0 = 0 , a convergent to the smallest root is, according to Piirstenau, 1904-5.] Dr Muir on the Theory of Continuants. 665 - C£0 d2 aB 1 ax a2 a3 . a* % al and therefore by the preceding for the two lengthiest elements, — a,Q a2 a1 af - a3aY a0 a2a1 - a3a0 U a2a0 Y and consequently O'O a2 Ob a0 ai a2% , a-L a2 and consequently that the continued fraction is I Cbo I a2 a3 1 an 1 ai ax a2 a3 I al a3 \ a0 ax a2 z.2(z2 - Zi)|l x2y3\, 2_>|1 x.2z3\; but there is an error in the first part as well. The four-line determinant, which is the denominator of the fraction sought above to be expressed as a continued fraction, is really transformable into I 1 VlZ2 I Z2~ Z1 I X0VlZ2 ! I xlz2 I X2~X1 I #1*2 I Va -Vi z2 - z1 I 1 X2Vz I I 1 X2ZZ I -r | yxz2 I {z2 - zx) {x2 - xx) and the four-line determinant, which is the numerator, is obtainable from this by putting 0 for x0, y0, z0 , — a substitution which only changes the first two elements of the first column into | yxz2 | , 0 . The continued fraction thus is I VlZ2 I I I v&2 1 (z2 ~ gj) 1 xoI/lz2 1 I X1Z2 I (x2 - Xx) I y^z2 1 (z2-zx) I 1 x2ys ; | 1 x2z3 | 2/2 - 2/i 668 Proceedings of Royal Society of Edinburgh. [sess. consisting of twenty-two very short paragraphs, almost every one of which contains a concisely stated property, accompanied, where necessary, by an indication of the mode of proof. ‘ Continuant ’ is formally defined as being a determinant which has the elements lying outside the principal diagonal and the two bordering minor diagonals each equal to zero, and which has the element of one of these minor diagonals each equal to negative unity. The continuant «i \ — 1 ^2 ^2 ~ 1 ai , a2> , A ax + a2 + • • • + a2 4- a1 + 2A + . . . rzf b2 b2 \ * * '^\a1 a2. ... a2 aj the deduction is made that XT ( bl b2 ’ ‘ \A, a1 , a2 • b2 \ \ a2 aY A ) K 2 2 a2 , . . . , a2 ax K b\ b2 b2 bY \ b2 b2 b1 A, alt a2,...,a2, ax, 2 A , a1 , a2,....a2, alf A K b2 bl bl b2 ax, a2 , . . . a2 , alt 2 A , a1 , a2, ... ,a2, aY Any other results given belong properly to the theory of con- tinued fractions.* * Some of these results and others are dealt with more fully in a pamphlet of 32 pages printed about the same time at the University Press in Glasgow, and entitled “ The Expression of a Quadratic Surd as a Continued Fraction.” 670 Proceedings of Royal Society of Edinburgh. [sess. Mum, Th. (1874, Feb.). [Further note on continuants. Proceedings Roy. Soc. Edinburgh , viii. pp. 380-382.] Proceeding from the fact, obtained in the previous paper, that the order of a continuant may be depressed if the first element of the main diagonal be unity, viz., that and that K - (bl + a^)(b2 + a2) b2 b3 . . . V 1 K ( b2 bi ■ L a2 aS . • - . J \ai + 01 a2 a3 rnb-L b2 . . . ) = ra-K ( bl ' ' i ct2 a3 . . • / \a^ a2 a3 . ma the author shows that f b1 ip1 + ai ) b% (b2 + a2) b3 \1 rtj a2 a3 and this is at once used to obtain as an equivalent for dYd2d3 .... • • • • the continued fraction given in Stern’s monograph of 1833 ( Grelle’s Journal , x. p. 267). The fact communicated by Cayley, but now known to be found in Nachreiner’s paper of 1872, viz., that any continuant is expres- sible by means of a simple continuant, is noted; likewise the identities K (aqar1 , a2x , a3x~l , a^x ,...)„ = K(a1 , a2 , . . . , uf) if n be even and = ar1 K (a1,a2, ... , an)if n be odd. Wolstenholme, J. (1874, May). [(Evaluation of a simple continuant whose diagonal is univarial) (Problem 4391). Educ. Times , xxvii. pp. 45-67 ; Math, from Educ. Times , xxi. pp. 83-85.] The problem is to prove that K(a,-1 a~\ . . . , a)n = sin m+ 1)0/ sin 0, if a = 2 cos 0. Two proofs are given, the more interesting depending on the fact that K n = - Kn_2, 1904-5.] Dr Muir on the Theory of Continuants. and the fact that 671 sin nO = a sin (n - 1)0 — sin {n — 2)0 ; in other words that Kn and sin nO satisfy the same difference- equation.* Gunther, S. (1874, Nov.). [Lehrbuch der Determinanten-Theorie fiir Studirende. viii + 236 pp. Erlangen.] In view of the attention which Gunther had previously given to the subject, it was natural that when he came to write his text-book on Determinants he should assign space to the consideration of the special form connected with continued fractions. We are not sur- prised, therefore, to find a whole chapter (Kap. vi.) with the head- ing “ Kettenbruchdeterminanten.” It extends to 31 pages, and is mainly a clear and detailed reproduction of his own and other previous work. In the paragraph dealing with the early history of the functions Sylvester is not now referred to. Gunther, S. (1875, Oct.). [Das independente Bildungsgesetz der Kettenbriiche. Denksehr. d. k. Akad. d. Wiss. in Wien : Math.-Nat. CL xxxvi. pp. 187-194. Of this paper the portion which is not introductory and semi- historical concerns the development of X — cq cq X — a9 a2 x X - <*n-l an— 1 X or A say, in a series arranged according to powers of x, this being considered * In connection herewith it may be noted that corresponding problems in the theory of continued fractions date much earlier : for example, problem No. 40 of Crelle’s Journal , ii. (1827), p. 193, a solution of which is given by Th, Clausen in a paper with the title “Die Function — — - a + a -f- a -(- . . . durch die Anzahl der a ausgedriickt,” published in Crelles Journal , iii. pp. 87-88. In our analysis of Ramus’ paper of 1856 the first of the two values there given for the continued fraction is that obtained by Clausen. 672 Proceedings of Poyal Society of .Edinburgh. [sess. of importance because of the author’s peculiar view that the con- tinued fraction h, CL i + ^ a2+ . K + - an is best expressed by means of two determinants of the form /A \/ <2^ The series obtained is, as might have been expected, that to which he would have been led by the use of the combinatorial “ rule ” more than once already referred to, and found fully enunciated in Stern (Crelle’s Journal , x. p. 6). It is indicated in substance by saying that the coefficient of x in A is the sum of all the products of p factors taken from a x2, a2’2, . . . . , , subject to the condition that no two factors with consecutive suffixes shall occur. Curiously enough, the finding of this sum is viewed as a problem with the following theorem for a solution : — “ Lehrsatz. — Der Coefficient der Potenz xn~2p in der Deter- minanten-Entwickelung hat den Wertli K = n — 2p + l r=p — 2 2, * a^+2-l ' al+2.2 * 1 * J a!+2r * M, k= 1 r— 0 unter M die (p — r — 1) fache Summe % = n - 2p + 2r + 3 s.2 = n- 2p + 2r + 3 + 2- 1 jr 2 Sj = k + 2r + 3 s.2 = k + 2 r + 3 + 2*1 sp_r_ 3 = ra-2p + 2r+3 + 2(p - r - 4) 2 ' Sp-r- 3 = « + 2?’ + 3 + 2 (p — r — 4 ) 1904-5. ] Dr Muir on the Theory of Continuants. 673 sp_r_ 2 = n- 2 p + 2r + 3 + 2 (p - r - 3) t = n Ya cj5-r-3 °p-r-2 jLmJ ' Z 2 ^2 “^2 a: Sp_r_2 = K+2r + 3 + 2(p-r verstanden.” 3) t = sp_r_ 2 + 2 As an example of the effectiveness of this formula, the case where n = 1 6, p = 7 is fully worked out. Diekmann, J. (1875). Guldberg, A. S. (1876, June). [Einleitung in die Lehre von den Determinanten und ihre Anwendung . . . viii + 88 pp. Essen.] [Determinanternes Teori. viii 4- 112 pp. Kristiania.] Of these two text-books, the first devotes a page and a half (pp. 23-24) to the relation between determinants and continued fractions ; the second indirectly touches on the subject by occupying a page (pp. 62-63) in showing that x V\ • -IIP* • . - 1 x p3 .-11 x + p1 p1 p2 x + p2 + Pz . Salmon, G. (1876, Sept.). [Lessons introductory to the Modern H-igher Algebra. Third Edition. xx + 318 pp. Dublin.] In this edition the sketch of the theory of determinants with which the book opens is extended to fifty pages, and half a page — a model of compact exposition — is assigned to the special form we are now considering. The name “ continuant ” is adopted. Muir, Th. (1877, Jan.). [A theorem in continuants. Philos. Magazine , (5), iii. pp. 137-138. The theorem in question is co + ape , o> + ape , )= co + ape , co + ape , + a? > ’ * * . aj Vq ) . . an + xj. PROC. ROY. SOC. ED1N. — VOL. XXV. 43 674 Proceedings of Royal Society of Edinburgh. [sess. The proof need not be reproduced, as it is included in another to be immediately given. The writer having become acquainted with Sylvester’s early papers on the subject, takes the opportunity to withdraw, in favour of the latter, the claim implied in the title of the paper Muir, Th. (1877, Feb.). [Extension of a theorem in continuants, with an important appli- cation. Philos. Magazine (5), iii. pp. 360-366.] The theorem referred to being, as we have seen, a relation (of equality) between two continuants, it was natural to expect the existence of a relation between the two continued fractions corresponding to those continuants. This expectation led to an acquaintance with Bauer’s paper of 1872, and thereafter to the extension here intimated. The extension for the case of the 5th order is of 1874. S + b- -c c2 r cyr bz r 1904-5.] Dr Muir on the Theory of Continuants. 675 the two sets of operations necessary to establish it being roWj + r row2 , row2 + r row3 , and col2 - r colj , col3 — r col2 , The case previously announced is that where Cj = c2 = c3 =....=== 1 and 8 - r = (3 . Bauer’s result regarding the product of two continued fractions having been noted in reviewing his paper, the generalisation of it here obtained may also be shortly alluded to. Denoting by F the continued fraction h(b2_a) | bJ,bt_a) fi + - a) P the author first shows, with the help of his theorem in continu- ants, that (3 + a 2 b2 + HhzT 1' P + b2-b3 + ^3(^3 a) /3 + b2-bi + a — [3 F — b1 # ’ Y+lf ; + K(K- a) P + bn - a thence, by merely changing the sign of a and the signs of all the b’s, that - a — (3 F + bT . 'F^~bf f3 ~ 5n + a and therefore by multiplication, that the product of the two con- tinued fractions on the left is equal to /F-a2 p - a 02{02 - a) 2 +v"aj -V', *,+/„+ - a) 4 676 Proceedings of Royal Society of Edinburgh. [sess. The paper concludes with two other curious theorems of similar character. * * The rather noteworthy theorem in continuants which is the basis of this striking result in continued fractions can be still more widely generalised as follows : — The continuant ! \ + A h ^ + i'A +5,Cl s2 7\ -3 + ^ A + S0C2 s3 r2 is unaltered in value by adding ?i + f!A + v> *4 *3 h + sAA+s4c4 TlCl y r2C2 " S1C1 5 r3C3 _ S2C2 J r4C4 ~ S3C3 > ~ S4C4 to the elements of the main diagonal, and changing the elements of the upper minor diagonal into Putting in this r2 , r2 , . . . = s1 , s2, . . .we have the identity - + A Cj — — + A + S2 — + A + SoC9 c3 —f + A + S3C3 c4 — - + A + s4 -4 Spl — — + A + SjCj -^-^2 % S2 cn — + A + s9c9 -3- + A + S3C3 ~b4 3 , s4 c _i + A + s4c4 i + A and specialising further by putting each of the s’s equal to s we come back to the theorem of the paper above reviewed. 1904-5.] Dr Muir on the Theory of Continuants. 677 Gunther, S. (1877, June). Baraniecki, M. A. (1878, Nov.). Mansion, P. (1878, June). [Lehrbuch der Determinantentheorie fur Studirende. 2te durchaus umgearbeitete .... Auflage. xii + 209 pp. Erlangen.] [Teorya Wyznacznikow (Determinantow) ; Kurs Universytecki. xxiv + 600 pp. Paris.] [Elemente der Theorie der Determinanten, mit vielen Uebungs- aufgaben. vi + 50 pp. Leipzig.*] Although continued-fraction determinants are dealt with in all of these text-books, there is nothing noteworthy in them to detain us. Gunther’s new matter refers more directly to the subject of the fractions than to the related determinants. Baraniecki gives six pages (pp. 447-453) of exposition, confining himself to what we have called “ simple ” continuants, and assigning them the first place (§ 108) in his chapter on skew determinants. Mansion, quite appropriately in view of the scope of his booklet, introduces (p. 18) two or three properties merely as exercises for the student. Muir, Th. (1878, Sept.). [On the word “ Continuant.” American Journ. of Math., i. pp. 344.] Sylvester having, without knowledge of the circumstances, complained of the introduction of the word “ continuant,” the introducer had to explain that the word had been proposed in ignorance of Sylvester’s papers of 1853, and that, as soon as this ignorance was removed, he had drawn pointed attention to those papers, persistently adhering, however, to the use of the new word for four reasons, which are shortly stated. In a note, Sylvester agrees that the second and third of the reasons afford “quite a sufficient justification for the use of the word in question.” * This the author reckoned as the second edition of his “Elements” published at Mons in 1875. 678 Proceedings of Royal Society of Edinburgh. [sess. Scott, R. F. (1878, Dec.). [On some symmetrical forms of determinants. Messenger of Math., viii. pp. 131-138.] The first of the forms referred to is c a b c a ... . b c .... which by means of its difference-equation is once more found to be equal to \c2 + Jc2 - kab J ~ \c2- Jc2 - 4 ab } 2“+1 7,2 - 4 ab Five special cases, more or less known, are mentioned, the last being that in which c2 = 4 ah and the value of the determinant n (ab)\n +1). Sylvester, J. J. (1879, March). [Notes on continuants. Messenger of Math., viii. pp. 187-189.] Here the main point of interest is the use of the old “ rule ” referred to in his paper of May 1853 to provide a proof that the number of terms in the simple continuant (a1 , a2 , . . . , an) is 1 + („_!) + (”-2)(”-3) + («-3)(n-*)(»-S) + . _ _ > 1-2 1*2*3 the various parts of this expression being shown to correspond with the various kinds of terms obtained in following the “rule,” viz., 1 term containing all the elements, n - 1 terms containing n - 2 elements, %(n - 2) (?i - 3) terms containing n - 4 elements, and so on. In stating some related results he uses the word “pro-con- tinuant ” for a determinant of the form a 1 1 b l ... . 1 c . . . . that is to say, for the continuant ( -i . -i . -i . , c , ,) 1904-5.] Dr Muir on the Theory of Continuants. 679 Scott, R. F. (1880, Feb.). Mansion, P. (1880, March). [A Treatise on the Theory of Determinants, and their applica- tions in analysis and geometry. xii + 251 pp. Cambridge.] [Elements de la theorie des determinants, avec de nombreux exercices. 3e edition. 64 pp. Mons.]. The title of one of Scott’s chapters (chap. xiii. pp. 169-179) is “Applications to the theory of continued fractions,” and it is accurately descriptive of the contents. As in Gunther’s text-book, both ascending and descending continued fractions are dealt with by means of determinants, the numerator of the last convergent to + b2 4- . . . + bn $2 ^71 viz., the determinant h -1 a2 -1 h a5 . . . K . an being actually spoken of as “ the continuant for an ascending fraction.” FTo new property of continuants is given. The continuant exercises in Mansion’s third edition occur on pp. 13, 21. LIST OF AUTHORS whose writings are herein dealt with. 1854. Smith . PAGE . 648 1875. Diekmann . page . 673 1872. Studni&ka . . 649 1876. Guldberg . 673 1872. Hattendorff . 650 1876. Salmon . 673 1872. Casorati . 650 1877. Muir . . 673 1872. Bauer . . 652 1877. Muir . . 674 1872. Nachreiner . 658 1877. Gunther . 677 1873. Gunther . 660 1878. Baraniecki . . 677 1873. Gunther . 663 1878. Mansion . 677 1873. Gunther . 666 1878. Muir . . 677 1874. Muir . . 667 1878. Scott . . 678 1874. Muir . . 670 1879. Sylvester . . 678 1874. Wo LSTEN HOLME . . 670 1880. Scott . . 679 1874. Gunther . 671 1880. Mansion . 679 1875. Gunther . 671 ( Issued separately May 17, 1905.) 680 Proceedings of Royal Society of Edinburgh. [sess. Suggestions towards a Theory of Electricity based on the Bubble Atom. By John Fraser, late Ordnance Survey, Edinburgh. Communicated by Dr W. Peddie. (MS. received December 12, 1904. Read May 15, 1905.) In a paper read before the Royal Society of Edinburgh, on 6th January 1902, and printed in its “ Proceedings,” I attempted to explain the constitution of matter by supposing the atoms of matter to be bubbles of ether. In order to fully understand what follows it is absolutely necessary to read that paper in its entirety, but for the benefit of those who may not have access to it, or who do not care to enter deeply into the subject, I give a short synopsis of it. 1. Well, then, the ether is supposed to consist of almost infinitesi- mally small, perfectly globular, smooth, hard and elastic particles of equal mass, filling the whole of space, and penetrating the pores of all bodies. It is endowed, according to Herschel, with a pressure of seventeen billion pounds to the square inch, and which pressure is suggested by me to be an effect of the radiations of the infinity of stars ; the waste heat of the universe, in fact. The ponderable atoms of matter are supposed to be, simply, bubbles of ether, the walls of which are only the thickness of one ethereal particle ; and inside of which there is perfect emptiness — an absolute vacuum in fact. The bubbles are kept' from collapse by supposing the particles * in the skin, or walls, to be in very rapid revolution round the vacuum, and so preventing the entrance of the in- crushing ether by “ centrifugal force.” The bubbles, or atoms, of different substances have different quantities of ether composing their skins or walls, and so accounting for the different atomic weights of different substances, blot only so, but the particles in the atoms of different substances have different velocities accord- ingly as they (the atoms) are large or small, and their walls dense or rare, or close or open-grained. Two of these bubbles would stick together by what may be called ethereal suction when brought so close together as to touch, * Particle = unit of ether. Atom or bubble = ordinary atom of matter. 1904-5.] Mr J. Fraser on Electricity based on Bubble Atom. 681 for, being perfect spheres, they could only touch at one point, and a certain area round the point of contact would be void of ether which would be all squeezed out by the act of bringing the atoms together. In this way the pressure, which was formerly supported by the particles in the screened space, would be now transferred to the particles at the point of contact of the bubbles, which, not being able to resist the increased pressure brought to bear on them, would be squeezed inwards, and the atoms flattened at these points ; in this way they would adhere together by what would amount to veritable suction, and form molecules. These molecules would vibrate in and out concertina-fashion ; and at each vibration outwards sending a pulse, or wave, of ether out into space, thus accounting for radiation of heat. The larger the surface area of these bubbles the greater the hold would they have of one another, and chemical afflnity is accounted for by the fact that small atoms would find a better hold on large ones than on those of their own size, and so would, whenever they got the opportunity, cling to them in preference.* I must refer the reader to the paper itself for the way in which gravity is accounted for, as to give any intelligible account of it here would be too long, and it has no particular bearing on the subject of the present paper. 2. I must admit that my very partial attempt to account for, or rather guess at, the nature of conduction was a failure in that paper, but I hope to be more successful in my present one. I ought to have dwelt a little longer in the paper referred to on the beautiful, almost miraculous, way in which the bubble atom makes its way through the ether — how the particles crowd together at the points where the pressure is greatest, and where it is least there will a fewer number of them be found ; the very act of pressure bringing them together, and the want of it causing them to separate farther apart. It seems as if they were furnished with a species of volition, for as soon as any part of their dominion is threatened with violence there they rush at once to protect it. I cannot help thinking of it and wondering, and yet it is all so mechanical. * Readers will gather from the present paper that I have altered my mind on this subject. 682 Proceedings of Royal Society of Edinburgh. [sess. 3. Before entering on the subject of electricity I should like to give what seems to me to be the explanation of “ Latent Heat,” which I very strangely omitted to consider in my former paper ; indeed the subject never entered my mind, although it was quite familiar to me, until thinking out the subject of my present paper, with which it is closely allied. Well, then, let us see what ac- count does the bubble atom give of “Latent Heat.” It is found that when a quantity of ice is melting the heat applied to this purpose disappears. The ice rises in temperature to the melting point and remains steadily at that point, no matter the quantity of heat applied, till the whole of it is melted. Afterwards the temperature of the resulting water rises, as the heat is continued, till it reaches boiling point, at which point it remains stationary no matter the quantity of applied heat, till it is all evaporated, Now what became of all the heat applied and absorbed during the times the thermometer was stationary ? It is said to have gone to change the state of aggregation of the molecules ; which is, no doubt, true, but after all this is only a hazy idea, and if the theory we are considering can give a clearer it ought to be a point in its favour. Well, then, according to this theory when two atoms, or bubbles, come together the ether in the medium within a certain area all round the point of contact of the globular atoms gets squeezed out, because the space inside of this area is too narrow to admit of the existence of an ethereal particle in it, as I have already said : hence the flattening of the atoms at their points of contact, also mentioned. The bubbles in fact partially collapse, and the more so the more they radiate out heat, drawing closer and closer together as they cool, their particles losing energy of position as they give out actual energy, the amount of flattening of their points of contact and the consequent amount of grip upon one another increasing hand in hand, till they have attained the temperature of their surroundings. Now this is what I should like to draw the attention of my readers to especially : — the loss of position by the particles of the atoms as heat is given out , i.e. the increase of collapse of the bubbles. Each particle, when originally elevated to the position where, along with its fellows, it helped to enclose a vacuous space, must have absorbed a quantity of energy proportional to the space enclosed and inversely as the number in 1904-5.] Mr J. Fraser on Electricity based on Bubble Atom. 683 the atom, and which energy was consumed in pushing the ether back so as to leave clear such a space. Inversely, then, when this space is being encroached upon the absorbed energy is given out again. It ought to be clear now what becomes of the heat absorbed by the melting ice ; it is expended in repairing the partial collapse of the molecules at their points of contact and rounding them out again till they separate. The inner working of it will be some- thing like this : at each inward vibration of the molecules the particles will be crowded close together and moving with their greatest velocity, some of their energy will be spent, in the sub- sequent outward rebound, in driving the ether back in a pulse or wave, and some in rounding out the collapsed part of the atoms. The heat which disappears does the latter part of the work, and this heat continues to disappear until the molecules part company, till, in fact, their points of contact are so rounded off that they have no longer a sufficient hold upon one another to retain them in the solid state. From this to the boiling point the applied heat is used up in increasing the motion of the molecules, causing them to take up more space, and, since increase of molecular motion is increase of temperature, manifesting an increased temperature. The heat which becomes “ latent ” during evaporation I have little new to say about ; no doubt part of it is used up in driving back the atmosphere, but a goodly proportion will be used up in complet- ing the rounding off of the points of contact of the molecules, and also in separating the constituent atoms of each molecule a greater distance apart, in fact rounding off their points of contact, and which process, if the heat were sufficiently great, would result in their dis- sociation, and the atoms would become complete spheres once again. 4. I now proceed to introduce my theory of electricity based on the constitution of the bubble atom. This atom the more it is examined the more marvellous will it appear. In concluding my former paper I expressed my confidence that within the folds of the theory with which it dealt lay hidden the mystery of electricity, and I hope my confidence in it may be found to be justified, for although I even now know only the facts connected with the most prominent points of the science, yet I hope to be able to account for those facts in a very fair way. I have not had time to read up and fix in my memory the technicalities of the 684 Proceedings of Royal Society of Edinburgh. [sess. science, a thing which I find more and more difficult as I grow older, but the more prominent points in it are easily grasped and retained. It is found that when two different substances are rubbed together they are said to be in a state of electrification. I need not describe this state, as all my readers doubtless know it, but shall proceed to explain it. What, then, should happen to bodies composed of atoms with a constitution such as the bubble atom when such bodies, if of different substances, are rubbed together % The constituent particles of the atoms of different substances having different velocities must, when they are pressed and rubbed together, transfer some of their speed from the one substance to the other. The substance with the slowest moving particles gains speed for its particles, and that with the quickest moving particles loses speed for them. What the one gains the other loses, the loss of the one being exactly equal to the gain of the other. This I take to be positive and negative electricity, that body being positively electrified whose particles have gained speed, and that whose particles have lost speed being negatively electrified.* 5. The Neutral State. The atoms of every element have their own peculiar con- stitution ; they may be very massive with a comparatively small and dense surface, or they may be of small mass with a com- paratively large and open-grained surface ; or they may be massive with a large surface, or of little mass with a small one, or in any state between these. All that is essential is that their constituent particles should have more or less motion according as their surfaces are large or small, rare or dense, as explained already. How the atoms with the swiftest moving particles will, other things being equal, create a greater disturbance in the ether by the particles’ greater centrifugal tendencies, sending it, or tending * Two substances of the same kind rubbed together may be electrified if in different physical states. For instance, rough and smooth glass. The ex- planation is, that in rough glass a greater proportion of the surface of each atom is free from its fellows, and therefore contains a greater quantity of motion than that of those of the smooth glass ; the latter is therefore posi- tively electrified, and the former negatively so. 1904-5.] Mr J. Fraser on Electricity based on Bubble Atom. 685 to send it, out from them in a continuous spray or rain in every direction. This may he realised by supposing a drum of a cage- like structure to he revolving very fast under a shower of hail. The hail striking against the bars of the cage-work would be scattered more and more violently the quicker the drum revolved ; and, indeed, if it revolved very fast it would be dangerous to eyes and face to stand near such a piece of machinery. I do not mean to suggest that the ether would be scattered in the same way as the hail, because I believe the ether to be too densely packed for any such scattering, but there would be stresses set up in it radiating outwards from the atoms in every direction. These stresses I take to be the “Lines of Force” in electricity. When the stresses at any point were equal in every direction there would be equilibrium, and the condition of things at that point would be in what is known as the “ Neutral State.” 6. Now the larger the atoms the greater the disturbance their particles would cause in the ether, or the greater their electricity , as I propose to call it after this. In fact, this disturbance, or their electricity, would, other things being equal, be precisely propor- tional to the square and their total energy to the cube of their radii. I think this may be readily seen when we consider that the work required to produce a vacuum in the ether, or the atmos- phere, is proportional to the cubical space out of which the ether or the atmosphere has been emptied ; and after the vacuum has been produced to keep it intact, a force at least equal to that which produced it must be continually exerted. In the case of our atoms, to double the radius of any one of them the speed of its particles would have to be increased in such a way that their total energy was increased by an amount equal to the work done upon the sur- rounding ether in clearing it out from the additional space now occupied by the atom. Thus the total energy of the particles of the atom is increased in proportion to the change of bulk, while at the same time the surrounding medium is further energised by an equal amount. Thus total energy is proportional to change of bulk and electrification to change of surface area. It would be as though the motion, or energy, which existed in the ether which had previously occupied the interior of the atom was now wholly located on the exterior, or surface. (It 686 Proceedings of Royal Society of Edinburgh. [sess. must be noted that the electricity is proportional to surface area irrespective of its density or close-grainedness, for though the particles of the densest kind of atoms have each of them less electricity, they will make up for that by their greater number.) The atoms, in fact, concentrate the energy, or motion, existing in the ether ; for that quantity of energy which existed in a space proportional to the cube of their radii is, by their peculiar con- stitution, concentrated into a space proportional to the square of their radii only, viz., their surfaces. A rough analogy will perhaps help here. Suppose an air-tight vessel full of air at atmospheric pressure to contain a number of empty bladders with a tube attached to each, accessible from the outside of the vessel. If, through these tubes, the bladders were blown up full of air, it is easy to see that the pressure in the vessel would be increased, and the more the greater the number of bladders. In much the same way, then, would the pressure in the ether be increased by the creation of these atoms, or by an increase in their size. 7. It will now, very naturally, be asked how can atoms such as these, with their various potentialities for increasing the ethereal pressure, be neutral at any time? In other words, how can the pressure in every direction be equal with atoms like these flying about? Or yet again, how is it possible to have the same electrical actions produced in the ether by atoms of different volumes ? The answer to this is not the least curious property of these atoms. Indeed, as I said already, the more their constitu- tion is studied the more marvellous will they appear. To answer the above shortly, I may say that the greater their quantity of electricity, or their potentiality for increasing the ethereal pressure, the greater proportion of it, through their collisions and vibrations, is converted into heat. Let me draw the reader’s attention again to what, according to this theory, a wave of heat is. When two atoms come together the independent particle movements which resist the in-crushing power of the ether, and which act within a certain area around the point of contact of the atoms, are, as it were, throttled ; the point of contact cannot resist the increased pressure brought to bear on it ; the atoms are therefore flattened in that locality ; the flattening produces a condensation of the particles, and when it has reached a certain point, over-balancing 1904-5.] Mr J. Fraser on Electricity based on Bubble Atom. 687 the pressure, a rebound and recovery of form takes place, the atoms at the same time sending out into space a volley of small shot, so to speak, instead of the scattered firing which would otherwise take place if they did not come into contact. The separate in- dependent particle movements of the area in contact during the time of contact are concentrated into one simultaneous movement of them all, and this is a wrave of heat. 8. I do not know of anything which better illustrates the difference between heat-waves and electricity than to compare heat-waves to volleys, and electricity to scattered firing. The particles of the atoms, when the atoms are not in contact, are each firing away their own small shot, independently of their neigh- bours, but wrhen the atoms are in the act of separation, after being in contact, the result of the cessation of this scattered firing during the time of contact is one simultaneous volley from all the particles which had been in contact, and which had been prevented from firing off their small shot during this time. This volley, then, constitutes a wave of heat, and what I mean to assert is that the greater the quantity of electricity possessed by any kind, or species, of atom the greater will be the quantity of it ultimately transformed into heat (see par. 9) by that species, both by their collisions and as a result of the vibrations of their molecules. If this be correct, then the quantity of electricity radiated by all kinds of atoms in the neutral state is the same, but a very different quantity of heat would be radiated by them ; and as waves of heat do not alter the average pressure of the ether (each condensation being followed by an equal dilatation), the result would be a state of equilibrium. 9. I said above that “the greater the quantity of electricity possessed by any kind of atom the greater will be the quantity of it ultimately transformed into heat.” I say ultimately , because it does not follow that because one species of atom has a greater quantity of electricity than another that therefore this excess is immediately transformed into heat. For the radiation of heat by any kind of atom or molecule will depend — everything else being the same — upon the elasticity of the atoms. Hence the highly elastic kind will take a comparatively long time in radiating their heat away, not only because they possess a greater share of 688 Proceedings of Royal Society of Edinburgh. [sess. potential heat — proportional to cubical space for their particles to get squeezed into — but they part with it more slowly because of their greater resistance to compression ; in other wrords, because of their great elasticity.* In fact, there is nothing to prevent us from imagining an atom whose elasticity is so great that it would take a practical eternity of time for its molecules to radiate their heat away. How, then, can the highly elastic kind he neutral ? To answer this, let us imagine an infinitely elastic atom. Mole- cules constituted of such atoms could vibrate for ever and yet send no heat-wave away into space. This seems a paradox, but it is easily answered. At each inward phase of the vibrations, pressure, electricity, or energy, whatever you like to call it, would be withdrawn from the ether in the immediate neighbourhood of the molecules — it is this energy which presses the atoms together — and upon each outward phase exactly the same quantity would be restored, and would proceed no farther than the locality from which it was withdrawn. As an illustration, suppose a perfectly elastic ball to be dropped from a height, in an air vacuum, on to a perfectly elastic pavement — it would rebound to the height from which it fell ; to fall again, and rebound, and so on con- tinually. On falling it would gain its energy of motion from gravity (a force the genesis of which I have attempted to explain in a former paper), and upon rising it would restore to the medium the energy it abstracted in falling. In this illustration none of the energy would be transformed into heat any more than in the case of our hypothetical perfectly elastic molecules, but in the latter case note what would be happening — at each outward phase energy would be added to the ether, and which at each inward phase would be withdrawn, these opposite actions alternating so rapidly that the average state of the medium would be normal, or neutral. In fact we might say that at one moment the state of the ether would be positive, the next moment equally negative, * “In the usual notation of dynamics, assuming simple harmonic motion, we have x= - n2x. Therefore, when the vibration frequency is increased n times, the displacement produced by the same force becomes l/?i2 of its former value ; and so, per vibration, under the action of the same force, the energy involved becomes 1/ri2 of its former value. But the number of vibrations per unit time is increased n times, so that the rate of emission of energy, under the usual law of damped vibrations, would become ljnth of the former rate.” 1904-5.] Mr J. Fraser on Electricity based on Bubble Atom. 689 so that the average state would be neutral. This property of atoms I propose to call elastic absorption. If the particles of the vibrating atoms lost position, or potential energy, so much would he sent away into space as a wave of heat, for the ether would rush in and occupy the space vacated by the crushed-in particles, and so would be energised to this extent, the heat sent into space re- presenting the potential energy lost, the remainder of the vibration restoring the pressure withdrawn during the inward phase. Thus no matter what the electricity of the atoms, provided their vibra- tions were proportionate to it, they would always be neutral. (The clause in italics will be understood later on.) On the other hand, if the temperature of an electrified body were kept constant, and it were perfectly insulated in an air vacuum, it seems to me that it ought to retain its electrification indefinitely. For only by a quickening of its rate or amplitude of vibration could it radiate away as heat any surplus electricity it might possess, or retain as electricity from heat supplied any deficiency of the same. 10. And now, can we not gain a glimpse of the reason why gases liquefy at such enormously different temperatures? Some of the metals, for instance, liquefy at almost the highest tempera- ture attainable by artificial means, whilst the so-called “ permanent gases ” do not liquefy till almost the zero temperature is reached. It appears to me that the solution of the enigma lies in the elasticity possessed by the atoms, those substances possessing the greatest atomic elasticity (and, it might be, the smallest mass) being the last to liquefy.* It appears that when gases are near their point of liquefaction equal volumes of them no longer contain the same number of molecules as other gases at the same temperature which are further removed from this point. They cannot, owing to their lack of elasticity, keep the same space clear for themselves , and so are compelled by the external pressure to crowd closer and closer together till they liquefy. The metals, owing to their generally great mass, possess a goodly quantity of electricity * “ If fj. represent the mass of a particle in an atom of radius r, while there are n such particles per unit area of the surface, the external pressure p is balanced when nuv2=pr. That is when Mv2 — SpY, where M is the mass and Y the volume of the atom.” PROC. ROY. SOC. EDIN. — VOL. XXV. 44 690 Proceedings of Royal Society of Edinburgh. [sess. even after they solidify, though they are greatly deficient in elasticity,* hut the permanent gases, oxygen, etc., retain their elasticity till almost all their electricity is gone, and that is almost to the zero of temperature. It is through this retention of their elasticity that I account for their maintaining the gaseous form through such a great range of temperature. For fear of being misunderstood, let us suppose two species of atoms of the same volume, hut one ten times the weight of the other. The lightest would have ten times the elasticity, for its particles would have ^/lO times the velocity of those of the other, and supposing them to start as perfect gases, at a very high tem- perature, the heavier would have cooled down far quicker than the other, for it would be the first to liquefy and solidify, and owing to the number of connections between the molecules in the liquid or solid state, emission of latent heat would proceed at a far more rapid rate. But this must be noted, that when the lighter had cooled down to the same temperature as the other (say to the zero temperature), it would have radiated precisely the same quantity of heat, for they both started with the same quantity of latent heat , and when they had passed through the same range of tem- perature they must have radiated the same quantity of heat away. 11. Contact Electricity. It follows from the foregoing that at the surface of contact of a gas with a liquid, or solid, the state of electrification cannot be the same in both, for the gaseous molecules at such surfaces not meeting with moleculeshaving the same motion as they have them- selves, do not get the same amount of their electricity converted into heat as if they encountered molecules of their own kind ; they are therefore left with an altered amount of electricity at such surfaces, and which change in amount is known in the Science of Electricity as “contact electrification,” giving rise to “difference of * Elasticity. — I am inclined to think that there must be two conditions of elasticity, viz. , the elasticity of great particle-speed and small density, and the elasticity of great particle-density, or close-grainedness, as I have called it, and slow speed. I should say that the permanent gases possess the former and the metals the latter, other substances ranging between these. The former can be overcome by great pressure, but the latter only slightly, or not at all. 1904-5.] Mr J. Fraser on Electricity based on Babble Atom. 691 potential.” The same is true of the surface of contact of a liquid with a solid, and also, hut in a much less degree, of two dissimilar solids. This fact will be put to its proper use, later on, when we come to consider current electricity. 12. By the kinetic theory of gases the molecules of all perfect gases at the same temperature and pressure occupy equal spaces ; hut the theory takes no account of the actual sizes of the molecules themselves, as their sizes are considered to he infini- tesimal compared with the space through which they move. The theory is that they all have the same average free path. If their sizes were doubled, say, it would, no doubt, shorten their free paths to some small extent, hut this would immediately give rise to an increase in the pressure. By an increase in their sizes there would he an increase in their electricity, but then the increase of electricity would he neutralised both by their heat and elastic absorption (see par. 9), and the state of equilibrium in the medium would be undisturbed. But now, suppose we had a means of practically increasing their sizes without at the same time increasing their heat vibrations, or lengthening their free paths ; it will be immediately apparent that in that case the state of equilibrium in the medium would be instantly upset. There would be a greater radiation of electricity from the locality occupied by the enlarged molecules than from the surrounding parts, because there was not a sufficiency of vibratory motion to convert the surplus electricity to heat or appearing in the phenomenon of elastic absorption. Or, again, if we had a means of decreasing their sizes without taking away their heat-motion, there would be less radiation of electricity from the locality occupied by the collapsed molecules than from the surrounding parts, because a greater quantity of it would be converted into heat or elastic absorption than when in the neutral state. I will now proceed to show how the foregoing principles can be applied to the explanation of electrical phenomena. 13. Electricity as it is Known. We have hitherto been considering electricity in its neutral state, but we will now consider it in its active or phenomenal state. In the former state all bodies are electrified alike, but 692 Proceedings of Royal Society of Edinburgh. [sess. in the latter some are more, and some less, electrified, and it is the difference of action of these differently electrified bodies on the medium and of the medium on the bodies which causes all the phenomena of electricity. We have seen that when two different substances are rubbed and pressed together the one becomes positively and the other negatively electrified — that is to say, that the constituent particles of the positively electrified body have gained speed, and those of the negatively electrified body have lost an equal amount, through their contact with one another. By the increase of speed thus gained the atoms and molecules of the positively electrified body would become more separated from one another by their recovery from collapse , as though by an increase of heat, and this without a commensurate increase in their heat or state of vibration. They would thus electrify the space in which they moved more strongly, and without a commensurate increase in their heat vibrations, etc., to nullify the electrification. On the other hand, the atoms and molecules of the negatively electrified body, by the speed lost by their particles, would cling more closely together through their greater collapse ; in this state they would electrify their spaces less strongly through having practically the same heat and elastic absorption and less electricity. The one would gain electricity without a gain in heat, or elastic absorption, and the other would lose electricity without a loss of either of the others.* They would have the same space to electrify — the one with more electricity to do it with and the other with less to do it with. The state of equilibrium existing in the medium would be thus upset, the positive body energising it more, and the negative body energising it less, than the surrounding neutral bodies. * It is found that electrified bodies when heated lose their charges, but that negative electrification is more readily discharged than positive. This is in accordance with the present theory, for negative electrification is a lack of electricity which heat can readily supply — that is to say, that some of the latter becomes transformed into the former till the neutral state is reached. In the case of positive electricity the heated body would retain its charge for some time, till by the increase of the vibrations the whole of it would be transformed into heat. In flames a chemical change is going on where both positive and negative electricity are present and being converted by their great affinity for one another into heat. 1904-5.] Mr J. Fraser on Electricity based on Bubble Atom. 693 14. We are now in a state to account for the attractions and repulsions existing between electrified and neutral bodies. But first induction must be accounted for. Induction, then, is the effect of the increase or diminution of ethereal pressure on the atoms of bodies (see par. 5). By increase of pressure in the ether the atoms contract or tend to contract in size, the orbits of their particles are more confined by the increased pressure, and if the body be a good conductor, and the inducing body is positive, a good deal of the motion of the particles escapes, as it were, to where the pressure is least, i.e. to the further end of the body under induction, and the end nearest the inducing body becomes negative, through its loss of motion, while the end farthest away becomes positive through increase of motion received from the end under induction. On the other hand, if the inducing body be negative, the atoms of the body under induction expand owing to the decrease in the pressure, and if it is a good conductor a good deal of the motion of the particles at the far end of the body flies to the end where pressure is least, and the end nearest the induc- ing body becomes positive, while the far end becomes negative. Good conduction or bad conduction (of which more hereafter) depends on the facility or difficulty with which an increase of motion in the particles of the atoms of different substances can be transferred from one end of the conducting body tp the other. 15. Let us now see how repulsion between two positively electrified bodies is brought about. The space between them is more strongly energised than that outside, hence there would be repulsion equivalent to the difference ; but if the electrified bodies are good conductors, they would, by mutual induction, drive, as it were, the greater part of the electricity to the sides farthest from one another, the sides next each other becoming more neutral ; but still there would be repulsion, though not so strongly as before. If the positive bodies happened to be bad conductors there would be less collapse of their atoms under their mutual induction, owing to the difficulty of the escape of their electricity, or motion, to the sides farthest away from one another, consequently there would be proportionately more electricity, or pressure, in the space between, and repulsion would be stronger than between good conductors. 694 Proceedings of Royal Society of Edinburgh. [sess. 16. Let us now see how repulsion between two negative bodies can be accounted for. In the space between the two bodies the ether would be less energised owing to their small radiation of electricity into this space ; it would become more densely packed, therefore, in this space, and motion or energy from the outside penetrating quickly into it, and energising the densely packed ether, sufficiently accounts for their separation. 17. Next, let us enquire how “Attraction” is brought about between positive and negative bodies. In the space between, the ether would he under a state of dilatation by the strong action of the positive radiations on the feeble negative radiations, sweeping, or tending to sweep, them entirely out of the field into the back- ground. If this state of matters could go on unchecked, a near approach to a vacuum would he formed ; hut it cannot go on un- checked, for the greater the dilatation the greater the resistance to it by the densely packed ether in the background, therefore there would be a strong tendency for the bodies to rush together. 18. We will deal next with the attraction between a positively electrified body and a neutral. The attraction between a positive and a neutral is brought about in precisely the same way as between a positive and a negative, only it is not so powerful, for the neutral may be looked upon, relatively to the positive, as a weak negative, i.e. its radiations are more powerful than those of a negative, therefore the action of those of the positive upon them is not so effective in driving them out of the field. If, though, the neutral is a good conductor, the attraction between them will approximate to that between positive and negative, for the side of the neutral next the positive becomes negative by induction, therefore there will he, and for the same reason, the same tendency to approach as between positive and negative, only, as said before, not so strong. If the neutral body were a had conductor, less motion would he pressed out of the side next the positive, i.e. it would become less negative, with the result that there would be less “ attraction.” 19. And now to examine the action between a negatively electrified body and a neutral. This action is also the same in kind as that between a positive and a negative. We may regard the neutral, relatively to the negative, as a weak positive, and acting 1904 — 5.] Mr J. Fraser on Electricity based on Bubble Atom. 695 upon the negative as a positive would do, only not so power- fully. If the neutral body were a good conductor, the attraction between them would approximate to that between a positive and negative, for the side next the negative would become positive by the induction of the latter, and they would “ attract ” one another as positive and negative. If the neutral were a bad conductor it would become less positive at the near end, consequently there would be less “ attraction.” The foregoing principles will be further illustrated as we advance. *20. In electrostatics the electricity always resides on the surface of bodies. Why1? Because confined motion always flies to the region of least restraint. Confined steam tries to make its way outwards. So the new motion of positive electricity flies to the surface of bodies, because there the atoms have a greater power of expansion, and it is there that the lack of motion constituting negative electricity would be first felt, i.e. the atoms at the surface would be the first to suffer, since a greater quantity of electricity, or motion, alivays resides at the surface, owing to the atoms there only being half in contact with their fellows, their upper surface being free. 21. The Action of Points on Electricity. From the foregoing it will be readily seen why electricity resides more on pointed surfaces, and on corners, than on plane surfaces. Electricity, like every other confined motion, tends to fly to the weakest spot, and break out there ; so, in the static state, it resides almost entirely on the surface atoms of bodies, because they, at their upper surfaces, offer least resistance to expansion, and, in the case of negative electricity, will be the first to lose their motion, since they contain most of it. Well, then, when we try to realise what a pointed or conical surface must be, we must see that in such a surface a greater proportion of the free surface of each atom must be exposed. If the reader resides in Edinburgh let him go to the Castle and look at the pyramids of cannon balls which he will see there at the first battery to which he will come, and he will see my meaning. He will see that a far larger proportion of the surface of each 696 Proceedings of Royal Society of Edinburgh. [sess. ball is exposed to view in this form than if they were built up in the form of a cube or cylinder. Pointed bodies, then, must be looked upon as pyramids or cones of atoms ; and if the point be as sharp as possible, it will consist of but one molecule, or, possibly, atom, if the molecule to which it belongs happens to be pointing in the right direction. 22. The Earth a Reservoir of Electricity. I think the reason for this will be readily seen. If any body be at a higher potential than the earth, and at the same time connected with it by a good conductor, the excess of motion in the body will escape into the earth, just for the same reason that steam would escape out of a boiler if a door were opened to it, or that water at a high level, or indeed anything else, con- stantly seeks to reach a lower. If the body be at a lower potential than the earth, or negatively charged, and connected with it by a good conductor, then motion would escape out of the earth to the body so as to bring it up to the same level as the earth, or to the neutral state — the earth in the above case illustrating the boiler. Positively charged bodies may be likened to water at a high level, the great neutral earth to the ocean, and negatively charged bodies to pits, or mines, under sea level. If the water from the high level were permitted to run into the pits it would fill them up to sea level — analogous to connecting two equally but oppositely charged bodies together. If the water from the high level Were permitted to fall into the sea — this would be analogous to connecting a positively charged body to earth, and if water from the sea were permitted to run into the pits it would be analogous to connecting a negative to earth. I think I need not elaborate this point any further, it seems perfectly obvious. 23. By a proper application of the foregoing principles the results of all the experiments in electrostatics can be explained. For instance, take that of an insulated conducting cylinder under the influence of an electrified body. If the body be negative, the end of the cylinder under induction will become positive and the other end negative, because there is less pressure on the end 1904—5.] Mr J. Fraser on Electricity based on Bubble Atom. 697 under induction, owing to the negative body’s lack of electricity. The greater pressure on the other end squeezes the motion to that end where it has freer play, and if the far end be now momentarily connected to earth, its loss of motion will be supplied from the earth’s great reservoir, making that end neutral (or even positive, if it he very near the inducing body) ; and if, now, the electrified body he removed, the whole cylinder will be found to be positively charged, because, upon equalisation of pressure over the whole cylinder, the excess of motion at the end which had been under induction is now spread equally over the whole cylinder. If, now, the cylinder he connected to earth, the excess of motion escapes to the earth from whence it came. We will now suppose the electrified body to he positive. In that case the end of the cylinder under induction will he under greater pressure than the other, squeezing the greater part of the motion to the far end — the end under induction becoming negative and the far end positive. This will be analogous to the case of a person stepping on the end of a highly elastic tube full of air or water. The air, or the water, would be partly squeezed to the end of least pressure, which would become distended. If, now, the far end of the cylinder be momentarily connected to earth while the other is still under induction, its excess of motion will escape to the earth, leaving that end neutral (or negative, if close .to the inducing body) ; and on the removal of the inducing body the whole cylinder will be found to be negatively charged. Obviously, this is because the quantity of motion left at the neutral end is insufficient for the whole body, a part of whose motion has been driven to earth, by the excess of pressure on one of its ends, but if it now be connected to earth, it will be supplied with a quantity of motion equivalent to that lost. 24. Why cannot a charge reside on the interior surface of a hollow conductor except an inducing body be insulated in the interior ? If the foregoing principles have been thoroughly grasped, the reason for the above will be easily seen. Suppose a positive charge to be given, then the atoms in the interior, as well as those on the exterior, would begin to expand, increasing the radiation of electricity there, which, with the tendency to expansion, would 698 Proceedings of Royal Society of Edinburgh. [sess. force the motion to the outside where pressure was least. If we suppose for a moment the charge could he retained there — as it is in hollow non-conducting bodies like the Leyden jar — the pressure would be greatly increased, owing to the opposite sides raining, as it were, electricity and encroaching on one another. The motion, in short, is self-forced to the outside, where it has greater freedom. Suppose the charge to he negative — then the greater pressure on the outside than in the interior would force so much of the motion as remained into the interior surface so as to bring it up to the neutral state. To put it in the language of the text-hooks — “the mutual induction ” of the opposite sides would retain the normal amount of motion in the interior atoms, leaving the exterior negative. If, though, an electrified body he lowered into the interior of a hollow conductor without touching it, as in the ice-pail experiment, the inside will he found to he electrified with electricity of the opposite kind to that of the body. This is explained by the fact that, supposing the body to he positive, the pressure in the interior is increased by the radiation from the body, and which forces the greater part of the motion in the atoms of the conductor to the outside, leaving the inside negative and the outside positive. On the other hand, suppose the body to be negative — then the greater pressure on the outside than in the inside, in presence of the negative body, forces the motion to the inside, making it positive and the outside negative. What follows if the electrified body, whether positive or negative, be allowed to touch the conductor is already explained in the text-books. 25. The Eledrophorus. The explanation of the electrophorus is very simple. When the metallic disc is placed on the negatively electrified resinous cake, the small radiation of electricity by the cake permits of the expansion of the atoms of the disc next it, i.e. motion is drawn to them at the expense of the atoms on the far side of the disc. In other words, the greater pressure on the side of the disc farthest from the cake presses the motion to the side of least pressure, which becomes positive, and the far side equally negative. When 1904-5.] Mr J. Fraser on Electricity based on Bubble Atom. 699 the upper part of the disc is touched motion flows in from the earth through the operator’s body and neutralises the negative electricity on the upper part of the disc, so that upon raising it from the cake it is found to he charged with positive electricity. If the disc remained on the cake while charged I have no doubt that the charge would slowly dissipate itself over the surface of the cake, and the reason it does not at once do so is, as it appears to me, the bad-conducting qualities of the cake ; but, as it appears to me, the disc, uncharged, might remain any length of time in contact with the negatively electrified cake without the disc losing any of its positive electricity, because, although the disc’s positive was in contact with the cake’s negative, the tendency for the positive to go back to its own negative would be at least as strong as the tendency to neutralise the negative of the cake, nay, more so, for the disc is a conductor, and the cake a non-conductor. 26. Specific Inductive Capacity. Some substances, such as glass, etc., if placed between an electrified body and a conductor not electrified, cause a greater induced charge to appear on the latter than if they were absent. The reason for this, as it appears to me, is as follows : Suppose the electrified body, or the supply of electricity from a machine, to be positive, then the extra pressure from the positive body to which the glass, or other dielectric, is subjected compresses the atoms into a smaller space, and since, practically, all the motion is conserved to each atom, none of it being able to escape, owing to the non-conductivity of the dielectric, the speed of the particles greatly increases by the conversion of their potential into actual energy. By the increase in their speed they absorb and radiate a greater quantity of the radiations , not only from the electrified body but from all other directions (see p. 41 of paper on “ Con- stitution of Matter,” etc.) ; not only so, but, by the contraction of their orbits, their “centrifugal force” is increased, and there is good reason to suppose, as will appear later, that the speed of the particles of dielectrics is far greater than that of those of conduct- ing bodies. For these reasons it will be apparent, then, that by the interposition of the dielectric the body under induction will 700 Proceedings of Royal Society of Edinburgh. [sess. be subjected to a greater battering of radiations of electricity than if it were absent, so that the end of the conductor nearest the electrified body becomes more negative, the motion escaping to where the pressure is least. If the electrified body were negative all the foregoing would be reversed, the atoms would expand, and the speed of their particles slow down by the conversion of their actual into potential energy. There would be less pressure on the body under induction than if the dielectric were absent, with the result that motion would flow to the place of least pressure. The thinner the dielectric the greater is its efficiency, because a limited supply of electricity, whether positive or negative, cannot have the same effect on an unlimited amount of matter as on a small quantity. If the electricity is positive and the quantity of matter small, there will be a greater concentration of the effect, as absolutely none of the motion can escape to more distant parts ; it is not subdivided between so many atoms of matter. And if the electricity is negative, the less number of atoms the less support, in the shape of electricity, will they get from their neighbours. I had intended touching on the Leyden jar and other condensers, but really there does not seem to be anything to say that has not been said already, or that cannot readily be deduced from what has been said. We will therefore pass on to consider the current. 27. Current Electricity. Without entering into the details of batteries, with which I have only a very slight acquaintance, I proceed to give my idea of the origin of current electricity, as deduced from the hypothetical bubble atom. Well, then, if two of these atoms, of the same hind , be united together to form a molecule, it appears evident, since the constituent particles of both atoms move with the same speed, that as much of the motion of the particles of the one atom as may happen to be transferred to those of the other must be exactly returned, neither more nor less. But it is also as evident that if atoms of different kinds, whose particles move with different velocities, be united in a molecule, that the transfer of speed from atom to atom will not be equal, but that 1904-5.] Mr J. Fraser on Electricity based on Bubble Atom. 701 the swiftest set of particles must lose speed and the slowest set gain an exactly equivalent quantity. The one set, then, will be electrified negatively, and the other set will gain an equal hut opposite positive charge. When they are liberated by electrolysis in an electrolytic cell, those having a positive charge go to the negative side of the arrangement and those having a negative go to the positive. As an example let us take water, whose com- position is two atoms of hydrogen to one of oxygen. In the water voltameter the hydrogen goes to the kathode with a positive charge, and the oxygen to the anode with a negative, from which we may conclude that the particles of oxygen move with a greater speed than those of hydrogen, and that when they unite into a molecule to form water the oxygen particles lose speed which the hydrogen particles gain, and which the latter deliver up at the kathode, to be carried through the outer circuit through the battery to the anode, and re-delivered there to the oxygen, both gases coming away in a neutral state. The current, then, according to this theory, is nothing more nor less than the excess of motion of one set of particles passing over by a suitable path to another set ichich are relatively deficient in motion. 28. There is a tendency in nature for all bodies to gravitate to the lowest attainable level. There is also a tendency in heated bodies to distribute their heat until all have attained the same level of temperature ; in the same way there would be, in my hypothetical atoms and molecules, a tendency to distribute their electricity until all had attained to the same electrical potential (see par. 11). When ordinary zinc is plunged into an acid the oxygen, or negative ion, of the acid tends to unite with the zinc, first because the oxygen has a greater supply of electricity than the zinc, and second because by uniting with the zinc the oxygen would gain a firmer hold upon it than it has of the hydrogen of the acid. It therefore loses its hold upon it and unites with the zinc. The process, would be somewhat as follows : The surface portions of the atoms of the zinc plate must be fully rounded hemispheres, their under surfaces, being united to their fellows, must be in a partially collapsed state, so that their upper surfaces contain a good deal of electricity. But the 702 Proceedings of Royal Society of Edinburgh. [sess. oxygen, or negative ion, of the acid, presumably, containing a good deal more,* acts first of all by induction, or, in other words, by excess of pressure on the outer atoms of the zinc, driving the motion, or electricity, inwardly, and so filling up, or tending to fill up, the collapse of the inner portions of the zinc atoms, and detaching, or tending to detach, them from one another. The partially detached zinc atoms now having a greater quantity of electricity on the side furthest away from the oxygen, the excess of pressure on that side and on the opposite side of the oxygen over that in the space between will drive the oxygen towards the zinc, with which it then unites. In the process of union a greater collapse takes place between the zinc and the oxygen than existed between the oxygen, or negative ion, and the hydrogen of the acid ; some of the electricity of the collapsed portion, or, in other words, the energy of position of the collapsed particles, is used up in separating the oxygen and zinc from their former partners, and should there he no path provided for the remainder to escape, it comes away in heat. Should, however, a path he provided, as in a galvanic battery, the surplus energy comes away as a “ current ” of electricity. 29. I have come to the conclusion that hydrogen, the metals, and the “ positive elements ” generally have the greatest surface density, or close-grainedness, because they always come away from combination with a positive charge. On the other hand, oxygen, chlorine, etc., the negative elements, have the least surface density. This seems to he confirmed by the great specific gravity of the positive elements compared with that of the negative. It will follow, then, that the particles of the positive elements, when in the neutral state, move with the least speed, and that when they (the positive elements) enter into combination * The sulphion of sulphuric acid is negative to the hydrogen with which it was united after the latter comes away from it, but before their union the sulphion was positive to the hydrogen, and in the act of union parted with some of its electricity to it, which made the hydrogen positive and the sulphion negative. Similarly the sulphion, before union, is positive to the zinc with which it unites, and during the act of union makes the zinc positive, leaving itself far more negative than when it parted with its hydrogen. This can be explained by the fact that its union with the zinc is far closer than it was with the hydrogen. 1904-5.] Mr J. Fraser on Electricity based on Bubble Atom. 703 with the negative their particles gain, or borrow, speed from the latter, and are thus made positive and the latter negative. To put it in another way, hydrogen and the metals before combina- tion with the components of their compounds are really negative, they being dense and small in proportion to mass, or atomic weight, and consequently having a relatively small quantity of electricity, and when they enter into combination with the opposite kind, which are possessed of a greater quantity, they deprive them of a part, and so become positive and the others negative. 30. In uniting with the opposite kind, oxygen, and the negative elements generally, i.e. those whose particles part with momentum, partially collapse as a result of some of their motion being given up to the opposite kind. The energy of position of the particles lost through the collapse of the atom would be taken up in enlarging, as a soap bubble is enlarged by blowing into it, the hydrogen, or positive element, and both atoms would he flattened at their point of union, as a result of their radiation of heat upon union. When oxygen and hydrogen unite to form steam, it seems to me that the hydrogen atom is enlarged till its surface density is equal to that of the oxygen. At this point each atom would be possessed of a quantity of electricity proportional to their masses, and evidently also to their surfaces, and of total energy pro- portional to the space which they occupied. For the hydrogen being smaller would, in the excursions of the molecules through this space, suffer fewer impingements, and thus a less quantity of the electricity of the hydrogen would he converted into heat and a greater proportion be available to electrify its domain, so that both the oxygen and hydrogen would electrify their domain equally, and the molecules would he neutral. It seems evident that when they share their electricity in proportion to their masses, their “attractions” or “affinities” must be satisfied, for at this point they have the same “centrifugal force,” they act on the ether equally, and it reacts equally upon them. Well, then, taking oxygen and hydrogen as our example, when they are satisfied with one another, the oxygen atom must have four times the radius of that of the hydrogen, with, of course, 64 times 704 Proceedings of Royal Society of Edinburgh. [sess. the total energy and 16 times the electricity. I am confirmed in supposing the above to be their difference in size by the angle of crystallisation of ice, viz., 60°. (See p. 62, “ Constitution of Matter and Ether.”) 31. We will now consider the origin of the current in the battery, which we will suppose to be a zinc-copper-sulphuric acid one. The acid first of all acts by induction both on the zinc and copper in the manner already pointed out (see par. 28), tending to send a current in both directions ; both the copper and zinc tend to unite with the negative ions of the acid, which, by their contact with the plates, give up a quantity of electricity to the latter ; this electricity tends to fill up the collapse at the junctions of the molecules and atoms of both the zinc and copper, but as, presumably, the collapse at the copper bonds is considerably greater, the filling up of the latter does not proceed further than would be sufficient to fill up a bond of zinc, and to detach it. In fact, the electricity in this case would act as water would which it was desirable to raise to a certain height, but which would not rise beyond half if a sufficiently wide opening were made in the pipe at that height — the electricity always expending itself in the direction of least resistance. In the process of union of the negative ions with the zinc the electricity which would be set free by the collapse at the bonds of the new molecule would be sufficient to detach the hydrogen, which would be attracted to the copper plate with a positive charge, the copper itself being negative owing to its electricity escaping to, and doing work on, the zinc through the connecting wire. In short, the energy of the union of zinc and sulphion being greater than that of hydrogen and sulphion, the former overbalances the latter, so to speak, and the surplus energy produced by the new union comes away as a “ current of electricity.” 32. We now come to electrolysis, and the first thing which seems to require explanation is why the current cannot be con- ducted without decomposition of the electrolyte. The solution of this enigma is not altogether on the surface, but yet it is thoroughly mechanical, and very simple, according to this theory All electrolytes are compounds ; and according to this theory all compounds are made up of atoms of different sizes and masses, 1904-5.] Mr J. Fraser on Electricity based on Bubble Atom. 705 whose particles move with different velocities .* Well, then, when anything tends to increase the motion of bodies moving with different velocities, the slowest are the first to accept the new motion. This is on the principle that any explosive, or, indeed, other force, will expend itself in the direction of least resistance. In an electrolyte the positive element is always the one whose particles possess the least speed, and therefore it is the first to accept the “ current.” Such being the case, the bond uniting the positive to the negative atom, when the “current” is turned on, becomes dissolved ; in other words, the collapse at the junction of the atoms becomes filled up, or rounded out, by the increase of speed in the particles of the positive element. As the collapse of the positive becomes filled up it gradually ceases to press upon, and by the reaction of its increased centrifugal force begins to draw away from the negative, whose particles consequently begin to round out, owing to the cessation of pressure upon them ; and when they become entirely separated they would both have the form of perfect spheres. It will, no doubt, be noted that the collapse of the positive atom is filled up by the “ current,” but that that of the negative is made good by the motion previously possessed by the particles of the negative atom. In fact, the negative atom must collapse as a whole in order to make good the deformation at the bond, while the size of the positive is increased by this quantity. The one is therefore made more negative, while the other is made more positive. To go a little more into detail, let us suppose the electrolyte to be water, then, as soon as the current is turned on, the hydrogen of the layer of molecules nearest the anode begins to accept the new motion ; some of this is passed on to that of the next layer, and so on, till all the bonds of the electrolyte are about to be dissolved ; none, or very little, of the current passing till this happens, because, as it seems to me, there is less resistance in * There seems to be some difficulty in accepting this statement. There is a liability to come to the conclusion that because the ions are in contact the speeds of their particles must be equalised. But this could never happen, for they cannot have the same speed with different radii or their “ centrifugal force ” would differ, nor can they have the same radii with different masses or their speeds must differ. The particles of the different ions never come into direct collision, because if they did the ions would break up, and it is chiefly by their centrifugal tendencies that momentum is exchanged. PROC. ROY. SOC. EDIN. — YOL. XXV. 45 706 Proceedings of Royal Society of Edinburgh. [sess. filling up the hydrogen bonds than would be met by the new motion passing into the circuit. For, observe that the oxygen is negative and the hydrogen positive, and there would thus be the strong attraction that exists between a positive and a negative body (see par. 18), and further, as the hydrogen becomes more positive, the oxygen becomes more negative , for the oxygen has to make good the state of collapse which existed at the bond by the motion which previously existed in the atom, while the collapse of the hydrogen is made good by the current. After separation the hydrogen would, as a positive body, be repelled from the anode and attracted to the kathode ; the latter, being now more negative than the oxygen, would greedily absorb the excess of motion in the hydrogen, and pass it on into the circuit. The oxygen would remain at the anode until it received all the electricity of which it was deprived when it entered into combination with the hydrogen to form water, and the hydrogen would remain at the kathode till it had delivered up all the electricity of which it had deprived oxygen at that same time. Please observe that it is the electricity which H carries forward to the kathode which keeps the circuit going, and if H, as it does, carries more forward than it deprived O of, on their before-mentioned combination, 0 remains attached to the anode till it receives its due share, and H at the kathode till it parts with its excess, when they both come away in a neutral state. They are practically in touch with one another, for they are connected by a good conductor, and as soon as 0 receives its due share, and H parts with its due share, they are ousted by more needy and richer new-comers — in other words, by more negative and positive bodies. If by any possibility the ions could come away, some positively and some negatively charged, i.e. before they had completed the delivery of their charges at the electrodes, they would very soon thereafter, upon mixing with one another, re- adjust the balance. I particularly request that it will be observed that I base my explanation of electrolysis on the fact that one of the ions is positive and the other equally but oppositely negative. In any other liquid formed of simple bodies, such as mercury, or other molten metals, each increment of electricity, however small, provided a conducting path were open to it, would be conducted 1904-5.] Mr J. Fraser on Electricity based on Bubble Atom. 707 away at once; but the “attraction ” existing between positive and negative bodies is so great that the charge is retained till it bursts its bonds in the manner described. I do not think I need say much as to the way in which the hydrogen passes over to the kathode. It is very }vell, so far as I can see, described in the text-books. As I have already said, the ions of the whole electrolyte are on the point of dissociation before any but a small quantity of current passes, for as H grows more positive O becomes more negative, untii 0 itself begins to absorb the current, then the hydrogen of the layer next the anode is repelled in direction of the kathode, and coming in contact with that of the next layer, transfers some of its electricity to it, which has the effect of divorcing the hydrogen of the second layer from its oxygen, the hydrogen of the first taking its place, the H of the second displacing that of the third, and so on, in the manner described in the text-books, till the kathode is reached.* The foregoing is, I am aware, but a crude explanation, but as I have more than once hinted, I am only a novice in electrical matters ; all I claim is that by much thought I have gained a little insight into the properties of the atom which I, myself, was the first to conceive, so far as I am aware, and which I believe to be the true atom of nature, and I have done my best to explain this particular portion of electrical science in accordance with the properties which, I believe, attach to this particular atom. 33. Conduction and Resistance. One of the greatest difficulties in the construction of this theory was to account in a tolerably feasible way for the enormous differences of the conducting-powers for heat and electricity of different bodies. Heat being caused, as we have seen, by a periodical condensation and dilatation of the particles of which the atoms are composed, with a consequent quickening and slowing down of their motion ; and electricity also, though in a different way, being caused (one kind of it) through a * Compounds would be dissociated by heat in much the same way, the bonds of the positive body being the first to fill up, and the charges of the components would be neutralised by the surrounding neutral bodies. 708 Proceedings of Royal Society of Edinburgh. [sess. quickening, and the other kind through a slowing down of the motion of these same particles, one would think that as the molecules are all in contact the motion should spread with equal facility through bodies of all kinds, generally speaking ; at least that there should not he the enormous differences that there actually are without something special to account for them. And there is something very special indeed, and complicated, hut, broadly speaking, very simple though complicated in its effects. The whole secret lies in the difference of speed of the particles of different bodies. When bodies in motion are placed in contact the exchange of motion between them will depend upon the difference between the motion of the one and that of the other, if their motion is both alike, each will receive from the other as much as it gives, and there is nothing lost or gained by either, but if their motion is greatly different the one will lose a great deal and the other gain as much. As a partial confirmation of the above, viz., that the secret lies in the difference of particle-speed, I appeal to the broad fact that the greater the atomic volume compared with weight of bodies the less will those bodies conduct both of heat and electricity. Now the atomic volume of my hypothetical atoms depends entirely upon the speed of the particles, and upon the number of particles (the atomic weight) upon which that speed is impressed. For, granting the same speed to be impressed upon different quantities of ethereal particles, the radii of the resulting bubbles would be proportional to the cube roots of the atomic weights, and, as I have already pointed out, the volume would be proportional to the square of the speed multiplied by the number of particles. But there is another and more striking fact to which I appeal for confirmation of my idea that difference of particle-speed is the secret cause of the difference in the conducting powers of bodies. And that fact is that the greater their radiating powers for heat the less is their conducting powers for electricity and also for heat. The latter fact may seem to follow from the former, for what is radiated cannot be conducted ; but wait a little. It is true that conducting bodies the more they are heated conduct electricity worse, but this is not true of insulators. Heat helps their conducting powers. Now, it is evident that in differently 1904-5.] Mr J. Fraser on Electricity based on Bubble Atom. 709 constituted bodies there must be differences, and in some cases great differences, in the size of the spaces existing between the atoms and molecules ; and especially will this be so in the case of compound bodies, for the latter are made up of atoms of different sizes and weights. It would follow from this that the ether which fills these spaces will have a greater difficulty or facility of passing from space to space, according to their constitu- tion, so as to readily admit of their heat-vibrations. In cases where there is a difficulty of passage, owing to pockets and corners, the ether, during the inward phase of the vibration, will be under great pressure, which will react on the atoms, increasing the speed of their particles enormously, and so preventing their, acceptance of new motion, such as that of electricity, and greatly increasing the subsequent outward rebound and loss of potential energy of the particles. In the cooler portions of bodies of this nature the spaces will be narrower, thus increasing the difficulty of the escape of the ether during the inward phase of vibration and increasing the pressure on the particles of the cooler portion, or at any rate tending to make up the difference in speed which the lessened amplitude would cause. This would prevent the conduction of heat to the cooler portions, for as the speed of the particles of the cooler portion would be nearly equal to that of the hotter, there would be little difference in the exchange between them, and thus the heat, instead of spreading, would be radiated in the locality where it was generated.* We can now account for the fact that insulators conduct electricity better when they are hot. They do so because the spaces between the atoms are wider ; there is greater facility for the passage of the ether from space to space, and consequently less pressure on the atoms and less particle-speed. 34. It requires only a superficial study of the subject, in view of the present theory, to arrive at the conclusion that heat must resist the passage of electricity through — all bodies, I was going to say — at any rate through most ; and even in the case of insulators, if there was no heat — that is at the zero temperature — and if the molecular contact was good, and the electrical potential This property of bodies I propose to call by the name of “Self- Compression. ” 710 Proceedings of Royal Society of Edinburgh. [sess. high enough, I do not see why even insulators should not become good conductors. For the heat vibrations, even without the pockets and corners, which resist the free circulation of the ether, must trap a good deal of the new motion of electricity. That is, the particle-speed produced by the condensations must be increased by the electrical motion, and consequently the heat vibrations increased, and a good deal of the electrical motion transformed into heat. But at the zero temperature, when all vibration has ceased, and the pressure of the ether throughout the body has become constant, and especially where there is free circulation of the ether, so that any small tremors which might possibly be generated by the electrical motion would have very little effect, it is easy to see that ordinary conducting bodies would become perfect conductors. For then none of the motion could be trapped and absorbed in the vibrations, because none of the latter existed. 35. While trying to puzzle out the enigma of conduction I came to the conclusion, whether rightly or wrongly, that com- munity of atomic volume involved also community of mean particle-speed. It does not necessarily follow that because their apparent volumes are the same their real or mean volumes are so, for the latter are proportional to the cubes of their mean radii, and the former is a combination of this with their amplitude of vibration. Every atom while executing a complete vibration passes from a state of expansion to a state of compression, and back again ; and its radius will pass through all stages from a maximum to a minimum, and back again. We can only measure the volume of any body at the maximum phase of its vibrations, not at the minimum ; therefore when testing the specific gravity it is the maximum volume which counts. In two bodies of the same atomic volume that body whose atoms possess the greater number of particles will have the greater mean atomic volume, but it seems to me, and my reasoning is supported by analogies from the kinetic theory of gases, the body with the less massive atoms occupies the same extreme or maximum space by reason of its atoms’ greater amplitude of vibration. I mean, of course, these remarks to apply to bodies in the solid state. In the gaseous state we know, of course, that the mean space occupied 1904-5.] Mr J. Fraser on Electricity based on Bubble Atom. 711 by all molecules at the same temperature and pressure is pro- portional to the square of their speed, and so here, if we look upon the particles as molecules, the mean space which they occupy is proportional also to the square of their speed. Again, in the kinetic theory the lighter atoms make up for their lightness by their speed, so in the solid state, if they are also small, they make up for their smallness by their greater amplitude of vibration. Remember in weighing this point that their maximum volumes are equal , but that their minimum volumes may be greatly different, being always less for the lighter elements, so that their mean volumes may be greatly different. 36. We are now in a position to test whether and in what degree the radiation of heat affects the electrical conduction of bodies. For the radiation of heat by solid bodies depends upon the amplitude and period of vibration, and the strength of the bonds uniting the molecules ; and, since bodies of the same atomic volume must, according to my theory, have the same elasticity or resistance to compression, they must also have the same period of vibration.* We have then in our hands, in order to calculate their radiation of heat, the atomic weight, the amplitude of vibration (the periods not being necessary since we are choosing conditions under which these are the same), and the strength of their bonds, which is measured by their melting points. The rule, then, according to these assumptions, for calculating their radiation of heat and consequent resistance to electrical con- duction is as follows : — Rule to Find the Electrical Resistance of Metals. 1st. It is inversely as the square of the cube roots of the atomic weights ; 2nd. Directly as the melting points in the scale of absolute temperature ; and 3rd. Directly as the atomic volume. I found when I tried this rule that it answered admirably in the case of silver, copper and aluminium ; their resistances * Pendulums of the same length have the same period of vibration irre- spective of amplitude or weight of bob. 712 Proceedings of Royal Society of Edinburgh. [mss. worked out almost to the of an ohm. They worked out also^ very closely when I paired zinc and platinum together, and also when I paired lead and antimony, but not at all when gold was. tried with either silver, copper or aluminium, nor when zinc or platinum, lead or antimony, were paired with any of those metals. I found, though, that if I multiplied the resistance found for gold^ when paired either with silver, copper or aluminium, by 2, the result would he very close to the observed resistance ; and also that if zinc or platinum were tried with either silver, copper or aluminium, and the result multiplied by 5, it would be very close to the observed resistance ; and further, if either zinc or platinum were tried with gold, the result had to be multiplied by 2J to- bring the resistance of the two former metals up to the observed. Similarly the resistance of lead and antimony, though working out. very closely when paired with one another, had to be multiplied by 25 when paired with either silver, copper or aluminium, and when paired with gold by 12J, so that the rule had to be modified as follows : — Rule to Find the Electrical Resistance op Different Metals, 1st. It is inversely as the square of the cube roots of the atomic weights; 2nd. Directly as the melting points in the scale of absolute temperature ; and 3rd. Directly as the atomic volume. The result to be multiplied by 2 when gold is paired with either silver, copper, or aluminium ; by 3 when iron is paired with either of those metals ; by 5 when either zinc or platinum is paired with them; by 6 when nickel is paired with them; by 14 for tin; by 25 for antimony or lead ; and, generally, by numbers proportional to their silver-copper-aluminium multipliers when paired pro- miscuously one with the other. 37. These results delighted as well as disappointed me. They delighted me because it was my assumed knowledge of the constitution of atoms which led me to try this method of finding the electrical resistance ; and I could not suppose that they were mere coincidences, for they were too close and intricate for that.. I reasoned that if my atoms were real things, and not “mere 1904— o.] Mr J. Fraser on Electricity based on Bubble Atom. 713 figments of the imagination,” they ought to answer to this test ; and I was disappointed that they did not answer more fully to it. It ultimately became clear to me that there was some factor in the problem of which I took no account ; and that this factor, what- ever it was, acted equally on silver, copper and aluminium ; and also equally on zinc and platinum, though differently from its action on the three former ; and also equally on lead and antimony, though differently on these from all the others. After casting about in every direction I could think of for some feasible solution of the problem, the most feasible — and, indeed, one which ought to be accounted for if this theory is not the mere ravings of a dis- ordered imagination — is self-compression, as I have termed it. It cannot be supposed that in solid bodies, constituted of atoms such as are postulated in the theory under discussion, that the ether should have the same freedom of circulation through them all. It must be that in some of them, according to the sizes and arrange- ment of the molecules, the ether must be absolutely trapped in a corner or pocket, so that the pressure of the vibrating molecules on it, and its reaction on them, must produce a speed in the constituents of the atoms which would prevent their acceptance of new motion, in the way already set forth (see par. 33), and could only find relief in the direction of least resistance — namely, outwardly, or by radiation of heat. 38. I append a list of the resistances found by the above rule, along with the observed resistances for comparison; also the melting points * of the different metals used in the calculations, and the numbers used as multipliers to bring the calculated resistances up to that observed. It will be seen that the latter are not mere empirical numbers, for they hold good in their proportions throughout the calculation. They are empirical in so far as that they are the nearest ivhole numbers required to bring the calculated up to the observed resistances, but when once established they hold their ground. For instance, the resistance found for gold when paired with aluminium, silver or copper, had to be multiplied by 2 to bring it up to the observed resistance, as already said, seeming to show that some factor acted with twice the influence on gold as on the three former metals. Similarly the resistance found * 273° to be added for reduction to absolute temperature. 714 Proceedings of Royal Society of Edinburgh. [sess. for platinum and zinc when paired with any of the three former metals had to he multiplied by 5 to bring it up to that observed, seeming to show that some factor acted with 5 times the influence on zinc and platinum as on silver, copper and aluminium; but when gold is paired with either zinc or platinum the multiplier is only 2J, being in the same proportion as the multiplier of the former metal with silver, etc., as that of platinum and zinc with them. And so of all the others. The observed resistances quoted are the relative resistances of wires of chemically pure substances of the same length and sectional area at 0° Cent. I believe that the resistances for wires of the same length and weight can be found on the same lines if allowance be made for the difference in surface area for radiation of heat. I only tried one example, viz., silver and aluminium, and the result was very close to the observed resistance. My powers of calculation are very limited, and so also is the time I can spare. 39. It may not be amiss to put down in succinct form the rationale of the above rule, as it may not be perfectly obvious to everybody ; indeed, I am rather in danger of forgetting it myself, and did forget it for a time, and had some difficulty in recalling it, so I will put it down once for all for the general benefit. Well, then, 1st, the reason for the resistance to be inversely as the squares of the cube roots of the atomic weights is that the mean radii (see pars. 6 and 35) of atoms of the same atomic volume are proportional to the cube roots of their atomic weights ; * and since the molecules of the lighter element at the outward limit of their swing must occupy the same space as those of the heavier, if their mean radii are small, the greater must be the amplitude of vibration ; and as the energy of vibration is proportional to the square of the amplitude, the heat radiated must be in this proportion, and the conduction inversely, as the heat radiated. Or resistance will be proportional to radiation of heat. 2nd. The reason for resistance being directly as the melting points is that the higher these latter the broader or deeper must be the bonds uniting the molecules, with a consequent greater radiation of heat per vibration. And 3rd, that it should be directly as the * Assuming, of course, that when atoms have the same atomic volume their particles move with the same speed. 1904-5.] Mr J. Fraser on Electricity based on Bubble Atom. 715 atomic volume is because the latter is proportional to the square of the speed of the particles multiplied by their number ; and since the acceptance of new motion by these same particles is less as the square of the speed is greater, the resistance must be as the square of the speed, or as the atomic volume. 40. This is as far as I have explored this puzzling subject ; I have done no more than merely glanced at magnetism, and can offer no solution of it at present. The phenomena of radio-active bodies seem to confirm my idea that atoms are formed of smaller bodies ; and if I might hazard a, perhaps, wild guess, it is that the atom may get broken up into its constituents, or possibly form smaller ones, by an intensely negative charge which would suddenly take away a great proportion of the motion of the particles, and the heat vibrations still persisting, as they would do, this, with the sudden collapse of the atom, might very well break it up. I have not studied this part of the subject, so I shall say no more about it at present. Perhaps I have already said too much. Before closing I should like to correct an unaccountable error in my paper on the “ Constitution of Matter.” On page 39, line 24, I wrote “normal” where I meant “tangential.” One of the strongest points in favour of this theory, which I have not before expressed in words, is the fact that, when elementary substances unite to form compounds, the resulting compound is altogether different in all its qualities and properties from either of the constituents. This theory, in my opinion, accounts exactly for this ; for according to it a union of two or more of my hypothetical atoms altogether alters their constitution, by imparting speed to the particles and consequent volume to the atoms of one or more of the constituents at the expense of less speed and volume to others of the compound. Moreover, it seems to show that chemical affinity is altogether an electrical pheno- menon— how that some kinds of atoms with more electricity than others “ attract ” one another as positive and negative bodies. [ Table of Calculated Electrical Resistances . 716 Proceedings of Royal Society of Edinburgh. [sess, Table of Calculated Electrical Resistances , the Resistance of Silver taken as Unity. Metal, resistance of which is to be calculated. Metal whose resistance is known and with which the former is paired. Calculated resistance. Observed resistance. Multipliers. Melting ;• points taken as * Metal. De- cent. Metal. Deg. Cent. Aluminium . Silver 1-911 1-935 0 A1 700 Silver 1000 Copper . Copper 1-04 1-063 0 Copper 1045 }J Aluminium . 19464 1-935 0 A1 700 Platinum Zinc . 5 809 6-022 0 Pt” 2000 Zinc 430 Antimony Lead 6-023 0 Antimony 2100 Lead 24-10 23-60 0 425 334 Gold Silver 1-383 1-369 2 Gold 1037 Silver 1000 Aluminium . Gold 1-8933 1-935 A1 700 Gold Copper 1-388 1-369 2 Iron 1530 Copper 1045 Iron Silver 6-287 6-460 3 Silver 1000 Platinum >> 5 974 6-022 5 Pt 2000 Zinc >> 3-485 3-741 5 Zinc 430 Lead >) 13-86 13-05 25 Lead 334 ; t Antimony Aluminium 22-51 23-60 25 Antimony 425 Ai’ 700 Zinc 3-5217 3-741 5 Zinc 430 Platinum u 5-4325 6-022 5 Pt 2000 Zinc Copper 3-555 3-741 5 Zinc 430 Copper 1045 Platinum Gold '. ! 5-493 6-022 5 Pt 2000 Zinc 3-481 3-741 2£ Zinc 430 Gold 1037 Platinum 5-322 6-022 Pt 2000 ff Tin Silver 8-354 8-784 14 Tin 235 Silver 1000 >> Aluminium 8-4366 8-784 14 Al 700 ,, Copper 8-535 14 ,, ,, Copper 1045 Nickel . Gold . 8-344 7 j y Gold 1037 Tin . 8-638 8-285 H y Nickel 1450 Silver 81633 ” 6 Silver 1 1000 ” • ' Aluminium 8-0689 6 A1 700 ” ” * Plus 273° for reduction to absolute temperature. ( Issued separately May 18, 1905.) 1904-5.] Prof. Metzler on Axisymmetric Determinants. 717 Variant Forms of Vanishing Aggregates of Minors of Axisymmetric Determinants. By Professor W. H. Metzler. (MS. received March. 13, 1905. Read May 1, 1905.) 1. Vanishing aggregates of determinant minors have of late received considerable attention and are now becoming well known. Prom aggregates for axisymmetric determinants of the form given by Kronecker,* * * § Muir,f or the present writer J we may get other forms, and it is the object of this paper to consider some of these new forms, and in particular to show that the general theorem given by Professor Nanson § is readily obtained from the vanishing aggregates of the type given by the present writer. ( *2iV 1 1 f -4- 2. Let us here as elsewhere || use ^ 1 ^ j to denote the c^th combination (tf + s) at a time of 2 r given numbers, (^r 1 ^ + S I s \ to ' al a2/ denote the a9th combination s at a time of the numbers in the combination the combination r 1 t' + s\ /2r 1 1' + s 2r 1 1' + s to denote the complementary of , that is, the combination of the re- maining numbers after the numbers in the combination are taken from the given 2 r numbers, and 2 r It' + 8 to denote /2r 1 1' + s | s V «i <*2 the combination of the numbers left after the numbers in the * “ Die Subdeterminanten Symmetricher System,” Berliner Berichte , 1882. f “Aggregates of Minors of an Axisymmetric Determinant,” Phil. Mag., April 1902. X “ On certain Aggregates of Determinant Minors,” Trans. Amer. Math. Soc., October 1901. § “Minors of Axisymmetric Determinants,” Amer. Jour, of Math., January 1905. || Loc. cit ., § 2. Amer. Jour, of Math., vol. xxii., No. 1. 718 Proceedings of Royal Society of Edinburgh. [sess. combination ^ + S 1 6 ^ are taken from the given 2 r numbers, etc. V ai Vi A al ' K al a2 V C2r i t' + s Is V '2r 1 1' + s l*i A \ a\ a2/\ ^ ai °2 V 1904-5.] Prof. Metzler on Axisymmetrie Determinants. 71 9’ ( ' \( '' ) Vs'+/C/ V K /s—s' — l c=2,: 2* 1 1 1 Similarly, 2 where /2r | + t + if | S | k\ f 2 v 1 1' + s | s | s' + K\ V ai j \ al r , then D = 0 and A and B could not exist, as minors of order r could not have more than r rows constant. If s' + 1 — r, , then s = s and t = t' and A and B both reduce to the single term (2r\t' + s\ (2r\r\ l «J. V «J or (2r\t' + s\ /2r 1 r \ V «J V “i ) Similarly for t'>r and for s>r. Other forms may be obtained from these aggregates by applying the law of complementaries and the law of extensible minors to them. 4. If now we turn to Professor Hanson’s paper and observe that in his relation K = M = kK\ - !,My or M + ^MA=AKA' the expression M + ^M^ is a sum of the form of the conjugate of D, and AKA' is of the form of A, then it will be seen that his theorem is, except for the lack of a sign factor, the same as one of the relations in III. As examples of III. we have (1) 1234 5678 6781 4523 = -2 1236 4578 where ^ 1234 5678 1234 5678 1235 4678 and 2, 6781 4523 6781 4523 6782 4513 6783 4512 1234 V > 1456 1237 (2) 2 5678 -2 2378 = -2 4568 (3) 2 12345 6789r --2 45678 1239t = -2 12349 5678t Syracuse University, Syracuse, N.Y., February 1905. ( Issued separately May 20, 1905). PROC. ROY. SOC. EDIN. — YOL. XXY. 46 722 Proceedings of Royal Society of Edinburgh. [sess. The Constitution of Complex Salts. — I. Derivatives of the Sesquioxides. By Alexander T. Cameron, M.A. Communicated by Dr Hugh Marshall, F.R.S. (MS. received February 20, 1905. head same date.) Preliminary. In a recent communication * I described how I had obtained crystals of potassium hydrogen succinate showing only curved faces, from an attempt, up to the present unsuccessful, to prepare complex derivatives of succinic acid corresponding to the chrom- oxalates. In searching the voluminous literature of the subject for particulars of such complex salts I especially noticed two things, — first, the frequent but hitherto scarcely noted parallelism exhibited by these compounds ; and second, the noticeable lack of uniformity in the formulae attributed to them. The former I shall deal with in the general part of this paper, the latter in this preliminary portion. The complex sulphates and oxalates are typical examples of these salts, and may therefore be selected for consideration. Graham and Mitscherlich ascribed to Gregory’s blue chromoxalate the “ double-salt” formula 3K20.C203 + Cr203.3C203 + 6H20 , while Crofts f ascribed to the red salt which he discovered a similar formula K20.C203 + Cr203.3C203 + 12H20 . J Malaguti § considered that these and similar compounds should be regarded as complex derivatives of chromic oxide ; and E. A. Werner, for reasons which I shall mention immediately, considered that K6Cr2(C204)6 , 6H20 , and not the empirical formula, correctly * Proc. Roy. Soc. Edin., 25, p. 401. t Phil. Mag., iii., 21, p. 197. + These formulae are here written in accordance with modern atomic weights. § Compt. Rend., 16, p. 456. 1904-5.] Mr Cameron on the Constitution of Complex Salts. 723 represented Gregory’s salt, while to the other he ascribed the constitution with ten molecules of water, instead of twelve as previously written. Rosenheim and his collaborators have shown that in most cases these doubled formulae are unnecessary, and have uniformly used the simple formulae, though lately they have applied A. Werner’s Co-ordination Theory, and have, for example, ascribed to Crofts’ “ red salt ” the formula Recoura, in his many papers on the chromisulphates, and latterly on the ferrisulphates, consistently uses the doubled formulae, as for example in the anhydrous alum acid and Klobb, in his researches on similar compounds, has used “ double-salt ” f formulae. To give but one other example, Kohlschutter, in his investigations on the complex uranium oxalates, has used invariably the simple formulae. There appear to be three chief reasons for this absence of agreement among investigators. In the first place, the old idea of “ double-salts ” which is still so largely upheld causes the re- tention of doubled formulae even when the substances come to be regarded as salts of complex acids. Secondly, the old formulae for the hydroxides of trivalent metals, e.g. Cr2(OH6), have never been convincingly disproved. From the nature of these substances, constitutions can only be assigned to them by comparison with their derivatives, whereas hitherto in many cases the process has been reversed. Finally, in the case of the chromoxalates, Werner | has used the doubled formulae, on the ground that there exist perfectly definite compounds corresponding to the formulae * References, where not otherwise mentioned, will be found at the end of this paper. t In this paper by “double-salts” are meant molecular compounds of simple salts. X J. Chem. Soc. , 51, p. 383, and 53, p. 404. K2H2Cr2(C204)(0H)2 + 8H20, 724 Proceedings of Royal Society of Edinburgh. [sess. The blue salt (a) crystallises in the same system as the corre- sponding potassium compound, and is indistinguishable in appear- ance from it ; the red salt (b) is stated to be more freely soluble in water than is the corresponding potassium compound, but resembles it closely in all other respects. Subsequently to these researches of Werner on the Chromoxalates, Retgers * published his important papers on the relations of density and composition in various isomorphous mixtures. From theoretical considerations he showed that by plotting the specific volume against the composition, expressed in the percentage of one of the constituents, a straight line should be obtained if mixtures alone were present and no definite compounds were formed. The experimental results which he obtained in numerous cases of isomorphism were in complete accordance with this deduc- tion, and he came finally to the conclusion that two truly isomorphous compounds cannot unite together to give a definite compound.! In view of Rutgers* results, Rosenheim J assumed that Werner’s compounds should be considered as isomorphous mixtures of the potassium and ammonium salts. As, however, this has not been generally recognised, and as direct experimental results had not been obtained, I thought it advisable to apply Retgers’ method of investigation to the blue chromoxalates, which form well-defined crystals. To obtain the material for this purpose, following Gregory’s original method, I mixed solutions of different pro- portions of potassium bichromate, potassium and ammonium hydrogen oxalates, and oxalic acid, as indicated below : — Mixture. K2Cr207. khc2o4. nh4hc2o4. h2c2o4. Ratio K : NH4. 1 1 4 5 6 ... 2 1 3 1 5 5 : 1 3 1 H n 5 9 . 3 2 • 2 4 1 2 2 5 4 : 2 5 1 4 5 2 : 4 6 (NH4)2Cr207.l) 4 5 ... : 6 * Zeit. fur phys. Chem., 3, p. 497, etc. t Ibid., 15, p. 528. + Zeit. fur anorg. Cliem., 11, p. 314, footnote. 1904-5.] Mr Cameron on the Constitution of Complex Salts. 725 From the first five mixtures perfectly definite crystals were obtained, and these were in each case recrystallised. The crystals finally obtained were indistinguishable in appearance. The sixth solution yielded no crystals on evaporation, but left a gummy mass. The density of the crystals was determined in accordance with the method described by Retgers,* using a mixture of bromoform and turpentine, which was found to give good results. In each case I selected the densest crystals — those most free from air- cavities — by separating such as sank first in liquid of almost the same density, and determined the density of the crystals by adding bromoform to the same liquid till the crystals neither rose nor sank, and ascertaining the density of this liquid by the pyknometer. The temperature at which these determinations were made was about 10° C., though it may be pointed out that slight differences of temperature should produce no appreciable difference of density in the solid crystals, and hence the determina- tions should be unaffected (provided no transition temperature be passed through). The following results were obtained : — Crystals from Mixture - Density. Specific Volume. 1 2T33 •4689 2 2-111 •4737 3 2T09 •4742 4 2-099 •4764 5 2-054 •4868 The percentage of ammonia was determined by distilling very dilute solutions with alkaline carbonate and Nesslerising the distillate. The second and third mixtures by themselves seem to show that the crystals resulting from such mixed solutions have no definite composition. The percentages are as follows : f — * Zeit. fur phys. Chem ., 3, p. 289. t It will be noticed that in each case the percentage of ammonia found is less than half that present in the corresponding solution. The results were confirmed by a determination of the potassium (as sulphate) and of the ammonium (by titration method) in the case of the fifth mixture. 726 Proceedings of Royal Society of Edinburgh. [sess. Crystals from Mixture. Percentage of Ammonia. Mean. (1) (2) 1 •04 •04 2 *71 •68 •70 3 •89 •87 •88 4 1-23 1-20 1-22 5 3-31 3-33 332 The results obtained by plotting the specific volume against the percentage of ammonia are shown in the diagram. It will be seen that the density of the pure potassium compound appears to be too high. No explanation can be at present offered for this deviation. . The concordant results in the case of the four PERCENTAGE of AMMONIA. mixtures give considerable support to the application of Retgers’ hypothesis to the chromoxalates, and to the view that the potassium- ammonium salts of these series are merely mechanical mixtures, and not chemically definite compounds. No doubt similar experi- ments with the red series of chromoxalates would give corresponding results. 1904-5.] Mr Cameron on the Constitution of Complex Salts. 727 It has been pointed out from other considerations that the tendency in such solutions is for the formation of crystals in which the metallic radicals have a simple ratio. I have endeavoured to determine the molecular weight of Gregory’s salt by means of the freezing-point method, hut this compound presents some anomalies in that connection ; these are at present under investigation, and may form the subject of a future paper. Rosenheim and Koppel * have determined the conductivities of a considerable number of complex oxalates, and the result /x1024 — At32 = 33 -3 for Gregory’s salt would lead to the conclusion, from Ostwald’s empirical rule, that this is a salt of a tribasic acid. I conclude, therefore, that in the case of the chromoxalates and similar salts there is at present no special reason for using doubled formulae, and that until such reason is put forward I am justified in using the simple empirical formulae in every case. Should more weighty proofs he put forward for the doubling of these formulae, the reasoning in the following pages is not invalidated, though the formulae are rendered more cumbersome. In considering the constitution of salts, it must be remembered that in crystalline solids there exist molecular complexes whose nature is little known, and that solution breaks these up into simple molecules, often ionising the latter. Such considerations, then, are really concerned with the non-ionised molecules in solu- tion, and it is possible that many crystalline solids are outwith the subject, as their complexes may be incapable of existing in solution. In my subsequent remarks I have not taken into account water of crystallisation, other than water of constitution, although it may he pointed out that certain well-defined regularities exist. These are most marked in the case of potassium compounds. To give hut one example, salts analogous to the blue potassium chromoxalate almost invariably, like it, contain three molecules of water. Zeit. fur anorg. Chem., 21, p. 17. 728 Proceedings of Poycd Society of Edinburgh. [sess. General. The constitution of complex salts of dibasic acids of the type H2X , and metals forming oxides of the type M203 , may be best considered by taking as examples the complex chromoxalates, and treating them as derivatives of chromic hydroxide by the substitu- tion of half-saturated oxalate groups for hydroxyl radicals. If all the hydroxyls are replaced by the radical - C204K Gregory’s salt is obtained, to which accordingly must be given the constitution This type may be regarded as the saturated one, and will here- after be referred to as A. 1. By the elimination of potassium oxalate from two molecules of Gregory’s salt a compound is theoretically derivable. No such chromoxalate has up to the present been obtained, but Recoura has prepared an exactly analogous chromisulphate, having the constitution This type of salt will be referred to as A. 2. In type B. will be included salts which still retain one hydroxyl group, and in addition the compounds which can be derived from these by loss of water. The first class of type B. is obtained by substituting two - C204K radicals for hydroxyl groups in chromic hydroxide, as in the compound c204-k /A-k CrfCA-K >CA or CA = [Cr : (C204.K)2]2 CAA-K AA-k S04 : [Cr : (S04.H)2]2 . ca-k 1904-5.] Mr Cameron on the Constitution of Complex Salts. 729 This was first prepared by Werner,* who, on heating it to nearly 300°, obtained the corresponding anhydride having the constitution The type of compound will be referred to as B. 1. The acid salt corresponding to the undehydrated compound will have the constitution This also, according to the same author, when heated to nearly 300°, yields its “ anhydride,” having the formula therefore An alternative constitution for this anhydrous salt will be mentioned later. This type of salt will be designated B. 2. In his last paper Werner J describes a new series of salts, to which he gives, in the case of the ammonium compound, the formula (NH4)5Cr4(C204)6(0H)5 , 2H20. From this he concludes that the corresponding acid is H5Cr4(C204)6(0H)5 , 4H20. It seems unfortunate, in view of the probable chromammonium com- plex, that he has chosen the ammonium compound as designating the type. His formula for the corresponding salt of potassium is K4Cr4(C204)6(0H)4. If this is halved it is easily seen that the salt may be considered as derived from that of type B. 1 by elimination of potassium oxalate from two molecules, and hence * J. Chem. Soc., 53, p. 407. t Ibid. Cp. also Rosenheim and Platsch, Zeit. fur anorg. Chem., 21, p. 11, and Rosenheim and Cohn, ibid., 28, p. 337. X J. Chem. Soc., 85, p. 1438. or O : [Cr : (C204.K)2]2. I o2w4 - av whieh is half the formula that Werner f assigns to Crofts’ red salt. 730 Proceedings of Royal Society of Edinburgh. [sess.. probably has the constitution OH CrZc204-K \C204 or C204 : (H0.Cr.C204.K)2 . C ' C204 - K XOH Probably by the application of heat an anhydrous compound may be obtained, exactly as in the preceding cases. It is interesting to notice that in his first paper on the chromoxalates * Rosenheim, in putting forward a somewhat similar classification of doubled constitutions derived from the sesquioxide Cr203, has predicted the existence of this compound, though he failed in his efforts to obtain it. This type will be styled B. 3. The remaining series, C., is that in which but one hydroxyl group is replaced. The chromoxalate of this class and its anhydrous derivative would have the constitutions OH Cr^OH and 0 : Cr.C204.K xC204-K respectively, but these compounds have not been prepared. Members of this series are up to the present rare, but a potassium antimony oxalate 0 :Sb.C204.K, and tartar emetic 0 :Sb.C4H406.K, f may be taken as instances. Nearly all the complex derivatives of the sesquioxides can be referred to one or other of these types. Some of the important exceptions will be mentioned later. Most of the investigators in this field of research have recognised to some extent that analogies exist among these complex com- pounds. Thus E. A. Werner has extended his observations from the chromoxalates to the chromium compounds of other organic acids, and Rosenheim and his collaborators have investigated the derivatives of oxalic acid and a number of trivalent and quadrivalent metals. Again, Christensen | has compared the * Zeit. fur anorg. Ghem 11, pp. 212 et seq. f The constitution of this salt is doubtful. t J. pralct. Ghem., ii., 34, p. 44, and 35, p. 172. HaO HC. HF HCN H8CN hN02 h2so, | H2C204 h2c3h2o4 v A‘- B.2. V : (O.H)a C12:V.C12.K i 8 v:([CNj2.K)3 (3) v:([SCN]2.K)3 (3) - -1 0 : Cp.O.M Cl2 : Cp.C12.K l&X Cp:([CNJ2.K)3 (4) Cr:(lSCN]2.MMlS) S04:Cp.S04.M (14,16) (22vl3 HnAi B.2. Fesl O : Mll.O.H • F2:[Mn:(Fo.X F2:Mn.F2.Ag >2k (5) (5) Fe.(lCN]2.M3 1 Mn :(C204.SD3 (20) FeKCUDg 0 : Fe.O.M S : Fe.S.Cu -.Bissau Cl2:Fe.Cl2.NH4 Fe^SO^NH^ (17) ,(ia,n) FeUC204.K)3 (10) C204:Fe.C204.K (10) Co Coi(O.H)s ! Co:([N02]2.M>a (11) ' A1 : (O.M)j 0 : A1 : 0.M A1 (Cl2.Na)3 C12:A1.C12.M L(i$ ai;([scn]2.k)3(13) S04:lAl:(S04)2:Pb]2 S04:A1.S04.NH4 (16) Ai;(Ca04.M)j (10) csmseti* ns "4 0:T1.0.H S : TI.S.M Cl2 : Tl.CIj.M 1 Ho si? mi A/1: 0:£’®2k. 0 : As.O.K s::iia S : As.S.M | ? AS : (C 0 : Sb.C-)04 K B1 2. B.2. 0:[BI:(0.MW2 0 : Bi.O.M .-S S : Bi.S.M C12:[B1:3 0:[Cp:(0.H)2]2(15) 0 : Cp.O.M ' Cp : (C12.T1)3 C12:[Cp:(C12.K)2]2 Cl2 : Cp.C12.K Cp : (F2.M] F2 : [Cp : Cp • (C3H204.M)3 (23, 24) Cp.C3H204.M (22,23) .Cp.C3H204.H)2 (22) A. 1. Mn 2- B. 2. A. 1. F* B.l." 2. 0 : Mn.O.H . F2: [Mn :(F2.A| F2:Mn.F2.Ag . Fe:(O.H)3 0 : Fe.O.M S : Fe.S.Cu Fe :(Cl-2-K)3 Cl2 : [Fe : (C12.M)2]2 Cl2 : Fe.Cl2.JSTH4 Fei(F2.M: F2:[Fe:(F2.M; A. 1. Co B. 1. Co : (O.H)g A. 1. ai 2. A1 B.l. 2. Ai:(O.M)3 0 : Al : O.M Al :(Cl2.Na)3 Cl2 : A1.C12.M Al : (f2.m: F2 : [Al : (F2.M; A. 1. T1 B.L 2. 0 : Tl.O.H S : Tl.S.M T1 = (C12.M)3 C12:[T1:(C12.K)2]2 Cl2 : T1.C12.M A. 1. As 2- B. 2. As:(o.m)3 0 : [As : 02 : KH]2 0 : As.O.K As = (S.M)3 S : [As : (S.M)2]2 S: As.S.M A. 1. 2. Sb B-|; c. 0 : Sb.O.M Sb :(S.K)i3 S : [Sb : (S.K)2]2 S : Sb.S.M Sb : (C12.K)3 Cl2 : [Sb : (C12.M)2]2 Cl2 : Sb.Cl3.NH4 F2 : [Sb : (F2.M ■ A. 1. Bi 2. B. 2. Bi i(O.M)3 0 : [Bi : (O.M)2]2 0 : Bi.O.M S : [Bi : S2 : Pb]2 S : Bi.S.M Bi:(Cl2.NH4)3 Cl2:[Bi:(Cl2.M)2]2 Bi:(F2.K: F2 : Bi.F2.NH i M represents a univalent The numbers refer to the PROC. ROY. soc. EDIN. — YOL. xxv. — {To face page 731.) 1904-5.] Mr Cameron on the Constitution of Complex Salts. 731 complex halides with each other and with the “ double cyanides.” Weinland and Koppen * have shown that by the conception of the replacement of one atom of oxygen by two of fluorine, and by the comparison of the complex fluorides of bivalent metals with the aluminites and ferrites, perfectly consistent formulae can he assigned to the former, and Locke f has pointed out that “all the sesqui- oxides which form alums yield soluble double potassium cyanides.” But no one, so far as I have been able to ascertain, has recognised the great structural similarity in the constitution of all these complex salts ; no one has shown that to the derivatives of the sesquioxides, with few exceptions, can he ascribed definite con- stitutions on the basis of a few simple types ; and no one has pointed out the striking parallelism between the complex salts of various acids usually described as monobasic, and those derived from dibasic acids. The structural similarity referred to is best shown by the table on the opposite page. This table is by no means exhaustive either with regard to acids or to trivalent metals, but has been so chosen as to include most of the important series of compounds, and instances of every type. I have endeavoured to make it as complete as possible with regard to the acids and metals contained, and to give correct references to the chemists who have recently prepared and investigated these compounds. It is highly probable that once the necessary conditions have been found most of the vacant spaces in this table will be filled. A comparison of the chromium derivatives will best show the relationship between the different complex acid groups, while a glance at the complex chlorides, fluorides, and oxalates will best illustrate the close correspondence which exists between them. A few of the compounds included may be mentioned. Thus, in the first column are the hydroxides themselves, the chromites, ferrites, aluminites, arsenites, etc. ; in the second are found copper pyrites, and the thio-salts of arsenic, antimony, and bismuth ; the “ anhydrous alums ” form the complex sulphates of type B. 2. The formulae ascribed to the complex halides, cyanides, etc. may be best understood by considering the compounds of the * Zeit.fur anorg. Chem., 22, p. 275. t Amer. Chem. J., 20, p. 589. 732 Proceedings of Roy al Society of Edinburgh. [sess. saturated type. The derivatives of the dibasic acids have the general formula M3'M"'X3'', or M"' : (X".M')3, (where M'", M', are tri valent and univalent metals respectively, and X" is the radical of the dibasic acid). Those of the monobasic acids have the general formula M3'M'"X6' , which may be written m"' ; ([x'2].m')3 , when the analogy is at once seen. With regard to the question as to how these ‘univalent’ radicals are themselves united, Kohlschuttcr * has pointed out that if Blomstrand’s and Remsen’s views are correct, such com- pounds as FeClg , 3KC1 must be written C1.C1.K Fe^Cl.CLK X31.C1.K . This assumption of the single bond between the halogen atoms does not explain the constitution of such compounds as that pre- pared by Jones and Knight, f possessing the composition 3RH4Br , ZnBr2 , whereas, by the assumption of a double bond between these “univalent” radicals, concordant constitutions can be given to all their derivatives at present known, and the existence of such compounds as iodine trichloride IC13 agrees with this view. Whatever is true in this respect of one of the halogens is evidently true of all. This is shown especially by a reference to Christensen’s papers, J by the comparison of the complex halides of thallium, bismuth, etc., and finally by the existence of a series of compounds such as BiBr3, 3XH4C1. It will be noticed that the series of double halides belonging to the type A. 2 can equally well be represented by formulae half those used in the table, as for example F.Cr : (F2.K)2 . It is not impossible that these compounds may be found capable of existing in both conditions, but I have chosen the double formulae in order to bring out more strikingly the relation between them and those derived from dibasic acids. * Ber, , 35, p. 483. t Amer. Chem. J., 22, p. 136. t Loc. cit. 1904-5.] Mr Cameron on the Constitution of Complex Salts. 733 Apparently the metallic radical in these salts may he any univalent or bivalent metal, although in most cases the salts of potassium, sodium, and ammonium, or of but one of these, have been obtained. With tri valent metals simple salts such as Cr2(S04)3 , and a series such as AlFe(S04)3 , are obtained. The existence of such compounds as KSrCr(C204)3 would appear to show that the correct constitutions of these salts are (V ,so S04>,r 'SO. and S° A10O^Fe . The sesquioxide likewise should be written Cr^(ACr, XCr and not, as usually, 0 : Cr.O.Cr : 0 . From such considerations an alternative formula may be given for the anhydrous salts of type B. 2. Thus ; C204 :0-H H|C204 ^ g/c"6;Ih H-Of^Cr -> XC204-K k-c/v It is probable that in all cases where there is water of crystallisa- tion the hydroxyl formula is correct, and that treatment of the anhydrous salt with water results in the formation of the hydroxyl salt before solution is effected, so that the true constitution of such anhydrous salts cannot be readily ascertained. C204-KK-C204 Further application of the system of types already enumerated. There appears to be no reason to doubt that all dibasic acids can give rise to complex salts of the kind which have been discussed. In connection with the extension of this theory to monobasic acids, it is interesting to note the results of Jones and his collaborators,* in which they show conclusively by means of the conductivities of the respective solutions (as compared with those of the solutions of the separate constituents) that in the case of the alums, the “ double sulphates ” of the series M2'M"(S04)2 , 6H20 , the “ double chlorides, bromides, iodides, and cyanides,” * Amer. Chem. J ., 19, p. 83, 22, pp. 5 and 110, 23, p. 89, and 25, p. 349. 734 Proceedings of Royal Society of Edinburgh. [sess. complex ions exist in solution, whereas in the case of certain “double nitrates” there was little evidence to show the existence of such complex ions. Some such result might especially have been expected in the case of the alums, whose formula agrees with that of type B. 2 and may reasonably be expected to be some modification of it. Moreover, Recoura has shown* that the “anhydrous” alums belonging to that type can be obtained from the ordinary alums by the application of heat. The existence of complex ions in the salts of the monobasic acids, as shown by their conductivities, agrees perfectly with the constitutions which I have assigned to such salts. A similar series of compounds exists in the case of quadrivalent elements; and to illustrate this, a table including the complex chlorides, fluorides, sulphates, and oxalates of tin, thorium, titanium, and uranium, is appended.! Type A. has been again chosen to represent the “saturated” compounds, B. those in which one hydroxyl group remains un- replaced, and so on. 1 HC1 HF H2S04 h2c2o4 A. 1. 2. Sn ; (Cl2)4 : Pt Sn:(F2.NH4)4 Sn : (C204)4 • Ba2 C204:[Sn:(C204.K)3]2 Sn B. 2. Cl2 : Sn(Cl2.M)2 F2 : Sn : (F2.M)2 C. 1. (HO)2 : Sn : (C204.M)2 A. 1. Th:(Cl2)4:Pt Th;(S04.M)4 Th j (C204.Na)4 Th B. 2. Fo : Th : (F2.K)2 S04 : Th : (S04.M)2 C. 2. Cl3:Th.Cl2.K fs ! Th.F2.M Ti B. 2. Cl2:Ti :(C12.NH4)2 F2 : Ti : (F2.K)2 S04 : Ti : (S04.K)2 C. 1. (H0)2 : Ti : (S04.NH4)2 (H0)2:Ti:(C204.M)2 A. 1. u 2- U ; (S04.NH4)4 U ; (C204.M)4 C204:[U:(C204.K)3]2 B. 2. | S04 : U : (S04.K)2 C204 : U : (C204.M)2 | * Bull. Soc. Chim., iii., 9, p. 590. t For particulars of the compounds included in this table, see Rosenheim and others, Zeit. filr anorg. Chem. , 20, p. 308, 26, p. 239, and 35, p. 424 ; Pechard, Compt. Rend., 116, p. 1513 ; and Kohlschutter and Rossi, Ber., 34, pp. 1472 and 3619. 1904-5.] Mr Cameron on the Constitution of Complex Salts. 735 With bivalent metals type A. 1 is represented by such salts as the series M2'M"(S04)2 , 6H20 , and Hg : [(SClSr)2.M]2, and type A. 2 by K2Mn2(Cr04)3 , 4H20 , and K2Zn2F6 . Every normal or as belonging to the type A. 1 ; “ Double salts” as K.(CN)2.Ag and K.(F2).H afford examples of the corresponding derivatives with monobasic acids. I have already mentioned reasons for disbelief in the existence of definite chromoxalates such as K5NH4Cr2(C204)6 . Among compounds to which constitutions in accordance with the types cannot be given, are the aluminium oxalates prepared by Rosenheim and L. Cohn * having the constitution To explain the existence of these compounds the authors assume that in concentrated alkaline solution aluminium hydroxide can exist as Al2(OH)6 . Rosenheim and Bierbrauer f have prepared various antimonyl oxalates, which they consider to be double salts of the complex antimonyl oxalates with ammonium or potassium hydrogen oxalate. To some of these, however, formulae in accordance with the types can be assigned. Thus the compound 2(NH4)20, Sb203, 6C203, 6H20 may be written Finally, the amorphous “ sulphochromosulphates ” of Recoura | may be mentioned. These cannot be derived from the simple molecule Cr(OH)3 . acid salt of a dibasic acid with a univalent metal must be considered Compounds whose formulae, cannot be derived from the system of types enumerated. OH ,c2o4-nh4 * Zeit. filr anorg. Chew,.. 11, p. 184. X Bull. Soc. Chem. , iii. , 17, p. 934. f Ibid., 20, p. 303. 736 Proceedings of Royal Society of Edinburgh. [sess. The development of organic chemistry was the chief cause of the extension and wide application of constitutional formulae. To organic compounds perfectly definite formulas have always, as far as ’ possible, been assigned. The artificial distinction between organic and inorganic compounds, the slow death of the Berzelian method of formulae-writing, and the fallacious notion of “ double- salts,” perhaps give the explanation why wp to the present such definite constitutions have not in all cases been assigned to inorganic salts. By means of these definite formulae the chemist has been enabled to comprehend more thoroughly the nature of organic compounds, to predict the existence of new substances, and in many cases successfully to prepare them. Recent develop- ments have shown, not the too great rigidity of such formulae, but that they are not sufficiently exact. In this paper I have endeavoured to show the close connection between a certain class of organic compounds and a considerable number of inorganic salts, and how a definite constitution can be given to the latter. It seems possible, when due weight has been attached to the existence of isomorphous mixtures and solid solutions, and such substances have been removed from the list of definite compounds, that definite constitutions can be ascribed to all salts, organic and inorganic, and that the notion of molecular union can be finally ruled out. I have appended a list of references to the more important and recently prepared compounds in the table. Particulars of most of those for which no reference has been given can be obtained in works of reference. In conclusion, my thanks are especially due to Mr J. Kerr, B.Sc., under whose direction this investigation has been carried on; also to Dr Hugh Marshall, F.R.S., for many valuable suggestions. Chemical Laboratory, Surgeons’ Hall, Edinburgh. 1904-5.] Mr Cameron on the Constitution of Complex Salts: 737 REFERENCES. (1) Petersen, J. prakt. Chem., ii., 40, p. 44. (2) Brierley, J. Cliem. Soc., 49, p. 822. (3) Locke and Edwards, Amer. Chem. J., 20, p. 594. (4) Christensen, J. prakt. Chem., ii., 31, p. 163. (5) Christensen, J. prakt. Chem., ii., 35, pp. 57 and 161. (6) Wagner, Ber., 19, p. 896. (7) Wagner, Chem. Zeit., 12, p. 1726. (8) Weinland and Koppen, Zeit. anorg. Chem., 22, p. 266. (9) von Helmholt, Zeit. anorg. Chem., 3, p. 115. (10) Rosenheim and Cohn, Zeit. anorg. Cliem., 11, p. 175, and 28, p. 337. (11) Rosenheim and Koppel, Zeit. anorg. Chem., 17, p. 35. (12) Rosenheim and Bierbrauer, Zeit. anorg. Cliem., 20, p. 281. (13) Rosenheim and Cohn, Zeit. anorg. Chem., 27, p. 280. (14) Recoura, Compt. Rend., 114, p. 477, and 116, p. 1367. (15) Recoura, Compt. Rend., 120, p. 1335 (for basic hydroxide), and 137, pp. 118 and 189. (16) Klobb, Compt. Rend., 117, p. 311, and Bull. Soc. Chim., iii., 9, p. 663. (17) Lachaud and Lapierre, Compt. Rend., 114, p. 915. (18) Marshall, Proc. Roy. Soc. Ed in., 24, p. 305. (19) Marshall, J. Chem. Soc., 59, p. 760. (20) Kehrmann, Ber., 19, p. 3101, and 20, p. 1594. (21) Werner, J. Chem. Soc., 51, p. 383, and 53, p. 404. (22) Werner, J. Chem. Soc., 85, p. 1438. (23) Howe, J. Amer. Chem. Soc., 25, p. 444. (24) Lapraik, J. prakt. Chem., ii., 47, p. 319. ( Issued separately May 25, 1905.) PROC. ROY. SOC. EDIN. — VOL. XXV. 47 738 Proceedings of Royal Society of Edinburgh. [sess. A Report on the Medusae found in the Firth of Clyde (1901-1902). By Edward T. Browne, B.A., Zoological Research Laboratory, University College, London. Com- municated, by Sir John Murray, K.C.B., F.R.S. (MS. received April 26, 1905. Read June 5, 1905.) CONTENTS. PAGE Introduction . . . 739 List of Medusae previously recorded for the Clyde . . 740 Medusa and their Hydroids 741 Medusa; as “Inhabitants” of or “Visitors” to the Clyde . 742 Comparison of the Hydromedusa; of the Clyde with those found in Valencia Harbour and at Plymouth . . .743 The Scarceness of Hydromedusa; during 1901-2 in the Clyde 743 The Seasonal Changes in the Medusoid Fauna .... 744 Limit of the Area for the Investigations of 1902 . . . 745 The Surface Temperature of the Sea during 1902 . . . 746 The Shape and Mesh of the Tow-nets 747 HYDROMEDUSiE. Anthomedusa;. Leptomedusa:. Corymorpha nutans . . 748 Dipleurosoma typicum 761 Cytceandra areolata . 748 Irene pellucida 761 Ectopleura dumortieri . 748 Melicertidium odocostatum 762 Euphysa aurata . 749 Melicertum and Melicertidium , Gemmaria implexa . . 750 revision of species 764 Hippocrene pyramidata . . 751 Mitrocomella yolydiademata 767 Hybocodon prolifer . . 752 Obelia dichotoma (reared in a Ear sabellarum . 753 bell -jar) .... 769 Lizzia blondina . 753 Obelia lucifera 770 Margelis britannica . . 754 Obelia nigra . ' . 770 Margellium odopundatum . 755 Odorchis gegenbauri 771 Perigonimus . . 761 Phialidium buskianum . 771 Podocoryne carnea . . 755 Phialidium cymbaloideum 771 Sarsia eximia (reared in a bell-jar) 756 Phialidium temporarium 772 Sarsia gemmifera . . 75 7 Saphenia mirabilis . 773 Sarsia tubulosa . 758 Tiaropsis multicirrata 773 Thamnitis, nov. sp. ? . 758 Tiara pileata . . 760 SCYPHOMEDUSiE. Lucernaria guadricornis . . 774 j Aurelia aurita 775 Depastrum cyathiforme . . 774 Rhizostoma octopus . 776 Cyanea capillata . 775 1 References to Literature 776 Tables I., II. . • . . . . . . following 778 1904-5.] Report on Medusae found in Firth of Clyde. 739 Introduction. Records relating to the occurrence of medusae in the Firth of Clyde have not been numerous, though its waters have long been a noted resort for marine naturalists. Forbes, in his Monograph on the British Naked- eyed Medusae, states that he paid special attention to the medusae of the Clyde, and that those which he collected while on a yachting cruise in the autumn of 1839 were the foundation of his well-known monograph. Amongst those who have made additions to the list of species I may mention the names of Landsborough, Alder, Allman, Herdman, and two well- known foreigners, Claparede and Haeckel. In June 1902 Dr Clemens Hartlaub, of Heligoland, made a short stay at the Millport Biological Laboratory, solely for the purpose of collecting medusae, but the complete results of his labours have not yet been published. Early in the year of 1901 I arranged with Mr Alexander Gray, who was then the curator of the Biological Laboratory at Millport, but is now residing in New Zealand, to take for me a series of tow-nettings in the Firth of Clyde. The main object which I had in view was to become acquainted with the medusae of the Clyde before beginning work on the group at the Laboratory in the autumn. I* asked Mr Gray to take one or two tow-nettings every week, and to preserve the whole contents of the net in formalin. This series of tow-nettings was begun on 11th April, and was continued to 31st July. A second series of tow-nettings was taken during my stay at the Biological Laboratory from 17th September to 23rd October. Whilst at the station in 1901 I arranged with Mr Gray for a more extensive programme of work for 1902. He willingly agreed to take a tow-netting once a week from January to December, in order that the seasonal changes in the plankton might be observed. Just as in the previous year, the plankton was sent to me in formalin. After I had removed the medusae and noted the occurrence of some of the other animals (see pages 779-91), the bottles were sent to Dr Thomas Scott at Aberdeen, who had kindly undertaken the determination of the Crustacea. 740 Proceedings of Royal Society of Edinburgh. [sess. In 1902 I worked in the Laboratory from 5th September to 21st October. Without Mr Gray’s assistance the work could not have been undertaken. I wish here to express my sincere thanks to him for collecting the material, and for the kindness which he showed during my two visits to Millport. Medusa previously recorded for the Clyde. The following is a list of the medusae which have already been recorded for the Clyde. The names used in this report are enclosed within square brackets. H YDROMEDU SiE. ANTHOMEDUSE. Bougainvillia britannica (Forbes). Kyles of Bute. Forbes. Lamlash Bay. Hartlaub. Euphysa aurata, Forbes. Lamlash Bay. Herdman. Oceania octona, Fleming. Lamlash Bay. Forbes. Lizzia claparedei , Haeckel. Arran. Claparede. Sarsia pulchella , Forbes. Skelmorlie ; Rothesay. Allman. [. Margelis britannica. ] [. Euphysa aurata.] [Tiara pileata.] [Lizzia blondina.] [Sarsia tubulosa.] Leptomeduse. Stomobrachium octocostatum (Sars). Arran. Landsborougli . Bute. Forbes. Thaumantias quadrata , Forbes. Loch Fyne. Forbes. Thaumantias aeronautica, Forbes. Lamlash Bay. Herdman. [Melicertidium octocostatum. ] Phialidium cymbaloideum .] [Phialidium cymbaloideum.] 1904-5.] Report on Medusae found in Firth of Clyde. 741 Thaumantias octona, Forbes. [Phialidium cymbaloideum .] Tarbert, Loch Fyne. Forbes. Arran. Haeckel. Thaumantias thompsoni, Forbes. [ Phialidium temporarium. ] Lamlash Bay. Herdman. SC YPHOMEDU SJE. [Aurelia aurita. [Cyanea capillata. ] [Depastrum cyathiforme . Aurelia aurita , Linn. (In the “ Fauna of the Clyde.”) Cyanea capillata (Baster). Lamlash Bay. Herdman. Lucernaria cyathiformis, Sars. Arran. Landsborough. Russell. Cumbraes. Russell. Lucernaria fascicularis, Fleming. [Lucernaria quadricornis. Ardrossan. Alder. Rhizostoma pulmo. (In the “ Fauna of the Clyde.”) [Rhizostoma octopus. Medusae and their Hydroids. The medusae found in the Clyde include 17 species of Antho- medusae, 12 species of Leptomedusae, and 5 species of Scyphomedusae. There are altogether 30 species of Anthomedusae and Leptomedusae, belonging to about 25 genera, for which there should be a corresponding number of hydroid genera. There are 77 species of Hydroids given in the compiled list of Hydroida in the “Fauna of the Clyde.” Out of these only 10 species, belonging to 6 genera, are known to liberate medusae. At Plymouth the proportion of non-medusa-budding hydroids to medusa-budding hydroids is very nearly the same as that in the Clyde. It therefore follows that either many of the Antho- medusae and Leptomedusae have a direct development, or that many more hydroids have yet to be discovered. My own observations tend to show that the hydroids have yet to be found. 742 Proceedings of Royal Society of Edinburgh. [sess. The medusoid fauna of the Clyde is distinctly littoral, and the true oceanic medusae take no share in it. Not a single Tracho- medusa or Narcomedusa was seen. The littoral character of the fauna of this region is also well marked for other groups of animals. Medusa classed as “Inhabitants” or “Visitors.” The Clyde Sea-area covers about 1100 square miles, and is simply a large inlet of the sea. Within this large area one finds that a certain number of the pelagic animals may be regarded as “ local inhabitants ” which have been established there for countless generations. The wide opening of the firth to the North Channel, between Ireland and Scotland, gives facilities for other animals to enter its waters from the south, and these may be regarded as “ visitors.” In many cases the evidence is not sufficient to show definitely whether a species belongs to the local inhabitants or is a visitor from the south. There can he no doubt that the pelagic fauna of the Cumbraes is largely recruited by animals which come up the firth from the south, hut some of them may be the “local inhabitants” at the southern end of the firth. Until the fauna at the southern end has been examined on the same lines as those recorded in this report, it is impossible always to draw definite conclusions. I have attempted to separate the medusae into these two groups, and have placed a query against the species about which I am in doubt. (a) Inhabitants of the Clyde. Corymorpha nutans. Cytceandra areolata. Euphysa aurata. Hybocodon prolifer. Lar sabellarum. Margelis britannica. Margellium odopundatum. Podocoryne carnea. Sarsia eximia. Sarsia tubulosa. Thamnitis, sp. Tiara pileata. Melicertidium odocostatum. Obelia dichotoma. Obelia lucifera. Obelia nigra. Phialidium buskianum. Phialidium cymbaloideum. Phialidium temporarium. Tiaropsis multicirrata. Aurelia aurita. Cyanea capillata. 1904-5.] Report on Medusae found in Firth of Clyde. 743 (b) Visitors to the Clyde . Ectopleura dumortieri . (?) Gemmaria implexa. (?) Ilippocrene pyramidata. Lizzia blondina. Sarsia gemmifera. Irene pellucida. Mitrocomella polydiademata. Octorchis gegenbauri. Saphenia mirabilis. Rhizostoma octopus. Dipleurosoma typicum. Comparison of the Hydromedus^i of the Clyde with those found in Valencia Harbour and at Plymouth. All the Hydromedusse found in the Clyde have been taken in Valencia harbour, with the exception of the following species, — Sarsia eximia , Thamnitis, sp., Irene pellucida , Mitrocomella polydiademata. In Valencia harbour about 20 species of Hydromedusse have been taken, which have not yet been seen in the Clyde. All the Hydromedusse found in the Clyde have been taken at Plymouth, with the exception of the following species, — Ilippocrene pyramidata , Thamnitis , sp., Dipleurosoma typicum , Melicertidium octocostatum , Mitrocomella polydiademata. At Plymouth about 15 species occur which have not yet been seen in the Clyde. The Scarceness of Hydromedusse during 1901-1902 in the Clyde. The result of tow-netting during the eighteen months has brought together a fair list of species, but I wish to draw attention to the scarcity of the Hydromedusse during this period. For the six months of 1901 only three species are recorded (Table I.) as being abundant or very abundant ; namely, — Hybocodon prolifer, in Loch Eanza on May 8th. Obelia nigra , off Little Cumbrae on June 6th. Lizzia blondina , off Little Cumbrae and Millport on July 18th and 20th. 744 Proceedings of Royal Society of Edinburgh. [sess. During 1902 (Table II.) only two species were found to be abundant or very abundant ; namely, — Margellium odopundatum, on May 5th and 12th. Hybocodon prolifer, on May 5th. For comparison I must select Yalencia harbour, as it is the only place I know of wdiere continuous records on medusae have been kept for a whole year. In 1897, the following species of Hydromedusse were found in shoals or in great abundance : — Corymorpha nutans , May and June. Sarsia prolifer a, July. Dipleurosoma typicum , July and August. Euchilota pilosella, June. Obelia nigra, July and August. Phialidium cymbaloideum , March, May, June and July. Phialidium temporarium, May, September and October. Solmaris corona, July and September. In 1898, all the above species, except Sarsia prolifera, again occurred in vast quantities, and Laodice calcarata occurred in shoals in July and August. I can only account for the scarceness of the Hydromedusse by the scarcity of hydroids. Although the hydroids found in the Clyde make up a long list of species, yet I noticed (on my two visits), when out trawling in the “Mermaid,” and when looking at the material which was brought into the Laboratory, that hydroids were usually scarce. The Seasonal Changes in the Medusqid Fauna. As a rule in our seas during the winter months — December, January and February — medusse are very scarce. They begin to make their appearance about the middle of March. The time of their first appearance depends mainly upon the temperature of the sea, so that in one year they may be earlier than in another year. Certain species (belonging to Obelia and Phialidium), which occur early in the spring, will be found throughout the summer 1904-5.] Report on Medusae found in Firtli of Clyde. 745 and autumn. These come from hydroids which are constantly liberating medusae, and several generations occur during the year. A few species of the spring medusae are liberated from hydroids (Corymorpha, Hybocodon ) which have only one generation. These medusae are only present for about two months, and die off early in the summer, though at times a stray specimen may he seen in the autumn. Most of the medusae in our seas appear in the summer months — June, July and August. More species are found in July than in any other month of the year. In October medusae begin to die off, and practically disappear by the end of [November. The Tables I. and II. have been specially arranged to show the seasonal changes in the medusoid fauna of the Clyde. At Valencia, where the sea is a little warmer during the winter than in the Clyde, the medusae appear earlier in the year, and several species are present for a longer period. For instance, Lar sabellarum first appears in the Clyde in July, whereas at Valencia it appears in March, or even earlier. Limit of the Area for the Investigations of 1902. It was obvious to me, after the experience gained in 1901, that to include all the localities visited by the Laboratory steamer would only lead to confusion, as it would be necessary to take into consideration the physical conditions of those localities. As most of the tow-netting would have to be done close to the Laboratory and from a rowing boat, I fixed the limits so as to include all the tidal waters which flow past the two islands of Cumbrae. The northern boundary extended from Largs westward, across the northern end of Great Cumbrae, to Mount Stuart on Bute. The southern boundary extended from Portincross Castle to Gull Point, at the southern extremity of Little Cumbrae, and then across to Garrock Head, which is the southernmost point of Bute. The flood-tide which passes by the Cumbraes comes up the centre and the eastern side of the firth, and after passing the islands, flows up Loch Long, several small lochs, and the estuary of the river Clyde. The favourite place for tow-netting was in the main tideway, 746 Proceedings of Royal Society of Edinburgh. [sess. about half a mile off the Laboratory. There the channel is about 15 to 20 fathoms deep, and the flood-tide runs about 2 to 3 knots an hour. The strength of the tide was sufficient to keep the net well expanded and stretched out from the boat at anchor. So far as time and weather permitted, the tow-netting was done on the flood-tide, between half flood and high water. Although the tide runs fast, it alone is not sufficient to carry the pelagic animals up the firth from the south. The wind is the most important agent, for moving the plankton over long distances, and a secondary agent is the slow movement of water due to variation in tempera- ture and density. A shoal of Pelagia , to reach the Cumbraes after rounding the Mull of Cantyre, would have to travel at least forty-five miles, taking the nearest route ; or if the shoal were in the neighbour- hood of Ailsa Craig, it would have to travel about thirty-five miles on a straight course. With this distance to travel, the chances of going into the wrong direction or being drifted back again are great, so one must not expect to see many oceanic species in the neighbourhood of the Cumbraes. The surface temperature of the sea and the nets used are recorded in the “Notes on the Pelagic Fauna,” pages 781-82. The Surface Temperature of the Sea during 1902. The temperature of the sea was taken at the surface whilst the tow-net was down, and the readings of the thermometer are given in the “Notes on the Pelagic Fauna,” p. 781. The lowest reading was on 19th February, when the temperature went down to 41-6° F., and the highest reading, 56° F., occurred on 23rd July and 25 th August. The surface of the sea was coldest in February, and it did not rise above 45° F. until the middle of April. Then there was a quick rise to 47° F., where it remained until early in June. About the middle of June the temperature reached 50° F., and within a week it quickly rose to 53-54° F. During July, August and September it oscillated between 53° and 56° F. The fall in temperature began in October, when 52° F. was recorded, and 51° about the middle of November. Then, within a week, there was a 1904—5.] Report on Medusae found in Firth of Clyde. 747 sudden drop to 48° F., which was probably due to a long spell of cold easterly winds. During December the temperature was about 48° F. until the middle of the month, and it decreased to 45*3° F. by the 30th. After allowing for short spells of extreme cold and hot weather, the records tend to show that the winter temperature was about 44° F. and the summer about 54° F. There is an account of the physical conditions of the Clyde Sea- area by Dr EL R. Mill in the “Fauna of the Clyde,” and it contains tables showing salinity and sea temperatures in different parts of the Clyde. A table for 1887 shows that in the Arran basin (just south of the Cumbraes) the surface of the sea was coldest in February and March (42'9° F.), and warmest in August and September (55*2° F.). The Tow- nets. The tow-nets which were generally used during 1902 were similar in pattern and size to those used by me at Valencia. These nets have a circular mouth of 17 inches in diameter and are about 5 feet in length, gradually tapering down to 3J inches in diameter, which is the diameter of the zinc can attached to the end of the net. The nets were made of the usual Bolting silk, and the series consisted of four nets, having respectively 30, 50, 60, and 76 threads per inch. The net used for each haul is recorded in the “Notes on the Pelagic Fauna,” p. 781. It must be remembered that a net, after it has been used for some time, becomes much finer; as the threads flatten and fray out, the meshes become smaller. As a rule, we used a net which ought to catch any organism about 0‘5 mm. in diameter. For general use I recommend a net with about 60 threads to the inch. This net (of the size mentioned above) wrnrks best with a pull of about 3 lbs., measured on a spring-balance; or, when sitting in the stern of a rowing boat, the pull on the net should not exceed the holding strength of one finger. 748 Proceedings of Royal Society of Edinburgh. [sess. HYDRO MEDUSAE. Order — Anthomedus^. Corymorpha nutans, Sars. (Tables I. 11 ; II. 14.) Steenstrupia rubra , Forbes, 1848, p. 73, pi. xiii. Corymorpha nutans , Allman, 1872, p. 388, pi. xix. Browne, 1896, p. 463, pi. xvi. In 1901 and 1902, it appeared about the end of May, and dis- appeared about the middle of July. It was most plentiful during the early part of June, when both young and adult stages were present. At Plymouth and Valencia Island this medusa usually appears about the end of March or early in April, reaches maturity early in May, and disappears during the summer. The hydroid Corymorpha nutans has not yet been recorded for the Clyde. Cytseandra areolata, Haeckel. (Tables I. 5 ; II. 6.) Cytceandra areolata , Browne, 1898, p. 817, pi. xlviii. In 1901, a few specimens were taken during April and July. In 1902, it was taken from March to July. It was generally very scarce, but was more plentiful in May than in the other months. Young stages occurred in March and the beginning of April. Adults were present in May. Ectopleura dumortieri (van Beneden). (Table I. 27.) Edopleura dumortieri , Hincks, 1868, p. 124, pi. xxi. In 1901, a single specimen was taken on 15th October, and another on 18th October. Both were adult males. Description of the adult medusa : — The umbrella is somewhat conical, a little longer than broad, with an inverted margin and fairly thick walls. Upon the ex-umbrella there are eight longitudinal rows of nematocysts, extending from the basal bulbs of the tentacles (two rows from each bulb) to near the top of the umbrella. The nematocysts are more numerous in each row near the margin of the umbrella than near the 1904—5.] Report on Medusae found in Firth of Clyde. 749 top. The velum is moderately broad. The stomach is large, cylindrical in shape, having its base composed of a cellular tissue. The mouth is small, circular in shape, and its margin is lined with nematocysts. The length of the manubrium is about half to two-thirds the length of the cavity of the umbrella. There are four fairly broad radial canals and a circular canal. The gonad completely surrounds the stomach, forming a large swelling. The four tentacles are of equal length, one opposite each radial canal, and have transverse circular bands of nematocysts. The basal bulb of a tentacle is broad, somewhat triangular in shape, and is without an ocellus. Size. — Umbrella 3 mm. in length and 2*5 in width. Colour. — A dark brownish transverse band of pigment near the base of the stomach (conspicuous in one specimen, but very faint in the other). A circular band of dull carmine pigment just above the mouth. Basal bulbs of the tentacles of a dark brownish colour. There is only one species in the British seas. The medusa can be easily distinguished from a Sarsia by the presence of the eight longitudinal rows of nematocysts upon the ex-umbrella and by the absence of ocelli. The hydroid Ectopleura dumortieri (van Beneden) has not yet been recorded for the Clyde. Euphysa aurata, Forbes. (Tables I. 8 ; II. 12.) Euphysa aurata , Forbes, 1848, p. 71, pi xiii. In 1901, it was first seen near the end of May, but was absent during June. On 20th July it was common. Very scarce during September, and occasionally taken during October. Two specimens were taken on 16th November. In 1902, a large specimen with immature gonads was taken on 24th January. There can be but little doubt that this medusa was born in 1901. During February, March and April not a single specimen of Euphysa was seen. It was not until 15th May that Euphysa began to appear, and after this date it was usually present in the nets until 22nd October. From 11th June to 4th August it was fairly common, but was very scarce from the middle of August to nearly the end of October. Early stages occurred in June and July. Adults were taken during July, August and 750 Proceedings of Royal Society of Edinburgh. [sess. September. On 17th December a large adult specimen was taken, and its umbrella measured 5 mm. in length. Euphysa aurata has been taken in Lamlash Bay by Herdman (1880). Gemmaria implexa (Alder). (Table I. 7.) Zanclea implexa, Hincks, 1868, p. 59, pi. ix. fig. 3. Gemmaria implexa, Allman, 1872, p. 289, pi. vii. In 1901, single specimens were taken off Little Cumbrae on 24th and 28th May. This medusa, when liberated from its hy droid ( Gemmaria implexa), has two, opposite, tentacles, bearing peculiar nematocysts upon long stalks. I have taken at Port Erin and in Valencia harbour medusae which have all the characteristic features of Gemmaria implexa, but have four perradial tentacles instead of two, opposite, tentacles. As specimens were taken at the same time, some with two tentacles and some with four tentacles, the latter with ripe gonads, I have come to the conclusion that the medusa with four tentacles is the fully developed medusa of Gemmaria imjplexa. I do not think that they are distinct species, as they are similar in every detail except in the number of tentacles. I have also taken Gemmaria implexa with ripe gonads at the two-tentacle stage. But I have noticed in other genera of British medusae that the gonads frequently become fully developed and ripe before the medusa has reached its maximum growth. Gegenbaur (1856) established the genus Zanclea for Zanclea costata found at Messina, and this species has four tentacles. McCrady (1858) found at Charleston, U.S.A., a medusa somewhat similar to a Zanclea, but with only two opposite tentacles. He called it Zanclea gemmosa, but suggested the generic name of Gemmaria if it should, later on, prove to be a distinct genus. Allman (1872) regarded McCrady’s medusa not to be a species of the genus Zanclea of Gegenbaur, and therefore adopted the name Gemmaria. Hartlaub (1904) mentions the occurrence of a Zanclea with four tentacles in Lamlash Bay. Description of Gemmaria implexa with four tentacles taken at Port Erin on 22nd September 1900 : — The umbrella is somewhat globular in shape, about as broad as high, with fairly thin walls. Upon the top of the umbrella there is a 1904-5.] Report on Medusce found in Firth of Clyde. 751 broad dome-shaped mass of jelly. The velum is rather narrow. Upon the ex-umbrella there are four perradial channels, running from the basal bulbs of the tentacles to about half way up the umbrella ; the channels contain nematocysts. The stomach is upon a short peduncle, and the mouth is small and circular. Four radial canals. Upon each canal there is a slight linear swelling, occupying the central part of the canal and about one-third of its length. It is similar to the swelling found upon the radial canals of Dipurena halterata. There is no evidence at present that these swellings are immature gonads ; they are simply thickenings of the endoderm. The gonads surround the stomach, forming a large swelling, which is separated into four parts by perradial ridges. (The specimen is a female, and the large ripe ova project in a most conspicuous manner.) The four tentacles are uniform in size, and have along their outer side a double row of nematocysts, like those figured by Allman for Gemmaria implexa, with two tentacles. The basal bulbs of the tentacles are globular, and are without an ocellus. Colour. — Basal bulbs of the tentacles have a bright crimson centre, and along each tentacle extends a central orange line. Size. — Umbrella l-5 mm. in length and 1*75 mm. in width. Hippocrene pyramidata, Forbes and Goodsir. (Tables I. 20 ; II. 23.) Hippocrene pyramidata , Forbes and Goodsir, 1851, p. 312, pi. x. Margelis pyramidata, Browne, 1900, p. 709. In 1901, a single specimen was taken on 20th July and another on 2nd October. In 1902, a specimen was taken on 6th November. This is rather a rare species. It was first found by Forbes and Goodsir off Mull, and by Haeckel at Handa Island, on the west coast of Scotland. I have also taken a few specimens at Port Erin and in Valencia harbour. Description of the specimen taken at Millport on 2nd October 1901 : — The umbrella is semi-globular, about as high as broad, and very thick ; the upper half of the umbrella is a thick mass of jelly. The stomach is situated upon a short, broad, cone-shaped peduncle, 752 Proceedings of Royal Society of Edinburgh. [sess. and has four perradial lobes which extend along the whole of the peduncle. Mouth circular. There are four oral tentacles which are twice dichotomously branched. Four narrow radial canals. The gonads are along the basal margin of the stomach and its lobes. Four perradial marginal groups of tentacles, each group with four tentacles ; the compound basal bulbs are globular and very small. Ocelli black and situated upon the basal bulb, one opposite each tentacle. Colour. — Basal bulbs reddish-brown. Size. — Umbrella 2’25 mm. in length and 2’5 mm. in width. Hybocodon prolifer, L. Agassiz. (Tables I. 1 ; II. 9. ) Amphicodon amphipleurus, Haeckel, 1879, p. 37, taf. i. Hybocodon prolifer, Browne, 1806, p. 466. In 1901, it was found during April and May, and it disappeared about the middle of June. There was a great shoal of Hybocodon prolifer in Loch Ranza, Arran, on 8th May. The shoal chiefly consisted of fine large adult specimens having three tentacles. Most of them had actinulse inside the cavity of the umbrella, the ova having developed up to that stage without breaking away from the wall of the stomach. Free floating actinulse were also common in the tow-nek In 1902, Hybocodon first appeared on 3rd April, and was last seen on 11th June. It was most plentiful during May. There was a shoal in tideway off the Laboratory on 5th May. Specimens with actinulse were taken on 12th May. The hydroid Hybocodon prolifer has not yet been found in British waters. To judge from the abundance of the medusa and the presence of free-floating actinulse, the hydroid is almost certain to live in the Firth of Clyde, probably in the neighbourhood of Arran. I think that it is absolutely necessary to see the liberation of the medusse from the hydroid to make sure of its identification. At Port Erin in 1893 and 1894 the medusse of Hybocodon prolifer were very abundant, but in 1896 not a single specimen was seen. I made a special search after the hydroid when it should have been breeding, but failed to find it. 753 1904-5.] Report on Medusae found in Firth of Clyde. Lar sabellarum, Gosse. (Tables I. 18 ; II. 18.) Lar sabellarum , Hincks, 1872, p. 313, pi. xix. Willsia stellata, Forbes, 1848, p. 19, pi. i. Lar sabellarum , Browne, 1896, p. 468, pi. xvi. ; 1898, p. 818, figs. 1-9. In 1901, it was taken from the middle of July to the middle of November. Early and intermediate stages were fairly common at the end of July. At the end of September adults were present in the nets, and also a few early stages, but most of the specimens belonged to the third stage in development and had eighteen tentacles. In 1902, it first appeared about the middle of July, and dis- appeared in the middle of November. It was not so plentiful as in 1901. On 6th October the earliest stage with six tentacles and the adult stage with twenty-four tentacles were taken. Description of an abnormal specimen with two stomachs : — This specimen possessed two perfect stomachs. One stomach was in its proper position, but had only three lateral lobes instead of the normal six. The second stomach was on one of the radial canals, about half way down the sub-umbrella. Both stomachs were provided with mouths, each of which had seized an Oikopleura . There were six main radial canals (the normal number), two from each lobe of the central stomach. The specimen had reached the third stage in development, and had eighteen tentacles. This medusa is liberated from the hydroid Lar sabellarum . Lizzia blondina, Forbes. (Tables I. 12; II. 20.) Lizzia blondina , Forbes, 1848, p. 67, pi. xii. Browne, 1896, p. 475. In 1901, it first appeared at the beginning of June, and was last seen on 18th October. It was very abundant on 20th July; evidently a shoal had come up the firth. Specimens taken on 17th September belonged to the first stage in development. They had eight single tentacles, but a few specimens showed the commencement of the second tentacle in the perradial groups. Minute medusa-buds were present upon the stomach. PROC. ROY. SOC. EDIN. — VOL. XXV. 48 754 Proceedings of Royal Society of Edinburgh. [sess. In 1902, it was only taken on three occasions — two specimens on 11th July and a single specimen on 25th August and on 11th October. Lizzia claparedei , Haeckel, is regarded by me as a stage in the development of Lizzia blondina. It was taken by Claparede off Arran in 1859. Margelis britannica (Forbes). (Tables I. 13 ; II. 8.) Hipjpocrene britannica , Forbes, 1841, p. 82, pi. i. fig. 2. Bougainvillia britannica , Forbes, 1848, p. 62, pi. xii. fig. 1. Bougainvillia britannica , Allman, 1872, pi, ix. fig. 8. Bougainvillia bella, Hartlaub, 1897, p. 470, taf. xv.-xvi. In 1901, a large adult specimen was taken on 3rd June. In 1902, some very early stages were taken between 22nd March and 25th April, but I am not quite sure about the identification. On 11th July a large adult was taken. Description of the specimen taken on 3rd June 1901 : — Umbrella somewhat conical in shape and very thick, about 7 mm. in length and width. Stomach with perradial lobes. Oral tentacles contracted. Gonads (female) surrounding the lateral wall of the stomach, isolated perradially into four groups. Four perradial groups of tentacles, situated upon large compound U-shaped basal bulbs, each basal bulb with twenty-three to twenty-four tentacles. Basal bulbs situated in niches on the margin of the umbrella. Ocelli dark brown (in formalin), one at the base of every tentacle. Description of the specimen taken on lltli July 1902: — Umbrella somewhat conical in shape and very thick, about 7 mm. in length and 5 mm. in width. Stomach with four perradial lobes. Four oral tentacles, about four to five times dichotomously branched ; the terminal branches long and slender, ending with very small knobs containing nematocysts. Gonads (male) surrounding the lateral walls of the stomach, isolated perradially into four groups. Four perradial groups of tentacles, situated on large compound Y-shaped basal bulbs, each basal bulb with eighteen to twenty tentacles. Ocelli dark brownish to black, one at the base of every tentacle. In 1897, Hartlaub described Bougainvillia bella as anew species 1904-5.] Report on Medusae found in Firth of Clyde. 755 from Heligoland, but after his visit to Millport in 1902 he has stated (1904) that it is identical with Bougainvillia britannica of Forbes. Soon after Hartlaub described Bougainvillia bella I recognised that it was identical with Allman’s figure of Bougain- villia britannica , but was doubtful about its being identical with Bougainvillia britannica , Forbes (1848). Forbes, in his original description (1841), states that the ocelli are black, but in his monograph (1848) he states that they are red. At Port Erin in 1893 and 1894 I found some young Margelis with red ocelli, and also some larger adult specimens with black ocelli. These specimens I described (1895) under the name of Margelis britannica (Forbes). After Hartlaub published his revision of the Bougainvillidse (1897), I revised my manuscripts on this genus and isolated the medusae with red ocelli under the name of Margelis britannica , Forbes (1848), and called the others Margelis bella. I have never again met with any specimens of a Margelis with red ocelli, and now think that the red colour may be reasonably regarded as a variation from the normal black. Margellium octopunctatum (Sars). (Tables I. 3 ; II. 2.) Lizzia odopunctata , Forbes, 1848, p. 64, pi. xii. Margellium octopunctatum , Browne, 1896, p. 479. In 1901, it was taken in April, May and July. It was generally very scarce, except on 8th May, when ten specimens were seen. In 1902, it occurred in the nets from 19th February to 23rd July, but was absent during June. It was abundant during the first half of May. Specimens taken up to the end of April had medusa-buds upon the stomach. In May gonads were develop- ing round the stomach. In July either gonads or medusa-buds were present on the stomach, so that there was a mixture of adults and intermediate stages. Podocoryne carnea, Sars. (Tables I. 23; II. 4.) Podocoryne carnea , Hincks, 1868, p. 20, pi. v. Allman, 1872, p. 349, pi. xvi. In 1901, a single specimen was taken on 31st July. In 1902, it was occasionally seen from 11th March to 23rd April, and on 23rd July, when a single specimen was taken. 756 Proceedings of Royal Society of Edinburgh. [sess. This medusa is liberated from the hydroid Podocoryne carnea , which has not yet been recorded for the Clyde. As all the medusae belonged to very early stages, the hydroid is likely to be found there. Sarsia eximia, Allman, 1859. Sarsia eximia , Allman, 1872, p. 282, pi. v. On 17th September 1902, I found a colony of Syncoryne eximia attached to the wooden piles of Keppel pier. This colony was about 30 mm. in height and had a bush-like appearance, with the stems irregularly branched. As medusa-buds were present upon the hydranths, the colony was placed in a bell-jar in which was working my plunger apparatus. It soon began liberating medusae, and the supply was so plentiful that I had occasionally to preserve a few dozen young medusae to prevent overcrowding. The bell- jar was kept well supplied with copepods, upon which the hydroid and its medusae fed and flourished. The colony was suspended by a thread in the bell-jar, and some of its branches just touched the side of the glass. At first it made very little growth, and it was not until gemmation ceased that growth really began, then it proceeded at a rapid rate. The branches which touched the glass attached themselves to the glass and became stolons. These stolons grew very quickly and ran almost straight along the surface of the glass. From the main stolons numerous lateral stolons grew out, usually at right angles, and upon them the hydranths developed. The hydranths when first formed were usually sessile, but soon a stem was developed. Later on, hydranths began to appear upon the sides of the stems. At first these were sessile, but soon a stem developed, and thus the original stem became branched. The branching of the stems was only a small part in the growth of the colony, as the branches were short and few in number. The great growdh of the colony was by means of stolons bearing isolated and single hydranths upon short stems. A change of habitat produced a change in the form of the colony. The original colony was like a little bush, whereas the new growth in the bell-jar was distinctly a creeping form of growth. This shows that it is not safe to base specific characters upon the exact shape and form of a colony. 1904-5.] Report on Medusae found in Firth of Clyde. 757 The medusae on liberation resembled Allman’s figure, and they reached the adult stage in about seven to ten days. Description of the adult : — The umbrella is somewhat oval in shape, a little longer than broad and moderately thick. Velum very broad. The stomach is cylindrical in shape, and is about as long as the cavity of the umbrella, but does not extend beyond the velum. The mouth is circular. Four radial canals. The gonad forms a swelling round the whole stomach, extending from its base nearly to the mouth. Four tentacles, with circular clusters of nematocysts and an extra large terminal cluster. The basal bulbs of the tentacles are large, and oval in shape ; upon each one there is a large circular ocellus. Colour. — Stomach and basal bulbs reddish-brown. Ocelli black in the early stages, but crimson in the adult. Size. — Umbrella about 3 mm. in length and 2 mm. in width. Sarsia gemmifera, Forbes. (Table I. 21.) Sarsia gemmifera , Forbes, 1848, p. 57, pi. vii. In 1901, two specimens were taken on 22nd July. It suddenly became fairly common on 30th September, but was not seen after 2nd October. The sudden appearance and disappearance were probably due to a small shoal drifting up the Clyde from the south. In 1902, it was not seen. The specimens taken on 30th September had two to four medusa-buds upon the long manubrium. The largest bud was usually at the top of the series. After the medusoids are liberated a second series of buds is developed, and these are situated on the stalks of the first series. The young medusae at the time of their liberation have also buds just beginning to develop. All the specimens had a gonad surrounding the stomach, which is at the end of the long manubrium. No females were seen. The presence of a gonad on the stomach of Sarsia gemmifera and Sarsia prolif era indicates that these medusae have a hydroid stage in their life-histories, but up to the present the hydroids remain unknown. 758 Proceedings of Royal Society of Edinburgh. [sess. Sarsia tubulosa (Sars). (Table II. 10.) Oceania tubulosa , Sars, 1835, p. 25, pi. v. fig. 11. Sarsia macrorhyncha , Busch, 1851, p. 10, taf. iii. figs. 7-10; taf. iv. figs. 1-2. In 1902, it appeared at the beginning of April and disappeared at the end of June. Adults and also some early stages were taken at the end of April. Sarsia pulchella :, found by Allman at Rothesay, probably belongs to this species. Thamnitis, nova species 1 (Table I. 24.) Generic character. — Margelidse with branched oral tentacles and four single perradial tentacles. (Haeckel, 1879.) In 1901, two specimens of an early stage were taken, — one on 21st September' and the other on 8th October. Description of the specimen taken on 8th October : — The umbrella is bell-shaped, with thin walls ; the ex-umbrella has a few nematocysts scattered over its surface. Yelum very broad. The stomach is cone-shaped, with a quadrangular base, and is about half as long as the cavity of the umbrella. Four oral tentacles, which are fairly long and once dichotomously divided, and terminate with very small knobs containing nematocysts. The gonads have not yet begun to develop. Four perradial marginal tentacles, which are rather short and thin, and have cone-shaped basal bulbs. Ocelli are absent. Colour. — Stomach yellowish-brown. Basal bulbs of an orange colour. Size. — Umbrella about 1 mm. in length and width. The specimen is, without doubt, an early stage, as the gonads have not yet begun to develop. There is also an apical stalk, over the base of the stomach. This stalk is the rudimentary remains of the canal by which the medusa was connected with its hydroid. It is frequently present in very early stages, but soon disappears by absorption. The medusa was placed in a plunger bell-jar, kept there for six days, and then preserved. During the six days the oral tentacles developed another branch. Description of the specimen taken on 21st September : — 1904—5.] Report on Medusae found in Firtli of Clyde. 759 The stomach is cone-shaped. Four oral tentacles, which are two to three times dichotomously branched. Four radial canals. The gonads have not yet begun to develop. Four perradial marginal tentacles with large basal bulbs. Ocelli absent. Colour. — By transmitted light, stomach bright yellowish-brown. The lower half of the basal bulbs bright yellow, the upper half (embedded in the jelly of the umbrella margin) yellowish-brown. By reflected light, stomach and basal bulbs bright orange. Size, — Umbrella about 1*5 mm. in length. (This specimen was taken with its umbrella turned inside out.) The genus Thctmnitis was established by Haeckel (1879), and the type species is Thamnitis tetrella , Haeckel, which was found on the coast of Brazil. There is no figure published of the type species, and its description is rather brief. In this genus Haeckel has placed Bougainvillia nigritella, Forbes (1848). This species is not a Thamnitis , but belongs to the genus Margelis , and its hydroid is probably a Bougainvillia. The medusae, which belong to the genus Margelis , begin their free-swimming life on liberation from their hydroid, with four perradial groups of tentacles. In each group there are two tentacles, and a further increase in number takes place as the medusa grows larger and older. The basal bulb of a Margelis is a compound bulb, from which spring two or more tentacles. In the Millport Thamnitis there is only a single tentacle in each perradius, and it is situated in the centre of a large conspicuous bulb. All the British species of Margelis have coloured ocelli, which are situated either on the extreme margin of the compound bulb or on the base of a tentacle. The number of ocelli corresponds with the number of tentacles. The Millport T'hamnitis has not an ocellus (the specimens were examined alive). The presence of single perradial tentacles and the absence of ocelli indicate that it is not a young Margelis. Judging from the appearance of the basal bulbs, I do not think that any more tentacles are likely to develop. These specimens, in general appearance, are not like a young Margelis , so that I do not consider it to be a case of numerical variation. They are certainly early stages, and at present there is no clue to the adult form. Before describing these 760 Proceedings of Royal Society of Edinburgh. [sess. specimens as a new species I should like to see another specimen with gonads, so I shall leave the specific name in abeyance. When a Margelis is just taken out of a tow-net it usually has its tentacles more or less contracted. Occasionally a specimen is found with all its tentacles rigidly contracted, forming mere stumps or lobes round the margin of the compound basal bulb. When a specimen in this condition is placed in a glass of sea water, the tentacles, within a few hours, begin to expand, and nearly always those at the corners of the basal bulbs are the first to expand. At this stage the medusa may have one or two tentacles expanded on each of the four bulbs. Now Forbes’s figure of Bougainvillia nigritella (Monograph, pi. xiii. fig. 2) shows basal bulbs with only one tentacle, and the tentacle is not in the middle of the bulb, but at one end. In the description of the species Forbes says, — “It (the umbrella) is contracted at its opening, which is quadrangular, each angle bearing a compact, oblong, or almost kidney-shaped mass of tentacular bulbs, apparently four in number, closely united together, so that, but for the indications of lobations at the lower part of the pad, the number of these bodies would be indeterminable. On one side of each pad arises a very short, thick, yellow tentacle, and only one.” It is clear from Forbes’s description that he was describing a Margelis which had four out of five tentacles in a state of contraction, though the figure itself (like many other figures in that monograph) is not so clear and defined as the text. It was an error on the, part of Haeckel to place this species in the genus Thamnitis. Tiara pileata (Forskal). (Tables I. 16 ; II. 19.) Tiara yileata, Haeckel, 1879, p. 58, taf. iii. In 1901, it first appeared about the middle of July and dis- appeared about the middle of October. It was fairly common in Lamlash Bay on 14th September. In 1902, it was taken from the middle of July till the beginning of October. Within the Cumbrae area it was very scarce ; only five specimens were taken. On 9th September a few specimens were taken in Lamlash Bay, and on 11th September it was fairly common in Etterick Bay, on the west side of Bute. All the specimens taken in 1901 and 1902 belonged to early 1904-5.] Report on Medusae found in Firtli of Clyde. 761 and intermediate stages. No full-grown adults were seen. About twenty specimens were collected in Lamlash and Etterick Bays. Nearly half of these had a cone-shaped crown on the top of the ■umbrella, variable in shape, either pointed or rounded at the apex. The remainder had a globose crown, which varied, greatly in size. The specimens also showed variation in colour, being either pale yellowish-brown, or pale brown, or reddish-brown. This medusa is liberated from a Perigonimus, probably the species commonly called Perigonimus repens , and starts its free- swimming life with two tentacles, many more developing as the medusa grows. Most of the specimens in the Clyde had four to eight tentacles, and a few had twelve tentacles. A fully-grown adult has about forty tentacles. The hydroid Perigonimus repens has been found in the Clyde, off the west coast of Arran. The following species, -which have been described and figured in Forbes’s monograph, are regarded by me as stages in the life- history of Tiara pileata. Oceania turrita , Forbes, p. 28, pi. ii. fig 2. Four tentacles. Oceania octona (Fleming), Forbes, p. 27, pi. ii. fig 3. Eight tentacles. Oceania episcopalis , Forbes, p. 27, pi. ii. fig. 1. Twelve tentacles. Order — LEPTOMEDUSiE. Dipleurosoma typicum, Boeck. (Tables I. 14; II. 16.) Dipleurosoma typicum , Browne, 1898, p. 826, pi. xlviii. In 1901, it was first seen on 5th June and disappeared after :20th July. Only a few specimens taken. In 1902, a specimen was taken on 11th June, and another on 18th June. Two were taken on 15th July. This species is at times very abundant in Valencia harbour. Irene pellucida (Will). (Table I. 26.) Geryonia pellucida , Will, 1844. Irene pellucida, Claus, 1881, p. 102, taf. iii. figs. 21-30. In 1901, a single specimen was taken on 30th September. 762 Proceedings of Royal Society of Edinburgh. [sess. Description : — The umbrella is somewhat conical, with a rounded summit, the upper half a thick mass of jelly ; its cavity is very small. The velum is narrow. The stomach is upon a funnel-shaped peduncle. The base of the peduncle is 5 mm. in diameter, and tapers off to about 1 mm. ; its length is about 4 mm. The stomach projects a little way beyond the margin of the umbrella ; it is small, and has four perradial lobes. The mouth has four lips and its margin is slightly folded. Four narrow radial canals. The gonads are linear, and are situated upon the outer two-thirds of the radial canals upon the sub-umbrella, but do not quite extend to the circular canal. Upon the margin of the umbrella there are altogether sixty tentacles and bulbs ; their number in the respective quadrants being 12, 16, 17, 15. The tentacles are very much contracted, and it is difficult to make sure whether some of the smaller bulbs have tentacles or not, but half the bulbs certainly have tentacles. The perradial, interradial, and adradial tentacles are much larger than the others, which vary very much in size. Some of the bulbs have excretory pores on their inner side, just above the velum. Probably all of them have excretory pores, but owing to contraction the papillae are not visible. Marginal cirri absent. There are forty-nine marginal sensory vesicles, their number in the respective quadrants being 11, 11, 13, 14. Each vesicle has usually two otoliths ; a few (the smallest in size) have one otolith, and three were seen with three otoliths. Colour. — Stomach and bulbs pale brownish. By transmitted light, yellowish. Size. — Umbrella 7 mm. in length and 10 mm. in width. Melicertidium octocostatum (Sars). (Tables I. 10; II. 15.) Stomobrachium octocostatum , Forbes, 1848, p. 30, pi. iv. In 1901, a specimen was taken on 28th May and another on 6th June. In 1902, it was first taken on 20th May, and last seen on 11th October. The specimens taken in May were adults. In July young stages and also adults were seen. It was generally very scarce. On 9th September two specimens were taken in Lamlash Bay. In August 1897, this medusa was abundant in Lamlash Bay. 1904-5.] Report on Medusae found in Firth of Clyde. 763 Many fine adults were collected by Messrs Jenkinson and Montagu, and examined by me. It was first found in Lamlash Bay by David Landsborough (1847). Forbes found this species abundant in the Kyles of Bute during July 1839. I expected to find the earliest stage of the medusa in the Clyde during 1902, but my expectations wrere not realised. Description of the smallest specimen : — The umbrella measures 2 m5 mm. in length and width. The gonads are just beginning to appear, and they extend over the proximal half of the radial canals. There are about twenty large tentacles. The tentacles opposite the eight radial canals are slightly larger than the others, indicating that the medusa probably begins its free-swimming life with only eight tentacles. There is a minute tentacle between every two large tentacles. Description of an intermediate stage : — Umbrella about 3‘5 mm. in length and 4 mm. in width. The gonads extend over the central third of the radial canals, forming two narrow bands along each side of every canal. About forty large tentacles and forty minute tentacles, alternating with one another. Description of the adult : — Umbrella somewhat cone-shaped, with a thick mass of jelly above the stomach. Yelum narrow. The stomach is octagonal, as broad as the top of the cavity of the umbrella (it is occasionally on a short broad peduncle), but only extending down about one-quarter the length of the cavity of the umbrella. The margin of the mouth has eight lips and some small folds. Eight radial canals, which are large and project outwards from the wall of the sub-umbrella. The gonads extend over the outer two-thirds of the radial canals, reaching down to the velum, and are sinuous. About sixty-four large tentacles, with laterally compressed basal bulbs, and sixty-four small colourless tentacles, which alternate with the large ones. Colour.- — Yellowish-brown or yellowish gonads, stomach, and basal bulbs of the large tentacles. Size. — Umbrella 11 mm. in length and width. The largest specimen collected by Jenkinson and Montagu in Lamlash Bay was 13 mm. in length and 10 mm. in width. 764 Proceedings of Royal Society of Edinburgh. [sess. On the surface of the sub-umbrella there are a number of fine lines (about three to five between every two radial canals) which extend from the stomach to the margin of the umbrella. Many of the lines bifurcate near the stomach, and also near the margin of the umbrella. Occasionally a line has two or three branches, and even a slight anastomosing with an adjacent line occurs. In large adult specimens lines were found which only proceeded a short distance from the margin of the umbrella towards the stomach. Romanes (1876) noticed these lines, and regarded them as longitudinal muscle-bands. Hartlaub (1894) states that they bear a resemblance to streaks of nematocysts. I also am inclined to the view that they are nematocyst-tracks. Romanes ( 1 87 6), in his description of Stomobrachium octocostatum found in Cromarty Firth, pointed out that his specimens were not quite like those described by Forbes, and he regarded them as a distinct variety. The tentacles are arranged in a double series ( i.e . long and short tentacles alternating with one another), and not in a single series as figured by Forbes. Now, Forbes has given his own figure, but the description is partly based upon Ehrenberg’s account of the species, and the alternating series of large and small tentacles is mentioned by Forbes on the authority of Ehrenberg. Forbes clearly states that he did not thoroughly examine his specimens, for he says, — “I have not met with (it) since my first season’s study of medusae in 1839, when, though I made a careful drawing of it, I did not examine its minute structure, trusting to meet with it again, as it seemed to be one of the most abundant of its tribe.” There can be no doubt that Forbes overlooked the small tentacles when drawing the specimen while on his yachting cruise. On the Genera Melicertum and Melicertidium. According to Haeckel’s classification, Oceania ( Stomobrachium ) octocostata , Sars, belongs not to the genus Melicertidium but to the genus Melicertum. The genus Melicerta was established by Peron (1809), and the spelling was changed to Melicertum by Oken (1815). One of the species in this genus was Medusa campanula 1904-5.] Report on Medusae found in Firth of Clyde. 765 of Fabricius (1780). It was not the type species of the genus Melicerta, but was considered so by Oken in 1835. Fabricius’s description of Medusa campanula is rather vague, and no figure is given. In the description there is no mention made of eight radial canals and eight gonads, but the description implies only four radial canals, and this was the view held by all the early writers. Lamarck (1817) transferred it to the genus Dianoea , and Lesson (1843) to the genus Campanella , and re-named the species C. fabricii. Up to that date the early authors had simply been dealing with the original description given by Fabricius, who found the medusa on the coast of Greenland, and they themselves had not seen a single specimen. In 1862, L. Agassiz called a medusa which he found at Grand Manan in the Bay of Fundy, Melicertum campanula , Peron. In 1865, A. Agassiz described and figured specimens found in Massachusetts Bay. This medusa has eight radial canals, and is very like the species first found by Sars. There is no evidence whatever that Agassiz’s medusa has any connection whatever with Fabricius’s medusa. Haeckel was also of this opinion, for he has placed Medusa campanula , Fabricius, as a doubtful synonym of Catablema campanula. Haeckel, however, has retained the genus Melicertum for Melicertum campanula of Agassiz, and he has defined the genus thus “ Melicertum , A. Agassiz, 1862. Thaumantidae with eight gonads on the course of eight radial canals. Numerous tentacles (sixteen or more). No marginal clubs or cirri.” Melicertum has really become a new genus, and with a new type species, M. campanula , A. Agassiz (non Fabricius). Haeckel (1879) introduced a new genus, Melicertidium , for Oceania octocostata , Sars, 1835, and defined the genus thus : — “ Thaumantidae with eight gonads on the course of eight radial canals. Numerous tentacles (sixteen or more). Between them numerous marginal clubs (or cirri). Haeckel himself had never seen a specimen of Melicertidium octocostatum , so that his description is based upon the work of other writers. He placed a wrong interpretation upon the figures given by Ehrenberg, and thought that the small tentacles figured by 766 Proceedings of Royal Society of Edinburgh. [sess. Ehrenberg, alternating between tbe large tentacles, were marginal clubs, similar to tbe marginal clubs (cordyli) found in Laodice. The manner in which Ehrenberg has figured tbe small tentacles makes them resemble cordyli in appearance. As Melicertidium octocodatum has no marginal clubs or cirri, the sole distinction which separates it from the genus Melicertum disappears. After due deliberation, I think it would be best to retain and amend the genus Melicertidium , and to do away with the genus Melicertum. To retain the latter genus would only lead to more confusion, as it is clear that Melicerta or Melicertum of Oken is not the same genus as Melicertum of Agassiz. It is really a new genus, with a new type species. I propose the following alteration : — Genus Melicertidium, Haeckel, 1879. Thaumantkhe, with eight gonads on the course of eight radial canals. Numerous tentacles. Species. — M. octocostatum (Sars), 1835. (The type species of the genus.) Distribution. — North Atlantic ; Europe. Northern limit; Norway, Bergen. Southern limit; England, Falmouth. M. campanula (A. Agassiz), 1865 (non Fabricius). Distribution. — North Atlantic ; North America. Northern limit; Bay of Fundy, Grand Manan. Southern limit ; Massachusetts Bay. M. georgicum (A. Agassiz), 1862. Distribution. — North Pacific ; British Columbia,, Gulf of Georgia. Note on Melicertum proboscifer, Maas, 1897, p. 19, taf. ii. figs. 5-7. I do not think that this medusa can be included in the genus Melicertidium , as it looks like a Trachomedusa, belonging to the genus Agliscra. It was collected on the “ Albatross ” Expedition in the Gulf of Panama. Maas considered it to be one of the Thaumantidse because he did not see any marginal sense-organs. The “ Albatross ” Collection was sent to Dr Mass for examination, so that he had only preserved specimens to work upon. 1904-5.] Report on Medusae found in Firth of Clyde. 767 I know from experience that sense-organs of Aglantha are not always to be found in preserved specimens. I remember spending several days searching for them on the margin of the umbrella of a large number of Aglantha preserved in formalin. It was necessary to find out whether there were four sense-organs or eight sense-organs for the purpose of determining the species. In many specimens the sense-organs were not to be seen ; in others one, in others two or three, and in others more were found. These sense-organs are minute ; and unless the specimens are very carefully preserved and in good condition at the time of preserva- tion, the chances of seeing the sense-organs are very small indeed. Melicertum proboscifer has its stomach on a long and con- spicuous peduncle ; the gonads are upon the eight radial canals on the sub-umbrella, and the tentacles (taf. ii. fig. 6), as shown in one octant of the umbrella, are quite characteristic of the Aglauridae I think that this species had better be transferred to the genus Agliscra. Mitrocomella polydiademata (Romanes). (Table II. 17.) Tiaropsis polydiademata , Romanes, 1878, vol. xii. p. 524; vol. xiii., pi. xv. fig. 3. Mitrocomella polydiadema , Haeckel, 1879. Browne, 1895, vol. ix. p. 279. In 1902, a specimen was taken on 27th June and another on 11th July. Description of the specimen taken on 11th July: — The umbrella is somewhat globular (the shape is partly due to the contracting inwards of the margin of the umbrella), with very thick walls; a little broader than high. Velum narrow. The stomach is small, with a quadrangular base. Four radial canals. The gonads are linear, extending over the outer half of the radial canals, and nearly touching the margin of the umbrella. Large ova are present along the whole length of the gonads. Tentacles thirty-six, which are long and slender, with cone-shaped basal bulbs. Between every two tentacles there are numerous cirri, about four to ten, the number depending upon the distance which the tentacles are apart. The cirri are very long and slender when fully expanded, and terminate in a small oval cluster of nemato- 768 Proceedings of Royal Society of Edinburgh. [sess. cysts. Sixteen large oval marginal sense-organs, containing many otoliths. The sense-organs are not closed vesicles, but open sacs. They are attached to the inner margin of the umbrella on their outer side and to the velum on their inner side. The opening is large and oval in shape, and is on the inner side of the velum, at its juncture with the umbrella. Colour. — Pale yellowish-brown for stomach, gonads, and basal bulbs (in formalin). Size. — Umbrella about 7 mm. in length and 10 mm. in width. Description of the specimen taken on 27th June : — The umbrella is watchglass-shaped, about twice as broad as high, with moderately thick walls. The umbrella is much thinner and flatter than in the one described above. The stomach is short and flat, with a quadrangular base. The mouth has four small lips. The gonads are linear, and extend over about three- quarters of the length of the radial canals, reaching almost to the margin of the umbrella. The ova are laterally situated upon the canals, and many are very large and ready for liberation. About forty-eight tentacles. Numerous cirri. Sixteen marginal sense- organs. Size. — Umbrella about 5 mm. in length and 10 mm. in width. Note on Mitrocomella fulva : — In my “ Report on some Medusae from Norway,” I described a new species of Mitrocomella called M. fulva. The specific characters are based partly upon a single specimen taken and examined alive at Plymouth in 1898, and partly on a single specimen in formalin from Byfjord, near Bergen. Both specimens are described, and the Norwegian one is figured. The intermediate stages of Mitrocomella polydiademata , which I saw alive at Port Erin (Isle of Man) in 1893 and 1894, had the mouth and basal bulbs of the tentacles of a purplish colour, and the gonads either yellowish-brown or purplish. Romanes de- scribed his specimens from Cromarty Firth with all the organs of a rich rose colour. The Plymouth specimen had yellowish- brown basal bulbs. When the specimens are once in alcohol or formalin the purple colour disappears, and a yellowish-brown colour is substituted for it, so that M. fulva is no longer distinguishable from M. polydiademata by its colour. After comparing the Millport specimens and some intermediate stages 1904-5.] Report on Medusae found in Firth of Clyde. 769 from Port Erin, which I have lately found in my collection, with the figures of M. fulva , I find that they agree so closely that they must he the same species. I think now that the Norwegian specimen must he regarded as an intermediate stage in the growth of M. polydiademata. With regard to the Plymouth specimen, I am still uncertain, and should like to see another specimen from the English Channel before coming to a decision. The geographical distribution of M. polydiademata is at present restricted to certain localities, where its hydroid no doubt lives. Romanes first found it in the Cromarty Firth, and states that it was somewhat rare. I found it at Port Erin in the spring of 1893 and 1894, and Chadwick recorded it for June and July in 1899. It has not yet been recorded for the west coast of Ireland. Obelia dichotoma (Linnaeus). Obelia dichotoma , Hincks, 1868, p. 156, pi. xxviii. fig. 1. On 17th September 1902, hydroid colonies of Obelia dichotoma were taken from the piles of Keppel pier and placed in a bell- jar for the purpose of rearing its medusa to the adult stage. As the colonies were loaded with gonophores containing medusa-buds, within three days the bell-jar became crowded with young medusae. About a hundred were transferred to another bell-jar in which was working the plunger apparatus. The young medusa on liberation from its hydroid has sixteen tentacles and eight sense-organs. It is quite colourless and is with- out gonads. On 26th September, I examined all the medusae in the bell-jar. The largest were about 2-2*25 mm. in diameter, and had sixty-four tentacles and ripe gonads. On 9th October, the largest specimen measured 2*5 in diameter and had eighty-four tentacles. A few specimens were kept in the bell-jar until 17th October, but they showed no further increase in the number of tentacles ; the gonads had decreased in size owing to the shedding of the ova. Description of the adult medusa reared in a bell-jar : — The umbrella is disc-shaped, being circular and almost flat. The stomach is very short and the mouth has four lips. Four radial canals. The gonads are very small, oval in shape, and are situated PROC. ROY. SOC. EDIN. — YOL. XXV. 49 770 Proceedings of Royal Society of Edinburgh. [sess. upon the radial canals, a little more than half way between the stomach and the circular canals, and are nearer to the margin of the umbrella than to the stomach. Tentacles sixty to eighty-four. Their basal bulbs are very small, and some contain yellowish-brown or brown pigment. The amount of pigment is very small and is not visible to the naked eye. The root of the tentacle, within the margin of the umbrella, is semi-globular or oblong, and is usually without a transverse septum, but occasionally has one. Eight adradial marginal sense-organs, with a single otolith, situated on the inner side of the basal bulbs. Colour. — Gonads and stomach yellowish-brown or brown. Size. — Umbrella up to 2*5 mm. diameter. The medusa Obelia lucifera has not yet been traced to its hydroid. Obelia nigra can at once be distinguished by the black or very dark brown pigment in some of the basal bulbs. What I have called Obdia lucifera no doubt includes Obelia dichotoma, and very likely another species (but not Obelia nigra). I have twice failed to rear the medusa of Obelia geniculata , and the failures were probably due to my not succeeding in finding out the proper food for the young medusae. Until all the British species of Obelia have been reared from their respective hydroids, I do not think that I can determine the adult medusae with certainty. Obelia lucifera (Forbes).. (Tables I. 17 ; II. 22.) Thaumantias lucifera , Forbes, 1848, p. 52, pi. x. In 1901, it was only taken between 26th June and 22nd July, and was fairly common on the later date. In 1902, it appeared on 30th September and disappeared on 15th November. Very scarce during October. Obelia nigra, Browne. (Tables I. 2; II. 5.) Obelia nigra , Browne, 1900, p. 721. In 1901, it appeared at the beginning of April and disappeared at the beginning of October. It was abundant off Little Cumhrae on 6th June. In 1902, it was taken from the middle of March up to the 1904-5.] Report on Medusae found in Firth of Clyde. 771 end of September. It never became abundant, and was only occasionally taken after the middle of June. Obelia nigra may be easily distinguished by the presence of dark brown or blackish bulbs at the base of the tentacles. Octorchis gegenbauri, Haeckel. (Tables I. 25 ; II. 24.) Octorchis gegenbauri , Haeckel, 1879, p. 171, taf. xiii. In 1901, a single specimen was taken on 30th September. In 1902, a single specimen was taken on 15th November. Description of the specimen taken on 30th September : — The stomach is on a long peduncle. The gonads are just beginning to develop upon the radial canals in about the middle of the peduncle, and also upon the radial canals on the sub- umbrella. Four perradial tentacles and many marginal bulbs, most of which have one cirrus, and a few have two cirri. Eight marginal sense-organs, each with three to five otoliths. Colour. — The gonads, tentacles, stomach, and marginal bulbs have a yellowish tinge in transmitted light. Size. — Umbrella 5 mm. in length and 8 mm. in width. This is a rather rare medusa on the British coast. Distribution : Cornwall and Devon, west coast of Ireland, Mediterranean. Phialidium buskianum (Gosse). (Table II. 21.) Thaumantias buskiana, Gosse, 1853, p. 385, pi. xxii. figs. 5-11. Phialidium buskianum , Browne, 1896, p. 448, pi. xvi. fig. 6. In 1902, it was fairly common at the end of September, and was occasionally taken during October. It was last seen on 15 th November. Phialidium cymbaloideum (van Beneden). (Tables I. 22 ; II. 13.) Phialidium cymbaloideum , Browne, 1896, p. 491, pi. xvii. In 1901, it was occasionally taken from 20th July to 15th Oct. In 1902, it was occasionally taken from 20th May to 11th Oct. This medusa is liberated from a hydroid belonging to the genus Campanulina. It is figured in Hincks’s monograph (pi. 38, fig. 1), 772 Proceedings of Royal Society of Edinburgh. [skss. and called Campanulina repens , but the colonies are more like those of Campanulina turrita in form. I first connected this medusa with its hydroid when working in the Marine Laboratory at Plymouth in 1899, and confirmed my observations at Millport in 1902. I found the hydroid growing on mussel shells and Laminaria roots attached to the piles of Keppel pier. It was placed in an aquarium and soon liberated a few^medusse. The medusa is a common British species and is often very abundant. It usually appears early in the spring and remains until late in the autumn. The following species described in Forbes’s monograph are probably stages in the life-history of Phialidium cymbaloideum. Thaumantias aeronautica , Forbes, p. 44, pi. ix. fig. 3. Four tentacles. The first stage in development. Lamlash Bay. Herdman (1880). Thaumantias quadrata , Forbes, p. 43, pi. ix. fig. 2. Four tentacles. This species was found by Forbes at Tarbet, Loch Fyne, in the autumn of 1845. Thaumantias octona , Forbes, p. 44, pi. viii. fig. 4. Eight tentacles. The second stage in development. It was found by Forbes at Tarbet, Loch Fyne, in 1845. Thaumantias maculata, Forbes, p. 44, pi. ix. fig. 4. Sixteen tentacles. The third stage in development. Thaumantias globosa , Forbes, p. 46, pi. x. fig. 4. Thirty-two tentacles. The fully-grown adult. Phialidium temporarium, Browne. (Tables I. 4 ; II. 1.) Phialidium temporarium , Browne, 1896, p. 489, pi. xvi. In 1901, it was taken from April till November. In 1902, it occurred throughout the whole year. During the early part of the year up to April only very early stages were seen. Adults were taken at the end of May. During the summer months, all stages in development, from the earliest to the adult, were present in the nets. In the autumn, adults were more numerous than the early and intermediate stages. The medusa is one of the commonest speeies on the British coasts. 1904-5.] Report on Medusae found in Firth of Clyde. 773 The following species described in Forbes’s monograph are probably stages in the development of Phialidium temporarium : — Tliaumantias thompsoni, Forbes, p. 49, pi. xi. fig 5. Sixteen tentacles. The third stage in development. Lamlash Bay, Herdman (1880). Thaumantias sarnica, Forbes, p. 48, pi. xi. fig. 4. Twenty tentacles. Thaumantias pileata , Forbes, p. 47, pi. xi. fig. 6. Twenty tentacles. Thaumantias inconspicua, Forbes, p, 52, pi. viii. fig. 3. Sixteen to twenty tentacles. Thaumantias p>unctata , Forbes, p. 53, pi. x. fig. 1. Thirty-two tentacles. Thaumantias lineata , Forbes, p. 48, pi. xi. fig. 1. Thirty-six tentacles. As Forbes has omitted in his descriptions and figures the marginal sense-organs, which are most important for the de- termination of the species, it is impossible to be absolutely certain about their identification. The six species given above were taken by Forbes in localities far apart, and this probably strengthened his view that they were distinct species, and prevented him from realising that they were only stages belonging to a single species. Saphenia mirabilis, Wright. (Table I. 19.) Saphenia mirabilis , Browne, 1896, p. 493, pi. xvii. In 1901, a single specimen was taken on 18th July and another on 20th July. This species is not uncommon during the summer months on the south coast of Devon and Cornwall, and is also often found on the west coast of Ireland. Tiaropsis multicirrata (Sars). (Table II. 7.) Tiaropsis multicirrata, Browne, 1900, p. 728. In 1902, a few early and intermediate stages were taken between 22nd March and 12th April. Description of the smallest specimen, about 1 mm. in length and width: — The umbrella is bell-shaped and has thin walls. Velum narrow. The stomach is very small, with a quadrangular base ; 774 Proceedings of Royal Society of Edinburgh. [sess. the mouth has four small lips. The gonads have not yet begun to develop. Twenty-four tentacles. As the basal bulbs of the perradial tentacles are much larger than the others, it is probable that the medusa on leaving its hydroid has four tentacles. The basal bulbs of the interradial tentacles are next in size. Eight adradial marginal sense-organs (the otoliths are not visible ; specimens in formalin), and at the base of each sense-organ, adjacent to the circular canal, there is a large, roundish, black ocellus. Description of the largest specimen, about 1 *5 mm. in length and 2*5 mm. in width : — The umbrella is bowl-shaped and has moderately thick walls. The stomach is short and flat, and the mouth has four small lips. The gonads are just beginning to appear along the central part of the four radial canals. The tentacles, about seventy, are closely packed together round the margin of the umbrella. The basal bulbs of the tentacles are spherical in shape, with a thick pad of nematocysts on the inner side. The tentacles are small and slender, covered with transverse circular bands of nematocysts. Eight adradial marginal sense- organs, each with a black ocellus at its base. SCYPHGMEDUSiE. Lucernaria quadricornis, 0. F. Muller, 1776. Lucernaria fasicularis , Johnston, 1847, p. 244, and p. 252, pi. xlv. figs. 3-6. Found by Joshua Alder at Ardrossan in 1846. (See Johnston, 1847, p. 252.) Depastrum cyathiforme (Sars), 1846. Lucernaria cyathiformis, Sars, 1846, p. 26, taf. iii. figs. 8-13. Lucernaria cyathiformis , Johnston, 1847, p. 475, fig. 86. Carduella cyathiformis , Allman, 1860, p. 125, pi. v. Depastrum cyathiforme , Russell, 1904, p. 62, pi. v. Depastrum was found by Landsborough in the south of Arran (see Johnston, 1847), and by Russell in the same locality in 1903. The latter also found it at Little Cumbrae and near Keppel pier. 775 1904-5.] Report on Medusae found in Firth of Clyde. Cyanea capillata (Linnaeus). (Table II. 11.) In 1901, adult specimens were frequently found washed ashore near the Laboratory during October. In 1902, on 5th September, a young Cyanea about 15 mm. in diameter, with tentacles just beginning to develop, was taken in the tideway off the Laboratory. Early in September I noticed several small shoals of Cyanea between Millport and Arran. During September many specimens were found stranded on the rocks near the Laboratory. Mr Gray informed me that Cyanea was very common and generally distributed in the Clyde area during the summer of 1902. Its abundance was particularly noticeable in July. Lamlash Bay, Herdman (1880). Aurelia aurita (Linnaeus). (Table II. 3.) In 1902, the Ephyra stage first appeared on 25th February, and was last seen on 3rd April. Only five specimens were taken. The following notes are based upon information received from Mr Gray : — Aurelia aurita was not so abundant in the Clyde during 1902 as in 1901. There was an absence of shoals, and usually only isolated specimens were seen. From the beginning to the middle of June Aurelia measuring 30-100 mm. were fairly common. Loch Riddan, up the Kyles of Bute, appears to be the head- quarters of Aurelia. The loch contained a shoal in 1901 and 1902. On 20th June 1902 thousands were seen in the loch, swimming about 1-2 fms. below the surface. On 21st September 1901 I visited Loch Riddan in the “Mermaid,” and used a trawl, but failed to catch a single Aurelia. The shoal which Mr Gray saw there earlier in the summer had evidently disappeared. Loch Riddan is very shallow, and its water was then very muddy and of a dark brownish colour, due to peaty water coming down from the mountains after heavy rains. The dirty appearance of the water reminded me of the river Tamar at Saltash, near Plymouth, which is a celebrated spot for Aurelia. Apparently Aurelia does not object to slightly brackish water, as there is at times a good deal of fresh water in the tidal water of the Tamar at Saltash. Lamlash, Herdman (1880). 776 Proceedings of Royal Society of Edinburgh. [sess. Rhizostoma octopus, Linnaeus. Rhizostoma cuvieri , Gosse, 1356, p. 37, pi. i. Pilema octopus, Haeckel, 1880. In 1901, on 30th September, a large specimen was seen swimming at the surface in the tideway off the Laboratory. On 31st October a perfect specimen was caught among the rocks on the coast of Little Cumbrae. The umbrella measured 30 cm. in diameter and 25 cm. in length. The arms projected 30 cm. beyond the margin of the umbrella. Rhizostoma pulmo is recorded in the “Fauna of the Clyde Area ” as being common. It is not stated who saw the specimens. Rhizostoma jpulmo is a Mediterranean species. University College, London, 10^ April 1905. REFERENCES. Agassiz, A., 1865, “North American Acalephae,” Illus. Catal. Mus. Comp. Zool. Harvard , No. 2, Cambridge, U.S.A. Allman, G. J., 1860, “On the Structure of Carduella cyathi- formisf Trans. Micro. Soc. London, vol. viii. pp. 125-128, pi. v. Allman, G. J., 1871-72, A Monograph on the Gymnoblastic or Tubularian Hydroids, Ray Soc., London. British Association, 1901, Fauna, Flora, and Geology of the Clyde Area, Glasgow. Browne, E. T., 1895, “Report on the Medusae of the Liverpool Marine Biological District,” Trans. Liverpool Biol. Soc., vol. ix. pp. 243-286. Reprinted in Fauna of Liverpool Bay, vol. v. Browne, E. T., 1896, “On British Hydroids and Medusae,” Proc. Zool. Soc., pp. 459-500, pis. xvi., xvii., London. Browne, E. T., 1898, “On British Medusae,” Proc. Zool. Soc., 1897, pp. 816-835, pis. xlviii., xlix. Browne, E. T., 1900, “The Fauna and Flora of Valencia Harbour, Ireland,” Report on the Medusae (1895-1898), Proc. R. Irish Acad., ser. 3, vol. v. pp. 694-763, pis. xx., xxi. 1904-5.] Report on Medusae found in Firth of Clyde. 777 Browne, E. T., 1903, “Report on some Medusse from Norway and Spitzbergen, ” Bergens Mus. Aarbog., 1903, No. 4, 36 pp., 5 pis. Busch, W., 1851, Beobacht. ueber Anatomie und Entwickelung einiger wirbellosen Seetlviere , Berlin. Claus, C., 1881, “Beitrage zur Kenntniss der Geryonopsiden- nnd Eucopiden-Entwickelung,” Arbeit. Zool. Instit., Wien, Bd. iv. pp. 89-120, taf. x.-xiii. Forbes, E., 1841, “Contributions to British Actinology,” Ann. Mag. Nat. Hist., vol. vii. pp. 81-85, pi. i. Forbes, E., 1848, A Monograph of the British Naked-eyed Medusae , Ray Soc. Forbes and Goodsir, 1851, “On some Remarkable Marine Invertebrates new to British Seas,” Trans. Boy. Soc. Edin., vol. xx. pp. 307-315, pis. x.-xi. Gosse, P. H., 1853, A Naturalist1 s Rambles on the Devonshire Coast , London. Gosse, P. H., 1856, Tenby : A Seaside Holiday, London. Haeckel, E., 1879-1880. Das System der Medusen, 2 vols., Jena. Hartlaub, C., 1897, “Die Hydromedusen Helgolands,” Wiss. Meeresunter , N. F., Bd. ii., Abt. Helgoland, pp. 449-536, 10 tafn. Hartlaub, C., 1904, “Bericht. liber eine zoologische Studien- reise nach Frankreich, Gross-Britannien, und Norwegen, ausge- fiihrt im Friihjahre 1902,” Wiss. Meeresunter, N. F.. Bd. v., Abt. Helgoland, pp. 97-106. Herdman, W. A., 1880, “On the Invertebrate Fauna of Lamlash Bay,” Proc. Roy. Phys. Soc. Edin., vol. v. pp. 193-219. Hincks, T., 1868, A History of the British Hy droid Zoophytes, Ray Soc. Hincks, T., 1872, “ On the Hydroid Lar sabellarum, Gosse, and its Reproduction,” Ann. Mag. Nat. Hist., ser. 4, vol. x. pp. 313-17, pi. xix. Johnston, G., 1847, A History of British Zoophytes, 2nd edit., London. Maas, O., 1897, “Die Medusen” (“Albatross” Expedition during 1891), Mem. Mus. Comp. Zool. Harvard, vol. xxiii. pp. 1-92, 15 pis. 778 Proceedings of Royal Society of Edinburgh, [sess. Marine Biological Assoc., 1904, “Plymouth Marine Inverte- brate Fauna,” Journ. Mar. Biol. Assoc., vol. vii. pp. 155-298. Romanes, G., 1876-77, “An Account of some New Species, Varieties, and Monstrous Forms of Medusae,” Journ. Linn. Soc., vol. xii. (Zool.) pp. 525-531, vol. xiii. pp. 190-194, pis. xv.-xvi., London. Russell, E. S., 1904, “ Notes on Depastrum cyathiforme,” Ann. Mag . Nat. Hist., ser. 7, vol. xiii. pp. 62-65, pi. v. Sars, M., 1835, Beskrivelser og lagttagelser, Bergen. Sars, M., 1846, Fauna litto ralis Norvegix, fasc. i., Christiania. Will, F., 1844, Horce tergestince , Leipzig. ( Issued separately July 5, 1905.) Off L. Cumbrae. July , anc 26 (1) 11 15 a3 a> "2 1» o 18 ) (5 (1) (1) (0 VI. Aban taken. 1 Off Keppel Pier. Tauls I. — Distribution of Medusie. 1901, April to July , and September to November. Firtli of Clyde. April. May. Jury IVLY SRPTEMBPR. October. Nov. nlis 90 22 94 30 1 3 8 11 17 99 j 94 28 29 3 5 3 15 1 25 90 11 13 18 20 22 29 31 17 21 24 95 30 » 2 * • 11- 15 18 19 21 93 16 23 No. _ 1 J s . SE o J 1 £ 1 £ 1 « s 5 I5 | l - z H | 1 | § 1 g J § 1m 1 § | O § ►4 1“ \l I .2 1 >4 o ja. 1 J. 3 « 3 m 1 1 s M 1 m . pr (S £ l S’ o E ! o ! 1 | o O 1 Ji s W o E i. a e 1 o E 1 5 | Off Keppel Pier. No. 2 3 Hybocodon prolifer IV. I. Date 1902. Se a-temperatur e , Surface. F. Depth of Tow- net. Fms. Duration of Haul. Minutes. Net. Threads per inch. Predominant Species. Remarks. June 11 49*5 3 10 60 Diatoms. Corymorpha nutans. Euphysa aurata. „ 18 49-8 3 15 60 Diatoms. Euphysa. „ 23 53-8 3 20 60 Calanus. Phialidium cymbaioideun. Sudden rise in temperature. ,, 27 54 3 20 30 Phialidiumtemporarium. Coarser net used. Cope- pods escaped. July 4 53 5 20 76 Very poor haul. „ 11 53 4 25 76 Euphysa. Oithona simi- lis. Oikopleura. Sagitta bipunctata. „ 15 55 6 30 76 Diatoms. Evadne nord- manni. Oikopleura. Sagitta. Euphysa. Diatoms (? Rhizolenia). Very thick. „ 23 56 4 20 76 Diatoms. Oikopleura. Lar sabellarum. Eu- physa. Diatoms very thick. „ 30 54-1 5 20 76 Diatoms. Paracalanus parvus. Acartia. Oithona. Diatoms very thick. Aug. 4 54-6 6 20 76 Diatoms. Cyphonautes. Oikopleura. Oithona. Euphysa. ,, 11 53 6 20 76 Diatoms. Fritillaria. „ 18 54 5 30 76 Cyphonautes. „ 25 56 5 30 76 Acartia. Oikopleura. Cyphonautes. Sea at its warmest. Sept. 1 55-6 6 20 76 Oikopleura. Oithona. Phialidium tempo- rarium. „ 8 54-7 10 30 76 Acartia. Pseudocalanus. „ 17 54 8 20 76 Ceratium tripos. Tide very strong. „ 19 10 30 76 Pseudocalanus. Acartia. Ceratium. „ 30 53 10 20 60 Acartia. Pseudocalanus. Oikopleura. Oct. 3 52 8 30 50 Oikopleura. „ 4 52 10 20 50 Acartia. Cyphonautes. Tide running about three knots. „ 6 2 60 50 Acartia. Pseudocalanus. „ 8 5 30 50 Oikopleura. Pseudo- calanus. ,» 11 10 20 50 Oikopleura. „ 16 4 30 50 Oikopleura. Pseudo- calanus. „ 17 5 30 50 Very poor haul. „ 22 52 5 30 60 Acartia. „ 30 52 5 20 60 Acartia. Pseudocalanus. Nov. 6 52 5 30 60 Sagitta. Oikopleura. Pseudocalanus. Acartia. „ 15 51-2 4 30 60 Sagitta. Oikopleura. Blowing hard from S.E.- S.W. for past four days. „ 20 48-1 4 20 60 Pseudocalanus. Cold east wind blowing for over a week. Decrease in surface temperature. „ 26 49-6 8 30 60 Pseudocalanus. Dec. 2 48-6 8 30 60 Pseudocalanus. Acartia. „ 9 46 8 25 60 Calanus. Pseudocalanus. Acartia. Fritillaria. Weather frosty. ,, 16 48-2 2 30 60 Pseudocalanus. Gales for past three days. Water very dirty. Keppel Pier. ,, 17 48-2 8 30 60 Pseudocalanus. Water very dirty. „ 23 8 30 60 Pseudocalanus. Acartia. Oithona. 1904-5.] The Pelagic Fauna of the Firth of Clyde. 783 stituent of the plankton during the winter and spring, were less conspicuous during the summer, owing to the appearance of other animals. They occurred, however, in nearly every haul of the tow-net, but Paracalanus occasionally took a long leave of absence. The three summer months — June, July and August — were the best and richest months for plankton in the Clyde. The characteristic feature of the summer was the vast quantity of Diatoms, which frequently became a nuisance, as they quickly clogged up the meshes of the tow-net, and thus reduced its catching capacity. Amongst the forms which occurred during the summer, I may specially mention Eupliysa aurata, Evadne nordmanni , and Cyphonautes towards the end of August. During the autumn months the predominant species were Pseudocalanus elongatus, Acartia clausi , Oikopleura dioica , and Sagitta bipunctata for a short period in November. COELENTEBA. Hydromedusae and Scyphomedusae. (See Keport by Browne on pages 738-778.) SlPHONOPHORA. Cupulita sarsii, Haeckel, 1888. Cupulita sarsii , Browne, 1900, p. 678. Two isolated nectocalyces were taken on 15th November 1902. They were probably the swimming bells of Cupulita sarsii. This siphonophore is common on the west coast of Ireland, and has also been occasionally taken in the Irish Sea. Anthozoa. Arachnactis bournei, Fowler, 1897, p. 805. A single specimen taken on 8th May 1901. This larval stage is not uncommon during the spring and summer at Plymouth 7 84 Proceedings of Royal Society of Edinburgh. [sess. and Valencia. It has also been recorded from St Andrews and the Isle of Man. Ctenophor^. Pleurobrachia pileus (Fabricius). Pleurobrachia pileus, Chun, 1898, p. 15. Pleurobrachia pileus, Vanhoffen, 1903, xi. p. 3, figs. 4-6. In 1901, Pleurobrachia was taken on 5th June. The largest specimen measured 12 mm. in length. During June and July it was very scarce. On 17th September young stages up to 5 mm. in length were taken, and up to the middle of October Pleurobrachia was always present off the Cumbraes, and often fairly common. The specimens taken did not exceed 10 mm. in length. On 21st October there was a sudden increase in quantity. A small shoal appeared, containing both very early stages and adults (up to 15 mm.). The shoal rapidly diminished, and Pleurobrachia became scarce towards the end of the month. Tow-nettings taken during the third week in November did not show the presence of any specimens. On 2 1st September young and intermediate stages were fairly common in the Kyles of Bute. In 1902, Pleurobrachia was seldom seen. It was first taken on 20th May. During June and July a few specimens (5-10 mm. in length) were obtained. It was absent during August and the first half of September. Towards the end of September young stages (3-4 mm.), and during October early and intermediate stages (2-6 mm.) were taken. It was only once seen in November (on the 16th), and not at all in December. From the middle of July to the end of the year only sixteen specimens were taken in the tow-nets, so that Pleurobrachia was much scarcer in 1902 than in 1901. There are apparently two generations in the year ; one during the spring and another during the autumn. Bolina infundibulum (Fabricius). Mnemia norvegica , Sars, 1835. Bolina hibernica, Patterson, 1838. 1904-5.] The Pelagic Fauna of the Firth of Clyde. 785 Beroe bilobata, Daly ell, 1848, ii. p. 254, pi. liv. Bolina norvegica, Vogt, 1888; Browne, 1900, p. 682. Bolina infundibulum , Chun, 1898; Vanhoffen, 1903, xi. p. 5, fig. 11. Aleinoe Smithii, Forbes and Goodsir, 1840, p. 86. In 1901, from 17th September to 23 rd October, Bolina was always present in the tow-nets. Usually a few were taken in every haul, but it was fairly common on 25th September. The specimens were mostly early stages from 1 mm. to 5 mm. in length, and a few intermediate stages up to 10 mm. In 1902, Bolina was first observed on 8th September, and last seen on 3rd October. Only four specimens were taken. Three early stages in September and intermediate stage (10 mm.) in October. Beroe cucumis (Fabricius). Beroe ovata, Browne, 1900, p. 684. Beroe cucumis , Vanhoffen, 1903, xi. 77, fig. 16. In 1901, from 17th September to 21st October, fourteen specimens were taken — usually one or two on each day the nets were used. The specimens measured from 4 mm. to 20 mm. in length. In 1902 not a single specimen was seen. ECHINODERMA. Auricularia. In 1901, Auricularia was first taken on 26th June, and was fairly common between 18th and 22nd July. In 1902, it was not seen. Bipinnaria. In 1901, Bipinnaria was first taken on 25th June. A few specimens were seen on 22nd and 29th July. In 1902 it was taken on the following dates: — 19th March, three specimens. 22nd March, one. 18th June, one. 4th July, one. 15th July, scarce. PROC. ROY. SOC. EDIN. — VOL. XXV. 50 786 Proceedings of Royal Society of Edinburgh. [sess. Pluteus. In 1901, it was first noticed in the tow-net on 30th April. A few were taken early in May, and towards the end of the month it became common. It was very scarce during June and up to the middle of July. It was abundant from 18th July to the end of the month. A few were seen on 18th August, and in the Kyles of Bute on 21st September. In 1902, Pluteus was scarce. It was first taken on 29th April, hut not seen during May. Only once taken in June, on the 18th, when it was very scarce. A few about the middle of July. Yery scarce early in August, and absent during September. One was taken on 3rd October, and another on 26th November. No attempt was made to identify the species of the larval Echinoderms. POLYCHAETA. Tomopteris onisciformis, Eschscholtz. In 1901, Tomopteris was first seen on 24th September, and again on 30th September. Specimens were taken on 1st, 2nd, 4th, and 19th October. Most were about 5 mm. in length, and none exceeded 10 mm. In 1902, specimens were taken on the following dates : — Jan. 24, July 15, Aug. 25, Sept. 30, Oct. 17, Nov. 6, Nov. 15, Dec. 23, One, 20 mm. in length. One, 5 mm. „ Two, 3 mm. ,, One, One, 5 mm. ,, Five, 5-10 mm. ,, Four, 3-12 mm. ,, One, 12 mm. ,, The rare occurrence of Tomopteris indicates that it is a “ visitor ” which comes up to Cumbrae from the south. I found at Valencia that large adult individuals were rather scarce during the early part of the year. Early stages became common about May. These increased rapidly in size during the summer months, and produced another generation in the autumn. 1904-5.] The Pelagic Fauna of the Firth of Clyde. 787 The early stages in the autumn were far more numerous than those in the spring, and occasionally occurred in shoals. The Free-swimming Larval Stages of Polych^tes. In 1902, larval stages were found in the tow-net from January till the beginning of May, and again from the end of October to the end of December. They were usually scarce, and never became even fairly common. Not many different kinds were seen, and most of them were not identified. Magelona papillicornis, F. Muller. The larval stage was seen on the following dates : — In 1901, eleven specimens were taken between 18th and 22nd July. In 1902, one specimen taken on 30th July. Mitraria. Korschelt and Heider, 1895, i. p. 276, fig. 124. Watson, 1901, p. 254, pi. xxv. fig. 17. In 1901, a specimen was taken in Millport Bay on 22nd July. This is the free-swimming larval stage of Owenia fusiformis. CELFTOGN ATH A. Sagitta bipunctata, Quoy et Gaimard. In 1901, Sagitta was very scarce from May till October. On 8th May two specimens were taken, and no more were seen until 30th September. It was found throughout October, but was always scarce. In 1902, Sagitta was taken throughout the year in every month from January to December. Up to the end of February only large adults (20-28 mm. in length) were seen. These, after breeding, began to die off during March and April, and had completely disappeared by May. 788 Proceedings of Royal Society of Edinburgh. [sess. About the beginning of March early stages (2 mm.) began to appear. These developed during the summer months, and reached maturity in September and October, when they produced an autumn generation. The breeding season apparently extends over about two months, as a mixture of early stages and large adults are usually found together. Sagitta was very scarce up to the end of June — usually only one or two specimens in the nets, and it was frequently absent. About the middle of July it became fairly common, but was scarce during August and September. In July the specimens taken were intermediate stages (5-10 mm.), and large adults were entirely absent. In September the specimens were about 10-15 mm. in length. At the beginning of October early stages began to make their appearance, and during that month large adults (20 mm.) and early stages (3-5 mm.) were present, hut they never became common. On 6th November Sagitta suddenly became abundant, and the increase in quantity was probably due to a fresh supply coming up the firth from the south. This shoal consisted of adults and intermediate stages. After the middle of November Sagitta be- came scarce, and continued scarce till the end of the year. In December only large specimens (15-20 mm.) were seen. The adults which are found in the spring of the year are larger than those which are found in the autumn. The spring race is about 20-28 mm. in length, and the autumn race is about 15-20 mm. CRUSTACEA. (See Report by Dr T. Scott, page 792.) POLYZOA. Cyphonautes. In 1902, Cyphonautes was taken from the beginning of August up to the end of December. It was common during August, abundant on 8th September, but scarce towards the end of the month. It was common on 4th October, but very scarce during 1904-5.] The Pelagic Fauna of the Firth of Clyde t 789 the latter half of the month. Fairly common during the first half of November, and then very scarce till the end of the year. Cyphonautes is the free-swimming larval stage of Membranipora pilosa. PHORONIDEA. Actinotrocha. In 1901, Actinotrocha was only seen between 13th and 22nd July. On 20th July twelve specimens were taken, and on the 22nd it was fairly common. In 1902, only two specimens were seen — one on 13th June and the other on 11th July. TUNICATA. Fritillaria furcata, Moss. .Fritillaria borealis , Lohmann, 1896, 1901, iii. p. 13, figs. 14-15. In 1901, it was fairly common about the middle of July, and a few specimens were taken about the middle of August. It was not seen during April, May, or June. In 1902, from January till the end of April Fritillaria was taken in the nets. As a rule it was scarce, but was fairly common on 24th January and common on 19th March. It was more abundant from January till March than Oikopleura. Specimens with gonads were taken early in February and also about the middle of March. It was not seen during May, June, or July. On 4th August a few specimens were taken, and on 11th August it was fairly common, but no specimens were seen towards the end of the month. On 1st September it was common, but was not seen again until 4th October, when only one specimen was taken. Solitary specimens were taken on 22nd and 30th October, and 15th, 20tli, and 26th November. On 2nd December it was very scarce, but fairly common on the 9th. A few specimens were taken on the 23rd. Fritillaria appears to be more common than Oikopleura during the winter months. 790 Proceedings of Royal Society of Edinburgh. [sess. Oikopleura dioica (Fol). ? Oikopleura flabellumr J. Muller. Oikopleura d,ioica , Lohmann, 1901, iii. p. 17, fig. 20. In 1901, during April it was fairly common, but became scarce in May. On 3rd June a shoal suddenly appeared. The shoal quickly decreased in number, and after the middle of June Oikopleura again became very scarce. During July it was fairly common. Records were not kept for the remaining months of the year. In 1902, it was taken in every month throughout the year.. During January, February, and March Oikopleura was always very scarce, and specimens were only occasionally taken. On 3rd April it suddenly became common, and was very abundant on 23rd April. It was common during May, but was decreasing in numbers towards the end of the month, and was very scarce throughout June. During June and July both young stages and small adults were taken. About the middle of July Oikopleura became common, and remained fairly common till early in August, when it began to decrease in numbers. On 25th August it again suddenly became abundant, and during the first week in September there was a dense shoal of large adults. They rapidly disappeared about the middle of the month, but there was an increase in numbers again towards the end of the month and in the early part of October. On 8th October there was another sudden increase in numbers, and large adults with gonads became very abundant. This shoal remained for about a week, and then quickly disappeared. Oikopleura was very scarce at the end of October. During the second week in November Oikopleura became common, when large adults with gonads were taken ; but again they soon disappeared, and there was a great scarcity towards the end of the month. Throughout December a few specimens, young stages and adults with gonads, were usually present in the nets. The most remarkable character about Oikopleura was the 1904-5.] The Pelagic Fauna of the Firth of Clyde. 791 appearance of shoals, followed by a scarcity. This occurred conspicuously in April, September, and October, and less so in July and November. The increase was not entirely due to young forms, for on two occasions (in September and October) only large adults were present. The appearance of the shoals is probably due to fresh shoals drifting up the firth. HEMICHORDATA. Tornarnia. In 1901, a few specimens were taken on 18th July. In 1902, it was not seen. REFERENCES. Browne, E. T., 1900, “The Fauna and Flora of Valencia Harbour, Ireland.” Notes on the Pelagic Fauna, 1895-1898, Proc. R. Irish Acad., ser. 3, vol. v. pp. 669-693. Chun, C., 1898, Die Ctenophoren der Plankton- Expedition. (“National.”) Dalyell, E., 1847-48, Rare and Remarkable Animals of Scotland, 2 vols., London. Forbes and Goodsir, 1840, “ On the Ciliograda of the British Seas,” Report, Brit. Assoc, for 1839, London. Fowler, G. H., 1897, “Contributions to our Knowledge of the Plankton of the Faeroe Channel,” No. III., Proc. Zool. Soc ., pp. 803-809, London. Haeckel, E., 1888, “ Siphonophora,” Challenger Reports. Korschelt and Heider, 1895, Text-book of the Embryology of Invertebrates. (English Translation.) Lohmann, H., 1896, Nordisches Plankton, III. Appendicularien, Kiel and Leipzig. Vanhoffen, E., 1903, Nordisches Plankton, XI. Ctenophoren. Watson, A. T., 1901, “On the Structure and Habits of the Polychseta of the Family Amnocharidee,” Jour. Linn. Soc., vol. xxviii. pp. 230-260, pis. xxiii.-xxv., London. (. Issued separately July 6. 1905.) 792 Proceedings of Royal Society of Edinburgh, [sess. 1904-5. A Report on the Free-Swimming Crustacea found in the Firth of Clyde, 1901 to 1902. By Thomas Scott, LL.D., F.L.S., etc. Communicated by Sir John Murray, K.C.B., F.R.S. (MS. received April 26, 1905. Read June 5, 1905.) Introduction. The material upon which this report is based was collected by Mr Alexander Gray, curator of the Biological Station at Millport. The tow-nettings were specially taken for Mr E. T. Browne, to aid his investigation of the Medusae of the Firth of Clyde. After the material was examined by Mr Browne, all the Crustacea were forwarded to me for identification. In 1902 most of the tow-nettings were taken off the Cumbrae Islands, within a limited area between the northern and southern extremities of the two islands. The temperature of the sea, the mesh of net, etc., are given in Mr Browne’s “Notes on the Pelagic Fauna” (pp. 781-782). Notes on the Crustacea mentioned in the Table for 1901. Table I. The collection examined in 1901 consisted of twenty-nine plankton samples. Seven of these samples were collected in April, ten in May, three in June, seven in July, one in August, and one in September. Moreover, seven were from the neigh- bourhood of Little Cumbrae ; one was collected off Largs and off Loch Ranza ; one in Lamlash Bay and in Inch Marnoch Sound, and also in Loch Striven and Loch Long ; all the others were from the vicinity of Greater Cumbrae. Seventeen species of the Crustacea observed in these samples belonged to the Copepoda, four to the Cladocera, and one each to the Isopoda and Amphipoda. Several groups of Crustacea were also represented in their larval or post-larval stages. Table I. — Distribution of Crustacea. 1901, April to September. Firth oj Clyde. Lamlash Bay. 2 I Near Marine Station. I Balloch Bay, M C umbrae. Loch Long. Near Marine Station. Off Lesser Cumbrae. ! 2 Near Marine Station. 2 Near Marine Station. Near Marine Station. Off Lesser Cumbrae. Near Marine Station. N ear Marine Station. Inchmarnoch Sound. 2§ Off Lesser Cumbrae. Off Lesser Cumbrae Lighthouse. §! Off Lesser Cumbrae. Off Tan Buoy, Cumbrae. Off Tan Buoy, Cumbrae. Off Cumbrae. oo Off Loch Ranza. Balloch Bay, Cumbrae. N ear Marine Station. Balloch Bay, Cumbrae. Near Marine Station . Loch Striven. Off Lesser Cumbrae. Off Largs. N ear Marine Station. N.W. ot Lesser Cumbrae. 'll ' 5s' W %-p' r- -C CS . WP3 ^ ? b 2? so ? £ S3 8 8 $ seS2 II §<1> II ■f%l I U-gs I fv® I gVc | s | Si'S M 3"®fi £3 > ®.r- O Hi =3 • l-l S o3 o< Sr8$ S e-8 - o <3 <3 V ►SiCi, K]CbCql>i o.„ HI IS « « o IWCO^IOOJ ^lMrjnCON vr = veryrare. r = rare. f=few. fr = frequent. c = common. ab = abundant. The figures show the actual number taken. 794 Proceedings of Royal Society of Edinburgh. [sess. Remarks on the Species. (1) The Copepoda. * Calanus helgolandicus , Claus. — The Calanus mentioned here is not the typical C. finmarchicus (Gunner), hut the form described by Claus, which G. 0. Sars considers to be specifically distinct. This form occurred in considerable numbers from the end of April to the first week in June, and also in September^ but was only sparingly represented in the samples collected in July and August ; indeed, in four of these samples this species appeared to be entirely absent. Paracalanus parvus (Claus) was observed in five of the samples, but only a few specimens were obtained ; these samples were all from the vicinity of the Marine Station. Pseudocalanus elongatus , Boeck. — This Calanoid, though not so plentiful as the Calanus , was observed in nearly the same number of samples, and appeared to have a somewhat similar seasonal distribution. Euchceta norvegica , Boeck, was only noticed in the sample from Loch Striven ; it is abundant in Loch Fyne, but usually near the bottom and in the deeper parts of the loch. Centropages hamatus , Lilljeborg. — This species occurred in all the samples examined, save two ; its seasonal distribution was somewhat similar to that of Calanus , being generally common or frequent from April till June, after which time it appeared to become scarcer. Temora longicornis (Muller), though sometimes occurring in considerable abundance, was only sparingly observed in the plankton samples under consideration, and its seasonal distri- bution appeared to be somewhat the reverse of that of the species already referred to. It was only noticed in four of the seventeen samples collected in April and May, and was only absent in three of the remaining twelve samples. Anomalocera Patersoni , Templeton. — This species occurred more or less sparingly in twelve of the samples collected during April, May, and June, but was absent in all the others. Parapontella brevicornis (Lubbock) was only noticed on four * The names and classification of Prof. G. 0. Sars’ great work on “The Crustacea of Norway ” are followed here. 1904-5.] Free-Swimming Crustacea of Firth of Clyde. 795 occasions — three times during April and once in May. Para pontella brevicornis, though occasionally found in the open sea, is more truly a littoral species. Acartia Clausi , Giesbrecht, was absent from only one of the samples examined in 1901 ; its seasonal distribution resembled that of Centropages hamatus , being more plentiful during April, and becoming subsequently rather scarcer. Oithona similis , Claus, was observed only once during April and May, but occurred more frequently during the following months, and is recorded as abundant in the sample collected on 31st July, in Balloch Bay. The following species were noticed only once or at most twice in the twenty-nine samples examined, and very few specimens at most were obtained. Cyclopina littoralis was only observed in the sample collected on 14th May. Dactylopusia tisboides in that collected on 5th June. Dactylopusia Stromi on 22nd May. Diosaccus tenuicornis was obtained in the two samples collected on 18th and 31st July. While Tigriopus fulvus , of which only one or two specimens were observed, occurred in the same sample with the Diosaccus. Another species, Harpacticus chelifer , closely allied to the one last mentioned, was observed in several of the samples collected during April and May, but only in one of those collected subsequently. These Copepods are all more or less demersal in their habits, and therefore, though sometimes common in gatherings from the bottom, they are not often present in plankton collections. (2) The Cladocera. This suborder of the Crustacea was represented in the collection for 1901 by Evadne Nordmanni, and by three species of Podou , viz., P. polyphemoides, P. intermedins, and P. Leuckarti. The Evadne occurred in most of the samples examined, but appeared to be rather more frequent in those collected after the end of May. Podon polyphemoides and P. intermedius were only noticed in the samples collected in July ; while P. Leuckarti , on the other hand, was present in all of those, save two that were collected during April, May, and June, but was absent in all the others; this seems 796 Proceedings of Royal Society of Edinburgh. [sess. to indicate a difference in the seasonal distribution of the species of Podon. (3) The Isopoda. Eurydice achata , Da Costa. — A single specimen of this Isopod was obtained in a plankton sample collected near the Marine Station on 24th April. This species, which is not uncommon in some parts of the Clyde estuary, is an active swimmer, and this may account to some extent for its absence in these gatherings. (4) The Amphipoda. G-ammarus locusta (Lin.) was the only Amphipod observed, and it occurred in three of the earlier gatherings ; it is a demersal species, and therefore its presence even in these three may have been accidental. (5) Larval and other Young Forms. Young Balani, especially in the Cypris stage, were moderately common in the samples collected in April, and they occurred, though only at intervals, up till the end of May, but after that time no more w'ere observed. Other young Crustacea, representing various groups, as the Brachyura, Macrura, Carida, Schizopoda, etc., were observed at more or less regular intervals throughout the summer, sometimes sparingly and at other times moderately common. They were present in all the samples collected from about the middle of May till the first week in June, but both before and after that time they were only occasionally observed. It will be observed, from the remarks on the various species and also from the table (Table I.), that four of the Copepods have a distribution more or less continuous throughout the six months during which the collection was made ; there is an apparent increase and decrease in the numbers of individuals captured belonging to each species, which may possibly be due to seasonal variation ; this variation is, however, rather more marked in one or two of the species whose distribution is not so continuous as those specially referred to, as, for example, in Temora longicornis. 1904-5.] Free- Swimming Crustacea of Firth of Clyde. 797 Most, if not all, of the species mentioned in Table I. appear to be “ residenters ” within the Clyde estuary, for, though they may disappear for a time, their appearance or disappearance may only be the result of periodic reproduction. Species are occasionally observed, sometimes in considerable numbers, the presence of which can only be explained by their having been transported thither by tidal or other currents. Notes on the Crustacea observed in the Plankton Samples collected during 1902. Table II. The Crustaceans observed in the plankton samples collected during 1902 comprised forty-nine species of Copepoda, four species of Cladocera, and two species of Ostracoda ; while the Amphipoda were represented by six species, the Isopoda by two, and the Sympoda by three; and also young forms belonging to the Decapoda, the Cirripedia, and various other groups. A few of the species were of frequent or common occurrence, but a large proportion of them occurred very sparingly; while several were observed only once, or at most only a few times, during the year. The number of samples examined for 1902 amounted to sixty-eight. In the following observations on the distribution of the various species, those belonging to the Copepoda, which are most numerously represented, will be noticed first, and the others in the order indicated above. Copepoda. An examination of the subjoined table (Table II.) shows, even more distinctly than the previous one (Table I.), that only certain species have a distribution more or less continuous throughout the year ; and of those, Calanus helgolandicus , Pseudocalanus elongatvs , and Acartia Clausi (Nos. 1, 3, and 17 on the table) are the most common. The Calanus was observed in each of these sixty-eight samples ; and on several occasions, from February till the end of June, it occurred in considerable abundance, but in the majority of the samples its numbers were more limited. Moreover, though it appeared to be scarcer in the samples collected in August 798 Proceedings of Royal Society of Edinburgh. [sess. than during the rest of the year, the difference was not very marked. The distribution of Pseudocalanus, on the other hand, showed a fairly distinct variation in the larger numbers obtained during the earlier and later months of the year than during those of summer. It occurred in considerable numbers from January till the end of March ; but after that the numbers became fewer, till about the beginning of* September, when there was again a per- ceptible increase that continued till December. The distribution of Acartia Clausi exhibited changes somewhat similar to those of the Pseudocalanus , but the changes were scarcely so well marked ; it also appeared to become proportionally more plentiful from the end of August till the beginning of October than at any other time during the year. Paracalanus parvus (No. 2 in the table). — This species was present in every sample from January till about the middle of April, but from that time till the beginning of July it was only observed once, and for the remainder of the year its appearance was more or less irregular. Centropages hamatus (No. 9). — This species, in curious contrast to the Paracalanus , was observed in none of the samples till about the middle of March ; but after that time it occurred, though at first very sparingly, in nearly every sample collected, till about the middle of November, when no more specimens were noticed. The distribution of Temora longicornis (No. 11) was somewhat similar to that of the Centropages. Like that species, it appeared to be entirely absent during the early part of the year. It was noticed for the first time in the sample collected on the 19th of March ; but thereafter it occurred at intervals, and for the most part very sparingly, till near the end of June it then occurred more regularly, though still in limited numbers, till the beginning of October, when it became more scarce and intermittent in its appearance. The only other species present more or less throughout the year was Oithona similis (No. 18), and its distribution was somewhat similar to that of Acartia , except that it was absent in nearly all the samples collected in April, and in half of those collected in May and June. 1904-5.] Free- Swimming Crustacea of Firth of Clyde. 799 Among the various Crustacean species observed in 1902, the seven just referred to were by far the most numerous, and con- stituted almost the whole of the contents of several of the gatherings in that year. The majority of the other species mentioned in the table are, for the most part, demersal in their habits, and this may explain to some extent their rare occurrence in the collections. Stephos Scotti, G. 0. Sars (No. 4), was only observed in a sample collected in January. It was at first ascribed to Stephos gyrans (Giesbrecht), but was afterwards shown to be a new species. S. Scotti, though not very common, appears to have a fairly wide distribution, and is one of the species found in Norway by Professor G. 0. Sars.* Undinopsis bradyi , G. 0. Sars (No. 5). — This species, which occurred on several occasions, may be found in the Clyde at nearly all seasons, though usually not very plentiful. It is a species that has had various names, i.e., Pseudocalanus armatus , Bradyidius armatus, and now Undinopsis bradyi. f Fuchceta norvegica (No. 6). — This species was observed in only one of the samples under consideration. It is abundant in the deep water of Upper Loch Fyne. Diaixus hibernicus (A. Scott), (No. 7), was noticed several times during the year. It is a deep-water species, and is moderately frequent in Upper Loch Fyne. It has been found in other parts of the British seas, and is also represented in the marine fauna of Norway.! Diaixus pygmceus (No. 8) is a smaller species than the last, and is also a moderately rare form. It has not yet been recorded outside of the British islands. Isias clavipes (No. 10) is also a comparatively rare species in the Clyde. It was only observed in one or two samples collected late in the autumn. Metridia lucens, Boeck (No. 12), though observed very sparingly in the present collections, is widely and generally distributed throughout the British seas. * Crustacea of Norway, by G. 0. Sars, vol. iv. p. 63, pi. xliii. (1903). t Op. cit., p. 32, pis. xix. and xx. + Op. cit., p. 59, pis. xxxix. and xl. 800 Proceedings of Royal Society of Edinburgh. [sess. Candacia armata , Boeck (No. 13). — This species was observed for the first time early in February, when a single specimen was obtained, and it did not occur again till September, but after that it was noticed at odd times till near the end of the year. As stated by the late I. C. Thompson, in his remarks on the Copepoda of Valencia Harbour,* this species, though widely distributed, is “generally rare in our seas,” and appears to some extent to be affected by seasonal influences. Labidocera Wollastoni (No. 14) is a moderately rare species in the Clyde. It was represented in the collection by only two specimens, which occurred in a gathering collected at the end of October. Anomalocera Patersoni (No. 15). — This species is widely, but at times not very regularly, distributed. Sometimes it occurs sparingly, and at other times it may be the most common form in the gathering. In the present collection there was no trace of it till September, and from that time onwards no more specimens were noticed. Parapontella brevicornis (No. 16). — This species occurred very sparingly towards the end of April, and again in September, October, and November. Gi/clopina littoralis and C. gracilis (19 and 20). — These two species are demersal in their habits, and therefore, though frequent in gatherings made with the dredge, they are only occasionally taken with the tow-net. Longipedia Scotti and L. minor (21 and 22) are also demersal forms of frequent occurrence, especially the former (21). Till recently, this species has been recorded under the name of Longipedia coronata, Claus ; hut Prof. G. 0. Sars has shown that this common British form is not the species described by Dr Claus, and he has therefore renamed it as above, f Microsetella norvegica (No. 23) \Microsetella (or E dinosoma) atlantica , Brady and Robertson]. This minute species was obtained in a sample collected about the end of January, and this was the * “The Fauna and Flora of Valencia Harbour,” Proc. Roy. Irish Acad., 3rd ser., vol. v. No. 5 (1899). t Crustacea of Norway, vol. v., Copepoda Harpacticoida, parts 1 and 2, pp. 10, 11 (Jan. 1904). 1904-5.] Free- Swimming Crustacea of Firth of Clyde. 801 only time it was observed. It differs from its nearest allies in being truly pelagic in its habits, and is at times moderately common in the open sea. Tegastes falcata, Norman (No. 24), is the species that has frequently been described as Amymone sphcerica, Claus ; but Rev. Canon Norman has shown,* however, that the generic name Amymone is preoccupied, and that the species is his Amymone falcata, described in 1868. f A single specimen of this curious form was observed in a plankton sample collected on 9th December. Ameira longicaudata Laophonte horrida Diosaccus tenuicornis \Dadylopusia tisboides , , Stromi ,, similis „ brevicornis The three species of Thalestris, as well as the Harpadicus and Westwoodia mentioned in Table II. (Nos. 32-38), are all of them bottom forms, and are more or less frequent amongst the roots of Algae and Zoophytes within the laminarian and littoral zones. They are all very sparingly represented in the present collection. Tigriopus (. Harpadicus ) fulvus (Fischer) and Porcellidium fimbriatum, Claus, are each represented in the • collection by a single specimen. The Tigriopus was observed in one of the December gatherings, and the Porcellidium in one of those collected in October. The first is sometimes not uncommon in shore pools even above high-water mark, and the other is frequent on the fronds of Laminaria and other sea-weeds, on the surface of which it can run quickly and adhere firmly when alarmed. Tisbe (or Idya) fur cata, longicornis, cluthce and minor, though not so free swimmers as some of the Calanoids, they all appear to have, to a certain extent, adopted pelagic habits, as they are frequently found in tow-net gatherings collected near the bottom. Tisbe cluthce, which has only hitherto been observed in such * Ann. and Mag. Nat. Hist. (7), vol. xi. p. 368 (April 1903). t Brit. Assoc. Report for 1868 (pub. 1869), p. 296. X Canon Norman points out (Ann. and Mag., April 1893) that, as Dactylopus is preoccupied, he has substituted Dadylopusia for it. PROC. ROY. SOC. EDIN. — VOL. XXV. 51 These are all demersal in their habits, and are therefore more fre- • quently obtained by the dredge than the tow-net. They only occurred at a few odd times throughout the year. 802 Proceedings of Royal Society of Edinburgh. [sess. gatherings, was first noticed in a deep-water sample from Upper Loch Fyne. Thaumaleus rigidus and Monstrilla longicornis (45 and 46) belong to a somewhat remarkable group of Copepoda, and were first made known to science by the late Mr I. C. Thompson of Liver- pool. The life history of the species belonging to this group does not yet appear to be very well known, but it is generally con- sidered that they are parasitic — at leasts at some stage of their life. The first of the two species mentioned here was observed only twice, and the other once during the whole year. The next two species, 47 and 48, belong to a family on which an interesting and elaborate monograph has been published by Dr Giesbrecht of Naples. Nearly all the members of this family appear to live as commensals with other organisms, several being found living in the water passages of various sponges. The two mentioned in the table were only noticed in samples collected in December. They appear to live about the roots of sea-weeds. Caligus rapax (49) was noticed on two occasions, once in October and once in November. It is the only species of a group of fish parasites which adopts, to a large extent, the free-swimming habits of the pelagic Copepoda ; and though numerous examples may be found running over the skin of large Gadoids, the species is also of frequent occurrence in tow-net gatherings collected in the open sea. Remarks on the Species enumerated in Table III. In the preceding notes, the Copepoda only are referred to, but, as previously stated, species belonging to various other groups of Crustacea were also observed; these are recorded in Table III. They were, however, with a few exceptions, very seldom noticed, and chiefly towards the end of the year. Four species of Cladocera, viz., Evadne Nordmanni and Podon polyph emoides, mtermedius, and Leuckarti were moderately frequent, so also were some larval and young forms. The first two species occurred more commonly in July, August, and September, while the third was more frequent in the latter month than at any other time during the year. Podon Leuckarti , on the other hand, occurred sparingly from March till near the end of July. Larval Balani were, with one or two 1904-5.] Free- Swimming Crustacea of Firth of Clyde. 803 exceptions, observed only in April and May ; but young Decapoda appeared to be more generally distributed. One other point of interest in connection with the distribution of the larval forms is that minute organisms, generally known by the name of Microniscusi which at times are found adhering to Calanus , Pseudocalanus , and other free-swimming Copepods, were sparingly observed during the first three and the last three months of the year. These Micronisci are now considered to be the larvae of parasitic Isopoda which live in their adult stages in the higher Crustacea, as, for example, on various hermit crabs, shrimps, etc. The occur- rence of these larvae during the early and later months, and their apparent absence during summer, seems to indicate that the pro- pagation of these parasites takes place chiefly during the months from October till March. Notes on Plankton Samples collected outside the “ Cumbrae Islands ” Area in 1902. In 1902 a few plankton samples were submitted for examination, which had been collected outside the Cumbrae Islands area. These samples — seven in number — were collected in April, May, and September, but chiefly during the latter month. Three were collected in Ettrick Bay, on the west side of the Island of Bute ; and the others at different places off the Island of Arran, two being from Loch Ranza, one from Mauchrie Bay, and one from Brodick Bay. Twelve species of Crustacea were observed in these samples ; nine of the species belonged to the Copepoda and three to the Cladocera ; a few young Decapoda, Isopoda, Balani, and perhaps one or two larval forms, were also noticed. The following are the species that were of most frequent occurrence, viz. : — Calanus helgolandicus , Claus ; Pseudocalanus elongatus , Boeck ; Centropages hamatus (Lilljeborg) ; Temora longi- cornis (0. F. Muller) ; and Acartia Clausi, Giesbrecht. These five species were present in all the samples. The Calanus was abundant in the sample collected in May, but only sparingly represented in the others ; Pseudocalanus , on the other hand, was common in four of the samples collected in September ; Centro- 804 Proceedings of Royal Society of Edinburgh. [sess. pages hamatus was common in April, but less so in May and September ; Temora , though present in the seven samples, appeared to be scarce in all of them. The Acarlia was the most common of the five species referred to, especially in the September gatherings, as shown in the following tabulated list of all the species : — Month | April May September Date 25 15 5 9 11 24 26 Locality Ettrick Bay, Bute. Mauchrie Bay, Arran. Loch Ranza, Arran. Brodick Bay, Arran, j Ettrick Bay, Bute. Ettrick Bay, Bute. Loch Eanza, Arran. Copepoda. Calanus helgolandicus, Claus, fr ab f fr fr f r P seudocalanus elongatus, Bk., . fr f c c c fr c Centropages typicus, Kr 2 ,, hamatus (Lillj.), Isias clavipes, Bk., .... c fr fr f f f fr r Temora longicornis (Mull.), . f f f f f r r Anomalocera Pater soni, Tempi., f f r r Acartia Clausi, Griesb., fr fr c ab c c c Oithona similis, Claus, .... fr f fr fr fr Crustacea (ceter). Evadne Nordmanni , Loven, fr fr f f fr Podon intermedius, Lillj., . f f f ,, Leuckarti, Gr. 0. Sars, f fr Microniscus (larvae of Isopod species), r r Young Crustacea — Decapoda, Bal- ani, etc. , f f f fr r Centropages typicus, Kroyer, so frequent round the north-east and north of Scotland, was only observed in one of the September samples; so also was Isias clavipes, Boeck, a species though not unfrequent round the south and west of the British Islands is very sparingly distributed along the whole east side of Scotland and on the west side north of the Firth of Clyde. Anomalocera Pater soni, Templeton, one of the most finely coloured of the pelagic Cope- poda found in the British seas, and which sometimes occurs in considerable swarms, was only noticed very sparingly in four gatherings. Oitliona similis , Claus, which was more or less frequent in the September gatherings, was absent in those collected in April and May. October T“ I4 8 16 22 30 T~ _j •— — fk fr r f fr fr Jr c fr c 1 *J4 IT Jr 4 fr f f f f 'f > r r f t 1 . 3 1 2 r b ir f c c r r fr fr !. ]• l {• - 1 1 i i 2 ? 2 Tabus II. — Distribution of the Copepoda. 1902, January to December. Chmhrae Islands. 1 bTOBER November December u 22 30 6 15 20 26 2 9 16 17 23 - I ■ ' 1 • f f • . 1 1 • 1 • i 1 1 1 1 1 " ' 1 1 ? • • 1 • • • • ' 1 1 ! . r f f f vr 1 , f r r * 4 11 3 r 1 1 1 1 4 I Tablb n I. — Distribution of Crustacea , other than the Copcpoda. 1902, January to December. Cumbrae Islands. 1904-5.] Free- Swimming Crustacea of Firth of Clyde. 805 Cladocera were not very numerous in the gatherings under con- sideration. Evadne Nordmanni was observed in those collected in April and May and in three of the September samples. The two species of Podon differed in their distribution in rather a marked way, Podon intermedius being present in three of the September gatherings, but absent in those collected in April and May ; while P. Leuekarti was present in the two earlier gatherings, but was absent in all those collected in September. It will be observed from these remarks on the various species, and also from the tables referred to, that there is a tendency for the distribution of several of the more common of the free-swimming Copepoda to be influenced by the seasonal changes that take place throughout the year. But without a study over a lengthened period of these seasonal changes, and of their effect on the dis- tribution of marine organisms, the results obtained will be incomplete. {Issued separately July 7, 1905. ) 806 Proceedings of Royal Society of Edinburgh. [sess. Certain Mathematical Instruments for Graphically In- dicating the Direction of Refracted and Reflected Light Rays. By J. R. Milne, B.Sc., Carnegie Scholar in Physics. (MS. received March 10, 1905. Read June 19, 1905.) The refraction equation sin i = /jl sin r, though simple in itself, is apt to give rise, in problems connected with refraction, to formulae too involved for arithmetical computation. In such cases it may be necessary to trace the course through the optical system in question of a certain number of arbitrarily chosen rays, and thence to find the course of the other rays by interpolation. The Fig. 1. — The divisions on the edge of the arm A G are not shown in the above figure. linkage about to be described affords a rapid and accurate means of determining the paths of the rays through any optical system. This linkage consists (see fig. 1) of five strips of metal, freely jointed at the points ABCD. If PA be the directionjof 1904-5.] Instruments for Graphically Indicating Light Rays. 807 a ray of light incident on the surface (plane or spherical) of a medium of refractive index = g, at the point A ; then A G will be the direction in the refracted ray, provided that the division in the scale A G corresponding to the value of the refractive index g be brought to the edge of the link C D. The proof is as follows. The divisions on A G are equally spaced, and are numbered from 0 50 to 2*00, and the length from the centre A to the division 1 *00 is equal to the length of the links A D and B C. Accordingly, if H be the division on the scale corresponding to a refractive index g, then we have the equation AH = |x, AD . . . (1) Further, the links AB and DC are of equal length, so that the perpendicular distances of the points D and H from the link A B are always equal. Accordingly we have, using equation (1), So sin i = ED E D _ ED aiF^Th ~~ ^'Ih ' sin i — g sin r. To use the linkage, the point A is brought to the point of intersection of the incident ray with the trace on the paper of the refracting surface. The edge of A L is laid along the trace if the latter be a straight line ; if it be the arc of a circle, then A L is made the tangent to that arc at the point A by arranging A B to pass through the centre of the circle (say at M). A F is then turned about A till it coincides with the incident ray, and the division on A G corresponding to g is brought to the edge of C D by turning A G about A. The edge of A G then gives the direction of the ray after refraction. If the medium above the boundary surface have a refractive index different from 1, then g must be taken as the ratio of the refractive indices of the two media, and so may be > < 1, but as the scale on AG ranges from '500 to 2 ,00, the procedure is exactly the same whatever the value of g. Should the incident ray lie on the other side of the line B N from that shown, the linkage is simply rotated through an angle of 180° about BN as axis. To avoid using values of g < 1, F may be moved to the other side of L, and the link A G then rotated till it 808 Proceedings of Royal Society of Edinburgh. [sess. lies on the other side of AD. In this case 1/yu, takes the place of g, and a somewhat more accurate setting can he made. The case of reflection is obtained by having A G- and A F both on the same side of AL, and by setting g to l'OO. The linkage is to be applied to the trace on the paper of the reflecting surface (whether plane or spherical) exactly as before described for the case of refraction. It is convenient to have the ends of the links shaped as shown in the figure, that the eye may see at a glance which is the “ working edge ” of the link. A small hole through the rivet at the joint A is necessary to enable its centre to be set as above described. Since writing the above the author has continued to investigate the matter, and he has found three other graphical methods of which he thinks it may be worth while to give a brief account. Each of these new methods proceeds by two steps or stages. I. The instrument consists simply of two straight strips of suitable material jointed together at one end, and having the distances from the joint marked along each of them so as to form a scale (or, better, a succession of scales) ranging from 1 to 2. If AO, fig. 2, be a light ray incident on the surface 0 B of a medium of refractive index g, let one leg of the instrument be laid along 0 A in such a way that 0 B intersects the legs O A and 1904—5.] Instruments for Graphically Indicating Light Bays. 809 A B at their unit graduations. The point B is now to be marked, and the instrument placed as shown by the dotted lines, so that the points of intersection at 0 and B each lie at the division corresponding to y. Then OD is the refracted ray ; for sin P O A = cos AOC = OC/OA = /i. OC/OA' = /x. cos A'O C = sin D 0 P'. It is to be observed that in proceeding from a more to a less optically dense medium, the above procedure must be reversed, and the g graduations used for the first step, and the unit graduations for the final one. II. The instrument consists of a piece of transparent celluloid shaped as shown in fig. 3a. Its straight edge E being set along Fig. 3a. Fig. 3b. the incident ray AO (fig. 3b), the intersection B of the inner semicircular edge (if the second medium be more dense than the first), or the outer semicircular edge (if the second medium be less dense than the first), with the surface BO is marked on the latter line. If the diameter of the semicircle 0 C be taken as unit length, then, because angle A 0 P = angle 0 C B, OB is the value of sin A 0 P. The instrument is now to be so placed that the semicircle whose diameter is equal to g takes the place of the semicircular edge with respect to the points 0 and B. We thus have, as before, sin P'O D = OB/OD = OB//q and therefore sin P'O D = sin A 0 P / g. Hence the straight edge of the in- strument which now lies along 0 D gives the direction of the 810 Proceedings of Royal Society of Edinburgh. [sess. refracted ray. For greater convenience, each semicircle drawn on the celluloid hears two numbers, one giving the ratio of its diameter to the diameter of the semicircle formed by the inner edge, and the other the ratio of its diameter to the diameter of the semicircle formed by the outer edge. III. The instrument consists merely of an ordinary “ 45° set square,5’ graduated in identical fashion along each of the two equal sides. The number attached to any graduation line gives the distance of the latter from the right angle corner in terms of an arbitrary unit, and the scale ranges from 1 up to 2. It is best to provide several such scales, each beginning where the preceding one ends. In use, one of the equal sides is laid along Fig. 4a. Fig. 4b. the incident ray A 0, fig. 4a, so that the surface B 0 intersects it at 0 at the graduation on one of the scales marked with a number equal to the value of g. The intersection B of the other equal side with the line B 0 is then marked on the latter. If the square be now placed so that the equal sides still pass through 0 and B, but with 0 at the graduation 1 of the scale, 0 D gives the direction of the refracted ray. Sin P 0 A = sin 0 B A = AO/OB = /x. CO/OB = /i. sin D 0 P'. When the ray passes to a less dense medium the procedure is reversed, the unit graduation being used for the first step and the g graduation for the second. When a large size square is being used on a blackboard for 1904-5.] Instruments for Graphically Indicating Light Rays. 811 teaching purposes, it simplifies the demonstration to apply the square as shown in fig. 4b. In this case the second step is taken with the right angle corner below the line 0 B. The lines 0 A, A B, B C, and C 0 are all drawn in ; and the line 0 D is then drawn at right angles to CO by means of the square. In this case A 0 and 0 D are as before the rays, while A B and 0 C are the traces in the two media of the plane wave fronts, of which the relative velocities are represented by A O and B C. An alternative way of using this instrument, which is preferable when the angle of incidence is small, is to employ not the surface but the normal to it, as shown in fig. 4c. Here sin P 0 A = AF/PO = /x. PC/PO = /x. sin P'OD. Of these four instruments, each seems to have its particular advantages. The linkage is the most useful for class demonstra- tion, because it shows simultaneously both of the rays and also the surface. The jointed strip arrangement is extremely portable, while the celluloid device gives directly the actual sines of the angles involved. The set square instrument is found to be the most convenient form for private use in the graphical solution of optical problems. In dealing with spherical surfaces, too, it is an advantage that with this instrument the normal to the surface may be used instead of the tangent, because the former can be obtained very easily by drawing a line through the centre of the circle. 812 Proceedings of Royal Society of Edinburgh. [sess. In order to obtain the reflected ray in each case the instrument is to be re-applied after having been rotated through an angle of 180° about the line BO as axis (except in figure 4c, where the line P 0 must be used for this purpose). {Issued separately July 7, 1905.) 1904-5.] Ankylostomiasis, or the Miners’ Worm Disease. 813 Ankylostomiasis, or the Miners’ Worm Disease. By Thomas Oliver, M.A., M.D., LL.D, E.R.C.P., Physician to the Royal Infirmary, and Professor of Physiology, University of Durham, College of Medicine, Newcastle-upon-Tyne. (With Two Plates.) (Address delivered at the request of the Council, March 27, 1905.) By the terms “ankylostomiasis,” “miners’ anaemia,” and the “miners’ worm disease,” is meant a malady due to the presence in the small intestine of numerous slender worms called Ankylostoma duodenale , — dy/aiAos, crooked, o-ro/xa, a mouth, and duodenale , because usually found in the upper part of the small intestine. Although the disease is known to have existed for long in Egyptian and Tropical countries, it was not until the huge mining engineering operations connected with the tunnelling of the Alps at Mont Cenis and St Gothard for railway extension were in progress that the disease attracted public attention in Europe. During the piercing of these Alpine heights the parasite was the cause of considerable ill-health and of loss of life among the miners, especially at the St Gothard. For a considerable length of time the true nature of the malady was not recognised. It was owing to the fact that as anaemia was one of the principal physical signs of the malady the disease came to be called miners’ anaemia , and as the men worked in tunnels, the term “la maladie des tonnelles ” was also given to it. After the discovery of the parasite in the small intestine of affected miners, the designation miners’ worm disease came to be applied to it, and it is by this name that it is commonly known in this country. Although admittedly a medical subject, ankylostomiasis yet presents many economic problems for solution, biological questions waiting to be answered, and hygienic requirements that have yet to be met. On the Continent the spread of the disease has given rise to considerable friction and ill-feeling between nation and nation, and has been the cause of occasional international mis- understanding. Although, therefore, very largely a medical question, ankylostomiasis, from its many-sidedness, is a subject worthy of the consideration of this learned Society. 814 Proceedings of Royal Society of Edinburgh. SESS. The disease presents both local and general symptoms. In such hot countries as India, Assam, Egypt, and certain parts of South America, ankylostomiasis is found among the agricultural labourers. As the men and women in these countries work in the fields with bare feet, and the soil is often polluted with human and animal excrement, rich in parasitic ova, these ova, under the influence of heat and moisture, develop into actively moving larvae, which have the power of penetrating human skin, thereby giving rise to local inflammation and to skin eruptions, known as “water itch,” u water pox,” and so on, or they enter the general circulation, and ultimately reach the alimentary canal. Once there, they become the cause of anaemia, shortness of breath, puffiness of the feet and legs, symptoms which may become progressive and end in death. Having in the early part of last summer visited the Dolcoath mine in Cornwall, which was reported to be infected, and having examined, through the kindness of Mr Thomas, the manager, several of the miners who harboured the ankylostoma, I felt that I wanted to know more of this interesting malady. Accordingly, at the end of June 1904, I proceeded to Westphalia and to Hungary, in order to see for myself something of the ravages caused by the parasite in the mining districts of these countries. Accompanied by Mr Belger, of the Armstrong College of Science, Newcastle-upon-Tyne, I made my way to Bochum, and entered the Westphalian coal district from here. I wanted to meet Dr Tenholt, who is the recognised authority on ankylostomiasis in Germany, and who is also the medical head of the Knapp- schaftsverein, or miners’ union, whose headquarters are in Bochum. Besides, it is in the valley of the Ruhr that the disease has played havoc with the miners, been the cause of acute friction between the colliery proprietors and the workmen, and the cause of considerable expense to the owners. At the Elizabeth Hospital in Bochum, a well-appointed institution with four hundred beds, one wing is specially set aside for the reception and treatment of patients suffering from ankylostomiasis, and there are pathological labora- tories and annexa replete with apparatus for the examination of the dejecta of infected subjects. Dr Nagel, principal assistant to Dr Tenholt, is in charge of these laboratories, in which nearly three hundred young doctors have been specially trained in the methods of 1904-5.] Ankylostomiasis , or the Miners Worm Disease. 815 diagnosis and treatment of ankylostomiasis. These men are now holding medical mining appointments all through Germany. On the date of my visit to the hospital I found thirty patients suffering from the miners’ worm disease. On the following day we visited the Lothringen mine, about three miles from Bochum, and, with Dr Tenholt and a mining official, descended to one of the levels in the pit, fully a thousand feet below the surface. Along the sides of some of the main ways were seen every forty or fifty yards a covered iron box containing a pail, which served as the underground closet for the miners. Occasionally these receptacles were placed in recesses in the rock and screened off by a piece of sacking, while the soil round about was strewn with quicklime, supposed to be destructive to any faecal matter that might be dropped upon the soil or upon the boots of the miner. Two thousand men are employed at the Lothringen mine, and of these 1600 work underground. A few years ago the number of infected miners in this pit was 72 per cent., but under Dr Tenholt’s supervision and treatment there were last June only 8 per cent, of the men infected. Within the last ten years Dr Tenholt has treated four thousand miners for ankylostomiasis at this pit. One of the disused galleries which we visited Dr Tenholt had voluntarily allowed to become infected, in order to ascertain the length of time it required for the ova deposited by infected miners to develop into larvse, and he found in this particular part of the mine, where the temperature was fairly high and moisture sufficient, that in fourteen days the ova had become converted into mobile larvae. All along the main ways in the pit were accumulations of muddy water and sludge, in which were myriads of the larvae of the ankylostoma. These active organisms live and thrive upon any organic matter in the water, and they attack the wooden props, wriggling upwards to the extent of fully three feet above the soil, causing the props to become extremely moist and soft, and rendering them unsafe as supports. These wooden props have in consequence to be fre- quently changed, thus adding to the cost of working the mine. At the Erin pit, a few miles further away, I w^s particularly struck with the sanitary arrangements provided for the men at the surface. Close to the mouth of the shaft were large bathrooms 816 Proceedings of Royal Society of Edinburgh. [skss. and dressing-rooms, heated by warm pipes ; these rooms led into another large room, which was divided off into sixteen excellent waterclosets, provided with automatic flushing appliances. A little distance from the mouth of the pit was the hospital, in which on the date of my visit twenty-five miners were being treated for ankylostomiasis. Origin of the outbreak. — It is not exactly known how ankylostomiasis reached Westphalia. Some persons attribute it to Italian miners coming there after the opening out of the St Gothard tunnel in 1892; others blame infected miners who came from Belgium. Dr Tenholt is of the opinion that it was carried into Westphalia by miners from Hungary. At the present time no miner is taken on at any colliery until he brings a medical certificate stating that a microscopical examination of his faeces has been made, and that they are free from the ova of the ankylostoma. For this certificate the workman pays himself one shilling to the doctor — an arrangement wdiich the employers found necessary to enforce in order to check the frequent flitting about from place to place of the miners. Although Italian, Belgian, and Polish miners who have passed the doctor are accepted in Westphalia, miners from Hungary are upon no conditions accepted at all. The rapid spread of the disease through Westphalia is attributed to the opening out of new mines and the enormous demand for coal. Although coal mining in Westphalia originated about the year 1760, it was not until 1840 that the impetus was given to the industry which has made this part of Germany so prosperous to-day. Some opinion of the enormous demand for coal can be formed when it is stated that in one year within very recent times twenty thousand miners were introduced into Westphalia. These miners came from Posen in Prussia, from Poland, Hungary, and Italy. It was probably at the time of this large influx of foreigners that ankylostomiasis was introduced into the country. Until very lately the Westphalian coal mines were frequently the seats of explosions, due to the firing of coal dust. As these explosions were attended by considerable loss of life, the German Government in 1900 passed a law requiring the use of water- sprays in the mines. Whether as a consequence of this, or PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH \ Vol. XXV. No. vii. ERRATUM. Page 562, § 33, last line, for “ more ” read “ less. 1904-5.] Ankylostomiasis , or the Miners' Worm Disease. 817 whether simply as a coincidence, the number of cases of ankylo- stomiasis in the Ruhr valley rapidly increased. In 1896 . . 107 cases. „ 1897 . . 113 „ „ 1898 . . 99 „ In 1900 . .275 cases. „ 1901 . . 1030 „ „ 1902 . . 1355 „ The headquarters of the mining industry are in Bochum. Here is the Knappschaftsverein, or miners’ union. The building is a large one. Attached to the union is a well-appointed school of mining, which is attended by six hundred students. The Knapp- schaftsverein is the insurance bank of the miners. It has a capital of £2,000,000, none of which can be used for strikes. To the funds of the union the employers contribute two-thirds and the workmen one-third. The outbreak of ankylostomiasis has already cost the union upwards of £100,000, to say nothing of the additional expenses incurred by the owners of collieries. The systematic manner in which the Government and the mine- owners are co-operating to stamp out ankylostomiasis commands at once our respect and admiration. Medical men have been appointed to all the infected pits, and the miners who are the subjects of the malady are obliged to go into the hospital for a fortnight. Formerly when these men were off ill they received 3s. a day, out of which they paid Is. to the union and Is. for their keep in the hospital, leaving therefore only Is. a day for their wives and families. This reduction to a minimum allowance not only led to the attempted perpetration of all kinds of fraud on the part of the miners, but was nearly the cause of a riot and a strike. These were only averted by the owners making the concessions demanded by the men, viz., the receipt of the whole of their wages, and that hospital treatment and residence should not be charged against them. I have alluded to the excellent sanitary arrangements proyided at the surface of the Erin mine for the men. The miners in going into the pit don their working clothes, and on coming >out of the pit they have a warm bath and put on the clothing which they left in the dressing-room before going to work. The miner leaves overnight his wet working clothes in the warm dressing- room, suspended by a cord from the ceiling, and on his return to PROC. ROY. SOC. EDIN. — YOL. XXV. 52 818 Proceedings of Royal Society of Edinburgh. [sess. work next day lie finds them dry, warm, and comfortable. The result of this washing at the pit-mouth and change of clothing is that you never, as in this country, meet a begrimed collier on the road. He is so clean and properly dressed that you cannot tell whether he is going to or returning from work. As ankylostomiasis is known to have existed for many years in Hungary, I proceeded to Sopron-Brennberg, one of the worst of the infected mines of that country. Here I was the guest of Dr Goldman, medical officer to the mines, and who is a recognised authority on ankylostomiasis. The coal obtained at Sopron is of a pitch-like character and is extremely fiery. The temperature of the mine is high. In some places it runs up to 106° F., and at other places, where the ventilation is not good and where water-spraying is not carried on, it may rise to 170° F. Here, as in Britain, the miners work in couples, but so high is the temperature and so exhausting the work, that although the number of hours spent in the mine is nominally eight, the men can only work four hours. Half of the time is spent by the workmen resting and in trying to cool themselves. One man works while his mate is cooling himself. Fires are constantly breaking out in the pit. Owing to the high temperature the men are bathed in perspiration, and as a consequence they drink enormous quantities of cold water containing a small quantity of citric acid. Boys with water-barrels fixed upon their shoulders walk in couples up and down the main ways in the pit. The provision of the drinking-water costs the owners £100 a year. Eight years ago, fully 90 per cent, of the miners at this colliery were suffering from ankylostomiasis ; to-day only about 30 per cent. When the disease first showed itself many years ago the miners suffered very severely. So pronounced was the anaemia, and so much did the men suffer from dyspnoea, swollen feet, and muscular debility, that they could scarcely crawl. There is this to be said of ankylostomiasis : When it affects for the first time a district, the symptoms, as a rule, are generally very severe, but as time goes on the miners seem to suffer less, owing to a diminution of the virulence of the parasite, or to an increased resistance on the part of the miners to it. It is with ankylostomiasis as with ordinary infectious diseases. There is an individual idiosyncrasy 1904-5. j Ankylostomiasis , or the Miners' Worm Disease. 819 to the parasite. All patients who harbour the worm do not equally suffer. It is the ill-fed, the poorly-clad, and the badly-housed miners who suffer most. Although the Sopron colliery is well conducted, and is in many respects a model mine, yet the officials have great difficulty in getting the men to use when underground the receptacles provided for their dejecta. In Westphalia, not only does the law enforce obedience to this requirement, the miners themselves see that none of their colleagues break the rule ; but in Austria there is no power given to mining officials to enforce this salutary recommendation. The hospital at Sopron-Brennberg is in the village, a mile or s© from the mine. It is the colliery hospital, and is not exclusively devoted, as most of those in Westphalia are, to the treatment of ankylostomiasis. There is accommodation for twenty-four patients. I examined six infected miners at the hospital, one of whom had been put upon treatment a few hours before my visit, and who had passed seventy fully-developed worms, some of which were gorged with blood. In some of the female worms there could he seen fertilised and unfertilised ova. In Hungary, coalminers are liable to skin eruptions as a con- sequence of the pitch-like character of the coal; in the Dolcoath mine in Cornwall the men suffer from a peculiar eruption known as “bunches.” Since the coolies of Assam and agricultural labourers in hot countries, who work in the fields with their bare feet, suffer from a similar kind of eruption, it is believed that the dermatitis and the accompanying boils are a consequence of the irritation caused by the entrance of the ankylostoma larvae into the skin. The date of the introduction of ankylostomiasis into Cornwall is not known. The manager of the Dolcoath mine, Mr Thomas, informed me that the men had been for a long time the subjects of anaemia and shortness of breath on the slightest exertion, and that they were unable to work. At first it was thought that the symptoms were caused by the presence of bad air in the mine owing to faulty ventilation, but chemical analysis of the air showed that, on the whole, the air was pretty pure. It was not until a microscopical examination of the stools of some of the anaemic miners was made, and the presence of excess of eosinophile 820 Proceedings of Royal Society of Edinburgh. [sess. corpuscles noticed in the blood, that the ill-health of the miners was traced to its proper source. As the high temperature and humidity of the Cornwall tin mines are extremely favourable to the development of the larvae of Ankylostoma duodenale , and as the mines have become infected through the irregular disposal of the excreta of the workmen, pails are now provided underground for the use of the miners. These pails are taken to the surface daily, rinsed with boiling water and disinfected. Anatomy and Physiology of the Miners ’ Worm. The Anhylostoma duodenale is one of the helminthozoa of the nematode class, and is included under the head of the Uncinaria, lienee the occasional substitution by some writers of the word uncinaria for ankylostoma. There is an ankylostomiasis not only of man, but of the dog, wolf, fox, and sheep ; and there is a form described by Stiles as the American uncinaria. It is only the Ankylostoma duodenale and the American uncinaria that attack man. Although several attempts have been made to introduce the other forms of ankylostoma into man, they have failed. There is apparently no intercommunicability between the various types of the parasite. When examined in the fresh state, the fully-developed worm of man is seen as a slightly blunted fili- form body, white or greyish- white in colour, or rose- white if it contains blood. There are male and female ankylostomes. The males are slightly shorter than the females ; the males measure 8- 11 millimetres, f to fully J inch in length, and the females 18 millimetres, or about f of an inch. They are about J a millimetre or of an inch in breadth. Probably the size of the worm varies in different countries. The males are not only shorter in length than the females, they are less numerous, the proportion being one male to three females. The tail end of the male swells out into an umbrella-shaped expansion which is the genital sac, whereas the tail of the female ends in a very fine point. The worms have an external covering or cuticle composed of two layers. The alimentary canal, commencing at the buccal cavity, leads into the oesophagus, a well-developed muscular tube, which is guarded, according to Brian^on, by valve-like structures, to prevent the 1904-5.] Ankylostomiasis, or the Miners Worm Disease. 821 regurgitation of the liquid material swallowed. From the oesophagus onwards the intestinal canal is, practically speaking, a straight tube, which in the female is continuous with a narrow rectum, ending in the anus, and in the male is deflected slightly, so as to open into a cloaca. At the buccal entrance there can be seen four hooklets, two on the right and two on the left of the median line, which serve to fix the worm to the intestinal mucous membrane, while on the dorsal aspect there may be observed in addition two small projecting teeth. There are six glands con- nected with the alimentary canal : two cervical glands, composed each of an unicellular secreting apparatus ; two cephalic glands, similar to the cervical, placed behind them, opening into the buccal cavity near the external hooklet, and secreting, according to Megnin, an irritating form of saliva, analogous to that secreted by ascarides, and which is capable of inducing catarrh of the intestinal mucous membrane ; there are also two glands near the anus. The muscular system is composed of two layers of transverse and longitudinal fibres. The nervous system is simply a collar around the oesophagus. The genital sac of the male is large ; it is composed of four lobes. At the depth of the sac there are poured, as into a cloaca, the secretions from the anal glands, the rudimentary testes, and the intestinal contents. The vulva of the female appears as a small protuberance about the middle of the terminal third of the body. The vagina leads into a double uterus. Where the two uteri meet, ovules and spermatozoa may be detected. It is here that fecundation takes place. The American type of the uncinaria differs slightly from the human ankylostoma. It is shorter, its mouth is slightly different, and it has only five instead of six hooklets or teeth. This variety is met with in Virginia, North and South Carolina, Texas, Brazil, Cuba, and Porto Rico. As the sexually developed worm has been found in the chimpanzee of West Africa, it is maintained that the American uncinaria had its origin in this animal. The female ankylostome, when in the human intestine, keeps passing off myriads of ova. It was Grassi who, in 1878, detected the ova in the stools of infected miners, and who demonstrated the meaning thereof. They are oval bodies, 55 to 65 micromillimetres 822 Proceedings of Royal Society of Edinburgh. [sess. in length and 32 to 43 in breadth. Although the fully-developed American ankylostoma is smaller than that of man, the ovum of the parasite is somewhat larger. The ova of the human ankylostoma have a well-defined external covering. Occasionally a small space is left between the contents of the ovum and the capsule. Usually the protoplasm is observed to he undergoing segmentation, when four or more blastomeres may be noticed. When the segmentation is complete, the ovum is said to have reached the morula stage, but this does not last long, for shortly afterwards the developing larva can be seen rolled up on itself, and sooner or later the capsule ruptures and the organism escapes. On examining the stools of infected miners a distinction has to be made between the ova of ankylostoma and those of other parasites, for miners who harbour the ankylostoma are often unconsciously the hosts of other intestinal parasites as well. The ova of Oxyuris are haricot-bean-shaped, while those of Tricocephalus dispar are smaller than those of the ankylostoma, are lemon-shaped, and often exhibit an iron-grey colour. The ova of Tcenia solium are round and have a thicker capsule ; those of Bothricephalus latus are still larger, and have a thin capsule, which is completely occupied by the contents. The ova of Ascaris lumbricoides are smaller and are rounder than those of the ankylostoma ; they are mulberry-looking and have a thicker capsule, which often exhibits a double contour. The ova of the Ankylostoma duodenale do not undergo segmenta- tion in water, and yet complete deprivation of water kills them. They develop, however, in soft liquid material. They require, it is generally stated, a temperature from 20° to 30° C., or from 68° F. to 86° F. Coal mines with a temperature below 60° F. would therefore not be very favourable to the development of the ova. Tenholt found in Westphalia, when the temperature of the mines was reduced by freer ventilation, that the disease ceased to spread in the pits ; but Lambinet and others have demonstrated that the ova can become transformed into larvse in coal mines at even lower temperatures than 57° F., although at this temperature the larvse come into existence very tardily, and, as a rule, are short-lived. Higher temperatures than 98° F. destroy the ova ; the ova do not hear very well sudden variations of temperature. The ova must 1904-5.] Ankylostomiasis , or the Miners Worm Disease. 823 have oxygen. If, for example, they are retained in the deeper portions of the faeces they die. We can understand how it is that the ova of ankylostoma do not develop in the intestine : (1) the temperature is too high ; (2) there is not sufficient oxygen. It is not known how long the fully-developed parasite can live in the intestine ; some say only a few months, others as long as four or five years. As time goes on the patient tends to cure himself ; for as the worm cannot propagate itself in the alimentary canal, if no re infection occurs the disease gradually wears itself out. It is external to the human body, therefore, that the ova become hatched into larvae, and it is the larvae gaining entrance into the body that cause ankylostomiasis. When at the Erin mine in Westphalia I was told by Dr Perner that the larvae could live eight to ten months at least in the water and sludge by the sides of the main ways. They thrive upon organic matter present in the liquid. Other filiform bodies known as rhabdites are also present in the liquid, and both of these organisms attack the wooden props, rendering them unsafe. So active and wandering are the ankylostoma larvae in their habits that, at the present time, in some of the agar cultures which Mr Belger and I have been making, the larvae leave the solid matter and pass out into the liquid, even moving into the clear drops of water that have condensed on the under surface of the lid of the Petri dish. It has been stated that outside the body the larvae can develop into the sexually matured worm. I have no experience of this, and am therefore inclined to doubt the occurrence of it. After escaping from the ovum, the larvae moult two or three times. Mode of entrance of the larvae into the human body. — It was formerly believed that the larvae gained an entrance into the alimentary canal by men drinking contaminated water or by eating with unwashed hands. Dr Looss, of Cairo, whose lantern slides I have his permission to show you, sometime ago accidentally infected himself by a drop of an ankylostomal culture falling upon his finger. A few hours afterwards the skin was red and irritable, and a few weeks afterwards he found the ova of the worm in his faeces. He therefore experimented upon dogs, and he found that larvae applied to the skin penetrated into the deeper subcutaneous tissues, and piercing the wall of a small vein, were carried by the 824 Proceedings of Royal Society of Edinburgh. [sess. blood to the right side of the heart and the pulmonary artery to the lungs. Here the larvae made their way out into the air-spaces of the lung, travelled up the bronchi, and wriggled up the wind- pipe. Then reaching the entrance of the gullet," they passed down it into the stomach, and thence made their way into the intestine, where they became fully-developed worms. In twenty-one days after the experimental infection of a dog, the ova of the ankylo- stoma can be found in its faeces. I regard Looss’ discovery as a very important contribution to scientific medicine. Causes of the anctmia. — Those who believe in the blood- sucking propensities of the worm attribute the anaemia not so much to the abstraction of the red blood globules as to the removal of the plasma. Lassano, in 1890, by injecting under the skin of a rabbit an extract obtained from the urine of a patient who was suffering from ankylostomiasis, succeeded in producing a profound anaemia. He therefore propounded the theory of poisoning by toxins secreted by the worms as the cause of the anaemia. Others have also obtained blood-changes by the injection of watery extracts of the ankylostomes. By means of such extract made for me by Messrs Brady and Martin, of Newcastle, I have succeeded in inducing anaemia and leucocytosis in rabbits. Looss of Cairo, Herman of Mons, Malvoz, and Lambinet of Liege are in favour of the view that the ankylostoma forms a toxin which has a destructive effect upon the red blood corpuscles and a dissolving influence upon their colouring matter. The toxins that are found are probably secreted by the glands in the neighbourhood of the mouth and oesophagus. It is thought that during the act of abstraction of blood some secretion is thrown out which prevents the blood from coagulating; and on the other hand, that this is absorbed by the blood-vessels of the host, and causes toxaemia. In favour of the loss-of-blood theory is the important fact an- nounced by Professor Stockman, of Glasgow, viz., that in the liver and spleen of five persons who had died of ankylostomiasis in Fiji and Ceylon he found a marked absence of iron — a circum- stance which points to an actual loss of blood rather than to destruction of it. Lambinet has just been carrying out a series of experiments on dogs — ending in the production of acute ankylostomiasis. In the 1904-5.] Ankylostomiasis , or the Miners' Worm Disease. 825 intestine he found large quantities of blood and mucus, marked evidence of catarrh of the mucous membranes. He also found that the worms attached to the intestinal wall contained blood. It is possible, therefore, that in acute cases the cause of the anaemia is rapid abstraction of blood and concurrent subacute enteritis, and that in the chronic cases toxaemia is more important. The question has sometimes been raised as to why the worms in the intestine are not digested by the trypsin of the pancreatic juice. It may be that their protoplasm offers some natural resistance to the action of proteolytic ferments, or that the worms, in defence, produce some antiferment or other substance that inhibits the action of the trypsin. The treatment of ankylostomiasis is preventive and curative. The curative or medicinal part of the treatment may well be left to the medical man in charge of the patient. It consists mainly in the administration of purgatives and of anthelmintics. In this country the administration of large doses of thymol has been followed by good results. On the Continent filix mas is frequently given, large doses of which have caused blindness. Preventive. — It is known that the ova require for their develop- ment into larvae, moisture, oxygen, and a fairly warm temperature. On the whole, the mines on the Continent have a higher tempera- ture than those in this country. Ankylostomiasis, however, has already gained a foothold in Cornwall. Here the mines which are metalliferous have a greater depth and higher temperature than the coal mines generally throughout the country. There are many coal mines in the county of Durham and other parts of England (I cannot speak for Scotland) where the tem- perature at the working place is over 60° F. British mine-owners and mining officials are inclined to attribute their freedom from ankylostomiasis to the lower temperature and better ven- tilation of their coal mines compared with those abroad. May it not be that they are closing their eyes to possibilities, and are allowing themselves to be lulled into a sense of false security? Ankylostomiasis takes a long time to travel from one country to another — even from one mine to another. Experience shows that it goes on silently developing in a mine for months, or it may be years, before there is an outbreak. This was certainly what 826 Proceedings of Royal Society of Edinburgh. [sess. occurred in Westphalia, and it is this which took place in the Dolcoath mine in Cornwall. We have no proof, therefore, that the disease may not at the present time he making its way into British mines other than those of Cornwall. Personal cleanliness on the part of the miners, cessation of the irregular disposal of their dejecta when working underground, microscopical examination of the blood of suspected miners for excess of eosinophile white corpuscles, also, if need he, of their faeces for ova, medical ex- amination of miners returned from South America, India and the Colonies for evidences of anaemia, keeping the temperature of the mines low and their humidity to a minimum, are prophylactic measures which should be at once resorted to if perchance the disease should invade our coalfields. Fig. 1.- — AnTcylostoma duodenal e (human), natural size. The smaller worm is the male. (. Issued separately July 10, 1905.) Proc. Roy. Socy. of Edin. ] [Vol. XXV. Fig. 4. — Ankylostoma Caninum , ova , of in various stages of development, x 200 diameters. Fig. 2. — Ankylostoma duodenale (human), x 12 diameters. Prof. Thomas Oliver. Proc. Roy . Socy. of Edin.~\ [Vol. XXV. Fig. 3. — Ankylostoma duodenale (human). Conjugation of male and female worms, x 7 diameters. Fig. 5. — Larva of Ankylostoma Qaninum. Young larva, 72 hours after inoculation on agar at 20° C. x 300 diameters. Prof. Thomas Oliver. 1904-5.] Form of Bolometer for Physiological Investigation. 827 A Form of Bolometer adapted for Physiological Investi- gation. By Walter Colquhoun, M.A., M.B., Physio- logical Laboratory, University of Glasgow. (Read May 15, 1905.) After a lecture on animal heat towards the end of last session, in which I described Langley’s original form of bolometer, with its two iron gratings, and mentioned that Dr Stewart, of Philadelphia, had referred to the use of tinfoil and leadfoil gratings for physiological purposes in his text-book, I started to make a bolometer for our department. I should mention that some time ago Professor M‘Kendrick, impressed by the probability of the bolometer being of use to physiologists, had communicated with Professor Langley, who kindly sent him, from Baltimore, literature dealing with the subject, and stated that the instrument was not made by an instrument-maker. The form I adopted for experimental purposes was as figured. Into a board were screwed terminals A, B, C, D, E, F, G, which are connected by wires as shown. In the gaps D E and F G are placed gratings. The galvanometer is placed in the circuit C D'. By means of a sliding contact along A B the point D' is found such that the galvanometer indicates no current in C D'. If heat be now applied to one of the gratings so as to alter its resistance, the balance of the bridge is destroyed and the spot of light from the 828 Proceedings of Royal Society of Edinburgh. [sess. galvanometer mirror at once swings from the zero position. The gratings may conveniently be cut out of very thin tinfoil, and mounted on three-quarter inch or seven-eighth inch microscope cover-glasses, which are cemented on wooden blocks, the terminals being screwed into the blocks through lugs of the tinfoil proceeding from the ends of the gratings. The galvan- ometer employed was a Wiedemann with low-resistance coils (1 ohm). It was found that the construction of a sensitive instrument by experimental observation was by no means easy. I had not read Langley’s Annals of the Astrophysical Observatory for 1900, in which, with the help of Mr Abbot, he gives the mathematical theory of his instrument. I had used short coils of high-resistance wire for my connections, and, in turn, gratings of tinfoil, leadfoil, aluminium, silver, iron, copper were used, with disappointing results. The movement of the spot of light for radiant heat from the hand was only about three feet on our class-room scale (about twelve feet from the mirror of the galvanometer), a result rather inferior to that obtained by our delicate thermopiles. I then investigated the question mathe- matically on the supposition that A and B were kept at a fixed difference of potential by a shunt current from the mains of reduced voltage, and I found that the most advantage was gained by making the arms A C and C B of as low resistance as possible, and of equal resistance. Thick copper wires were substituted for the connections, and the gratings were made of a resistance of from one to three ohms, with six or seven bars to the grating and very fine inter-channels. The result was a great improvement in sensitiveness. Radiant heat from the hand now gave a twenty-foot swing, and touching a grating caused the heavy ring magnet to spin round and round. The spot of light was caused to swing with every draught in the room, and the instrument was already so sensitive that its value was much lessened unless special precautions were taken to enclose it from accidental influences. In the complete instrument all connections as Avell as the gratings must be covered in and protected from such influences. I would draw the attention of physiologists to the fact that no especially delicate galvanometer is required for our purposes. Langley uses special galvanometers, 1904-5.] Form of Bolometer for Physiological Investigation. 829 wound to an internal radius of 1 mm., and having a space of 2 mm. between the coils. He uses arrangements of six flat needles suspended by a quartz fibre, needles and mirror weighing only from 2#4 to 6*5 milligrammes. In my arrangement the heavy ring magnet of the Wiedemann does all that is requisite for our purposes. A low-resistance galvanometer with light needle would answer better to very small increments of temperature, hut would possibly be unmanageable if muscles or heart were laid on the grating. The instrument will be very useful both for teaching purposes and for purposes of research, but, owing to its delicacy, will have to be used with care. If gratings are placed in both bolometer arms, and a half-crown from the pocket be placed on one and a penny on the other, the spot of light goes to the side of the penny, which is the better conductor of heat, but after some time the spot returns to zero, and then crosses to the half-crown side, the half-crown retaining its heat longer. The Du Bois Reymond induction coil cannot be used for stimulating through its nerve a muscle placed on a grating, because, even when the wires are led down from the ceiling and the electrodes placed at right angles to the grating, there is a swing of the spot of light at each break, followed by an arrest of swing at each make. Under certain atmospherical conditions, the apparatus shows that the heart of a frog is hotter than its muscles, and the tempera- ture of the isolated heart gradually rises as it continues beating. The heavy magnet does not show a rise for each beat, but rather a gradual ascent with stops. A lighter magnet would probably show the effect of each beat. With regard to the material to be used for the gratings, I find that tinfoil is quite convenient. Since, with the arrangement I adopted, a low resistance in the grating is advantageous, theoreti- cally silver would be the best material to use, but one is met with practical difficulties as regards thickness of the commercial article. Silver leaf gives too great resistance, and silver foil is too thick. It seems to me that Professor Langley attaches too much importance to the material of which his bolometer strips are 830 Proceedings of Royal Society of Edinburgh. [sess. composed. Most metals lose at 100° C. about thirty per cent, of their conductivity at 0° C. Yet they vary very much regarding their conductivity, and one consequently chooses the metal according as one wants a grating of low or of high resistance for a given cross section and length. ( Issued separately July 10, 1905.) 1904-5.] A New Method of Preparing Esters. 831 A New Method of Preparing Esters. By W. W. Taylor. Communicated by Professor Crum Brown, F.K.S. (Head June 5, 1905.) In the preparation of esters, one of the main difficulties is the removal of the water produced by the interaction of the acid and the alcohol. This difficulty is very pronounced in the case of those esters which are readily hydrolysed, e.g. oxalic and tartaric esters ; the methods of preparation of such esters are long and troublesome, and the yields are not always satisfactory. The method described in this paper is rapid and easy, requires little attention, and gives satisfactory yields. The essential idea of the process is to remove the water produced in the reaction between the alcohol and the acid, by the addition of benzen, and distillation of the ternary mixture of benzen, alcohol, and water. Young, in his paper, “The Preparation of Absolute Alcohol from Strong Spirit,”* showed that when a mixture of ethyl alcohol, benzen, and water is fractionated, a mixture of all three distils first at 64*85° C. ; followed by the binary mixture — alcohol, benzen at 68*25° C., or water, benzen at 69*25°. In this way he obtained absolute alcohol from aqueous alcohol by careful fractionation, after addition of a sufficient quantity of benzen. Since methyl alcohol does not form a ternary mixture with water and benzen, the method cannot be employed for the preparation of methyl esters, nor can it be used unless the acid and the ester are sufficiently non-volatile not to distil over with the ternary mixture. It was at first thought that the use of hydrochloric acid or sulphuric acid as catalyser might be dispensed with if the benzen was continuously dropped into the mixture of alcohol and acid, and the ternary mixture removed. As a rule, the reaction proceeded too slowly aud too irregularly, and it was necessary to add a small quantity of aqueous or alcoholic solution of hydro- chloric acid. It was also found impracticable to carry out the continuous process. * Chem. Soc. Journ., 81, p. 707, 1902. 832 Proceedings of Royal Society of Edinburgh. [sess. The following way has been found to give good results: — A quantity of dry acid and an excess of absolute alcohol are placed in a round-bottomed flask, provided with an efficient fractionating column and a tap -funnel ; 1 cc. of alcoholic solution of hydrochloric acid is added, and the mixture boiled for 20-30 minutes. The fractionating column (Young’s rod and disc pattern, with seventeen discs and contractions on the tube) serves as a reflex condenser. A quantity of benzen, sufficient to remove one-quarter of the total quantity of water produced by the reaction, is then run in and the ternary mixture slowly distilled off. As soon as all the benzen has come over, the distillation stops, and the residue boils under reflex condenser as before until a further quantity of benzen is added.* This process is repeated three times, and finally the excess of alcohol is boiled off, and the residue purified by distillation in the usual manner. As the ternary mixture, according to Young, contains 1 8*5 per cent, of alcohol, 7 ‘4 percent, of water, and 74T per cent, of benzen by weight, each gram of water requires 10 gm. (1Y5 gc.) of benzen. In practice, 10-15 per cent, excess of benzen was added. In the experiment described in detail below an additional 5 cc. of benzen was added ; the result showed that it was unnecessary. As an illustration, one experiment will be described in full ; in the others the quantities and yield only will be given. Diethyl tartrate. 30 gm. tartaric acid, 80 cc. ethyl alcohol, 1 cc. alcoholic hydrochloric acid, boiled under reflex condenser for 30 minutes. Added 25 cc. benzen + 5 cc. alcohol. 10.30 a.m. temp. 64’8° C. 11.0 ,, „ 66*2° C., distillate 29 cc. 25 cc. benzen + 5 cc. alcohol. 11.25 ,, „ 67‘8° C., distillate 35 cc. 25 cc. benzen + 5 alcohol. 12.5 p.m. temp. 65 *0° C. .10 ,, ,, 66 -7° C , distillate 35 cc. * This circumstance is one of the causes which make the process so convenient. 1904-5.] A New Method of Preparing Esters. 833 Added 25 cc. benzen + 5 cc. alcohol. 12.13 p.m. temp. 65*4° C. .17 .20 .50 1.0 55 55 55 55 55 55 651° 65-4° 65*4’ 66*7, distillate 35 cc. 5 cc. benzen + 5 cc. alcohol. 1.5 „ temp. 66*7 .10 „ „ 67 -0, distillate clear. After the last addition the distillate was quite clear, i.e. con- tained little or no water. The contents of the flask were then transferred to a fractionating flask and distilled under reduced pressure. The distillation gave no trouble and the ester came over at constant temperature ; weight of ester 37 gm., yield 90 per cent. The whole preparation took less than 5 hours, and did not require continuous attention at any time. Summary of Test preparations : — Acid. Alcohol. HC1. Benzen. Ester. Percentage. Ethyl Tartrate. 1. 30 gm. 80 cc. 1 cc. 100 cc. 34 gm. 83 2. „ „ 3 3 3 3 1 „ 3 3 3 3 37 „ 90 3. „ „ •5 3 3 4 „ 3 ’ 3 3 36 „ 87 4. 45 ,, 3 3 3 3 2 „ 3 ’ 3 3 51 „ 83 Ethyl Oxalate. 5. 18 gm. 80 cc. 1 CC. 100 cc. 23 „ 79 6. ,, ,, 3 3 3 3 1 „ 3 3 3 3 27 „ 93 7. „ „ 3 3 3 3 2 „ ’3 3 3 23 „ 79 8. „ „ 33 33 4 „ 3 3 3 3 24*5 ,, 84 *9. ,, 60 „ 1 „ M 33 20 „ 69 *10. ,, ,, 3 3 3 3 1 ,5 3 3 3 3 22 „ 76 Ethyl Succinate. 11. 25 gm. 80 cc. 4 cc. 100 cc. 34-5 „ 94 *12. 23-5 „ 60 „ 1 ,, 3 3 3 3 29 „ 83 *13. 23-5 ,, 3 3 3 3 1 „ 3 3 ; > 28 „ 81 Ethyl Benzoate. 14. 25 gm. 80 cc. 2 cc. 100 cc. 20 „ 66 *15. 24-5 „ 60 „ l „ 3 3 3 3 16 ,, 53 *16. 24*5 ,, 3 3 3 3 1 ,, 3 3 3 3 18 „ 60 PEOC. EOY. SOC. EDIN. — VOL. XXV. 53 834 Proceedings of Royal Society of Edinburgh. [sess. The yields in the preparations marked with an asterisk were somewhat lower than the others ; this was certainly due to a less efficient fractionating column, — a Young’s rod and disc pattern, with only eleven discs and no constrictions on the outer tube, being used in these cases. If considerable quantities of ester are required, it is not convenient to greatly increase the quantities in any one operation, as the time necessary for distilling off the ternary mixture would be proportionately lengthened. Several lots could be esterified simultaneously, and the product worked up in one lot. If this were done the yields would be larger, for a vacuum distillation cannot be carried out on a small quantity of substance without considerable loss. The benzen can easily be recovered by addition of water to the ternary mixture, and separation from the aqueous alcohol, which forms a separate layer. The benzen is well washed with water, dried, and distilled. Several of the test preparations were made with benzen recovered in this way, and no difference was observable. No doubt the method could be extended to esters of other alcohols besides ethyl alcohol, employing either benzen or some other liquid which forms with water and the alcohol a ternary mixture of suitable boiling-point. I am much indebted to Mr T. F. Cowie for testing the method by making some of the preparations of ethyl oxalate, succinate, and benzoate. Chemistry Department, University of Edinburgh. {Issued separately August 29, 1905.) 1904-5.] Action of Radium Bromide on Eyeball of Frog. 835 On the Action of Radium Bromide on the Electromotive Phenomena of the Eyeball of the Frog. By John G. M‘Kendrick, M.D., F.R.S., and Walter Colquhoun, M.A., M.B. (MS. received June 3, 1905. Read July 3, 1905.) It has been known for the last thirty-four years that when the fresh excised eyeball of a frog is connected by non-polarizable electrodes with a sensitive galvanometer, an electrical current (travelling through the eye from the retina to the cornea) may be detected, and that variations occur in this current, due solely to the action of light on the retina.* It is also well known that salts of radium are luminous in the dark, and that if a tube containing radium f is pressed against the closed lid of the eyeball, or even pressed against the temple, one has the consciousness of luminosity. This being so, it was of interest to ascertain whether this luminosity was due to the radium causing fluorescence of any of the structures of the eyeball, or whether it was due to the direct action of one or other of the emanations of radium on the retina itself. Dr Hardy of Cambridge kindly lent us a specimen of radium bromide enclosed in a small leaden capsule and covered on one side with mica. This was used in the experiments to be described. The mica cover prevents the escape from the radium of the a particles, so that any effect observed was due to the action of the /3 or y rays, or of both conjointly. * This phenomenon was first observed by Holmgren, of Upsala, in 1871 : it was investigated independently by Dewar and M ‘Kendrick in 1872-3 ; and since then it has been examined by Kiihne and Steiner in 1880-1, by Engelmann and Grijns in 1891, by Fuchs in 1894, by Beck in 1899, and by A. D. Waller in 1900. The bibliography is fully given by Waller at the end of his paper, “ On the Retinal Currents of the Frog’s Eye, excited by light and excited electrically,” in the Phil. Trans. Roy. Society, vol. cxciii., B. 1900, p. 163. The time relations of the phenomenon have also been elabo- rately investigated by Gotch, Jl. of Physiology, vol. xxix. p. 388, 1903, and vol. xxxi. p. 1, 1904. In the last paper he specially studies the effects of monochromatic light. t By “ radium ” is always meant “a salt of radium.” 836 Proceedings of Royal Society of Edinburgh. [sess. The galvanometer employed had a resistance of 8498 ohms. The scale was 15 feet from the mirror, and the source of illumina- tion was a Nernst lamp. The non-polarizable electrodes were of the trough form, first used by Du Bois Reymond.* We con- structed a dark box, of which we give a drawing in outline. The box is 29 cm. in length, 10*5 cm. in breadth, and 11 cm. in height. On the bottom is a groove, having thick edges, which is exactly the width of the troughs, so that these can he kept securely in position, while they can be slid longitudinally (that is, approximated or sepa- Arrangement for experiments with Radium on Frog’s eye. A.B. Non-polariz- able electrodes. O. Holder for radium. D. Dotted line shows an out- line of the lead plate, which can be interposed between radium and eye. The dotted outline shows the dark box, with the lid open, so as to admit light, when radium was not used. rated) as required. In the middle of the upper surface of the box, corresponding to the lid, there is a little shutter for admitting or excluding light. The box is provided with binding screws, by which the troughs may be connected with it and with the galvanometer. On one side of the box, just in the middle, and at a sufficient height, we cut a rectangular hole through which we passed an accurately fitting piece of lead 85 mm. in length, 20 mm. broad, and 3 5 mm. in thickness. The end of the lead inside the box ended in a T-shaped portion, the T being 38 mm. in length. This piece of * These I used because I have been accustomed to them for thirty-five years. — J. G. M‘K. 1904-5.] Action of Radium Bromide on Eyeball of Frog. 837 lead was used as a screen, which could be placed between the radium and the eye at pleasure. We have found this little dark chamber of great service in these experiments. Recognising the fact that the luminosity of radium, or of bodies rendered fluorescent by radium, is most apparent after the eye has been kept for some time in the dark, we made use of the eyeballs of frogs that had been kept for at least forty-eight hours in absolute darkness, and the animal was killed and the eyeball was usually dissected out in monochromatic red light, such as is used in a photographic chamber. We found that this procedure greatly increased the sensitiveness of the eye to light, when the experiments were made in the usual way with a lighted match or taper, or when the shutter in the upper surface of the box was opened so as to allow the light from a few incandescent lamps to fall on the eyeball from an electrolier hung about 12 feet above the apparatus. In the dark box a small brass forceps was arranged so as to hold the leaden capsule containing the radium in such a position that the radium was directed to the cornea of the eyeball placed on the clay pads of the electrodes. As already described, the movable lead screen could be pushed out and in. When “ in,” the T-shaped piece screened off the radium from the eyeball : when “ out,” the radium acted on the eyeball. “ Radium on ” was obtained by pulling the lead out ; “radium off,” by pushing it in. Expt. 1. Eye placed on the mica cover of the capsule and the clay points brought into contact with fundus and centre of cornea. Resting current, 60 divisions on scale. Current steadily fell in five minutes from 60 to 28. Steady for five minutes at 24 divs. ; then “light on,” rise to 27, fall to 26, rise to 29 divs. ; “light off,” rise to 30, then fall to 21 divs. Expt. 2. (a) Eye readjusted on electrodes with radium capsule screened off by lead plate. Resting current, 25 divs., fall in two minutes to 22 divs. Radium on, rise to 24 divs., remained steady for one minute; radium off, rise to 26 divs., fall to 21 divs. (&) Resting current, 18 divs. Radium on, rise to 19 '5 divs., fall to 19, rise to 20 divs. ; radium off, rise to 21 divs., fall to 17 divs. These experiments are typical of others. It would appear that radium rapidly diminished the initial resting current, but the per- centage of increase produced both by radium “on” and radium “off” was sometimes greater than with ordinary light “on” and “off.” 838 Proceedings of Royal Society of Edinburgh. [sess. Expt. 3. Comparison of action of light and of radium on same eye. Eye adjusted on clay pads, so that it could be submitted to action either of radium or to the light from a taper held 2 feet from eye. Resting current, 40 divs. Radium on, rise of 1 div. ; very slight fall ; very slight rise ; radium off, rise of 1 div., then fall to nearly 40. Radium removed from box. Eye in dark for five minutes. Light on, rise of 10 divs., slight fall ; rise of 1 div. ; light off, rise of 5 divs., then fall to somewhat below starting point. Rest for three minutes. Light on, rise of 6 divs. ; slight fall ; light off, rise of 2, then fall. The eye was then readjusted on the pads.. Total resting current, 70 divs. Light on, rise of 8 ; slight fall ; light off, rise of 5 divs., then fall. The radium was again introduced and was placed nearer the eyeball. Total resting current, 70 divs. ; radium on, rise of 7 divs. ; radium off, rise of 5, then fall. Two other experiments may be quoted, the one showing action of light and the other the action of radium. Light. Fresh Eye. A. (1) Resting current, 22 divs. ; light on (taper, 2 feet off), rise to 26 divs.,. steady for one minute ; light off, rise to 30 ; fall to 21 divs. (2) Resting current, 19 divs. ; light on, rise to 26, fall to 20, rise to 27 divs. ; steady ; light off, rise to 30, fall to 21 divs. (3) Resting current, 19 divs. ; light from red lamp, 2 feet off, rise to 20, fall to 18 '5 divs. ; light off, rise to 21, fall to 18 ’5 divs. (4) Resting current, 13 divs. Red light on, rise to 19, fall to 18, rise to 19, fall to 17 divs. ; light off, rise to 21, fall to 16 divs. It is interesting to note that in this experiment the eye was- sensitive to the rays of red light from a lamp which we employ in a photographic chamber. Radium. Fresh Eye. B. (1) Large resting current; TV = 20 divs. ; radium on, rise of ’5 div., slight fall ; radium off, rise of *5 div., then fall. (2) Full current used, without shunt = 120 divs. Radium on, rise of 3 '5 divs., slight fall ; radium off, rise of 3 divs., then fall. (3) Repeated, radium on, rise of 2 divs., fall of 15, rise of 1*5, fall of 1 div. ; after two minutes’ exposure, radium off, rise of 3 divs., then fall to original position. (4) Full current, 54 divs. ; radium on, rise of 2 ‘5, fall of ’5, rise of l-5 div. ; radium off, rise of 3 divs., fall to 53 divs. The radium was removed and eye kept in dark. We note also that ten minutes thereafter the resting current was 44 divs. ; light on, rise of 11 div. ; steady ; light off, rise of 6 divs. , and then fall to 43 divs. Repeated experiments similar to Expt. (3 B) gave similar results. With radium on there was always a rise of 2 to 3 divs., then a slight fall, say of 1-5, then a second rise of 1 div., and then a slight fall. With radium off there was a slight rise of usually 1 div., and then a rapid fall off towards original position. After 1904-5.] Action of Radium Bromide on Eyeball of Frog. 839 the radium was removed the light from the overhead electric lamps gave the usual phenomena, namely, a rise of from 5 to 8 divs. when light on, and a rise of 4 to 6 divs. when light off. We next examined the fluorescing properties of the specimen of radium in our possession. This was done with the aid of a blackened box 43 cm. long, by 27 cm. broad, and 36 cm. in height. There was a hole in the end of the box, and when the box was inverted on the table, and a cloth was placed over the observer’s head when he looked through the hole (as in focussing a camera), there was total darkness. Various minerals and fluids were placed before the radium, and fluorescence was observed. One substance in particular, willemite (zinc ortho-silicate), gave beautiful results. The radium was placed within two pill boxes, with the radium facing the bottom ; the bottom of the pill box was covered with black paper, and a bit of thin aluminium was also interposed, but still fluorescence, although faint, could be observed. When the pill box was directed to the eye of the observer, with the coverings before mentioned, it appeared to be absolutely black, that is to say, no rays emerged which acted on the eye of the observer. The interposition of a lead plate produced absolute blackness. When the pill box was reversed so that the bottom of the leaden capsule was towards the observer’s eye, there was absolute darkness. Expt. 4. A sheep’s eye fresh was placed in the dark chamber, with the radium opposite. No fluorescence of the cornea was observed. The anterior segment of the eyeball was cut off, leaving the lens and the vitreous tumour ; no fluorescence. The lens alone gave no fluorescence. The vitreous was evacuated without injuring the retina ; no fluorescence. Finally the vitreous and retina were removed so as to expose the brightly shining sclerotic ; this showed no fluorescence. The eyeball of a large frog was examined in the same way with negative results. The lenses of several eyes were examined, but no fluorescence was observed. It would appear, therefore, that none of the structures of the eyeball are fluorescent, and that the action of radium in the retina cannot arise from light so produced. Expt. 5. The willemite that fluoresced with radium was now placed in the black box between the electrodes ; an eyeball was so placed on the pads that its cornea was directed downwards towards the fluorescing mineral ; and the radium holder was so adjusted that the radium was directed past the side of the eyeball, downwards towards the fluorescing mineral. On looking into the little box with a cloth over the head the mineral was seen to be fluorescent. The lead plate could be interposed between the radium and the fluorescent surface. 840 Proceedings of Royal Society of Edinburgh. [sess. In this way it was possible to examine the action of the fluorescent light on the eye. The usual phenomena occurred, but the amount of increase with radium on and radium off was only about one-eighth part of that produced by light on and light off in the same eye in a subsequent experiment. Expt. 6. The surface of the mineral was covered with black paper. No fluorescence. Still radium on and radium off gave a slight + effect, about 1 div. Black paper was then placed over the radium. There was still a slight effect, about '5 div. Expt. 7. Another eyeball placed on pads, so that the cornea faced upwards. The mineral was removed. Radium was placed so as to be directed to cornea, but lead plate could be interposed ; the usual phenomena were detected. A glass slide 1 -5 mm. thick was placed over eye ; usual effects observed, but much smaller. A strip of aluminium 1*5 mm. thick was placed over glass slide. Still an effect of 1 div. could be observed with radium on and radium off. In Expt. 7 it may be assumed that some or most of the /3 rays were cut off ; if so, the small effect was due to the y rays. The next experiment is adduced as an example of several, which appear to indicate that after the influence of radium on an eye for a short time the eye becomes more sensitive to the action of ordinary light. Expt. 8. Eye placed on pads with cornea directed upwards. Radium above, in usual position, facing cornea. Yery large resting current, and, by means of a shunt, only x^-th part of it was used, represented by 20 divs. on scale. With the full current, radium on gave a rise of 5 divs., then a slight fall, then a rise of 1'5 divs., and again a slight fall. Radium off gave a rise of 3 divs., and then a fall to near the original point. The radium was then enclosed in a pill box having the bottom painted black, the radium being directed towards the blackened bottom. Radium on, rise of 2 divs. ; radium off, rise of 2 divs., and then a fall to 4 divs. below original position. Again, radium on, rise of 2 divs., slight fall, rise of 5 divs. ; radium off, rise of 2 divs., fall to original position. After an interval of three minutes, light from the electric lamps was allowed to fall on eye by opening shutter on upper surface of blackened box ; a rise of 35 divs., then a slight fall ; light off, rise of 5 divs., then fall to original position. The eye was kept in the dark for thirty minutes (in the small black box). When the lid was opened, in the darkened room, with no electric lamps, there was a rise of 15 divs. ; when the lid was closed there was a rise of 1 *5 divs. , and then a fall to the original position. This was the most sensitive eye we have ever seen.* The next experiment is illustrative of an attempt to exclude the * Note by J. G. M‘K. I have seen hundreds of the original experiments during the last thirty years, but I have never met with an eye so sensitive as this one. 1904-5.] Action of Radium Bromide on Byeball of Frog. 841 J3 rays by means of glass. A little frame was made into which was fitted by superposition thirteen microscopic cover -glasses, giving a total thickness of 4 mm. This frame could be interposed between the radium and the eye by the same method as that followed with the lead plate. Expt. 9. Eye placed on pads. Resting current, 60 divs. Radium on, rise of 1 div., slight fall, rise of 5 divs. ; radium off (by interposition of glass), just a perceptible rise, then a fall to original position. After three minutes, experiment was repeated. Radium on, rise of 2 divs., fall of 5 divs., then a rise of 5 divs. Radium off (glass interposed), barely perceptible rise, then fall to original position. This was not a conclusive experiment. Several other experi- ments were performed, which generally showed that the effect of radium was less when the glass slips were interposed, but we are not quite confident on this point. Our general conclusions are : — (1) That the light emanating from radium bromide affects the electromotive phenomena of the living retina of the frog in a manner similar to that of ordinary light, although to a considerably less degree. (2) That this action is not due to fluorescence of any of the structures of the eyeball, but to direct action on the retina. (3) That the retina of the frog’s eye will still respond to emanations of radium passing through cardboard, blackened paper, thin glass, and aluminium foil, emanations which, when allowed to fall on the human eye in a perfectly dark chamber, do not give rise to a luminous sensation. (4) That the frog’s retina is susceptible to the feeble light emitted from the surfaces of fluorescible minerals and fluids rendered fluorescent by radium. (5) That the /3 rays are responsible for most of the effects observed, but that after those have been largely excluded, a slight effect still persists which, presumably, must be due to the y rays. (6) That monochromatic light which is employed in a photo- graphic chamber may still alter the electromotive phenomena of the living retina of the frog. Note. — We note that Kiihne and Steiner, and also Gotch, found the advantage of using the eyes of frogs that had. been kept for 842 Proceedings of Royal Society of Edinburgh. [sess. twenty-four hours in absolute darkness. We kept the animals in darkness for a much longer time — in some cases for three or four days. We also used a specially constructed trough, by which the animals were subjected to red, green, or blue light for long periods by the use of appropriate filters. It was not difficult, as could be proved by a spectroscopic examination of the fdtering medium, to obtain fairly pure red and green light, but we cannot say the same of blue. The retinas of the animals could thus be, as it were, “ adapted” to red, green, or blue rays. As Professor Gotch is working at this subject, we do not propose to go further, in the meantime, with these experiments, but we recognize their great importance as being an objective method of investigating the validity of the various theories of colour vision. With eyes so “adapted” we obtained electromotive effects considerably greater in magnitude than those noted by Gotch. We also made some experiments with Wood’s ultra-violet light filter, and with “light off” we detected a slight upward movement of the light on the galvanometer screen. As, with a sensitive eye, the smallest leakage, or the slightest movement of the box in performing the experiment, might account for this, we agree with Gotch that no proof has yet been given that the ultra-violet rays produce any effect. ( Issued separately August 29, 1905.) 1904-5.] Cape Hunting Dogs (Lycaon pictus). 843 Cape Hunting Dogs (Lycaon pictus) in the Gardens of the Royal Zoological Society of Ireland. By D. J. Cunningham, F.R.S., Professor of Anatomy, University of Edinburgh. (With Two Plates.) (MS. received July 3, 1905. Head same date.) In October 1894 a pair of Cape hunting dogs were acquired by the Royal Zoological Society of Ireland and added to their collection in Phoenix Park. They were purchased from Hagen- beck, in Hamburg, and at the time they came to Dublin they were not quite full grown. Although still existing in considerable numbers over a very wide area in Africa, the Lycaon is by no means a common specimen in Zoological Gardens, and it is rare to meet with it on the lists that are periodically issued by dealers in wild animals. The characters of the Cape hunting dog are so fully described in most books on natural history, that is not necessary to dwell on them in this communication. Although placed in a separate genus, there is little either in general appearance or in structural detail that distinguishes it from the lupine members of the genus Canis. As is well known, the dog has five toes on the front foot and four on the hind foot. The Lycaon has -four toes on both fore and hind feet (fig. 1) ; and this, with certain minor dental peculiarities, constitutes the chief structural difference between it and the genus Canis. In size and general form it resembles an English collie, but its legs are longer and more slender and its head is remarkable on account of its breadth. The feature which chiefly catches the eye is its peculiar coloration. The prevalent or ground colour is a dusky, dull black, but this is interrupted by numerous blotches and spots of light yellow and white, which are scattered very irregularly over the body and limbs. Ho two Cape hunting dogs are marked precisely alike, and yet the general effect is the same in them all and very different from the uniform and more sombre hues which as a rule distinguish the members of the genus Canis. 844 Proceedings of Royal Society of Edinburgh. [sess. The superficial resemblance which the Lycaon is said to present to the spotted hyena (Hyena crocuta) is commented on by most authors, and it is generally regarded as affording an instance of mimicry. It is difficult to conceive how such borrowed plumes could he of any advantage to the Cape hunting dog, seeing that it is in every respect bolder and more self-reliant than the cowardly and skulking hyena. For my part I must confess that this resemblance, except in the shape of the head, never impressed me. The Lycaon holds its head erect ; its limbs are slender and long ; it is not so bulky ; its coloration and its action are quite different (fig. 2). Still, this fancied resemblance has earned for it the name of the “Hyena dog.” In captivity the Cape hunting dog is very intractable. The pair under consideration were in the Zoological Gardens of Dublin for nine years, and during the whole time they showed the same savage temper and never acquired any appreciable liking for their keeper. The Lycaon does not bark like a dog, but this is not remarkable, seeing that the “ bark ” is said to have been acquired by the latter through domestication ; nor does it snarl or howl like the wolf. When excited, as on the approach of food, it sets up a continuous jabbering or chattering cry something like the whinny of a horse, which is very distinctive hut very difficult to describe. This was the only sound which the Dublin specimens emitted except when they were separated from each other, and then, although on these occasions the male was placed in a remote part of the Gardens, they managed to keep up constant communication with each other by a series of loud, piercing cries. But the object of this paper is to put on record certain points which were observed in connection with their breeding. Between January 1896 and January 1900 no less than six litters were horn. It is sufficiently rare for these animals to breed in captivity to make this a matter of some interest. Two or three litters are known to have been horn on the Continent (notably in Amsterdam), but so far as I am aware in no case have any of the young survived. Personally I never saw the act of coitus : but Flood, the keeper of the lion house, and a man of large experience in 1904-5.] Cape Hunting Dogs (Lycaon pictus). 845 the breeding of carnivora, informs me that during the act the male does not become “ locked” to the female as in the case of the domestic dog. The following table gives the leading details regarding the six litters born in the Dublin Gardens : — Date of Birth. Number of Puppies in Litter. Period of Gestation. First litter Second litter . Third litter . Fourth litter . Fifth litter Sixth litter Jan. 6, 1896 Jan. 4, 1897 Jan. 1, 1898 Nov. 8, 1898 May 16, 1899 Jan. 1900 4 5 (1 reared) ? 12 (2 reared) ? 80 days 80 ,, 78 „ 86 ,, 80- ,, 80-82 (?) What strikes one first in studying this table is that four out of six litters were born within the first few days of January, and that in the case of the first three litters the births were separated from each other by an interval of one year. Shorter intervals, viz., one of ten months and two of nine months, intervened in the case of the last three litters. It is not easy to offer a satisfactory explanation of the irregularity of the fourth and fifth litters. I am inclined to believe, however, in the absence of definite information on this point, obtained from the animals in a state of nature, that the Lycaon breeds only once a year, and that the irregularity noticeable in the case of the fourth and fifth litters is due to a tendency on the part of the Dublin specimens to adapt themselves to the climatic conditions of Ireland. At the same time it should be mentioned that certain indications were observed in connection with the demeanour of the parents towards each other which seemed to indicate that the sexual instinct was excited at more than one period in the year. The period of gestation was accurately ascertained in the case of the first five litters, and approximately in the case of the last litter. It may be reckoned as being eighty days. This is seventeen days longer than in the case of the domestic dog, and, as might be expected, the young when they are born are more lusty and more advanced in development than new-born puppies of the dog. Still, they are born with their eyelids closed. On one occasion (fourth 846 Proceedings of Royal Society of Edinburgh . [sess. litter) the period of gestation was lengthened out to eighty-six days, but this was no doubt due to the unusually large size of this litter. All the puppies of the first litter died within a few days of their birth. The conditions under which they were born were very unfavourable. The only preparation which was made was the removal of the male from the cage. The cage was in the small carnivora house, and the only means of secluding the mother was by boarding up the front of the den. This was not sufficient. The noise of the visitors in the house alarmed the mother so much that during the day-time she kept continually careering round her compartment with one or more of the puppies in her mouth, seeking a place where she could conceal them. The puppies stood this treatment for three days and then they all succumbed. On the second occasion elaborate precautions were taken to reproduce as far as possible the conditions under which these animals breed in a state of nature. In a secluded part of the Gardens a den was prepared from the back of which a narrow passage, constructed to resemble a burrow, led into a second smaller compartment. The burrow, and the recess to which it led, were buried deeply under a mass of closely packed straw and peat- moss, with the object of deadening the many noises that take place in a zoological garden. The prospective mother took very kindly to her new quarters, and when her young were born she showed none of the former restiveness and came out at regular intervals to the front den to feed. After a day or two had elapsed a mistake was made. A foster-mother in the form of an Irish terrier having become available, the temptation to remove some of the puppies and place them under her care proved too great, and accordingly two were selected for this purpose. The next day one of the remaining three puppies was found dead at a distance from the others. Evidently the keeper’s hand had touched it, and the mother had thrust it out from the others and had allowed it to die of cold. This alarmed us for the safety of the remaining two, and we determined to rear three with the foster-mother. One only was left with the mother, and on the morning following the second removal it had totally disappeared. It had been devoured by the mother. 1904-5.] Gape Hunting Dogs (Lycaon pictus). 847 This was a very unfortunate circumstance, because everyone who has experience in the breeding of wild forms of carnivora knows that when the mother has once acquired the habit of eating her offspring, it is useless to expect that she will ever again properly perform the maternal duties. Of the three puppies which were placed with the foster-mother, two died — one from natural causes and the other from an accident. The survivor, a male, was reared until he became six months old, and then he was presented to the Zoological Society of London (fig. 3). He was, however, very difficult to bring up, and required constant care on the part of one of our most experienced keepers. Part of the treatment carried out was to rub cod liver oil well into the skin. This was done under great difficulties, because the puppy was very savage, and as early as six weeks after its birth it snapped viciously at anyone who touched it. When nearly four months old, a curious incident occurred. It was given a little terrier puppy as a companion, and in the course of their play the sharp teeth of the terrier scratched one of the fore feet of its mate, so that blood began to flow. Ho sooner did the young Lycaon see the blood than it began to attack its own foot with the greatest fury, and, before it could be stopped, it had torn off a toe and had lacerated the foot to a very considerable extent (fig. 4). The third litter came two days before it was expected. The male had not been removed. Not a trace of this litter was ever seen. The fourth litter was remarkable on account of its great size. The puppies, however, were considerably smaller than those of the first two litters. On this occasion a foster-mother had been pro- cured, hut she was quite unable to provide for so numerous a family; consequently, although in three days two other foster- mothers were obtained, ten of the puppies died. Of the two survivors one (a male) succumbed when very nearly full grown, whilst the other (a female) lived for four or five years in the Gardens (fig. 5). The last two litters were destroyed and devoured by the mother before the keeper had an opportunity of removing them. It is interesting to note that certain features which are very 848 Proceedings of Royal Society of Edinburgh. [sess. characteristic of the adult Lycaon are absent in the new-born puppy. In the latter, the coloration and markings are different. There are no yellow patches. The body and head, in almost every case, were uniformly black ; whilst the legs, and in some cases the thighs, were mottled black and white ; further, in every specimen the terminal half of the tail was white. The yellow patches do not make their appearance until the third month, and it is long before they assume the vivid tone of the adult. At an early period two light patches begin to appear on the forehead — one on either side. The dark median band which separates these was a striking feature in both the parents, and in the figures of other specimens of the Lycaon which have come under my notice it is generally more or less distinctly represented. The ears of the new-born puppy are small and by no means obtrusive. In the adult they are large, wide-spreading, and erect, and give a peculiarly rakish look to the animal. It is towards the end of the second month of puppyhood that the ears begin to shoot out, and at the end of the fourth month they are relatively as large as in the adult. An attempt was made to obtain a cross between the Lycaon and the domestic dog. For this purpose a female collie was purchased, and when the proper time came she was placed with the male Lycaon. I need hardly say that, in view of the savage nature of the Cape hunting dog, this was not done without some misgiving and certain precautions being taken for the safety of the collie. During the few days that the latter remained in the cage she showed the greatest fear of her companion, whilst he on his part treated her with the utmost contempt, and took not the slightest notice of her. In view of the very manifest discomfort and terror evinced by the collie while in the cage, the experiment was not repeated. In putting these few notes together regarding the breeding of the Cape Hunting Dogs, I must express my indebtedness to Mr Thomas Hunt, superintendent of the Zoological Gardens in Dublin, for the material help that he has given me. ( Issued separately August 29, 1905.) Proc. Roy. Socy. of Edin.\ [Vol. XXV. Fig. 1. — The fore feet of a newly- born Lycaon. Fig. 2. — Male Lycaon to the right ; young female, bred in the Dublin Gardens, on the left. (From a photograph by Professor Alfred Scott.) Fig. 3. — Young Lycaon two months old (second litter). (From a photograph by Mr C. A. K. Ball, F.R.C.S.) Pkof. D. J. Cunmngham. Proc. Roy. Socy. of Edin."\ [Vol. XXV. Fig. 4. — Same specimen as seen in Fig. 3, when four and a half months old. (From a photograph by Mr C. A. Iv. Ball.) Fig. 5. — Two specimens of the fourth litter when a few weeks old. (From a photograph by Lafayette.) Prof. U. J. Cunningham. 1904-5.] On the Magnetic Properties of Demagnetised Iron. 849 Note on Some of the Magnetic Properties of Demagnetised and Annealed Iron. By James Russell. (Read June 19, 1905.) In a paper laid before this Society in July 1902, the magnetic seolotropy of iron demagnetised by decreasing reversals of co- directional and transverse magnetising forces, and also of iron left transversely magnetised, was established. In later communications (July 1903 and July 1904) it has further been shown that iron and nickel demagnetised by decreasing reversals of a directional force, develop an induction component at right angles to the subsequent magnetising force, which tends to disappear as saturation values are reached, when the angle between these two forces is other than 0° and 90°. In annealed iron this property is absent. The present preliminary communication is limited to experiments made with one sample of transformer iron, demagnetised by de- creasing reversals of co-directional (C) and transverse (T) forces and also by annealing (A). The letters C, T, and A will be used to represent these three conditions of demagnetisation respectively. The magnetic properties determined are: — permeability, reten tivity, coercive force, and the energy loss due to hysteresis. Permeability. — B-H curves of induction have been plotted for values of the magnetising force between the limits of H = 0*1 and H = 10. One set of curves, three in number, measures the induction from zero, due to the first application of many given values of H, superposed upon conditions C, T, and A respectively. Another set of curves measures one-half the induction change on reversal of the given values of H, after conditions C, T, and A respectively have been subjected to or modified by 200 reversals of that force. If any given value of H be represented by h, then Ch , T h, and Ah may conveniently signify that before the readings, from which these curves were plotted, had been recorded, h had first been superposed upon the molecular conditions of demagnetisa- tion and reversed 200 times. PROC. ROY. SOC. EDIN. — YOL. XXY. 54 850 Proceedings of Royal Society of Edinburgh . [sess. When the values of H are low — about 1 C.G.S. unit — the B-H curves are in the following ascending order : — T, Th, Ah, A, C, Ch, . . . (1) When the values of H are taken somewhat greater than 1*8 C.G.S. units, the ascending sequence is as follows T, Ah, Th, C, Ch, A, (2) And when H reaches about 5 C.G.S. units, the sequence is : — The more important conclusions are : — First. Reversals of H produce opposite effects in annealed and demagnetised iron. In annealed iron successive repetitions of a magnetising force give, as is well known, “a gradually diminishing range of magnetic change ” (Ewing). The permeability of the iron is decreased. In demagnetised iron, on the other hand, one- half the magnetic change of induction produced by the 1st or the 10th or the 1000th reversal is always greater than that produced by the first application of a given magnetising force. In other words, the permeability of the iron is increased. This has been verified over a wide range, and is true irrespective of whether the iron has been demagnetised by decreasing reversals of co-directional or transverse forces. (See (1), (2), and (3).) Second. To a first application of the magnetising force, and when the values of H are low, annealed iron is less permeable than iron demagnetised by a co-directional force, but more permeable than iron demagnetised by a transverse force. (See (1).) When H exceeds the value of T8 C.G.S. units, annealed iron is more permeable than iron demagnetised either by a co-directional or by a transverse force. The greater permeability of annealed iron in comparison with iron demagnetised by a co-directional force is well known (Ewing), but it does not apply when the values of H are low. (See (1), (2), and (3).) The B-H curves for annealed and co-directionally demagnetised iron cross ; that for transversely de- magnetised iron remains lower than both throughout a wide range. Third. Reversals of the magnetising force modify the molecular condition of annealed and demagnetised iron, so that co- T, C, A, (3) 1904-5.] On the Magnetic Properties of Demagnetised Iron. 851 directionally demagnetised iron remains more permeable than annealed (Ewing, 1885 ; Searle, 1905) and transversely demagnetised iron until these curves coalesce, when H approximates to 5 C.G.S. units. Under the same conditions of reversals, annealed iron is more permeable for low values of H than transversely demagnetised iron; but there are indications that these curves cross to some slight extent before all three unite, as above mentioned. (See (1), (2), and (3).) Retentivity. — Measurements have also been made on the with- drawal of the magnetising force after its first application. The curves of residual magnetisation so obtained, accentuate the relative differences which exist in the induction curves under the conditions C, T, and A of demagnetisation. The hysteresis loops, still to be described, also show that the same result obtains when the residual magnetisation is measured on the withdrawal of the magnetising force after it has been reversed 200 times. Coercive Force. — The iron was also carried through six sets of cycles between the positive and negative limits of B == ± 70 and B= ±2230. Each set consisted of three hysteresis loops plotted from observations recorded after the particular values of H required to produce the same induction for each set, under the three con- ditions of demagnetisation, had been reversed 200 times. It was found that the curves of each set of cycles cross the horizontal axis and each other at the same point ; and that, consequently, equal negative values of H are required to reduce the iron to zero magnetisation from equal positive values of induction, whether the iron had been demagnetised by a co-directional or a transverse force or by annealing. The coercive force of the iron, therefore, appears to be absolutely independent of the molecular condition impressed upon the iron by these three methods of demagnetisation. Hysteresis Loss. — The differences which exist between the three hysteresis loops for each set of cycles, having the same maximum values of induction, are most easily described as relative differences of shear. The iron being more permeable under the C h conditions, these loops necessarily attain to + and - maxima at lower values of H (see Permeability — Third), and retain a greater proportion of their magnetisation when H is being reduced and finally withdrawn (see 852 Proceedings of Royal Society of Edinburgh. [sess. Retentivity), than they do under the T h conditions of lower permeability. When H is reversed and reaches that particular value which measures the coercive force for each set of cycles, the curves cross, and the consequence is that the hysteresis loops following upon transverse demagnetisation are sheared over to a greater extent than the loops following upon co-directional demagnetisa- tion. Annealed iron ta,kes its place between these two extremes ; but on the whole, and within the limits above given, the hysteresis cycles approximate much nearer to those of transversely demagnet- ised iron than they do to those of co-directionally demagnetised iron. The areas of the three curves, however, appear to remain the same, so long as the maximum induction is the same. The conclusion is therefore arrived at that the energy dissipated as heat when the iron is subjected to cyclic alternation between positive and negative maxima is not affected by demagnetisation, by co-directional or transverse forces, or by annealing. The above summary of the more important results observable in the curves plotted for one sample of iron is only to be regarded as a preliminary communication on this subject. The publication of the curves, and any discussion following thereon, is reserved until the experiments have been repeated for other samples of iron and also for nickel. It may also be stated that ratio curves have been exhibited, the curve under the Ch conditions having been taken as unity. When H is sufficiently reduced the curves rapidly approximate to one another, and may even cross in some cases in the neighbourhood of H = 0’05. Although the initial permeability of the various curves cannot differ greatly, it is proposed to repeat these experiments at the lowest possible values of H (after the sensibility of the ballistic galvanometer has been adjusted so that maximum readings may be obtained under the given experimental conditions) before attempting a final conclusion. All the experiments have been conducted in zero magnetic field. The importance of the results obtained, in their bearing on any theory of magnetic induction, is obvious. As on a former occasion, I acknowledge my indebtedness to the Royal Society of London for having placed at my disposal a Govern- ment grant for these researches. ( Issued separately August 29, 1905.) 1904-5.] Vanishing Aggregates of Determinant Minors. 853 Vanishing Aggregates of Determinant Minors. By Professor W. H. Metzler. (MS. received May 15, 1905. Read June 5, 1905.) 1. Since a persymmetric determinant is a particular case of an axisymmetric determinant, it follows that every type of vanishing aggregate for axisymmetric determinants is also a vanishing aggregate for persymmetric determinants. The principal object of this paper is to give a series of theorems (I., II., III., IV., V.), by the application of which to any vanishing aggregate of minors of persymmetric determinants new vanishing aggregates are obtained (7-12), which, though true for persymmetric, are no longer true for axisymmetric determinants. It is also shown that certain theorems given by Muir* come out as particular cases of a theorem given by the present writer.! 2. The following types of vanishing aggregates of determinants are known : — (a) Tor axisymmetric determinants : 2 | 1234 15678 1234 1235 + 1236 1237 + 1238 1 5678 4678 4578 4568 4567 2 1234 5678 § = 0 (1) (2) = 0 (3) * Muir, “Vanishing Aggregates of Secondary Minors of a Persymmetric Determinant,” Trans. Roy. Soc. Edin., vol. xl., 1902. This will be referred to hereafter as Muir, paper I. t Metzler, “On Certain Aggregates of Determinant Minors,” Trans. Amer. Math. Soc., October 1901. Referred to hereafter as Metzler, paper I. X Kronecker, “Die Subdeterminanten Symmetricher Systeme,” Berliner Berichte, 1882. § Metzler, l.c., paper I. || Muir, “Aggregates of Minors of an Axisymmetric Determinant,” Phil. Mag., April 1902. Referred to hereafter as Muir, paper II. 854 Proceedings of Royal Society of Edinburgh. 2 1234 5678 = - 2 1236 4578 = 2 6781 4523 (4) (b) For persymmetric determinants : 1 k : : 1 l 1 h h l \ \h k + \ k l j 1 k+ 1 i : 1 /+1 ; 1 h l ! h k + ! k (5) (6) Other aggregates may be obtained by applying the law of complementaries and the law of extensible minors to these.§ 3. In what follows the umbral notation will be used, and the usual law for the sign factor of a term observed. Theorem I. Given any identical relation between the minors of order m of a persymmetric determinant of order n, we may obtain another identity by adding a to the column numbers of each minor , leaving the row numbers the same. The effect of increasing the column numbers is evidently to increase by a the subscript of each element entering the minors of the given identity, and hence the theorem follows at once. Theorem II. Given any identical relation between the minors of order m of a persymmetric determinant of order n, we may obtain another identity by adding a to each row number of each minor , leaving the column numbers the same. This has the same effect as increasing the column numbers, and hence the theorem. Theorem III. Given any identical relation between the minors of order m of a persymmetric determinant of order n, we may obtain another identity by increasing every row number by a and every column number by ft. * Nansen, “Minors of Axisymmetric Determinants,” Amer. Jour, of Math., January 1905. — Metzler, “Variant Forms of Vanishing Aggregates of Minors of Axisymmetric Determinants,” Proc. Roy. Soc. Edin., xxv., 1905, p. 717. t Muir, “The Automorphic Linear Transformation of a Quadric,” Trans. Roy. Soc. Edin., xxxix. L.c., paper I., theorem (A). X Cazzaniga Tito, “Relazioni fra i minori di un determinante di Hankel,” Rendiconti del R. 1st. Lorrib. di sc., e lett., Serie ii., vol. xxxi., 1898. § Muir, l.c., paper I. “The Law of Extensible Minors and Certain Determinants, ” Proc. Edin. Math. Soc., vol. xx., 1901-1902. 1904-5.] Vanishing Aggregates of Determinant Minors. 855 As this has the effect of increasing the subscripts of every element in each minor of the identity by a + /3, the truth of the theorem follows. Theorem IY. Given any identical relation between the minors of order m of a persymmetric determinant of order n, where k of the row numbers are invariant ( the same for each minor), we may obtain another identity by increasing by a each of the other m — k row numbers in each minor , leaving the column numbers the same. The effect in this case is to increase by a the subscript of each element in each row of every minor except in those rows whose row numbers are invariant throughout the identity. If we expand by Laplace’s theorem each minor of the identity in terms of minors of order k, with their complementaries, formed from the k in- variant rows, then since these complementaries are minors of a persymmetric determinant, it follows that the total coefficient of any minor of order k formed from the k invariant rows vanishes,* and the theorem is established. Theorem Y. Given any identical relation between the minors of order m of a persymmetric determinant of order n, where k of the row numbers and h of the column numbers are in- variant (k + hk, and therefore the theorem follows as in IY. It is obvious that instead of increasing the numbers as has been supposed in these theorems, we might have diminished them. It is also obvious that certain restrictions are placed upon the magnitude of a and /3. For instance, in theorem I. the largest row number plus a^f>n, and similarly for the others. 4. If now we apply these theorems to the vanishing aggregates for axisymmetric determinants, we get results true for per- symmetric determinants, but in general no longer true for axi- symmetric determinants. For instance, if we take the Kronecker aggregate, Metzler, l.c., paper I., theorem (1). 856 Proceedings of Royal Society of Edinburgh. [sess. a k h l a k h l a h k l + a l k h = o, or that obtained from it by replacing each minor by its com- plementary, n.lr n h n. 1 = 0, a k a h \ a l . — ■ + : \ h l j : k l : \ k h \ and apply to it theorem I., we get : a k : a h a l . h + a l + CL : — : + : ■■k + a 1 + a '.k + a h + a ■ = 0 which when a = 1 = a becomes (5), or (A) of Muir’s paper. Applying both theorems I, and IV., we have (7) a h + a k + p l + p a k + a h + p l + p Starting with the aggregate 124 356 136 245 + a l -H a k+ph+p = 0 123 123 456 456 + 125 346 145 | 236 I 126 345 146 235 + 134 256 156 234 (8) 135 246 and applying theorem I., we have, making a= 1, 123 124 + 125 126 j + 1 134 i 567 467 457 456 367 1 , 145 146 156 + 347 346 + 345 135 357 + = 0 136 356 = 0. (9) Applying theorem IV. we have, making a = 1 , 134 456 135 I 356 i + + 136 137 + 145 | 346 345 256 156 157 i + 167 336 235 1 234 146 246 + 147 245 = 0. (10) Similar results are obtained from applying the other theorems. Starting with the aggregate 123 456 123 456 + 125 346 126 345 135 246 + 136 245 156 234 = 0 1904-5.] Vanishing Aggregates of Determinant Minors. 857 and applying theorem V. we have, making a = /3= 1, or 134 467 1341 467 ! 136 447 146 347 + 137 446 147 146 347 + 147 346 167 344 346 Starting with the aggregate 1234 = 0. (11) 2 5678 = -2 1236 4578 or 1234 1235 1236 + 1237 1238 5678 4678 4578 4568 4567 and applying theorem IV. we have, making a — 1, 1235 5678 1236 4678 1237 4578 1238 4568 1239 4567 (12) Theorem V. is not applicable in this case. 5. It has been shown that n-k 9 (V) •2 (-1)* ix=i /2n\h$2n\ k\n-k\ \ a a i\ ) (2 n \k\n-k\ V a /2 n-k\ \h+2g) = 2 (-ir’Ph where P,, denotes the product of the two aggregates : (T) Z^1)’3 * 2=1 2n\k\h\2n\k\h + 2g\g a /3 a ix icA /2n—2g—h—Tc\ V n—h—g ) x-vr* 2n\k\h + 2g\g\ CL 1%) 2n\k\h\2n\k\h + 2g\n-k- g a fS a iY iz f2n | k | h + 2g \ n - k - g V a v~9\ ^3 / If the determinant from which these minors are taken be axisymmetric, then these aggregates vanish. '2n\ V If in this relation some of the numbers in be put equal Metzler, l.c., paper I. theorem (2). 858 Proceedings of Royal Society of Edinburgh. [sess. to some of those in 2 n | k a , then some of the terms on the left vanish, and we have the special case given by Muir,* which, as stated by him, is as follows : — “ If to n - 2 - a columns of n elements each there be appended the cf, c2th, . ... , cath and rth columns of a given determinant of the n order , and from the resulting array the rih row be deleted , there being thus produced a square array of the (n - 1)^ order, the determinant of which is Dr , then the aggregate will vanish when the given determinant is axisymmetric.,> As an example, take the case (n , k , h , g) = 5 , 4 , 2 , 0) 12345 | _ 12345 12346 12356 12456 78916 “ 78916 ~ 78915 + 789l4 — 78913 13456 78912 23456 7 89 1 1 12 78 2 1345 916 - 13 78 2 245 916 + 14 78 2 15 78 2 234 916 + 16 78 2 234 9l5 + 123 78 2 25 78 2 134 916 - 26 78 2 134 915 + 34 78 2 36 78 2 124 915 - 45 78 2 123 916 - 46 78 2 235 916 145 I 916 125 916 123 915 + 24 78 35 78 56 78 135 916 2 2 124 916 123 914 and put 9 , 1 = 1,2 respectively, then the last two terms on the left will vanish, having identical columns, and the relation becomes : 12345 12 345 13 245 78126 — 78 2 126 “ 1 78 2 126 56 | ^ 123 + 78 1 2 124 + L.c. , paper I. arts. 17 to 28. 1904-5.] Vanishing Aggregates of Determinant Minors. 859 If 123456 123456 is axisymmetric, the aggregates 2 345 126 ’ 2 245 126 ’ 123 124 all vanish, and therefore the aggregate on the left vanishes. It will be observed that this is entirely independent of the elements in the seventh and eighth rows and columns, which may be any whatever. This is the example given in article 23 of Muir’s paper. We may obtain various other interesting results as special cases of this same theorem. For instance, let us form a determinant of order 2 p + q according to the following diagram : p + r (0) p + q - r (B) (X) (B) (X) (0) (0) (B') j>p + A: r — k h > p + q - r - h p + k r- k h p+q- r-h where in the upper left-hand corner there is a square of p + r rows and column of zeros. The complementary minor of this square has h rows and h columns of zeros, and for convenience they are represented as the first h rows and columns of the minor, but may be any h whatever. The remaining elements of the minor are 860 Proceedings of Royal Society of Edinburgh. [sess. represented by B'. In the upper right-hand corner we have p + k rows of elements represented by B, followed by r -Jc rows of elements represented by X. The elements in the lower left-hand corner are the same as their conjugates. Our theorem applied to the determinant thus formed would be : (2p + q\p + r\h\q \/2p + q\p + r\r + k\k\ \ ai Si ft A a] a2 i ' 2p + q \p + r\f2p + q\p + r\r - Jc\f2p + q\p + r\r - a, a2 / \ a2 i) ff) (p+q-r-h. \P+K-h / i where P* denotes the product of /2 p + q\p-srr\r-k V a, a, 1 2 (clp + q\p + r h \ /2p + q\p + r\h\p + K-h\ V “i 111) \ ai Si 'i ) and the aggregate (2p + q\p + r \h\q\ k' \ ai Si S2P (2p + q\p + r \r- k\i ) '2 p + q \p + r\h\p + Jc-h\ {2p + q\p + r\h\q\n\ \ ! (i) Z(-x)" 3=1 an a0 2 p + q p + r r - K\{2p + q\p + r\r - k\k /2p + q\p + r\ q\(2p + q\p + r\r - k\k \ ai ft A (2p + q\p + r^ /2 p + q\p + r\r- k\ V ai a2) 2p + q p + r \p + k ( X-i O-o i (2p + q\p + r \q\ k \ ai ft J 2p + q\p + r\r- *\(2p + q \p + r \p + + q \p + r \ q | k «i ft J 1904-5.] If Vanishing Aggregates of Determinant Minors. 861 (2p + q\p + r\q\ \ al @2/ (2p + q | p + r | q\ \ ai /V is axisymmetric, the aggregates in the product P< vanish. It will he observed that this is entirely independent of the elements denoted by X. If in addition to ?i = 0 we put h= 1 , then we have the theorem of arts. 29 and 31 of Muir’s paper. As stated by him in its most general form (art. 3 1 ) it is as follows : 11 If two arrays B and B' be taken, B containing q + 1 rows and p + q - r columns and B' containing p + q — 1 rows and q columns , and a new determinant , /\p, of the (p + q)*71 order be formed having for its first p rows all the rows of B except the pth, each preceded by r zeros, and for the first column of the remaining space the last q elements of the vth row of B , and for the other columns the p + q - 1 rows of B', then p=p+ i 2Ap(-r‘ p= i vanishes if the last coaxial minor of the ofh order in A be axisymmetric” In this statement of the theorem, as pointed out by Muir, it is evident that we might substitute for “ the last q elements ” the words “ any q elements,” with the proper change in the statement of the minor which is to he axisymmetric. If we put h — 0 and Jc = q-r= 1 we have the case given in art. 29. Syracuse University, April 1905. ( Issued separately August 29, 1905.) 862 Proceedings of Royal Society of Edinburgh. [sess. Les Concretions phosphatees de l’Agulhas Bank (Cape of Good Hope). Par Dr Leon W. Collet, Mem. de la Soc. Geol. Suisse, assistant de Sir John Murray, K.C.B. Avec une note sur la Glauconie qu’elles contiennent, par Gabriel W. Lee, B.Sc. Communique par Sir John Murray, K.C.B. (With Four Plates.) (MS. received June 9, 1905. Read June 19, 1905.) Introduction. L’liiver passe je regus une invitation de Sir John Murray a venir, en qualite d’assistant, au Challenger Office etudier sous sa direction une nombreuse collection de concretions phosphatees et nodules provenant de depots dragues par les bateaux du “ Department of Agriculture” du Cap de Bonne Esperance et envoyee par Dr J. D. F. Gilchrist, “ Government Biologist of the Cape of Good Hope.” Ces concretions sont quelques fois accompagnees des depots dans lesquels elles se sont formees, d’autres fois les parties fines des depots ont ete lavees et perdues durant la montee du filet. Neanmoins nous pouvons affirmer en nous hasant sur notre etude et sur celle des depdts du Challenger , de la Gazelle , et de la Valdivia dragues dans le voisinage de l’Agulhas Bank, que ces con- cretions phosphatees se forment aujourd’hui surtout dans les sables verts (green sand) et quelques fois dans des sables coquillers grossiers (coarse shell sand), sur toute l’etendue de l’Agulhas Bank et sur la pente continentale. Notre materiel se compose de concretions provenant de 13 stations differentes echelonnees sur toute la longueur de 1’ Agulhas Bank, de la Station 7, lat. 33° 15' S., long. 28° E. ; a la Station 4, lat. 33° 50' S., long. 17° 55' E. ; a partir de la ligne de 100 fathoms (183 m.) jusqu’a la profondeur de 800 fathoms (1460 m.). L’etude de ce materiel nous amena a la decouverte de nou- veaux problemes comme celui de la formation des nodules jaunes ou et le phosphate et la Glauconie nous paraissent jouer un grand role ; aussi nous contentons nous aujourd’hui de donner une de- 1904-5.] Les Concretions phosphates de V Agulhas Bank. 863 scription generale de cette importante collection avec les resultats detailles que nous possedons deja. Une etude subsequente detaillee nous permettra peut-6tre d’elever a la hauteur de verites scien- tifiques ce que nous donnons comme hypotheses. Mon cousin Mr Lee, a eu l’amabilite d’etudier quelques coupes microscopiques de ces concretions; je donnerai quelques unes de ses diagnoses dans le texte, et le reste concernant plus specialement l’etude de la Glauconie en Appendice. Je dois de sinceres remerciements a Sir John Murray qui m’a donne l’occasion de travailler sous sa savante direction une de ces questions d’Oceanographie qui touchent de si pres a la Geologic et h la Chimie. Distribution Geographique des Concretions Phosphatees. Avant de faire la description des concretions de T Agulhas Bank, il me parait interessant de dire quelques mots de la distribution geographique de ces formations. Les geologues ont depuis longtemps reconnu que bon nombre de gisements de phosphorites des depots sedimentaires avaient du etre formes sur le fond des mers des temps passes. Parmi les decouvertes faites par l’Expedition du Challenger , celle de la formation des concretions phosphatees dans les mers actuelles fut d’une grande importance, car comme nous le verrons plus loin cette formation parait etre liee etroitement a d’autres phenomenes oceanographiques qui doivent nous donner une indica- tion sur l’etat des mers des periodes geologiques dans lesquelles nous retrouvons ces memes concretions phosphatees et les con- ditions sous lesquelles elles se sont formees. En 1898 Sir John Murray publie un memoir e d’une grande im- portance, accompagne d’une carte et intitule : “ On the Annual Range of Temperature in the Surface Waters of the Ocean and its Relations to other Oceanographical Phenomena,”* dans lequel il fait entr’autres remarquer que dans tous les endroits de la carte ou nous trouvons les grands ecarts de temperature annuelle de l’eau de surface la Glauconie et les Concretions phosphatees furent draguees premierement par l’expedition anglaise du Challenger f * Sir John Murray, Geographical Journal, vol. xii. p. 113, August 1898. t Reports of the Challenger, “ Deep-$ea Deposits,” p. 891. 864 Proceedings of Royal Society of Edinburgh. [sess. sur 1’ Agulhas Bank, la cote E. du Japon, la cdte d’Espagne, la cote E. d7Australie, la cote du Chili, entre les lies Falkland et l’em- bouchure de la Plata ; puis par l7 expedition allemande de la Gazelle aussi sur l’Agulhas Bank ; par l’expedition americaine du Blake * sur la cote atlantique de FAmerique du Nord et dans le Detroit de Floride, plus tard (1898-1899) par l’expedition allemande de la Valdivia f sur F Agulhas Bank, et dernierement par Alexandre Agassiz sur les cotes du Pacifique nord. Nous devons aj outer a ces collections Fimmense materiel envoye de F Agulhas Bank par le “ Department of Agriculture 77 du Cap et qui vient confirmer la theorie que Sir John Murray donnait en 1898. Comme le montre le dit memoire ces grands ecarts de tempera- ture de Feau de surface amenent dans les regions precitees une immense destruction d’animaux qui a ete specialement observee sur la cdte atlantique de FAmerique du Nord et dans le Detroit de Floride. Sir John dit: “During 1880 and 1881, Professor Yerrill dredged along the Gulf Stream slope, obtaining in this warm belt, as he terms it, many species of invertebrates character- istic of more southern localities. In 1882 the same species were scarce, or totally absent from places where they had previously been abundant, and this, taken in connection with the occurrence of heavy northerly gales and the presence of much inshore ice at the north, leaves little doubt that some unusual lowering of tem- perature in the warm belt brought immediate death to many of its inhabitants. This is more probable, as it is a well-known fact that sudden increase of cold will bring many fish to the surface in a benumbed or dying condition, and there are no indications of any shock or earthquake having occurred at the time the dead fish were first noticed. . . . “It has been estimated that the bottom of the ocean in this region must at the time have been covered to the depth of about six feet with the dead bodies of the tile-fish and other marine organisms , * John Murray, “Report on the Specimens of Bottom Deposits,” Bull. Mus. Comp. Zool ., Cambridge, U.S.A., vol. xii. No. 2. Yoir aussi: Alex- ander Agassiz, “Three Cruises of the Blake,” vol. i. pp. 275-276, Bull. Mus. Comp. Zool., Cambridge, U.S.A., vol. xiv., 1888. t Les dep6ts de la Valdivia sont actuellement en cours d’etude, et la publi- cation des resultats se fera dans WissenscJiaftliche Ergebnisse der deutschen Tief see- Expedition, 1898-1899. Herausgegeben von Carl Chun, Jena. 1904-5.] Les Concretions phosphatees de V Agulhas Bank. 865 and it seems evident, from the subsequent researches of Professor Libbey, that their destruction was due to the lateral shifting of currents from different sources and of different temperatures, thus producing a wide range of temperature even at depths of 50 and 100 fathoms.”* Ce fut precisement a l’endroit ou ces poissons furent tu£s ainsi que dans le Detroit de Floride que de grosses concretions furent draguees par le Blake et V Albatross. Si maintenant nous jetons un coup d’oeil sur la carte des courants marins nous remarquons que Bt oil nous avons les grands ecarts annuels de temperature de l’eau de surface nous avons la rencontre d’un courant froid avec un courant chaud. Les animaux vivant dans le courant chaud seront tues par l’abaissement de temperature a la rencontre du courant froid et vice versa. L’ Agulhas Bank est le lieu de rencontre du courant chaud venant de PEquateur par le Detroit de Mozambique avec le courant froid venant de 1J Antarctic. Des lies Falkland a l’embouchure du Rio de la Plata nous avons la rencontre du courant chaud du Brezil avec le courant froid du Cap Horn. Sur la cote E. de l’Amerique du Nord c’est le courant froid du Labrador qui vient meler ses eaux a celles du Gulf Stream. La cote E. du Japon est le lieu de rencontre du courant froid, venant de la mer de Behring, avec le Kouro Sivo. Sur la cote E. d’Australie nous trouvons un courant chaud venant de l’Equateur qui vient meler ses eaux a celles du courant froid venant de P Antarctic et qui probablement a certaines epoques de l’annee passe le detroit de Bass. Quelle relation existe-t-il entre les concretions phosphatees et les brusques ecarts de temperature de Peau de surface ? Comme nous l’avons vu, ces ecarts de temperature amenent la mort d’un grand nombre d’animaux qui s’accumulent sur le fond de la mer et qui par leur decomposition produiront de l’Ammoniaque et du phosphate de Chaux qui servent a former les nodules et concretions phosphatees. Nous venons de voir quelles sont les conditions sous les- quelles se forment aujourd’hui sur le fond des mers les con- * Loc. cit., p. 130. PROC. ROY. SOC. EDIN. — YOL. XXV. 55 866 Proceedings of Royal Society of Edinburgh. [sess. cretions phosphatees ; si maintenant nous retrouvons dans les- etages geologiques les phosphates et la Glauconie nous pourrons je crois affirmer que ces depots se sont formes non loin de la cote d’un continent, dans une mer peu profonde, sujette a des change- ments de temperature et de salinite. Les nodules phosphates du Tertiaire de Malte furent envisages- par les geologues comme des cailloux roules jusqu’a ce que John Murray* en 1890 eut demontre dans son etude geologique de Malte que ces nodules etaient semblahles a ceux dragues par le Challenger , qu’ils contenaient les mdmes organismes que le calcaire qui leur sert de matrice et que par consequent nous avions la une formation marine sur le bord d’un continent, im- pliquant une mer sujette a de fortes variations en temperature ou salinite. CARACThRES GeNERAUX. Avant de faire la description des concretions de chaque station, il est je crois preferable d’en donner une description gendrale (fig. 1). La plus grande des concretions mesure 23 x 16 x 12 cm., c’est la plus grosse qui ait ete draguee pres de l’Agulhas Bank. La moitie du materiel se compose de concretions de 8 a 16 cm., le reste se compose de specimens variant de 5 mm. a 6 cm. Surmontees de protuberances ou perforees de nombreux trous et cavites, les concretions phosphatees ont en general une forme tres- capricieuse avec des contours plus ou moins arrondis et quelques fois presque anguleux. La matiere qui les recouvre empeche d’en connaitre la structure. Cette matiere est de deux sortes ; foncee et brillante ou grise et mate. Cette derniere est due d’une part a un lavage par l’eau de mer, d’autre part a une foule d’organismes qui ont cru sur la concretion tels que : Coraux, Bryozoaires, Annelides^. Alcyonnaires, Eponges et Eoraminiferes. Cette difference de couleur externe, souvent tres nettement marquee sur un meme- specimen, peut peut-etre nous donner une idee sur la position de la concretion au fond de la mer. La partie grise, surmont4e de restes d’organismes etant dans l’eau, tandis que la partie brillante- et noire se trouverait enfouie dans la vase. * John Murray, “ The Maltese Islands, with special reference to their geological structure,” Scottish Geographical Magazine , vol. vi. p. 449. 1904-5.] Les Concretions phosphates de V Agulhas Bank. 867 Examinees de plus pres ces concretions apparaissent comme formees par une plus ou moms grande quantite d’elements hetero- genes cimentes les uns avec les autres par une pate dont l’tltment principal est le phosphate de Calcium [(P04)2Ca3]. Sur une cassure fraiche ou mieux sur une coupe faite a la machine a travers la concretion, la nature retlle de cette derniere apparait; nous la voyons en effet constitute par des nodules de differentes grandeurs, de couleur grise, jaune ou brunatre, cimentes par une substance compacte jaunatre, dans laquelle se trouvent emprisonnees des coquilles de Foraminiferes, des grains de Glau- conie, de la Calcite en paillettes et des mineraux detritiques. Cette matiere formant le ciment, comme celle qui constitue les nodules,, donne la reaction caracteristique des phosphates. On peut observer souvent des nodules ou des concretions avec des fentes remplies d’une substance verdatre qui me parait pouvoir etre attribute a de la Glauconie. Nous aurions 1& un fait semblable a celui signalt par Mr Cayeux* dans les nodules de phosphates du Cap de la Heve et par Mr Sollas dan's les nodules de l’Upper Green Sand. Concretions de l’Agulhas Bank. Les concrttions phosphattes regues du Cap proviennent de 13 stations differentes ; 9 se trouvent grouptes pres du “ Cape Point ” et les 4 autres sont rtparties sur le reste de 1’ Agulhas Bank. Station. Orientation. Profondeur. Fathoms. Metres. 4 Lion’s Head, S. 82° E. 27 miles (49 km.) de la c6te, 125 228 11 Vasco de Gama, S. 75° E. 13£ ,, (25 km.) ,, 166 304 12 id. N. 71° E. 18 J „ (33 km.) 230 421 17811 Cape Point, E.N.E. 36£ ,, (67 km.) ,, 660-800 1210-1460 17946 id. N. 41° E. by D.R. 38 „ (68 km.) 315-400 576-732 17989 id. N.E. | N. 39 „ (70 km.) 310-560 567-1024 14605 id. N.E. | N. 20 ,, (36 km.) 130 238 17856 id. N. 50° E. 34£ ,, (63 km.) ,, 380-475 690-860 17781 id. E. byN. § N. 34 ,, (62 km.) ,, 480-600 878-1100 1882 Cape St Blaize, N. by E. 73 ,, (133 km.) ,, 125 229 1921 id. N. by E. J E 90-100 165-183 9 Lat. 34° 27' S., Long. 25° 42' 45" E. .. 256 468 7 Cove Rock, N.W. | W 13| .. (25 m.) 80-130 146-238 * L. Cayeux, Contribution a V Elude micrographique des terrains sedi- mentaires. Lille. 1897. 868 Proceedings of Boyal Society of Edinburgh. [sess. Nous ne decrirons que les concretions et nodules les plus in- teressants, specialement ceux des stations 11 et 12 qui sont en grand nombre. Station 11. Yasco de Gama, S. 75° E. 13J miles (25 km.) de la cote. Profondeur 166 fathoms (304 m.). Le materiel de cette station, environ 20 litres, provient de sables verts et se compose presque entierement de concretions phosphatees. La drague a aussi apporte une quinzaine de cailloux roules de quartzites dont le plus gros est de 7J x 6 x 4 cm., les autres varient de 2 a 4 cm. Un fragment roule de schiste pro- vient aussi de cette station et comme semblable roche n’a pas ete trouvee dans d’autres stations en voici la diagnose qu’en donne Mr Lee : (sections 15 et 15') Typique schiste quartzeux, c’est a dire micaschiste pauvre en mica ; il consiste en quartz en quantite pre- dominante ; en muscovite en fines lames et en quelques cristaux 1904-5.] Les Concretions phospliaUes de V Agulhas Bank. 869 de Zircon et de Tourmaline, cette derniere montrant le dichroisme suivant : Ng (fonce) brun olive, Np (clair) verdatre. On y trouve aussi de l’oxyde de Fer. La teneur en Silice est de 82*85 %. Concretions Phosphatees. Une concretion mesure 23 x 16x12 cm., une autre de 12x12x9 cm., puis une quinzaine de 6 a 8 cm. ; le reste du materiel de cette station se compose de concretions de 3 a 6 cm. Un fait nouveau est a noter ; c’est la presence parmi ces concre- tions de quelques fossiles de Lamellibranches et Gasteropodes. J’aurai l’occasion de revenir sur ces fossiles dans la descrip- tion du materiel de la station 12 oil ils sont particulierement abondants. La couleur externe de la pluspart de ces concretions est par places souvent jaunatre ; les sections transversales nous donnent l’explication de cette couleur qui donne aux specimens de cette station un caractere tres particulier. La plupart sont formees par la reunion de plusieurs nodules ciment^s les uns avec les autres, d’une couleur jaune-brun nettement differente de celle du ciment qui les unit. Fait egalement a noter; il n’y a pas de Glauconie en grains dans ces nodules. Les coquilles de Fora- miniferes par contre sont toujours presen tes en plus ou moins grande quantite. J’ai pu sortir un nodule de sa matrice et j’ai trouve entre cette derniere et le nodule une substance jaune verdatre qui, comme je l’ai deja fait remarquer, pourrait etre due a de la Glauconie. Quel est la cause de la difference de coloration entre les nodules et le ciment1? Comme le montrent les analyses suivantes c’est une augmentation en peroxyde de fer. 1. Nodule jaune. Insoluble = 9 -76 % P205 =17-31 % = 37-79 % (P04)2Ca3 CaO =43-81% Fe203 =21-9 % 870 Proceedings of Royal Society of Edinburgh. [sess. 2. Nodule jaune. Insoluble = 4*15% P205 =21-39 % = 46-69 % (P04)2Ca3 CaO = 32-85 % Fe203 =23-70 % 3. Ciment. Insoluble = 31 -82 % (mineraux et Glauconie) P205 = 14-29 % = 31-19 % (P04)2Ca3 CaO =17-40% Fe203 = 4-29 % Ces trois analyses nous montrent : 1° Que le ciment contient plus de mineraux detritiques que les nodules, comme on peut du reste le voir macroscopiquement ; 2° La forte teneur en oxyde de fer des nodules jaunes. La difference du CaO entre les analyses 1 et 2 s’explique par le fait que l’echantillon 1 contenait une plus grande quantite de coquilles de Foraminiferes. Dans les analyses du Challenger nous trouvons 5 '80 % comme chififre maximum de la teneur en fer ; dans une analyse d’un nodule du Blake il n’y en a que des traces. Dans la description des concretions draguees par le Blake * dans le Detroit de Floride, Mr Murray decrit une concretion d’une couleur brune, consistant en une aggregation d’organismes calcaires cimentes par une matiere brun jaune, montrant souvent des anneaux concen- triques a la maniere d’une agate. II eut ete interessant de connaitre la composition cbimique de cette matiere brun jaune ; cette couleur etait probablement aussi due a une grande quantite de fer. Deux ou trois concretions de la station 1 1 ont des caracteres si particuliers qu’il me semble interessant de les decrire. Ce sont plutot des nodules isoles que des concretions, mais des nodules enormes puis qu’ils mesurent jusqu’a 10 et 11 cm. Ho. 21 (fig. 3). Hodule de forme arrondie dans la partie non recouverte d’organismes et de couleur jaunatre ; la partie recouverte d’organismes d’une couleur noire possede de nombreuses cavites et protuberances. Comme je l’ai dejk fait remarquer ces organismes Jphn Murray, loc. cit p. 58. 1904-5.] Les Concretions phosphaUes de V Agulhas Bank. 871 qui croissent sur le nodule ou la concretion doivent nous indiquer sa position sur le fond de la mer. La section nous montre qu’a la partie jaunatre ou inferieure correspond une partie formee presque entierement de coquilles de Foraminif eres et ressemblant aux nodules jaunes precedemment decrits. A la partie superieure ou noire correspond une matiere compacte avec une grande quantite de grains de Glauconie ; cette substance est la meme que celle qui forme le ciment dans les autres concretions. La partie inferieure est separee de la superieure par une ligne de \ mm. d’epaisseur, noire, dont la convexitC est tournee vers la base du nodule. A partir de cette ligne foncee nous voyons la partie formee de Foraminif eres coloree legerement en vert. La ligne foncee comme la couleur verte me paraissent etre dues a la Glauconie. No. 22. Nodule de section subtriangulaire, dont la partie superieure recouverte d’organismes represente la base du triangle et la partie inferieure le sommet. Une section transverse nous montre une structure concentrique autour d’un noyau a la base du nodule. Ce noyau de couleur gris verdatre est constitue par un petit nodule avec organismes ; la couleur faiblement verdatre est probablement due a de la Glauconie pigmentaire. Le cercle qui l’entoure, jaune brun, montre une augmentation en peroxyde de fer ; puis une nouvelle zdne gris verdatre n’entourant que la partie superieure et les cotes de la precedente. La masse qui recouvre ces zdnes, d’une couleur variant du jaune gris au jaune brunatre, ne montre aucune structure. Les organismes remplis par la substance et cimentes par elle sont nombreux, point de Glauconie en grains. No. 13. Concretion formee de 3 nodules cimentes, le plus gros de 10x7x3 cm. est une vraie aggregation de Foraminif eres, remplis et cimentes par une matiere ou pate brun fonce (fig. 5). Mr Lee donne la diagnose suivante d’une coupe mince de ce nodule (section 13). Mineraux tres petits et rares; se com- posant principalement de Quartz et de tres petits Feldspaths. Les grains de Glauconie sont peu nombreux, ils remplissent quelques fois les coquilles de Foraminif eres et sont alors legere- ment color4s et leur birefringence est faible. Les grains isoles ont les caracteres habituels de la Glauconie et montrent une mince zone marginale de matiere amorpbe non coloree et sans structure qui parait appartenir plutot a la matrice qu’aux grains 872 Proceedings of Royal Society of Edinburgh. [sess. de Glauconie eux-memes. Les Foraminiferes et les fragments de coquilles sont tres abondants. La matiere principale, brune, consiste en un melange de materiel amorphe qui contient du Phosphate de Calcium avec de tres petites paillettes de Calcite, qui sont absentes quand la matiere principale remplit l’interieur des coquilles de Foraminiferes. Cette section ainsi que d’autres niontre dans la matiere principale des espaces d’une couleur verdatre et de contours non definis d’un vert plus fonce dans le milieu que sur les bords. Cette couleur verte peut-etre attribute a la diffusion de petites particules de Glauconie. II n’est pas possible de dire si ce phenomene est accidentel ou si au contraire il marque le premier stage de la formation des grains de Glauconie. L’analyse chimique de ce nodule nous a donne les resultats suivants : (P04)2Ca3 48 70 C5 C03Ca - 31-86 fc! S04Ca = 3-39 s e < C03Mg = traces Fe203 2-35 rS A1203 — 3-38 SiO2 = M8 V Perte = 1-19 Residu insoluble = 8-18 100-23 Partie Insoluble. SiO2 = 87-83 Fe203 | = 8-65 A1203 / CaO = 3-10 MgO = traces 99-58 Un fait k noter est la faible quantite de fer de ce nodule comparativement a celle des nodules jaunes (21 et 23 %). La grande quantite de C03Ca est due aux coquilles de Foraminiferes. 1904-5.] Les Concretions phosphaUes de V Agulhas Bank. 873 No. 12. Ce nodule se compose d’un corail de 1*8 x L2 cm. de diametre, fossilise ou si Ton prefere infiltre de matiere phos- phatee. Mr Lee donne la diagnose suivante d’une coupe mince de ce corail (section 12). Parmi les mineraux, le quartz est comme toujours preponderant, en grains anguleux de meme grandeur. Feldspaths tricliniques avec made d’Albite. La Tourmaline et le Zircon sont presents mais rares. Deux autres mineraux n’ont pu etre identifies. La Glauconie est surtout en grains arrondis de plutot grandes dimensions, avec des contours francs, completement fraiche ou reduite a l’etat d’oxyde de fer. Elle est generalement isolee et quelques fois remplit une coquille de Foraminifere ou euveloppe un cristal de Quartz. Dans cette section la Glauconie n’est pas uniformement distribute a travers la matiere principale, mais a une tendance a s’agglomerer, et dans ce cas la matrice entre les grains est plus amorphe, c’est a dire plus pauvre en paillettes de Calcite que dans les autres parties de la section. Quand ils sont isoles les grains montrent souvent une partie externe sans couleur et d’une faible epaisseur, isotrope entre les nicols croises, done sans aucune espece de structure. Les septa du corail montrent surtout a leur terminaison exterieure, une coloration verdatre probablement due a de la Glauconie pig- men taire. Les fragments de coquilles sont peu abondants, mais leur Calcite est completement fraiche. La matiere principale ou pate est la meme que precedemment. L’analyse chimique donne les resultats suivants : 1 (P04)2Ca3 g COsCa it! S04Ca |J COsMg T] PeW | Al2Os 3 SiO2 Perte Residu insoluble 52*05 18-35 3-12 1-02 0-95 3-55 0- 90 1- 91 17-75 99-60 $74 Proceedings of Royal Society of Edinburgh. [sess. Partie Insoluble . SiO2 Fe203 ) A1203 i CaO MgO 87*5 10-0 1-05 1*02 99-57 Si nous comparons ces resultats a ceux du No. 13 nous xemarquons une augmentation dans le xesidu insoluble provenant de la plus grande quantite de minexaux, une forte diminution de C03Ca provenant du petit nombre de coquilles et une legere augmentation de Phosphate. Comparons maintenant ces resultats avec ceux du Challenger et du Blake. Station 142, 150 fh. (274 m.), Challenger (P04)2Ca3 = 43*57 143, 1900 fh. (3480 m.), „ = 5P38 143, 1900 fh. (3480 m.), „ = 49-57 317, 333 fh. (609 m.), Blake =51 -36 11, 166 fh. (304 m.), Nodule jaune = 37*79 id. i'l. =46*69 id. ciment des Nodules =31*19 id. No. 13 =48*70 id. No. 12 =52*05 En resume, ces chiffres nous montrent que la pate ou masse principale des nodules est composee en majeure partie de Phosphate de Chaux dont la. teneur varie de 30 a 50 %. La teneur en Carbonate est sujette a de grosses variations dependant de la plus ou moins grande quantite des organismes calcaires. Dans deux nodules de cette station on peut voir une sorte de passage graduel d’une partie noire qui est presque entierement formee de grains de Glauconie a une partie externe jaune brunatre. Dans un de ces nodules ce passage est particuliere- ment typique, la partie noire glauconitique faisant en quelque sorte office de noyau enveloppe par la matiere jaune bran ; la limite n’est pas franche entre les deux parties. Une idee qui vient naturellement a l’esprit est que cette 1904-5.] Les Concretions phosphattes de V Agulhas Bank. 875 ■couleur des nodules jaunes pourrait etre due a de l’oxyde de fer provenant d’une decomposition de la Glauconie ou que les conditions n’etait pas satisfaites pour la formation de la Glauconie ou hydrosilicate de fer et de potasse, il se soit forme un hydrate ou un oxyde de fer. Station 2624a. Yasco de Gama, S. 75° E. 13J miles (25 km.) de la c6te. Prc ondeur 166 fathoms (304 m.). Les quelques concretions de cette station (7 dont la plus grande mesure 14 x 10 x 8 cm.) ont les memes caracteres que celles de la station 11. Le point du draguage est le meme et le numero different doit probablement seulement indiquer un second draguage a un temps different. Dans une coupe j’ai pu extraire un nodule form 6 de meme substance que le ciment ou la matrice, et j’ai trouve entre cette derniere et le nodule cette substance jaune verdatre dont j’ai deja parl4. Ce nodule montre en outre deux fines zones concentriques de meme substance que le noyau, separees par une ligne plus foncee (fig. 4). Station 12. Yasco de Gama, N. 71° E. 18J miles (33 km.) de la cote. Profondeur 230 fathoms (421 m.). Les echantillons de cette station, env. 40 litres, represented -J- du materiel procure par deux draguages d’une heure chacun avec une large drague. La plus grosse concretion mesure 20 x 16 x 10 cm., nous trouvons en outre une trentaine d’echantillons de 17 a 8 cm., le reste se compose d’une quantite de concretions de 7 a 1 cm. Nous observons egalement un grand nombre de fossiles de Lamellibranches, Brachiopodes ainsi que des coquilles mortes, des fragments d’os, des dents de requins et des coraux. La drague apporta egalement melanges aux concretions, des representants vivants de Lamellibranches, Brachiopodes, Brachy- ures, Schizopodes, Isopodes, Annelides, Alcyonnaires, Holothuries, Coraux et Eponges qui temoignent d’une abondance de vie dans cette localite. 876 Proceedings of Royal Society of Edinburgh. [sess. Concretions Phosphatees. Generalement de couleur exterieure grise et recouvertes en partie ou totalite par des organismes. On est frappe lorsqu’on les compare avec celles de la station 11, de la petitesse des nodules cimentes les uns avec les autres. On ne retrouve plus cette couleur externe jaune des nodules a forte teneur en fer. Le fait de la presence des coquilles de Globigerines en grande quantite et formant souvent entierement les nodules, donne a ces concretions un caractere de mer plus profonde, en outre les mineraux clastiques inclus dans le ciment sont beaucoup plus petits que ceux de la station 1 1 . Quelques nodules se composent uniquement de grains de Glauconie cimentes par le phosphate. Comme on le verra plus loin ces deux manieres d’etre des nodules, tres differentes, me semblent devoir impliquer une dualite de mode de formation. La partie la plus interessante du materiel de la station 12 est formee par des fossiles de Lamellibranches, Brachiopodes et quelques Gasteropodes. Nous y trouvons tous les modes de passage depuis la coquille morte, blanche, a celle completement transformee en phosphate de couleur brillante brune. Les coquilles mortes contiennent du phosphate en plus ou moins grande quantite. La coquille semble avoir ete un point d’attraction pour la matiere phosphatee qui la reinplit. Ces fossiles ressemblent beaucoup aux phosphorites des gres verts de l’Albien de la Perte du Rhone a Bellegarde ou le phosphate s’est concentre dans les fossiles. Nous avons la un exemple de plus du mode de forma- tion des concretions. Ces fossiles remplissant le role de nodules pourront etre cimentes les uns avec les autres par de la matiere phosphatee et donneront des concretions ou pourront etre cimentes simplement par du carbonate de chaux ou de l’argile et donneront alors des gisements de phosphorites semblables a ceux que nous trouvons aujourd’hui dans la serie stratigraphique. 1904-5.] Les Concretions phosphates de V Agulhas Bank. 877 Station 2793a. Yasco de Gama, R. 71° E. 18J miles (33 km.) de la cdte. Profondeur 230 fathoms (421 m.). Le point de cette station est le meme que celui de la station 1 2 ; 11 indique done un autre sondage a un temps different. Les trois concretions phosphatees, les quelques coquilles de Lamellibranches et Gasteropodes rappellent le materiel de la station 12. Un os phosphatise appartenant a un cetace (Globiocephalus V) de 3 x 2 x 1 cm. provient du meme sondage. Station 7. Cove Rock, R.W. f W. 13J miles (25 km.) de la cdte. Profondeur 80-130 fathoms (146-238 m.). Environ deux douzaines de concretions ou plutot nodules, d’aspect ;assez different de ceux des autres stations. La plus grande con- cretion mesure 16x7 x 3 cm., la plus petite 5x5x3 cm. Rous retrouvons quelques unes de ces concretions et nodules a forte teneur en fer, de couleur externe brun jaune ; les autres bien differentes de ces dernieres ressemblent exterieurement a de la ponce. En coupe mince il y a une difference essentielle entre ces deux ■especes de concretions. Mr Lee dit ce qui suit (coupe Ro. YI. nodule riche en fer). Cette coupe ne contient pas de mineraux detritiques. Les nombreuses coquilles qu’elle renferme sont les unes encore fraiches, c.a.d. que la calcite (ou aragonite ?) dont elles sont formees montre la croix noire typique de la structure fibro- radiee entre nicols croises en lumiere parallele; les autres im- pregnees d’une matiere brune (phosphate) abaissant fortement leur birefringence. Quelques unes sont remplies d’une substance brunatre qui represente vraisemblablement un des derniers stades de la decomposition de la Glauconie. La pate brune est la plus amorpbe dans ses parties les plus foncees ; les parties claires sont celles qui renferment le plus de particules de Calcite. Deux dosages de Fer dans deux nodules differents ont donne 13-5 % et 14-9 % en Fe203. (Coupe Ro. V. nodule & aspect de ponce.) 878 Proceedings of Royal Society of Edinburgh. [sess. * Les mineraux sont constitues par du Quartz abondant. Quelques grands cristaux decomposes appartiement peut - etre a de l’Orthose, des cristaux de Plagioclases, quelques grains do Zircon et de la Glauconie. Comme le montrent ces deux diagnoses, il y a une difference essentielle entre ces deux esp&ces de concretions ; celles riche en fer ne contient pas de mineraux detritiques. Comment expliquer cette difference ? La premiere idee qui vient k l’esprit est que les concretions et nodules riches en fer et sans traces de mineraux detritiques pour- raient provenir d’affleurements sous marins ou d’un depot marin plus ancien effectue a un temps ou les conditions de la mer et du continent etaient autres qu’elles ne sont aujourd’liui. D’autre part la profondeur de cette station donnee entre les. limites de 80 a 130 fathoms (146 a 238 m.) pourrait peut-etre expliquer la difference essentielle entre ces concretions. Pendant la duree du draguage le bateau peut avoir subi une faible deriva tion qui de la profondeur de 80 fathoms l’a amene a celle de 130 ; il y aurait eu alors simplement un melange de depots, ceux con- tenant des mineraux detritiques appartenant k la plus faible pro- fondeur tandis que les concretions riches en fer avec sections de Globigerines indiqueraient un regime de mer plus profonde. Cette derniere maniere de voir me parait la meilleure, car on ne peut juger un d4pot a la vue d’une diagnose d’une seule coupe microscopique. Station 17989. Cape Point (approx.), N.E. J K 39 miles (70 km.), de la cote. Profondeur 310-560 fathoms (567-1024 m.). Au nombre d’environ trois douzaines les concretions de cette station sont de petite taille a Texception d’une qui mesure 13x9x8 cm. Toutes sont d’une couleur exterieure foncee. La plus grosse est a moitie recouverte d’organisuies. J’ai deja fait remarquer dans le chapitre des caracteres generaux que la partie brillante et non recouverte d’organismes devait se trouver dans la vase et l’autre partie exposee dans l’eau ; nous pouvons de cette maniere nous fair© une idee de la position de certains nodules sur le fond de la mer. 1904-5.] Les Concretions phosphoMes de V Agulhas Bank. 879' Les grosses concretions des stations 11 et 12 (166 et 230 fathoms) sont en tontes parts recouvertes d’organismes (fig. 1) en plus on moins grande quantite, ce qui prouverait non que les concretions aient ete changees de place sur le fond de la mer,. mais plutot un changement dans le niveau du fond, changement qui peut provenir de Faction plus ou moins forte des courants. II est plus que probable que cette action des courants diminue lorsque la profondeur augmente, ce qui expliquerait la difference d’aspect des concretions des stations 11 et 12 avec celles de la station 17989. Les nodules de cette station comme ceux des stations profondes sont presque entierement formes par des coquilles de Globigerines, cimentees par le phosphate et apportant une fois de plus cette preuve de la formation des nodules in situ , car dans les concretions phosphates la quantite de coquilles de Globigerines augmente avec la profondeur de la mer, ce qui est en accord parfait avec ce que nous connaissons des depots marins. Parmi les petites concretions nous en trouvons quelques unes de couleur externe brun fonce et jaunatres a la cassure, indiquant une augmentation de la teneur en fer. Nous trouvons encore dans le materiel de cette station des fragments d’os calcifies et phosphatises. Comme roches nous ne trouvons qu’un seul petit morceau de quartzite, subangulaire. Station 17946. Cape Point, R. 41° E. by D. R. 38 miles (68 km.) de la c6te. Profondeur 315-400 fathoms (576-732 m.). Le materiel de cette station se compose de petites concretions phosphatees et de nodules (la plus grande de 6 x 3 x 2 cm.), de 4 cailloux roules de quartzites (le plus gros de 4’5 x 4 x 2 cm.), de quelques fragments d’os completement calcifies et phosphatises, de coquilles de Lamellibranches et Gasteropodes, de coraux, quelques fragments de coquilles de Pteropodes et Eoraminiferes, des tubes d’Annelides ainsi que deux morceaux de charbon. Rous remarquons aussi quelques petites boules friables de boue agglomeree, tres legeres comparativement aux nodules phosphates de meme grandeur ; nous avons rencontre de semblables aggre- 880 Proceedings of Royal Society of Edinburgh. [sess. gations dans le materiel d’un draguage provenant de sables verts. Aurions nous peut-etre la un exemple d’une premiere phase dans la formation des concretions phosphatees ? Pour le moment nous ne pouvons qu’enregistrer ce fait. Station 17811. Cape Point, E.N.E. 36 J miles (67 km.) de la cote. Profondeur 660-800 fathoms (1210-1460 m.). La moitie du materiel de cette station est composee de cailloux roules et subangulaires. Le reste comprend de petites concretions phosphatees et nodules, quelques bons specimens et fragments d’os tympaniques de cetaces (Globiocephalus et Mesoplodon), quelques dents de requins et des fragments d’os plus ou moins pliosphatises. Mr Lee donne la diagnose suivante d’une coupe mince a travers un nodule de cette station (Coupe No. 19). Mineraux : Quartz, Plagioclases et de la Glauconie qui remplit frequemment des coquilles de Globigerines, montre ici tres bien ses divers stades de decomposition ; verte, puis jaune et moins bire- fringente, enfin brune et noire opaque. La Glauconie pigmentaire offre les memes phenomenes que les grains. Certaines zones de Glauconie sembleraient jalonner les contours d’un corps qui aurait disparu. Cette coupe se distingue des autres 1° par le fait qu’ici la Glauconie pigmentaire predomine sur la Glauconie en grains ; 2° par le fait que la pate, brune en lumiere naturelle, est ici le plus birefringente, la plus claire etant presque isotrophe. Dans ce dernier cas la Calcite des coquilles qui y sont renfermees ne montre plus de birefringence. La pate est aussi presque completement isotrophe a l’interieur des coquilles de Globigerines. Mode de Fokmation. L’origine de la matiere phosphatee dans les phosphorites a donne lieu a plusieurs explications dont nous trouvons le resume dans un memoire de Mr J. J. H. Teall,* “ Natural History of Phosphatic * J. J. PI. Teall. Presidential Address to the Geologists’ Association, February 2, 1900. Proceedings of the Geol. Association , vol. xvi., part 7. 1900. 1904-5.] Les Concretions phosphaUes de V Agulhas Bank. 881 Deposits.” Mr de Mercey pense que la matiere phosphatee est venue d’en has. Mr Lasne l’attribue aUx rivieres qui apportent dans la mer de 1’ Apatite en solution. MM. Renard, Cornet et Strahan pensent qu’elle provient des organismes dont on trouve de si abondantes traces dans les depots. Nous avons vu dans le chapitre “Distribution geographique, ” quelle nous paraissait devoir etre l’origine de la matiere phosphatee. Les nombreux restes d’animaux qui accompagnent les nodules de lAgulhas Bank et consistant en dents de requins et os tympaniques de cetaces sont une preuve de plus a notre maniere de voir. Pourquoi, dira-t-on, ne trouve-t-on pas de concretions phosphatees dans les fosses du Pacifique ou les os tympaniques et les dents de requins furent draguees en si grand nombre par le Challenger h A cette question nous repondrons que dans les grands pro- fondeurs les os sont en grande partie dissouts avan't, d’atteindre le fond et que le phosphate entre en dissolution dans un volume d’eau considerable tandis qu’il en est autrement dans les faibles profondeurs avoisinant 1’ Agulhas Bank ; la les corps des animaux marins, tues en grande quantite par les brusques changements de temperature, tombent sur le fond ou ils se decomposent et ou les os sont dissouts, tandis que les parties dures telles que les os tympaniques et les dents de requins restent sur le fond. Nous avons vu que les concretions phosphatees etaient dues a la reunion de plusieurs nodules, cimentes par une matiere dont l’element principal, tout comme dans les nodules, est le phos- phate de Chaux (P04)2Ca3 (fig. 2). Quel peut-etre le mode de formation des nodules ? Nous avons vu qu’ils se presentaient sous deux aspects bien differents : 1° Avec foraminiferes ou autres organismes dont les coquilles calcaires sont souvent pseudomorphosees par le phos- phate et qui dans quelques cas paraissent servir de noyau autour duquel viennent se d4poser d’autres zones concentriques. 2° Sans foraminiferes ou restes d’ organismes calcaires ; la matiere phos- phatee paraissant seulement cimenter les grains de Glauconie et les mineraux clastiques. Ces deux manieres d’etre, tres differentes, me paraissent devoir impliquer une duality de mode de formation des nodules. PROC. ROY. SOC. EDIN. — YOL. XXV. 56 882 Proceedings of Royal Society of Edinburgh. [sess. (a) Nodules avec foraminiferes ou autres organismes calcaires. Par sa decomposition la matiere organ ique produit de l’Am- moniaque qui reagissant sur le Phosphate de Chaux en solution donnera du Phosphate d’Ammonium. C’est Faction du Phosphate d’Ammonium sur le Carbonate de Chaux des coquilles calcaires qui me parait devoir etre le premier stade dans la formation de ces nodules. Cette action, comme du reste le prouve Fanalyse micro- scopique est une pseudomorphose. L’Acide Phosphorique du Phosphate d’Ammonium remplace l’Anhydride Carbonique du Carbonate de Chaux pour donner du Phosphate de Chaux ; ce qui peut s’expliquer comme suit : 2POH3 + 3CaC03 = 3H20 + 3C02 + (P04)2Ca3 ; ou mieux 2P04(NH4)3 + 3CaC03 = (P04)2Ca3 + 3C03(NH4)2. Ce Phosphate de Chaux provenant de cette pseudomorphose servira ensuite d’attraction pour les precipations subsequentes de Phosphate de Chaux dues peut-etre a des reactions entre le Phos- phate d’Ammonium et le Bicarbonate de Chaux en solution, pro- venant de l’attaque du Carbonate des coquilles par l’Anhydride Carbonique en dissolution dans l’eau de mer. Cette hypothese a l’avantage d’etre basee sur les experiences et les faits suivants : Dans les “ Reports ” du Challenger , MM. Murray et Renard, font mention deja d’un travail de MM. Robert Irvine et W. S. Anderson, entrepris sous la direction de Sir John Murray a la “ Granton Marine Station,” et intitule : “ On the Action of Metallic (and other) Salts on Carbonate of Lime.” * Dans ce memoire ces chimistes montrent que dans Vespace de six mois un corail plonge dans du Phosphate d’> Ammonium se trouva contenir 60 % de Phosphate de Chaux. Nous avons peut-etre dans cette experience une synthese des nodules phosphates. C’etait du meme coup donner l’explication de la formation des phosphates des lies coraliennes ; c’est ce que ces derniers auteurs font en disant : “ Without doubt, phosphate of lime deposits, especially those found in old coral islands, have had their origin in this manner, the phosphoric acid being derived from the excreta of * Proceedings of the Royal Society of Edinburgh, vol. xvii., pp. 52-54. 1891. 1904-5.] Les Concretions phosphaUes de V Agulhas Bank. 883 wild fowl, deposited upon dead coral or carbonate of lime, the amount of pseudomorphic change being in accordance with the quantity of guano deposited. Of course, transference between carbonate of lime and alkaline phosphates can only take place in the presence of water, so that we have no such pseudomorphs where the climate is rainless ; there the guano remains as deposited, whilst these deposits in rainy zones always assume the form of insoluble phosphate of lime.” * Plus loin ils concluent ainsi : “ From the results of numerous experiments, which it is unnecessary to record here, we have good grounds for assuming that carbonate of lime, either in a massive or comminuted condition, or in solution, carries out the most im- portant function of withdrawing metallic and other bodies from sea water which may be said to hold (often in a minute amount) almost every elementary substance in solution and fixing these in a concentrated condition.” f Nous avons au Challenger Office un bloc de coraux completement transforme en Phosphate de Chaux; il provient de Christmas Island (200 miles S.W. de Java) oil aujourd’hui sont exploites les plus riches phosphates du monde [env. 90 % de (P04)2Ca3]. Cette action pseudomorphosante du Phosphate d’ Ammonium n’agit pas que sur le Carbonate de Chaux; Mr Armand Gautier dans une etude des Phosphates d’Alumine et de Fer de la Grotte de Minerve arrive a la conclusion que ces phosphates sont dus a Paction pseudomorphosante du Phosphate d’ Ammonium, provenant de la decomposition de matiere animale, sur Pargile ; ce qu’il prouva par Pexperience en produisant du Phosphate d’Alumine par Paction d’une solution de Phosphate d’ Ammonium sur du Kaolin. Mr J. J. H. Teall]; dans une etude sur “A Phosphatised Trachyte from Clipperton Atoll,” dit ce que suit: “The chemical analyses show that the change is accompanied by the removal of silica and alkalies, and by the introduction of phosphoric acid and water, This change has probably been effected by solutions of alkaline phosphates, principally ammonium phosphate, and other compounds derived from the droppings of sea-birds.” § * Loc. cit., p. 53. t Log. Git., p. 54. + Quarterly Journal of the Geological Society, vol. liv., p. 230. May 1898. § Loc. cit., p. 231. 884 Proceedings of Royal Society of Edinburgh . [sess. Je crois qu’il est inutile de donner des exemples plus nombreux de cette interessante action du Phosphate d’ Ammonium en solution non-seulement sur le Calcaire mais aussi sur les Silicates. Comme je l’ai deja dit, cette hypothese sur la formation des nodules avec coquilles calcaires a le grand avantage d’etre basee sur des experiences et des faits. Une preuye a cette maniere de voir me semble apportee par les grosses coquilles de Lamellibranches et Gasteropodes de la station 12 en particular, qui montrent que le Carbonate de Chaux des coquilles est bien un point d’attraction pour la matiere phosphatee. Dans certains gisements de phosphates, l’Albien de la Perte du Rhone a Bellegarde par exemple, les fossiles semblent avoir con- centre la matiere phosphatee et des geologues out explique ce fait en disant qu’il provient d’une attraction de la matiere organique sur le phosphate. Les phosphorites de Bellegarde me paraissent avoir beaucoup de ressemblance avec les nodules avec fossiles de la station 12. Je crois que l’explication de leur formation due a l’attraction de la matiere organique doit etre ecartee ; la matiere organique ne fournissant que l’Ammoniaque utile si ce n’est necessaire a la formation des nodules et le Carbonate de Chaux etant en quelque sorte la matiere attractive. (b) Nodules sans organismes calcaires. Dans ces nodules le phosphate ne joue plus le meme role que dans les nodules avec coquilles calcaires, il agit simplement comme ciment entre les grains de Glauconie et les mineraux detritiques ; nous n’avons jamais rencontre de mineraux portant des traces d’une action pseudomorphosante du Phosphate. Ces nodules sont peut-etre dus simplement a une precipitation de Phosphate de Chaux due a une reaction entre le Phosphate d’ Ammonium et le Bicarbonate de Chaux, ou nous avons peut-etre la tout simplement une action en quelque sorte incrustante du phosphate sur ces boules ou nodules de boue agglomeree qu’on rencontre dans les sables verts et dont nous avons trouve des echan- tillons dans le materiel de la station 17946. Esperons qu’une etude detaillee nous donnera quelques eclaircissements sur cette question. 1904-5.] Les Concretions phosphaUes de V Agulhas Bank. 885 Nodules jaunes. Dans la description du materiel de la station 12, nous avons dit que l’oxyde de fer des nodules jaunes pourrait provenir d’une decomposition de la Glauconie ou du fait que les conditions n’etant pas satisfaites pour la formation de la Glauconie, il se soit forme simplement un oxyde de fer. Le calcul suivant peut nous donner une idee de l’oxyde de fer total contenu dans le ciment des nodules jaunes. Insoluble = 31 ’86 % dont les f sont composes par de la Glauconie, ce qui nous donne pour cette derniere seule une teneur de 23*89 %. Si maintenant nous prenons dans les “ Deports ” du Challenger la teneur en oxyde de fer du plus riche echantillon de Glauconie nous la trouvons egale a env. 40 %. Done 23*89 % de Glauconie, contenant 40 % d’oxyde de fer, nous donnent une quantite d’oxyde de fer egale a 9*55 %. Ajoutons k cela les 4*29 % d’oxyde de fer soluble et nous aurons (9*55 + 4*29) 13*84% comme teneur en oxyde de fer total dans le ciment au cas ou la Glauconie serait decomposee. Ce chiffre est quelque peu inferieur a celui des nodules de la station 12, mais par contre il se rapproche beaucoup de celui des nodules de la station 7, ou nous avions 13*7 % et 14*9 % d’oxyde de fer. Dotes sur la Glauconie des Concretions Phosphatees de l’ Agulhas Bank, par Gabriel W. Lee, B.Sc. Coupe Do. 1.* Station 4. 125 fathoms (229 m.). Tissu osseux forme d’un corps cristallin fibreux, birefringent (ng.-np. probablement compris entre 0*012 et 0*015), k extinctions onduleuses, d’allongement negatif et de signe optique negatif, biaxe a axes tres rapproches. Il n’y a rien qui puisse indiquer le systeme cristallin auquel appartient ce corps, dont les proprietes optiques semblent du reste etre variables (voir coupe 20). Ce corps doit probablement rentrer dans le groupe des Phosphates du Guano. Les canicules du tissu osseux sont remplies par une substance * Section a travers un os infiltre de matiere phosphatee. 886 Proceedings of Royal Society of Edinburgh. [sess. noire opaque, probablement un oxyde de fer. Certaines portions de la coupe sont occupees par de grandes plages homogenes de cette substance noire, qui prend aussi par . places la forme d’un mouchetage criblant le tissu osseux. II n’y a presque pas de mineraux clastiques, seulement quelques grains de quartz et d’un mineral peu birefringent non reconnaissable. La Glauconie , qui est rare, se presente sous deux formes : en rubans ou longues zones mal delimitees et en grains le plus souvent localises a l’interieur des plus grands d’entre les canaux de l’os. Un grain parfaitement frais presente un phenomene particulier : il contient 3 ou 4 petites plages irregulieres, qui aux plus forts grossisements se montrent formees d’un agregat de petits grains informes d’un mineral noir opaque (oxyde de fer ?), mais le grain de Glauconie lui-meme ne presente aucune trace de decomposition ni aucunes fentes ou craquelures. A la forme cristalline pres ces inclusions rappellent celles qui ont ete figurees par Mr Cayeux (fig. 12, pi. vi., Etude micrograpbique des Terrains Sedimentaires), le grain de Glauconie appartenant du reste aussi a la variete homogene. Coupe No. 2. Meme station. Mineraux : Quartz avec ses caracteres habituels en fragments plutot anguleux, tres abondants. Zircon reconnaissable a sa birefringence et a son relief eleve et dont une section est presque perpendiculaire a l’axe optique. La Glauconie est en grains nombreux, mais petits, tantot isoles, tantot inclus a l’interieur de Globigerines ou autres coquilles. Dans quelques cas elle n’est pas en grains, mais forme des taches ou plutot des plages pigmentaires a contours indefinis se fondant insensiblement avec la pate. Elle ne presente presque pas de phenomenes de decomposition, mais par contre sa couleur verte n’a pas partout la meme intensite. Les mineraux et les coquilles predominent sur la pate qui les cimente ; celle-ci est brune en lumiere naturelle et d’aspect floconneux. Entre nicols croises elle se montre amorphe, mais contient une multitude de paillettes de Calcite reconnaissables a leur birefringence tres elevee. 1904-5.] Les Concretions johosphaUes de V Agulhas Bank. 887 Coupe No. 3. Meme station. Mineraux : Quartz tres abondant, un peu de Zircon et quelques grains de Tourmaline. La Glauconie est, comme precedemment, tantot en grains fonces, a contours tranches, et montrant la polarisation d’aggregat, le plus souvent isolts, mais aussi parfois inclus dans des coquilles, tantot sous forme d’un pigment de couleur claire teintant la pate. D’assez nombreux petits grains noirs doivent etre un produit ferrugineux. Pate habituelle brune amorphe et avec paillettes de Calcite. Coupe No. 4. Meme station. Beaucoup de Quartzt mais en grains plus petits que dans la coupe precedente. Un peu de Zircon et de Tourmaline. Quelques petits cristaux macles de Plagioclases. Grains noirs ferrugineux. La Glauconie presente ici en sus des caracteres generaux deja vus, une mince zone incolore et isotrope entourant certains grains ; dans ce cas les grains montrant ce phenomene sont groupts en nids, et la pate qui les relie est teintee de vert, probablement par un pigment glauconieux. Cette bande incolore s’observe aussi dans des grains isoles, mais est moins apparente. Coupe No. 5. Station 7. 80-130 fathoms (146-238 m.). Les mineraux sont constitues par du Quartz , abondant, quelques grands cristaux decomposes diOrthose, des cristaux de Plagioclases dont l’un presente une bissectrice mal centree. Quelques grains de Zircon. La Glauconie a ici des caracteres speciaux. Elle s’observe : 1° En grains habituels, isoles, a contours tranches. 2° Sous forme de pigment. 3° En grains de forme generalement ovale, entoures d’une gaine incolore , montrant une structure radiee ty pique que je n’ai rencontree que dans cette coupe et dans le No. 11. Les fibres qui forment cette gaine sont allonges negativement et sont constitutes par un mineral rappelant par son aspect le Quartz, et polarisant dans le blanc de premier ordre. Le signe de l’allonge- ment et la birefringence font que ce mineral doit pouvoir etre 888 Proceedings of Royal Society of Edinburgh. [sess. considere comme de la Galcedoine , que se serait deposee posterieure- ment a la formation des grains de Glauconie. En effet, elle n’enveloppe non seulement la Glauconie mais aussi des fragments de Calcite organique et meme un gros grain de quartz detritique. Dans ce cas particulier cette game n’est pas constitute par une coquille dont la Calcite aurait ete remplacee par pseudomorphose, comme cela pourrait paraitre au premier abord par suite de la forme generalement reguliere qu’affectent ici les grains de Glau- conie ; son depart est indubitablement posterieur a la formation de la Glauconie. Cette Glauconie aureolee est localisee dans la coupe dans une plage arrondie de couleur verdatre, pouvant avoir \ cm. de diametre, et ou le ciment renferme une tres forte proportion, sous forme de minuscules paillettes, du mineral que je rapporte a de la Calcedoine. Comme autres phenomenes interessants, j’ai observe un grain de Glauconie ne renfermant pas moins de quatre assez gros grains de Quartz. Certains grains montrent une curieuse disposition par bandes alternativement tres birefringentes et beaucoup moins bire- fringentes ; dans ce cas les bandes sont placees selon les meridiens ; enfin dans un ou deux grains la partie la plus externe est plus homogene et plus birefringente que la partie interne, mais ne presente ni structure ni clivage. Je pourrai dire a ce propos que meme sur les particules les plus favorables, je n’ai jamais observe de polychroisme, et que les clivages, s’ils existent, sont presque impossibles a observer, meme aux plus forts grossisse- ments a immersion. Les produits de decomposition de la Glauconie sont les memes que dans les autres coupes, et la pate a son aspect habituel : melange de matiere amorphe et de paillettes de Calcite. Coupe No. 10. Station 11. 166 fathoms (304 m.). Les mineraux sont representes par du Quartz , un peu de Plagio- clases, et de Tourmaline. La Calcite des coquilles est fraiche. La Glauconie se presente : 1° En grains bien delimites, dont la couleur varie d’intensite. Leur pourtour montre quelquefois une bire- fringence plus elevee qu’a Finterieur, mais sans former de gaine 1904-5.] Les Concretions phosphaUes de V Agulhas Bank. 889 individualisee ; comme le reste du grain cette zone est cryptocris- talline et polarise en aggregats. 2° En grains inclus dans des coquilles, ce cas est plutdt rare, alors la couleur est plus claire que dans les grains isoles. 3° En plages formant un enduit vert clair ou brun par oxydation. La pate offre son aspect habituel, mais est plus pauvre en paillettes de Calcite a l’interieur des coquilles qu’k l’exterieur. Coupe No. 11.* Meme station. Comme mineraux detritiques il n’y a guere que du Quartz , qui est localise dans les parties de la coupe ou la Glauconie est k l’etat d’enduit. La Glauconie est plus souvent a l’etat d’enduit qu’a celui de grains definis. Dans ce dernier cas elle presente souvent une aureole radiee, constituee par des fibres allongees negativement et que je rapporte a la Calcedoine, comme dans la coupe No. 5 ; ici aussi ce mineral a du se deposer en dernier lieu, car il moule aussi par places les vacuoles du tissu osseux. La trame de la coupe est constituee par une pate a grain fin, peu birefringente parcourue par des fibres sinueuses du meme mineral que dans la coupe No. 1. La pate contient des petits batons noirs opaques, et la partie cristalline des mouchetages bruns doues de birefringence. Coupe No. 14. Meme station. Les mineraux clastiques sont represents par du Quartz tendant k former des agglomerations, et probablement par du Zircon. La Glauconie est en grains, en plages pigmentaires, et en longues trainees renfermant des mineraux. Les grains sont en general de couleur claire, et quelquefois Jeur pourtour est incolore et isotrope, mais ce dernier caractere est peu accentue, et il est difficile de savoir a quoi Tattribuer. Les coquilles sont en partie fraiches, en partie decomposes, c’est a dire que leur Calcite a perdu une partie de sa birefringence par suite de l’impregnation de la matiere brune attribuable au Phosphate de Chaux. La pate n’offre pas partout la meme birefringence, c.a.d. que les particules de Calcite sont irregulierement distributes. Section a travers un os infiltre de matiere phosphatee. 890 Proceedings of Royal Society of Edinburgh. [sess. Coupe No. 16. Station 12. 230 fathoms (421 m.). Grande abondance de mineraux clastiques : surtout du Quartz , un peu de Plagioclases et de Zircon. Tous ces mineraux sont uniformement repartis. La plupart des coquilles sont im- pregnees de Phosphate de Chaux (substance brune), mais montrent encore la croix noire typique de la structure fibroradiee. Peu de Glauconie, dont plusieurs grains sont inclus dans des Globigerines. Pate habituelle avec paillettes de Calcite et qui remplit certaines coquilles. Coupe No. 18.* Station 17946. 315-400 fathoms (576-732 m.). Comme mineraux clastiques surtout du Quartz , plusieurs grains de Zircon et peut-etre de la Tourmaline. La coupe est composee d’une pate parcourue par des fibres sinueuses ressemblant en lumiere naturelle a celles des coupes 1 et 11, mais beaucoup moins birefringentes et la plupart du temps isotropes. Comme dans les autres cas, elles sont foisonnees de batonnets noirs. La masse qui sep;ire ces fibres contient beaucoup de Quartz et de grains de Glauconie et est teintee de vert. Ses grains de Glauconie tres abondants ont souvent une forme angulaire et n’ont pas d’aureole. Des grains noirs opaques peuvent etre consideres comme un produit ferrugineux derivant de la decomposition de la Glauconie. La pate est tres isotrope ; elle ne contient pas, ou tres peu, de paillettes de Calcite. Coupe No. 20. t Station 17821. 660-800 fathoms (1210-1460 m.). Beaucoup de mineraux qui sont egalement repartis : Quartz , Plagioclases , Zircon, peut - etre Hornblende commune et des grains noirs qui sont probablement un produit ferrugineux. II y a aussi une ou deux sections d’un mineral en grains, peu birefringent et rappelant Y Apatite. Le tissu osseux est comme dans la coupe No. 1, jalonne par le Section a travers un os infiltre de matiere phosphatee. t Ibid. 1904-5.] Les Concretions phosphaUes de V Agulhas Bank. 891 mineral en fibres sinueuses, mais qui est ici moins birefringent ; des parties toujours eteintes entre nicols croises montrent une croix noire tres indistincte en lumiere convergente, et donnant avec le quartz teinte-sensible la figure des mineraux joositifs (les parties correspondantes de la coupe No. 1 etaient negatives). Je n’attribue pas beaucoup d’importance a cette difference, vu que le phenomene n’est pas tres distinct, et que si la difference existe reellement, elle peut-etre due soit a une difference de composition chimique, soit encore peut-etre a un entre — croisement des fibres elementaires du mineral. En tous cas ce mineral offre le meme aspect en lumiere naturelle dans cette coupe que dans les coupes 1 et 11, avec les m ernes points noirs et bruns. La Glauconie est en petits grains sans aureole, et en plages pigmentaires souvent de couleur brune, par suite de decomposition. Les tres rares coquilles qu’i.1 y a dans la coupe ont perdu toute birefringence. La pate est absolument isotrope. Remakques. La Glauconie , dans les coupes que j’ai eues entre les mains, est toujours nettement cryptocristalline et polarisant en aggregat. Je n’ai pas tente d’en mesurer exactement la birefringence maxima, les particules elementaires etant trop petites pour se preter a une mesure, mais elle semble, par comparaison, devoir atteindre dans certains cas une valeur comprise entre 0*015 et 0*02. Meme dans les parties ou les particules tendent a prendre une orientation uniforme (coupe 5) il n’y a pas de polychroisme, ou, s’il existe, il n’est pas appreciable. Je n’ai pas observe non plus de clivages ; cette absence des caracteres reconnus ailleurs (Lacroix, Cayeux, etc.) doit provenir de ce que, dans le cas particulier, les particules elementaires sont extremement petites et ont atteint un degre de cristallisation moins avance que dans les cas cites par les auteurs. Il n’y a de meme dans ces coupes aucun exemple de structure concretionnaire ni de structure radiee ; la Glauconie se presente toujours a l’etat de grains montrant partout la meme structure cryptocristalline et a Vetat d'enduit ou pigment. 892 Proceedings of Royal Society of Edinburgh. [sess. Les grains sont beaucoup plus gros que les mineraux clastiques (quartz) qui les accompagnent, et sont en regie generale isoles ; les grains inclus a l’interieur de Globigerines sont plutot rares, et sont plus petits que les grains isoles. II ne semble pas y avoir de relation bien nette entre la teneur en Glauconie et la richesse en coquilles : des coupes riches en coquilles sont pauvres en Glauconie et vice versa. Parmi les mineraux, les feldspaths presentent une Constance remarquable : tous les individus determinables rentrent dans la categorie des Plagioclases basiques, et sont dans un tres bon etat de conservation. La coupe Ho. 5 renferme seule de YOrth.ose, dont la determination n’est du reste pas certaine, qui est alors en grands cristaux tres decomposes ; il est interessant de constater cette absence presque complete de FOrthose et cette preponderance des Plagioclases. A part ce que je rapporte a de la Calcedoine, il ne semble pas y avoir (excepte peut-etre la Glauconie) formation de mineraux secondaires. Pour ce qui est du Phosphate de Ghaux, autant qu’il est permis de le dire, il n’est jamais individualise sous forme miner alogique, mais est diffuse, du reste inegalement, dans la masse en formant d’une part le ciment le plus souvent avec l’aide de paillettes de Calcite, et d’autre part en impregnant la substance des coquilles, et n’offre aucune tendance a la cristallisation. Quand a Torigine de la Glauconie dans les coupes etudiees, il serait liasardeux d’exprimer une opinion ; mais il est permis de faire la reflexion suivante. Les grains arrondis a contours tranches pourraient logiquement faire partie du nodule au meme titre que le quartz et les autres mineraux, c.a.d. avoir ete formes avant la formation du nodule, car s’ils s’etaient formes in situ dans le nodule par precipitation chimique il faudrait expliquer leur repartition quelconque dans le nodule ; car dans ce cas on devrait s’attendre a leur voir occuper dans le nodule une zone determinee ; en un mot le nodule devrait montrer une structure concretionnaire que n’existe pas dans les coupes en question. Cette maniere de voir serait justifiee par la presence des deux types de Glauconie : en grains et en enduit ou pigment : le premier etant relativement ancien puisqu’il est Proc. Roy. Socy. of Edin. ] [Vol. XXV Db. Leon W. Collet. Fig. 1. — Aspect general d’une concretion phosphatee recouverte d’organismes. Station 12. Prof. 230 fathoms (421 m.). \ grandeur naturelle. (Photo. Robert Dykes, Challenger Office.) Proc. Roy. Socy. of Edin. ] [Vol. XXV. Fio. 2. — Concretion formee par de gros nodules cimentes. Station 13. Prof. 166 fathoms (304 m.). § grandeur naturelle. (Photo. Robert Dykes, Challenger Office.) Dr Leon W. Collet. Proc. Pay. Socy. of Edin. ] [Vol. XXV. Fig. 3. — Section a travers un nodule (voir description, page 870). Grandeur naturelle. (Photo. R. Dykes.) Fig. 4. — Section a travers une concretion montrant un nodule avec 2 zones concentriques. Grandeur naturelle. (Photo. R. Dykes.) Dr Leon W. Collet. Proc. Roy. Socy. of Edin. ] [Yol. XXV. .Fig. 6 Fig. 5. — Section a travers un nodule forme essentiellement de coquilles de Fora mini feres cimentees par le phosphate. Grandeur naturelle. (Photo. R. Dykes.) . — Section a travers une concretion montrant les differents nodules dont elle est composee. A droite on remarque un corail qui joue le role de nodule. Grandeur naturelle. (Photo. R. Dykes.) Dr Iteon W. Collet. 1904-5.] Les Concretions phosphatees de V Agulhas Bank. 893 englobe dans le ciment. II n’en est pas de meme pour la Glauconie ; pigmentaire , qui est manifestement posterieure au depart des autres mineraux. II n’y aurait done rien d’invraisemblable a admettre que la Glauconie en grains se serait formee a un endroit quelconque de la mer, et que ces grains une fois formes auraient joue, dans la forma- tion du nodule, le role d’^lements detritiques, tout comme le quartz ou les feldspatbs. On pourrait done dire que la presence de la Glauconie, et que la cause de la formation de la Glauconie ainsi que le mode deformation de la Glauconie, sont deux questions distinctes ; la premiere seule pouvant eitre interpretee avec plus ou moins de verite au moyen du microscope dans l’etude des coupes minces. {Issued separately, September 6, 1905.) 894 Proceedings of Royal Society of Edinburgh. [sbbs. Evaporation of Musk and other Odorous Substances. By John Aitken, LL.D., F.R.S. (Read July 10, 1905. MS. received July 17, 1905.) In scientific literature the evaporation of musk has a considerable interest. Almost every writer on the divisibility of matter cites it as an instance of the extremely minute division of which matter is capable, our sense of smell enabling us to detect a more minute quantity of this form of matter than can be detected of any other kind of matter by any of the modern refined methods, such as the spectroscope, or chemical processes. It is possible we may shortly have to modify this statement, as extremely small quantities of some kinds of matter can be de- tected by their radio-activity ; but, so far as I know, no reliable numerical values have been obtained in this direction. To give an idea of the extreme minuteness of the particles of musk that are capable of affecting our sense of smell, the following figures may be given. Leslie, in his Natural Philosophy (1823), says, referring to a grain of musk that had perfumed a room for twenty years, “ that at the lowest computation the musk had been subdivided into 320 quadrillions of particles.” The following- table, for which I am indebted to Dr Gordon Blackheath, gives a more recent estimate of the amount of musk that can be detected by its smell, and it will be noticed that it is not so small as Leslie’s estimate. The table also shows the smallest amounts of some other kinds of matter that can be detected by the most refined methods. Delicacy of the Sense of Smell compared with that of SOME OF THE MOST DELICATE OBJECTIVE TESTS. Substance. Smallest part of a Gramme detected. Re-agent. Authority. Musk Iodoform . Sodium Lithium . Nitrite 0-000,000,000,000,000,01 0-000,000,000,000,01 0-000,000,000,03 0-000,000,001 0-000,000,001 Sense of Smell . > J Spectroscope 5 J Ilosvay’s re-agent Berthelot Bunsen k KirchofF Bunsen Warington 1904-5.] Dr Aitken on Evaporation of Musk. 895 As the extremely small amount of musk that can be detected is likely long to retain its classical interest, and as there is a point connected with the subject on which there still seems to be some dispute, I have thought it worth while to see if the doubt could not be cleared up by some experimental methods. There seems to be a difference of opinion as to the state in which the musk exists in the air after it leaves its visible form. While some consider that it passes off as a gas or vapour, others think it goes off in solid particles. It is somewhat difficult to understand how this idea that musk passes into the air as a solid could ever come to be so strongly held, as everyone has seen snow and ice evaporating during frosty weather, and have never supposed the particles leaving the ice to be different from those leaving water. There seem to be a number of ways in which we might test whether musk exists in the air in the form of solid particles, or as a gas. First, we might try the cloudy condensation test. If the musk is in solid particles, these particles will become nuclei of cloudy condensation in supersaturated air, and thus make their presence visible. Second, we might pass the musk-laden air through tightly-packed cotton-wool. If the musk passes through the wool, we may conclude it does so in the form of a gas, as cotton-wool keeps back all particles floating in the air. Third, we might try diffusion. If the musk is gaseous, it will diffuse through the air and not require air-currents to carry it, which would be necessary for solid particles. Diffusion through porous vessels, tightly-packed cotton-wool, etc., might also be tried, as we would hardly expect solid particles to diffuse through these. Fourthly, we might try gravitation. If the musk is in solid particles, it will settle at the bottom of the enclosure, as do the finest dust-particles in air. Before going further, it may be as well to refer to a point which requires attention. It might be asked, May not the subdivision of solids go on so far that they may be reduced to the dimensions of molecules? And if so, How would they differ from gaseous molecules, and how would they conduct themselves when sus- pended in a gas? Would they take up movements similar to those of the surrounding gaseous molecules? If so, they might diffuse through the gas, and both diffusion and gravitation tests 896 Proceedings of Royal Society of Edinburgh. [sess. would have no value. There are, however, some reasons for supposing that solids are never reduced to such minute dimensions. The simplest method of showing this is by a study of the phe- nomena of cloudy condensation in dusty air. If we take the usual apparatus for showing cloudy condensation, a few experi- ments will show that the solid particles seem to have a lower limit to their size, and that they are never so small as to be capable of diffusing or not being separated hut by the action of gravitation. The apparatus required for illustrating these points is shown in the figure. F is a glass flask provided with an india- rubber stopper, the stopper having two apertures in it, in which are fitted two tubes. One of the tubes, C, is connected with an air-pump P, and the other, DD, shown in dotted lines, with a cotton- wool filter W ; a stop-cock, S, being introduced in the pipe DD between the flask and the filter, as shown. A little water is put in the flask F to moisten the air. Suppose, now, there is ordinary unfiltered air in the flask F. If we close the stop-cock S, and then make the smallest degree of expansion by pulling out the pump-handle a very short length, it will he noticed that cloudy condensation at once takes place, the very smallest expansion being sufficient to cause the dust nuclei to become centres of condensation. That is to say, there are particles in the air 1904-5.] Dr Aitken on Evaporation of Musk. 897 sufficiently large to allow of condensation taking place on them with a very slight degree of supersaturation. Now, it is well known that the vapour pressure at a convex surface is higher than at a flat surface, and that the quicker the curvature the higher is the vapour pressure. From this we see that the smaller the dust-particle the higher the supersaturation must be before it can become a nucleus of condensation ; so we would expect, if the solid particles were of all sizes down to molecular, that while the larger particles might become centres of condensation in very slightly supersaturated air, the smaller ones would require a higher degree of supersaturation, and higher in pro- portion to their smallness. There is, however, no evidence of this, the slightest degree of supersaturation being sufficient to cause condensation on even the smallest. A simple way of show- ing this is to take part of the cotton-wool out of the filter W shown in the figure, and only leave enough of it to keep back all but a few particles. By this process we get not only a few, but these few in all probability the smallest in the entering air, and yet they require but the very slightest expansion to make them visible ; and if we clear the air of them by making successive very slight expansions so as to carry them down as the nuclei of rain-drops, when all drops cease to make their appearance with these very slight expansions, we shall find that higher expansions produce no further condensation though accompanied by much higher supersaturations. The supersaturation may be made to go on increasing without any sign of condensation making its appearance till at a very high degree of supersaturation ; as C. T. R. Wilson has shown, condensation takes place on the ions in the air. As all the dust-particles become centres of condensation with an extremely small amount of supersaturation, and when got rid of no condensation takes place on dust-particles with higher degrees of supersaturation, we are entitled to conclude that the particles are not of all sizes down to the mblecular. There is another experiment which supports these conclusions. If we leave the apparatus above described for a considerable time— it may be for days — after filling the flask with ordinary dusty air, it will be found that the sifting process, due to gravitation, will remove all the larger particles first, till in PEOC. ROY. SOC. EDIN. — VOL. XXV. 57 898 Proceedings of Royal Society of Edinburgh. [sess. the end the finer ones are also removed ; but if we test it just before the last of them fall, we shall find that the slightest ex- pansion is sufficient to make them centres of condensation and that higher expansions and supersaturations produce no further cloudy condensation — which we would be entitled to expect under the higher strain if extremely minute particles were present. We may therefore conclude that the finest subdivided solids are still acted on by gravitation, and seem to have a definite lower limit of subdivision; unless it can be shown that extremely minute particles do not form nuclei of condensation, a conclusion for which there seems to be no warrant. Of the different methods above described for distinguishing between solid and gaseous particles, the cloudy condensation test seems to be the best; accordingly, the odour of musk was first tested by it. The apparatus above described, and shown in the figure, was used for the purpose, a little musk being introduced into the flask F. It is evident that if the musk gave off solid particles, it would now be impossible to get the air in the flask in such a condition that no cloudy condensation would take place when the air was expanded, because the musk would keep up a continued supply of nuclei of condensation. However, on putting the musk to the test it was found that the condensation, due to the dust-particles, which were admitted along with musk, decreased, and finally entirely ceased, just as when no musk was present; thus showing that the musk did not give off solid particles. It was thought desirable to vary this experiment, as it was possible that the vapour-laden air in the test-flask might interfere with the result. The musk was therefore removed from the test-flask F, and put into a separate bottle, B, by itself. This bottle was provided with an air-tight stopper through which passed inlet and outlet tubes, and introduced into the apparatus between the filter and the test-flask in the manner shown in the figure. By this arrangement the musk evaporated in filtered air, of the ordinary dryness, before entering the test-flask. Tests made in this way also gave no nuclei from the musk, even when the apparatus had been left some time for a quantity of musk to evaporate. From these experiments we may conclude that musk does not give off solid particles, but evaporates as a gas or vapour like 1904-5.] Dr Aitken on Evaporation of Musk. 899 other substances — that it is gaseous particles from the musk that act on our sense of smell. In confirmation of these results some other experiments were made. It was thought that if musk passes into the air as a gas or vapour that it would be able to pass through a quantity of cotton-wool sufficient to stop all dust-particles. To test this, part of the apparatus shown in the figure was used. The air was first passed over the musk, then through the cotton-wTool filter, with the result that the perfume came freely through the cotton-wool. It did not come just at first ; but after pumping a short time the scent became quite distinct, apparently as strong as when not passed through the cotton-wool. Some of the gas which first entered the filter was trapped and held by the wool, but the wool soon became sufficiently saturated to allow the musk vapour to pass. The trapped vapour remained in the wool and could easily be detected afterwards. Having the apparatus arranged for testing the musk, it was thought advisable to test some other odorous solid substances ; camphor and naphthalene were accordingly experimented with. They both acted like musk and gave no nuclei of condensation, and the gas or vapour from both passed easily through cotton- wool ; so we may conclude that they, like musk, evaporate in gaseous form. It is intended to test a number of other solid odorous bodies to see if any of them give any support to the idea that they give off their perfume in solid particles. Note added 27th July. — Since the above paper was read on 10th July, a number of other odorous substances have been tested. The cloudy condensation method of testing was used in all cases, as it seems to be the most satisfactory, and definite results were obtained by it ; whereas filtering through cotton-wool and diffusion tests are at times uncertain owing to the sensitive surface — the nostrils of the observer — not always giving a definite answer, especially when fatigued ; and there is the further risk of subjective sensations interfering with the correctness of the results. Diffusion tests made with ordinary porous cells are somewhat unsatisfactory, owing to some of the vapour being condensed in the 900 Proceedings of Royal Society of Edinburgh. [sess. pores of the cell. Camphor, for instance, comes freely through the walls of the cell, hut at first only in small quantity ; but the smell outside becomes stronger with time, and if the camphor he removed from the interior of the cell, the outside of the cell continues to give off the smell of camphor for days. Some of the camphor is evidently condensed in the pores and is slowly given off, just as water vapour is condensed and slowly given off under similar conditions. Both the filter and diffusion tests were, however, used in some cases as checks on the condensation method. The following table shows the substances tested. Many of them are entered under their ordinary commercial names. All of them, with the exception of the metals, flowers, and herbs, were tested in the apparatus shown in the figure. For testing the metals, etc., a larger flask than B was used. The metals were in the form of wires — a quantity being coiled up and placed in the bottle. The result of the tests was that not one of the twenty three substances gave off their perfume in solid particles, nothing hut gases or vapours escaping from them. List op Substances Tested. i Natural Products, . . Chemical Products . . j Metals, . . . . | Flowers, . . <| Herbs, . . < Asafoetida gum — ground. Caraway — ground. Cinnamon „ Cloves. Cubebs ,, Lavender. Nutmeg ,, Pimento ,, Tobacco „ Sewage. Stink-wood (Kaizer Busuk). Ammonia carbonate. Menthol. Zinc valerianate. Brass. Copper. Iron. Lilies. Boses Sweet-peas. Peppermint. Kue. Sage. 1904-5.] Dr Aitken ok Evaporation of Musk. 901 All the substances entered under natural and chemical products were samples of ordinary articles of commerce, and I am indebted to Sir John Murray for the piece of Kaizer Busuk from Christmas Island which was used in the tests. This Avood has a very strong and extremely offensive smell, strong enough and heavy enough to suggest solid particles ; yet it, like the others, only gives off gas or vapour. It may be interesting to sanitarians to know that sewage does not communicate to the air any solid particles, that the offensive emanation is a gas. As there seemed to be some doubt on this subject it was thought advisable to test it — though one would hardly expect solid or liquid particles to leave a wet surface. Further, it is known that the air in sewers is remarkably free from germs of all kinds, as they do not leave the sewage ; and if they are in the air they soon settle. If sewage gave off solid or liquid particles these also would soon settle on the surface of the sewage. These remarks apply only to sewers in which the sewage flows easily and without break in its surface film. If it is stirred up or flows rapidly, especially if over falls, then both germs and particles of the sewage get mixed up with the air, as the bursting of each bubble scatters a number of minute particles of sewage. Our nostrils seem to confirm the conclusion that the perfume given off by substances is not in the same form, and probably often not of the same composition, as the matter from which it is emitted. Take the effect of tobacco-snuff, for instance ; the perfume from it is perfectly distinct from the sensation produced when the dust of tobacco comes in contact with the nasal passages. The perfume is a soft and velvety sensation ; while the effect of the solid is sharp and biting, more allied to pain than pleasure. It may be said that this painful sensation is only the natural effect of over- stimulation of the nerves, just as the feeling of a fire is pleasant at a distance, while contact with the live coals is painful. The two sense perceptions are, however, so dissimilar it would be unsafe to draw too close a comparison. If they were similar, then an excess of all perfumes ought to be painful if the dust effect of the snuff were only an excess of perfume. But this is not the case. Musk, when snuffed, has hardly any effect, only the musky odour felt when no musk dust touched the nostrils. Other substances, such 902 Proceedings of Royal Society of Edinburgh. [sess. as pimento, menthol, and many others, when snuffed also produce a sensation in the nostrils quite different from that of their perfume. Curiously enough, they all produce a similar sensation, and only vary in degree ; and all of them give a sensation similar to that of tobacco-snuff, which is more an irritation than a smell. Of course, when these substances are applied to the nostrils in the form of powders the sensation is compounded of the contact effect of the dust and of the perfume ; the latter is probably perceived by some part of the surface not affected by the dust. It is probable that none of the dust ever comes in contact with the more sensitive part of the olfactory surfaces, which are out of reach of the direct air-currents. When we consider that all these odorous substances in the form of fine powders give rise to almost the same sensation, though in varying degrees, the probability is they are all perceived by the branch of the fifth nerve, which serves the inside of the nostril over which the main air-currents flow, and have no effect on the olfactory nerve, on which only gases or vapours appear to act. (. Issued separately September 30, 1905.) 1904-5.] Opacity of Aluminium Foil to Ions from a Flame. 903 On the Opacity of Aluminium Foil to Ions from a Flame. By George A. Carse, M.A., B.Sc., 1851 Exhibition Science Research Scholar of Edinburgh University; Emmanuel Col- lege, Cambridge. (Read July 17, 1905.) The apparatus used to show that aluminium was opaque to the ions from a flame consisted (see fig. 1) of a tube A, which was Fig. 1. funnel-shaped at one end, the other end of which led to an enclosure B, one side of which (a b) was made of aluminium foil connected to earth, and on the other side there was an insulated metallic plate (cd), which could either be connected to earth or to a high potential battery. On the other side of the aluminium foil there was an electroscope in a closed case C. The electroscope was of the type used by C. T. R. Wilson* in his experiments on the natural ionisation of air in closed vessels. The ions were got from a bunsen burner placed beneath the funnel, the heated air being cooled by a water-jacket D, and * Proc. Roy. Soc., 68, p. 152, 1901. 904 Proceedings of Royal Society of Edinburgh. [sess. drawn through by a water-pump. The rate of leak of the electroscope was read by a low-power microscope provided with a micrometer scale, and was taken — 1°, when the flame was not lit and the field not on ; 2°, when the flame was lit and the plate c d to earth ; 3°, when the flame was lit and the field on. When the flame was first lit, the leaf of the electroscope was somewhat unsteady. This unsteadiness was due to convection currents of air in the electroscope case ; but after an interval of fifteen or twenty minutes the leaf became steady and readings could be taken. The air in the electroscope case was kept dry by means of calcium chloride. In order to be certain that the ions from the flame really reached the enclosure B in an uncombined state, the aluminium foil was removed and the rate of leak of the electroscope was taken — 1°, with the flame unlit; 2°, with the flame lit; -the plate cd being to earth in both cases. The result was that the rate of leak due to the ions was from 50 to 80 times the natural rate of leak, showing that a sufficient supply of ions was present. The following are two sets of observations of the kind taken in the course of the experiments. In all cases given, the leaf of the electroscope was charged to a potential of 360 volts. 1°. Flame unlit. (Plate cd to Earth.) Time in Minutes. Reading. Leak per 5 Minutes. 0 33*3 5 35-4 2*1 10 37*7 2*3 15 39*8 2*1 20 41*9 2*1 Average leak per 5 minutes, 2*15. 1904-5.] Opacity of Aluminium Foil to Ions from a Flame. 905 2°. Flame lit for 20 Minutes before Readings taken. (Plate cd to Earth.) Time in Minutes. Reading. Leak per 5 Minutes. 0 26-2 5 28*3 2’1 10 30-7 2-4 15 32-8 2'1 Average leak per 5 minutes, 2 '2. 3°. Flame lit {already fur 35 Minutes). (Plate cd to 360 volts.) Time in Minutes. Reading. Leak per 5 Minutes. 0 33-2 5 35-4 2'2 10 377 2-3 15 39-9 2-2 Average leak per 5 minutes, 2*2. 1°. Flame unlit. (Plate cd to Earth.) Time in Minutes. Reading. Leak per 5 Minutes. 0 22-8 5 24-7 1*9 10 267 2-0 15 28-7 2’0 Average leak per 5 minutes, 2’0. 906 Proceedings of Royal Society of Edinburgh. [sess. 2°. Flame lit. (Plate cd to Earth.) Time in Minutes. Reading. Leak per 5 Minutes. 0 28*9 5 30*8 1-9 10 32-7 1-9 15 347 2-0 Average leak per 5 minutes, 1 ’9. 3°. Flame lit. (Plate cd to 360 volts.) Time in Minutes. Reading. Leak per 5 Minutes, j , 1 0 36-0 5 37*9 1*9 10 39*9 2-0 15 41*9 2*0 Average leak per 5 minutes, 2'0. The maximum deviation of any reading from the mean was about 10 per cent., so that, since the leak of the electroscope due to the ions from the flame, when the foil was removed, was 50-80 times the natural rate of leak, the accuracy of the experiments, therefore, was such that if 1 per cent, of the ions had gone through the aluminium foil, their presence could have been detected. With the limits of accuracy in question it is concluded that no ions penetrate the aluminium either under no field or under the small field applied. M. Le Bon* has described an experiment showing that ions from a flame traversed a “cage de Faraday” formed of alumin- ium, the leak of his electroscope being very great when the gas from the flame was not cooled, but appreciably reduced when the gas was cooled. Now Campbell f has shown that M. Le Bon’s result that radio-activity accompanies chemical change * Revue Scientijique, iv. 18, 1902, p. 649. t Phil. Mag., vi. 52, 1905, p. 545. 1904-5.] Opacity of Aluminium Foil to Ions from a Flame , 907 was due to a heat effect, and to change of surface electrification on the sulphur which formed the floor of M. Le Eon’s vessel, and it may be that his result in the experiment described above, in which he used the same apparatus, is due to a similar effect, as the leak of his electroscope decreased as the gas was cooled. These experiments were carried out at the Cavendish Labora- tory, Cambridge, during the winter 1904-5; and I beg to tender my sincerest thanks to Professor J. J. Thomson for his valuable advice and criticism. Cavendish Laboratory, Cambridge, June 1905. {Issued separately September 30, 1905.) 908 Proceedings of Royal Society of Edinburgh. [sess. The Theory of General Determinants in the Historical Order of Development up to 1852. By Thomas Muir, LL.D. (MS. received June 12, 1905. Read July 3, 1905.) Cauchy (1844). [Memoire sur les arrangements qne Ton peut former avec des lettres donnees, et sur les permutations ou substitutions a l’aide desquelles on passe d’un arrangement a un autre. Exercices d’ Analyse et de Phys. Math., iii. pp. 151-252.] The nature of the connection of this with the theory of deter- minants is evident from the title. Some of the elementary portions of the memoir had in fact already appeared in Cauchy’s determinant papers of the years 1812, 1840, 1841, and have been noted in our accounts of the latter. In these papers, as was natural, only such isolated properties were given as might be of immediate application to the main subject : here we have a methodically arranged and lucidly written treatise. As, however, in dealing with permutations the question of signature is not taken up, there is no explicit reference to determinants : and all that is therefore necessary is to direct attention to a storehouse of informa- tion regarding a subject closely connected with them. Cauchy (1844). [Memoire sur quelques proprietes des resultantes a deux termes. Exercices d’ Analyse et de Phys. Math., iii. pp. 274-304.] By “ resultantes a deux termes ” are meant determinants of the second ord.er. The expression recalls “resultantes a deux lettres,” used by Binet in his memoir of November 1812 ; and as the said memoir is here referred to by Cauchy and contains the foundation of the latter’s results, it is not improbable that the one expression suggested the other. 1904-5.] Dr Muir on General Determinants. 909 Five theorems with attendant corollaries are carefully formulated and proved, extreme simplicity and fulness of exposition being in evidence throughout. The first three theorems are mere variants of the first case of Binet’s multiplication-theorem for two non- quadrate matrices, viz., in later notation — I ai^i d* a'2X2 d" a3^3 + • • • ^ll/l d~ a2^2 d" + • • • I fti^i + ft^ 2 + ftsXS + ’ ' ' ftlVl d" /^2 d- ft.$Z + ' ‘ ’ = °1 a 2 a3 • • • • 1 x1 x2 x3 .... ft ft Pz • • • • 1 Vi y 2 2/3 • • • • ai a2 X1 X2 + |a> CO e x} x3 + • ...+ h a3 Pi ft \Vl V2 Ift fts V\ y% I ft 2 ftz The real interest arises when the a’s and /3’s of this are so taken that the first determinant of every pair on the right is of the same form as the determinant on the left, and can therefore be expanded in exactly the same way as the latter. The outcome is “ 4e Theoreme. Soient P P P n fonctions homogenes et lineaires de n variables a , y , ^ , • • • • [viz., Px = xPxx + yPxy + zPxz + • • •, Py= • • • Jetnommons P P P ce que deviennent les fonctions Px , Py , P, , .... quand on remplace les n variables x , y ,z , ... par n autres variables x , y , z , .... [viz., Px = xPa,>a. + yPa.iy + zPl.fZ + * • • , Py=- • • ]. Concevons d’ailleurs, que l’on ajoute entre eux les termes de la suite p p p x a; 5 .2/5 x z 5 • • • • 5 ou de la suite P P P 1 X ) f 1 Z ) respectivement multiplies par les variables x,y,z, ou par les variables x , y , z , . . . .; 910 Proceedings of Royal Society of Edinburgh. [sess. et nommons P Q Q P les quatre sommes ainsi obtenus, P etant celle qui renferme les senles variables x ,y ,z , . . . , et P celle qui renferme les seules variables x , y , z , . . . , en sorte qu’on ait P = xPx + yPy + zPz + ■ ■ Q = xPx + yPy + zPz + • • • Q = xPx + 2/Py + zPz + • • • , P = xPx + yPy + zPz + . • • La resultante P P - QQ , formee avec ces quatres sommes, dependra uniquement des binomes qui represented les divers termes de la serie xy -xy, xz-xz, . , yz-yz, et sera une fonction de ces binomes, non-seulement entiere, mais encore homogene et du second degre.” The full meaning of the theorem and the mode of establishing it will be readily understood from working out the case where the number of terms in each element of the initial determinant is three. The process is — | P Q I- = I xPx + yPy + zPz xPx + yPy + zPz Q P' _ I xPx + yPy + zPz xPx + yPy + zPz I, p P Pz 1 \x y P P x x A y PZf x y z 1 P P 1 x y _ x y + X Z + Py P> |. y i P P 1 L x y x y p p x X x z X z Py Pi y z xPXtX + yPXty + zPXth xPy>x + yPyty + zPytZ I xy ^-Px ' x T y Rx , y b ^Py , z ^-Py ,x^~ y Py ,y ^Py , z y I xPx,x + yPx,y+zPx,z *Pz,x + yPz,v+zPz,z + I y Px>y + Z Pxz xPZiX + yP !, , y + zPZ)Z X z X Z + xPy,x + yPy,y + zPv,z xPz,x + yPZ,y+zPZ,Z xPy.x + yPy'.V + zPy.z xPz.x + y Pz,„ + zPz,t. y z y z 1904-5.] Dr Muir on General Determinants . 911 X y z\ P P P x , x x ,y x,z x y i xyz P P P -*• x,x J x , y M x,z X Z x y z| P P P x x, x ■*- y ,y x,z x y T xyz P P P J z,x M z,y x z , z X z xyz IP P P ' M y,x y ,y * y ,z xyz P P P \ *- z , x z , y -1- z , z x y p p x,x x, y + X Z p p \ -*■ XtX •X- 2 | + y z p p k1- x ,y x , z 1 « 2/ x y P P x y,* x y,y X z • p p i y , x j/,2 y z 1 p p \ y,y y ,z J x y .r y ' P P x,x x,y + p p a?, a; -*• a:, z + y « _ P P \ a? 2 x y P P z , x z , y X z P P x z, a? x 2: f z y z P P x 2 , 2/ x z , 2 ) x z ® y | P P y , x y ,y + X z 1 L P P y,% y,z + y z P P x y, y x j/ , 2 y z x y P P x z,x M z,y 1 X z • P P ■*- Z,X z , z J z P P M z ,y ± z,z i y z or, in still later notation, kyi k z i \y z | ip pi 1 fx,x Py,z\ \P*,V Py.z 1 k y ! 1 P*,x P,,y\ \Px,x Pzl lc,,„ p,' ,{ k z | \P*J .. P.. J \Py>x Pz>z\ !-pJ /’..j ly z |, — a result which loses half its interest if we do not note that each element of the initial determinant is presentable in the same form, viz., P P P M x, x x x,y •*- x , 2 P P P V y , x M y ,y y , z y P P P xyz Q i y z y z The fifth theorem, which is obtained from the fourth by further specialisation, viz., by putting in every instance Prs = Psr, is enunciated at equal length ; and then, evidently for the sake of historical connection, it is illustrated by the two simplest cases, that is to say, the case where the number of variables is two and where the number is three. In the former case 912 Proceedings of Royal Society of Edinburgh. [sess. “on obtiendra l’equation identique (ax2 + by2 + 2 cxy)(ax2 + by2 + 2cxy) - [axx + byy + c(xy 4- xy) }2 = (ab-c2)(xy-xy)2, qni a ete donnee par Lagrange dans les Memoires de Berlin de 1773”; in the latter case, it being explained that A = bc-d2 , B = ca- e2 , C = ab- f2, T) = ef-ad, F —fd - be , F — de-cf, and X = yz - yz , Y = zx — zx , Z = xy - xy , “ on obtiendra l’equation identique (ax2 + by2 + cz 2 + 2 dyz + 2 ezx + 2 fxy)(ax2 + by2 + cz2 + 2c7yz + 2ezx + 2/xy) - { axx + byy + czz + d(yz + yz) + e(zx + zx) + f(x y + xy) }2 = AX2 + BY2 + CZ2 + 2 DYZ + 2EZX + 2FXY , que l’on pourrait deduire de l’une des formules donnees par M. Binet dans le xvie cahier du Journal de VEcole Poly- technique.” This latter, for the sake of future reference, it is well to restate in the form X y z X y z a f e X a / e X f b d y f b d y X Y Z e d c z e d c z A F E X X y z X y z F E B D D Y a f e X a / e X C Z f b d y f b d y e d c z e d c z A concluding paragraph is devoted to noting that Pxx, Px . in the fourth theorem are expressible as halved differential- quotients of P, viz., Px,x=mp > Py,y=mp i PZ,Z = \B>\P, P.,BW>X>yP, P,.,= i DJD.P, = i 1904-5.] Dr Muir on General Determinants. that therefore 913 2 P = x2DlP+ y2D'2yP + z^DlP • • • + ^xyD^yP + 2^Da,DgP + • • ■ • and p — IT) p P — ID P p - ID P . . . . L x~ 2J-/a:x 5 1 y ~~ 2 LJyl J z — ’ After this the second part of the memoir, consisting of geometrical applications, is entered upon. Haissen, P. A. (1846, Aug.). [Ueber eine allgem eine Auflosung eines beliebigen Systems von linearischen Gleichungen. Berichte . ... k. sdehs. Ges. d. Wiss. (Leipzig), pp. 333-339.] The solution of a set of linear equations is here looked at from the point of view of an astronomical computer, and though determinants are not used — are, in fact, eschewed — it is interesting to note that the hidden identities on which the new process of solution depends are l a^)2 i _ x . Si Ton donne pour coefficients a deux clefs algebriques a , /3 dans deux fonctions lineaires X , g les termes qui renferment la premiere et la seconde ligne horizontal du tableau (1) on aura non-seulement (3) mais encore X = a^a + bJSf [a = a^ci. 4“ b2{3 , (4) I V I = aia2 1 «2 1 + &A I aP I + bla2 I V I + hA I £2 1 ; et, pour que le produit symbolique \Xfi\ se reduise a la resultante s , il suffira evidemment de poser (5) |o*|=0, I v entrera deux ou plusieurs fois comme facteur dans le produit k ; et poser, au contraire, (15) |*| = 1, ou (16) ! k\ = - l 918 Proceedings of Royal Society of Edinburgh. [sess. quand le produit k renfermera une seule fois chacune des lettres y , • • , y, la formnle (15) etant relative au cas oil Ton sera oblige d’operer entre ces lettres prises deux a deux un nombre pair d’echanges, pour passer du produit | a/3y . . . rj | au produit \k\” The obtaining of the results I aPy I = I fiy a I = I yaP 1 1 = - | a.y/3 | = - |/3ay| = - | y/3a | j from transformations of the form 1 a/5 | = ~ |/?a| is then shortly considered ; and this is followed by a concluding paragraph in which the statement occurs that “ cette decomposition (des sommes alternees en facteurs symboliques) une fois operee on peut s’en servir avec avantage pour decouvrir ou pour demontrer les principales proprietes des sommes alternees.” Cauchy’s position is thus seen to be very different from Grass- mann’s. Grassmann was not concerned with determinants : his problem was to solve the set of equations aYx + a2y + = a0 j \x + b0 + b3z = \ j- «i* + deducing from them two different triads of equations independent of U , V , W , solving these triads for u , v , w , and then comparing the results.* In connection with this two points have to be noted. The first is the use of the notation H I, which may be compared with Catalan’s of the year 1846, and with the modification of the vertical-line notation which the printers of Crelle’s and Liouville’s journals employed for two or three years in setting up Cayley’s papers. That Joachimsthal was familiar with Catalan’s paper of 1846 is made more probable by the occurrence of a footnote (p. 28) giving x +1 y z x y z 1 1 | \1 V * ' - x + V y' z - — det.- .r y' z [ + det.j r v * - y" z" x' y" z" J ! 1 \ i" y" z' an identity which Catalan was the first to formulate in a similar way. The second point is the unnaturalness, in view of the mode of proof, of not writing the second determinant of the theorem in the form ft Vi ft * The details of the proof not being given, one cannot guess how it was that a second theorem was not obtained, viz. , the theorem h +VVi +*(i +w 2 +«C2 1 1 1 h I2 I K ^ili + Vivi + ^iCi Xlk + VlVi + tlCz = j | xfi1z2 | Vi V2 j K + 2/2^1 + zzC\ X2%2 + 2/2^2 + ^2^2 1 1 xyM | Ci C2| 1904-5.] Dr Muir on General Determinants. 921 Towards the close of the paper (p. 44), his geometrical work having led him to use the identity ’P + cl" ft" + a"'ft'")(y'S' + y'T + y '"S'") - (a S' + a'S" + a"'S'")(ft'y' + ft"y" + ft'"y'") = (o'Y" - a'YW'S'" - ft'"S") + (ay" - a"'y')(ft'S"' - ft'"S') + (ay" - h *2 • • . . t2 k A= det.< ^2 V2 C2 • • • • r2 > , xn Vn ^ n • • .. tnJ M Vn Cn • • • • Tn j and N = det.. cT* O lo.i *0.2 * • • • Jo,.' h,o ^1,1 ^1,2 • • • • Ji.» < h.o l2> 1 l“2 , 2 • • • • I'i.n \.ln,0 ln,l , 2 • • • • *».» , where ^o.o = xo^o 4“ VoVo 4“ 2oCo + ■ • • + t0r() , k.i = 4" VoV\ 4- ^oCi + • • ■ + ^oTi , ln, 0 = Xn£() 4“ VnVo 4* Zn£0 + * * • + tnTQ , In, l ~ t 4" 4 * " ‘ 4" tnT-^ , ln,n ~ Xnftn "t" ynVn 4“ % n£n ' * * 4“ t'rJ’n ? and where therefore DA =N, he differentiates both members of this identity with respect to . . • tn, obtaining 0D , 0N , 0N 0N A;r- — Co g? 4- Ci 07 4- , n 0D 0N 0N 0N ~ ^° dl ^ 0/ 4- • • 4" Vn 0£ n 0D _ 0N 0BT 0N 3*» °34r»+Ti^+" ' ’ 4- rn , , n 922 Proceedings of Royal Society of Edinburgh. [sess. From these last equations, on multiplying by 0A 0A. 0A d$n ’ fyn ’ ’ 9r« respectively, and adding, there is obtained with the help of the known identities 0 A 0 A BA = 0, dL ' ' +t°bT n 0 A 0 A 0 A = 0, ZL + Vi + • • dyn • • + T1 — drv 0 A 0 A 0 A % + T the result 0D 0A 01) 0 A dx^dL + dy^dVn + 0D0A dL dr„ = A, m dL z.e. det.- + det. ' Vo ^0 ' Vo Co • T0 * *1 • - . det.- V\ ii • T1 < Vn-i 1 • • . . . Vn- -1 L- -1 • • • Tn-1 r X0 Zq K > ^0 Co • T0 X1 h • h 1 . det.- tl Cl * T1 v Xn- 1 *-l • L— 1 ) . fn- -1 in- -1 • ’ • Tn- 1 1 ( k ,0 lo ,i 1 0 , ti- | = det.- 1 K ,0 h , i ll ,n- -i 1 1 Jn- -1,0 In -1,1 • * K- 1, ,n- 1 j + Using later phraseology we may say in describing this that from the theorem regarding the product of two square matrices of order ra+1 there is obtained the theorem regarding the product of two rectangular but non-quadrate matrices, the latter product appearing as a principal coaxial minor of the former. Cauchy’s generalisation concerned any minor of the former product, but even this further extension was not beyond Joachimsthal’s reach, for he ends with the remark “ En differential de nouveau par rapport a xn_x , yn_x , ... on obtiendra d’autres formules ; et ainsi de suite.” 1904-5.] Dr Muir on General Determinants. 923 Sylvester, J. J. (1850, Sep.). [Additions to the articles in the September number of this journal “ On a new class of theorems . ... ” and “ On Pascal’s theorem.” Philos. Magazine (3), xxxvii. pp. 363-370 : Collected Math. Papers , i. pp. 145-151.] Of the three additions referred to in the title it is the last which concerns us, viz., that in which Sylvester introduces and explains his use of the term minor as applied to a determinant. Starting with the ‘square array’ of a given determinant, and leaving out one ‘line ’ and one ‘ column,’ he calls the determinant of the minor array which remains a ‘ First Minor Determinant ’ ; similarly ‘ Second Minor Determinant ’ is explained ; and then he adds, “and so in general we can form a system of rth minor deter- minants by the exclusion of r lines and r columns, and such system in general will contain j n(n- 1) ... (n — r+ 1) ( 2 t 1*2 . . rr j distinct determinants.” It is thus seen that ‘ minor determinant * is used as ‘ partial determinant’ had already been used by Lebesgue (1837), and as ‘ determinant of a derived system ’ had been used by Cauchy (1812), hut that, whereas Cauchy added a distinguishing epithet to specify the order of the determinant, Sylvester did so to indicate how many lines or columns fewer it had than the ‘ principal ’ or ‘ complete ’ determinant originally started with. The following proposition or ‘ law ’ is next given, viz. : The whole of a system of vth minors being zero implies only (r+1)2 equations , that is , by making (r + l)2 of these minors zero , all will become zero : and this is true , no matter what may be the dimensions or form of the complete determinant. Then, after some geometr cal applications concerned with first minors of a symmetrical deter- minant, there follows the explanation — “The law which I have stated for assigning the number of independent or, to speak more accurately, non-coe vanescent 924 Proceedings of Royal Society of Edinburgh. [sess. determinants belonging to a given system of minors, I call the Homaloidal law, because it is a corollary to a proposition which represents analytically the indefinite extension of a property, common to lines and surfaces, to all loci (whether in ordinary or transcendental space) of the first order, all of which loci may, by an abstraction derived from the idea of levelness common to straight lines and planes, be called Homaloids.” A further advance is made just before the close of his paper. Leaving the square array and taking m lines and n columns, he says “ This will not represent a determinant, but is, as it were, a Matrix out of which we may form various systems of determinants by fixing upon a number p and selecting at will p lines and p columns, the squares corresponding to which may be termed determinants of the pih order.” Here there is to be noticed the first use of the word matrix in connection with determinants, as well as the change back to Cauchy’s mode of particularising the minors. The corresponding more general ‘law’ is said to be — The number of uncoevanescent determinants constituting a system of the pth order derived from a given matrix , n terms broad and m terms deep , may equal but can never exceed the number (n-p + 1 )(m-p + 1) . Ho proof of this is given. Spottiswoode, W. (1851). [Elementary theorems relating to determinants, viii + 63 pp. London.] This is noteworthy as being the first separately-published elementary work on the subject, the author explaining that he had been led to write it because determinants had come to be in frequent use, and there was no accessible text-book to which students could be referred. It consists of a preface and ten short chapters or sections, the mode of partitioning and arranging the matter being such as has often subsequently been followed. 1904-5.] Dr Muir on General Determinants. 925 The preface contains a short sketch of the history of the theory, the first of the kind that had appeared. In the first section (§ 1) the reader is introduced to determinants of the second and third orders as they actually occur in the solution of geometrical problems, and certain of the simpler properties are incidentally pointed out; the next seven sections (§§ 2-8) deal with deter- minants in general ; and the rest of the hook is occupied with determinants of special form, viz., § 9 with skew determinants and § 10 with functional determinants. The concluding portions of most of the sections consist of worked examples illustrative of applications of the theory to co-ordinate geometry. The definition employed is that of Vandermonde * as expressed in Cayley’s vertical-line notation, viz. — (1.1) (1.2) (2,1) (2,2) = (1, 1)|(2, 2)|-(1, 2)|(2, 1)|, (1.1) (1,2) (1,3) (2.1) (2,2) (2,3) (3.1) (3,2) (3,3) -(1.1) (2.2) (2,3) (3.2) (3,3) + (1,2) (2.3) (2,1) (3.3) (3,1) + (1,3) 1(2,1) 1(3,1) (2, (3, The quantities (1, 1), (1, 2), . . . which Cauchy called ‘terms’ and Jacobi ‘elements,’ are named ‘constituents' ; and the deter- minant of the nth order having these constituents is denoted shortly by 2±(l,l)(2,2...(n,n) The first result, deduced in somewhat loose fashion from the * It may be worth noting that while both Vandermonde and Schweins used the recurrent law of formation as a definition, they did not write it in exactly the same form. Schweins followed closely the form used by the original discoverer, Bezout, putting for example | «Ac3^4 | = d4 |«AC3 | ~ ^8 | alb‘2C4 l + d2 | « AC4 \ ~ dl\ a263C4 | , the connecting signs being in all cases alternately positive and negative ; whereas Vandermonde wrote | a^c 3d4 | = a2 1 &2c3d4 | - a2 1 &3c4^1 j + a?t | &46'1c?2 ( - a4 1 &4 c2d3 | , where the cyclical change of suffixes causes the connecting signs to be alternately positive and negative when the order of the determinant is even, and to be uniformly positive when the order is odd. to to 926 Proceedings of Royal Society of Edinburgh. [sess. definition, is “ Cramer’s rule ” ; but the first that is actually formulated and numbered is one of much later date than Cramer, “ Theorem I. — If the whole of a vertical or horizontal row be multiplied by the same quantity , the determinant is multi- plied by that quantity .” In this form, as is well known, it afterwards became almost stereotyped. The second result, which is of about the same age, is that regarding a determinant whose vertical row consists of ^-termed expressions, second vertical row of ^-termed expressions, third vertical row of r-termed expressions, and so on, being to the effect that such a determinant is expressible as a sum of pqr . . . determinants with monomial constituents. The next seven results are, like the first, new only in form, the wording being, as in Theorem I., more topographical in character than formerly, on account of the determinant being now more consciously viewed as connected with a square holding n-n quantities situate in n vertical rows and at the same time in n horizontal rows. The tenth result, which is a converse of the ninth, is new but unimportant, viz. — “ Theorem X. — If a determinant of the nth order vanishes , a system of n homogeneous linear equations , the coefficients of which are the constituents of the given determinant , may always be established .” The eleventh result is the multiplication-theorem; and here anything that is noteworthy is not in the enunciation but in the proof. Beginning with two sets of equations, exactly after the manner of Joachimsthal, viz., he views them as six linear equations in x , y , z , uY , u2 , u3 , and seeks to find the value of one of the first three unknowns, say x, in two different ways. Firstly, by using the first set to eliminate ux , u2, u3 from the second set, he obtains + If I + ^3C1 )x d- (^1®2 d* If 2 d" l^C2 )y + (lyJ's + tf% + )z = ( m ^ + mfA + mycfx + (m1a2 + mf2 + m3c2)y + (m1a3 + mf3 + m3cB)z = v2 (fqtq + nfl + n3c x )x + (nxa2 + nf2 + n3c2 )y + ( n Ya3 + nfz + n3c3 )z = n3 viz. 1904-5.] and thence Dr Muir on General Determinants. 927 Vx d" ^2^2 "h l^’ 2 ^1^3 T ^2^3 ^3^3 v2 + m2&2 + W3C2 ^i®3 + m2&3 + m3c3 v3 nxa2 + n2b2 + n3c2 nxa3 +njbz +nzez l i$i + ^2^1 T ^3^1 ^1^2 "h ^2^2 ^3^*2 ^1^3 "b /2&3 ~b ^3^3 m-p^q + m2&j + m3cx mxa2 + m2b2 + m3c2 m^g + m2&3 + m3c3 +^2^1 + ^3Ci ^1^2 + w2^2 +^3C2 7iias + ^2^3 + ??'3C3 Secondly, — and here he differs from Joachimsthal, — by writing the six equations as one set in the form axx + a-iV + a3z - % = 0 ' bxx + \y + hz - U2 = 0 exx t o2 y t czz - ws = 0 hwi + l2u2 + /3W,3 = mlul + m2u2 + mzu3 = ^2 nxux + n2u2 + = V3 he obtains directly for x the value a2 az - 1 . ax a2 a3 -1 b2 h - 1 \ ^3 - 1 C2 c3 - 1 ci C2 C3 - 1 V1 h l2 h h h h V2 mx m2 m3 mx m2 m3 VZ nx n2 n3 nx n2 n3 A comparison of the denominators in the two values of x then gives the desired result.* The theorems of § 6, though, for some unexplained reason, not formulated and numbered like the others, are of the highest importance, the subject-matter being the determinant * Spottiswoode, like Joachimsthal, it will he observed, deduces nothing from a comparison of the numerators. Thus, by equating the two cofactors of vlf he might have obtained I mi m2 m3 1 | a2 b2 c2 1 1 ni n2 n3 1 1 a3 h c3 | a.2 a3 — 1 b2 b3 . - 1 c2 c3 . . - 1 . . mx m2 m3 . . nx n2 n3 . 928 Proceedings of Royal Society of Edinburgh. [sess. of what is called the “inverse determinant [1,1] [1,2] .... [1,»] [2,1] [2,2] .... [2 ,«] system, that is to say, the [n, 1] [n , 2] . . . . [n , n] where pqs] is the cofactor of (1 , 1) in 1 1 , 2 , . . . , n\. Cauchy’s theorem regarding the whole determinant is first proved, and then, instead of Jacobi’s more general theorem, there is established a theorem said to include Jacobi’s, viz. — \i + 1 , i + 1 ] [i + l,i + 2] .... p + 1 , n\ p -{- 2 , a + 1 ] \i + 2 , i + 2] .... p + 2 , n\ [«,* + !] [n , i + 2] [n,n] p+i + M'+Z+l] [i+j + l,i+j+ 2] ... [i+j+l,n] [i +j + 2 , i +j + 1] [i +j + 2 , i +j + 2] . . . [i +j + 2 , n] |l, 2,. ..,n\l 1 1,2, [n,i+j+ 1] [«,^+i + 2] ...\n,ri\ That it does include Jacobi’s is at once seen on putting i+j+ l=n, when we have p + 1 P + 1 ] p + 1 ,i + 2] . . p + 2 , i t 1 ] p' + 2 ji + 2] . . ,. pH-1, rz] .. p+2,w] \n,i+ 1] \n,i + 2] .. [5 n,n ] [»,«]■! 1,2, ... ,n I” ‘-1- 1 1 , 2 , . . . , » I’*-'-1 . | 1,2, It is equally true, however, that by a double use of Jacobi’s theorem Spottiswoode’s follows immediately. The next section (§7) deals with the differentiation of a deter- minant, and with an application of the same by Malmsten to find the nih particular integral of a certain differential equation when n- 1 particular intergrals are already known. The eighth section concerns the solution of what is called a “redundant system” of linear equations, that is to say, a system of m equations in n unknowns where m>n. Theorem XII. is the result obtained therefrom, and this being applied to the method of least squares, the last formulated result, Theorem XIII., is reached. • f +3 .'I n- if 1904-5.] Dr Muir on General Determinants , 929 Sylvester, J. J. (1851, March). [On the relation between the minor determinants of linearly equivalent quadratic functions. Philos. Magazine (4), i. pp. 295-305, 415 : Collected Math. Papers , i. pp. 241-250, 251.] In order to formulate the relation referred to in the title, that is to say, the relation between any minor of the determinant (later, discriminant) of a quadratic form and the £ pari-ordinal ’ minors of the determinant of the new form obtained from the old by means of a linear substitution, Sylvester found it necessary to introduce “a most powerful, because natural, method of notation” for deter- minants. He says — “My method consists in expressing the same quantities biliterally as below : a1 oq a1a2 . . . agxn ^2a2 * ' , . a2an ana- 1 ana2 . . , . ana.n where, of course, whenever desirable, instead of cq , a2 , . . . , an and cq, a2, . . . , an, we may write simply a, b, . . . , l and a , j6, . . . , A respectively. Each quantity is now represented by two letters; the letters themselves, taken separately, being symbols neither of quantity nor of operation, but mere umbrse or ideal elements of quantitative symbols. We have now a means of representing the determinant above given in a compact form : for this purpose we need but to write one set of umbrse over the other as follows : fa1a2... an \ jf we now wish to obtain the algebraic \cq a2 ... aj ° value of this determinant, it is only necessary to take a1? a2, . . . , an in all its 1*2 *3... w different positions, and we shall have j a\ a2 ... an i ^ \=2j±{aia' \ cq a2 ... an ) 0 ! X a2a6>2 X X an^6n } , in which expression _61 , 02 , . . . , 0n represents some order PROC. ROY. SOC. EDIN. — YOL. XXV. 59 930 Proceedings of Eoyal Society of Edinburgh. [sess. of the numbers 1,2, . . . , n , and the positive or negative sign is to be taken according to the well-known dichotomous law.” An obvious extension of the notation is also indicated, whereby what he calls “ compound ” determinants may be appropriately represented. Since, in accordance with the foregoing, i: ;} is used to denote he considers that aa . b/3 — a/3 . ba { ab cd ) a/3 yS ( “will naturally denote that is ab cd ab cd a (3 y8 y8 a/3 (aa x b/3 | ( cy x dS)j (a/3 x ba)\ x 1 - (cS x dy)\ And in general the compound determinant ) J ( (ay X bij) > 1 r (ca x d/3) a f - 1 ( - (aS x by)\ x 1 I - (c/3 x da) f a1 b1 . . lY bo . L al fil * ’ ^1 $2 * ' ’ ^2 * * will denote ar (3r ... A, 1 i ai \ • "h \ x , a2 J . 1 -X 1 ar br . „l > • “«! ft J ' ’ ae.2 • •• v 1 a6r Por ' where, as before, we have the disjunctive equation 01502, ... ,0r = 1,2, ... , r .” As an example of the power of this notation he gives the theorem aY a2 . . . ar ar+ 1 ax a.2 . . . a^ Ojy | o a1 a2 . • • ur ar+s «i a2 . . . ar ar+ 1 al a2 • • . ar ar_^_2 .... a, a2 . ■ • ar ar+s = i aY a2 . ar i ts_1 > x (axa2 ... ar ar+ 1 ar+ 2 . . . ar+s [ 1 ai a2 . ar 1 1 ai a2 . • • ar ar ar_^2 • • • ar+s ( adding, in his enthusiasm, that without the aid of his “ system of umbral or biliteral notation, this important theorem could not be 1904-5.] Dr Muir on General Determinants. 931 made the subject of statement without an enormous periphrasis, and could never have been made the object of distinct contempla- tion or proof.” The main object of his paper is then taken up, but the subject of the notation is twice recurred to, — once to say that it is “ very similar to that of Vandermonde ” as he had learned from “ Mr. Spottiswoode’s valuable treatise,” and the second time to point out that on second thoughts it is better to unite two umbral elements in the form a a rather than in the form aa , because then the analogy upon which the extension of the notation from simple to compound determinants is grounded will be better apprehended. The theorem used above to illustrate the power of the £ umbral ’ notation should not be lightly passed over, being far more deserving of the epithet ‘ new 5 than the notation employed in formulating it. Although at a later date it came to be of less moment because of its inclusion as merely one of a class of theorems, viz., the class known as £ Extensionals,’ there can be no doubt that at the time of its discovery it was, as Sylvester himself styled it, ££ a remarkable theorem.” Taking, for the sake of illustration, the case of it where r = 3 and s = 4, viz., I a-^b2c2d^ | i aAC364 I I a~ftc2pzf 4 | I a1b2c3gi | I «AC3^5 I I I I ai^2Csf5 I I aih2C*9$ I I ai^2CSd6 I ! aAC3e6 I ! «AC3 I I «AC3?6 i I aAC3^7 I | aYb2c^ | I aAc3 fi I I «Ac30V i = I aAc 3 !3- I aAcAebf(i9i I* we see that if we delete a^b2cz everywhere on both sides we are left with db dQ dyj e4 e5 e6 e7 f 4 J 5 f Q D 9± 9$ 96 97 I d^f&97 1; 932 Proceedings of Royal Society of Edinburgh. [sess. so that the theorem is seen to he the Extensional of a manifest identity.* Sylvester, J. J. (1851, Aug.). [On a certain fundamental theorem of determinants. Philos. Magazine , ii. pp. 142-145 : Collected Math. Papers, i. pp. 252-255.] After a characteristic introductory paragraph about the import- ance of the new theorem and his reasons for publishing it, Sylvester proceeds — “The theorem is as follows: — Suppose that there are two determinants of the ordinary kind, each expressed by a square array of terms made up of n lines and n columns, so that in each square there are n 2 terms. Now let n he broken up in any given manner into two parts p and q, so that p + q = n. Let, firstly, one of the two given squares he divided in a given definite manner into two parts, one containing p of the n given lines, and the other part q of the same; and secondly, let the other of the two given squares be divided in every possible way into two parts, consisting of q and p lines respectively, so that on tacking on the part containing q lines of the second square to the part containing p lines of the first square, and the part containing p lines of the second square to the part containing q of the first, we get hack a new couple of squares, each denoting a determinant different from the two given determinants : the number of such new couples will evidently he n(n - 1) ... (n -p + 1) . 1-2 ... p ; and my theorem is that the product of the given couple of determinants is equal to the sum of the products ( affected with the proper algebraical sign ) of each of the new couples formed as above described The same is then stated in symbols, viz., See Trans. P.S.U., xxx. p. 4. 1904-5.] Dr Muir on General Determinants. 933 l a1 a2 . . . an ) | aj a2 . . , an j t \ b2 . . . b„ f X 1 ft & . . . ft ) a1 a2 an ) j ax a2 an ) ... bp foop+i fidp+'Z ••• fion ' ^ $6\ ft 02 ••• @0p ^p+ 1 ^jp+2 • • • ' where 01, 02 . . . , 0P are any p different integers taken from 1 , 2, . . n, or where, as Sylvester puts it, 6lt 02, . . 0n are * disjunctively ’ equal to 1 , 2 , . . . , n. A proof of a verificatory character is given at some length, the aim being to show that the terms arising from the expansion of the products occurring on the right-hand side are classifiable under two heads : (1) those which appear twice, viz., once with a positive sign and once with a negative sign ; (2) those which appear only once, and which in their aggregate agree with those arising from the expansion of the single product on the left. An improvement of it by Faa di Bruno will be given later. By removing to the right the solitary product at present on the left, the theorem is seen to belong to the class of vanishing aggre- gates of products of pairs of determinants, and ■ therefore to be not entirely new, the first instances of it, viz., \ab'\-\cd'\ - | ac |-| bd! | + \ ad'\\bc'\ — 0, | ab'c” |*| def" | - | abrd" |*| ce'f" | + | acd" |-j bef" \ - \ he'd" |-| acf" \ = 0, that is to say, the cases where n = 2, p — 1 , and n = 3 ,p = 1 , being found in Bezout (1779). Nothing, however, done by Bezout, Cauchy, or Schweins ought to dissociate Sylvester’s name from the theorem. His claim, too, is all the stronger from the fact that he it was who in 1839 first formulated the case n = n, p= 1, — a fact which seems to have dropped entirely out of remembrance, writers giving the date 1851 when referring to the case enunciated a dozen years earlier. Sylvester, J. J. (1851, Oct.). [On a remarkable discovery in the theory of canonical forms and of hyperdeterminants. Philos. Magazine , ii. pp. 391-410 : Collected Math. Papers , i. pp. 265-283.] Here, amid matter of great algebraical importance, there is incidentally suggested the discarding of the use of the term 934 Proceedings of Royal Society of Edinburgh. [sess. ‘ determinant ’ as connected with a single function, — that is to say, Gauss’ original use of the term, — and the substitution of the term * discriminant ’ in its place. The introduction of a new word, it is explained, is for the purpose of avoiding the obscurity and con- fusion which arises from employing the same word in two different senses, and “ ‘ discriminant ’ because it affords the discrimen or test for ascertaining whether or not equal factors enter into a function of two variables, or more generally of the existence or otherwise of multiple points in the locus represented or characterised by any algebraical function.” * Cayley, A. (1851, end). [On the theory of permutants. Cambridge and Dubl. Math. Journ., vii. pp. 40-51 : Collected Math. Papers , ii. pp. 16-26.] The second part of his paper of 1843, as we have seen, Cayley devoted to the consideration of a class of functions obtainable from the use of m sets of n indices in the way in which a deter- minant is obtainable from only two sets. The general symbol used for such a function was fV °1 T1 ' P2 °"2 r2 • < Pn Tn • • • this standing for the sum of all the different terms of the form -- V — 5 A x • • • • x A Pn o-8l rh • • • Prn • • • 5 In J denote any permutation whatever, the same or different, of the series of integers 1,2, ... ,re, and where ± r denotes the sign + or — according as the number of inversions in , r2 , . . . , rn is even or odd. Using a f over the column of p’s to indicate that these are unpermutable, he shows that f A 1 f A 1 Pi 0-1 . . . Pi (Ti . . . - = 1*2 • ■ • • m - - ^ Pn • • • - . Pn °"n • • • . when the number of columns, m, is even ; and vanishes when m is odd. In the former case it is clear that the placing of the f over any other column would have had the same result, and therefore that it is better to mark this indifference by placing it over the A. The other theorems, including a multiplication theorem, need not be given, our object being simply to show the position occupied by determinants among the new functions ; and this we can now do by quoting one sentence, viz., “ an ordinary determinant is represented by t t 1 A „ 1 A., “i& 1 1 .... - or .... j v a w fin - „ n n ) the latter form being obviously equally general with the former one.” In his paper of 1845 a further generalisation was made, the functions then reached being called ‘hyperdeterminants,’ and a hyperdeterminant defined as an expression representable as a homogeneous pth-degree function, H^, of certain of the deter- minants of a rectangular array, each of whose elements is 936 Proceedings of Royal Society of Edinburgh. [sess. denoted by n umbrse, and each umbra one of the integers 1 2 , . . . , m. Thus when n — 3 and m— 2, the array is or Ill 112 121 122 211 212 221 222, 111 112 211 212 121 122 221 222, 111 121 211 221 112 122 212 222, according as the first, second, or third umbra is made invariable throughout the two rows ; and if p = 1 we have the ‘ incomplete 9 hyperdeterminants 111 122 + 112 121 211 222 212 221 111 212 112 211 121 222 + 122 221 111 221 + 121 211 112 222 122 212 whereas if p= 2 we have the hyperdeterminants 111 122 211 222 111 212 121 222 111 221 112 222 112 121 j y 212 221 J 112 211 122 221 121 211 122 212 i F- 111 121 211 221 | 111 211 121 221 111 211 1112 212 112 122 2121222 112 212 122 222 121 221 122 222 which being really identical, have their common expression designated a * complete J hyperdeterminant. The general form of H p is not specified. Further details would here be out of place : the one important point to be noted is the relation between hyperdeterminants and the functions of Cayley’s paper of the year 1843, and this is shortly indicated by saying that the latter functions are hyperdeterminants in which y — 1 and n is even. 1904-5.] Dr Muir on General Determinants. 937 In his paper of the year 1847 an altogether different generalisa- tion was formulated, the corresponding symbol being £±(1, 2,. and one of the objects aimed at being to extend the definition of a determinant so as to include within it the Pfaffian. (See Collected Math. Papers , i. p. 589.) Having thus attempted to make clear the stage which the process of generalisation had reached with Cayley prior to 1851, we are prepared to appreciate the notable advance made by him in his paper of that year. The widely embracing conception therein formulated was that of the functions called on the suggestion of Sylvester ‘ permutants.1 For the sake of easy exposition we shall follow him in his special usage of the words ‘ form,5 * blank,5 4 characters,5 1 symbol.5 “ A form,” he says, “ may be considered as composed of blanks which are to be filled up by inserting in them specialising characters, and a form the blanks of which are so filled up becomes a symbol.” If the ‘ characters 5 (previously called by him * nombres symboliques ’) be 1, 2, 3, 4, ... . the ‘ symbol 5 may always be represented in the first instance, and without reference to the nature or constitution of the ‘ form,5 by V1234 . . . ; for example V1234 . . . may stand for -Pl2Q3-^4 • • • J 0r ^12-^34 • * • j 0r • • ' • How, let the characters 1, 2, 3, 4, . . . in such a symbol be permuted in every possible way, and the resulting symbols have the sign + or — prefixed to them in accordance with Cramer’s rule, then the aggregate of all these symbols is a ‘ simple permutantd The originating symbol being V1234 , the corresponding permutant might have been denoted by % ± V1234 ... as in his paper of the year 1847, but as a matter of fact Cayley now makes use of (Vim. ..:)•• It is thus seen that, taking for shortness5 sake only three characters, we have 0^123) = ^123 ^231 + V312 — ^132 ~ ^213 — ^321 > (V123) = (Y231)=-(V132)=-**- 0^113) == 0 • 938 Proceedings of Royal Society of Edinburgh. [sess. These preliminaries having been grasped, “it is easy,” in Cayley’s own words, “ to pass to the general definition of a permutant. We have only to consider the blanks as forming, not as heretofore a single set, but any number of distinct sets, and to consider the characters in each set of blanks as permutable inter se, and not otherwise, giving to the symbol the sign compounded of the signs corresponding to the arrangements of the characters in the different sets of blanks.” Thus, if the first and second blanks form a set, and the third and fourth blanks form a set, the per- mutant whose originating symbol is V1234 is The idea is hereupon suggested of arranging the blanks of a compound permutant so as to show in what manner they are grouped into sets. For example, instead of doing as we have just done, viz., using V1234 accompanied by a verbal explanation as to its sets, we might write From this it is a simple step to the idea of grouping the blanks in lines and columns, that is to say, to such a symbol as One case of this is that in which it is viewed as a function of the symbols Vapy . . . , Va'/3y • • • , etc., and a less general case that in which it is viewed as the product. Cayley then proceeds : — “ Upon this assumption it becomes important to distinguish in the different lines and columns. The cases to be con- sidered are : (A) The blanks of a single set or of single sets are situated in more than one column, (B) The blanks of each single set are situated in the same column, (C) The blanks of each single set form a separate column. The case B (which 34 and so obtain the different ways in which the blanks of a set are distributed 1904-5.] Dr Muir on General Determinants. 939 includes the case C) and the case C merit particular considera- tion. In fact, the case B is that of the functions which I have, in my memoir on Linear Transformations in the Journal , called hyperdeterminants, and the case C is the particular class of hyperdeterminants previously treated of by me in the Cambridge Philosophical Transactions , and also par- ticularly noticed in the memoir on Linear Transformations. The functions of the case B, I now propose to call ‘ Inter- mutants,’ and those in the case C, ‘Commutants.’ Corn- mutants include as a particular case ‘ Determinants,’ which term will be used in its ordinary signification.” To arrive at the position of determinants, therefore, in the great theory of permutants, we have first to seek out the particular permutants whose originating symbol is of the form p y ... . a' P 7 then in this restricted field to look for those in which the symbol just given is viewed as a product of symbols Vapy . , Va'p y ....,• • • • ; next to confine ourselves in this smaller domain to those in which the ‘ blanks ’ of each single c set ’ form a separate column ; and lastly to isolate those in which the number of such columns is 2. In his paper Cayley goes on to expound the theory first of commutants , and then of intermutants. Neither exposition, how- ever, needs attention here, because the one has already been dealt with under the year 1843, and the other is outside our subject. Sylvester, J. J. (1852, Jan.). [On the principles of the calculus of forms. Cambridge and Dublin Math. Journ ., vii. pp. 52-97 ; Collected Math. Papers , i. pp. 284-327.] A postscript added by Cayley to his paper of the year 1851 makes evident that Sylvester had a share in the latest generalisa- tion, and, as was natural, did not wish that share to be lost sight 940 Proceedings of Royal Society of Edinburgh. [sess. of. It made clear that the two workers had during the year been deeply engrossed in what Sylvester then called the ‘ calculus of forms,’ that they had been in close communication with one another, and that Sylvester’s discovery that the function ace + 2 bed - ad 2 - b2e - c3 could be expressed as a commutant, viz., /0 0\ 1 1 \2 2 J by considering 00 = a, 01 = 10 = /;, 02 = 11 = 20 = c, 12 = 21 =d> 22 = e had led Cayley to the conception of intermutants. The famous paper which we have now reached, and which was doubtless completed very shortly after Cayley’s, contains the results — numerous and suggestive — of Sylvester’s labours. The only section, however, which directly concerns the theory of determinants is the third, bearing the heading “On Commutants.” It opens with a page regarding the simplest species, “the well- known common determinant,” and then proceeds : — “ If, instead of two lines of umbrae, three or more be taken, the same principle of solution will continue to be applicable. Thus, if there be a matrix of any even number r of lines each of n umbrae «1 b i •• .. a2 h ■■ .. i2 ar br . . .. lr the first may be supposed to remain stationary, and the remaining r— 1 lines each be taken in 1*2 ’...n different orders : every order in each line will be accompanied by its appropriate sign + or — ; and each different grouping in each line will give rise to a particular grouping of the letters read off in columns. The value of the commutant expressed by the above matrix will therefore consist of the sum of (1*2* . . . n)r~l terms, each term being the product of n quantities respectively symbolised by a group of r letters and affected with the sign + or - according as the number of 1904-5.] Dr Muir on General Determinants. 941 negative signs in the total of the arrangements of the lines (from the columnar reading off of which each such term is derived) is even or odd. For example, the value of a b c d e f g h will be found by taking the (D2)3 arrangements, as below, ab ab ab ab ab ab ab ab cd dc cd dc cd dc cd dc ef ef fe fe ef ef fe fe gh gh gh gh hg hg Kg Tig , the signs of cd , ef , gh being supposed + , those of dc , fe , hg will be each - . Consequently the sum of the terms will be expressed by aceg • bdjli - adeg ■ bcfli — acfg • bdeli + adfg • bceh - aceh • bdfg + adeh • bcfg + acfh • bdeg - adfh • bceg It will be observed that the example here given is the quadratic function which Cayley would have denoted by / V \ \ 0 0 0 0 I \ ] 1 1 1/ ’ and which, on the supposition that generally Ya,^,y,s =Va+)g+v+5 and in particular that V0 = a, V1 = b , Y 2 — c , . . . . would represent ae-bd — bd + c2 — bd + c2 + c2 — db i.e. ae - ibd + 3c2 . In his applications of the theory of commutants to that of £ forms 5 Sylvester first uses differential operators as umbrae, speaking, for example, of the commutant a_ a_ a_ dx1 ’ dg1 5 dz1 5 a„ dx2 ’ dy2 ’ dz2 ’ 942 Proceedings of Royal Society of Edinburgh . [sess. He also uses effectively such umbrae as an , an~1b , a~nb 2 ,...., — a usage which is most appropriately illustrated by taking a commutant having two lines of three umbrae each, that is to say, the determinant of the third order a2 ab b2 a2 ab b2 . This is conveniently taken to represent a4 • a2b2 • 64 - a4 • abB • ab 3 - aBb ■ aBb • 54 + azb • ab 3 • a2b 2 + a2b2-azb-abz - a2b2 • a2b2 . a2b2 . and consequently if (ckc + fa/)4 = A«4 4- 4Bx3y + 6C x2y2 + 4D xyB + Ey4, it is an expression for ACE + 2BCD - AD2 - B2E - C3 , that is to say, for the special determinant ABC BCD C D E . When he comes to speak of 1 partial ’ commutants, which are identical with intermutants, he devotes a page (pp. 88-89) to the subject of his relations with Cayley. As it would appear that he was not quite satisfied with the wording of the postscript above referred to, Cayley published a modified form of it as a note, headed “ Correction of the Postscript to the Paper on Permutants,” and there the matter between the two friends happily rested. Betti, E. (1852, Feb.). [Sulla risoluzione delle equazioni algebriche. Annali di sci. mat. ejis., iii. pp. 49-115.] In this important memoir dealing with the theory of substitu- tions, and with the application of the same towards finding the conditions of resolvability of algebraic equations, the author defines on page 80, in the manner afterwards so familiar, the expression 1904-5.] Dr Muir on General Determinants. 943 ‘ determinant of a substitution ’ : and on the following page there occurs the passage — “ Quindi dal noto teorema della moltiplicazione delle determinant e facile dedurre che, se si chiama A la deter- minante del prodotto delle due sostituzioni ( h ) e (li) [whose determinants are D and D'], avremo A =D1)'; cioe la determinate del prodotto di due sostituzioni e eguale al prodotto delle loro determinanti .” Bruno, F. Faa di (1852, May). [Demonstration d’un theoreme de M. Sylvester relatif a la decomposition d’un produit de deux determinants. Journ. de Liouville (1), xvii. pp. 190-192.] The theorem is that which appeared in the Philosophical Magazine for August 1851, and which is there formulated in the umbral notation as follows : — | a, a2 ... . an lb1 b2 ... . bn i x { ? aJ ■ ■ . . CLn | J \ /?! P2 . . • • Pn ) a^ a2 an 1 j a2 an &i b2 ... bp @0p+ 2 • • ■ @6n * ' fio j 2 • • • fiop bp+1 bp^_2 • • • bn where 61 , 02 , . . . , 0n are ‘ disjunctively ’ equal to 1,2, ... n . Faa di Bruno prefers to write it in the form (±«? 01 ™02 ^ . . . a*") • 2( + sf1 . . . b*n) 0 n / V — 1 2 p n / ,0 p J*p+ i „'!'p+ 2 P+ 1 P+ 2 using two other sets of letters like 01} 02, . . . 0n. This change in notation being allowed for, the new proof is in general character exactly the same as the old ; it is, however, more concise and more clearly set forth. It starts with the fact that any term arising from the expansion of the typical product on the right-hand side may be written 01 02 a1 d>p \fjp+ 1 tin i//! jp2 p p+\ n 01 0-2 npp 702>+l 7 0P+2 7 0n °0p °0p+ 1 %+ 2 * ‘ * °6n 944 Proceedings of Royal Society of Edinburgh. [sess. Then observing the ‘ indices superieures 5 attached to the V s in this, we are asked to consider two possible cases. In the first place, we have to note that if no one of the i/^’s be identical with any one of the <£’ s, the term is a term of the expansion of the product on the left-hand side, and that the number of such terms in the expansion of each product on the right-hand side being (1.2.3 . . . n) • (1.2.3 . . . p) • (1.2.3 . . . hf^p) and the number of products n(ii -\)(n — 2) .... (n - p + 1) 1.2.3 . . . p the total number of such terms is (1.2.3 . . . nf , which is exactly the total number on the left-hand side. In the second place, if one of the i/^s be identical with one of the <£’s, say ^ i = ^P+h 5 it is pointed out that there must exist another term in which, in place of having jfi lfp+h °i 6p+h we shall have jfi jfp+h ®p-\-h and that these two terms having necessarily different signs, must cancel each other. Sylvester, J. J. (1852, Oct.). [On Staudt’s theorems concerning the contents of polygons and polyhedrons, with a note on a new and resembling class of theorems. Philos. Magazine (4), iv. pp. 335-345 : Collected Math. Papers , i. pp. 382-391.] After a page of introduction, written in a light semi-historical, semi-critical style, Sylvester prepares the way for considering his main subject by giving as a basis two algebraical lemmas. The first he formulates as follows : — “ If the determinants represented by two square matrices are to be multiplied together, any number of columns may be 1904-5.] Dr Muir on General Determinants. 945 cut off from the one matrix, and a corresponding number of columns from the other. Each of the lines in either one of the matrices so reduced in width as aforesaid being then multiplied by each line of the other, and the results of e multiplication arranged as a square matrix and bordered wicn the two respective sets of columns cut off, arranged sym- metrically (the one set parallel to the new columns, the other set parallel to the new lines), the complete determinant represented by the new matrix so bordered (abstraction made of the algebraical sign) will be the product of the two original determinants. ” In illustration he gives three forms for the product of a b , a [ 3 ctiid. c d 1 y viz. — aa + b/3 ay + bS aa ay b 2 2 a b Ca + d/3 cy + dS > Ca cy d 2 2 c d P 8 . 1, a /? . . i y 8 . . In regard to the 2’s which occur in the last form his remark is : — “Any quantities might be substituted instead of 2 .... , as such terms do not influence the result : this figure is probably, however, the proper quantity arising from the application of the rule, because .... the value of the determinant represented by a matrix of no places is not zero but unity.” In the case where the two given determinants are of the third order, say a b c a P y a V c and d p' y n a b" c" a P" y" he gives only the second and third of the four (w+1) possible forms, viz. — aa + bp ad + b/3' aa" + b/3" c a' a + b'/3 a a + b/3' ad' + b'p" c a' a + b"/3 d'd + b"f3' a" a" + b" /3" c" y i y" PROC. ROY. SOC. EDIN. — YOL. XXY. 60 946 Proceedings of Royal Society of Edinburgh. [sess. aa ad ad' b c \ da do! a a" b' c a” a ,, , n n i n a a a a a DC P p P" ■ ■ y y y" ■ ■ pointing out by way of demonstration that the former of these is arrived at hy transforming the given determinants into a b c . a (3 y a b' c . and - a /S' . 7 a" b" c" . a" (3" . 7 . . 1 . 1 and applying the ordinary rule of multiplication, and similarly that the latter is got by multiplying a b c a .. (3 y a b' c . d .. (3' y a" b" c" . . by d' . . /r / . . . 1 . . i . . . . . . . 1 . . i . . He thereupon leaves the subject with the remark : — “This rule is interesting as exhibiting .... a complete scale whereby we may descend from the ordinary mode of representing the product of two determinants to the form .... where the two original determinants are made to occupy opposite quadrants of a square whose places in one of the remaining quadrants are left vacant, and shows us that under one aspect at least this latter form may be regarded as a matrix bordered by the two given matrices.” The second lemma is the identity — a\2 aiZ ai n 1 - An -^12 • . . . Aln 1 «S1 (%22 • • • • a2n 1 An ■^22 • ■ • • -^~2n 1 U„2 . . . . &nn 1 A -Aj-w2 • • • • Kn 1 1 1 . . . . 1 1 1 . . . . 1 1904-5.] Dr Muir on G-eneral Determinants. 947 where Ars = ars + hr + Jcs, and the h’s and &’s are perfectly arbitrary quantities, the transformation being of course effected by adding multiples of the last column to the other columns, and thereafter multiples of the last row to the other rows. The geometrical applications which follow, it may be interesting to note, are connected with the subject of Cayley’s paper of 1841, — his well-known first paper on determinants. LIST OF AUTHORS whose writings are here dealt with. 1844. Cauchy . PAGE . 908 1851. Sylvester page . 929 1844. Cauchy . . 908 1851. Sylvester . 932 1846. Hansen . . 913 1851. Sylvester . 933 1847. Cayley . . 913 1851. Cayley . . 934 1847. Cauchy . . 915 1852. Sylvester . 939 1849. JOACHIMSTHAL . 919 1852. Betti . 942 1850. Sylvester . 923 1852. Bruno, Faa di . 943 1851. Spottiswoode . 924 1852. Sylvester . 944 ( Issued separately September 30, 1905.) 948 Proceedings of Royal Society of Edinburgh. [sess. Note on some generally accepted Views regarding Vision. By Dr W. Peddie. (MS. received June 29, 1905. Read July 17, 1905.) The following beliefs regarding vision meet with very general acceptance : — First. Very intense light of any wave-length produces prac- tically the sensation of whiteness. Second. Very weak light of any wave-length produces prac- tically the sensation of whiteness. Third. A coloured area of normal brightness retains its colour, though with diminished purity, when gazed at steadily for a long time. Fourth. Small, faintly luminous, objects are seen more easily by indirect vision than by direct vision. The first and second of these supposed facts are readily accounted for on any of the usual theories of vision. The Young-Helmholtz theory, for example, gives quite as easy an explanation of them as Hering’s theory gives. Yet the truth of these supposed facts is by no means a necessary result of any of the theories. In a recent paper “ On Colour-Vision by very Weak Light” ( Proc . Roy. Soc., B 508, 1905), Dr G. J. Burch describes experiments which lead him to the conclusion that the second statement is not necessarily true. In that paper he also refers to the first statement in the following words : “ In my paper on Artificial Colour-Blindness” {Phil. Trans., B vol. 191, 1899), “ I described experiments showing that Hering’s argument in favour of a black-white sensation is invalid, in so far as it rests on the statement that by intense light all colours tend towards white. For the apparent whiteness — in the green region, for instance — is only a transitory stage in the production of green blindness, and is reached when the green sensation is reduced to the strength of the underlying blue and red, the mixture of the three being 1904-5.] Dr W. Peddie on some Views regarding Vision. 949 equivalent to white by candlelight, and, therefore, by courtesy, white.” In the majority of the instances given in Dr Burch’s paper the region of the spectrum, in which the light used to produce blindness lies, is entirely blotted out, so that evidence of ‘ whiteness ’ cannot appear. In the case of blinding by green light the region is not blotted out, and, between the red part of the spectrum on the one hand and the blue on the other, there is a narrow band of an indescribable neutral tint. This indicates practical whiteness in the green region when the strong blinding light is replaced by weaker light. Farther blinding may alter this condition, but does not affect the question whether the intense coloured lights do not themselves appear to be white. It would be of great interest, in the above case, to determine if mixture of the red and blue lights which occur on either side of the neutral band cannot give rise to a neutral light. There is no a priori reason why a mixture of lights should not be neutral to a blinded eye although they appear to it to be similar to lights which, when viewed by the eye in an unblinded condition, are not mutually complementary. It is known that apparent absence of colour in light viewed by a colour-blind eye does not prevent that light from exercising its property of complementariness ; so that lights which are complementary in normal vision are also complementary in abnormal vision. But the converse is often untrue. Whatever may be the case with regard to intense light, Dr Burch’s conclusion with regard to weak light seems to be fully supported. He finds that some hours of entire rest in darkness may be necessary to get rid of ‘dazzle-tints,’ that is, coloured luminosity in the eye due to previous exposure to light ; and that, when the dazzle-tints have entirely disappeared, “there is no interval between the threshold of light-sensation and the threshold of colour-sensation,” so that the feeblest visible light has its colour manifest. With regard to the third belief, Dr Burch’s statement as to the transitoriness of the stage of whiteness in blinding by intense light, would, if verified, prove a negative. A somewhat different phenomenon which I have observed points in the same direction. About three years ago I was making observations on after-images 950 Proceedings of Royal Society of Edinburgh. [sess. of coloured objects. In the course of these I looked steadily for some time, in strong lamp-light, at a red table-cover and watched the gradual weakening of the colour, which ultimately became very grey. Quite suddenly the colour changed from greyish but distinct red to a fairly strong green, which could be looked at for some time, though a slight motion of the eyes would cause it to change back to red. The process could be readily repeated. The suddenness of the change was quite startling at first. I ascribed it, at the time, to an action analogous to mus- cular fatigue. If one pushes against a reverse force, which can just be overcome, the muscles ultimately become fatigued and resist less and less strongly and more and more spasmodically. A sudden uncontrollable diminution of effort at last enables the reverse force to produce reverse motion. About two years ago I made, quite unintentionally, an observa- tion which negatives the universality of the truth of the fourth statement. Being awake during the night, I was watching the coloured luminosity in the eye — presumably Dr Burch’s ‘dazzle- tint ’ — and noting its changes. The main colours are greenish and violet, and these appear to be nearly complementary, for they give rise to a whitish light when they seem to border on each other and presumably overlap. They sometimes change with great rapidity, suddenly spreading out from centres, suddenly breaking up in centres and rolling off throughout the field of vision. At other times they are more fixed. I could see them even against the dark sky, some of the colours being brighter and some darker than the background. As usual, faint stars were visible when regarded indirectly but disappeared when looked at directly. After a time, when the colours were more steady, I found that, by motion of the eyes, it was possible to get the patches removed temporarily from the central parts of the field ; and I then saw the faint stars well by direct vision. The usual want of power to see faint objects directly is very tantalising. The pleasure associated with the abnormal power of seeing them best by direct vision is quite indescribable. Continuous with- drawal of the line of vision from them produced continuous diminution of visibility ; and, whenever the line of sight was such as to bring the star to the edge of a dark patch of colour in 1904-5.] Dr W. Peddie on some Views regarding Vision. 951 the field of vision, the star disappeared. It was quite invisible through a dark patch ; through a brighter patch it was visible, though apparently less distinct. It seems therefore that direct vision, when unobstructed by patches of self-colour in the eye, is most effective for perception of small luminous objects. Such a conclusion removes the basis from some theories of the mechanism of vision. {Issued separately October 23, 1905.) 952 Proceedings of Royal Society of Edinburgh. [sess. Note on the Boiling Points of Aqueous Solutions. By the Rev. S. M. Johnston, B.A. Communicated by Professor J. G. MacGregor, F.R.S. (MS. received July 17, 1905. Read same date.) In the course of a research on the boiling points of aqueous solutions, certain points came under my notice which have been introduced into this note. After considerable experience with various forms of Beckmann’s boiling point apparatus, and due consideration of the Jones type, a boiling point apparatus was designed which embraced what were considered the best points of each, in view of the research anti- cipated. The body of the tube was of the Jones type, and had a side tube fitted with a rubber stopper for the introduction of the salt at a short distance from the top of the tube. On the opposite side of the boiling tube, about the same height up, went off a condensing tube of the Beckmann pattern. The thermometer — one of Beckmann’s — read to hundredths of a degree, and, with the aid of a Beckmann reading glass, could be estimated to thousandths of a degree. It passed through a close-fitting rubber stopper at the top of the tube. In carrying out an experiment, garnets and platinum tetrahedra were used for filling material. The thermometer, when in position, was surrounded to a point above the surface of the solvent or solutions by a cylinder of platinum foil. Beneath the thermometer a few pieces of platinum foil were placed. The boiling tube was surrounded externally by a cylinder of glass of considerably larger diameter, and the space between was packed with asbestos wool. The heat was supplied by a gas jet, which was prevented from coming into contact with the boiling tube by wire gauze and asbestos paper. The whole apparatus was surrounded by a zinc cylinder in two portions, one of which could be removed at pleasure. With these precautions, a steady boiling temperature could be 1904-5.] Note on Boiling Points of Aqueous Solutions. 953 quickly obtained, — so steady that, notwithstanding the delicacy of the thermometer used, no change of reading could be detected frequently for five or ten minutes, and sometimes for longer periods. In the experiments, the amount of solvent delivered by a fifty c.c. pipette was used. As the result of several experiments to determine the amount of vapour in the tube during an experi- ment, it was found to be ’41 grammes, and was allowed for. The distilled water used was redistilled to guard against impurities. The filling material, after each series of experiments, was thoroughly cleansed with boiling water and dried before being used again. The platinum foil, in addition, was heated in a Bunsen flame. Series of solutions were made from each salt by the addition of compressed pellets of salt successively to the solvent or solution during ebullition. The pellets were made at first by the aid of a steel press, but later by one with ivory fittings, to safeguard their purity, which was essential when deliquescent salts were the subject of research. The procedure adopted was to bring the solvent to a steady boiling temperature, which was noted. Then pellet after pellet of salt was added at intervals of from twenty to twenty-five minutes, the boiling temperature of the successive concentrations being noted. It was found essential to the success of an experiment to allow at least twenty minutes for the diffusion of the salt. Corresponding to the successive readings of the thermometer, a succession of readings of the barometer was taken, so that any change in atmospheric pressure might be allowed for. The barometer gave readings corresponding to four thousandths of a degree, but could be estimated to the equivalent of two thousandths. The salts used were supplied by Messrs Merck & Co. as specially pure, and were tested quantitatively and spectroscopically. In the calculation of results ionization coefficients were necessary at high temperature, as near the boiling point as possible. These were obtained from conductivity values as given by Kranhals * as follows. Kranhals gives the molecular conduc- * Zeit. fur phys. Chem. , 5, 250. 1890. 954 Proceedings of Royal Society of Edinburgh. [sess. tivity at 99° '4 C. for solutions containing one, one-half, one-fourth, one-eighth, etc. and one-thousandth gramme equivalents per litre. The ionization at any of these concentrations was obtained by dividing the conductivity value, as given by Kranhals, by the value at one-thousandtli gramme equivalents. The concentration ioniza- tion curve was drawn on sectional paper for the range of a series of experiments. From the amount of salt added to the solvent the percentage composition was obtained, from which, by the aid of tables,* the concentration in equivalent gramme molecules per litre was obtained, and for this the ionization by the use of the ionization concentration curve already referred to. Ivranhals claims to work with an error limit of from two to three per cent. Having repeated many of his experiments, I found this claim well justified. Schaller, and Lyle and Hosking have also done some conductivity work at 99° or 99° ’4. Kranhals’ values were chosen because they were best suited to series of experiments within the range of this note. Lyle and Hosking f deal chiefly with sodium chloride solutions. Schaller J worked principally at 256, 512, and 1024 litres per gramme equivalent. Values up to 80° have been given by Trotsch,§ and Campetti and Nazari,|| which would be too low a temperature for my purpose. Those who have given con- ductivity values up to 99° or 99° -4 have only given them to about one-thousandth gramme equivalents per litre, which dilution could scarcely be supposed to give the molecular conductivity at infinite dilution for every salt. I therefore intend to make determinations of conductivity at greater dilution. When calculating the results obtained by experiment, at first , total elevations above the boiling point of the solvent were used. The calculations were made from the formula c_ m.W.E (1 +n~ la )w where C is the value of the so-called boiling point elevation * B. A. Report on the Present State of our Knowledge of Electrolysis and Electro- Chemistry , 1 893. t Phil. Mag. (6), 3, 487. 1902. + Zeit. f. phys. Chem ., 25, 497. § Wied. Annalen, 41, 259. 1890. || Acad. Science Torino , 40, Nos. 2 and 3, pp. 155, 163. 1904-5. 1904-5.] Note on Boiling Points of Aqueous Solutions. 955 constant expressed per gramme particle (molecule or ion) in one gramme of solvent — m = molecular weight of salt added. W = weight of solvent used in grammes. E = elevation of boiling point. w = weight of salt added in grammes. a = ionization coefficient. n = number of free ions into which a molecule of salt dissociates. From this formula values of C were obtained, at one time high, at another low, when compared with theory. Thus, for potassium chloride the values 858, 704, 684, 643, 614, 596, 572 were obtained from one series; a second series gave 460, 467, 514, 518, 523. For potassium nitrate the values were 637, 617, 603, 573, 571, 549, 547, 540, and a second series gave 874, 702, 696, 686, 643, 608, 609, 593 ; for a third series the values were 605, 556, 550. For sodium nitrate 518, 516, 520, 529, 534, 530, 535. For sodium chloride 617, 621, 592, 587, 579. Such values as these being obtained, it was desirable to see what values would be given by calculations from the boiling point data of other experimenters. Elevations of boiling point as given by Biltz * gave for potassium nitrate as values 638, 589, 596, 628, and for sodium chloride 585, 598, 611, 609. Those given by Walker and Lumsden f gave for potassium nitrate 648, 618, for sodium chloride 598, 593, and for potassium bromide 620, 614, 645, 665. Smitz’s % elevations gave for sodium chloride 463, for potassium chloride 497, for potassium nitrate 522, and for sodium nitrate 594. From observations I made, it would seem that these high values are the result of a difficulty in the determination of the exact boiling point of water. Thus, for the solvent, a steady boiling temperature could be raised or lowered by increasing or decreasing the strength of the source of heat, within the range of several hundredths of a degree. A solution, on the other hand, took up a definite boiling temperature, which was independent of small changes in the strength of the source of heat so long as ebullition was maintained. * Practical Methods for determining Molecular Weights, translated by Jones and King, 189. 1899. t Journal of the Chemical Society, 73, 502. 1898. t Zeitschrift fur physicalische Chemic, 39, 420. 1902. 956 Proceedings of Royal Society of Edinburgh. [sess. Several series of experiments were performed on each of a number of salts to find the relation between the boiling point elevation of different series on the same salt. It was seen from plotting elevations of boiling temperature against weight of salt added, and drawing in the curves for different series on the same salt, that the curves obtained were approximately straight lines, and parallel to each other. Specimens of these are given for potassium nitrate, barium chloride, and lithium chloride on page 957 ; ammonium sulphate and potassium chloride on page 958 ; and sodium nitrate on page 959. The straightness of the curves in the vicinity of the origin was also tested in some cases, and it was found that, so far as experiment could he carried, the curves continued approximately straight lines. The boiling temperature of the solvent under these considera- tions being looked upon as at fault, that is, its experimental value varying by one or two hundredths of a degree, and the boiling temperature of a solution being steady, it became desirable, in determining the boiling point constant, to use only elevations above the boiling point of a solution. I consequently computed, not the elevation of the boiling point per gramme particle produced by adding a given number of grammes of salt to one gramme of solvent, hut the elevation per gramme particle produced by adding given numbers of gramme molecules of salt to a solution, the expression employed being n m.W.AE O “ - - j (1 + n - la)A w where m, W, n and a are as before, and AE and A w increments of elevation of boiling temperature and grammes of salt added respectively. According to theory, the values obtained should he the same as those from the first formula if the E could he AE accurately determined. The ratio was found as follows : — J A w Let OW and OE he axes of weight of salt added and elevation of boiling temperature respectively. Let LR, the curve for any series of observations, found as seen above to he approximately a straight line, be produced to meet the axes in P. Through any near points Q and R on this curve draw parallels to the axes. WEIGHT OF SALT ADDED. 10 12 14 16 1-8 20 1904-5.] Note on Boiling Points of Aqueous Solutions, 957 Fto. 1 WEIGHT OF SALT ADDED. 958 Proceedings of Royal Society of Edinburgh. [sess. / "aC J ELEVATION OF BOILING TEMF Fig. 2. WEIGHT OF SALT ADDED. 1904-5.] Note on Boiling Points of Aqueous Solutions. 959 Fig. 3. 960 Proceedings of Royal Society of Edinburgh. [sess. AE _ QS A w ~RS PT ~ TR OT-OP TR E-OP w Hence C - E - OP/ mW \ w \1 + n—fa/’ w Fig. 4. AE Values of — were obtained from those of E and w by reading A w J off OP and deducting it from the observed value of E and dividing by iv. The following tables contain the results of the determina- tion of C. As Kranhals only claims an accuracy in his conductivity data of two to three per cent., I have usually considered it sufficient to calculate ionizations to two places of decimals. In the case, of sodium nitrate the elevations of boiling temperature used were the observed values, but for the other salts the elevation values were taken from the curves. Potassium Nitrate. First Series. Grins. Salt added. Per cent. Composi- tion. Grm. eqs. per Litre. Elevation of Boiling Point. Ionization Co-eff. Elev. Constant. •2118 •42 •041 •063 •665 519 '445 •89 •089 •112 •657 511 •6986 1-39 •139 •160 •642 514 •9318 1-85 •187 •206 •629 521 1-2126 2-39 •244 •252 •616 518 1-5044 2-95 •301 •292 •611 516 1-8366 3-57 •364 •348 •608 516 2-1876 4-23 *431 •403 •605 516 Second Series. •4300 •86 •086 •086 •657 512 •8120 1-61 •162 •149 •635 512 1-493 2*92 •298 •265 •611 516 1904-5.] Note on Boiling Points of Aqueous Solutions. 961 Potassium Chloride. First Series. Grms. Salt added. Per cent. Composi- tion. Grm. eqs. per Litre. Elevation of Boiling Point. Ionization. Co-eff. Elev. Constant. *1754 •35 •048 *054 •89 527 •3546 •71 •124 •101 •88 521 •5424 1*08 •144 •146 *87 503 •7426 1-47 •202 *190 •85 500 •9740 1-93 •266 •247 •83 500 1-1520 2-26 •316 •291 •81 505 1-3684 2-69 *370 •343 •79 504 1*5924 3-11 *428 •394 •77 511 1-7278 3'37 •466 •425 •76 512 1-8918 3-68 •508 •471 *75 517 Second Series. •1975 •39 •050 1 •058 •89 522 •3164 •63 •084 •078 •88 502 •5386 1-07 •146 •129 •87 501 •6736 1-34 •164 •171 •85 495 •8236 1-63 •224 •216 •84 497 1-0228 2-02 •298 •258 •81 497 1-1742 2*31 •318 •297 •81 502 1-2970 2-55 •356 •329 •80 503 1-5382 3-01 •414 •372 •78 508 1*7364 3-39 •468 •421 •76 512 1-9388 3-77 •516 •489 •74 523 2-1434 4-15 '570 •535 •73 525 Third Series. •3300 •66 •090 •120 •88 503 •5500 1-09 •248 •191 •87 509 •8084 1-60 •230 •260 •84 510 1-0460 2-07 •288 •312 •81 516 1-3558 2-66 •366 •388 •79 518 1*6300 3-19 •440 *444 •76 520 1-9224 374 *512 •510 •74 521 2-2144 4-28 •590 •582 •72 529 2-5328 4-87 •674 •666 •71 530 PROC. ROY. SOC. EDIN. — YOL. XXV. 61 962 Proceedings of Royal Society of Edinburgh. [j Sodium Nitrate. First Series. Grms. Salt added. Per cent. Composi- tion. Grm. eqs. per Litre. Elevation of Boiling Point. Ionization. Elev. Constant. •2054 •36 •042 •053 •87 500 *4860 •87 •105 •111 •82 500 1-0198 1-81 •218 •220 •76 500 1*4880 2-50 •302 •312 •70 505 1-9852 3-60 •435 •420 •65 530 2-5216 4-80 •578 •530 •62 536 3-0242 5-54 •667 •632 •59 540 3-5682 6-58 •744 •700 •54 531 Second Series. •2156 •37 •046 •066 •87 499 •4625 •82 •101 •125 •82 517 •7628 1-43 *173 *186 •78 517 1-0879 2-04 •247 •262 •76 525 1-3831 2-64 •319 •316 •70 530 1-5883 3-02 •367 •359 •67 536 1-8682 3*56 ‘431 •428 *65 550 2*2619 4-32 •521 •509 •63 552 Potassium Bromide. First Series. Grms. Salt added. Per cent. Composi- tion. Grm- eqs. per Litre. Elevation of Boiling Point. Ionization Co-eff. Elev. Constant. •4250 •85 •088 •112 •796 504 •6854 1*36 •140 *161 •774 502 •8813 1-75 •170 •198 *758 509 1-0293 2-03 •208 •223 •744 519 1-2945 2-55 •260 •252 •732 520 1 -5705 3'07 *312 •312 *720 525 1-9564 3-88 •396 •374 *706 528 2-3074 4-45 •456 •435 •692 535 1 904— 5. j Note on Boiling Points of Aqueous Solutions. 963 Second Series. Grms. Salt added. Per cent. Composi- tion. Grm. eqs. per Litre. Elevation of Boiling Point. 1 • Ionization Co-eff. Elev. Constant. *5530 1-14 •116 •078 •786 520 *8060 1-G0 •168 •105 *764 515 1*0248 2*02 •208 •131 •744 519 1-1754 2-32 •332 •157 •734 521 2-2978 4-44 •456 •342 •694 530 2*5470 4-88 •500 •379 •688 531 2-8726 5-48 •592 •428 •676 535 3-2479 6*16 •632 •483 •660 536 3*4952 6-60 •680 •529 •652 537 Sodium Chloride. First Series. Grms. Salt added. Per cent. Composi- tion. Grm. eqs. per Litre. Elevation of Boiling Point. Ionization Co-eff. Elev. Constant. •2070 •48 •080 •096 •79 503 •4294 •91 •162 •169 "76 518 •6143 1-23 ■218 •228 •71 522 •8314 1*66 •294 •294 •68 523 1-0277 2-01 •354 •356 •67 525 1-2160 2*38 •404 •421 •66 523 1-5870 2-98 •528 •541 •65 526 2-0284 3-88 •634 •680 •65 525 2-5044 4-80 •856 •826 •64 524 2-9744 5-68 1-004 •986 •64 525 3-4182 6-47 1-148 1-144 •63 525 Second Series. •2384 •483 •082 •136 •79 509 •4018 •80 •140 •179 •76 518 •6852 1-36 •242 •285 *71 518 ■8862 1*76 •312 •347 •68 522 1-1136 2-06 •356 •499 •67 526 1-3978 2-74 •486 •494 •66 527 1*7802 3-47 •614 •610 •65 526 2-1962 4-25 •752 •715 •65 521 2-6150 5-02 •892 •821 •64 525 2-9736 5-67 1-008 •929 •64 527 3-2832 6*22 1-102 1-013 •64 525 964 Proceedings of Royal Society of Edinburgh. [skss. If the values just given for C be compared with those obtained when elevations above the boiling point of the solvent were used, as in the calculations on page 955, it will be obvious they are in much greater harmony for the same series. It will also be seen that the values of C for one series, when compared wuth those for another on the same salt, are in greater harmony ; and the increased agreement is maintained when the values for series on different salts are considered. The agreement of the values with theory is also much greater. Most of the values obtained for C indicate an increase of the value with increase of concentration ; but it would be premature to draw that inference, as in solutions so dilute as some of those used, a small ionization error would cause a considerable variation ; but in addition it has to be remembered that for some of the dilutions used, one-thousandth of a degree variation of boiling temperature would have made a difference of 10 in the value of C, and for any of the concentrations a few thousandths of a degree would have made a considerable change. It has also to be borne in mind that the barometer used, although an excellent instru- ment, only read to the equivalent of about four thousandths of a degree, and was estimated only to two thousandths. The first five values obtained for sodium nitrate in the first series are very approximately the same : during the time this series of observations was taken, no barometric change was detected. For potassium bromide the barometer remained steady for the last three experiments of the second series ; and here, again, there is closer agreement than usual in the values of C. Also for the first series on potassium nitrate the barometer was steady, except in one observation, and here likewise the harmony of the values is increased. It would therefore seem probable that barometric changes, even after eliminating their effects by the ordinary method, have had considerable influence in producing variations in the value of C ; consequently, were these deducted, the changes of value would be proportionately diminished. This is a source of error which it will be possible more fully to eliminate in later experiments. The advantages of the method adopted become more apparent when it is applied to find molecular weights. 1904-5.] Note on Boiling Points of Aqueous Solutions. 965 Prom the expression for C given above, page 956, we have C.w.(l +n - la) m= W(E-OP) ' To illustrate this application of the method, I calculated the values of m for the bromide, chloride, and nitrate of potassium, and for sodium nitrate. The first series , as given above, in each was taken. In the calculations the theoretical value of C, i.e. 520, was used. The values of m for potassium bromide were 121, 123, 120, 118, 118, 116, 115, 114 : the mean value being 118T, the recognised value 1 18*7. For potassium chloride the molecular values were 73, 73*3, 76, 76, 76, 76, 76, 74, 74, 74 : their mean value is 74*83, the recognised value 74*59. For potassium nitrate the values were 101, 104, 102, 99*4, 100, 103, 103, 101 ; mean value, 101*2; recognised value, 101*17. For sodium nitrate the values were 86, 87, 87, 86, 85, 82, 80, 83, the arithmetic mean being 84*4, and the recognised value 85*08. Had my object been the determination of molecular weights, greater care would have been taken when drawing the curves. The molecular weight calculations I have made indicate how accurately my method might be employed in such observations. Up to the present the boiling-point method has only been applied roughly to determine molecular weights, and generally* with considerable divergence of value. This divergence would frequently have been much greater had not one error helped to counterbalance another. An inaccurate determination, usually too low, of the boiling point of the solvent when water was used, resulting in too high elevation of the boiling temperature of the solution, was largely overcome by the assumption of total ioniza- tion when the latter was only from seventy to ninety per cent. The variation is accentuated when molecular weights obtained by * Ber. Der. Chem., 31, 471. 1898. Practical Methods for determining Molecular Weights , by ... . Biltz, translated by Jones and King, p. 189. 1899. Zeitschrift fur Anorg. Chemie, 17, pp. 435 and 450. 1898. Sakurai, Journal of the Chemical Society , 61, 987. Walker and Lumsden, Journal of the Chemical Society, 73, 509. 1898. 966 Proceedings of Royal Society of Edinburgh. [sess. different experimenters are considered, these varying for the same concentration by as much as twenty per cent. It will thus be seen that molecular weight determinations by the boiling point method have been set on a much more satis- factory basis, and at the same time one giving better results. It is claimed, therefore, for the method adopted — namely, the deter- mination of elevation per gramme equivalent by adding salt to a solution rather than to the solvent — that it gives to boiling point work on aqueous solutions greatly increased accuracy, whether we view it from the standpoint of values obtained for C, or from that of molecular weight determinations. It may also he noted that as the manner in which the ionization coefficients were obtained and the formula used in calculating values of C were based, each on the dissociation theory, conse- quently the theory has been put to a somewhat severe test ; and as the results agree so fully with theory, it has been entirely favourable. The research was carried out at the Physical Laboratory of the Edinburgh University, and is to be continued. ( Issued separately November 4, 1905. 1904-5.] Flora of Scottish Lakes. 967 A Comparative Study of the dominant Phanerogamic and Higher Cryptogamic Flora of Aquatic Habit, in Three Lake Areas of Scotland. By George West. (With Fifty-five Plates.) SCOTTISH LAKE SUBYEY. Under the direction of Sir John Murray, K.C.B., F.R.S., D.Sc., LL.D., etc., and Laurence Pullar, F.R.S.E. (Read June 19, 1905.) Introduction. In this contribution an account is given of the dominant plants of aquatic and semi-aquatic habit existing in and about the lakes of the following districts of Scotland : — 1. The Loch Hess area. 2. The lakes in the Island of Lismore, Argyll. 3. Lakes situated between Nairn and the Culbin Sand Hills. 1. The Loch Ness Area. — The most casual observer, in passing through the Caledonian Canal, must have noticed the yellow-brown appearance of the water, which is due to the water supply from the mountains having to percolate enormous quantities of peat before reaching the lower level. It is the presence of this peat extract in the water that is the dominating factor governing the aquatic flora of this area ; it makes the water untenable to a large number of plants, and restricts also the zone of plant-life, by rendering the water so dark that plants are unable to carry on their functions beyond a very limited depth owdng to want of light. When looking over the side of a boat in Lochs Oich and Ness, one is not able to see the bottom beyond a depth of seven or eight feet. The paucity of vegetation in peaty water is evident to the most casual observer. The prevailing and frequent strong winds are westerly ; consequently there is upon the eastern shore of a lake a very considerable and sustained wave action. Acting upon a rocky or stony shore, this erosive power entirely prevents 968 Proceedings of Royal Society of Edinburgh. [sess. the growth of the higher plants in the shallow water, where its influence is felt. Unless sheltered by adjacent hills, all the lakes will he almost or quite devoid of vegetation on their eastern shores ; whilst the western shores and hays, sheltered from the prevailing wind, will have an abundance of vegetation (figs. 47, 48). We do find, however, even in exposed parts of the lakes, large rocks often covered with mosses, hepatics, algae, etc. By reason of the pre- serving action of humic acids, the organic remains about the lakes do not readily decay, but undergo a slow process of dis- integration and form a sort of liquid peat. Owing to this action, suitably situated shallow places about peaty lakes become reclaimed by the growth of plants quicker than in waters free of humic acids. 2. The Lismore Area. — Here we find conditions absolutely different from those existing in the Loch Hess area. There is no moorland peat formation at Lismore that can possibly drain into the lakes. The geological formation throughout the island is limestone. The land is almost entirely in a more or less culti- vated state, and supports a large number of sheep and cattle. Instead of humic acids an appreciable supply of ammonia salts will therefore find access to the lakes. The three lakes on Lismore are hut slightly elevated above sea level, and are sheltered from wind by adjacent low hills (figs. 108, 109). A marked difference from the Hess area is, that the waters of the lakes are heavily charged with calcium carbonate. In contra- distinction to the lakes of the Hess area, the water of these lakes is pellucid. It is so clear that one may look over the side of a boat and see the bottom through twenty-five feet of water. In consequence of this clearness, the photic zone of vegetation is much less restricted than in the Hess area. The rocks and stones are covered with an incrustation of lime which gives them a peculiar sponge-like appearance (fig. 1). The rounded, water- worn, and polished stones found on the shores of the Hess district are not to he seen at Lismore (fig. 2). The lakes being sheltered from the wind by hills, their shores are not subjected to frequent and powerful erosion by the waves ; they are consequently more or less surrounded with a littoral vegetation. Many of the plants in these lakes are heavily coated with an incrustation of calcium 1904-5.] Flora of Scottish Lakes. 969' carbonate, a phenomenon unknown in the Ness area (fig. 3, p. 1021). As may he inferred from the foregoing remarks, the flora of the Lismore lakes differs considerably from that of the lakes in the Loch Ness area. 3. The Lakes near Nairn. — These differ in many respects from those of the two areas already described. The lakes in the two foregoing areas mostly owe their existence to the action of glaciers, are frequently situated in deep valleys overshadowed by hills, or in excavations upon the mountains themselves, rock and precipice being a characteristic feature of their rugged and frequently tree- less shores, while considerable and often great depth is a marked feature. Here, however, we have extensive sheets of water existing in mere depressions among former sand-hills of the sea- shore. Their shores are flat, muddy, and, but for the artificial forest about them, featureless (fig. 103). Where vegetation is abundant the mud is deep, and evil-smelling when disturbed. In the two former areas described a continuous flat and muddy shore has not occurred, neither has the mud often been of the stinking kind. In the deeper lakes of the two former areas a large portion of the bottom is destitute of flora. The scattered organic detritus is therefore much less than in these shallow lakes which have abundant vegetation all over the bottom. The refuse-eating fauna, existing at the bottom, are consequently, in the former case, able to maintain an equilibrium between supply and demand ; and the lake bottom consists essentially of the non-fetid excrement of these creatures. Here, however, we have lakes whose floor is wholly carpeted with vegetation, and the supply of organic detritus is greatly in excess of the demand of any refuse-eating organisms that may exist, and therefore fetid mud results from the processes of unhindered decomposition. In these lakes we find but little evidence of lime, and little or no acid peat extract. The water is somewhat stagnant, and, from the considerable amount of decomposing organic matter, it presents a turbid and unwholesome appearance. In these respects this district again differs from those of the two former areas considered. In conse- quence of the depressed situation, and with surrounding forest, these lakes are much sheltered from wind. Although in close proximity to the sea, the water is not brackish. A certain 970 Proceedings of Royal Society of Edinburgh. [sess. restricted flora occurs here that is not found in the other areas under consideration. We are not at present able to give a comparative analysis of several of the lakes under investigation. It may, however, be interesting to give that of Loch Baile a Ghobhainn at Lismore, by W. E. Tetlow, along with that of Lake Geneva as published by Forel. One litre (or one million parts) contains (parts or) milligrams : — Lake Geneva. Loch Baile a Ghobhainn. Sodium and potassium chlorides 1*8 3*725 Sodium sulphate ..... 15-0 Sulphuric acid trace Ammonium sulphate .... trace ... Ammonia ...... trace Calcium sulphate ..... 47*9 Basic calcium phosphate 0-094 Calcium nitrate i’-o Nitric acid ...... trace Calcium carbonate 73*9 151-161 Silica ....... 3*7 2-635 Lithium ....... trace Alumina and ferric oxide 1-9 Iron carbonate ..... 1-158 Magnesium carbonate .... 1-414 Organic matter and loss .... 11*9 30-913 Total solids ..... 157 parts in 191 parts in one million. one million. I. The Plants. Regarding the purely aquatic vegetation no ambiguity can exist as to what constitutes an aquatic plant. With the semi-aquatic plants, however, there is considerable scope for personal equation on the part of the observer. In the following pages the application of semi-aquatic has been restricted to plants that one habitually finds preferring decidedly wet places, with leaves and flowers elevated in the air. Attention must be called to the fact that no search has been instituted for the so-called rare plants. The object in view is rather to present before the reader the dominant plants of the districts investigated. 1904-5.] Flora of Scottish Lakes. 971 LIST OF THE PLANTS. In a future contribution I hope to deal especially with the internal and external morphology of the plants here enumerated ; such matters are therefore excluded from the present pages. The occurrence of the plants in each of the three areas under discussion is indicated by the numerals after the authority, viz. : — I. The Ness area. II. Island of Lismore. III. Lochs at Nairn. ranunculaceh:. Ranunculus hederaceus, L. I. Very scarce. Ranunculus Flammula, L. Normal forms. I., II., III. Abundant everywhere below 1000 feet. Ranunculus scoticus , Marsh. I. Abundant about the shores of lochs over 1000 feet above sea. This is merely a depauperated form of R. Flammula, L. From the non- flowering specimens, 3 inches or less in height at great elevations, every stage to the normal lowland forms may be obtained as one proceeds towards sea level. Ranunculus circinatus, Sibth. II. Very scarce. Caltha palustris, L. I., II., III. Abundant in lowland situations. Caltha palustris, var. minor , Syme. I. The remarks to R. scoticus , Marsh., apply equally well to this depauperated form of C. palustris. nymphhiaceh:. Castalia speciosa, Salisb. I., II. Abundant in places where the water is less peaty. Castalia speciosa, Salisb ., var. minor, DC. I. In peaty hill lochs, often growing on mud. An intermediate form also occurs in peaty lochs at less elevation; the leaves are smaller than the type and purplish, lobes more divergent and acute, reticulations below more prominent. These variations from the normal are probably due to environ- ment. 972 Proceedings of Royal Society of .Edinburgh. [sess. Nymphsea lutea, L. II. Fairly abundant outside the belt of C. speciosa. Nymphsea pumila, Hoffm. I. Lowland ; distribution re- stricted. CRUCIFERAE. Radicula officinalis, Groves. II., III. Hot common. Cardamine pratensis, L. I., II., III. Universal about the shores of lakes, even the highest hill lochans. CARYOPHYLLACEiE. Silene maritima, With. I. Abundant about the shores of L. Ness. Stellaria uliginosa, Murr. I., II., III. Marshy places about lochs ; not common. ROSACEiE. Spiraea Ulmaria, L. I., II., III. Universal in wet places- about lakes chiefly lowland. Comarum palustre, L. I., II., III. Remarks as above plant. LYTHRACEiE. Peplis Portula, L. I. Aquatic and terrestrial forms about the shores of lowland lakes. Lythrum Salicaria, L. II. I have only observed this remark- able plant on the shore of Loch Fiart. ONAGRACEiE. Epilobium angustifolium, L. I. General but not common. Epilobium palustre, L. II. Fairly abundant. Epilobium hirsutum, L. I. Distribution restricted. HALORAGACE^E. Hippuris vulgaris, L. II. Very abundant. I. Only seen at L. Dunmaglass, the water of which, owing to the position of the loch, is not, or but slightly, peaty. III. Scarce. Myriophyllum alterniflorum, DC. I. Abundant in almost every loch. III. Less abundant. Myriophyllum spicatum, L. II. Abundant. 973 1904-5.] Flora of Scottish Lakes. CALLITRICHACE^E. Callitriche stagnalis, Scop. I., III. Aquatic and terrestrial forms ; scarce ; not seen in very peaty water. Callitriche hamulata, Kiltz. III. Scarce. I. Extremely abundant in almost every loch ; a dominant plant. Never seen here with a rosette of spathulate floating leaves ; all the leaves are linear and emarginate. Mr A. Bennett of Croydon has written me respecting this species as follows : — “It is unusual for this species to occur over wide areas without floating rosettes ; but it does occur so, without them, here in the south, and then when in the water it looks somewhat like C. autumnalis, L., on a small scale, but the fruit is very different. I have specimens before me that are quite like your plant from 1 Scalloway, Shetlands, 1890. R. M. Barrington.’” PORTULACEiE. Montia fontana, L. Aquatic form, syn. M. rivularis , Gmel. I. II. Scarce ; not observed in very peaty water. SAXIERAGACEiE. Parnassia palustris, L. I. Scarce. II. Abundant. ITMBELLIEERiE. Hydrocotyle vulgaris, L. I., III. Abundant about the shores of lochs. II. Scarce. Apium inundatum, Reichb. I. Distribution restricted, but abundant in a few of the less peaty lochs. (Enanthe crocata, L. I. Very abundant about the shores of Urquhart Bay, L. Ness. RUBIACE^E. Galium palustre, L. I. In marshy places on the shores of lakes; scarce. COMPOSITE. Eupatorium cannabinum, L. II. Only observed in this district. 974 Proceedings of Royal Society of Edinburgh. Senecio aquaticus, Hill. I., II. Universal about the shores of lowland lakes. CAMPANULACEiE. Lobelia Dortmanna, L. I. Abundant in almost every loch. III. Scarce. GENTIAN ACEiE. Menyanthes trifoliata, L. I., II., III. Very abundant every- where. BOR AGIN ACEAE. Myosotis palustris, With. I. Scarce, limited to a few small lowland ponds beyond the influence of peat. II. Abundant. III. Scarce. SCROPHULARIACEiE. Yeronica Beccabunga, L. I. A small depauperated form creeping upon sand in Urquhart Bay ; only record. Yeronica Anagallis, L. II. Not abundant. Scrophularia aquatica, L. I. About the shores of L. Ness. Pedicularis palustris, L. I., II., III. Universal about the shores of lakes. LABIATiE. Scutellaria galericulata, L. I. Abundant about the shores of L. Ness and a few other places. Mentha arvensis, A., var. prsecox, Sole. III. Abundant. Mentha arvensis, var. agrestis, Sole. I. Shores of the less peaty lakes ; not common. Mentha sativa, L. II., III. Abundant. Mentha sativa, var. rubra, Huds. I. Shores of the less peaty lakes ; not common. LENTIBULARIACEiE. Utricularia vulgaris, L. I., II., III. Generally distributed. Utricularia intermedia, Hayne. I. Common in the hill lochs. Flora of Scottish Lakes. 975 1904-5.] PRIMULACEiE. Lysimachia nemorum, L. I. About the shores of the less peaty lowland lochs ; not common. Lysimachia Nummularia, L. I. As above. Lysimachia vulgaris, L. I. Only observed at a small loch near Aldourie. Samolus Yalerandi, L. II. Only observed at L. Kilcheran. PLANTAGINACEiE. Littorella lacustris, L. I., II., III. Abundant everywhere. POLYGONACEiE. Polygonum amphibium, L. I. Restricted to the less peaty lakes. II. Aquatic and terrestrial forms abundant. Polygonum Hydropiper, L. I. Only observed about the shores of Urquhart Bay, L. Ness. AMENTIFERiE. Alnus glutinosa, Gxrt. I. Abundant. II., III. Less so. Salix aurita, L. I. Abundant. II., III. Less so. Betula glutinosa, Fries. I. Abundant. II., III. Less so. The above three species are the most dominant trees or shrubs in the wet places about the shores of lakes, especially in Area I. Many other genera and species occur, but mostly on drier ground. IRIDACEiE. Iris Pseud-acorus, L. I., II., III. Generally distributed. ALISMACEiE. Alisma Plantago, L. I. Only observed at Urquhart Bay,. L. Ness. II. L. Fiart ; not abundant. Alisma Plantago, Z., app. var. lanceolata, With. II. L. Fiart; not abundant. A weak form induced by the overshadowing of adjacent plants. Alisma ranunculoides, L. III. Abundant. '976 Proceedings of Royal Society of Edinburgh. [sess. JUNCAGINACEJE. Triglochin palustre, L. I., II. Generally but sparsely dis- tributed about the shores of lochs. MELANTHACE^E. Tofieldia palustris, Huds. I. About shores in peaty places ; not common. Narthecium ossifragum, Huds. I. About shores in peaty places ; abundant. JUNCACE^E. .Juncus effusus, L. I., II., III. Abundant everywhere. Juncus conglomeratus, L. I., III. On drier ground than J. effusus and much less abundant. •Juncus bufonius, L. I. Abundant about some of the low- land lochs. •Juncus articulatus, L., including J. lamprocarpus, Elirh. I. II., III. One or another of its protean forms; abundant nearly everywhere ; a very curious form with flowers and nodes viviparous abounds by a small loch near Aldourie. Juncus supinus, Mcench. I. This is one of the most protean species imaginable ; its various forms almost defy diagnosis. The normal type is of terrestrial habit, and is found spar- ingly about the shores of lakes. Opposed to this is a submerged aquatic plant, with tresses of numerous long hair-like leaves, without flowTers ; one might therefore easily be puzzled as to their identification. By careful search, however, a whole chain of intermediate forms may be found. The clue to the submerged hair-like leaved forms (t Juncus Jluitans , Lam.) is found in shallow places with but a few inches of water. Here we find forms bearing •degraded and abortive flowers, with the leaves of the sub- merged plant. In drier places we find intermediate forms again ; often with degraded flowers, and frequently vivipar- ous at nodes and inflorescence. The terrestrial forms may resemble J. bufonius or certain varieties of J. articulatus. These terrestrial forms are usually erect, about 6 inches 1904-5.] Flora of Scottish Lakes. 977 high, leaves with very obscure septa and slightly channelled, flowering, not often viviparous ; such represent J. supinus, Moench. Another form, more csespitose and dwarfed, with finer leaves, in wetter situations, flowering, not often vivi- parous, may he regarded as var. uliginosus. Then we have a prostrate form resembling supinus in size hut with finer leaves, inflorescences more abundant, and in whorls, often viviparous ; this may be taken as var. subverticillatus. Then we have the half - submerged forms with abortive flowers and hair-like leaves from which we recognise the submerged form with tresses of hair-like leaves, and non- flowering ; var. fluitans. This latter form is extremely abundant in nearly all the waters of Area I., from the highest mountain loch to L. Ness. The other varieties are all scarce. These forms are of extreme interest; in them we seem to be able to trace the phylogenesis of an extremely abundant and dominant aquatic plant : from plastic terrestrial and sub-aquatic forms ; not now dominant nor abundant in this district. TYPHACEiE. Typha latifolia, L. III. Only observed at Lochs Loy and Cran. Sparganium ramosum, Huds. I. Scarce. III. Abundant. Sparganium ramosum, Huds., var. neglectum, Beeby. II. Not abundant. Sparganium natans, L., app. S. simplex, Huds. I. About lowland lochs ; not abundant. Sparganium natans, L. I. General, chiefly lowland lochs. Sparganium minimum, Fries , very small terrestrial form on mud. I. Hill lochs; scarce; aquatic forms abound in the water near these. Sparganium minimum, Fries. I. Abundant in all waters, even in the highest mountain lochs. Often not flowering, in which state its floating leaves may easily be mistaken at a distance for those of aquatic forms of Glyceria fluitans, R. Br. The remarks to Juncus supinus apply similarly to Sparganium. I am of the opinion that S. minimum PKOC. ROY. SOC. EDIN. — VOL. XXV. 62 978 Proceedings of Royal Society of Edinburgh. [sess. and natans are aquatic forms of S. simplex, Huds. Plastic forms of simplex are seen in var. longissimus, Fries., from which a course to minimum is quite open. The terrestrial forms of minimum mentioned above seem indicative of a reversion towards a terrestrial ancestor. POTAMOGETONACEiE. Potamogeton natans, L. I., II., III., Abundant everywhere. Potamogeton natans, L. I. Dwarf terrestrial forms about the shores of lochs ; not common. Potamogeton natans, L., app. polygonifolius, Pourr. I. A curious dwarf plant about 4 in. long, with the leaves of polygonifolius. From a cold spring at the margin of a small loch in Ealmacaan Forest, elevation 1600 ft. The temperature of the water of this spring was 51*8° F. At 12 ft. distant the temperature of the water was 57*2° F. At the other side of the loch the temperature of the water was 64'2° F. Air temperature, 54'8° F. There were numbers of the normal P. natans about the loch ; but none of this depauperated form beyond the cold spring. This plant has probably been depauperated from normal forms by its habitat ; the specimens were fruiting. Potamogeton natans, L ., app. polygonifolius, Pourr. I. Large forms universal in peaty lochs. Potamogeton polygonifolius, Pourr. I. In less peaty water • not abundant. P. natans and polygonifolius, with the various intermediate forms, are probably deviations from or towards the typical natans. The recent remarks on other variable plants may be applied to these. Potamogeton heterophyllus, Schreb. III. Extremely abundant in L. Cran. Potamogeton lucens, L. I., II. Abundant, and universally distributed. I have seen very large specimens of this plant in Lochan a Chait, below Ben Lawers. Potamogeton prselongus, Wulf. I. In less peaty lochs distribution very restricted. Potamogeton crispus, L. I. Distribution restricted. Potamogeton perfoliatus, L. I. Only observed an attenuated 1904-5.] Flora of Scottish Lakes. 979 form in L. Ashie. II. Extremely abundant in deep water. I have seen these at Lismore growing in 24 ft. of water and yet producing their flowmrs above the surface. Potamogeton pusillus, L. I. Only observed in two lakes. II. Abundant. Potamogeton pusillus, var. tenuissimus, M. fy K. I. Only observed at L. Meiklie in 8-10 ft. of water. II. In water about 12 ft. deep. Merely a deep water form. Potamogeton filiformis, Pers. II. In shallow water. I have not observed P. densus, L., nor P. pectinatus, L., in these districts. It may interest Edinburgh botanists to know that P. pectinatus, L., produces abundantly its hiber- nating shoots in Duddingston Loch. CYPERACEiE. Heleocharis palustris, Br. I., II., III. Abundant everywhere. 1 found an interesting form on a sand-bank, on the shore of L. Ness. In order that it might not be buried too deeply by the growing sand-bank, the rhizome had discarded the diageotropic habit and assumed negative geotropism. Scirpus lacustris, L. I., II., III. Generally distributed and abundant in lowland lakes under 1000 ft. elevation. I have seen the stems of these 14 ft. long — 6 ft. above the surface of water, 8 ft. deep. When cut off near the rhizome such large specimens shoot up out of the water 3 or 4 ft., owing to the air contained in the intercellulars. The long linear grass-like leaves I have only seen in water 3-8 ft. deep. Eriophorum vaginatum, L. I. Abundant about the peaty shores of hill lochs. Eriophorum polystachion, L. I. Abundant about the peaty shores of lochs, chiefly lowland, but also quite common about mountain lochs. II. Small specimens. Carex dioica, L. I. Shores of mountain lochs ; not common. Carex elata, All. I. A carpeting form with diageotropic rhizomes in wet places, and a csespitose form with negative geotropic rhizomes forming tussocks in water 2 or 3 ft. deep. Inchnacardoch Bay, L. Ness. 980 Proceedings of Royal Society of Edinburgh. [sess. Carex aquatilis, Wahl. I. In various forms, excluding the tall variety ; this is one of the most widely distributed and dominant plants. It covers considerable tracts of bog and shallow water at the peaty margin of lakes, most frequently on the shore side, behind C. rostrata, Stokes, which is a deeper water species. II. Less abundant. Carex flacca, Schreb. II. Fairly abundant on the shores. Carex flacca, Schrcb ., var. stictocarpa, Sm. III. Shore of L. Cran. Carex flava, L., var. argillacea, Town. III. Shore of L. Cran. Carex flava, L., var. minor, Town. I. Shores of mountain lochs. Carex flava, L., var. lepidocarpa, Tausch. I. Sandy shores of lowland lochs. Carex binervis, Sm. I. Peaty places about the shores of hill lochs. Carex filiformis, L. I. Abundant about the shores of peaty lochs, on the mountains between Glen Moriston and Glen Urquhart. Carex rostrata, Stokes. 1., II., III. Beyond doubt the most widely distributed and dominant plant in Areas I. and III. It occurs in water up to 18 ins. deep, always in advance of C. aquatilis, where the two are found together, which is very usual. By its large and rapid growth, a considerable amount of detritus is thrown down annually ; it is therefore a most important plant in converting shallow lochs and shallow places about large lakes into terra firma. The largest specimens I have seen were at exposed lochs 2300 ft. above sea. Carex vesicaria, L. I. Similar in habit to C. rostrata, but requiring less water, and not so robust. Not nearly so common or abundant as rostrata. GRAMINEiE. Phalaris arundinacea, L. I. Abundant about L. Ness, especially so on Cherry Island ; scarce elsewhere. Phragmites communis, Trin. I., II., III. Generally distri- 1904-5.] Flora of Scottish Lakes. 981 buted and abundant, usually under 6 ft. high, and seldom covering very large areas except at Lismore. Deschampsia csespitosa, Beauv. I. Generally distributed, mostly about lowland lochs. Glyceria fluitans, Br. I. Aquatic and terrestrial forms abound everywhere in this area. II., III. Scarce. EQUISETACE^E. Equisetum limosum, L. I., II., III. Abundant everywhere in I. and III., often covering large areas. It prefers deeper water than Carex rostrata ; sometimes even in water 5 ft. deep. When the two are growing in the same locality, which is very usual, the colonies are always distinct from one another, with Equisetum in advance. LY COPODIACEiE. Isoetes lacustris, L. I. Abundant everywhere in peaty water, forming a bottom carpet from about 2 to 1 6 ft. deep. In some lochs they are about 4 or 5 ins. high, with stout, erect leaves, forming stiff little plants. In other places, apparently under similar conditions, the leaves are 18 ins. long, weak and recurved. CHARACEiE. Messrs H. and J. Groves most kindly gave me the benefit of their unrivalled knowledge of this difficult order. Nitella opaca, Ag. I. Generally distributed in peaty lochs ; it occurs at a greater depth in these lakes than any other plant, save Fontinalis antipyretica. Nitella opaca, Ag ., slender forms, app. var. attenuata, H. fy J. G. I. In L. Ness and other lochs. Nitella translucens, Ag. I. Only observed at L. Meiklie in 8-10 ft. of water. Chara aspera, Willd., not incrusted with lime. III. Carpets the entire bottom of L. Cran ; also in L. Loy, etc. Chara aspera, Willd ., app. var. desmacantha, H. fy J. G.y incrusted with lime. II. Carpeting the bottom of the lakes from 2-20 ft. deep. 982 Proceedings of Royal Society of Edinburgh. [se'ss. Chara aspera, Willd ., var. desmacantha, H. fy J. G ., incrusted with lime. II. Carpeting the bottom of the lakes from 2-20 ft. deep. Chara fragilis, Desv., app. var. barbata, Gant., not incrusted. I. Lochs in Balmacaan Forest. Chara fragilis, Desv., var. delicatula, Braun., app. barbata, not incrusted. I. In L. Tarff. Chara fragilis, Desv., app. var. delicatula, Braun., not incrusted. I. Abundant in L. Uanagan at 6-20 ft. deep. Chara fragilis, Desv., var. delicatula, Braun., not incrusted. I. In L. Uanagan margin to 10 ft. deep, and universally distributed throughout the whole area. Chara fragilis, Desv., var. delicatula, Braun., incrusted with lime. II. Carpets the bottom of the lakes from 10-20 ft. deep. Chara hispida, L., var. rudis, Braun., incrusted with lime. II. A large coarse plant abundant at a depth of 25-35 ft. SPHAGNACEiE. Sphagnum cymbifolium, Ehrh. I. Very general about the margins of small lochs ; abundant. Sphagnum acutifolium, Ehrh. I. As above ; abundant. Sphagnum subsecundum, Nees, var. viride, Bout. I. As above ; scarce. Sphagnum cuspidatum, Ehrh., var. plumosum, Nees ty Hornsch. I. As above; scarce. No doubt many other species of this difficult genus might be observed about the lochs by giving them particular attention; they are of course abundant on the moors and mountains. DICRANACEiE. Blindia acuta, B. S. I. Submerged rocks about the shores of lochs ; frequent. FISSIDENTACEiE. Fissidens adiantoides, Hedio. I. Wet rocks about the shores of lochs ; frequent. Flora of Scottish Lakes. 983 1904-5.] GRIMMIACE^. Rhacomitrium aciculare, Brid. I. Wet rocks about the shores of lochs, especially near burns ; not common. BARTRAMIACEAE. Philonotis fontana, Brid. I. In shallow places about mountain lochs ; scarce. FONTINALACEiE. Fontinalis antipyretica, L. I. Very abundant everywhere from half-submerged rocks to a depth of 30 ft. II. Less abundant in shallow water, but an attenuated form is very abundant in deep water, even to 40 ft. deep. HYPNACE^E. Brachythecium rivulare, B. ty S. I. On rocks about shores, especially about the estuary of burns ; abundant. Eurhynchium rusciforme, Milde. I. As above. Hypnum uncinatum, Hedw. I. Wet rocks about the shores of lakes N. of Invermoriston ; not frequent. Hypnum fluitans, L. I. Shallow places about small lowland lochs ; not common. Hypnum falcatum, Brid. I. Shallow places on stones, etc., in lochs N. of Glen Urquhart ; scarce. Hypnum ochraceum, Turn. I. About the shore of mountain lochs ; not abundant. Hypnum scorpioides, L. II. Very large specimens of this fine moss very abundant about the rhizomes of Scirpus lacustris, 3-5 ft. deep. I have only observed it at Lismore. “ Hypnum scorpioides, L., forma ad var. miquelonense, Ren. Card ., proxime accedens.” “ An interesting and unusual form, differing from the type form in the pale, golden-brown colour, more delicate texture, and especially in the leaves gradually tapering to a fine acuminate point, the latter character being the most important distinguishing character of the var. miquelonense, Ren. & Card. I thought the Loch Ruthven plant might, in spite of the colour, be referable there, and accordingly I 984 Proceedings of Royal Society of Edinburgh. [sess. submitted a specimen to Mons Cardot, who wrote : ‘ La forme de l’Hypnum scorpioides . . . est en effet bien voisine de la var. miquelonense.’ Mons Cardot kindly- sent me a small specimen of the variety {leg. Delamare) which scarcely differs except in the dark purple-blackish colour, the more rigid texture, and the slightly more tapering and enrolled points to the leaves. The Loch Ruthven plant must therefore be considered to approach the variety miquelonense very closely.” (Signed) “ H. N. Dixon.” I. L. Ruthven, L. Ness, and L. Uanagan, in water 5-10 ft. deep. Mr H. N. Dixon has kindly furnished the above note for this variety, new to Britain. Hypnum stramineum, Dicks. I. Shallow places about lochs in Portclair Forest ; abundant in places. Hypnum trifarium, W. fy M. I. As above. Hypnum cuspidatum, L. I. Wet places about shores of lochs ; not common. SCAPANIOIDEiE. Scapania undulata, L. I. Very abundant on rocks about the shores of lochs. EPIGONIANTHEiE. Nardia emarginata, Ehrh. I. Forms of this plant are abundant in shallow places about lochs. Nardia compressa, Hook. I. Abundant on rocks, etc., of the mountain lochs especially. ALGiE. A few dominant species that were noticed. Batrachospermum moniliforme, Rotli. I. Very general. Enteromorpha intestinalis, L. III. Only seen here. Spirogyra crassa, Kutz. III. Only noticed in abundance here. Cladophora fracta, Dillw. II. Very abundant in places. CEdogonium capillare, L. III. Abundant. Conferva fontinalis, Berk. I. Very abundant in Inchna- cardoch Bay, L Ness, covering stones and other plants; very general. Zygnema Vaucherii, Ag. I., II. Covering rocks; universal. 1904- 5.] Flora of Scottish Lakes. 985 Zygogonium ericetorum, De Bary. I. Purple variety is very abundant on other vegetation in Lochan Dubh at Brin. Dickieia and similar gelatinous Diatomaceae. I. Abundant in some of the mountain lochs. Other diatoms are of course abundant everywhere. The following plants, usually associated with water-scenes in the south, have entirely escaped my observation in these areas : — Symphytum officinale, Sagittaria sagittifolia, all the Lemnacese, Elodea canadensis, Butomus umbellatus, Potamogeton densus, Typha angustifolia, Hydrocharis Morsus-Ranae, Sium angustifolium, Apium nodiflorum,. Rumex Hydrolapathum, many of the Batrachian Ranunculi,, Salix viminalis, S. fragilis, Ricciocarpus natans, Ricciella fluitans, etc. Many moorland plants not to be seen, or scarce in the south, grow here (Area I.) in great profusion. The following may be mentioned as being conspicuous by their abundance Antennaria dioica, Arctostaphylos Uva-Ursi, A. alpina, Betula nana, Cnicus heterophyllus, Cornus suecica, Cystopteris fragilis, Drosera intermedia, extremely abundant, Empetrum nigrum, Galium boreale, Trientalis europaea, etc. II. The Lakes. Loch Ness is the largest fresh-water loch in Scotland, it is 221- miles long and J of a mile to If miles broad. It is also one of the deepest of the Scottish lakes, and drains an area of nearly 700 square miles. Its surface is 52 feet above sea level. It is situated in a huge depression carved by glaciers, and mountains rise almost precipitously from its waters on either side, throughout its whole length (fig. 4). At the north-east and south-west ends, however, the land is low-lying and comparatively flat, being in fact the strath, or bottom of the valley known as the Great Caledonian Glen, that bisects the Highlands from Loch Linnhe to the Moray Firth (fig. 26). The lower slopes of the adjacent mountains are abundantly clothed with forest to the water’s edge. Here and there bold, bare crags of grey or red rock contrast beautifully or harmonise softly with the various shades of green afforded by 986 Proceedings of Royal Society of Edinburgh. [sess. the coniferous or deciduous wood. Far above, the purple heather and the sombre greens of the various grass-like formations lend a beauty to the whole, so charming that we are apt to ignore the never-ceasing antagonism urging on the mighty gladiators of nature — moorland and forest, for instance — to unrelenting mortal combat. All this grace, further embellished and emphasised by the magnificent sky effects that obtain here so frequently, gives this superb lake a high position among the gems of Scottish scenery. Abundant and beautiful as is the terrestrial flora, that of the water is extremely scanty; the cause of this paucity has already been mentioned (p. 967). One may traverse miles of the shores of this lake and find scarcely an aquatic plant, unless it be the lithophilous bryophyta or algae, that defy the erosive power of the waves (fig. 5). The only places in Loch Ness where aquatic plants are abundant are Urquhart Bay, Inchnacardoch Bay, about the south-west portion from Borlum to the railway pier, where the water is comparatively shallow with a pebbly, sandy, or muddy bottom ; also, but more scantily, about the estuaries of the rivers Moriston and Foyers, and in a few small sheltered bays here and there about the lake. Generally the shore is so steep that deep water occurs immediately. Opposite Invermoriston, for example, a depth of 652 feet occurs at 120 yards from the shore. This great depth so near the shore is of course exceptional, but it serves as an example to show the impossibility of there being an abundant bottom flora of the higher forms under such conditions. The limit of the photic zone is therefore reached, as a general rule, within a few feet of the shore. During the past summer (1904) Sir John Murray afforded the staff of the Lake Survey the exceptional opportunity of dredging the bottom of Loch Ness and the other lochs forming part of the Caledonian Canal, by aid of the fully equipped steamer Mermaid , of the Millport Marine Biological Station. The result of several days’ dredging in the deep water of Loch Ness* — 100 feet to 750 feet deep — fully corroborated the results previously and subsequently obtained by hand-dredging from a row-boat. No living, light-demanding, * The physical and zoological results, obtained by aid of the Mermaid , -will be treated by other workers. 1904-5.] Flora of Scottish Lakes. 987 plant was obtained from this deep water. This was quite in accordance with expectation, seeing that the photic zone in Loch Ness does not extend beyond a depth of 30 feet, owing to the amount of matter held in solution by the water. From even the deepest parts of the loch there was found an appreciable quantity of vegetable remains, but entirely that of the terrestrial or aquatic flora washed out from the shore ; or of aquatic forms not found living in abundance in the loch, but brought into it by rivers and burns. It was possible to identify branches, twigs, leaves, fruits, ■etc., of Scots Pine, Birch, Alder, Ash, Oak, Beech, Willow, Bog- Myrtle, Equisetum, Carex, Sphagnum, etc., all undergoing a process of disintegration by carbonisation. On 13th September, after heavy rains had caused the rivers to be in considerable flood, I found the surface of Loch Ness below Beinn a Bhacaidh covered for the distance of about a mile with the fruits of Betula glutinosa, Fries ., — distinguished from the fruit of its congener, Betula verrucosa, Fhrh., by the persistent stigmas exceeding the wings. These were probably brought into the loch by the river Tarff and the Allt Doe, and borne thence by westerly winds. This example serves to show how quantities •qf material foreign to the loch find an ultimate resting-place on its bottom. It also exhibits an interesting method of plant distribution : such prodigal scattering perhaps occurs annually. The sudden rise and fall of the water of Loch Ness must be mentioned as probably a further factor antagonistic to the well- being of plants. The records kept by the canal authorities at Fort- Augustus give the maximum of 7 feet 4 inches from the lowest in dry periods to the highest in wet weather. A rise of 2 feet within a few hours is quite a usual occurrence. At Loch Garth there is a rise and fall of 22 feet, caused by artificial agency ; its effect upon vegetation is there very evident (p. 1015). The following extracts from my field note-book will afford evidence regarding the photic zone of Loch Ness : — “Dredged the bottom from the point beyond the railway pier south of Cherry Island to the estuary of the river Oich in from 30 feet to 50 feet of water. A great number of hauls were taken, but I obtained not a single evidence of any living plant being at the bottom.” 988 Proceedings of Royal Society of Edinburgh. [sess.. “Dredged the bottom of Loch ]STess for about 2 miles along the shore off Portclair Forest. In 30 feet to 60 feet of water no plants whatever were obtained : the bottom in many places consists of a stiff yellow clay, probably the same that is exposed at sections along the roadside from Fort- Augustus to Invermoriston. In sheltered bays Myriophyllum alterniflorum, DC ., occurs in water 10 feet and even to 15 feet deep, often with an interrupted bottom carpet of Littorella lacustris, L., and Isoetes lacustris, L. In 20 feet to 30 feet of water Nitella opaca, Ag ., is fairly abundant,, and usually covered with diatoms.” “Dredged about Cherry Island; at a depth of 15 feet to 20 feet- dense masses of Nitella opaca, A g., were obtained with Myrio- phyllum alterniflorum, DC. At 400 yards west of the island, Isoetes lacustris, L., forms a dense bottom carpet at a depth of 14 feet to 16 feet. In water 35 feet to 50 feet outside Cherry Island, east and west, for some distance the bottom is of stiff yellow clay. No plants whatever were obtained from these depths.” “Dredged about the south-west end of Loch Ness from St Benedict’s Abbey towards Borlum and Glen Doe pier. Littorella lacustris, L., and Isoetes lacustris, L., sparingly in patches. Myrio- phyllum alterniflorum, DC., and Nitella opaca, Ag., fairly abundant in places from 5 feet to 12 feet deep ; beyond this depth N. opaca and Fontinalis antipyretica, L., only ; form scattered growth to 30 feet and an occasional plant in even deeper water. Beyond 40 feet no plants were obtained. The bottom here is mostly gravel down to 30 feet or 40 feet; in deeper water mud obtains. This seems to imply the action of the waves being sufficient at that depth to prevent a mud deposit. The Nitella here were heavily invested with diatoms, filamentous algge were scarce, young plants of Batrachospermum moniliforme, Roth., were common on some of the Nitella, but no large specimens were procured from the deep water, although they are abundant and grow to a full sixe in shallow water at the estuary of the river Tarff.” “ At Urquhart Bay abundant and varied vegetation was obtained to a depth of 15 feet ; exceeding this depth, Nitella opaca occurs to 30 feet. No plants were found in deeper water. The bottom is firm and sandy to 20 feet or 25 feet ; beyond this depth mud occurs. 1904-5.] Flora of Scottish Lakes. 989 This apparently denotes wave action at this depth sufficient to prevent a mud deposit. From the sheltered position of Urquhart Bay one might expect the disturbing power of the waves to be felt at a less depth than at Borlum. The dredging results give the difference between the two batfs of about 10 feet. I have, however, made no close investigation into this subject, but merely record an observation that occurred during botanical work.” Enough has been said to show that the photic zone in Loch Ness does not exceed a depth of 30 feet, and that from about 15 feet to the photic limit the only dominant plant is Nitella ■opaca, Ag ., and occasionally Fontinalis antipyretica, L. Perhaps the most favourable way of representing to the reader a sketch of the features presented by the flora of the littoral, and of such shallow water as may exist at Loch Ness, will be in the form of an imaginary tour round the loch. Starting from Borlum at the east corner of the south-west end, we proceed towards Fort- Augustus, thence along the north-west .shore to Lochend, returning to Borlum by the south-east shore. A general view of the loch from our starting-point is presented by fig. 4. The shore from here to the embouchure of the Tarff consists of gravel and sand, forming a large high beach (fig. 5). As already explained, no semi-aquatic plants can exist here. The aquatic flora extends from about 5 feet to 30 feet deep, as described on p. 988. On the crest and rear of this high beach is a con- siderable flora, tending, in accordance with the cecological con- ditions, from xerophilous plants in the more elevated parts (fig. 6) to hygrophilous vegetation at a lower level (fig. 7). Galium boreale grows in great luxuriance on this beach and presents a most pleasing feature when in flower. Potentilla anserina and Silene maritima are also abundant. Behind the beach is an extensive marsh containing the usual plants of such an environment common to the district (figs. 7, 8). The vegetation here is composed chiefly -of the following : — Alnus glutinosa, Spiraea Ulmaria, Deschampsia •caespitosa, Comarum palustre, Caltha palustris, Ranunculus Flammula, Myosotis palustris, Equisetum limosum, Heleocharis palustris, Carex rostrata, C. aquatilis, Stellaria uliginosa, Meny- •anthes trifoliata, Glyceria fluitans, and Potamogeton natans. At the estuary of the river Tarff is an island, a mere gravel bank 990 Proceedings of Royal Society of Edinburgh. [sess.. consisting of stones, sand, and other detrital matter brought down by the river. Although this little spot is swept by every considerable flood, yet it has a great variety of plants, some of which are alpines, brought down by the river. Fig. 9 illustrates this apparently barren spot, which, however, contains sixty-two species of flowering plants, as follows : — Ranunculus Flammula, R. acris, R. repens, Trollius europseus, Yiola palustris, Cardamine palustris, Sagina procumbens, Cerastium vulgaris, Geranium molle, G. Robertianum, Spiraea Ulmaria, Alchemilla vulgaris, A. alpina, Rosa canina, Potentilla Tormentilla, P. anserina, Galium saxatile, G. palustre, G. horeale, Trifolium procumbens, Veronica scutellata, Brunella vulgaris, Myosotis palustris, Peplis Portula, Epilobium montanum, E. alpinum, E. tetragonum, Euphrasia officinalis, Crepis paludosa, Beilis perennis, Centaurea nigra, Senecio vulgaris,. Leontedon autumnalis, Tussilago Farfara, Plantago media, P. lanceolata, Rumex Acetosella, R. Acetosa, R. obtusifolius, Polygonum viviparum, Betula glutinosa (young), Alnus glutinosa (young), Salix. two sp. (young), Triglochin palustre, Juncus squarrosus, J. articulatus, J. bufonius, J. trifidus, J. effusus, Luzula campestris, L. sylvatica, L. multiflora, Carex rigida, C. aquatilis, C. rostrata, Eestuca ovina, Lolium perenne, Deschampsia flexuosa, Alopecurus geniculatus, Anthoxanthum odoratum, Glyceria aquatica (terrestrial form). The plants dominating this hank are of the tenacious rooting type, as Rumex, Juncus, etc. In the shallow water hereabout are quantities of Batrachospermum moniliforme attached to the stones. The Caledonian Canal entrance into Loch Ness has a luxuriant aquatic flora upon its embankments, but almost limited to Lobelia Dortmanna, Juncus fluitans, Callitriche hamulata, and Myrio- phyllum alterniflorum. From here, past the river Oich embouchure to the point beyond the railway pier, the flora is extremely scanty (p. 987). There is practically no shore; the rocks have occasional patches of Nardia emarginata or Scapania undulata, and are sometimes green with Zygnema. Rounding this point we enter Inchnacardoch Bay. The water over a considerable area here is under 20 feet deep, with a sandy or muddy bottom, bearing a luxuriant vegetation. The only island of Loch Ness is at the entrance to this bay — Cherry Island (fig. 10). The aquatic flora. 1904-5.] Flora of Scottish Lakes. 991 although extremely abundant, is restricted, as follows : — Littorella lacustris, Lobelia Dortmanna, Isoetes lacustris, Myriophyllum alterniflorum, Utricularia vulgaris, Juncus fluitans, Chara fragilis, var. Potamogeton natans, P. lucens, Callitriche hamulata, Spar- ganium natans, Glyceria aquatica, Polygonum amphibium, Nitella opaca, Fontinalis antipyretica, Menyanthes trifoliata, Equisetum limosum ; filamentous algse as Spirogyra and Conferva abound, as also do the epiphytic Diatomacese. The littoral and marsh plants, beyond those enumerated above, that also inhabit such places are : — Carex aquatilis, 0. rostrata, C. elata, C. flava, Phalaris arundinacea, Valeriana officinalis, Angelica sylvestris, Cnicus palustris, Juncus effusus, J. articulatus, Iris Pseud-acorus, Heleocharis palustris, Comarum palustre, Caltha palustris, Senecio aquaticus, Ranunculus Flammula, R. acris, Spirsea Ulmaria,, Mentha sativa, Hydrocotyle vulgaris, Eriopliorum polystachion, Deschampsia csespitosa, Viola palustris, Alnus glutinosa, Betula glutinosa, Salix aurita, etc. The shore at the extremity of the bay is flat, with sandy or peaty mud, protected from the erosive power of the waves by the projecting headlands at the entrance of the bay. The littoral vegetation consequently thrives luxuriantly (fig. 11). The tufts standing up in the water, in the foreground of fig. 11, are those of Carex elata, All. Immediately to the left, the short growth out of the water is the same species, with a creeping or carpeting habit, extending unto the shore from very shallow water. The tussocks are in water 30 inches deep. It is curious that the plant should adapt itself to these two environmental conditions. On ground that is merely wet or that has but a few inches of water, this Carex grows in a horizontal spreading mass, carpeting the ground with a tangle of rhizome and root so dense that it is scarcely possible to get the fingers through them in order to tear up a specimen. As the deeper water is approached, this carpeting habit gives way. The rhizomes discard the diageotropic growth, assume negative geotropism and a csespitose habit, forming thereby the tree-like stem of each tussock that enables them to elevate their leaves and inflorescences above the surrounding water. With some considerable labour I extracted one of these tussocks ; its weight when wet was about 70 lbs. Fig. 12 is from a photograph taken after it had dried somewhat. At the base are '992 Proceedings of Royal Society of Edinburgh. [sess. the active roots ; thence to the top of the chair -hack are the combined rhizomes, bearing above the leaves and flowers. I noticed about this bay a quantity of Sparganium natans that for several days had their flowers submerged by the raising of the water level through floods. No doubt but such accidental submersions of their inflorescences induce in aquatic plants a disuse of sexuality, as previously remarked upon. The inflowing burn at Inchnacardoch Bay is rather remarkable in that it entirely disappears into the ground during dry weather, within the space of a few yards, owing to its course at that part being through an ancient lacustrine beach, formed by Loch Ness before its water had sunk to the present level, through the gradual reduction of the level of the outflow, between Lochend and South Kessock, by ■erosion. Anent this subject, it occurred to me when at XJrquhart Bay, that the reduction of level undergone by Loch Ness since itlie building of XJrquhart Castle might be measured. This castle was built on a small rocky peninsular, or perhaps island at the ■time ; at any rate a moat was made by cutting through the neck of the peninsular. The apparent bottom of this moat is now several feet above the level of Loch Ness, notwithstanding the surface of the loch being raised 10 feet or thereby at the time of the construction of the Caledonian Canal. By careful excavation .the original bottom of the moat might be found ; allowing for a .sufficient depth of water above that bottom, we should have .approximately the level of Loch Ness at the building of the ■castle, from which, to the level of the loch, previous to its being raised by the canal construction, we should arrive at the reduction of level undergone since the building of the castle. Returning to the burn at Inchnacardoch Bay, below the point •of its disappearance, its bed is thickly covered with very large plants of Eontinalis antipyretica ; although no water can pass except in time of flood (fig. 13). I also noticed near this bay an interesting example of seed dispersal, Calluna vulgaris and other moor plants being covered with the seeds of Eriophorum poly- ■stachion, blown thence by the westerly winds from an adjacent marsh (fig. 14). At the northern side of Inchnacardoch Bay the shore is unique •as to Loch Ness. It is rather flat, is composed of boulders and 1904-5.] Flora of Scottish Lakes. 993 gravel, and covered with a vegetation exhibiting more or less xerophilous characters, Erica, Myrica, Calluna, Juniperus, Betula, and Pteris being the dominant forms, encroaching in patches over the beach from the adjacent moor (fig. 15). Leaving this bay, we meet with scarcely any aquatic flora except such as may occur in little bays (p. 986) until Invermoriston is reached. Here again there is a paucity in the variety and quantity of aquatic plants, nothing calling for special remark. The erosive power of the waves upon the shore here is shown by the washing away of the soil from the roots of trees on the littoral, as seen by fig. 16. From Invermoriston to Urquhart Bay, a distance of some 10 miles, there is absolutely nothing in the way of aquatic flora to demand attention. In Urquhart Bay, however, conditions prevail similar to those of Inchnacardoch Bay, the bottom being of firmer sand. The aquatic plants are similar, with the following excep- tions : — Polygonum amphibium more abundant, and Potamogeton polygonifolius abundant at the mouth of the river Enrick, and not found anywhere else in Loch Hess. Regarding the marsh or semi-aquatic plants, those of Inchnacardoch Bay are also repre- sented here, with the exception of Carex elata. There are also several additions for Urquhart Bay : — Mentha sativa, var. rubra ; Mentha arvensis, var. agrestis ; Sparganium ramosum, Alisma Plantago, Scrophularia aquatica, Cnicus heterophyllus, Polygonum Hydropiper, Polygonum amphibium, terrestrial form, Salix alba, and Veronica Beccabunga, a small depauperated form. These additions may no doubt be accounted for by the less peaty con- dition. At Urquhart Bay two rivers enter Loch Hess, the Enrick, draining the populous and highly cultivated Glen Urquhart, and the Coiltie, from Balmacaan Forest, which also drains a consider- able area of cultivation. The nitrogenous substances ; and lime from a district north of Glen Urquhart, brought down by these rivers, undoubtedly, to a certain extent, extinguish the action of the humic acids. Again, a considerable marsh delta has been formed here, and upon it there is a luxuriant vegetation of the woodland type ; the mild humus of this has also to be borne in mind. The water of the bay, owing to the great bulk of the loch, is probably but very little if at all reduced in peatiness; the similarity of the vegetation to other portions of the loch bear out PROC. ROY. SOC. EDIN. — YOL. XXV. 63 994 Proceedings of Royal Society of Edinburgh. [sess. this remark. The marsh about the embouchure of the rivers is more under the influences mentioned, and here the mud is of the black and fetid kind (p. 969). The accompanying photographs illustrate some of the features of the marsh vegetation here. Fig. 17 affords an idea of the sandy shore and its vegetation at the south of the bay. The two rivers enter Loch Ness through the wood seen in the middle distance. Fig. 18 shows one of the rivers passing through the wooded marsh. Owing to the dense vegetation, the light here is very weak ; under the same conditions of sky, i.e. overcast, the negative for this photograph received thirty times the exposure of that for fig. 17, viz., half a second and 15 seconds respectively. This is of course a somewhat hap-hazard method of measuring light intensity, but it agrees closely with the results obtained by J. Wiesner with special apparatus. Wiesner * found the light under a spruce- tree to be about of the intensity of that in the open. Fig. 19 presents a marsh view near the mouth of the rivers, looking out towards the bay. Fig. 20 represents a group of Alisma Plantago, a plant of rare occurrence in this area. Passing out of Urquhart Bay, there is very little more regarding aquatic flora to arrest our atten- tion in Loch Ness. At the north-east end of the loch, from Lochend to the lighthouse at the entrance to Loch Dochfour, there is a re- markably large high stony beach (fig. 21). During westerly gales, the waves, gathering strength from the whole length of the loch, break with great force upon this beach ; which resembles, but on a much smaller scale, the noted Chesil Beach in Dorsetshire. The pebbles for the photograph (fig. 2) were gathered here. At Dores Bay a similar but smaller and less stony beach may be seen. Fig. 22 affords an illustration of the shore at Inverfarigaig which is typical of this portion of the loch. In wet situations, throughout the eastern shore of Loch Ness, are large quantities of Scutellaria galericulata (fig. 23). A few aquatic plants are found in Foyers Bay, but only such as have been already mentioned as common to the loch ; neither is there any abundance of aquatic vegetation here. The bay has been formed by detrital matter brought into the loch by the river Foyers. Fig. 24 will give some idea of the extent of this delta. So great has been the * “ Photometrische Untersuchungen auf pflanzenphysiologischem Gebiete,” Erst Abh., Sitzungsberichte der Wiener Akademie , Bd. cii., Abth. I., 1893, etc. 1904-5.] Flora of Scottish Lakes. 995 amount of detritus brought down by this swift river, that the bottom of the loch opposite its delta has been silted up to the ■extent of about 200 feet in vertical height. The large works of the British Aluminium Company give employment to a considerable number of persons. The selection of this remote spot as the site for an extensive mechanical industry is due to the water of the river Foyers affording a cheap motive power for the large turbines and dynamos that generate the enormous electrical force required for the operations of the Company. The winds carry the dust of cryolite from the works over the adjacent vegetation. The coniferous trees, by reason of their evergreen leaves, are being killed by this dust, the deciduous - leaved trees remaining apparently uninjured (fig. 25). A noted landmark of Loch Ness is the “ Horse-shoe,” an enormous scree of that shape on the slope ■of Beinn a Bhacaidh, with its free ends rising from the water (fig. 10). A view taken from the middle of the loch, looking towards Fort- Augustus, is represented in fig. 26. This also shows the passage of the Great Glen between the mountains. Nearer Fort- Augustus is “ Corrie’s Cave,” formed by the falling away of a portion of the rock from the main body of the cliff, and said to have been the stronghold of an outlaw of that name. A view from this cave, looking towards Fort-Augustus (fig. 27), illustrates the steep and wooded slopes so common to Loch Ness. The nature of the shore below may be seen by fig. 28, which was photographed from Glen Doe pier. A little above the pier there is an enormous Alnus glutinosa with a bole about 17 feet in circumference ; the stem branches at about 9 feet from the ground. Growing in the fork is an ash-tree about 6 inches in diameter, sending its roots to earth by way of the hollow bole of the alder. The power of the waves to damage littoral trees is illustrated in fig. 29, in which the roots of Alnus glutinosa have been laid bare, and subsequently wounded by the rolling of the pebbles over them. Fig. 30 is a photograph of a transverse section of one of these wounded roots. Almost needless to say, no aquatic phanerogams can exist on such shores as recently described. Only in the little sheltered bays do we find a few of the common plants. The rocks, however, are frequently covered with algae and hepatics, chiefly varieties of Zygnema, Nardia, and Scapania. The 996 Proceedings of Royal Society of Edinburgh. [sess.. only other object of botanical interest about the shores is an ash- tree with an enormous base near Borlum (fig. 31). This is caused- by a rotting of the duramen ; the disease probably induced by the wet habitat. A little beyond this tree we arrive at the place whence we set out on our tour of Loch Ness. Loch Uanagan is situated in the Great Glen, about a mile south-west of Fort- Augustus ; it is about half a mile long and is 43 feet deep in its deepest part. Its shores enter the water at a gentle slope, are sandy or stony, and its water rather peaty. The inflowing burn at the south-west end has introduced a large amount of detrital matter into the loch ; a considerable area of shallow water thus formed is covered with vegetation (fig. 32). At the opposite end of the loch, although the water is shallow,, there is little vegetation, owing to the erosive power of the waves, caused by the prevailing westerly winds. The general features of the aquatic and marsh flora are similar to what is found in the shallow water and marshes of Loch Ness. Loch Uanagan differs, however, in certain respects. Here we have a colony of Scirpus lacustris growing in water 4-7 feet deep and from 2-5 feet above its surface (fig. 33). Peplis Portula occurs in wet places about the shore. There is also an abundant bottom carpet of Characese,, Chara fragilis, var. delicatula, from the margin to 10 feet deep, Chara fragilis, approaching var. delicatula, 6-20 feet deep, Nitella opaca, 10-30 feet deep. Potamogeton lucens is very abundant to 15 feet deep. Sparganium natans grows very abundantly in places (fig. 34). The photic zone extends to about the same deptli as in Loch Ness. Standing by the railway at the south-west end of the loch, one obtains an excellent example of the gradual change from aquatic to' moorland vegetation, arranged in the following order (fig. 35). Out in the loch Scirpus lacustris ; then for some distance no vege- tation rises above the surface of the water ; this space is filled with various aquatics — Littorella lacustris, Lobelia Dortmanna, Potamogeton natans, P. lucens, Myriophyllum alterniflorum, Characese, etc. Then we have a great belt of Carex rostrata advancing into the loch ; these in the drier places are mixed with Carex vesicaria, nearer the shore C. aquatilis abounds. In still drier places numerous bog plants obtain, Juncus bufonius 1*904-5.] Flora of Scottish Lakes. 997 ■being very abundant. Then Myrica Gale dominates a slightly ■drier area, followed by Erica and Calluna, intermingled with the numerous herbaceous plants common to such associations. Beyond (those enumerated, the following plants occur here : — Utricularia vulgaris, Isoetes lacustris, Fontinalis antipyretica, Hypnum scorpioides, var. app. miquelonense, Apiuni inundatum (in pools near shore), Callitriche hamulata, Juncus fluitans, Menyanthes trifoliata, Glyceria fluitans, Sparganium natans, S. minimum, Equisetum limosum, Heleocharis palustris, Comarum palustre, Eriophorum polystachion, Ranunculus Flammula, R. acris, Juncus articulatus, J. supinus, var. uliginosus, Caltha palustris, Cardamine pratensis, Hydrocotyle vulgaris (fig. 36), Pedicularis palustris, ■Senecio aquaticus, Galium palustre, Spirsea Ulmaria, Mentha arvensis, var. agrestis, M. sativa, var. rubra. I noticed Lobelia Dortmanna here growing in 5 feet of water and producing its flowers at the surface. From the north-west shore of the loch [rises a considerable hill ; this is clothed with a coniferous forest extending beyond the length of the loch and over the hill to the bank of the Caledonian Canal: the trees were planted in 1880. This wood affords an excellent example, in the way of thoughtless forestry, well exhibited on the banks of the canal. Owing to the scarcity of food in the spring, in a coniferous forest the squirrels attack the trees at from 3 to 5 feet below the apex, biting off the bark in rings; consequently the apex weakens and dies; finally it is blown off by the wind and the tree remains an unsightly ruin, practically worthless (fig. 37). Quite half the trees hereabout have been thus ringed by the squirrels. When oak, beech, etc., are planted with the conifers, food is assured to the squirrels by the fruits of these trees, and they very seldom attack the conifers. Mr Maclean, forester at Glen Garry, assured me that this matter had always been attended to on the estate under his care, and that he had very seldom observed damage to the conifers by squirrels. Rabbits are very destructive to Pyrus Aucuparia growing on the ■canal bank ; almost every tree has been more or less gnawed at the base by these animals in times of scarcity, and thus injured or billed (fig. 38). Passing along the canal from Fort- Augustus to Loch Oich, we 998 Proceedings of Royal Society of Edinburgh. [sess. encounter in places, where the canal has been made through small and shallow lochs, a very abundant aquatic flora. The submerged sides of the canal are also well clothed. All the plants, however, are those quite common to the waters of the district, and call for no special comment except at Coiltry Loch, which in parts is simply filled with five dominant plants, viz., Lobelia Dortmanna, Isoetes lacustris, Littorella lacustris, Juncus fluitans, and Callitriche hamulata. The river Oich is a rather large- stream. Fig. 39 is from a photograph taken near Coiltry; its> bank here is, covered with Juncus eflusus. Loch Oich is the highest of the lakes in the Great Glen ; it i& about 4 miles long, with shores and islands abundantly wooded. Set amongst lofty and rugged mountains, it presents a magnificent piece of highland scenery (fig. 40). The aquatic flora is similar to- Loch Ness. Over a great area of this loch the water is shallow, the bottom being well within the photic zone, and aquatic vegetation fairly abundant, but of restricted variety. The water is peaty, very similar to that of Loch Ness. Littorella lacustris. Lobelia Dortmanna, and Isoetes lacustris are extremely abundant and form a dense bottom carpet; Juncus fluitans, Callitriche hamulata, Myriophyllum alterniflorum, Fontinalis antipyretica, Glyceria fluitans, Utricularia vulgaris, Carex rostrata, C. aquatilis, all very abundant and dominant ; Equisetum limosum, scarce and’ plants small; Potamogetons scarce, except natans and lucens; Characese are also scarce. The shores of this loch are stony or sandy, with very sparse vegetation or none whatever. Not- withstanding the innumerable small bays and shallow shores, there is very little marsh, so that plants of this habitat are not abundant. The Calder burn has brought down a great amount of detrital matter into the loch, forming large gravel banks ; but these are almost destitute of plants. The paucity of shallow water and marsh vegetation must, I think, be due to the abundance of stones and sand and scarcity of mud. The hills hereabout are faced with glacial drift gravel (fig. 42), which is brought into the loch by the burns (fig. 41). Nothing can be more antagonistic- to littoral phanerogams than gravel, shifting under the power of the waves. These long narrow lochs running in the direction! of the prevailing winds always have barren shores, owing to the- 1904-5.] Flora of Scottish Lakes. 999 waves having power over practically the whole of the loch ; this is more especially the case if the shores happen to be of gravel. Loch Lochy is not properly in the Ness area, as it drains into Loch Linnhe. Some dredging by the Mermaid , at depths to 500 feet, furnished exactly similar results to those already described for Loch Ness. Beyond this I have only examined the north-east end of the loch, which is practically the same in character and flora as Loch Oich ; the water, however, is less peaty. The mountains are here faced with glacial gravel, through which the numerous water - courses have carved enormous gullies, bringing down the gravel into the loch (fig. 42). By this action, two burns upon opposite shores have brought into the loch at Kilfinnan almost enough material to divide the loch into twain (fig. 42). We now proceed to smaller lochs of a more or less elevated position, situated on the mountains north-west of Lochs Lochy, Oich, and Ness. Some botanists have endeavoured in the past to distinguish mountain lochs by the presence of certain plants, as, for example, Isoetes lacustris, Lobelia Dortmanna, Potamogeton polygonifolius, Sparganium natans, S. minimum, and by the absence of reeds at the margin. This may undoubtedly be the case in some districts, but in the Loch Ness area the presence or absence of such plants and associations are certainly no criteria of the elevation of a loch. All the plants enumerated are to be found at so low a level as Loch Ness (52 feet above sea) ; and a reedy margin is found at quite highland situations, as will be shown later; whilst it is almost absent in such low-lying lochs as Oich and Ness. The reason is not one altogether of elevation for the presence or absence of certain associations of plants, but is rather due to the supply of food-salts, and the amount of exposure of the water to winds, coupled with the nature of the shore. The mountain lakes usually drain a very small area, poor in food-salts and rich in acid humus ; consequently only those plants are found in them that can obtain their requirements from an apparently scanty food supply, combined with the presence of humic acids. Such plants are those that have been associated with mountain lakes. Lowland lakes usually drain a wider area, and soils poor in peat and rich in food-salts; which, although 1000 Proceedings of Royal Society of Edinburgh. [sess. indispensable to most plants are poison to others. In the area of Lochs Ness and Oich there is but a small amount of soil rich in food-salts available for drainage, compared with the soil poor in food-salts and rich in acid humus. Consequently the effect of drainage from a small, rich food area is almost extinguished by the humic acids, and in such lowland lochs we find vegetation identical with that of the highest mountain lakes. Again, in Lochs Oich and Ness (and of course others) we have practically no reedy margin, neither have we in many mountain lakes. The reason for this is the nature of the shore, combined with the erosive power of the waves, leaving altogether out of the question food supply. On the other hand, in mountain lakes with a sheltered peaty or muddy shore, as in lowland lochs of like nature, we find a reedy or sedgy margin. The most luxuriant sedge association (Carex rostrata) that I have seen was at an elevation of 2300 feet ; but the factors are there suitable. Phrag- mites communis and Scirpus lacustris I have seen abundant at 800-1000 feet elevation. Highland lochs are usually in situations fully exposed to the fierce winds, their shores rocky or stony, consequently they have few plants about their margins. Their water, being poor in food-salts and rich in humic acids, has a restricted aquatic flora; but the same conditions may obtain in the lowlands, when the flora of the lakes will be similar. On the other hand, a highland loch having a supply of food-salts, with a suitable shore, and sheltered from prevailing winds, may quite well have the character of a lowland loch regarding its flora. Lochan Coire Glas, in Glen Garry Forest, is an extremely wild little lake about 1600 feet above sea level. Mountains rise precipitously from its margin to over 3000 feet, closing it in on three sides like an amphitheatre (fig. 43). Gusts of wind descending the mountains strike the loch with terrific force, not- withstanding its apparently sheltered position. This loch is gradually being silted up with detritus washed in by the burns, or rather waterfalls, that descend the mountains. A sand-bank in the middle of the loch is covered with Heleocharis palustris. The following plants also occur here : — Callitriche hamulata, Juncus lluitans, Myriophyllum alterniflorum, Isoetes lacustris, Littorella lacustris, Potamogeton natans, P. var. app. polygonifolius, 1904-5. ] Flora of Scottish Lakes. 1001 Sparganium minimum, Menyanthes trifoliata, Ranunculus Flam- mula, Carex flava, Caltha palustris, Juncus effusus, Carex aquatilis, Eriophorum vaginatum, Nardia compressa, Hypnum ochraceum. All the littoral plants were very much dwarfed. Lochan Diota is a small pool at about 1000 feet elevation north- west of Loch Lochy. It is in a depression, and is covered with the following plants : — Littorella lacustris, Lobelia Dortmanna, Juncus fluitans, Castalia speciosa, Menyanthes trifoliata, Heleo- ■charis palustris, Juncus effusus, Scirpus lacustris, Carex aquatilis, C. rostrata, Utricularia intermedia, all abundant. A number of old stems of Scirpus lacustris had been washed up on the east shore, 3 or 4 feet above the present w^ater level. Loch Lundie is north of Glen Garry, at an elevation of 445 feet. The shores are flat and peaty, sandy or stony. The water is peaty, and there is an abundant flora. The marsh plants grow luxuriantly ■on its western shore (fig. 44), but the eastern shores are com- paratively bare (fig. 45) ; the western side is also well wooded. A considerable island on the east is covered with dwarf birch and alder (fig. 45). Some of the shallow bays on the west are entirely filled with Phragmites communis (fig. 44), others with Scirpus lacustris (fig. 46). Isoetes lacustris is extremely abundant here, •carpeting the bottom from 2 to 20 feet deep ; in the deeper water these were frequently 18 inches long, being the largest specimens I have seen in this area. Littorella lacustris and Lobelia Dortmanna form a bottom carpet in many of the shallower places. Great beds of Carex rostrata, with C. aquatilis, occur on the western shore. Other abundant plants are Juncus fluitans, Potamogeton natans, P. lucens, Chara sp. rather scarce, Myrio- phyllum alterniflorum, Callitriche hamulata, Utricularia inter- media, Castalia speciosa, Sparganium natans, Equisetum limosum vather scarce, Comarum palustre, Menyanthes trifoliata, Heleo- charis palustris, Caltha palustris, Juncus articulatus, J. effusus, Ranunculus Flammula, Eriophorum polystachion, Pedicularis palustris. Lochan Doire Cadha is a small loch situated between Loch Lundie and Loch Oich, with peaty water. The west side is com- posed entirely of a deep and dangerous bog, sparsely covered with small Phragmites communis, Carex rostrata, and C. aquatilis 1002 Proceedings of Royal Society of Edinburgh. [sess. (fig. 47). The eastern shore is stony : large quantities of the dead stems of Phragmites communis have been washed high on this shore by the winter storms (fig. 48). This loch affords an excellent illustration of the difference between an eastern and western shore due to winds. Lobelia Dortmanna, Littorella lacustris, Juncus fluitans, Callitriche hamulata, Castalia speciosa, Potamogeton natans, Menyanthes trifoliata, Heleocharis palustris, Ranunculus Flammula, are the other plants that flourish here. A small colony of gulls were in possession of the bog at the western side. Some had made nests on the little elevated tussocks common to such places ; such nests consisted merely of a few grass leaves, etc. Others had nests quite on the bog, and liable to be flooded by a slight rise of the water ; such nests were rather large structures, built of Phragmites’ stems, so as to raise them several inches above the surface of the bog. On the west of Loch Ness, among the mountains, are a great number of lochs at an average elevation of about 1200 feet; some,, however, over 1600 feet above sea. Many of these bear a general resemblance in their flora. It is not essential therefore to treat- each loch separately ; they fall naturally into groups, and an enumeration of the plants of each group will be sufficient. We may group them as follows : — Taking the glens as boundary lines we have the lochs on the mountains south of Glen Moriston, those on the mountains between Glen Moriston and Glen Urquhart, Loch Meiklie in Glen Urquhart, and the lochs on the mountains- north of it. From the latter we shall pass across Loch Ness at Dochfour, and examine the numerous lochs east of Ness, working, back towards Fort- Augustus. South of G-len Moriston. — All these lochs are peaty and usually have a considerable colony of Carex rostrata upon their western shores, with C. aquatilis growing in shallower places in the rear of the former. The eastern shores are mostly stony or rocky, and < trees are entirely absent (fig. 49). The other plants that flourish at one or another of these lochs are as follows : — Littorella lacustris,. Lobelia Dortmanna, Isoetes lacustris, Fontinalis antipyretica, Chara fragilis, var. delicatula, Nitella opaca, Juncus fluitans, Calli- triche hamulata, Potamogeton natans, P. app. polygonifolius, P_ lucens, Sparganium minimum, Utricularia intermedia, Myrio- 1004-5.] Flora of Scottish Lakes. 1003 phyllum alterniflorum, Glyceria fluitans, Sphagnum acutifolium, S. cuspidatum, var. plumosum, Hypnum stramineum, H. trifarium, Rhacomitrium aciculare, Scapania undulata, Nardia compressa, Batrachospermum moniliforme, Zygnema Yaucherii, Menyanthes trifoliata, Comarum palustre, Equisetum limosum, Heleocharis palustris, Eriophoruni vaginatum, E. polystachion, Triglochin palustre, Juncus effusus, J. articulatus, Caltha palustris, Ranun- culus Flammula, Hydrocotyle vulgaris, Carex binervis, C. dioica. At Loch nam Faoileag (one of this group) the eastern shore presents a very curious appearance. It is almost jet-black, with white quartzite rocks protruding here and there (fig. 49). Upon examination the apparent black sand was found to consist of grains of carbonised vegetable matter looking exactly like coarse gunpowder. Microscopical analysis of these grains revealed them to be the remains of small woody plants with a close grain, but the fragments are too much burnt and too small for exact identi- fication. Probably they have been blown into the loch from the moor after extensive heather-burning by strong westerly winds. I have only seen a substance similar to this at one other loch, viz., Coire Glas, in Glen Garry Forest, but there it was brown in colour, not black. Fig. 50 illustrates a terrestrial form of P. natans found at a peat pool about a mile from Loch nam Faoileag. I have also observed them at other places. It is perhaps a state reverting towards a terrestrial ancestor, induced by an inadequate water supply through the filling up of the pool by the formation of sphagnum peat. Crossing the picturesque and charming Glen Moriston, through which flows a splendid river (fig. 51), we enter a desolate mountain region remarkable for the great number of its lochs. These are at an elevation of 1000 to 1600 feet. With the exception of dwarf birch or mountain ash on the islands of a few of them, their shores are treeless, and frequently entirely devoid of vegetation. Their waters are without exception peaty, often extremely so. At Loch a’ Mheig there is a great development of Carex rostrata, encroaching in a semicircular manner over the loch (fig. 52). The darker patches in the photograph indicate the Carex rostrata in 1 2 to 18 inches of water; the lighter patches, right and left of the island, with trees, are very shallow water or bog with Menyanthes. 1004 Proceedings of Royal Society of Edinburgh. [sess. trifoliata, Carex aquatilis, etc. It will be here noticed that the plants are growing upon the eastern shore ; this is due to the loch being entirely sheltered from westerly winds by adjacent high hills. Moreover a considerable stream passes through this loch, •and the effect of its detrital matter, assisted by the vegetation, is rapidly filling the loch. Mr Duncan Macmillan, keeper of the Invermoriston forest, informed me that forty years ago the only vegetation in this loch was that immediately about the island with trees, but it has gradually been encroaching over the loch, so that now its waters are not available for fishing from the shore. The reason for the vegetation encroaching in a crescent formation over the loch is owing to the gentle decline and even nature of the loch basin ; were its bottom irregular, such a crescent formation could not occur. The rocky, barren shore of the majority of these lochs is well illustrated by fig. 53. Occasionally Betula nana is found spreading over the rocks of the shore (fig. 54). This plant is very abundant in the district, and often of considerable size ; the largest specimens I have seen had stems as thick as one’s wrist ; they are always prostrate. The growth of Carex rostrata, etc., in the shallower water of many lochs of this series is illustrated by fig. 55. A similar feature is shown in fig. 56, the plant being Equisetum limosum. The dwarf birch on an island of an otherwise treeless district may be seen at Loch nan Eun (fig. 57) ; the birches shown here are mere shrubs. I suppose the reasons for the birch only being found on the islands of the lochs are due to the less peaty soil •of the islands, absence of deer, which are very destructive to trees, and also because the islands escape the periodic heather-burning. Adjoining Loch nan Eun, whose shores are almost destitute of plants, are several very small lochs, almost completely over- grown with plants, chiefly Carex rostrata ; but for the erosive power of the waves and the rocky shore of the large loch, these plants must certainly spread to it also. Fig. 58 is a photograph of Loch a Mhuilinn, showing Eriophorum polystachion growing in the water with Carex rostrata, Menyanthes trifoliata, etc. A small pool that has been almost converted into terra firma by the vegetation is shown in fig. 59 ; the existing plants are as follows : — Carex rostrata, C. aquatilis, Potamogeton natans, 1904-5.] Flora of Scottish Lakes. 1005 Utricularia intermedia, Menyanthes trifoliata, Juncus fluitans, and other terrestrial forms of J. supinus, Eriophorum polystachion, and over the drier parts tussocks of Scirpus csespitosus, Molinia coerulea, and Carex echinata. Loch Aslaich has an island with trees of considerable size, due to its sheltered position (fig. 60). These trees were probably planted, as there is a bothy on the little island, used by keepers when stalking deer. The terrestrial form of Sparganium minimum, mentioned on p. 977, is illustrated in the foreground of fig. 61, which is from a loch north of Loch, Aslaich. Dwarf forms of Castalia speciosa growing on peaty mud are shown in fig. 62. Menyanthes trifoliata, overgrowing peaty mud, with its rhizomes exposed, are seen in fig. 63. Perched rocks are a common feature of this desolate region. The one shown in fig. 64 is 26 inches high and 10 feet in circumference, in the form of a flattened sphere. It is so delicately poised that it can be rocked 2 inches with the little finger of one hand. The lochs of this extensive region, containing about 100 square miles of mountain and moor, are characterised by a general paucity, not only of variety, but also in quantity of phanerogamic plants. In the following list for this district many of the plants occur both in normal and in dwarf depauperated forms, in accordance with environment : — Ranunculus Flammula, Caltha palustris, Castalia speciosa, Epilobium angustifolium (about half-a-dozen plants at Loch a Choire Bhuidhe, probably introduced here by ducks ; large numbers of these birds are bred at the Balmacaan estate for sporting purposes), Myriophyllum alterniflorum, Callitriche hamu- lata, Lobelia Dortmanna, Menyanthes trifoliata, Littorella lacustris,. Utricularia vulgaris, U. intermedia, Juncus articulatus, J. supinus,, J. fluitans, Triglochin palustre, Sparganium natans, S. minimum, Potamogeton natans, P. app. polygonifolius, do. depauperated form in cold spring (p. 978), P. lucens, P. prselongus, Heleocharis palustris, Eriophorum polystachion, E. vaginatum, Carex filiformis, C. rostrata, C. aquatilis, C. binervis, Glyceria fluitans, Equisetum limosum, Isoetes lacustris, Chara fragilis, app. v. barbata, do. var. delicatula, Nitella opaca, Eontinalis antipyretica, Sphagnum sp., Blindia acuta, Brachythecium rivulare, Hypnum cuspidatum, H. uncinatum, Philonotis fontana, Scapania undulata, Uardia emarginata, N. compressa, Batrachospermum moniliforme, Zygnema 1006 Proceedings of Royal Society of Edinburgh. [sess. Vaucherii, Dickieia and similar gelatinous diatomacese very abun- dant in places ; the last may easily be mistaken for frog spawn. This list, with the foregoing description and photographs, will, I hope, convey a sufficiently clear idea of the nature of this series of lochs. There is such a similarity in their flora, that an enumer- ation and description of each is not only unnecessary, but its production would afford merely an unpalatable repetition. Loch Meiklie, situated in Glen Urquhart at an elevation of 372 feet above sea, differs from lochs hitherto considered, and demands special mention. Its shores are beautifully wooded, mostly stony or sandy : but about the entrance of the river Enrick, at the west end, there is a considerable swamp. Some of the sheltered bays, notably at the north-east, have also swampy margins (fig. 65). Besides moorland, it drains a small area of cultivation ; its water is therefore less peaty than usual. There is, however, a considerable amount of matter in suspension in the water, so that the photic zone here extends to about the same as at Loch Ness. In some parts of the loch the water was quite green with volvox. At the west end of the loch, proceeding from the drier ground of the swamp towards the water, we find associations of plants in some- what this order: — J uncus effusus, J. articulatus, Carex rostrata, Phragmites communis, Equisetum limosum in water 2 to 5 feet deep, Castalia speciosa in water 4 to 8 feet deep, Nymphsea pumila in water 8 to 10 feet deep ; beyond the latter, at the bottom, Potamogeton pusillus, var. tenuissimus, P. lucens, Utricularia vulgaris, Nitella translucens. All these associations are of course mixed with other plants ; but those mentioned are dominant over a certain area. The Castalia speciosa association is extremely well developed here, and presents a magnificent spectacle. Pig. 66 will afford some idea of the extent of this colony. Littorella lacustris is extremely abundant here, occurring in water 8 to 10 feet deep ; also upon the shores, where it flowers prolifically (fig. 67). There is another very large bed of Equisetum limosum at the north-west corner of the loch ; a portion of this had been cut for agricul- tural purposes. In places where it had not been cut, several cows were feeding upon it, two of these animals had advanced so far after this food that their backs were quite under water. Besides those already mentioned, the following plants occur here : — 1904-5.] Flora of Scottish Lakes. 1007 Eanunculus Flammula, Caltha palustris, Cardamine pratensis, Stellaria uliginosa, Spirtea Ulmaria, Comarum palustre, Epilobium hirsutum, Myriophyllum alterniflorum, Callitriche hamulata, Hydrocotyle vulgaris, Galium palustre, Senecio aquaticus, Lobelia Dortmanna, Lysimachia nemorum, Menyanthes trifoliata, Myosotis palustris, Pedicularis palustris, Mentha arvensis, var. agrestis, Mentha sativa, var. rubra, Polygonum amphibium, Juncus bufonius, J. fluitans, Sparganium natans, S. minimum, P. natans, P. app. polygonifolius, Heleocharis palustris, Scirpus lacustris, Des- champsia csespitosa, Glyceria fluitans, Isoetes lacustris, Nitella opaca, Chara fragilis, var. delicatula, Fontinalis antipyretica, Batrachospermum moniliforme, Conferva fontinalis. Near this loch I saw an enormous “witches’ broom” on Pinus sylvestris (fig. 68). Such a large, extremely compact and well- grown broom on Pinus sylvestris is not often met with. It is now in the museum of the Eoyal Botanic Garden in Edinburgh. Ascending the hills north of Glen Urquhart, we find a number of mountain lochs, differing somewhat in character from any hitherto seen. Here, with some exceptions, we have a great abundance of Castalia speciosa in its normal form, and often a luxuriant swamp vegetation of Scirpus lacustris, etc. Vegetation, although restricted in species, is more luxuriant than usual in hill lochs. This is no doubt due to two causes : — 1st. Most of these lochs are sheltered from wind by adjacent hills. 2nd. Seams of lime occur in these mountains, and undoubtedly its influence is felt in the lakes. The waters are usually but slightly peaty, moorland peat not being abundant above the level of the lochs ; so that we have in the general appearance of the flora of these lochs characters usually associated with lowland lakes. Fig. 69 is an illustration of a loch with an abundant flora upon its eastern shore ; this anomalous con- dition is due to the shelter afforded by hills on the west, south, and north sides. In fig. 70 a huge crescent of Castalia speciosa is seen to grow around the whole bay ; behind which are associations of Equisetum limosum and Carex rostrata. A similar feature is shown in fig. 71, with the addition here of Phragmites communis. The following plants occur here beyond those above mentioned — Eanunculus Flammula, Caltha palustris, Cardamine pratensis, Comarum palustre, Myriophyllum alterniflorum, Callitriche i 1008 Proceedings of Royal Society of Edinburgh. hamulata, Lobelia Dortmanna, Menyanthes trifoliata, Littorella lacustris, Pedicularis palustris, Utricularia vulgaris, Juncus effusus, J. articulatus, J. fluitans, Sparganium natans, S. minimum, Pota- mogeton natans, P. app. polygonifolius, P. prselongus, P. lucens,. Heleocharis palustris, Scirpus lacustris, Eriophorum vaginatum, E. polystachion, Carex rostrata, C. aquatilis, Phragmites communis,. Glyceria fluitans, Equisetum limosum, Fontinalis antipyretica,. Hypnum falcatum. At the north-east end of Loch Ness, behind the great beach (p. 994), there is a small loch entirely surrounded with forest trees, chiefly Pinus, Larix, Alnus, Salix, Populus, and having a large development of marsh vegetation. The chief plants here are Equisetum limosum, Phragmites communis, Carex rostrata, Juncus articulatus, J. fluitans, Caltha palustris, Comarum palustre, Myriophyllum alterniflorum, Littorella lacustris, Lobelia Dort- manna, Isoetes lacustris, Callitriche hamulata, Apium inundatum,. Potamogeton natans, P. lucens. Adjoining the beach of Loch Ness at Aldourie there is a small lake entirely surrounded and covered with vegetation. Erom Loch Ness shore, where not a water plant can be observed, 30 paces bring one to this little loch, entirely overgrown with aquatic plants (fig. 7 2). The following are plentiful : — Ranunculus Flammula, Hydrocotyle vulgaris, Comarum palustre, Montia fontana, Apium inundatum, Menyanthes trifoliata, Lysimachia vulgaris, L. nemorum, Myriophyllum alterniflorum, Polygonum amphibium, Potamogeton natans, Sparganium natans, Heleocharis palustris, Carex rostrata, Juncus effusus, etc. Surely ! but for the unsuitable nature of the Loch Ness shore, some of these plants would occur on it also. Other similar lochs occur hereabout; one near the high road 1 mile north of Dores, less closed in by trees than the last, contains the above-mentioned plants with the exception of Sparganium natans, Lysimachia vulgaris, and Montia fontana, but with the addition of much more Carex rostrata and C. aquatilis, Myosotis palustris, Mentha sativa, and Juncus articu- latus— a curious form having flowers and nodes viviparous, the young plants from the nodes quite large. Littorella lacustris carpets the bottom, and grows also on the muddy shore; the latter had flat, prostrate leaves, copious stolons producing young 1904-5.] Flora of Scottish Lakes. 1009 plants at every node, and with an abundance of flowers. Here again we have a dominant submerged and flowerless aquatic plant produced from plastic, semi-aquatic forms, and now, in its sub- merged aquatic state, propagated asexually by offshoots ; still retaining, however, within its protoplasm, the subtle powers of reproducing sexually that belongs to its semi-aquatic progenitors ; so that when removed from its submerged environment, either by the accidental subsidence of the water or by overgrowing a muddy flat, the latent force is rejuvenised and the plants flower abundantly. They retain also the character induced by the submerged environ- ment of reproducing by offsets. We next visit a series of lochs, many of considerable size, at elevations of from 600 feet to 1000 feet above sea level, lying to the east of Loch Hess. Loch Ashie is 716 feet above sea level on an open moor. It is about a mile and a half long, with flat and stony shores (fig. 7 3) and rather peaty water. The country on the east side is a bleak moor rising gradually from the loch and presenting a dreary aspect ; on the west the shores are clothed with coniferous forest. Towards the south-west the land has been recently deforested, so that this portion is as featureless as the eastern shore. It is very poor in plants : the only associations of marsh plants are a few colonies of Carex rostrata and C. aquatilis in bays on the east. Littorella, Lobelia, and Isoetes occasionally carpet the bottom. There are also groups of Sparganium natans, Potamogeton natans, P. crispus, P. pusillus, P. perfoliatus, P. lucens, Myriophyllum alterniflorum, Juncus fluitans, Fontinalis antipyretica, Hitella opaca, and Chara fragilis, var. delicatula. The littoral plants are, with the exception of the Carex colonies, limited to a few plants here and there of the following: — Equisetum limosum, Caltha palustris, Menyanthes trifoliata, Hydrocotyle vulgaris, Juncus effusus, J. articulatus, J. supinus, var. subverticillatus abundant, and Ranunculus Elammula. The larger rocks may have patches of Hardus, Scapania, and Zygnema. Loch Bunachton is an extremely desolate sheet of water, smaller than the last mentioned, but otherwise resembling it in character and flora (fig. 74). Loch Culcairn is a recent artificial lake, and the water, which PROC. ROY. SOC. EDIN. — VOL. XXV. 64 1010 Proceedings of Eoyal Society of Edinburgh. [sess. is very peaty, presents little of botanical interest. Originally there existed on the site a small tarn and extensive peat diggings. The dam is at the north end. Lochan Dubh, at Dunlichty, is a small peaty pool entirely surrounded with coniferous forest; near the margin the sandy bottom is entirely covered with a dense tangled mass of Hypnum fluitans, var. Arnellii, Sphagnum cuspidatum, var. plumosum, Nardia emarginata, and Zygogonium ericetorum, purple var. At other places Littorella lacustris, Myriophyllum alterniflorum, and Menyanthes trifoliata occupy considerable areas, while the shores, on the western side especially, have colonies of Carex rostrata, C. aquatilis, and Juncus effusus. In the rear of the latter a large tract, but slightly elevated above the surface of the loch, is occupied by a pure formation of Erica tetralix, the depressions filled with Sphagnum subsecundum, var. viride (fig. 75). Loch a Chlachain is 683 feet above sea level. The surrounding country is extremely wild and rocky. The water is clear, owing to the fact that the peat area drained by it is comparatively small. This loch drains Loch Duntelchaig, which in turn drains Loch Ceo Ghlas. The whole catchment area of these lochs consists greatly of bare rock, covered in many places with enormous patches of Arctostaphylos Uva-Ursi. Heather and peat is often restricted to interstices between the bare boulders, consequently the water of these lakes is unusually clear, but doubtless very poor in plant food-salts. The rocky nature of this area, together with the spreading habit of Arctostaphylos Uva-Ursi, are illustrated by fig. 76. The rock-bound shore is not conducive to a littoral flora; plants are consequently scarce, excepting at the west end, where the shore is flat owing to detrital matter brought into the lake by the inflowing stream. This portion is covered with vegetation, Equisetum limosum, Phragmites communis, Carex rostrata, C. aquatilis, Eriophorum polystachion, and E. vaginatum occupying considerable areas. The other plants of this loch are Littorella lacustris, Lobelia Dortmanna, Isoetes lacustris, Potamogeton lucens, P. natans, Sparganium natans, Juncus fluitans, Callitriche hamulata, ISTitella opaca, Chara fragilis, var., Myriophyllum alterniflorum, Juncus effusus, J. articulatus, and a few of the usual and common shore plants scattered here and there. 1904-5.] Flora of Scottish Lakes. 1011 Lochan a Choin is a small loch in a partially cultivated area ; its western shore is flat, with muddy peat. The eastern shore is stony and bare of plants. The water is peaty. The western shore is covered with a considerable area of vegetation presenting the usual features, Equisetum limosum, Carex rostrata, C. aquatilis, and Menyanthes trifoliata being the dominant forms. Lochan nan eun Ruadlia is near the last mentioned, but much larger, and very bare of plants. The south-west side has deep water quite up to the thick peat bank, with no shore whatever. The eastern and northern portion has a shore of stones and rock. The western side has a marsh area occupied chiefly by groups of Phragmites communis. No boat could be obtained here, and I could procure from the shore but very few aquatic plants, only Myriophyllum alterniflorum, Juncus fluitans, Littorella lacustris, Lobelia Dortmanna, Chara fragilis, var. delicatula, Fontinalis antipyretica. Beyond the above-mentioned Phragmites, the littoral plants are chiefly Carex rostrata and C. aquatilis, with a few others usual to the district. The strata hereabout consists greatly of a reddish conglomerate : on the ridges of this are several perched rocks of the same formation. A very similar strata occurs on the east shore of Loch nam Breac Deargh, below Meall Fuarvounie. Loch Duntelchaig is one of the largest lochs in the Ness area, and is a magnificent sheet of water 3 miles long by 1 wide, and 702 feet above sea level. It would take at least a week to do justice to this lake. I could only give it a short inspection, during which I saw nothing different in vegetation from what has usually occurred. The clearness of its water has already been remarked upon (p. 1010). Loch nan Gead’as, at the south-west end of Duntelchaig, and joined to it by a narrow channel which has wide, marshy flats on either side. This loch is more or less surrounded by a swamp bearing an abundant vegetation (fig. 77). Beyond those plants enumerated under the photograph, the vegetation is quite ordinary and common to the district. Loch Ceo Ghlas is a long narrow loch 766 feet above sea, below Tom Bailgeann. The clearness of its water has been already mentioned (p. 1010). The south-east shore has colonies of Carex 1012 Proceedings of Royal Society of Edinburgh. [sess. rostrata and Phragmites communis in sheltered hays. The north- west shore is bare and stony. The south-west end has an extensive marsh, covered with Equisetum limosum and Carex rostrata, etc., presenting no unusual features. I have noticed where the country people have mentioned lochs as being poor for trout-fishing, that the water has generally been clear; such is the case here. Loch Ruthven is a fine sheet of water some 2 miles long and 700 feet above sea level. Its water is peaty. The east and west ends are silted up with sand, so that there is a considerable area of shallow water at both ends ; but more especially so at the east. The shores are frequently sandy, more so than is general ; they usually slope gradually, and vegetation is abundant. The shallow areas at each end of the loch are often densely carpeted with the ordinary plants. Utricularia vulgaris is extremely abundant at a depth of 5 to 10 feet: with this Utricularia, Hypnum scorpioides, app. var. miquelonense (p. 983) occurs in plenty, so also does Potamogeton pusillus and Chara fragilis, var. delicatula. The photic zone here does not extend beyond a depth of about 23 feet, owing to the dark colour of the water. I noticed that the water was much more turbid at the east than at the west end ; the probable reason for this is due to the shallow area at the west end being of much less extent than at the east end. The greatest depth and bulk of water being at the west end, the sediment at the bottom is below the influence of the waves. At the east, however, a large area is within this influence, and the sediment is easily raised. Moreover, for some days previous to my visit, there had been a stiff westerly breeze. I have not seen this phenomenon at any other lake in the Ness area. The character of the vegetation at the sandy flat at the east end is shown by fig. 78. At the north-east end of the loch a large bay is filled with Equisetum limosum ; its existence here is due to the shelter afforded by the wooded hill from the westerly winds. It is interesting to notice how abruptly they terminate beyond the protective influence of the point (figs. 79, 80). At the west end of the loch a large sandy flat of several acres’ extent is entirely covered with a Juncus effusus association (fig. 81). There are also at the west end large colonies of Phragmites communis and 1904-5.] Flora of Scottish Lakes. 1013 Carex rostrata, the latter also at other places about the loch, particularly near the boat-houses at the east end, being under the lee of a point projecting into the loch. Beyond those enumerated the following plants occur here : — Ranunculus Flammula, Caltha palustris, Cardamine pratensis, Spiraea Ulmaria, Comarum palustre, Myriophyllum alterniflorum, Callitriche hamulata, Hydrocotyle vulgaris, Lobelia Dortmanna, Menyanth.es trifoliata, Littorella lacustris, Pedicularis palustris, Polygonum amphibium, Juncus fluitans, Triglochin palustre, Sparganium natans, Potamogeton natans, P. lucens, P. praelongus, Heleocharis palustris, Eriophorum polystachion, Carex flava, C. aquatilis, Glyceria fluitans, Isoetes lacustris, Nitella opaca, Fontinalis antipyretica, Scapania undulata, Nardia emarginata, Conferva fontinalis, Zygnema Yaucherii, Batrachospermum moniliforme. An Dubh Lochan, near Loch Ruthven, is a small pool entirely surrounded with vegetation. Owing to the wide swamp, the water is almost unapproachable. The plants are those quite usual to the district. Loch a Choire, a little north of Loch Ruthven, is 865 feet above sea level. The scanty vegetation is quite ordinary to the district and requires no special remark. The south-east shore is flat and mostly sandy, merging gradually into moorland; beyond a few sandy bays, the shores are otherwise rocky and stony. The water is not very peaty. Abruptly from its north-west shore a consider- able hill rises, the upper portion of which ends in a bold, perpen- dicular escarpment. Loch Dunmaglass is partially an artificial loch with the dam at the north-east end. Meall Nochd rises almost perpendicularly from its western shore, and the flank of Beinn Dubh-choire on the east is also steep. Being closed in by precipitous and bare rocky mountains, having but little peat, its water is clear. The scenery is very wild. It is remarkable for being the only loch in the Ness area in which I found Hippuris vulgaris, but only the submerged shoots. A flat, swampy portion at the north-east *end (fig. 82) is covered with Myrica, Calluna, and dwarf birch, with Carex at the margin. I was informed that previous to the making of the dam this place was quite dry, so that an example is here furnished of the conversion of moorland into swamp. The other 1014 Proceedings of Royal Society of Edinburgh. [sess. plants of this loch are of the usual type. Between Loch Mhor and Loch Ness are a number of small lochs very similar to one another in the character of their flora. They contain quantities of Castalia speciosa, which, with wooded shores, and general luxuriance of vegetation, give them a decidedly lowland appearance. The plants, however, notwithstanding the general luxuriance, are those usual to peaty lakes. A photograph of the south-west side of Loch an Ordain (fig. 83) shows Carex rostrata and C. aquatilis about the margins, Equisetum limosum and Phragmites com- munis standing out of the water, and growing among them, are quantities of Potamogeton natans and Castalia speciosa. The shores are clothed with alder and birch. A general view from the south-west (fig. 84) shows a large area of Carex rostrata that has almost completely overgrown this shallow portion of the loch; a pool in the foreground is, however, too deep for them and this is overgrown on the left side with Castalia speciosa. Such circular pools are known under the unpleasant appellation of “murder- holes.” Pig. 85 illustrates Phragmites communis advancing upon the loch in crescent formation, the water in front of them being covered with Potamogeton natans; this is from Loch Bran. So also is fig. 86, showing Carex rostrata growing into the water, behind them C. aquatilis on the drier ground, gradually merging thence into moor, the space between them being covered with Potamogeton natans. All the common plants of the area were found at one or another of these lochs, and need not be enumerated again. Loch Mhor. — In and about this large loch I found absolutely not a trace of any living plant. It is about 600 feet above sea level, and the water extremely peaty. Originally there were two lochs on this site, Loch Parraline and Loch Garth. In order to obtain a constant and efficient supply of water for their turbines, the British Aluminium Company at Foyers, who own the lochs, undertook operations by which the two lochs were joined, and the level of the lower raised some 20 feet by a dam ; so that one large loch was formed thereby, about 5 miles in length, and named Loch Mhor. The Company’s turbines utilise an enormous amount of water, consequently, in accordance with the rainfall, the surface- level of the loch is continually changing, the difference between 1904-5.] Flora of Scottish Lakes. 1015 maximum and minimum being about 22 feet. Now the water of this loch is so dark that I should imagine no plants could exist at a greater depth than 10 to 12 feet. The consequence therefore of an extra 20 feet of this dark water was to kill out the whole of the aquatic flora of the original lochs, and the ever- changing level has not favoured the introduction of a new flora ; in fact I doubt if a flora could exist there under the present conditions. Not only were all the aquatic plants destroyed, but the entire littoral flora was also extinguished by drowning, so that when the water is low the remains of the old littoral trees and shrubs form a desolate picture of death and destruction. Fig. 87 shows the shore of the present loch with the water fallen about 20 feet ; amongst the mud and stones are the remains of alder and birch. Fig. 88 is from another portion of the loch showing remains of birch, ash, and alder trees ; the shore is here of sandy mud and has been washed into terraces by the receding water. Another view is represented in fig. 89, where the peat covering has been washed from the underlying rock, the latter bearing evidence of glacial action. Loch Kemp is beautifully situated amongst hills, some of the lower slopes being wooded with birch. Its shores are mostly rocky, the water is very peaty, and vegetation extremely scanty. On the north-east side the bottom, within the photic zone, is to a great extent incrusted with a hard brittle layer, about half-an-inch thick, resembling moor-pan ; no plants grow in this substance. In other places there is a bottom carpet of Lobelia, Littorella, and Isoetes to about 12 feet deep; beyond this depth I could obtain no evidence of plant life. The photic zone here cannot extend beyond a depth of 12 to 15 feet. When looking over the side of a boat, the bottom was quite invisible at a depth of 5 feet. A small shallow bay with a sandy bottom on the west side has Potamogeton natans, not intermingled and covering the surface with their leaves in the usual way, but each plant quite isolated (fig. 90). With the latter are a few Castalia speciosa, with Equisetum limosum and Carex rostrata about the shores. Similar conditions also exist at the estuary of the inflowing burn from Meall na Targuid (fig. 91). Beyond those already mentioned, the only plants that I found here were Utricularia vulgaris, Callitriche / 1016 Proceedings of Royal Society of Edinburgh. [sess. hamulata, and Juncus fluitans ; none of them abundant. The littoral plants were merely isolated specimens of the commoner species here and there among the rocks. Loch Knockie much resembles Loch Kemp in general features. Its water is less peaty, and vegetation rather more plentiful, Car ex rostrata, Equisetum limosum, and Phragmites communis being abundant in sheltered bays. The photic zone extends to about 25 feet. No unusual features nor any but ordinary plants were observed. The loch, which is about 1^ miles long, is shown in fig. 92. Loch nan Lann possesses great natural beauty ; its shores are mostly stony and its water peaty. The aquatic flora is fairly abundant, but quite of the ordinary type and needs no comment. The features of this loch are similar in every respect to its neighbour, Loch Kemp. Fig. 93 represents the north end of the loch, the larger portion being obscured by the point projecting into the loch on the left. Loch Tarff is 956 feet above sea level ; its shores are mostly stony and rocky, and its water peaty. It has several small islands, the largest of which is the breeding place of a large number of gulls. This island is overgrown with stunted birch, alder, and willow, with an undergrowth of Calluna, etc. The branches of the trees are thickly invested with the lichen Alectoria j ubata, giving them a fantastic appearance. Another island has an undergrowth of Epilobium angustifolium and Capnoides claviculata ; a third has an abundance of Cnicus heterophyllus : yet none of these plants appear to be abundant anywhere else near the loch. Ranunculus hederaceus occurs sparingly on the shore, probably a mere casual, as I have not seen it at any other loch of this area. Menyanthes trifoliata, Carex rostrata, C. aquatilis are abundant in shallow bays. Littorella, Lobelia, and Isoetes carpet the bottom. Chara fragilis, var. Nitella opaca, Myriophyllum alterniflorum, Juncus fluitans, Callitriche hamulata, Utricularia vulgaris, Sparganium minimum, Potamogeton natans, P. lucens, Fontinalis antipyretica are all abundant as usual. Equisetum limosum not abundant. Wet rocks are frequently covered with Blindia acuta, Nardia compressa, and Zygnema Yaucherii. Ranunculus Flammula, Caltha palustris, Juncus effusus, Heleocharis palustris, Eriophorum 1904-5.] Flora of Scottish Lakes. 1017 polystachion occur about the shores, but mostly of dwarfed growth. Fig. 94 affords a general view of the loch with three of its wooded islands. There are several small lochs situated in the neighbourhood of the larger ones recently mentioned ; the flora of these is all of the common type usual to the lochs of the district, and as they possess no features of special interest they need not be enumerated. Loch Killin is situated at an elevation of about 1000 feet in a narrow and deep glen overshadowed by mountains. Its shores are rocky, excepting at the south end, and the water is peaty. The aquatic flora is quite ordinary to such lochs. Mention must, however, be made of the large quantities of Glyceria fluitans (fig. 95) and Sparganium natans, chiefly at the south end. The most interesting feature about this loch is the remarkable amount of detrital matter brought into it by the river Killin (fig. 96). The bottom of the glen south of the loch forms a flat strath, consisting of the alluvial sand and gravel of the river Killin, and extending a length of about 2 miles. Kear the loch many acres of this strath are covered with Juncus effusus. The south shore of the loch consists of this alluvium, and forms a beach of considerable extent. Fig. 96 illustrates this beach, and the manner in which it becomes overgrown with plants. From the main body of the vegetation of the strath we see extending over the gravel ; patches and isolated plants of Kardus stricta, Deschampsia flexuosa, Festuca ovina, Molinia cserulea, Scirpus csespitosus, etc. ; in the rear of these ; isolated tussocks of Juncus effusus occur as the vanguard from the large colony farther up the strath (fig. 97). Such sward as exists between these tussocks is mostly composed of dwarf and densely matted Equisetum arvense. A view of the loch from the north-west, and the steep wooded escarpment entering it on the western shore, is shown in fig. 98. About six miles to the south-east of Fort- Augustus, between the mountains of Carn a Chuilinn and Cairn Yangie, is an extensive plateau some 2200 feet above sea level ; wild and desolate in the extreme, it is knowTn locally under the sobriquet of “ Siberia.” Upon this plateau are a series of lochs numbering about twenty. As this is probably the highest series of lochs in the British Islands, they merit special mention. The shores of 1018 Proceedings of Royal Society of Edinburgh. [sess. these lochs are mostly rocky and stony ; where littoral marsh plants are found, they always occur on the western side, or in sheltered hays. Carex rostrata, C. aquatilis, Equisetum limosum, Eriophorum vaginatum, and E. polystachion are the plants that dominate such sites ; all other marsh plants are hut poorly represented. Carex rostrata grows most luxuriantly, in fact the largest specimens I have seen were at these lochs. Equisetum limosum also grows well in some of the lochs ; hut I have observed that when growing near the Carex rostrata they scarcely grow taller than the latter, whereas in the lowland lochs they grow twice as high : no doubt this is due to the stronger action of the wind at this elevation. On 11th July, at midday, the temper- ature recorded at Lochan na Stairne, elevation 2154 feet above sea level, was as follows : — Bright sun all the morning ; fresh N.E. wind. Air temp, (thermometer swung in the air), 65 ’2° F. „ „ under the shade of a peat bank and facing wind, 59*5° F. „ „ on the heather in the sun, 6 ins. from ground, 72° F. Water at S. end of loch, 65*4° E. „ „ 1ST. „ „ 56*8° E. „ „ half way down the loch, F. „ „ N.E. end in a sandy bay, 50'43 F. ,, ,, the same bay, but at the estuary of a burn from Dubh Lochan, 67 '5° F. „ „ a spring on the shore half way down the loch, 43 ‘2° E. The difference of 8*6° between the S. and N. ends of the loch being due to the -N.E. wind driving the upper strata of warm water to the S. The low temperature recorded at the sandy bay was probably due to a wide gully, down which the wind came with considerable force, driving back the upper strata of warm water. The water of a loch S.E. of the last mentioned, but about 200 feet higher, after brilliant sun all day, registered 64*5° F. at 9.15 p.m. Air temperature, 53’8° F. I am not able to give winter temperatures, but the record would no doubt be very low. There is no boat on any of these lochs ; I was therefore unable to gain much information regarding the bottom flora. Besides the previously mentioned, the following plants occur, mostly of dwarf 1904-5.] Flora of Scottish Lakes. 1019 growth : — Ranunculus Flammula, Caltlia palustris, Littorella lacustris, Lobelia Dortmanna, Isoetes lacustris, Carex aquatilis, Juncus fluitans, Myriophyllum alterniflorum, Sparganium mini- mum, Potamogeton natans, P. polygonifolius, Callitriche hamulata, Utricularia intermedia, Chara fragilis, vars. Scapania undulata,, Nardia compressa, Blindia acuta, Fontinalis antipyretica, Sphagnum sp. About stagnant places, Batrachospermum moniliforme and Zygnema Vaucherii ; Armeria maritima upon some of the rocks. Colonies of gulls occupy a few of the islands. The whole plateau is entirely devoid of trees. The photographs illustrate the character of the dominant flora and the nature of the land about these lochs. Fig. 99 shows Carex rostrata growing into a loch, and the manner in which it thins out as mud is approached, and the luxuriant growth where the depth of water is suitable. Fig. 100 illustrates Carex rostrata near the shore, and beyond them a zone of Equisetum limosum; both of equal height. Fig. 101 shows a loch that has become reduced in size by the detrital matter of a stream, together with that formed by plants. Carex rostrata is growing in the water : behind it, in less water, is Carex aquatilis ; and the boggy flat is covered with Eriophorum vaginatum (mostly past seeding), Scirpus csespitosus, Molinia cserulea, etc. Fig. 102 represents one of the western lochs of this series, with islands ; it is also one of the largest. Between Nairn and Forres there occur lakes that have already been referred to at considerable length (p. 969). It now remains to enumerate the plants that thrive there. Those of this district, not general to the peaty lochs of the Ness area, are marked with an asterisk: — Ranunculus Flammula, Caltha palustris, Radicula officinalis,* Cardamine pratensis, Stellaria uliginosa,Spirsea Ulmaria, Comarum palustre, Hippuris vulgaris,* Myriophyllum alterni- florum, Callitriche stagnalis,* Hydrocotyle vulgaris, Lobelia Dort- manna not abundant, Menyanthes trifoliata, Myosotis palustris,* Pedicularis palustris, Mentha arvensis, var. prsecox,* M. sativa,* Utricularia vulgaris, Littorella lacustris not abundant, Iris Pseud-acorus, Alisma ranunculoides,* Juncus effusus, J. con- glomeratus, J. articulatus, Typha latifolia,* Sparganium ramosum,* Potamogeton natans, P. heterophyllus,* Heleocharis palustris, Scirpus lacustris, Carex flacca, var. stictocarpa,* C. flava, var. 1020 Proceedings of Royal Society of Edinburgh. [sess. argillacea,* C. rostrata, Phragmites communis, Equisetum limosum, Chara aspera,* Enteromorpha intestinalis,* Spirogyra crassa,* lEdogonium capillare.* Vegetation here is in general more luxuriant than in the peaty lochs, and occurs all round the loch, more or less, and not particularly at the west side, as in the lochs of Area I. The flat, sandy-muddy shore, without vegetation, is shown in fig. 103 : in the winter this shore is covered with water. Typha latifolia is very luxuriant at Loch Loy (fig. 104). Loch Cran has a bottom carpet of Chara aspera and Potamogeton heterophyllus over the greater portion of it. Large associations of Carex rostrata are frequent. Being disappointed in the only available boat on the last-named loch, which could not be kept afloat for more than a few minutes at a time, I spent the remainder of a rather wet day on the Culbin sand-hills, and give herewith a short description of this interesting place. Behind the sand-hills a large belt of forest, chiefly Pinus sylvestris, has been planted in order to check the inroad of the sand over the land, and to reclaim from the dunes land already taken possession of by them. After one or more generations of the Pinus sylvestris have been cropped, the detritus, formed by the loppings and natural remains of the trees, together with that of such plants as associate with them, mixing with the sand, renders it fit for agricultural purposes or for the planting of a more valuable timber. The sand-hills here are of immense size, being amongst the largest in Britain. In places where the distance is shut out of view by dunes, nothing but an enormous tract of bare shifting sand can be seen, wearying the eye by its monotony. Hearer the forest, however, the sands are less shifting, and a vegetation is found encroaching over the dunes, partly of such plants as find their natural habitat thereon, as Ammophila arun- dinacea, etc. (fig. 105); and upon the border of the forest; plants also of the heath and moor formations, spreading gradually outwards over the sand-hills (fig. 106). A most interesting example in oecology is seen in the wonderful manner in which a trailing and straggling moor plant, Salix repens, adapts itself to the environmental conditions of the sand-dunes here. Instead of trailing, as amongst the heather, we find the 1904-5.] Flora of Scottish Lakes. 1021 plants associating and forming themselves into dense, dome-shaped tussocks about a foot high (fig. 107), by which means they are able to protect themselves against the cutting wind and sand. Being normally a xerophilous plant of the moorland, the scant water supply of the sand-dune does not hinder its growth there ;, moreover its roots are more largely developed, and are much longer than when growing in the peat moor. The physical conditions of the lakes at Lismore have already been discussed (p. 968), where it was remarked that the flora differed notably from that of the Ness area. The peculiar lime- incrusted stones upon the shores of the lochs have been already mentioned (p. 968). This incrustation is calcium carbonate, CaC03 (fig. 1); it is formed by minute lithophilous filamentous algae in the process of their metabolism, in a similar manner by which the same substance is deposited on the stems of aquatic phanerogams (p. 968). Loch Fiart, in the south of Lismore, has a reedy margin of Phragmites communis (fig. 108) and Scirpus lacustris. Loch Kilcheran is about 2 miles north of the above, and, like it, has a reedy margin of the same plants, which at the north end cover an extensive area. A circular pool is shut off from the main body of the loch by these plants, forming thereby a “ murder-hole ” (fig. 109). Loch Baile a Ghobhainn, at the north of the island, has also a similar reedy margin to that of the other lakes. The south end is occupied by an extensive tract of Scirpus lacustris, and at the north end, behind the belt of Scirpus lacustris, there is an extensive bed of Phragmites communis; the latter had been cut for economic purposes (fig. 110). Not only in the reedy margin, in the water, in the shores, and in the general aspect, do thd^e three lakes agree with one another, but also in their general flora, so that an enumeration of the plants of one will answer for either ; those not general to the Ness area are marked with an asterisk : — Ranunculus Flammula, Caltha palustris, Castalia speciosa, these three abundant but only in normal form ; Nympliaea lutea,* Radicula officinalis,* Cardamine pratensis, Stellaria uliginosa, Spiraea Ulmaria, Comarum palustre. Lythrum salicaria* only at Loch Fiart; Epilobium palustre.* 1022 Proceedings of Royal Society of Edinburgh. [sess. Hippuris vulgaris,* extremely luxuriant and abundant, growing in water as deep as 10 feet, with the flowering stems above the surface. Looking over the side of the boat at the subaqueous meadow of foliage formed by the barren shoots of this elegant plant, bathed in the soft refulgence afforded by the blue sunlit water, was a sight not easily forgotten. Myriophyllum spicatum* very abundant even to 10 feet deep. This plant is so incrusted with lime that it is unable to rise to the surface to produce its flowers ; and although plentiful I saw but few flowering or fruiting specimens. Montia fontana, Parnassia palustris,* Hydrocotyle vulgaris, Veronica Anagallis,* Pedicularis palustris. Utricularia vulgaris down to 12 feet deep. Eupatorium cannabinum* about the lochs, a sure indicator of lime ; Senecio aquaticus, Menyanthes trifoliata, Myosotis palustris.* Samolus Valerandi * only seen at Loch Kilcheran ; Littorella lacustris much less abundant than in the Ness area ; Polygonum amphibium, Iris Pseud-acorus, Alisma Plantago,* Triglochin palustre, Juncus effusus, J. articulatus, Sparganium ramosum.* Potamogeton perfoliatus* growing in water 10 to 24 feet deep, and pro- ducing their flowers above the surface from even the greatest depth ; P. natans to 20 feet deep ; P. lucens, P. pusillus,* 2 to 12 feet deep; P. filiformis* in shallow water; Heleo- ■charis palustris. Eriophorum polystachion, small specimens ; Scirpus lacustris very abundant ; Carex rostrata, Cb aquatilis, neither of these so much in evidence as in the peaty lochs ; C. flacca.* Phragmites communis very abundant ; Equisetum limosum not abundant ; Chara aspera, var. desmacantha,* heavily incrusted with lime, carpets the bottom from 2 to 20 feet deep ; C. fragilis, var. delicatula, incrusted with lime,* carpets the bottom from 10 to 20 feet deep; C. hispida, var. rudis,* incrusted with lime at 25 to 35 feet deep; Eontinalis antipyretica abundant in deep water down to 40 feet deep ; Hypnum scorpioides,* a very robust form, from 3 to 5 feet deep, abundant ; Cladophora fracta,* floating in the water and about aquatic plants; Zygnema Vaucherii on smooth rocks. From the foregoing chapters it will be seen that some plants flourish best in water poor in food-salts and lime ; others in water rich in food-salts and lime ; others, as Typha, where there 1904-5.] Flora of Scottish Lakes. 1023 is an abundance of marsh gas ; while a considerable number are indifferent, and can adapt themselves to any of these conditions. It would be interesting to plant artificially aquatic plants in oecological conditions opposed to their usual natural habitat, and to study the results. I hope to continue the work during the summer of the present year (1905) in other areas of Scotland, and to publish,/ the result as a continuation of the present contribution. All the lakes mentioned in this paper may be found in Bartholo- mew’s latest half-inch maps of Scotland, Nos. 11, 15, 20, and 21. ( Issued separately November 11, 1905.) “ Yet methinks it is not unreasonable to propose, that words standing for things which are known and distinguished by their outward shapes should be expressed by little draughts and prints made of them. . . . Naturalists, that treat of plants and animals, have found the benefit of this way : and he that has had occasion to consult them will have reason to confess that he has a clearer idea of apium or ibex, from a little print of that herb or beast than he could have from a long definition of the names of either of them.” — John Locke ( ob . 1704). Proc. Roy. Socy. of Edin.~] [Vol. XXY. Fig. 1. — Stone from the shore of a loch at Lismore, showing the incrustation of calcium carbonate caused by the metabolic processes of minute lithophilous algre. Reduced one-half natural size. Fig. 2. — Waterworn and polished stones from Loch Ness shore at Loc^iend, of various geological formations. Reduced one-quarter natural size. [Plate 1. — Referred to on page 968. a Mr George West. Proc. Roy. Socy. of Edin.~\ [Vol. XXV. Fig. 3. — Portion of a stem of Potamogeton natans from a lake at Lismore, showing incrustation of calcium carbonate. (Magnified three diameters.) Fig. 4. — General view of Loch Ness from Borlum, near Fort- Augustus, looking north-east. [Plate 2. — Referred to on pages 969 and 985. Mr George West. Proc. Roy. Socy. of JEdin.] [Vol. XXV. Fig. 5. — Loch Ness shore, near the embouchure of the river Tarff, looking towards Beinn a Bhacaidh. Waves breaking on the gravel shore during easterly breeze. L.S.Y. Susan at her station on the loch. Fig. 6. — Crest of the beach of Loch Ness near Borlum, showing the xerophilous nature of the vegetation : Ulex europaeus, Silene maritima, Thymus serpyllum, etc. Mr George West. [Plate 3. — Referred to on pages 986 and 989. Proc. Roy. Socy. of Edin.] [Vol. XXV, Mr George West [Plate 4. — Referred to on page 989. Proc. Roy. Socy. of Edin. ] [Vol. XXV. Fig. 9. — Portion of a gravel bank in Loch Ness, at the Tarff estuary. Although the vegetation is scanty, yet it contains sixty-two species of flowering plants. Beinn a Bhacaidh in the distance. L. S.Y. Susan at her station on the loch. Fig. 10. — Inchnacardocli Bay, Loch Ness, witli Cherry Island and the “ Horseshoe ” in the distance. A view of the beach on the left, opposite the island, is pre- sented by fig. 15. Mr George West, [Plate 5 .—Referred to on page 990, Proc. Roy. Socy. of Edin. ] L V 01. AAV. Fig. 11. — Marsh vegetation at Inchnacardoch Bay, Loch Ness. Tussocks of Carex elata standing out of the water in the foreground ; immediately to the left of them are the same species with a carpeting habit ; behind both a large Carex rostrata association is advancing into the loch ; Alnus glutinosa in the rear. Fig. 12.— One of the tussocks of Carex elata seen in Fig. 25. [Plate 6. — Referred to on page 991. Mr George West. Proc. Roy. Socy. of Edin. ] [Vo]. XXV, Mr George West [Plate 7. — Referred to on page 992. Fig. 13. — Fontinalis antipyretica in the dry bed of Balantoul Fig. 14. — Calluna vulgaris, etc., covered with the seeds of Burn, Inchnacardoch Bay, Loch Ness. The burn has Eriophorum polystachion carried by the west winds from water in it at this part only at times of flood. an adjacent marsh. Proc. 'Roy. Socy. of Edin. ] [Vol. XXV. Fig. 15. — Shore of Loch Ness, north-east of Inchnacardoch Bay ; stony shore, with a more or less xerophilous vegetation encroaching over the beach from the adjacent moor. Fig. 16 — Shore of Loch Ness at Invermoriston. Alnus glutinosa, that has had the soil partially washed from its roots by the water of the loch. Me Geokge West. [ Plate 8. — Referred to on page 993. Proc. Roy. Socy. of Edin.~\ [ Vol. XXV. Fig. 17. — Urquhart Bay, Locli Ness, showing sandy shore, behind which Jnneus effusus is covering the low ground, with isolated bushes of Alnus glutinosa spread from the dense wood in the rear. The tall trees of lighter colour are Salix alba and Fraxinus excelsior. Fig. 18. — View in the interior of the wooded marsh at Urquhart Bay shown in Fig. 17. Alnus glutinosa, Salix alba, and Fraxinus excelsior very dense ; huge clumps of Nephrodium Felix-mas overhang the river, with a tangle of other shade-loving plants. Mr George West. [Plate 9.— Referred to on page 994. b Proc. Roy. Socy. of Edin.] [Vol. XXV. Fig. 19. — Marsh scene at Urquhart Bay, looking out towards Loch Ness. Menyan- thes trifoliata in foreground. Phalaris arundinacea on right and left. Groups of Alisma Plantago in centre. On the left of them Carex rostrata. Alnus glutinosa on both sides ; same again in middle distance, with Equisetum limosum. Dead tree washed up on the shore. Cultivated land on opposite side of bay. Fig. 20. — Group of Alisma Plantago in Urquhart Bay. Me George West. [Plate 10. — Referred to on page 994. Proc. Roy. Socy. of Edin. ] [Vol. XXV. Fig. 21. — High stony beach at east end of Loch Ness ; view from near the light- house, looking towards Lochend. Ulex europseus on crest of beach, the foremost plants dwarfed by the wind. Fig, 22. — Loch Ness shore at Inverfarigaig. Mr George West. [Plate 11. — Referred to on page 994. Proc. Roy. Socy. of Edin. ] [Vol. XXV. Fig. 23. — Group of Scutellaria galericulata (sun form) on the shore of Loch Ness near Inverfarigaig. Fjg. 24. — View at Foyers, looking across Loch Ness towards Meall Fuarvounie. The tree-covered flat, with stretch of sand beyond it, consists of detrital matter brought into the loch by the river Foyers. Mr George West. [Plate 12 . — Referred to on page 994. Proc. Roy. Socy. of Edin.'] [Yol. XXV. Fig. 25. — Coniferous trees killed by dust of cryolite at Foyers, by Loch Ness. Fig. 26. — View from the middle of Loch Ness, about two miles from Fort Augustus, showing the passage of the Great Glen through the mountains on the left centre of picture ; Beinn Tee in the distance. Mr George West. [Plate 13. — Referred to on page 995. Proc. Roy. Socy. of Eclin.] [Vol. XXV. Fig. 27. — Shore of Loch Ness, clothed to the water’s edge with birch, ash, hazel, alder, etc. View from Corrie’s Cave, looking towards Fort Augustus. The rectangular projection into the water is Glen Doe Pier. Fig. 28.- — Shore of Loch Ness from Glen Doe Pier, looking towards Corrie’s Cave. The rocky nature of the shore, combined with the constant wash of the waves, prohibits phanerogamic vegetation in the littoral waters. Mr George West. [Plate 14. — Referred to on page 995. Proc. Roy. Socy. of Edin.] [Vol. XXY. Fig. 29. — Roots of Alnus glutinosa on the shore of Loch Ness that have been exposed by the action of the waves, and then continuously wounded by the stones of the beach being washed over them during floods. Fig. 30. — A transverse section of a wounded root of Alnus glutinosa, as shown in fig. 29, magnified three diameters. Nearly half of the root has been worn away ; the living portion below has again and again attempted to heal the wound by the formation of a callus, but the erosive action of the stones has frustrated this. The only living part of the root now is the light portion at the bottom of the picture. On the left an attempt is again being made to occlude the upper dead wood. Mr George West. [Plate 15. — Referred to on page 995. Proc. Roy. Socy. of Edin. ] [Vol. XXV. Fig. 31. — Fraxinus excelsior, with very much enlarged base, on the shore of Loch Ness, by Borluin. Fig. 32. — View at the south-west end of Loch Uanagan, showing extensive marsh covered with Carex rostrata, etc. The inflowing burn passes through the pool in the foreground. Mr George West. [Plate 16. — Referred to on page 996. Proc. Roy. Socy. of Edin, ] [Yol. XXV. Fig. 33. — West end of Loch TJanagan, with Scirpns lacustris growing out in water. Eriophorum polystachion, Carex, and other marsh plants in the foreground. Beinn a Bhacaidh in the distance on the left. Fig. 34. — Sparganium natans, with floating leaves and flowers above the surface of the water. Carex rostrata in the rear. [Plate 17. — Referred to on page 996. C Me George West. Proc. Roy. Socy. of Eclin. ] [Yol. XXY. Fig. 35. — Loch Uanagan. Yiew south-west to north-east, showing the various zones of vegetation described in the text. Fig. 36. — Hydrocotyle vulgaris on the shore of Loch Uanagan. Mr George West. [Plate 18. — Referred to on page 996. Proc. Roy. Socy. of Edin ] [Vol. XXV. Mr George West. [Plate 19. — Referred to on page 997. Fig. 37. — Pinus sylvestris on bank of Caledonian Canal. The Fig. 38. — Pyrus Aueuparia on the bank of Caledonian Canal, apex, having been ringed by squirrels, has been blown off Entirely killed by rabbits gnawing the bark at the by the wind, as described in the text. base. Proc. Roy. Soey. of Edin.] [Vol. XXV. Fig. 39. — River Oicli, near Coiltry. View looking south-west, Beinn Tee in the distance. Bank covered with Juncus effusus. Fig. 40. — Loch Oich, with Calder Burn in the foreground, showing gravel bank at its embouchure, island in the loch, Sron a Choire Ghairbh and Beinn Tee on the right. Mr George West. [Plate 20. — Referred to on page 998. Proc. Roy. Socy. of Edin.] [Vol. XXV. 05 +3 "Hp ® 2 05 rQ J ^ 1 £ [Plate 21. — Referred to on page 998. Mr George West. Proc. Roy. Socy. of Ed in.] [Yol. XXY. Fig. 43. — Lochan Coire Glas, view looking west. Sron a Choire Ghairbli rises precipitously from the margin of the loch ; patches of snow still remain. Fig. 44. — Loch Lundie. View looking north-east. Reed margin of Phragmites communis. Island, with birch and alder, at the other side of loch. Mr George West. [Plate 22. — Referred to on page 1000. Proc. Hoy. Socy. of Edin. ] [Vol. XXV. Fig. 45. — Loch Lundi, looking south-west, showing the bare eastern shore. Island with birch and alder (see fig. 44). Beinn Tee in the distance. Fig. 46. — Bay on the north-west side of Loch Lundie, filled with an association of Scirpus lacustris, and showing the manner in which they thin out as the deeper water is reached. Mr George West. [Plate 23. — Referred to on page 1001. Troc. Roy. Socy. of Edin. ] [Vol. XXV, Mr George West. [Plate 24. — Referred to on page 1002. IU.aU. Fig. 49. — Loch nam Faoileag, showing eastern shore, composed of black vegetable sand through which white quartzite rocks protrude ; colony of Carex rostrata near the opposite shore. Fig. 50.-- Terrestrial form of Potamogeton natans ; Juncus effusus in the background. [Plate 25.— Referred to on page 1003. d Mr George West. Proc. Roy. Socy. of Edin. ] [Vol. XXY. Fig. 51. — The river Moriston, with its banks abundantly wooded. Locb a’ Mheig. Carex rostrata advancing into the loch in crescent formation. Fig. 52.— Mr George West. [Plate 26. — Referred to on page 1003. Proc. Roy. Socy. of Ed in. ] [Vol. XXV. Fig. 53.— Lochan an Ruighe Dhuibhe (south of Carn Tarsuinn). Yiew at the west end of the loch, looking north-east, showing rocky shore and a few Equisetum limosum (dwarf) in the water. Fig. 54. — Betula nan a overspreading the rocks of the shore of loch, as fig. 53. [Plate 27. — Referred to on page 1004. Mr George West. Proc. Roy. Socy. of Edin.'] [Vol. XXV. Fig. 55. — In the deeper water is a zone of Equisetum limosnm (dwarf) ; nearer the shore Carex rostrata occupies a considerable area ; in the shallower water still Carex aquatilis is mixed with Eriophorum polystachion, merging gradually into the plants of the moorland. Fig. 56. — Loch na Criche. View from a bay at the south-west end, looking north-east, showing a considerable belt of Equisetum limosum around the hay. Mr George West. [Plate 28. — Referred to on page 1004. Proc. Roy. Socy. of Edin. ] [Vol. XXV. Fig. 57. —Loch nan Eun, looking west, showing island with dwarf birch, district otherwise treeless ; shore without vegetation. Fig. 58. — Loch a Mhuilinn, looking south-east ; Eriophorum polystachion grow- ing in the water with Menyanthes, beyond which is Carex rostrata reaching out towards the island. Me Geokge West. [Plate 29. — Referred to on page 1004. Proc. Roy. Socy. of Edin. ] [Vol. XXV. Fig. 59. — Site of a loch that has become almost filled by the accumulation of plants that have grown in it. Fig, CO. — Loch Aslaich, looking south-west ; island with moderate-sized trees, owing to shelter afforded by the hills. Mr George West. [Plate 30. — Referred to on page 1004. Proc. Roy. Socy. of Edin. ] [Yol. XXV Fig. 61. — The south-west shore of a small loch north of Fig. 62. — Bog at the margin of a loch, with Castalia speciosa growing on the Strath an Fiacail, showing terrestrial form of Sparganium mud, and much dwarfed ; footprints of a bird in the mud also, minimum in the foreground, with Eriophorum, Carex, etc. beyond. Proc. Roy. Socy. of Edin. ] [Vol. XXV. Fig. 63. — Shore of a loch with Menyanthes trifoliata, having its rhizomes exposed on the surface of the mud. Fig. 64. — Perched rock on the mountain top between Loch Aslaich and Loch nam Meur. Portions of five small lochs can be seen in the distance. Mr George West. [Plate 32. — Referred to on page 1005. Fig. 65. — Bay at the north-east of Loch Meiklie, looking towards the bridge over the outflowing river. In the foreground is a zone of Phragmites communis ; on the shore side of these occur Carex rostrata, Juncus eflusus, etc. Fig. 66. — Association of Castalia speciosa at the west end of Loch Meiklie, with Equisetum and Phragmites nearer the shore. Proc. Roy. Socy. of Edin. ] [Vol. XXV. Mr George West. [Plate 33. — Referred to on page 1006. Proc. Roy. Socy. of Ed in. \ [Vol. XXV, Mr George West. [Plate 34. — Referred to on yage 1006, Fig. 67.— Sandy shore at Loch Meiklie, covered with Littor- Fig. 68. — “Witches’ broom’’ on Pinus sylvestris. The walk- ella lacustris in the form of a green sward ; behind the ing-stick on the second branch below is 39 inches long, boat is an extensive belt of Equisetum limosum. Proc. Roy. Socy. of JSdin.] [Vol. XXV Fig. 69. — Vegetation upon the eastern shore of a highland loch (see text). On the shore in the foreground Carex aquatilis ; next beyond is Carex rostrata, then Equisetum liinosum ; in still deeper water is a zone of Scirpus lacustris, and beyond that Castalia speciosa, which also encroaches towards the shore in places where other plants are sparse. Fig. 70. — A western hay of Locli nan Faoileag, showing Carex rostrata, Equisetum limosum, and Castalia speciosa encroaching upon the water in crescent forma- tion ; Erica cinerea in the foreground. Mr George West. [Plate 35. — Referred to on page 1007. Proc. Roy. Socy. of Edin.] [Vol. XXV. Fig. 71.- Loch na Ba Ruaidhe. View of a western bay, showing Carex rostrata, Phragmites communis, Equisetum limosum, and Castalia speciosa encroach- ing on the water in crescent formation. Islands with dwarf birch and alder. Fig. 72. — Little loch near Loch Ness beach at Aldourie, entirely surrounded and covered with vegetation. On the water, among others, are chiefly Potamo- getoti natans, Polygoninm amphibium, and Menyanthes trifoliata. Mr George West. [Plate 36. — Referred to on page 1008. Proc. Roy. Socy. of Eclin. ] [Vol. XXV. Fig. 73. — Loch Ashie from the north-east, looking south-west, showing barren flat and stony shore. Fig. 74. — -Loch Bunachton. A desolate loch, situated in the bottom of a vast treeless moor. Mr George West. . [Plate 37. — Referred to on page 1009. Proc. Roy. Socy. of Edin ] [Vol. XXV. Fig, 75. — Dubh Lochan, with Carex rostrata and Juncus effasus on its western shore ; gradually merging into moorland. Fig. 76. — Margin of Loch a Chlachain, with Arctostaphylos Uva-TJrsi overgrowing rocks in the foreground. Mr George West. [Plate 38. — Referred to on yacje 1010. Proc. Roy. Socy. of Ed in.'] [Voi. XXV. Fig. 77. — Loch nan Gead’as, with a zone of Castalia speciosa, behind which are belts of Equisetum limosum, Carex rostrata, Comarum palustre, Myrica Gala, etc. Fig. 78. — Sandy flat at the east end of Loch Ruthven, showing the moorland vegetation encroaching over the sand. The foreground is thickly clothed with Calluna vulgaris, Myrica Gala, Juncus squarrosus, Nardus stricta, Deschampsia flexuosa, Juncus effusus, etc. Nearer the water the plant- covering is thinner, then isolated clumps and plants finally give way entirely to sand. Mr George West. [Plate 39. — Referred to on page 1012. Proc. Roy. Socy. of Eclin.~] [Yol. XXY. Fig. 79. — Equisetum limosum in a bay at the north-east end of Loch Ruthven, showing how abruptly they terminate beyond the protection afforded by the wooded point Mr George West. [Plate 40. — Referred to on page 1012. Proc. Roy. Socy. of Edin. ] [Vol. XXV. Fig. 81. —West end of Loch Ruthven, looking east, showing the Jnncns effusus association : these gradually become less packed as the drier ground is reached ; finally they extend towards the moorland in distant isolated tussocks. Fig. 82. — Loch Dunmaglass, looking south-west, showing swampy portion at the north-east end and the steep escarpment of Meall Nochd on the right. [Plate 41. — Referred to on 'page 1012. / Mr George West. Proc Roy. Socy. of Ed in.'] [Vol. XXV. Fig. 83. — Loch an Ordain, looking north-east, giving a general view of' the luxuriant vegetation of the south-west shore. Fig. 84. — Loch an Ordain, general view looking north-east, showing a portion of the loch only ; a large area covered with Carex rostrata, excepting the circular area in the foreground, which is too deep for them. Mu George West. [Plate 42. — Referred to on page 1014 Proc. Roy. Socy. of JEdin.] [Vol. XXV. Fig. 85. — Loch Bran. A crescent formation of Phragmites communis in one of the bays. Fig. 86. — Loch Bran. A small bay with Carex aquatilis and Carex rostrata. Mr George West. [Plate 43. — Ref erred to on page 1014. Proc. Roy. Socy. of Edin.'] [Vol. XXV. Fig. 87. — Loch Garth, showing the shore when the water is low, with remains of dead vegetation ; view looking north-east. Fig. 88. — Loch Garth at the south-west end, showing the shore when the water is low, with remains of dead trees. Mr George West. [Plate 44. — Referred to on page 1014. Proc. Roy. Socy. of Ed/in. ] [Vol. XXV. Fig. 89. — Loch Garth. View of the south-east shore when the water is low ; rocks that have been denuded of their peat covering exhibit glacial striation. Mr George West. [Plate 45. — Referred to on page 1015. Proc. Roy. Socy. of Edin. ] [Yol. XXV. Fig. 91. — Loch Kemp. View from the inflowing burn, looking north-west. Estuary in the foreground with Potamogeton natans, Castalia speciosa, and Carex rostrata ; dwarf birch on the shore ■ Meall Fnarvounie in the distance. Fig. 92. — A general view of Loch Knockie from the shoulder of Beinn a Bhacaidh, looking north-east, showing islands, wooded shores, and adjacent moorland. Mr George West. [Plate 46.— Referred to on page 1016. Proc. Roy. Socy. of Pd in.] [Vol. XXV. Fig. 93. — Loch nan Lann, looking south-east from the outlet into Loch Ness, showing wooded shores and a colony of Carex rostrata on the left. Fig. 94. — A general view of Loch Taiff, looking north-east, showing wooded islands and Carex associations in shallow places. Mr George West. [Plate 47. — Referred to on page 1016. Froc. Roy. Socy. of Edin. ] [Yol. XXV. Fig. 95. — Groups of Glyceria fluitans in Loch Killin. The isolated floating leaves are those of Sparganium natans. Fig. 96. — Large beach of sand and gravel at the south end of Loch Killin, looking south, showing vegetation encroaching over the beach. In the rear of the isolated tufts of grasses, Scirpus, etc., Juncus effusus is extending from a large colony farther up the strath. Mr George West. [Plate 48. — Referred to on page 1017. Proc. Roy. Socy. of Edin.] [Vol. XXV. Fig. 97. — Nearer view of the Juncus effusus vanguard mentioned in fig. 96, showing the isolated tussocks extending out over the recently formed beach from the main body farther up the strath. The sward existing between these tussocks is chiefly composed of dwarf and densely matted Equisetum arvense. Fig. 98. — Loch Killin, showing the steep wooded escarpment on the western shore, looking south-east. The escarpment shuts out the view of the south end of the loch. [Plate 49. — Referred to on page 1017. 9 Mr George West. Proc. Roy. Socy. of Edin.] [Vol. XXV. Fig. 99.— Portion of a locli on Carn a Chuilinn, with Carex rostrata encroaching on the water. Fig. ICO. — View of Dabh Lochan, showing a large belt of Equisetum limosum outside a colony of Carex rostrata, both of equal height ; Eriophorum vaginatum on the bank in the foreground. Mr George West. [Plate 50. — Referred to on page 1019, Proc. Roy. Socy. of Edin.] [Vol. XXV. Fig. 101. — A small loch on Carn a Chuilinn ; filling up from the western side as described in text. Fig. 102. — One of the westernmost lochs on Carn a Chuilinn, with islands ; illustrates the desolate nature of this elevated plateau. Mr George West. [Plate 51. — Referred to on page 1019, Proc. Roy. Socy. of Edin. ] [Vol. XXY. FrG. 103.— Loch Loy, looking west : with a flat sandy-muddy shore, having no aquatic vegetation save algse. Coniferous forest at margin of loch. Fig. 104. — West end of Loch Loy, with Typha latifolia at the margin of the water. In the foreground, and extending to the left, is a large colony of Carex rostrata, dividing the loch into two portions, so that one may walk over the Carex to the other side of the loch. Me Geoege West. [Plate 52. — Referred to on page 1020. Fig. 105. — View at the rear of the Cnlbin sand-hills, looking towards the sea. Ammophila arundinacea encroaching up the great sand-dune in the distance. Proc Roy. Socy. of Edin.\ [Vol. XXV. Fig. 106. — View at the rear of the Culbin sand-hills outside the belt of pine forest. Some of the foremost pines are partially engulfed in sand. In the foreground are numerous low dome shaped tussocks of Calluna vulgaris encroaching upon the sand-dune over the domain of Ammophila, dense masses of which cap the top of the dune. Mr George West. [Plate 53. — Referred to on page 1020. Proc. Roy. Socy. of Edin. ] [Vol. XXV. Fig. 107. — Salix repens growing in isolated dome-shaped tussocks on the Culbin sand-hills and encroaching over the domain of Ammophila arundinacea ; some of the latter may be seen growing out of the tussocks of Salix. The xero- philous habit assumed here gives it an entirely different appearance from that seen when growing on the wet moors. — . - - ---- • - i Fig. 108. — Loch Fiart, looking south-west, showing zone of Phragmites communis extending along the east shore. Mr George West. [Plate 54. — Referred to on page 1021. Proc. Roy. Socy. of Edin. ] [Vol. XXV. Fig. 109. — Loch Kilcheran, looking south-west, A circular pool has been shut off from the main body of the loch by dense zones of Phragmites communis and Scirpus lacustris. Fig. 110. — Loch Baile a Ghobhainn, looking west, showing a portion of the loch only. A large bed of Phragmites has been cut for economic purposes as far out as the depth of bog would allow, some are still standing in cocks ; Iris Pseud-acorus, etc., in the foreground. Mr George West. [Plate 55. — Referred to on page 1021. 1904-5.] Magnetic Quality in Molecular Assemblages. 1025 Magnetic Quality in a Boscovichian Assemblage of Molecular Magnets. By Dr W. Peddie. (MS. received May 15, 1905. Read same date.) CONTENTS. Sec. Page 1. Statement of Problem . 1025 2. Statement of Assumptions 1026 3. 4. Weiss’s Experimental Re- sults . . . 1027, 1029 5. Wallerant’s Formula . . 1030 6. Components of Field due to an Ideal Magnet . .1032 7. Parallel Component of Force due to an Infinite Homo- geneous Assemblage . 1032 8. Proof that 2(3 Cos2 0 - 1) = 0 1034 9. Modified Expression for the Parallel Component of Force .... 1034 10. Direction Cosines of the Transverse Component of Force .... 1036 11. Components of the Trans- verse Force . . .1036 Sec. Page 12. Modified Expressions for these . . . . 1037 13. Directions of Equilibrium in Zero Field . . . 1038 14. Transverse Force under Magnetisation in Princi- pal Planes . . . 1039 15. The Magnetisation Quartic 1042 16. 17. Magnetisation in Princi- pal Planes . . 1043, 1047 18. Magnetisation and Field along Principal Axes . 1048 19. Condition at a Boundary. — Residual Magnetisation . 1049 20. Estimate of Size of Mol- ecular Magnets and of Molecular Susceptibility 1053 21. Conclusions . . . 1054 22. Approximate Evaluation of Constants . . . 1055 1. The gradual growth of the theory of molecular magnetism from the original suggestions of Poisson and Weber is well known. The recent great development, made by Ewing, and tested experi- mentally by means of models, has placed the theory on a fairly firm basis, and has made essentially secure the fundamental postulate that magnetic phenomena in material bodies are due to magnetic molecules which may possibly be regarded as free from any directional control other than that supplied by their own mutual action. Since, on the modern view of the constitution of matter, solids are supposed to be aggregates of crystalline groups, the study, at the very outset, of magnetic quality in a crystalline medium, is a necessity. The fact that the more notable magnetic materials crystallise in forms belonging to the cubic system makes the study PROC. ROY. SOC. EDIN. — YOL. XXY. 65 1026 Proceedings of Boy al Society of Edinburgh. [sess. of that system most desirable. Ewing, in his treatment, assumed that the molecular magnets were arranged in consecutive and adjacent groups of four, placed at the corners of a square, and that the distance between nearest centres only slightly exceeded the dimensions of the molecule. Thus, in the magnetised condi- tion of the medium with no external field, a pole of one molecule was regarded as being practically under the control of the opposite pole of the consecutive molecule alone ; and a line of such consecu- tive molecules realised one of Faraday’s lines of induction. Ewing’s aim was mainly to account for the characteristic form of the induction curve in strongly magnetic materials and for the observed magnitude of residual magnetisation. The primary object in the present investigation is to determine whether or not a satisfactory explanation can be given of the characteristic phenomena manifested in the magnetisation of crystals of the cubic system. A secondary purpose is to extend the Boscovichian theory of the constitution of matter so as to include the subject of magnetism. 2. The assumptions made are to some extent different from those made by Ewing. As in his work, it is assumed that the molecule possesses the qualities of an ideal magnet. Should it be the case that the effective magnetic moment of the molecule is not actually independent of its distance or orientation, full account of the fact can be taken, in the expressions subsequently found (§§ 9, 11), by the alteration of constants in a manner which would be perfectly definite when the actual conditions were given. It is assumed further that the space distribution of the centres of molecules is that of the closest-packed homogeneous assemblage of Boscovichian points. Other arrangements are not excluded, but their treatment is not taken up in the present paper. It is conceivably quite possible that a comparison of results obtained with different arrangements may lead to magnetic tests discrimi- nating the actual arrangement of the magnetic constituents of molecules from amongst those which are theoretically possible on the cubic system. It is assumed, at first, that the medium is of practically infinite extent, so that demagnetising force is not evident; but the effect at boundaries is specially discussed (§ 19). 1904-5.] Magnetic Quality in Molecular Assemblages. 1027 Finally, it is assumed that the dimensions of the molecidar magnets are of such size in comparison with their average distance apart, that the fourth and higher powers of that ratio can he neglected. 3. Weiss’s Experime7ital Results. — An extended series of observa- tions has been made, by P. Weiss, upon the magnetic properties of magnetite. His results were given in full in his thesis (Paris, Ho. 890, 1896), and in V itclairage electrique , 1896. A resume was also given in the Journal de Physique , 1896. I have only been able to obtain the latter account. The thesis is now out of print. Figs. 1-4, taken from the resume, show the main results. In fig. 1 the abscissae represent external field, while the ordinates represent magnetisation. The observations were made upon bars cut from the crystal in various directions, and special care was taken to avoid self-demagnetisation. The field varied from zero to 500 c.g.s. units. The curves Q, B, T, refer respectively to magnetisation parallel to the quaternary, the binary, and the ternary axes; i.e. to the directions respectively of the edges, the face diagonals, and the body diagonals of a cubic crystal. At the higher fields, the order is T>B>Q; while in weak fields the order is reversed, the three curves crossing in the neighbourhood of H = 30. Weiss observes that this peculiarity does not present itself in all specimens. The curves given were obtained with a dodecahe- dral specimen from Brozzo, in Piemont. In the case of an octahedral specimen from Zillerthal, in the Tyrol, the curves are “in the same order, in high fields, and do not intersect in the neighbourhood of the origin.” This point is of importance in view of the results obtained in the present investigation. Fig. 2 shows the effect of magnetisation, in its own plane, of a disc cut parallel to the faces of the cube. The longitudinal effect, i.e. the magnetisation parallel to the external field, is shown in the large full curve. The eight-lobed curve (six lobes only shown) in the centre represents the component of magnetisation transverse to the external field. This component vanishes along directions parallel to the edges and the face-diagonals of the cube. The flatness of each loop on the side next the lines parallel to the edges of the cube (horizontal and vertical in the diagram), and the 1028 Proceedings of Royal Society of Edinburgh. [sess. greater proximity of the maxima to these lines than to the face- diagonals, is noteworthy. Weiss remarks that “the magnetisation turns more quickly than the field when it separates from an axis n B » » binaire » B' » •» binaire » Q » » quaternaire » Q' » » quaternaire » 0 Voir ie texte. 3" “ en fonction de I! Courbe direction de i’axe lernaire » Bj » » - binaire » Q$ » quaternaire of minimum magnetisation and less quickly when it separates from an axis of maximum magnetisation.” Tig. 3 shows the similar results in the case of a disc cut parallel to a diagonal plane of the structural cube. The line parallel to a 1904-5.] Magnetic Quality in Molecular Assemblages. 1029 cube edge is now vertical only. The horizontal line is parallel to the face diagonal. The main difference lies in the relative magni- tude of alternate lobes. In directions perpendicular to body diagonals the parallel component was constant while the transverse component was practically zero; so that “the magnetite acts as an isotropic substance for all directions contained in the face of the octa- hedron.” Weiss remarks that the evident irregularities are probably due to fissures in the disc. 4. Weiss’s Experimental Results. — Fig. 4 represents results similarly to fig. 2. In this case the observations were made upon a disc of iron-wire network. This disc is regarded as being a slice cut from a face of a cube constituted of three mutually perpendicular sets of sheets of magnetic material, successive sheets being separated by layers of non-magnetic material. The actual network has nothing in its structure corresponding to the alternate layers parallel to its own plane. The effect of these would be to add a constant magnetisation to the component of magnetisation parallel to the field. The pointed curve inside the outer circle r T 1030 Proceedings of Royal Society of Edinburgh. [sess. represents the component thus modified. “ These curves strongly resemble those of magnetite parallel to the face of the cube.” 5. Wallerant’s Formula. — The next contribution to the in- vestigation was made by Wallerant ( Gomptes Rendus, Oct. 1901). His work is purely mathematical, and is not based upon any assumption as to the structure of the magnetic material. He remarks that the components, X, Y, Z, of induction along the quaternary axes are functions of the components of the field along these axes — i.e. of the direction cosines cos a, cos f3, cos y, of the Fi$- 8. Magneiite de Brozto. Premier disque parallels k la face du doditotalre Aimantatkm parallele et perpendicaialre an champ. Lea Hgftes pom till yes Indiqucnt 1*8 maxima et minima. field. He then develops these functions in increasing powers of the cosines, and, neglecting powers beyond the third while expressing the necessary conditions of symmetry, obtains the expressions X = E cos a(l + &cos 2a) , Y = E cos /?(! + h cos 2/3) , Z = Ecos y(l + A: cos 2y ) , where E is the induction along a binary axis, and h is a numerical coefficient whose value depends on the intensity of the field. To verify these expressions, he deduces the relation 3T + Q = 4E, where T and Q have the meanings given in connection with fig. 1, 1904-5.] Magnetic Quality in Molecular Assemblages. 1031 while R takes the place of B as previously used. He then calculates by this formula the values of R corresponding to two pairs of values of T and Q, as observed by Weiss. The calculated values were 323 and 403; Weiss’s observed values were 325 and 404. I have calculated other values. The numbers in the first row below give the field ; those in the second and third rows respectively give calculated and observed values of R, the data being taken from Weiss’s diagram reproduced in fig. 1. 10 20 40 60 80 100 120 140 160 200 240 280 320 360 400 440 91 159 250 299 330 351 363 374 381 389 395 400 404 407 411 414 100 166 252 299 330 352 364 373 380 388 395 400 404 406 407 409 Ft§.4. Dissque de tutlc inelaliique. Aimantation pamlUMe el porpendtculatre tttt tdiftinp. The correspondence is practically perfect for values of the field ranging from 50 to 360 ; while, outside these limits, the difference is relatively considerable. Weiss’s data are for one specimen only, which, as fig. 2 shows, obviously possesses defects ; and further ■data are very desirable. The peculiar form of the curve Q suggests the existence of fissures in planes parallel to the faces of the cube. Weiss essentially, and purposely, introduces these in his theoretical model. On any view, the partial identity of results is remarkable. Wallerant further shows that his expressions lead to the value B' = R + R&(cos2a cos 2a + cos2/? cos 2/3 + cos2y cos 2y) 1032 Proceedings of Royal Society of Edinburgh. [sess. for the component of induction parallel to the field, and points out that it gives the constancy in all directions perpendicular to the ternary axes which Weiss found. He points out the diamagnetic quality which would ensue in certain directions, if k did not lie between - 1 and + 3, and remarks that k is probably most often less than unity in absolute value. “One sees,” he says, '“that these formulae reproduce all the peculiarities observed experi- mentally.” His formulae certainly give the general nature of observed' peculiarities. It will be considered later whether or not they give their detailed nature. His primary remark that the components of induction are functions of the components of the field might be reversed. On the molecular theory, the field acting upon any molecule has an internal as well as an external constituent, and the former is determined by the magnetisation. Further, it is the internal constituent which must exhibit relations to the crystal- line symmetry. 6. Components of Field due to an Ideal Magnet. — Angles being measured from the direction proceeding from the south pole to the north pole of a magnet, and r being distance from the centre of the magnet, whose moment and semi-length are M and a, it is easy to verify that, to the second order in a/r, the components of the total force, F, along and perpendicular to r, respectively, are F cos = 2~ cos 0^1 + ~g(2 + 5 sin2 0)J , Fsin<£= ^ sin #[~1 + ^ ^-(5 cos2 0—1)1. rd L 2 r2 J From these we obtain, for the components parallel and perpen- dicular to the magnet, the expressions F cos (6 + ) = *[(, cos2 6 - 1) + L?f(35 cos4 0-15 cos2 0+3)J, F sin (0 + <#>) = ^ sin 6 cos 6 |^3 + 1 ~(35 cos2 6 - 15) J . 7. Parallel Component of Force due to an Infinite Homogeneous 1904-5.] Magnetic Quality in Molecular Assemblages. 1033 Assemblage. — As stated in § 2, the assemblage of magnets con- sidered is that having centres at the centres of spheres in the single homogeneous closest packed arrangement. The distance r between a pair of such centres is given by the formula A2 + p2 + v2 , where p is the least distance between centres, and A, g, v, are positive or negative whole numbers ; for the homogeneous arrange- ment under consideration is the same as that of points situated at the centres, and the mid-points of the edges, of homogeneously arranged, closest packed, cubes filling all space. If we put r2/p2=p, we see that p must be an integer; for either one or all of A, g, v must be even integers. If we consider the origin of co-ordinates to be at the centre of one of the magnets, while the axes of co-ordinates are parallel to edges of the cubic arrangement ; and if we take a, /3, y, as the common direction cosines of the axes of the infinite system of magnets regarded as constituting a homogeneously magnetised body ; the expressions at the end of § 6 give the components of force at the origin, provided that we put cos 6 = (aA + (3g + yv)/'(2p)1/2 , and sum for all possible values of A, g, v. But the force which we require is not that at the origin. It is the force at the pole of the magnet whose centre is at the origin. If we consider the north pole, it is therefore the force at the point + aa > P^ + r P\/2 + Q ^ ’ S° we have to toke cos v = aA + /3g + y v + Jo, - P A + V2ap)2 + (p- + \/2/? — ja P Developing the quantity (3 cos2 6 - 1) in the value of F cos (0 + <£),. neglecting powers of a/p greater than the second, and summing 1034 Proceedings of Royal Society of Edinburgh. [sess. throughout space, we find that the term involved contributes to the force at the pole the amount 2-2 ^5Ma2 [4 + 105 cos4 e - 75 cos2 0](2p)f* , where cos0 has the value (aX + /3p + yv)/(2p)112 as before. Terms involving the first power of a/p vanish because they contain odd powers of X, etc., so that they cancel in pairs in the summation for each value of p, positive and negative values for X, etc., occurring symmetrically. It is necessary also to note that P = oo 2(3 cos2 6 — 1) = 0. The proof is given in next section. p= i To the quantity just obtained we have to add, from the expres- sion for F cos (6 + <£), the terms involving «2/r2, for these have practically the same value at the pole as at the centre. Thus we get finally, for the component of the force, at the pole, taken parallel to the magnet, the expression [245 cos4 <9-165 cos2 6 + ll](2p)-»2 . £>«00 8. Proof that 2 (3 cos2 6 - 1) = 0. — The sum vanishes for every p=i value of p independently. Consider 2(aX + /3g + yv)2 = 2 (a2 A2 + /32/x2 + y V2) + 21(a /3Xp + fiygv + yavX). The second sum on the right hand side of the equation vanishes since, with a given value of p, positive and negative values of A, /x, v, occur symmetrically, so that each positive product is cancelled by an equal negative product. Again, by the symmetry of the expression 2 p = X2 + p? + v2, we see that the number of points having a given X , /x, or v respective^ are equal. Thus 2-A2 = 2-^,2 = 2-v2 = J2(A2 + /x2 + 1/2). Therefore 2(aA + /3p + yv)2 — J2(A2 + f2 + v2). This proves the theorem. It is interesting to find that the truth of this theorem in topology, regarding points in any homogeneous cubic arrangement, necessi- tates also the condition that these points are loci of zero force if magnetic or electric, similarly directed, double-points are centred at them. 9. Modified Expression for the Parallel Components. — It is 1904-5.] Magnetic Quality in Molecular Assemblages. 1035 desirable to obtain the expression in a form in which the direction cosines of the magnetisation are separate from those giving positions of centres. In the summations of last section, we must carefully remember that each sum is not merely a sum of distinct numerical values. Account must also be taken of the number of times that a given numerical value appears. In this way, from the condition 2p = A.2 + /x2 4- v2, we get 32(A2) = 2p2-N, where N is the number of times that a given A.2 occurs with the given p. Remembering again that sums of quantities which involve odd powers of A, ,u, or v vanish, we find (aA + fig + yv)4 — 2(a4A4 + /34/x4 4- y4c4) + 62(a2/32A2//,2 + (32 y2g2v2 4- y2a2i/2A2) - (a4 + /34 + y4)2-A4 + 6(a2)S2 4- fly 4- y2a2)2-Ay = (a4 4- p4 4- y4)2-A4 4- (a 2/32 + /52y2 4- y2a2)[(2p)2S-N - 32-A4] , since 62(A>2) = 32.A2(/a2 4- v2) = 32-A2(2 \p - A2). But 1 = a4 4- P4 + y4 4- 2 (a 2j82 4- /32y2 4- y2a2), and so we get 2(aA + pg + yv)4 = J(a4 4- /34 4- y4)(52-A4 - 2-(2^)2) - 1(32-A4 - 2-(2 p)2) . Therefore, writing 2-(2 \p)2 in the form (2p)25-N, the parallel component takes the form ![^{(a4 + /34 + /)(52.^-2.N) _\y WY (32' A.4 m -S-N)] 442-N (2 P) -5/2 where the 2 p outside the square bracket comes under the signs of summation also. The summations are easily carried out to a sufficient approximation, and will be given subsequently (§ 22). The expression reduces to A — B(a4 + p4 + y4) , where A and B are positive, and A>B. Since the k in Wallerant’s formula for the induction (§ 5) is a negative quantity, it appears that the form here deduced for the internal component of force parallel to the induction is identical with that which Wallerantgave for the component of induction parallel to the external force. The a used here corresponds to his cos a, etc. This result justifies to some extent the remarks made at the end of § 5. Further justification will appear when we consider the transverse components of force and induction (§§ 14, 16). 1036 Proceedings of Royal Society of Edinburgh . [sess. 10. Direction Cosines of the Transverse Component of Force . — It is desirable to find expressions for a sin 0, b sin 6, c sin 0, where a, b, c are the direction cosines of the transverse component. We have at once aa + b/3 + cy — 0 . Also, if l, m, n be the direction cosines of the normal to the plane containing (a, /I, y) and (X, g, v), we have la + mb + nc — 0 . But la + m/3 + ny = 0, and l\ + mg + nv = 0, so that Igm :n — /3v — yg : yX — av : ag — /3X. Therefore a(/3v — yg) + b(yX — av) + c{ag — /3X) = 0 , and we get a :b : c =* (3{gg — /3X) — y(yX - av):y((3v - yg) - a(ag - /3X) :a(yA - av) — /3(/3v — yg) = a(aA + /3g + yv) — X : (3(aX + /3g + yv) — g : y(aA + /3g + yv) — v . Writing a — &[a(aA + j3g + yv) - A], etc., we find Xa + gb + vc — A[(aA + /3g + yv )2 — (X2 + g2 + v2)] = - k( X2 + g2 + v 2) sin2 0 . But Xa + gb + vc = (X2 + g2 + v2)1 sin 0 , so that k = - 1/(A2 + g2 + v2)* sin 6 . Hence (X2 + g2 + v2fa sin 0 — X — a(aX + /3g + yv) , the other two expressions being got by cyclical interchange of a, b, c; a, (3, y; X, g, v. 11. Components of the Transverse Force. — The components of the first term in the expression for the transverse force at the origin (§6) are 2* sin 0 cos 0 = + f3g + yv)[A - a(aX + fig + y^)](X2 + g2 + v2)~B/2 , r6 p6 and two other quantities obtained by cyclical interchange of a, f3,y ; X, g, v. At the positive pole, distant a forwards in the direction (a, (3, y), this becomes 6J2M aX + f3g + yv+ X + J2 a— — a( aX + f3g + yv + ■4 (X2+a2 + v2yv(l + 2 J2~y, a aX 4- (3g 4- yv + g2 + v2 + 2 a* X2 + i y/2 g2 + v2) 1904-5.] Magnetic Quality in Molecular Assemblages . 1037 Expanding, neglecting terms involving powers of a/p beyond the second, and writing P = aX + ftp. + y v, this reduces to 210^M-2-(A-aP)F(2p)-^. To this we have to add the second term in the expression for the transverse force (§ 6), which, on summation, reduces to 35V2M_q^.(X _ ap)P8(2j))-W . P The total components at the pole are therefore 245N/2Ma2^ (X _ ^ps^-t/s P5 and two cyclically related quantities. 12. Modified Expressions for the Components of the Transverse Force. — For the purpose of separating magnetisation cosines from position cosines, we can put the above sums into the form ^"X[a3A.3 + 3aA(/32p2 + y2v2)] — a2*[a4A.4 + /P/u.4 + y4^4 + 6 (a 2/32A2yU,2 + p2y2p,2i/2 + y2a2i/2A2)] , with the two other cyclically related quantities. Multiplying respectively by l , m, w, subject to the conditions at + Bm + yn = 0 , Z2 + m2 + n2 = 1 , and adding, we get (a H + j$m + y %)2-(^4 - 3AV2)(2 V)~w = |-(a3Z + /3Bm + y3 N (2 P)~m in which the sum is (§ 22) negative. The condition for this quantity vanishing is a 3Z + + y 2n = 0 ; whence l :m :n = /3Q3 2 - y2)y : y(y2 - a2)a : a(a2 - /32)/3 . Now the transverse force is perpendicular to (a, /3, y) and also to (Z, m, n), as above conditioned. Therefore its direction cosines 1038 Proceedings of Royal Society of Edinburgh. are proportional to a(a2-Q), (3((32 - Q), y(y2 - Q), where Q = a4 + /34 + y4. Inserting these quantities divided by the square root of the sum of their squares, in place of l, m, n in the factor outside the sign of summation, it becomes Ja6 + /36 + y6-Q2, the proper sign having yet to be found for the cosines of the force. To determine the sign put in (a3l + (33m + y3n), a=l-2£2, (3 = rj, y — 0, where £ and r] are small positive quantities, and we get 7] = 2£. Now assume l— - 2£, m= 1 - 2£2, and (a3Z + (33m + y3n) becomes - 2£ ; so that the force is outwards along ( - 2£, 1 - 2£2), and its component, in the direction indicated by l, is - 4£2 multiplied by % This component must be identical with ±a(a2 + Q)/x/a6 + /36 + y6 — Q2 multiplied by % Substitution of the values of a, (3, y gives the result ± 4£2. Therefore the negative sign must be taken. Consequently the magnitude of the transverse force is and its direction cosines are a(Q — a2)/ J a6 + (36 + y6 - Q2 , etc. 13. Directions of Equilibrium in Zero Field. — The expression for the magnitude of the transverse force shows that the cones constant transverse force. The particular case, when c = 0, is of special interest since it gives the directions of equilibrium under the action of the internal field alone. If we put z= 1, the equation is a symmetrical cubic in x2 and y2. If it be arranged in descending powers of x2, it is easy to prove that the term independent of x is positive or zero, and that the sum of the other three terms is also necessarily positive or zero. The two zero values occur together when x and y have the real values 0 and ± 1. Thus the only directions of equilibrium are the 13 lines of cubic symmetry — i.e. the three quaternary axes, the four ternary axes, and the six binary axes. 245 j2Ma2 2p5 r2(x 6 + y6 + z6) - (ic4 + ?/4 + z4)2 = c2r8 , where x2 + y2 + z2 = r2, and c is an arbitrary constant, are loci of 1904-5.] Magnetic Quality in Molecular Assemblages . 1039 It is necessary now to discriminate the directions of stable and unstable equilibrium. When in the quantities a [a4 + /34 + y4 - a2], /3 [a4 + /34 + y4 - yS2], y[a 4 + /24 + y4 - y2], we make a nearly equal to unity, f3 and y small, we find that the transverse force acts oppositely to and more strongly than the parallel force so as to increase displace- ments from the quaternary axes, which are therefore directions of unstable equilibrium. Similarly, putting a, /3, y, each nearly equal to 1/ J 3, we find that the ternary axes are directions of stable equilibrium. Lastly, putting a and /3 nearly equal to 1 / J 2, with y small, we find that the components of displacements from a binary axis in the direction of a ternary axis are aided, while displacements in the direction of a quaternary axis are resisted, by the transverse force ; and the opposite effect of the parallel force is overcome in the former case. Thus we find that, for molecules subject to random displace- ments, the direction of a ternary axis is the only direction of stable equilibrium. This result is of vital importance in any discussion of magnetic quality in a random aggregate of crystals. 14. Transverse Force under Magnetisation in Principal Planes. — Since the component of the transverse force in the direction (l, m, n) is proportional to a H + fPm -f y sn, we can find the trans- verse force when the magnetisation is in a face plane of the cubic arrangement, say the (a, /3) plane, by putting y = 0, at + fim = 0, n = 0. Writing a = cos0, we get as the value of the force where B (§ 9) is proportional to the magnetic moment per unit volume. Similarly, taking (a, /3 , y) and (l, m, n) in the plane perpen- where cos 6 = y, as the value of the force in a diagonal plane of the cubic arrangement. These values are plotted respectively in figs. 5 and 6. In fig. 5 JB sin 40, , so that a + j3 = 0 , l + m= 0 , 2a l + yn — 0 , we find JB sin 20(3 cos2 0-1), 1040 Proceedings of Royal Society of Edinburgh. [sess. the axes are parallel to edges of the cubic arrangement, and the other direction of zero transverse force is parallel to the face diagonal. In fig. 6 the vertical axis is parallel to a face diagonal, the horizontal axis is parallel to an edge, and the other direction of zero transverse force is parallel to a body diagonal of the cubic arrangement. Now, Wallerant’s expressions for the components of induc- tion (§5) lead to precisely the above results as expressions for the transverse component of induction, taken as" positive in the direction of increasing 6 , provided that we write B = - 2&R. This gives no crucial test, so far as the sign of the effect is concerned, between his expressions for the components of induc- tion and those deducible from the theory here developed ; for B is positive while k is negative. Therefore the transverse component of induction when the force is nearly coincident with a quaternary axis should, on his view, be directed from that axis — so that the induction is inclined at a greater angle to the quaternary axis than the external force is ; and the same' result follows from the present theory. For a component of the outside field is required to balance the component of internal force 1904-5.] Magnetic Quality in Molecular Assemblages. 1041 transverse to the direction of magnetisation, which component, in the neighbourhood of a quaternary axis, is directed from that axis. Similarly, on either view, the induction in the neighbour- hood of a ternary axis makes with that axis a smaller angle than the external force makes. The direction of the induction always lies within, or on the boundary of, the trihedral angle formed by the three planes which pass through pairs of co-initial lines drawn in the directions of the external force and the two nearest ternary axes. These results are in entire accordance with Weiss’s state- ment, already quoted (§ 3), that the magnetisation turns more quickly than the field when it separates from an axis of maximum magnetisation. But, when the curves in figs. 5 and 6 are compared with the corresponding curves in figs. 2 and 3, with which they should agree if Wallerant’s formulae were correct, it at once becomes evident that the characteristic flatness of the loops on the sides next the axes is absent. The curve of fig. 5 is quite symmetrical ; and the curve of fig. 6 is actually very slightly flatter on the inner side of its smaller loop than it is on the outer side, though the opposite is true of the larger loop. PROC. ROY. SOC. EDIN. — YOL. XX Y. 66 1 042 Proceedings of Royal Society of Edinburgh. [sess. Weiss does not give, in his abstract at least, any investigation of the transverse magnetisation along a ternary axis when the external force lies in a plane perpendicular to that ternary axis. The case is one of considerable interest. If we presume, con- versely, that the magnetisation lies in that plane, the condition is a 4- (3 + y = 0, from which we find a4 + /34 + y4 = 1/2. Hence (§ 9) the component of internal force in the direction of magnetisation is constant in amount. Also the factors a (Q - a2), /3 (Q - /3 2), y(Q - y2), in the expressions for the cosines of the transverse component of the internal force, become each equal to — a/3y. Therefore the transverse component is entirely along the ternary axis. Its magnitude is - 4^/3 B a/3y. Transforming to co- ordinates in the plane of magnetisation, this becomes where 0 is measured from a binary axis counter-clockwise when we look inwards along the ternary axis. Hence, as the direction of magnetisation revolves in the plane, the transverse force alternates along the ternary axis, changing sign at intervals of 60° as the direction of magnetisation passes through a binary axis. It is positive in the three sextants which contain the planes passing through the ternary axis and the three conter- minous edges of the cubic arrangement. This is simply a result of the fact that the direction of magnetisation tends to approxi- mate to the nearest ternary axis. The graph is shown in fig. 8, in which the radial scale is less than that used in figs. 5, 6, and 7, in the ratio ^2/4^3. In all cases in these figures the diagram scales must be used, for the absolute scales have been altered in the process of reproduction by photography. On Wallerant’s view, the above expression should represent the component of magnetisation along the ternary axis when the external force is perpendicular to it. 15. The Magnetisation Quartic. — The quartic surface cc4 + y^ + z* = 1 is of fundamental importance in the geometrical representation of the magnetic properties of the cubic arrangement of molecular magnets here considered. Its form is roughly that of a cube with 1904-5.] Magnetic Quality in Molecular Assemblages. 1043 rounded edges and corners, and it is everywhere concave to its centre. If a, /3, y be the direction cosines of the radius, r, drawn from the origin to a point on the surface, the direction cosines of the outwardly drawn normal at that point are a3/ Ja6 + /36 + y6, etc. ; and the direction cosines of the line drawn perpendicular to the radius vector, in the plane containing it and the normal, so that the angle between it and the outward normal is obtuse, are a(Q - a2)/ Ja6 + /36 + y6 - Q2, etc. Also, if p be the length of the perpendicular drawn from the origin to the tangent plane at the extremity of r, we have a6 + /36 + y6 = 1 /phs, and Q = 1 /r4. Thus the magnitude of the transverse force is B^/r2 -p2/2pr4:. Now - B/2r4 is the variable part of the internal force in the direction of magnetisation. Therefore, if the inwardly drawn radius vector be taken to represent this component, the subnormal will represent the transverse component. So that, on this scale, the intercept of the inwardly drawn normal by the central plane drawn perpendicular to r represents the total variable part of the internal force. 16. Magnetisation in Principal Planes. — Experimental facts to 1044 Proceedings of Royal Society of Edinburgh. [sess. be accounted for are represented in figs. 2 and 3. Weiss’s state- ment is, “ If one lays off along radii proceeding from a point the magnetisation which the matter acquires in a field of constant strength, directed along the radius considered, one obtains a surface having cubic symmetry. For the value of the field which we have used it resembles a cube with hollow faces and rounded edges. This surface has four circular sections parallel to the face of the octahedron. The value of the magnetisation varies much with the magnitude of the field. The aspect of this magnetic surface should then be very variable ; what is of more importance to note than its form in such or such a particular case, is the very complete concordance of its symmetry with that of the cubic system.” The properties of the magnetisation quartic show that, when the magnetisation is along a given radius vector, the external force must have a component, perpendicular to the radius vector, which will be representable by the subnormal on the same scale as that on which the subnormal represents the transverse component of internal force. Therefore the external force will, on that scale, be representable by a line drawn from the extremity of the subnormal to some point on the line of the radius vector. But it is quite 1904-5.] Magnetic Quality in Molecular Assemblages . 1045 impossible to tell the position of that point until the law connect- ing magnetisation with magnetising force is known. The special case in which the point lies on the quartic is of importance. For, since the internal force has then its variable part balanced by the external force, the medium is left magnetised under the constant force A (§ 9). The magnetisation is therefore constant in all directions. We then get, iu the previous notation, B.p/r = B/2r4 = 6I/r4, if we put B = 25I where b is an absolute constant. This gives I = K/bJaQ + f3Q + yQ. Now, if the medium were of such a nature that, in a given direction, I was proportional to H, this expression would also give the value of the induction under a force which was constant in all directions. But the curves of fig. 1 exclude this supposition. On the other hand, if we regard the curves B and T as normal, we see that the conditions when I is sufficiently large may be fairly well represented by the relation I — 10 = AH, where I0 is an absolute constant and A varies from one curve to another. At least the representation is probably sufficiently close to indicate the general nature of the true relation over a range of force large enough to give equal magnetisation in all directions. If, therefore, there is any reason to modify the above expression for the force under constant magnetisation, so that the left-hand side is I - I0 instead of I, we could identify A with l/bJa6 + /36 + yQ and test the resulting values of the components of magnetisation under constant force in different directions. Now the assumptions made in § 2, as a basis for the present theory, cannot hold rigidly in an assemblage of molecules obeying the postulates of the kinetic theory. They can only represent an average condition. And in view of the extremely small range of molecular directional control (§ 19), it seems quite certain that, in actual materials and at ordinary temperatures, a considerable pro- portion of molecules are free to turn under the action of the external field without reference to crystalline direction. These molecules will therefore contribute to the magnetisation a term which is in- dependent of direction. Consequently a term I0must be added, giving I = I0 + H/Va6 + /36+y6. 1046 Proceedings of Royal Society of Edinburgh. [sess. We shall therefore assume that this formula gives the value of I, at constant H, over the range corresponding to all possible directions. But it should be noted that any necessity for this particular interpretation of the meaning of I0 may disappear when an accurate expression for the magnetisation, in terms of force, is obtained. Under the conditions now postulated we have to take B = 2 b (I - 10), and the extremity of the line representing the external force lies on the quartic at all values of the force and the induction within the limits considered. Hence the component of magnetisa- tion, I - I0, parallel to the external force is H a4 + /I4 + y4 b a6 + /36 + y6’ and the component perpendicular to it is H Ja6 + /36 + y6 — Q2 b a 6 + /36 + y6 the direction cosines of the force being a = az/Ja6 + + y6, etc. In a plane parallel to a face of the cubic arrangement, these expressions become H 1 - 2a2(l - a2) H aj\ - a2(2a2 - 1 ) b 1 — 3a2(l — a2) ’ b 1 — 3a2(l — a2) ’ a =2a3/x/l-3a2(l-a2). In a plane parallel to a diagonal plane of the cubic arrangement, they are 0H 1 — 2a2 + 3a4 b 1 — 3a2(l — a2 — a4) * aj\ — a2(3a2 — 1) 1 — 3a2(l — a2 — a4)’ a =2a3/Vl-3a2(1-a2-“4)- The corresponding curves are shown in fig. 7, the full lines referring to the face plane and the dotted lines to the diagonal plane, the radii being proportional to I - I0. The flatness of the loops, which represent the transverse effect, on the sides remote from axes of maximum induction in a plane is apparent. In this respect Weiss’s experimental results are reproduced. The curve representing the longitudinal component in the face plane is very similar to Weiss’s curve of the effect in 1904-5.] Magnetic Quality in Molecular Assemblages. 1047 iron gauze ; and both curves of the longitudinal effects simulate very well his curves for magnetite (figs. 2 and 3) when a constant amount, corresponding to I0, is added to the radii. The points of difference requiring special consideration are (1) the acuteness of the angle at which the curves of the parallel component cut the axes of minimum magnetisation ; (2) the great relative size of the smaller loop of the transverse effect in the diagonal plane. With regard to (1), there seems to be little evidence in Weiss’s curves to make it certain that they should cut the axes at right angles. They might quite readily, so far as the observational points in these diagrams — with possibly one exception — indicate, be drawn so as to cut at an acute angle. In the case of the iron gauze, the angle is acute. With regard to (2), the difference is readily explainable by the existence of crystalline flaws perpendicular to the quaternary axes. The peculiar form of curve Q, fig. 1, practically necessitates this assumption. Weiss essentially made it in his theoretical discussion of the question ; he also ascribes, as we have already seen (§ 3), the great differences in the sizes of the loops in fig. 2 to the existence of flaws. Since, in the region between the binary and ternary axes in the diagonal plate, the transverse magnetisation does not depart much, in the neighbourhood of its maximum, from the quaternary axis, its magnitude must be greatly reduced by the existence of fissures perpendicular to that axis. 17. Magnetisation in Principal Planes. — The only remaining principal plane is one perpendicular to a ternary axis. Under the experimental conditions which he employed, Weiss found (§ 3) that the parallel component of magnetisation was constant, and that the transverse effect was practically zero. Yariations of the former component amounted to 0T6 per cent, of its value ; the magnitude of the latter did not lead to an obliquity of half a degree between force and magnetisation. This plane differs from the other principal planes in that the force and the magnetisation do not in general both lie in it. Two distinct cases arise, therefore, according as we regard the plane as the locus of the force or as the locus of the magnetisation. The latter case has been already considered (§ 14). When the external 1048 Proceedings of Royal Society of Edinburgh. [sess. force is always in the plane, the transverse field, parallel to the ternary axis, which arises because of the magnetisation, brings in, if unbalanced, a transverse component of magnetisation along that axis. This component alternates along the axis six times per complete revolution of the force, so that the arrangement could act as the core of a six-pole dynamo. The case of magnetisation always in the plane probably more nearly coincides with the conditions under which Weiss worked; for his disc of magnetite, though 20 mm. in diameter, was only 0*3 mm. in thickness. Self-demagnetising force would therefore act strongly, so that the resultant force was not really in the plane ; the magnetisation would practically be in it, and he constant, as TFeiss found. 18. Magnetisation and Field along Principal Axes. — From the expression (§ 16) connecting magnetisation and field, we can deduce relations connecting the magnetisations and fields in the directions of the axes of crystalline symmetry. Taking the suffixes T, B, Q to refer to the ternary, binary, and quaternary axes respectively, and taking account of I0, we get the result It + Iq = 2Ib . Using the data given by fig. 1, the numbers in the second row below are calculated values of IB corresponding to values of H given in the first row. The observed values of IB are given in the third row. 10 20 40 60 80 100 120 140 160 200 240 280 320 360 400 440 107 167 245 286 311 329 340 350 358 368 376 383 389 394 401 405 100 166 252 299 330 352 364 373 380 388 395 400 404 406 407 409 In view of the marked crystalline defects which are indicated by Weiss’s diagrams, the differences between observed and calculated values do not seem to he excessive. Yet, apart from other facts, the very remarkable agreement between calculation and experi- ment, in the case of Wallerant’s formula (§ 5), would settle the question as between his formula and that given in § 16 in favour of his. On the other hand, as already pointed out (§ 14), the non-correspondence of the shape of the loops in figs. 5 and 6 to the shape of the observed loops, figs. 2 and 3, and the correspondence 1904-5.] Magnetic Quality in Molecular Assemblages. 1049 of the shape of those deduced from the present theory, fig. 7, with the observed shape, seems to be quite decisive in favour of the view here taken. The existence of the crossing point in the three curves, fig. 1, which is not present in all cases, and the apparently abnormal shape of the curve Q, must, if they are really abnormal conditions, have an effect tending to bring about the coincidence. On any view, the coincidence is remarkable, and, in conjunction with the apparent absence of transverse magnetisation, or variation of parallel magnetisation, in the case of the field lying in a plane perpendicular to a ternary axis (§ 17), fully justified Wallerant in connecting the quantities as he did. 19. Condition at a Boundary. — Residual Magnetisation. — The expressions representing the force due to the assemblage of magnets show that the magnetic effect of a given distribution of molecular magnets is, at any given point, external or internal, proportional to the magnetic moment per unit volume. There- fore, when a bounding surface exists, the effect of the magnetisa- tion is representable in the usual way as being due to an imaginary surface distribution of magnetism. Yet it is necessary, on the molecular theory, to obtain a definite view of the mechanism of self-demagnetisation, residual magnetisation, and hysteresis. The existence of coercive force, in the case of magnetisation of an unbounded assemblage magnetised along a ternary axis, has already been found (§ 13). In such an assemblage, magnetised so, at the absolute zero of temperature, there would be no demagnetisa- tion on withdrawal of the external field if we suppose the magnets to have constant magnetic moment. But, when molecular motions are taken into account, the magnetic moment would be appreciably smaller unless infinite external field acted. Considerable residual magnetisation would be left, since self-demagnetisation from sur- face effects do not take place in the unbounded medium. In the case of magnetisation along a binary axis in an unbounded medium, withdrawal of the external field would be followed by alignment of the molecules along the two nearest ternary axes. The effective component along the binary axis is therefore reduced to two-thirds of its original value, apart from possible effects of molecular motions. In the case of magnetisation along a quaternary axis, 1050 Proceedings of Royal Society of Edinburgh. [sess. withdrawal of the field would be followed by alignment along the ternary axes, so that the residual magnetisation would be only one- third of the original magnetisation even if there were no molecular motion. The effect of molecular motions is to make the residual magnetisation less than the original magnetisation along a ternary axis, for these motions are controlled by smaller magnetic force after the external field is removed. The tendency is similar in the other cases ; but the fact that the internal field is stronger along the ternary axes, to which the molecules set from the binary or quaternary axes, works oppositely. It is probable that the large value of the reduction factors, 1/3 and 2/3 respectively, will ensure that the magnitudes of the residual effects are in decreasing order from the ternary to the quaternary axes. Because of the entire withdrawal of the magnetisation I0, which takes place under the action of an external field on groups of molecules whose constituents are randomly conditioned because of heat motions, the actual residual magnetisations will be uniformly less than the above considerations indicate. Weiss’s curves T' and B', fig. 1, verify these conclusions, but the curve Q' is in conflict with them. These curves of the residual effects indicate ver}^ strongly the abnormal nature of magnetisation parallel to a quaternary axis. For the binary effect is not inter- mediate between the ternary and quaternary effects as it is in the other curves ; on the contrary, the usual conditions are so entirely departed from that Q' lies on the remote side of T\ Now the existence of flaws perpendicular to the quaternary axes might naturally be expected to lessen, not to raise, the residual magnetisation along these axes; for large demagnetising forces might be expected to exist because of the effective intro- duction of boundaries. As a matter of fact, the present theory leads to the result that the effect of such flaws may really be to raise the residual magnetisation along a quaternary axis. To prove this we have first to determine the stable directions of magnetisation, under internal force, in the neighbourhood of a boundary which we assume to be a plane perpendicular to a quaternary axis. In the evaluation of the constants involved in the expressions for the parallel and transverse components of internal force we have now to consider the action of molecules lying in, or on one side of, the 1904-5.] Magnetic Quality in Molecular Assemblages. 1051 bounding plane. Thus, in the data given in § 22, we have to omit the reckoning for negative values of v. We thus find, for the parallel component on a magnet at the boundary, the quantity V.^f![18-6(a4 + 13* + y *) - 2] approximately. This is always positive. In the same way the transverse component is found to be ^~“21 8 -6(a« + + / - Q2)1/2 . The longitudinal effect has therefore the same sign as it had in the interior, while the sign of the transverse effect is reversed. Thus the turning moment is, in the neighbourhood of a quaternary axis, always directed towards that axis, which is therefore a direction of stable equilibrium. In the neighbourhood of a ternary axis, the moment of the transverse component overcomes that of the parallel component, so that this axis is one of unstable magnetisation. In fact, the conditions of stability are the reverse of those which hold in the interior. How the values of H(2p)_5/2 and HA.4(2p)-9/2, given in § 22, show that molecular control in the interior is effectively determined by very near neighbours. The effect of those at a greater distance than seven times the least distance between molecules in the postulated homogeneous arrangement does not seem to be capable of making serious change in the values of the constants given above. If it does not, it follows that flaws, of thickness far smaller than the range of molecular forces, effectively introduce boundaries. Consequently, so far as the terms now under dis- cussion go, a considerable amount of magnetisation parallel to a quaternary axis may be retained. And this effect of the flaws tends also to diminish the residual internal magnetisation parallel to the binary and the ternary axes. In the case of a cubic crystal, on removal of the magnetising force, the tendency is to retain on the whole magnetisation along the ternary axis most nearly coincident with the original direction of magnetisation. At a surface of the cube, on the other hand, the magnetisation tends to be normal ; and the change from the one condition to the other takes place in an extremely thin film. 1052 Proceedings of Royal Society of Edinburgh. [sess. Thus, apart from the action of terms of different order from those now under consideration, the resultant magnetisation would he determined mainly by the internal part. But it is impossible to leave out of account in this connection the effects of the first terms in the expressions for the components of force (§ 6). These terms, being independent of the ratio a/r9 are the terms which give rise to the action at distant external points, and also to the self-demagnetising action of the so-called surface magnetisation. The term 2x/2M/p3^-(3 cos2 0 - l)(2p)~3/2 becomes 2^2M/p3-S- [3v2 - N(2p)](2p)_5/2, if we put y=l, so that the magnetisation is along a quaternary axis. Now, in the evaluation of these sums from the data in § 22, the convergence of terms is not nearly so rapid as it was in the case of the expressions which involved the ratio a2 Ip2 ; so that the approximations to the values of the sums are not so exact as in the former cases. As a test, we may note that the sum of those terms in ^ which involve v2 should be equal to the sum of the terms which do not involve v when the summation is carried to infinite values of v. When it is carried to the values v— ± 10, as in § 22, the value of the former sum is 19 '75 and the value of the latter is 14-54. The difference is not so excessive as to make it likely that results deduced from the limited summation would be reversed when the summation was extended farther. When the limited summation is taken for zero and positive values of v only, the whole term is found to be positive, its value being T39 M/p3. And a similar treatment of the term fi^/lM/p3-^- sin 0 cos Q( 2jp)~3/2 shows that this transverse component of force is practically zero so long as the angular displacement of the direction of magnetisation from the quaternary axis is so small that its square can be neglected. It therefore seems certain that magnetisation along a quaternary axis which is normal to a boundary possesses a fair amount of stability. It is needless to give a more full discussion of self-demagnetisa- tion relative to this orientation of the boundary alone. Full treatment would be somewhat lengthy, and may be deferred mean- while. But in support of the conclusion just reached, it should be noted that Weiss observed an obliquity between the external field and the direction of magnetisation, which, on allowance for 1904-5.] Magnetic Quality in Molecular Assemblages. 1053 the effect of self-demagnetisation, amounted to about 20°. And the theoretical results, as exhibited in fig. 7, indicate a possible obliquity of about 31°, which is subject to considerable reduction because of the magnetisation I0. Thus the internal field is quite comparable with the external field, and is therefore still more comparable with — indeed, may possibly exceed — the field which is due to the existence of boundaries. 20. Estimate of Size of Molecular Magnets and of Molecular Susceptibility. — We can now test directly the validity of the assumption (§ 2) that the semi-length of a molecular magnet bears to the average distance between molecules a ratio which is of such magnitude that terms, involving the fourth and higher powers, in the expressions for the components of force, can be neglected. The magnitude of the transverse component of force in the diagonal plane is (§ 1 4) given by If we take 16° as the value of 0 corresponding to maximum obliquity between the external field and the direction of magnetisa- tion, we get F = 0*237B. And if we take Weiss’s value, 20°, for the angle of maximum obliquity, we find that the external field, H, is practically three times the internal transverse component. by the formula of § 12 and the data of § 22. Now, in Weiss’s observations, the value of H was 353 c.g.s. units, and the value of the magnetisation, I, may be taken about 400 c.g.s. units. So, since in this closest-packed homogeneous arrangement of centres the number of molecules per unit volume is J2 /p3, we get MN/2/p3 = I, and p2/a2 = 21. This gives practically p = 4*6a. The first of the neglected terms, though appreciable, could not make any fundamental change in the results. The absolute value obtained for the ratio is probably of little importance ; consistency of order is all that can be looked for. F = JB sin 20(3 cos 20 - 1) . Thus H = 0*712 B 1054 Proceedings of Royal Society of Edinburgh. [sess. From the above expression we can obtain also an estimate of the value of p. The ratio M/H is the molecular susceptibility. Consistent determinations of the value of that quantity, obtained from observations on solutions of different salts of iron, have been made by Liebknecht and Wills (Du Bois, Rapports, Oongres International de Physique, tome ii., 1900). The mean value is 0*014, the mass of a hydrogen atom being taken as unity. To obtain the value of this mass independently of any estimate of the number of molecules contained in unit volume, we may postulate that the atomic charge is identical with the ionic charge. From the magnitude of this quantity, together with the value of the electro-chemical equivalent of hydrogen, we find that the mass of the hydrogen atom is 1*2(10)-24 grammes. Multiplying 0*042 by this number, we obtain 5(1 0)-26 as the absolute value of the molecular susceptibility in a molecule containing three atoms of iron. If, now, disregarding the fact that the susceptibility of magnetite is not constant, we identify the number just obtained with the ratio M/H, we find p = 3(10)-9, a result not greatly different from the values usually given for molecular distance. If, on the other hand, we adopt the usual estimate of molecular distance, we obtain a value for the molecular susceptibility of magnetite which is about twenty times greater than that found above from observations on dissolved salts of iron. This is by no means an impossible result. 21. Conclusions. — The following conclusions may, I think, be drawn from the foregoing results. (1) The theory of molecular magnetism, when applied to magnetic crystals of the cubic class, leads to results which are not in discordance with any observed results, but which, on the contrary, are in general agreement with observation. (2) Wallerant’s formula is correct in mathematical form, but should be interpreted with reference to internal force instead of with reference to magnetisation. (3) It is possible that parallel investigations of the properties of other assemblages having cubic symmetry may lead to a discrimina- tion of actual molecular arrangement. 1904-5.] Magnetic Quality in Molecular Assemblages. 1055 (4) The results obtained may serve as a basis for the treatment of magnetic quality in a medium consisting of randomly arranged crystalline particles. (5) The Boscovichian theory of the constitution of matter is capable of extension so as to include applications to magnetic properties. 22. Approximate Evaluation of Constants. — The data given in Tables I. and IL, below, serve for the calculation of the leading terms in the infinite sums which appear in the preceding work. The columns headed v = 0, 2, 4, etc., give the values of 2 p corre- sponding to the given values of X, p, v. Table I. X P N 2-m4 V=0 v= 2 v=4 v = 6 v— 8 v= 10 0 0 2 0 [0] 4 16 36 64 100 1 1 4 4 2 6 18 38 66 0 2 4 32 4 8 20 40 68 2 2 4 64 8 12 24 44 72 3 1 8 328 10 14 26 46 74 0 4 4 512 16 20 32 52 80 3 3 4 324 18 22 34 54 82 4 2 8 1088 20 24 36 56 84 5 1 8 2504 26 30 42 62 90 4 4 4 1024 32 36 48 68 96 5 3 8 2824 34 38 50 70 98 0 6 4 2592 36 40 52 j 72 100 6 2 8 5248 40 44 56 76 5 5 4 2500 50 54 66 86 7 1 8 9608 50 54 66 86 6 4 8 6208 52 56 68 88 7 3 8 9928 58 62 74 94 0 8 4 8192 64 68 80 100 8 2 8 16448 68 72 84 6 6 4 5184 72 76 88 7 5 8 12104 74 78 90 8 4 8 17408 80 84 96 9 1 8 26248 82 86 98 9 3 8 26608 90 94 7 7 i 4 9604 98 In the particular case v = 0, p = 0, we of course take N = 0. 1056 Proceedings of Royal Society of Edinburgh. [sess. Table II. A ix N 2-NA4 V=1 v — 3 v = 5 v = 7 v=9 0 1 4 2 2 10 26 50 82 2 1 8 68 6 14 30 54 86 0 3 4 162 10 18 34 58 90 3 2 8 388 14 22 38 62 94 4 1 8 1028 18 26 42 66 98 0 5 4 1250 26 34 50 74 4 3 8 1348 26 34 50 74 5 2 8 2564 30 38 54 78 6 1 8 5188 38 46 62 86 5 4 8 3524 42 50 66 90 6 3 8 5508 46 54 70 94 0 7 4 4802 50 58' 74 98 7 2 8 9668 54 62 78 6 5 8 7684 62 70 86 8 1 8 16388 66 74 90 7 4 8 10628 66 74 90 8 3 8 16708 74 82 98 0 9 4 13122 82 90 9 2 8 26308 86 94 7 6 8 14788 86 94 8 5 8 18884 90 98 9 4 8 27268 98 It is convenient to pick out from these tables the values of N corresponding to given values of v andp, say We thus find q]St3 = 0, 0^6 = 0, etc., which we may briefly express by the notation 0N3, 6, ... =0. In this way we obtain 1904-5.] Magnetic Quality in Molecular Assemblages. 1057 Table III. 0^0, 3, 6, 7, 11, 12, 14, 15, 19, 21, 22, 23, 24, 27, 28, 30, 31, 33, 35, 38, 39, 42, 43, 44, 46, 47, 48 = 0 . 1^2, 4, 6, 8, 10, 11, 12, 14, 16, 17, 18, 20, 22, 24, 26, 28, 29, 30, 32, 34, 35, 36, 38, 39, 40, 42, 44, 46, 47, 48 = 2^5, s, 9, 13, 14, 16, 17, 21, 23, 24, 25, 26, 29, 30, 32, 33, 35, 37, 40, 41, 44, 45, 46, 48 = 0 . 3^6, 8, 10, 12, 14, 15, 16. 18, 20, 21, 22, 24, 26, 28, 30, 32. 33, 34, 36, 38, 39, 40, 42, 43, 44, 46, 48 = 0 . 4^11, 14, 15, 19, 20, 22, 23, 27, 29, 30, 31, 32, 35, 36, 38, 39, 41, 43, 46, 47 = 0 . 5N14, 16, 18, 20, 22, 23, 24, 26, 28, 29, 30, 32, 34, 36, 38, 40, 41, 42, 44, 46, 47, 48 = 0 . 6^21, 24, 25, 29, 30, 32, 33, 37, 39, 40, 41, 42, 45, 46, 48, 49 = 0 . ) j ; 7N 26, 28, 30, 32, 34, 35, 36, 38, 40, 4l, 42, 44, 46, 48 = 0 . 8^35, 38, 39, 43, 44, 46, 47 — 0 . 9N42, 44, 46,48 = 0 . 2^2 = 4^8 = 6^18 = 8^32 = 10^50 = 0^1,2,4,8,9,16,18,25,32,36,49,50 = I • 1-N”i? 5, 13, 25, 41 = 4. 2^3, 4, 6, 10, 11, 18, 20, 27, 34, 38 = 4 . 3^5,9,17,29,45 = 4 . 4^9, 10, 12, 16, 17, 24, 26, 33, 40, 44 = 4 . 5^13^7,25,37 = 4. Nl9, 20, 22, 26, 27, 34, 36, 43, 50 = 4 . 7^25, 29, 37, 49 = 4 . ^33, 34, 36,40,41,48,50 = 4. 9^41, 45 = 4 . 0^5 , 10, 13, 17, 20, 25, 26, 29, 34, 37, 40, 41, 45, 50 = 8 . 1^3, 7, 9, 13, 15, 19, 21, 23, 27, 31, 33, 37, 43, 45, 49 — 8 2^7, 12, 15, 19, 22, 27, 28, 31, 36, 39, 42, 43, 47 = 8 . 3-^7, 11, 13, 17, 19, 23, 25, 27, 31, 35, 37, 41, 47, 49 = 8. 4^13, 18, 21, 25, 28, 33, 34, 37, 42, 45, 48, 49 = 8 . 5^i5} 19, 21, 25, 27, 31, 33, 35, 39, 42, 45, 49 = 8 . 6^23, 28, 31, 35, 38, 43, 44, 47 = 8 . 7^27,31,33,37,39,43,45,47 = 8. 8^37,42,45,49 = 8 . 1^43,47,49 = 8 . The numbers which are underlined in the values for FT — 8 indicate a double occurrence. From these data we can now *=10 calculate the value of 2'NA.4(2p)_9/2. Values of the parts of this sum corresponding to v = 0, 1, 2, etc. are given in successive columns of the first half of the following table. The numbers in successive rows correspond to the different values of p. The *=10 second half of the table gives the similar data for 2*N(2^)_5/2. *=o PROC. ROY. SOC. EDIN. — VOL. XXV. 67 1058 Proceedings of Royal Society of Edinburgh. Table IY. i/=0 V = 1 v=2 V- =3 V =4 v=5 v=6 II -a v=8 0-17680 0*08841 0-00126 0-00006 000001 0*00002 o-ooooi o-ooooi 0-00001 0-06247 2141 276 47 4 2 1 1 1 552 512 19 36 4 3 1 1 1087 270 230 35 14 5 1 1 0*00002 195 231 72 44 9 5 2 1 73 111 29 33 4 4 1 1 152 58 67 20 11 4 1 1 107 40 56 17 12 2 1 17 17 10 7 3 3 2 0-00007 36 18 22 9 6 2 2 26 10 16 6 5 3 1 32 15 21 8 7 2 1 25 7 19 4 8 4 1 12 18 8 10 4 2 12 6 9 4 4 0*00016 6 3 5 2 2 0-00043 9 8 7 5 4 2 3 2 2 1 5 3 4 1 5 4 0-00295 2 6 0-12312 5 4 4 0-00136 1 4 0-01081 0*26245 v=0 V = 1 v=2 V =3 V- :4 1! v—6 v=7 II 00 v=9 0-70730 0-70730 0-06248 0-01265 0*00195 0-00080 0-00026 0-00023 0-00006 0-00007 1250 9069 4535 1091 291 162 45 36 11 12 2210 1265 2210 291 222 59 40 16 10 5 2530 1091 802 352 142 90 31 26 9 9 391 589 1091 232 232 70 56 23 17 8 291 1 348 224 178 69 68 91 25 7 447 162 176 90 59 37 19 15 7 0-00041 232 90 284 56 103 26 34 12 12 69 70 162 45 70 23 26 5 10 120 56 51 37 25 20 10 9 4 51 23 90 16 45 8 20 4 8 79 36 40 26 21 15 S 1 4 68 26 62 20 34 12 16 0-00194 41 46 56 34 34 21 17 0-00105 31 17 21 13 21 8 11 11 7 26 5 17 — 9 i 21 24 11 18 7 0-00699 4 9 10 18 8 12 17 8 8 — 6 0-00392 14 15 0-03777 10 13 0-83667 12 9 i/=10 10 12 8 4 9 12 0-01632 0-00002 0-78651 For negative values of v the numbers are necessarily the same as for positive values. 1904-5.] Magnetic Quality in Molecular Assemblages. 1059 The following numbers give the values of S-NV2(2p) 5/2 from v = 1 to v = 10 : — 0-83667, 0-64640, 0-33993, 0-26112, 0*17475, 0-14112, 0*09506, 0-06721, 0-03321, 0*00200. v=10 The next table gives the values of the parts of 2 •N(2p)-3/2. v=0 Table V. v = 0 v=l v = 2 v = S V — 4: v = 5 v=6 v=7 v = 8 v=9 i/ = 10 1-41460 1-41460 0-24992 012650 0-03120 0-02080 0-00936 0-01150 0-00384 0-00574 0-00200 0-05000 54414 27210 15274 5238 4860 1710 1944 726 1032 •17680 12650 17680 5238 4440 2006 1600 928 680 450 25300 15274 9624 7744 3408 3420 1364 1612 648 846 6256 10602 15274 6032 6032 2940 2576 1518 1258 784 5238 9048 4480 6052 2208 3400 1092 1850 560 8940 4860 3872 3420 2006 1998 1026 1170 574 0-03686 6032 3420 6816 2576 3708 1612 1904 1032 1008 2208 2940 4860 2250 2940 1518 1612 450 900 4080 2576 1836 1998 1150 1400 680 846 384 1836 1150 3420 928 2250 592 1400 392 784 3160 1944 1600 1612 1092 1170 648 400 3400 1612 2728 1400 1904 1032 1216 0-12892 2132 3036 3024 2516 2244 1890 1462 0-08306 1798 1258 1176 1066 1428 784 968 704 574 1612 450 1258 846 1428 2064 748 1692 560 0-30702 400 648 900 1296 784 1008 — 1258 784 608 — 528 0-21430 1120 1170 0-73682 900 1066 2-70566 1008 864 900 1032 784 392 846 1200 — 0-49070 1-36912 2-43236 The calculations have been carried out to five decimal places in the earlier tables so as to have as little error as possible in Table V. and the preceding set of numbers, where large factors are used to multiply the smaller numbers of the earlier tables. Except in these earlier tables, none of the figures beyond the first two after the decimal point are probably of any value. ( Issued separately November 20, 1905. ) 1060 Proceedings of Royal Society of Edinburgh. [suss. Deep Sea Ship-Waves. {Continued from Proc. R.S.E., January 23, 1905.) By Lord Kelvin. (Read July 17, 1905.) § 65. Referring to § 63, we must, for the present, as time presses, leave detailed interpretation of the curves of fig. 17 : merely remarking that, according to § 44, if 3 = 0, (which means that J is an integer), the disturbance, d, is infinitely great; of which the dynamical meaning is clear in (70) of § 39. § 66. Let us now find the depression of the water at distance x from the origin, when the disturbance is due to a single forcive, expressed by the formula * <95>’ travelling uniformly with any velocity v. If this forcive were applied steadily to the surface of water at rest it would produce a steady depression — Tl(x), as we are taking the density of the water, unity. Thus the forcive II (x) would shape the water to an infinitely long trough, of cross-section shown in fig. 25, representing z = Jcb2/(x2 + b2) on the scale of k = 10 cm. and 5 = 1 cm. 1 fx Taking — / dx of (95) we find tan_1(a;/&).5&. Hence the area 9 J o of fig. 25 is 2 tan-1 S.bJc, or n rbk, and the total area of the diagram extended to infinity on each side is 7 rbk. Hence the area of fig. 25 is , or '92, of the total area. This total area, 7 rbk, I 180 call, for brevity, the forcive area ; and 7 rb, I call the mean breadth of the forcive area. The breadth of the forcive where z = *8 k (as shown by the dotted line B B in the diagram) is b. § 67. Now let the forcive be suddenly set in motion, and kept moving uniformly with any velocity v in the rightward direction of our diagrams. This will produce a great commotion, settling * What is denoted by x in this and following expressions, is the (x - vt ) of §§ 36 . . . . 40 ; the origin of co-ordinates being now fixed relatively to the travelling forcive. 1904-5.] Lord Kelvin on Deep Sea, Ship- Waves. 1061 1062 Proceedings of Poyal Society of Edinburgh. [sess. ultimately into more and more nearly steady motion through greater and greater distances from O. The investigation of §§ 1-10 above (Feb. 1904), and particularly the results described in §§ 5, 6, and illustrated in figs. 2, 3, show that in our present case the commotion, however violent, even if including splashes ,* divides itself into two parts which travel away in the two direc- tions from 0, ultimately at wave-speed increasing in proportion to square root of distance (according to the law of falling bodies) ; and leaving in their rears, through ever broadening spaces, what would be more and more nearly absolute quiescence if the forcive were suddenly to cease after having acted for any time, long or short. § 68. But if the forcive continues acting, and travelling right- wards with constant speed, ?>, according to § 67, the travelling away of the two parts of the initial commotion in the two directions from 0 (itself merely a point of reference, moving uniformly rightwards), leaves the water, as shown by fig. 26, in a state of more and more nearly quite steady motion through an ever broadening space on the rear side of 0, and through a small space in advance of O ; provided certain moderating conditions are fulfilled in respect to k, b, v. § 69. To illustrate and prove § 68 ; first suppose v infinitely small. The water will be infinitely little disturbed from the static forcive-curve shown in fig. 25, and described in § 66. Small enough velocities will make very small disturbance with any finite value of k/b. § 70. But now go to the other extreme and let v be very great. It is clear, on dynamical principles without calculation, that v may be great enough to make but very little disturbance of the water-surface, however steep be the static forcive curve. A “skipping stone” and a ricochetting cannon shot, illustrate the application of the same dynamical principle in three-dimensional hydrokinetics. By mathematical calculation (§ 79 below) we shall see that, when v is great enough, we have (97), A * However sudden and great the commotion is, the motion of the liquid is, and continues to be, irrotational throughout. _2'812 1063 1904-5.] Lord Kelvin on Deep Sea Ship-Waves. Fig. 26. d(a) - \h sin 1064 Proceedings of Royal Society of Edinburgh. [sess. where h denotes the height of crests above mean water-level in the train of sinusoidal free waves left in the rear of the travelling forcive ; A denotes the area of the forcive curve (fig. 25) ; being given in § 66 by the equation A = irbk (98): and A, given [§ 39, (71)] by A = 27 TvPJg (99), denotes the wave-length of free waves travelling with velocity v. § 71. A very important theorem in respect to ship-waves is expressed by (97). Without calculation we see that, if A is very great in comparison with 7 rb, (the “ mean breadth ” of the forcive curve according to § 66), h must be simply proportional to A, for different forcives travelling at the same speed. This we see because, for the same value of b, h/k is the same, and because superposition of different forcives within any breadth small in com- parison with A, gives for h the sum of the values which they would give separately. Farther without calculation, we can see, by imagining altered the scale of our diagrams, that hX/A must be constant. But without calculation I do not see how we could find the factor 47t of (97), as in § 79 below. § 72. The effect of the condition prescribed in § 71 is illustrated and explained by considering cases in which it is not fulfilled. For example, let two forcives be superposed with their middles at distance JA ; they will give h = 0, that is to say no train of waves. The displaced water surface for this case is represented in fig. 27. Or let their distance be JA or §A ; the two will give the same value of h as that given by one only. Or let the two be at distance A ; they will make h twice as great as one forcive makes it. § 73. In figs. 26, 27, 29, 30, representing results of the calcula- tions of §§ 78, 79 below, the abscissas are all marked according to wave-length. The scale of ordinates corresponds, in each of figs. 26, 27, 29, to k = 243’89, and irb = 1*0251. 10-3. A. This makes by (98) and (97) A = JA, and Ii — tt. Fig. 30 represents the curve of fig. 29 at the maximum, in the neighbourhood, of O, on a greatly magnified scale: about 1720 times for the abscissas, and 39 times for the ordinates. § 74. Fig. 26 shows, on the right-hand side, the water slightly 1904-5.] Lord Kelvin on Deep Sea Ship-Waves. 1065 heaped up in front of the travelling forcive, which is a distribution of downward pressure whose middle is at 0. On the left side of 0, we see the water surface not differing perceptibly from a curve of sines beyond half a wave-length rearwards from O. A small portion of a wave-length of true curve of sines in the diagram shows how little the water’s surface differs from the curve of sines at even so small a distance from 0 as a quarter wave-length. It must be remembered that in reality the water surface is everywhere very nearly level ; and in considering, as we shall have to do later, the work done by the forcive, we must interpret properly the enormous exaggeration of slopes shown in the diagrams. It is interesting to remark that the static depression , h , which the forcive if at rest would produce, is about 87 times the elevation actually produced above 0 by the forcive, travelling at the speed at which free waves, of the wave-length shown in the diagrams, travel. It is interesting also to remark that the limita- tion to very small slopes is not binding on the static forcive curve. Thus for example, a distribution of static pressure, everywhere perpendicular to the free surface, producing static depression exactly agreeing with fig. 25, would, if caused to travel at a spefed for which the free-wave-length is very large in comparison with b, produce a disturbance, represented by fig. 26 with waves of moderate slopes : and, as said in § 69 above, would produce no disturbance at all if the speed of travelling were infinitely great. § 75. Fig. 27 is interesting as showing the waveless disturbance produced by two equal and similar forcives with their middles at distance equal to half the wave-length. This disturbance is essentially symmetrical in front and rear of the middle between the two forcives. By dynamical considerations of the equilibrium of downward pressures, we see that the area of fig. 27 (portion above line of abscissas being reckoned as negative) must be exactly equal to 2 A, the sum of the areas of the two forcives, representing their integral amount of downward pressure. This area, being 2 t rbh, with the numerical data of § 73, is numerically JA, ; that is to $ay a rectangle whose length is JA., and breadth the unit of our vertical scale. Approximate mensuration, with a very rough estimate of the area beyond the range of the diagram, continued to infinity on the two sides, verifies this conclusion. 2-845 1066 Proceedings of Royal Society of Edinburgh. I I t I I I lc i id Fig. 27. d(a-- +d # + 7 1904-5.] Lord Kelvin on Deep Sea Ship-Waves. 1067 § 76. Fig. 28 is designed on the same plan as fig. 27 but with eleven half-wave-lengths as the distance between the two forcives instead of one half- wave-length. Like fig. 27, it is symmetrical on the two sides of the middle of the diagram ; hut, instead of being waveless, as is fig. 27, it shows four and a half waves, all very approximately sinusoidal, with two depressional halves of waves at their two ends, and elevations coming asymptotically to zero beyond the two ends of the diagram. The curve represented by fig. 26 is very accurately the right-hand extreme of fig. 28 : and the same figure, turned right to left, is the left-hand extreme of fig. 28. If we commence with the water wholly at rest, and start the forcives at the proper speed, with force gradually (or somewhat suddenly) increasing up to the prescribed amount, the motion produced will be that represented by fig. 28, with, superimposed upon it, a disturbance quickly disappearing in ever lengthening waves of diminishing amplitude, travelling away in both directions from our field. If now, with the regular regime represented by fig. 28, we suddenly cease to apply the forcives, we have left a free procession of four and a half very approximately sinusoidal waves, between a front and a rear deviating from sinusoidality as shown in the diagram. From the instant of being left free, the front of this procession and its rear will rapidly become modified ; while for three periods the central part of the procession will have travelled three wave-lengths, with very little deviation from sinu- soidality. But, after four or five periods from the instant of being left free, the whole procession will have got into confusion. After twenty or thirty or forty periods, the water will be sensibly quiescent, not only through the whole space where the procession was, but through the whole space over which it would have travelled if its front and rear had been kept guarded by the continued action of the two travelling forcives. At no time after the cessation of the forcives can we reasonably or conveniently assign a “ group velocity ” to the group or procession of waves with which we are concerned. A prevalent idea is, I believe, that such a group of deep sea waves could be regarded as travelling with half the “ wave-velocity ” of waves of the length given in the original group. In § 30 above, reasons are given for accepting the theory of “ group velocity ” only in the case of mutually supporting 1068 Proceedings of Royal Society of Edinburgh. [ SESS. 1904-5.] Lord Kelvin on Deep Sea Ship-Waves. 1069 groups, given by Stokes in his Smith’s Prize examination paper, published in the Cambridge University Calendar for 1876 : and for rejecting it for the case of any single group of waves. In reality the front of a group, left to itself, travels with accelerated velocity exceeding the velocity of periodic waves of the given wave-length, instead of with half that velocity. § 77. Fig. 29 shows the steady motion , symmetrical in front and rear of a single travelling forcive, which is a solution of our problem; but it is an unstable solution (as probably are the solutions of the problem of § 45 above, shown in figs. 13, 14, 15). If any large finite portion of the water is given in motion according to fig. 29, say, for example, 50 wave-lengths preceding 0 (the forcive) and 50 wave-lengths following 0, the front of the whole procession, to the right of O, will become dissipated into non-periodic waves travelling rightwards and leftwards with increasing wave-lengths and increasing velocities ; and the approximately steady periodic portion of it will shrink backwards relatively to the forcive. Thus before the forcive has travelled fifty wave-lengths, the periodic waves in front of it are all gone : but there is still irregular disturbance both before and behind it. After the forcive has travelled a hundred wave-lengths, the whole motion in advance of it, and the motion for perhaps 30 wave-lengths or more in its rear, will have settled to nearly the condition represented by fig. 26, in which there is a small regular elevation in advance of the forgive, and a regular train of approximately sinusoidal waves in its rear ; these waves being of double the wave-height given originally. This motion, as said above in § 68, will go on, leaving behind the forcive a train of steady periodic waves, increasing in number ; and behind these an irregular train of waves, shorter and shorter, and less and less high the farther rearward we look for them (see R in fig. 10 of £§ 26, 27 above). It is an interesting, but not at all an easy problem, to investigate the extreme rear (with practically motionless water behind it) of the train of waves in the wake of a forcive travelling uniformly for ever. I hope to return to this subject when we come to consider the work done by the travelling forcive. § 78. Pass now to the investigation of the formulas by the calculation of which figs. 26, 27, 28, 29, 30 have been drawn, and 1070 Proceedings of Royal Society of Edinburgh. 10-4X 1904-5.] Lord Kelvin on Deep Sea Ship-Waves . 1071 Fig- 30- d(x) - d(0). 1072 Proceedings of Royal Society of Edinburgh. [sess. the theorem of (97) proved. Go back to the problem of § 41 above: but instead of taking e= *9, as in§§ 46-61, take e = 1 — 10-4* and c= 1/(2/+ 1). By (86) and (87) of § 45 we have the following solution d= tf+ $ (100) where J= { \ sin (./ + 1)0 tan"1 - £ cos ( / + \)6 log 1 + 2 >/e cos +_e 1 ( , 01 < 1 - e " 1 - 2 Je cos -ktf + e ) and ^=1 • 3 2; + 1 + 2/ e cos 0 e2 cos 20 , .. 1 + 9* + Be^cos jO Je cos J0 + e (102). Fig. 29 has been calculated by putting 0— — . and A j + h1 taking j = 20. The explanation is that, as we shall see by (78) of § 43 above, (100), (101), (102), express the water disturbance due to an infinite row of forcives at consecutive distances each equal to (20|r) A ; the expression for each forcive being cbafeir (103), b2 + (x - naf where n is zero or any positive or negative integer ; and by (79) we have 20-5. lO"4. A b = 27 T (104). Thus we see that the pressure at O due to each of the forcives next to O, on the two sides, is l/{ 1 +(27r.l04)2} of the pressure due to the forcive whose centre is O. Thus we see that the pressures due to all the forcives, except the last mentioned, may be neglected through several wave-lengths on each side of O : and we conclude that (100), (101), (102) express, to a very high degree of approxi- mation, the disturbance produced in the water by the single travelling forcive whose centre is at O. §79. To prove (97) take 0=180° in (100), (101), (102); we thus find ( - l)>d(180->*y { tar' 1 -£ + £ + « - e)~> ■ } (105). Instead now of taking e= 1 - 10-4, as we took in our calculations 1073 1904-5.] Lord Kelvin on Deep Sea Ship-Waves. for d(0), let us now take e = 1 . (-iyd(i8o°)=^ + i-J+i . This reduces (105) to , (-ly-* 1 1 (-iy + 2/ — 1 2 2/+1 (106). Lastly take j an infinitely great odd or even integer, and we find d(180°) = (-iy- £ (107). Kow fig. 26 is, as we have seen, found by superimposing on the motion represented by fig. 29 an infinite train of periodic waves represented by - Jh . sin 27 TX and therefore h = 7r, which proves (97). § 80. To pass now from the two-dimensional problem of canal- ship-waves to the three-dimensional problem of sea-ship-waves, we shall use a synthetic method given by Rayleigh at the end of his paper on “ The form of standing waves on the surface of running water,” communicated to the London Mathematical Society in December 1883.* In an infinite plane expanse of water, consider two or more forcives, such as that represented by (95) of § 66, with their horizontal medial generating lines in different directions through one point O, travelling with uniform velocity, v, in any direction. The superposition of these forcives, and of the disturb- ances of the water which they produce, each calculated by an application of (100), (101), (102), gives us the solution of a three- dimensional wave problem ; which becomes the ship-wave-problem if we make the constituents infinitely small and infinitely numerous. Rayleigh took each constituent forcive as confined to an infinitely narrow space, and combated the consequent troublesome infinity by introducing a resistance to be annulled in interpretation of results for points not infinitely near to O. I escape from the trouble in the two-dimensional system of waves, by taking (95) to express the distribution of pressure in the forcive, and making b as small as we please. Thus, as indicated in §§ 79, 73, 76, by taking b = 10^A./(104.7t) we calculated a finite value for d(0). But for values of x, considerably greater than half a wave-length, we were able to simplify the calculations by taking 6=0. * Proc. L.M.S., 1883 : republished in Bayleigh’s Scientific Papers , vol. ii. art. 109. PROC. ROY. SOC. EDIN VOL. XXV. 68 1074 Proceedings of Royal Society of Edinburgh. [sess. § 81. For the three-dimensional system let, in fig. 31, if/ he the inclination to 0 X of the rearward wave-normal of one of the constituent systems of waves. This is also the inclination to 0 Y of the medial line of the travelling forcive to which that set of waves is due. Take now for the forcive obtained by the super- position of an infinite number of constituents, as described in § 80, -1%, y)= f’ctyfr — ^ ^ . . (108), g y y J o r [(x cos xf/ + y sm xj/)2 + b2] where k may be a function of xf/, and b is the same for all values of \f/. For the case of a circular forcive system we must take k constant ; and we find - II(r) = 7r^.— wher er2 = x2 + y2 . . (109). 9 Jif + b2) § 82. Let now the forcive, whether circular or not, be kept travelling in the direction of x negative * with velocity v : and * This is opposite to the direction of the motion of the forcive in fig. 26. 1904-5.] Lord Kelvin on Deep Sea Ship- Waves. 1075 let A. denote the corresponding free wave-length given by the formula 27 rv^/g. This is the wave-length of the constituent train of waves corresponding to if/ = 0. For the ^-constituent, the component velocity perpendicular to the front is v cos i f/, and the wave-length is X cos 2i f/. Looking now to fig. 26, with X cos 2i f/ instead of X; and to fig. 31; and to equations (97), (98); we see that the portion of the depression at ( x , y) due to the constituent of forcive shown under the integral in (108) is 47 r2bk. dif/ . 27 t{x cos if/ + y sin if/) X cos2i f/ X cos2i {/ (110), provided x cos if/ + y sin if/ is considerably greater than JA. cos 2t f/. Hence for the depression at (x, y) due to the whole travelling forcive, we have d(®, y) = 47 r2b Hf-0 Jcdif/ 2tt(x cos if/ + y sin if/) X cos 2if/ X cos 2i fr (in). §83. The reason for choosing the limits ^ ^ to ^ is that each constituent forcive gives a train of sinusoidal waves in its rear, and no perceptible disturbance in its front at distances from it exceeding half a wave-length. Look now to fig. 31, and consider the infinite number of medial lines of the forcives included in the integrals (108), (111) ; all as lines passing through O. Four examples, Q P, Y'Y, LK, XX' of these lines are shown in the diagram: corresponding respectively to i f/= ~ 0j3 lf/ = 0,if/ = any positive acute angle, if/ = ^ . On each of the first three of these lines R R indicates the rear. The fourth, X X', is in the direction of the motion, and has neither front nor rear. The integral (111) must include all, and only all, the medial lines which have rears towards P. Hence Q P is one limit of if/ in (111) because it passes through P; XX' is the other limit because it has neither front nor rear. Thus all the lines included in the integral, lie in the obtuse angle POX'. Thus the integral (111) expresses the depression at P(&, y) due to the joint action of all the constituent forcives, because none except those whose medial lines lie in the angle P O X', contribute anything to the disturbance of the water at P. 1076 Proceedings of Royal Society of Edinburgh. [sess. § 84. For interpreting and approximately evaluating the definite integral, we may conveniently put M jWTf, and tt = 008 (’/' - *> . . . (112), V y ’ COS2^ and write (111) as follows : **v)-*#> P x2^sin2F • -(113)- Now if we suppose r/X very great, there will be exceedingly rapid transitions between equal positive and negative values of sin (fhrrujX), which will cause cancelling of all portions of the integral except those , if any there are, for which du/di Jr vanishes. We shall see presently that there are two such values, i/q, x J/2, both real if tan0< Fil u being a maximum (uf) for one of them, and a minimum ( u2 ) for the other ; and that, when 0 has any value between tan -1 and - tan -1 the values of xj/v x J/2 are both imaginary. Consideration of this last-mentioned case shows that, in the whole area of sea in advance of two lines through the centre of the travelling forcive inclined at equal angles of tan -1 (or 19° 28') on each side of the mid- wake, there is no perceptible disturbance at distances of much more than a half wave-length from the centre of the forcive. The main disturbance by ship-waves, therefore, lies in the rearward angular space between these two lines. It is illustrated by fig. 32, as we now proceed to prove by the proper interpretation of (113). Expanding the argument of the sin in (113) by Taylor’s theorem for values of xj/ differing from xf/1 by small fractions of a radian, we find 27 rru , . 27rrr aT= ” A L ^xh+<$), ■ where df From the second of (115) we find dxf/ = dq1/(^1 Jtt), where dxf/2Ji (116). Dealing similarly in respect to x[/2 and values of xf/ differing but 1904-5.] Lord Kelvin on Deep Sea Ship-Waves. 1077 o Fig. 32. — Isophasal Carves. 1078 Proceedings of Royal Society of Edinburgh. b d(x, y) = little from it, we take + q2 instead of the -qf of (111), and (d2u/dx]/2)2 instead of the - (d2u/dx{/2)1 of (115); because ux is the maximum and u2 the minimum. Calling kv k2 the values of k corresponding to x /q, x}/2, and using these expressions properly in (113), we find, for the depression of the water at ( x , y), 4 &7T3/2 S1 COS 2xf/1 f dqx sin (ax - q-f) + — ^ [ dq2 sin (a2 + ?22)1 . ( 1 1 7). J Kin COS Xj/nJ j /32 cos 2xf/2 The limits oo , - oo are assigned to the integrations relatively to q1 and q2 because the greatness of r/A in (115) and correspond- ing formula relative to xf/2, makes q1 and q2 each very great, (positive or negative,) for moderate properly small positive or negative values of xf/-xf/ 1 and xj/-xf/2. Now as discovered by Euler or Laplace (see Gregory’s Examples , p. 479), we have r oo /*oo I dq sin q2= I dq cos q2= Jtt/2, and using these in (117) we find d(x !/) - 2^27r^ f ^i(sin ai ~ cos ai) , *g(sin a2 + cos a2)1 (118\ h L cos 2«/q fi2 cos 2xf/2 J Substituting for ap a2 values by (115) we find 4t r2b . 2t r( sm ( ru j — A N ) + ^2 • 27 T[ sin A COS 2x[/1 A \ 8 / > fi2 cos 2xJ/2 A\ (118)'. § 85. To determine the quantities denoted by /3V j32 in (116) . . . (118)', we write (112) as follows : — ru = (x + yt) Jl+t2, where t = tan xf/ . . .(119). Hence, by differentiation on the supposition of x, y , r constant, we find y{ i + 2*2)] Ji du r#=L' xt + + t2 d2uV x(l + 2<2) + yt(5 + 6i!2) L/l + t . (120). • (121). By (120) we find for tm , which makes u a maximum or minimum, xtm + y( l + 2^) = 0 (122); a quadratic equation which, when (y/x)2<^, has real roots as follows, — ~Ty V[(f,)‘- i]' V[(5)’- ?] <123>’ 1904-5.] Lord Kelvin on Deep Sea Ship-Waves. 1079 ther of \wl=[x(1~tl)+2yt’ And substituting tm, (either of these,) for t in (121) we find / d2u\ Jl+t*. . .(124), or with simplification by (119), r($)m=2™™-^(1+C>3/i (124)'- Eliminating t2m from the first factor of (124) by (122) we find which, with m — 1, and m — 2, gives /31 and /32 by (116). §86. Using (123) we see that (d2u/dij/2)m vanishes when x = y J8, and that it is negative for and positive for t2, when x>y */8. Hence tY makes d2ujd\\r2 negative. Therefore u1 is the maximum ; and t2 makes it positive. Therefore u2 is the minimum ; and (119) gives for these maximum and minimum values ru1 = (x + yt1) Jl +t12, ru2 = (x + yt2) Jl+t2 . (125). By (122), (123) we see that when yjx= 0, we have -t1 = + oo , and — t2 = 0. If we increase y from 0 to 4- x / J8, — 11 falls continuously from oo to and - 12 rises continuously from 0 to J\. Thus - tx and - 12 become, each of them, ; which is the tangent of 35° 16'. § 87. Geometrical digression on a system of autotomic , monopara- metric co-ordinates * §§ 87-90. In (119) put ru = a (126), where a denotes the parameter 0 W of the curve 0 C C, fig. 32, which we are about to describe ; being the curve given intrinsi- cally by (119) and (122) with suffix £ m 3 omitted from t. In the present paper these curves may be called isophasals, because the argument of the sine in (130) below is the same for all points on any one of them. Solving (119) and (122) for x and y, we find 1 + 2^ / _ -t (l + *2)3/2’ y~a ( T+Wp ■ (127). * Of this kind of co-ordinates in a plane, we have a well-known case in the elliptic co-ordinates consisting of confocal ellipses and hyperbolas. 1080 Proceedings of Royal Society of Edinburgh. [sess. The largest of the eight curves shown in fig. 32 has been described according to values of x, y calculated from these two equations, by giving to - lvalues tan 0°, tan 10°, tan 20°, . . . . tan 90°. The seven other isophasals partially shown in fig. 32, all similar to the largest, have been drawn to correspond to seven equidifferent smaller values, 19 A., 18A . . . . 13 A, of the parameter a, if we make the largest equal to 20A. § 88. It is seen in the diagram that every two of these isophasals cut one another in two points, at equal distances on the two sides of O W. If we continue the system down to parameter 0, every point within the angle COC is the intersection of two and only two of the curves given by (127), with two different values of the parameter a. If we are to complete each curve algebraically, we must duplicate our diagram by an equal and similar pattern on the left of O : and the doubled pattern, thus obtained, would show a system of waves, equal and similar in the front and rear, which (§77 above) is possible but instable. We are, however, at present only concerned with the stable ship-waves contained in the angle ± 19° 28' on the two sides of the mid-wake ; and we leave the algebraic extension with only the remark that all points in the angle C O C of the diagram, and the opposite angle leftward of O, can be specified by real values of the parameter a : while imaginary values of it would specify real points in the two obtuse angles. § 89. By differentiation of (127), we find ^—=-t—-tdca\l/ 0^8); dy which proves that tan-1£ is the angle measured anti-clockwise from O Y to the tangent to the curve at any point ( x , y), in the lower half of the diagram. Elimination of t between the two equations of (127) gives, as the cartesian equation of our curve, {x2 + y2)z + a2(8y4 - 20a;2?/2 - a4) + 16a4y2 = 0 . . (129). But the implicit equations (127) are much more convenient for all our uses. It is interesting to verify (129) for the case -t=± in (127), corresponding to either of the two cusps shown in the diagram. 1904-5.] Lord Kelvin on Deep Sea Ship- Waves. 1081 § 90. Going back now to § 86 and the continuous variations con- sidered in it, we see that - 11 and - t2 are respectively the tan- gents of the inclinations, reckoned from OY clockwise, of portions of the long arc 0 C and of the short arc W C, in the upper half of the diagram. Thus, if we carry a point from 0 to C in the long arc, and from C to W in the short arc, we have the change of in- clinations to OY represented continuously by the decrease of tan -1( - L) from 90° to 35° 16', while y increases from 0 to x JS ; and the farther decrease of tan -1( - t2) from 35° 16' to 0°, while y diminishes from xJ8 to 0 again. The inclination to O Y of the two branches meeting in the cusp, C, is 35° 16' (or tan -1 N/J). For any point in the short arc GWC of the curve u or cos (if/ - 0)/cos 2 if/, is a minimum. In each of the long arcs u is a maximum. At every point of the curve the value of u, whether minimum or maximum, is a/r. Hence for different points of the curve, u is inversely proportional to the radius vector from O. § 91. Going back to (118)' we now see that for all points on any one of our curves, rux and ru2 have both the same value, being the parameter O W of the curve. The first part of (118)' is one constituent of the depression at any point on either of the long arcs; and the second part of (118)' is one constituent of the depression at any point on the short arc. Taking for example the largest of the curves shown in fig. 32, we now see that for any point of either of its long arcs, the second constituent of the depression of the water is to be calculated from the second part of (118)'; while for any point of its short arc, the second con- stituent of the depression is to be calculated from the first part of (118)'. § 92. Explaining quite similarly the determination of d(&, y) for every point of each of the smaller curves which we see in the diagram cutting the longer arcs of the largest curve, we arrive at the following conclusions as the complete solution of our problem. The whole system of standing waves in the wake of the travel- ling forcive is given by the superposition of constituents calcu- lated according to (127). with greater and smaller values of the parameter a with infinitely small successive differences. Hence, what we see in looking at the waves from above is exactly a system of crossing hills and valleys, with ridges and beds of 1082 Proceedings of Royal Society of Edinburgh. [sess. hollows, all shaped according to the isophasal curves shown in fig. 32. Looking at any one of the short arc-ridges and following it through the cusps, we find it becoming the middle line of a valley in each of the long arcs of the curve. And following a short arc mid-valley through the cusps, we find, in the continua- tion of the curve, two long ridges. Every ridge, long or short, is furrowed by valleys. All the curved ridges and valleys are parts of one continuous system of curves, illustrated by fig. 32 and expressed by the algebraic equation (129). With these explanations we may write (118)' as follows : d(x, y) = Arr2bk, sec2i f/ where XfS sin — l ru (130), (131). § 93. An important, perhaps the most important, feature of the wave-system which we actually see on the two sides of the mid- wake of a steamer travelling through smooth water at sea, or of a duckling* swimming as fast as it can in a pond, is the steepness of the waves in two lines which we know to be inclined at 19° 28' to the mid-wake. The theory of this feature is expressed by the coefficient of the sine in (130), and is well illustrated by the A * S6^ ~ ^or e^even P°inls °f any one of the curves of fig. 32, the results of which are shown in column 6 of the following table. They express the depression below, and elevation above mid-level, due to one constituent of the system of crossing hills and valleys described in § 92. Column 1 is -if/. Columns 2, 3 are xja and y/a, calculated from (127). Column 4 is u, calculated by (126) from columns 2, 3. Column 5 is ^ • d2u/dif/2, calculated from (124) and columns 2, 4. Column 6 calculation of "\/r sec 2if/ calculated from columns 1, 6. bein g, as we * In the case of even the highest speed attained by a duckling, this angle is perhaps perceptibly greater than 19° 28', because of the dynamic effect of the capillary surface tension of water. See Baltimore Lectures , p. 593 (letter to Professor Tait, of date 23rd Aug. 1871) and pp. 600, 601 (letter to William Froude, reprinted from Nature of 26th Oct. 1871). 1904-5.] Lord Kelvin on Deep Sea Ship- Waves. 1083 have seen, a maximum for values of — if/ from 0 to 35° 16', and a minimum for values from this to 90°, we see that the proper suffix in columns 4, 6, for the first four lines of each column is 1, and for the last six lines is 2. Col. 1. Col. 2. Col. 3. Col. 4. Col. 5. Col. 6. -rP X a y a u r d2u a d\f/2 fa sec 2if/ V A’ £ 0° 1-0000 o-oooo 1-00000 1-00000 1-0000 10° 1-0145 •1685 •97239 •93782 1-0647 20° 1*0497 •3201 •91587 •73497 1-3210 30° 1 -0825 •3750 •87290 •33333 2-3094 35° 16' 1-0887 •3849 •86602 o-ooooo OO 40° 1-0826 •3773 •87225 - -40830 2-6660 50° 1-0201 •3166 •93624 - 1-84070 1-7839 60° •8750 •2165 1-10941 - 5-00003 1-7888 70° •6441 •1100 1-53041 -14-0987 2-2793 80° •3421 •0297 2-91222 -63-3341 4-1672 90° o-oooo 0 0000 OO — OO OO §94. In (130), k is generally a function of if/; hut if the forcive is circular, (§ 81 above) A is a constant, and for points on one of the isophasal curves (a = constant) the only variable coefficients of the sine are sec 2if/, and /3~l. But for different isophasal curves the coefficient in (130) expressing the magnitude of the range above and below mean level, varies inversely as Ja. For mid-wake (if/ = 0) a is simply the distance from the forcive : and we conclude, not merely for our point- forcive, but for a great ship, that the waves at a very large number of wave-lengths right astern, are smaller in height inversely as the square root of the distance from the forcive or from the middle of the ship. § 95. The infinity for if/ — ± 35° 16' represents a feature analogous to a caustic in optics. There is in nature no infinity for either case, if the source is finite and distributed, not infin- itely intense and confined to an infinitely small space. According to the methods followed in §§ 1-72 above, we have in every case a finite intensity of source, or of forcive, except in § 80 where we have supposed b infinitely small, in comparison with A, we avoid the infinity shown in column 6 : and can, by great labour, calculate a table of mitigated numbers, rising to a very 1084 Proceedings of Royal Society of Edinburgh. [sess. large maximum at if/= ±35° 16'; but not to infinity; and so arrive mathematically at an expression for the very high waves seen on the two bounding lines of the wave-disturbance, inclined at 19° 28' to the mid-wake. But it is interesting to remember that we see in reality a considerable number of white-capped waves (would-be infinities) before the well-known large glassy waves which form so interesting a feature of the wave-disturbances. §§ 80-95 of the present paper are merely a working out of the simple problem of purely gravitational waves with no surface- tension on the principle given by Rayleigh* in 1883 for the much more complex problem of capillary waves in front, in which surface-tension is the chief constituent of the forcive, and waves in the rear, in which the chief constituent of the forcive is gravitational. In all the work arithmetical, algebraic, graphic of §§ 32-95 above, I have had much valuable assistance from Mr J. de Graaff Hunter ; who has just now been appointed to a post in the National Physical Laboratory. *Proc. Lond. Math. Soc., xv. pp. 69-78, 1883 ; reprinted in Lord Rayleigh’s Scientific Papers , vol. ii. pp. 258-267. ( Issued separately December 11, 1905.) 1904-5.] Dr W. T. Ritchie on Complete Heart-block. 1085 Complete Heart-block, with Dissociation of the Action of the Auricles and Ventricles. By W. T. Ritchie, M.D., F.R.C.P.E. Communicated by Dr George A. Gibson. (Read July 3, 1905.) The ventricular rhythm differs from the auricular, firstly, on the occurrence of a ventricular extra-systole, and, secondly, in cases where there is allorhythmia due to depression of conductivity of the heart muscle. When conductivity is depressed, the contraction stimulus at regular or irregular intervals may he blocked at the auriculo-ventricular muscle bridge ; so that whereas some stimuli induce both auricular and ventricular systole, others induce auricular systole alone, the ventricular systole being missed. That con- dition, incomplete heart-block, is of not infrequent occurrence in the human heart, and has been graphically recorded by Mackenzie (1), Finkelnburg (2), and other writers. The block at the auriculo-ventricular bridge may, however, be complete, as after the application of a Stannius’s ligature around the auriculo-ventricular junction of the frog’s heart. Bering (3) has conclusively proved the contention of His (4) and Max Humblet (5), namely, that complete heart-block occurs after section of the auriculo-ventricular muscle bundle (or bridge) of His. The auricles then continue to contract rhythmically, whilst, the con- duction of contraction stimuli being completely blocked by the division of that bridge, the ventricles manifest their inherent power of automatically generating contraction stimuli, and beat less frequently than the auricles and with an independent rhythm. Persistent bradycardia in man, with a pulse rate of 30 to 36 beats per minute, is probably in every instance the result of a lesion at the auriculo-ventricular bridge. In the cases of brady- cardia recorded by Adams (6), Stokes (7), and many subsequent writers, there is, however, no conclusive evidence of complete dissociation of the ventricular rhythm from the auricular. Complete heart-block in man has been demonstrated by few observers. 1086 Proceedings of Royal Society of Edinburgh. [sess. Chauveau (8) recorded a case, and reproduced tracings which indicate that while the left ventricle contracted at the rate of 21 to 24 beats per minute, the left auricle contracted 60 to 65 times per minute, and that there was complete dissociation of the ventricular rhythm from the auricular. Chauveau was not able to obtain a tracing from the jugular pulsations, hut he observed that they had the same rhythm as the auricular waves seen in the tracing taken from the cardiac impulse. The two auricles, therefore, beat at the same rate. W. His, jun. (9), recording a case of the Adams-Stokes syndrome, reproduced tracings which show that the jugular pulsations were three or four times (sometimes ten times) more frequent than the infrequent arterial pulse, and that the right auricle and left ventricle beat in dissimilar rhythm. In Mackenzie’s cases (1), (10), the condition of complete heart- block is conclusively proved. The ventricles contracted simul- taneously at the rate of 30 to 32 beats per minute, and some of the tracings demonstrate that the two auricles contracted synchron- ously about 60 times per minute. D. Gerhardt (11) interprets the imperfect tracings from the case he records as indicating complete heart-block. In the three cases recorded by Gibson (12), the complete heart- block is proved by a number of tracings. ' In the record of Joseph Erlanger’s case (13), no tracings are reproduced. The heart-block was at most times complete, “ the ventricular rhythm being totally independent of the rhythm of the venous end of the heart. In one determination the rate of ventri- cular beats was 27'6 per minute, of auricular beats 98 per minute.” H. E. Hering (3) refers to two cases he has observed but not yet published, and he also describes complete heart-block in a human heart restored to functional activity eleven hours after death.* The case I have had under observation is that of a man, fifty-five years of age, who has complained of dyspnoea and occasional * J. Rihl ( Zeitschr . /. exper. Path. u. Therap ., 1905, Bd. ii. S. 83) has recently recorded two cases ; and John Hay ( British Med. Jour. 1905, ii. p. 1034) also records a case. 1904-5.] Dr W. T. Ritchie on Complete Heart-block. 1087 syncopal attacks for four and a half years. Since he first consulted me, fourteen months ago, the rate of the arterial pulse has been almost constantly 32 to 34 heats per minute, though occasionally after physical exercise as frequent as 40 beats per minute. In July 1904, tracings, for which I am indebted to Dr Oliphant Nicholson, were taken simultaneously from the jugular vein and radial artery, by means of Mackenzie’s polygraph and Dudgeon’s sphygmograph. Those tracings demonstrated that the right auricle contracted more frequently than the left ventricle, and that there was dissociation of the ventricular rhythm from the auricular. I have since obtained many tracings from the patient, by means of the Knoll-Hering kymograph. Fig. 1 is a reproduction of a portion of the tracings taken simultaneously on the 19th May 1905. The upper tracing is from the jugular and carotid movements, the middle tracing is from the right brachial artery, the lower tracing is from the apex beat of the heart. In this and all other tracings the time is recorded by Jaquet’s chronograph, recording 0-2 of a second. In the jugular and carotid tracing, the waves marked with the letter C are carotid waves, those marked with the letter A are waves due to auricular systoles, and those marked with the letter V are ventri- cular waves. Fig. 1 shows that the left ventricle contracted rhythmically at the rate of 3 2 ’8 beats per minute, and that the right auricle contracted at the rate of 59*3 beats per minute. Some of the systoles of the left auricle are represented by distinct waves in the tracing from the apex beat. In the jugular and carotid tracing a ventricular wave occurs after each carotid wave. The administration of 90 c.c. of whisky was found to increase the frequency of the auricular contractions by 2*95 beats per minute, whereas the increase in frequency of the ventricular contractions was only 0*4 of a beat per minute. The systolic blood pressure, estimated by Gartner’s tonometer, immediately after the tracings reproduced in fig. 1 had been taken, was equal to 85 mm. Hg. In the numerous tracings taken from this patient at intervals during a period of fourteen months, there is no evidence of depres- PROC. ROY. SOC. EDIN.— VOL. XXV. 69 Fig. 1090 Proceedings of Royal Society of Edinburgh. [sess. sion of auricular or ventricular excitability. The two auricles always contracted together, and the two ventricles always contracted simultaneously, the condition being identical with heart-block experimentally induced. The independence of the ventricular rhythm from that of the right auricle was, moreover, manifest on examination of the patient by means of the Rontgen rays. The constancy and permanence of the heart-block point to it being due to some intrinsic cardiac lesion rather than to dromo- tropic nerve influence. This view was confirmed by tracings taken after the administration of atropin to the patient. In fig. 2, a portion of tracings taken after administration of atropin is reproduced. The upper tracing is from the jugular and carotid movements, the middle tracing is from the right brachial artery, the lower tracing is from the apex beat of the heart. The tracings show the auricular rate of contraction to be 274*73 per minute, while the ventricular rate is 36*58 per minute. The heart-block is still complete, and it is therefore due to an intrinsic cardiac cause — a lesion, probably chronic interstitial myocarditis, involving the auriculo-ventricular bridge. The independent auricular contractions have, in this case, never given rise to audible sounds. REFERENCES. (1) Mackenzie, J., The Study of the Pulse , arterial , venous , and hepatic , and of the Movements of the Heart , Edin. and London, 1902, chap, xxvii. p. 279. (2) Finkelnburg, R., Deutsches Arcliiv f. Min. Med., Leipzig, 1905, Bd. lxxxii. S. 586. (3) Hering, H.!E., Archiv f. d. ges. Physiologie , Bonn, 1905, Bd. cviii. S. 267. (4) His, W., jun., Wiener med. Blatter , Wien, 1894, Bd. xvii. S. 653. Also reference in Centralb. f. Physiol ., Leipzig und Wien, 1896, Bd. ix. S. 469. (5) Humblet, Max, Arch, intern, de physiologie , 1904, tome i. 1904-5.] I>r W. T. Ritchie on Complete Heart-block. 1091 (6) Adams, R., Dublin Hosp. Reports and Communications in Medicine and Surgery , Dublin, 1827, vol. iv. pp. 396-400. (7) Stokes, W., Diseases of the Heart and the Aorta , Dublin, 1854, pp. 312, 313. (8) Chauveau, A., Revue de medecine , Paris, 1885, tome v. p. 161. (9) His, W., jun., Deutsches Archiv f. klin. Med ., Leipzig, 1899, Bd. ixiv. S. 316. (10) Mackenzie, J., British Medical Journal , London, 1902, ii. p. 1411. Ibid., 1905, i. p. 521. (11) Gerhardt, D., Arcli.f. exper. Path. u. Pharmak ., Leipzig, 1903, Bd. li. S. 11. (12) Gibson, G. A., The Nervous Affections of the Heart , Edin. and London, 1904, p. 61. Edinburgh Medical Journal , Edin. and London, 1905, N.S. vol. xviii. p. 9. (13) Erlanger, J., “Proceedings of the American Physiological Society,” Amer. Jour, of Physiology , Boston, 1905, vol. xiii. p. xx vi. Bulletin of the John Hopkins Hospital , Baltimore, 1905, vol. xvi. p. 202. ( Issued separately December 14, 1905.) 1092 Proceedings of Royal Society of Edinburgh. [sess. A Regular Fortnightly Exploration of the Plankton of the two Icelandic Lakes, Thingvallavatn and Myvatn. By C. H. Ostenfeld, Inspector of the Botanical Museum, Copenhagen, and Dr C. Wesenberg-Lund. Com- municated by Sir John Murray, K.C.B., F.R.S. (With Three Plates.) (Read July 17, 1905.) I. INTRODUCTION. During the last five years the greater part of my time has been taken up by the study of the plankton in the fresh-water lakes of Denmark, and in the spring of 1904 the first part of an extensive paper upon this subject was published by me. In that paper I have compared the results arrived at by me with the results of plankton explorations in other countries, and have tried to collect together everything known at the present moment regarding the periodicity and geographical distribution of the European fresh- water plankton. At the time I wrote my paper, extensive and regular plankton explorations were carried on no further north than in Denmark. On the other hand, plankton explorations had been commenced in Holstein and North Germany at an earlier period than mine. As the distance between these places, geographically speaking, is inconsiderable, it has been impossible for me to ascertain whether the differences and similarities between my observations and those arrived at further south were due only to the northerly situation or to other facts. This is especially the case with regard to the plankton of some of the northern lakes in Jutland. Very little is known about the plankton in lakes in the northern parts of the temperate zone, as well as in arctic regions. Regular fortnightly explorations in lakes further north than the Danish ones are non-existent. The knowledge obtainable with regard to the fresh-water plankton of higher latitudes was restricted to an examination of some few samples of phyto- or zoo-plankton 1904-5.] The Plankton of Thingvallavatn and Myvatn. 1093 respectively, which had been gathered during journeys with quite other objects in view. Explorations on a very large scale were started years ago by Mr Huitfeldt Kaas in the Norwegian lakes; but to my knowledge only a minor part has as yet been published. When comparing the results of my own explorations with those in foreign countries, I arrive at some general conclusions. These, I suppose, may be considered as facts of great probability. I have taken the liberty to give an account of some of the points which may be supposed to be of the greatest interest, in the following pages. (Owing to the frequent use of the words “temperature” and “maximum development,” I shall in the following abbreviate these to “tp.” and “max.” respectively.) 1. Myxopliycece. — The bulk of these belong to the pond-like lakes with high summer tp. and rich in organic matter ; most of them reach their max. only at a tp. of 20° C., and the only plankton Myxophycese 'which play a somewhat conspicuous part in the cold, clear alpine lakes are Oscillatoria rubescens (max. at tp. 5°-10° C.) and Anabcena flos aqua} (max. 16°-18° C.). 2. All the European fresh- water Diatoms seem mainly to attain their max. at a tp. below 15°-16° C. Only the max. of Fragilaria crotonensis is reached at a tp. of 13°-16° C. The greater part of the remainder reach their max. at a much lower tp. (7°-10° C.). 3. Chlorophycece. — Nearly all of these are pond forms and only very few belong to the pelagic region of the larger lakes. As such may be mentioned Spheerocystis schroeteri. Dictyosphcerium pulchellum and a few species of Oocystis, Botryococcus braunii , Raphidium braunii , etc. Only very few of these species are of any importance in the pelagic regions, and the rest may all be regarded as tycholimnetic. 4. Peridinece. — The only common plankton-organism within this group to be found in the European lakes is Ceratium hirundinella. It is a summer form, with max. occurring at the highest tp. of the water. Different species, especially of the genera Peridinium and Glenodinium , appear in the pelagic region, but they generally appear in small quantities and have been studied but little. 1094 Proceedings of Royal Society of Edinburgh. [sess. 5. Euflagellata.— Of these the species of Dinobryon are the only real plankton organisms in the larger lakes. The remainder are all tycholimnetic, their home being in the smaller lakes or ponds. 6. Rhizopoda. — It seems that we have in the European lakes, and especially in the clearer and colder ones, a very peculiar but slightly studied fauna of Rhizopoda , consisting of but a few and very fragile species. Further investigations upon this point will presumably increase the number of species as well as give more detailed information regarding the periodicity and biology of these interesting animals. 7. Infusoria. — 'These are of hardly any importance in the pelagic region of the greater lakes, all having a surprisingly short and clearly defined max., which rarely extends beyond a longer period than one or one and a half months, and which generally occurs during spring. ( Dileptus track elioides, Tintinnidium jluviatile , Staurophrya elegans.) The only perennial Infusorium is Codonella lacustris. 8. Rotifera. — These may he referred to two groups. One of these contains cosmopolitan poly- or di-cyclic perennial species in larger lakes. They have two max. and two sexual periods, one in spring and another in autumn. The other, containing monocyclic periodical species, has its max. and sexual period in summer at the highest tp. of the water, and is of a more restricted distribution. The poly- or di-cyclic group generally attains its greatest max. in ponds, but may also reach a considerable max. in larger lakes. The max. reached by the monocyclic group is commonly rather small. All in all, the Rotifera in the pelagic region of the greater part of the larger lakes play but an inconspicuous part. 9. The association of plankton Crustacea in Danish lakes does not differ in any way from that of the lowland lakes of Central Europe. As shown by the explorations of Lilljeborg (1900), G-. 0. Sars (1861-1901), and by the considerations of Steuer (1901), it seemed probable, when I wrote my work, that a closer examination of the arctic regions would prove the existence of an association of plankton Crustacea, which differed from those inhabiting warmer countries. This association was, however, at that time but inconsiderably known. 10. During the last four years I have been occupied by the study 1904-5.] The Plankton of Thingvallavatn and Myvatn. 1095 of the propagation of the plankton Cladocera in nine of our Danish lakes. These explorations will he published in the second part of my plankton work. I think they will bring out some new facts. Still, all in all, they are in accordance with Weismann’s (1876-79) elaborate investigations of the Cladocera in Germany. On the other hand, it is shown by my own exploration of the Greenland Daphnids (1895) that the propagation in all probability is quite different in arctic lakes. I shall particularly point out, that the Cladocera of Greenland are always monocyclic, never poly- or acyclic, as is the case with many of the species to be found in temperate countries. If species which are polycyclic in southern countries become monocyclic in Greenland, then it is the sexual period occurring in autumn which thus is lost. The cycle is abbreviated as far as possible, if the parthenogenetic propagation is to be preserved at all. Lastly, I shall draw attention to my supposition that the number of eggs produced by the partheno- genetic females is smaller than in countries of a temperate climate. None of these assertions must be regarded as exact, because the material which I have had at my disposal was not collected with studies of this kind in view. The possibility of incorrectness is so much greater since Zschokke (1892), who has studied the life cycle in alpine lakes in Switzerland, arrived at quite different results. He maintains that the Cladocera of the alpine lakes are ordinarily polycyclic and not monocyclic, and that if Cladocera in lakes situated at a great elevation above the level of the sea are monocyclic, this is not owing to the loss of the autumnal sexual period, but to the merging of the two sexual periods into each other, the first of these having set in later and the second having commenced somewhat earlier than usual. However that may be, one thing may be concluded from Weismann’s, Zschokke’s, and my own explorations, — the manner in which the life cycle of the Cladocera goes on is not the same all over the world, but depends on latitude and the height above the sea-level. According to my knowledge, this very interesting fact has not been established with so much certainty with regard to any other group of animals. 11. In 1900 I pointed out that in several very different plankton organisms the longitudinal axis is simultaneously lengthened 1096 Proceedings of Royal Society of Edinburgh, [sess. during summer and shortened during winter, and that the forma- tion of all the various structures (spines, floating apparatus, etc.), considered necessary to enable the organisms to float, are most dis- tinctly visible in summer forms and summer individuals. I also pointed out that the explanation must he looked for in the varying external conditions, which, so to speak, compel the organisms to vary regularly in accordance therewith. I ascribed these variations mainly to the annual changes in the specific gravity of the water, caused by the regular annual fluctuations in the tp. I started from the supposition that if the velocity of the falling motion of the plankton organisms he not the same at all seasons, the organisms must — in order to exist as such during the seasons when the velocity of the falling motion is invariably greatest — of necessity he capable of developing properties tending to reduce the velocity of the falling motion. Knowing that the spherical form in all bodies has the quickest falling velocity, and seeing that so many organisms with the increasing tp. and decreasing specific gravity of the water often obviously became lengthened in form, the thought struck me, that very probably the seasonal variations in the specific gravity of the water were the main factors in determining the seasonal variations in the shape of the organisms. It was subsequently pointed out by Ostwald (1902) that the lengthening of the longitudinal axis with increase of tp., and the shortening of the longitudinal axis with decrease of tp., cannot he attributed solely to the variations in the specific gravity of the water caused by the rising tp. in spring and falling tp. in autumn. He draws attention to the fact that the oscillations in the specific gravity of the water, with a tp. varying from 0° to 27° C., are too slight to account for these great seasonal variations in the form of the organisms. He agrees with me in taking it for granted that these seasonal variations in so many very different plankton organisms can only be due to variations in the external conditions. But he believes them to be due to the varying viscosity of the water, which, like the specific gravity, is dependent on the oscillations in the tp. of the water, while the variations in viscosity are far more perceptible than the variations in specific gravity. I think that Ostwald’s modification of my views is quite correct. 1904-5.] The Plankton of Thingvallavatn and Myvatn. 1097 While studying the seasonal variations in our own lakes, I was struck by the thought that if the variations are occasioned by outer conditions varying in accordance with the tp. varia- tions of the water, we must expect the variations to be most con- spicuous in those lakes which have the most pronounced annual variations in tp. It has now become evident that the seasonal variations are great and very conspicuous in a great many lakes of Denmark, South Sweden, and North Germany. If the theories held by Ostwald and myself prove to be correct, we might expect the seasonal variations to be inconspicuous or wholly absent in arctic or alpine lakes with their much slighter amplitude of the tp. scale. It will be easily understood, that the various results and sup- positions arrived at through my explorations would be strongly corroborated if it were possible to compare them with those from more northern latitudes. If the results mentioned above were correct, wre should expect to find the following conditions with regard to the arctic and sub-arctic lakes. The Myxophycese would most probably be almost wholly absent, perhaps with the exception of Anabcena flos aqua, and Oscillatoria rubescens. The main part of the phytoplankton will be the Diatoms, of which especially Melosira , Asterionella , and Tabellaria wrill be of importance ; on the other hand, Fragilaria crotonensis , with its higher max. tp., probably will be absent. The Chlorophycese will play only a small part in the phytoplankton : Sphcerocystis and some others form an exception to the rule. The Yolvocinese will probably be very scarce; according to A. Cleve (1899), Lagerheim (1900), and Levander (1901), no Yolvocinese have been noted in lakes in the Lappmark, the Bear Isle, and the Murman coast, while Yanhoffen (1897), Borgesen (1898), and Ostenfeld (1904), have found Volvox as well as Eudorina in small ponds in Greenland (c. 71° lat. north) and Iceland. Of the Peridinese, Geratium hirundinella , the only species which commonly is of importance in the plankton, probably will not attain a conspicuous frequency in more northern lakes. Here it is very rare, only a few specimens having been found by Levander (1901) in the lake Enare, and by Ostenfeld (1904) in 1098 Proceedings of Royal Society of Edinburgh. [sess. a small lake in Iceland. On the other hand, the occurrence of Geratium , as well as of Volvox and Eudorina in Greenland and Iceland, show how cautious we must he in drawing our conclusions. The tp. at which a species has its max. and occurs in large quantities in the lakes in the temperate regions and in the lowland, will not always be a necessary condition for the progress of the species towards the North. Consequently it is always rather hazardous to draw conclusions from its max. tp. in temperate regions as to the northern limits of its geographical distribution. Of the other genera of Peridinese we probably will meet species of Peridinium and Gymnodinium ; the P. willei seems, according to papers of Huitfeldt Kaas (1900), Levander (1901), Ostenfeld (1903, 1904), West (1903), and Lemmermann (1904 a), to he a species with northerly (and north-westerly) distribution, hitherto found in Norway, Finland, Iceland, and the Faeroes, Scotland and Sweden. Among the other Flagellata the genus Dinobryon will no doubt he common. We are aware of its occurrence in Greenland, Iceland, the Faeroes, the Lappmark and the Murman coast, as well as further south. It will, together with the Diatoms, be the prominent form in the phytoplankton of lakes in higher latitudes. One species has been found in samples from Iceland (Ostenfeld, 1904), two species predominate in Greenland (Vanhoffen), and one in Lule Lappmark (A. Cleve). The Eotifera will only be represented by the cosmopolitic perennial dicyclic group, the monocyclic periodical summer forms most probably being wholly absent. It appears that there is a difference between this plankton Crustacea and ours. The life cycle is, as mentioned above, much simpler, and the seasonal variations are inconspicuous. As I wished to have my results and suppositions as exact as possible before writing the second part of my plankton paper, there was only one thing to be done : to contrive regular fort- nightly plankton explorations in lakes from higher latitudes. I wished to effect such explorations in pronounced arctic lakes as well as in lakes with a low summer tp. (never more than 12° C.). I consequently endeavoured to procure regularly collected samples from Greenland as well as from Iceland. AVith regard to Green- land I was rather unfortunate. I tried in different ways to bring about explorations ; in the time from November 1902 to February 1904-5.] The Plankton of Thingvallavatn and Myvatn. 1099 1903, samples have been sent me from a small lake near Ivigtnt, but these samples contained only mud and bottom organisms and no plankton at all ; consequently they did not suit my purpose. With regard to the Icelandic plankton, I had the good luck to find the right man for an undertaking of this kind. It was the Icelandic naturalist, Mr B. Soemundsson, assistant teacher at the classical school in Reykiavik, who in several ways has promoted our knowledge of the Icelandic fauna. Hear the Thingvallavatn he found a young man, Mr Simon Pjetursson, whom he could re- commend as being capable of undertaking my task. Furthermore, he interested the Dean of Skutustodum, the Rev. Arni Jonsson, who resides near Myvatn, in the plankton explorations. Two men from his parsonage have procured the samples from this lake. It had, of course, been my intention to have the collections made simultaneously from both of the lakes, hut a sad accident prevented this. All the apparatus which first were sent to the Rev. A. Jonsson were, while on the way to Myvatn, according to a letter from him, destroyed by a great fire in the town of Husavik. Hew apparatus had therefore to be sent to Skutustodum, but these did not reach their destination until some nine months later. The explorations in Thingvallavatn were at that time already commenced. On the Thingvallavatn the samples have been collected from 14th July 1902 to 30th June 1903 ; on the Myvatn from 1st April 1903 to 2nd April 1904. Only qualitative nets have been used for the explorations, and nearly all the samples are surface samples ; from Thingvallavatn I have some summer samples from deep water. The samples have been taken with two different nets, the one Miillergauze Ho. 20, and the other my Bosmina net (Griesgauze Ho. 60). Only Crustacea and some of the Rotifers could be gathered in this last net, but no phytoplank- ton. The gatherings from Ho. 20 were preserved in formaline, the gatherings from the Bosmina net in alcohol. The tp. of the air and that of the surface water were taken by a centigrade thermometer of a very ordinary construction. In winter, when one of the lakes was ice-bound, samples were taken through a hole in the ice. It must be considered that the method used was only a very primitive one, but it must be remembered that all the samples 1100 Proceedings of Royal Society of Edinburgh. [sess. had to be taken by men who had not the slightest idea of science, who could not be controlled at all, and of whom I had no know- ledge whatever. Any man may throw a net into the water, row about for some minutes, and put the contents in a bottle. But it is always a very difficult thing to base scientific results upon samples from deep water collected by men who are in possession of no scientific education, and therefore I have omitted to do so with regard to the present exploration. With regard to the tp., I have supposed that the simpler the instruments used the more correct would be the statements. It is proved by the plankton samples that all my requests have been carried out to the letter, and I wish to offer all, especially Mr Soemundsson, my sincerest thanks for the readiness with which the explorations have been established. As it was impossible to get samples from Greenland, it will be seen that I could not in this paper give as much as I had intended. A regular fortnightly exploration of an arctic lake will always be a desideratum, the lakes of Iceland having only the low summer tp. in common with those in arctic countries, but, on the other hand, never being frozen over for as long a time as the arctic lakes. Still, the results of my exertions are not quite fruitless, seeing that Thingvallavatn and Myvatn are at this moment the most northerly lakes in which a regular plankton exploration has been carried out. Further, I hope that most of the above- mentioned results and suppositions, already arrived at through explorations of the Danish lakes, have been greatly corroborated through this little exploration. In 1904 Ekman’s extremely interesting and very valuable paper appeared. It treated of the Crustacea fauna of North Swedish alpine countries, together with their arctic and sub-arctic life conditions. In this paper Ekman stated the existence of a Crustacean fauna common for the arctic region, the Scandinavian and the Central European alpine region ; this region he calls the boreo sub-glacial region. The Crustacea of the lowland lakes in Sweden and the Central European plains differ greatly from those of this region. With regard to the plankton Crustacea of the arctic lakes the most common features may be the following : the great Crustacean plankton of the arctic lakes is mainly composed of the following 1904-5.] The Plankton of Thingvallavatn and Myvain. 1101 species : Holopedium gibberum, Bythotrephes longimanus, both having individuals of an extremely great size ; Daph7iia longispina ( = hyalina) in different varieties ; Bosmina obtusirostris, Cyclops strenuus, and C. scutifer ; the three species of Diaptomus, D. laticeps , laciniatus , and denticornis. The following species, which form the greatest part of the Crustacea plankton in the lowland lakes, Diaptomus graciloides , Leptodora kindtii , Hyalodaphnia cucullata, Bosmina coregoni , and Diaphanosoma brachyurum , are here almost entirely absent. With regard to the propagation of the Cladocera, Ekman has confirmed the correctness of my two above-mentioned suppositions, and supposes that when Zschokke has arrived at a result differing from mine, the reason may be looked for in the fact that the lakes explored by him have not had sufficiently arctic conditions. The number of eggs which the parthenogenetic females produce is, according to Ekman, by no means smaller than in more southern countries, it being, on the contrary, often much larger. Ekman states, with regard to the seasonal variations, that these are by no means as conspicuous as in more southern countries. Brehm (1902) has arrived at quite a similar result regarding the alpine lake Achen in Tyrol. Though I believe that the facts mentioned by Ekman are quite correct, I still suppose that his explorations have not made mine superfluous. Mine have been carried out in another country and have been based on principles quite different from Ekman’s, his being an examination of many localities once or only a few times, and all in a relatively short time of the year. I, on the contrary, have examined but two localities, but these examinations have been carried on regularly every fortnight all the year round. My explorations are, furthermore, carried on in a country which only in a very few places offers life conditions which may be called arctic. Still, it might be expected that the results of my explora- tions of the Crustacea would be very similar to those arrived at by Ekman. As I wished a botanist to work out the phytoplankton, I asked my friend Mr Ostenfeld, Inspector of the Botanical Museum in Copenhagen, to do it. He had recently published a paper on the phytoplankton of an Icelandic lake. To my great satisfaction he 1102 Proceedings of Royal Society of Edinburgh. [sess. complied with my request. The section Phytoplankton (pp. 1 106— 1 1 28) is therefore entirely his work. The common results have been prepared by both of us ; the rest of the paper is worked out by me. Our knowledge of the Icelandic fresh- water plankton is at this moment but slight. De Guerne and Richard (1892, p. 310) com- municated the zoological results arrived at by examination of some samples gathered by M. Rahot in three different regions of Iceland. One is gathered in the northern part near Akureyri, one in the western part in the neighbourhood of Reykiavik, and one in the eastern part, Lagarfjot, near Eskifiord. The samples contained 29 species : 16 Cladocera, 8 Copepoda, 2 Ostracoda, 2 Rotifers, and 1 Protozoan. The greater part of these species are bottom or shore animals, and only a smaller part of them are plankton animals. In Thingvallavatn M. Rabot had gathered the following species : Scapholeberis mucronata, O.F.M. ; Bosmina arctica, Lillj. ; Eurycercus lamellatus , O.F.M. ; Acroperus leucocephalus, Kock ; Alona affinis , Leyd. ; Chydorus sphoericus, Jurine. ; Polyphem,us pediculus, De Geer ; Diaptomus minutus, Lillj. ; Cyclops strenuus, Fischer ; Cyclops viridis , Fischer. In the samples from Lagarfjot, De Guerne and Richard have found Holopedium gibberumi Zaddach ; Diaptomus minutus , Lillj. ; and D. glacialis, Lillj. The result of the exploration may he summed up thus : Iceland takes an intermediate position between the arctic and the temperate region. The phytoplankton in a sample from a lake in south Iceland, 63° 28' lat. N. and 18° 55' long., has later on been described by Mr Ostenfeld (1904, p. 331). This paper will he mentioned in the botanical part. Besides this, several small papers by Hariot Bellocq and Borgesen deal with some fresh-water algae, among which a few plankton species may occur. As I wished, as far as possible, to test the tps. reported to me, I applied to the Meteorological Institute of Copenhagen, which also has meteorological stations in Iceland. Mr Willaume Jantzen, second director of the Institute, kindly informed me of the fact that there were no stations situated at the two lakes. But as there was one at Reykiavik, it thus became possible to test the tp. measured in Thingvallavatn. Another was situated at Storinupur, 1904-5.] The Plankton of Thingvallavatn and Myvatn. 1103 the first mentioned being a coast station, the second a much colder inland station. With regard to Myvatn, there was a similar coast station at Akureyri, and a very cold inland station at Modrudalur. The mean tp. of the months in which the plankton samples have been taken has, according to my request, been used for the calculation. I take the liberty to offer Mr Willaume Jantzen and the Institute my best thanks for their kind services in this respect As it was very difficult for me to find the widely spread literature treating on Myvatn, I begged of the well-known Ice- landic geologist, Prof. Thoroddsen, to give me his aid. He kindly provided me with a list of literature appertaining to this lake. The sketch of the physical and natural conditions of the lake is based upon this list, more especially on Prof. Thoroddsen’s own valuable papers on this subject. I beg to forward to Prof. Thoroddsen my very best thanks for the valuable assistance he has given me. For the beautiful photo of Thingvalla lake, my best thanks are due to Mr C. Y. Prytz, professor at the Royal Veterinary and Agricultural School in Copenhagen. C. Wesenberg-Lund. II. THING V ALL AY ATN. (a) General Remarks. With regard to the Thingvallavatn, Mr B. Soemundsson, in the journal edited by the Royal Danish Geographical Society 1904, has published an account of a thorough bathymetrical exploration of the lake, accompanied by a map, and some remarks pertaining to the environments, tp., vegetation, and geology. From this paper I have obtained the following information. The Thingvallavatn is situated in the south-western part of Iceland, at c. 64° north latitude. It is a combination of a lava and a glacial lake. The length of the lake is about 16 kiloms., the greatest breadth is 8 kiloms. The water covers an area of about 115 square kiloms., the greatest depth is about 110 m., the surface of the lake is 106. m. above sea-level, the mean depth is about 1104 Proceedings of Royal Society of Edinburgh. [sess. 35 m. ; it is the deepest of all known Icelandic lakes. It has two small islands, Sandey and Nesjaly. The bottom is, from the shore to the 10 m. curve, stone chips or dark volcanic sand, often covered with mud ; in the deepest part of the lake we find the mud absolutely predominant. This mud is of a dark, grayish-blue colour and con- sists chiefly of organic matter, especially diatom frustules. It is highly probable that the greater part of the water arises from springs in the bottom. According to Mr Soemundsson the surface tp. was, in the period from 16th July to 2nd August, 10 to 12, 2° C. The vegetation of higher plants along the shore is very poor ; on the other hand there is a luxurious growth of Characese ( Nitella ) in depths of 13 to 30 m. The rocks just beyond lake-level are covered with the gelatinous green alga, Tetraspora cylindrica. Insect larvae and Limncea are common near the shore. With regard to my own tp. explorations, I may refer the reader to the tp. curves and to the mean tp. for the months taken at the meteorological stations at Reykiavik and Storinupur. Monthly Mean tps. of the Air at Reykiavik and Storinupur. 1902-1903. Reykiavik. Storinupur. July, .... 11*1 August, 10-4 September, 9-2 October, 6*0 November, 3-5 December, . 1-2 January, . -2*0 February, . - 1*0 -l’*9 March, -1-6 -2*2 April, 0-5 -0*5 May, .... 5-5 4-5 June, 8-8 1 8*5 It will be seen that there, in spring, summer, and autumn, there is a fair conformity between the mean tp. of the month and the solitary observations taken of the atmosphere and of the surface water in the lake. On the other hand, it must be noted as a very remarkable instance, that during the entire winter no negative tp. 1904-5.] The Plankton of Thingvallavatn and Myvatn. 1105 was reported me from the Thingvallavatn, even though the mean tp. of the air at the nearest coast station in the months January, February, and March was — 1*6 to — 2, and at the inland station - 1’9 to -0*5. What may be the cause of this Ido not know; probably the tp. of the winter months given me from Thing- vallavatn have not been fully correct. All in all, we arrive through the observations made at the following facts : — The highest tp. of the lake during the period of observations is 11° C., which was reached on 14th August 1902. Then the tp. from 14th August to 31st October falls to 5° C. and keeps this tp. to 14th December, when the tp. further falls to 1° C. (16th March 1903), not rising until 16th April ; already (30th June) it has reached 8J- above zero. During the whole year the lake has not once been frozen over. Besides, it appears that the tp. of the lake is rather slow in following the variations in the tp. of the atmosphere ; of course this must be ascribed to the considerable depth of the lake. As I wished to know whether or not it was a rare case that the lake had not been frozen, I asked Mr Soemundsson to inform me as to this point, but as yet no reliable information has been obtained. PROC. ROY. SOC. EDIN. — YOL. XXV. 70 1106 Proceedings of Royal Society of Edinburgh. [sess. ( b ) Phytoplankton. By C. H. Ostenfeld. 1. General Remarks. Last year Dr Wesenberg-Lund asked me to examine the plant- organisms in a series of samples from Thingvallavatn. I was very pleased at his request, as I just had published a little note on a plankton sample from an Icelandic lake, as well as some smaller papers on fresh- water phytoplankton from the Faeroes and from Norway. But the samples from Thingvallavatn were of special interest, because they were collected regularly every fortnight during a whole year, thus giving an idea of the seasonal changes in the plankton of a lake in Iceland. I therefore took up the work with pleasure. Very little is known concerning the phyto- plankton of the northern countries ; in the arctic region we have small contributions from Greenland (E. Vanhoffen, 1897) and Bear Isle (G. Lagerheim, 1900); to these we must add contributions from the Lule Lappmark (Miss A. Cleve, 1899) and from the Murman coast of Finland (K. M. Levander, 1901). There are further published some papers on the phytoplankton of Swedish lakes (0. Borge, 1900 ; Lemmermann, 1904 a), but very little from Norway (Holmboe, 1900; Ostenfeld, 1903). From the United Kingdom we have publications from Ireland and Scotland (W. and G. S. West, 1902, 1903 ; O. Borge, 1897), and small notes from the river Thames (F. E. Fritsch, 1902, 1905) ; an examination of phyto- plankton from the Faeroes has also been published (F. Borgesen and Ostenfeld, 1902), as well as one of a single sample from a lake in South Iceland (Ostenfeld, 1904). All these publications have in common the drawback that they are based upon samples which have been collected only in the summer time and without any regularity. It is only in Denmark (Wesenberg-Lund), Germany (O. Zacharias, Lemmermann, etc.), Switzerland (C. Schroeter, R. Chodat, H. Bachmann, etc.); United States (Illinois, by C. S. Kofoid, etc.), and partly Hungary and Russia, that more regular investi- gations have taken place. The task undertaken by Dr Wesenberg- Lund — to obtain a series of samples from lakes in Iceland collected during an entire year — is therefore a very interesting one. 1904-5.] The Plankton of Thingvallavatn and Myvatn. 1107 With regard to the physical conditions of the Thingvallavatn and the surrounding country, I may refer to the remarks above written by Dr Wesenberg-Lund ; hut I must he allowed to quote some few words from my little note concerning Icelandic fresh- water plankton (1904, p. 235) : “ I think we may say that the plankton is like that of the lowland lakes of northern Central Europe and Southern Scandinavia, but much poorer, especially by the want of the summer forms ; this also is the case with the climate ; it is the climate of northern Central Europe and Southern Scandinavia with regard to the autumn, winter, and spring, but the summer is skipped over.” The insular climate causes the lakes, at least the lowland lakes in South Iceland, to be ice-covered during only a short period in winter or not at all, while the cold summer, with its abundance of cloudy and rainy days, is not warm enough to give the lake a high summer tp. These conditions will cause a plankton, in which the Diatoms predominate all the year round, and the Myxophycese are wanting or nearly so, as they reach their max. at higher tps. Such is the result of the examinations of the samples from Thingvallavatn. In the accompanying table (pp 1154, 1155) I have arranged the phytoplankton according to the dates of collection, and furnished them with the ordinary signs denoting the quantity. We learn from this that the number of species is but small, and when restricted to the true limnetic species only, this is even diminished by half its number. The species belong to the Chlorophycese and Ilacillaricere, to which two Flagellates (Mallo- monas and Peridinium ) are to be added. The Myxophycece are completely wanting ; but it must be noted that some of the samples contain specimens of bottom Myxophycese, viz., Lyngbya sp., Anabcena variabilis , Kiitz., but only very sparsely, the few specimens occurring being mixed up in the plankton by wind and waves. Such accidentally occurring bottom forms are rather common in most of the samples ; the climate is very windy, so it is but natural that the chance to meet with bottom forms in the plankton is great ; especially are bottom Diatoms met with very frequently in the samples, viz. Cymbella cistula, Ceratoneis arcusy Epithemice , etc. Such forms which are specified in the table, viz., Fragilaria construens, F. capucina , Synedra acus, S. ulnay 1108 Proceedings of Royal Society of Edinburgh. [sess. Surirella biseriata , Melosira varians, and M. arenaria , may also be considered as bottom forms ; they do not belong to the true plankton, but once broken off from their place in the bottom along the shores, they are capable of floating some time and perhaps of multiplying themselves while in a floating con- dition. True plankton Diatoms are only the following : Asterionella formosa , Fragilaria crotonensis , Cyclotella comta, Melosira italica and islandica, and the two Rhizosolenice. Of these the two Melosirce and Asterionella occur all the year round in the plankton, while the other may be found only during shorter or longer periods of the year ; the Rhizosolenice have resting spores, and it is evident that they form their spores when past the flowering period ; the spores sink to the bottom and there they rest until the next period. The same periodicity may occur with the Fragilaria crotonensis and the Cyclotella , but we have here no morphological sign to help us to decide when the period of flowering is ended. Among the Chlorophyceae the Desmids have no distinct period in which they disappear from the plankton ; Sphcerocystis and Oocystis, on the contrary, act as the Rhizosolenice. Such perio- dicity is to be found also in the Peridinium aciculiferum and the Mallomonas, both having resting spores. Although it thus be- comes evident that some of the plankton forms lack periodicity, inasmuch as they at no time of the year wholly disappear from the plankton, they still evidence periodicity in another way, viz., they attain at a given period their richest flowering or so-called max. ; before this period they become more and more numer- ous, and afterwards steadily decrease in number until they reach a minimum from which they then again commence to increase in number. This periodicity is not much different from the perio- dicity mentioned first ; if we suppose the minimum like zero, and if this minimum extends over some time, we have the first-men- tioned periodicity : the difference is consequently but gradual, except in the cases where a formation of resting spores completes the max. The causes which produce a periodicity in each species are partly inner causes, partly causes based upon physical and chemical conditions of the surrounding matter. We do not 1904-5.] The Plankton of Thingvallavatn and Myvatn. 1109 know anything about the inner causes, but we know a little with regard to the others. Based upon the numerous plankton in- vestigations of the last twenty years, it may be affirmed that the tp., including the physical conditions depending upon tp. (viscosity, gravity), of the water, and its chemical composition, together with the light, are the effective factors in relation to the plankton organisms. The chemical composition of the water (contents of air and of salts) plays an important part with regard to the marine plankton, but in fresh water the tp. and the light are the most effective factors. It is not easy to decide which of these may he said to predominate — or, more correctly, in some cases the tp. is the critical factor, in other cases (probably more exceptionally so) the light predominates. Our table will give some examples of both cases. Preceding this, it must he mentioned that in July-September 1902 the main part of the plankton consisted of Crustaceans, which occur in such large quantities as to hide the phytoplankton completely. Conse- quently, the signs of quantity with regard to the plant organisms in the samples obtained during these months stand very low in the table. Apart from this, we learn that Splicer ocystis and Oocyst is are dependent of the variations of the tp. as regards their frequency. They have their max. in October 1902 at a tp. of 5°-7-5°, Sphcer ocystis has a secondary max. in June 1903 at 7°-8’5° ; it follows that we are right in stating that the two species here and in the year in question reach their max. at about 7° ; the lower tp. as well as the higher thus being unfavourable for their propagation. Nor does their growth depend upon the light, as the light in June is of much greater power than in October, and Splicer ocystis is of about the same great frequency at these two periods. It is also the tp. which regulates the growth of the two Rliizosolenice and the Cyclotella ; they reach their max. in June 1903 at 7°-8,5°. The case is not so clear with regard to the three Diatoms, , which are the most characteristic forms in the plankton, viz., Asterionella, Melosira italica , and M. islandica. We learn that Asterionella is rare in July- August, and from that we conclude that 9°-ll° is too high a tp. ; hut it grows very well in tps. varying from l°-8'5°, perhaps with a faint decrease in quantity 1110 Proceedings of Royal Society of Edinburgh. [sess. at 1°-1*5° and at 8°-8'5°; if we must choose the most favour- able tp., it must be 4°-5°.* We do not find any tendency to relation to the light. Asterionella reaches one max. in the winter (November-February) and another in May- June. I think we may say that the growth of Asterionella in some degree depends upon the tp., but that the limits of the max. tp. are very wide, going from 1° to 8°. The two Melosirce act in a manner very similar to that of the Asterionella , although with some differences. They prefer a some- what lower tp. than the Asterionella ; their max. lies in March- May at a tp. of l°-5°, and they cannot endure a tp. of 7°-8° as well as the Asterionella. They have no distinct relation to the light. Finally, we take the Peridinium aciculiferum ; it appears suddenly in great quantities in the sample of February at 1*5° and flowers in the next samples at about the same tp. (l°-2°), but when the tp. rises it decreases in number ; consequently it has its max. at l°-2° and is dependent on the tp.f Nevertheless we have no explanation of its sudden occurrence, and here, I think, we must take the light as the moving factor. The remaining forms have no distinct max. ( Staurastrum pelagicum seems to follow . Sphcerocystis). Some of them occur rather evenly throughout the entire year, but not in quantities ; others, e.g., Fragilaria construens , show no regularity, and these last mentioned manifest thereby that they are only occasional guests in the plankton. If we summarise our remarks, they will be in accordance with my words quoted above. Tliingvallavatn has a phytoplankton consisting mainly of a few species of Diatoms ( Asterionella and Melosirce ), Myxophycese are wanting, Flagellates (in the widest sense) and Chlorophycese are without greater importance. The phyto- plankton has not at all an alpine character, but is very like the plankton of the lakes in the Central European lowland during ivinter and early spring. It is very poor in species and one of its most remarkable features is the number of organisms one might * Some authors (Marsson, B. Schroder) have suggested that the number of cells in the stellate colonies depends on the seasons, but this is not the case in Thingvallavatn, as I have found 4, 5, 6, or a still greater number of cells in each colony in all the samples. t For its relation to the tp. in other countries see p. 1128. 1904-5.] The Plankton of Thmgvallavatn and Myvatn. 1111 expect to find , but which are wanting. Of these we may mention : — Tabellaria fenestrata, Dinobryon sp., Scenedesmus, Pediastrum, Eudorina, etc.,* besides all the Myxophyceee. 2. Remarks on some Species. Chlorophyce^e. The Desmids do not play any important part in the plankton, but there are some few species which occur in nearly all the samples, consequently all the year round. These are some species of Staurastrum and one Cosmarium ; the long Closteria, which often have been found in plankton, do not seem to exist at all in the plankton of Thingvallavatn, nor do we find any species of the Xantidia. The max. of the Desmids occurs in October 1902, with a secondary max. in June 1903. The species observed are rather interesting, as they come near or are identical with some of the many plankton Desmids mentioned and figured in the papers on phytoplankton from Ireland and Scotland by W. West and G. S. West (1902, 1903). As my identi- fication of the species may be incorrect, I have drawn figures of them (see PI. II. figs. 11-15). Cosmarium phaseolus, Breb. — The specimens observed were 32-38 g long, 30-36 g broad, ab. 18 p thick, and the isthmus 12 p. It is with some hesitation that I have referred them to this ubiquitous species ; they greatly resemble Mr W est’s drawings of C. abbreviatum , Racib., var. on pi. xv. fig. 6 (1903); but the semi-cells of the latter are more flattened and more angular, and the dimensions are smaller.! Staurastrum pelagicum , W. West and G. S. West, l.c. (1902) pi. ii. figs. 26-27, p. 46. — This very characteristic species, which has been described from Lough Neagh and Lough Beg in Ireland, occurs regularly in the samples from Thingvallavatn and is the most abundant Desmid in the plankton. As my drawing * In a sample from the neighbourhood of Thingvallavatn, a Dinobryon occurs ; and also all the other species enumerated as wanting have been found in other lakes in Iceland. t O. Borge (1897) has given a drawing of a C. phaseolus, 0. achondrum (Boldt)? from a lake in the island Mull (Scotland), but it is smaller than our form. 1112 Proceedings of Royal Society of Edinburgh [sess. will show, the Icelandic form is quite like the Irish ; the dimen- sions of the cell are also about the same (long. 40 g, lat. cum spin. 67 g, sine spin. 46). W. West and G. S. West have later (1903) described a S. pseudopelagicum only differing from S. pelagicum by its hollow processes and a somewhat different shape of the cells ; but the Icelandic form is more like the true S. 'pelagicum. The two species have in common the two large spines at the apices of the processes, hut in a specimen from Thingvallavatn I have observed three spines at one of the processes. S. paradoxum , Meyen. — After S. pelagicum the most common plankton Desmid in Thingvallavatn is a form of the variable S. paradoxum. It is always quadrangular (I have not seen a single triangular specimen in the samples), and resembles some- what the form figured by W. West and G. S. West (1903) pi. xviii. fig. 4, hut is slenderer. Long, sine proc. ah. 40 g , lat. sine proc. ah. 22-24 g, lat. cum proc. ah. 100 g. It differs much from the commonest plankton form of S. paradoxum , viz., var. longipes, Nordst. S. breoispinum, Breb. — The form which I have placed under this name on account of its resemblance to Buffs’ figure of it is also a constant form in the samples. My drawings show the shape of it. Long. ab. 50 g, lat. sine spin. ab. 55 g , lat. cum spin. ah. 65 g, lat. isthmi ab. 12 g. S. Bieneanum, Babenh., forma. — Although this species does not occur as constantly in the plankton of Thingvallavatn as the above-mentioned ones, it has been found in so many of the samples that I think it is a planktonic species. I am not convinced of the identification of this species. It is larger than the ordinal’)' S. Bieneanum , being 60 g long and 52 g broad, hut Mr Borgesen, who has seen my drawing, agrees with me in counting the Thingvallavatn form as a variety of S. Bieneanum nearest to the var. ellipticum of Wille (1879, pi. xiii. fig. 49); the semi-cells are alternating. Besides these five species, several other Desmids have been observed in the samples ; but as they occur without any regularity, and only in one or a few specimens, I have reckoned them as strangers to the plankton and therefore omitted them in the list ; 1904-5.] The Plankton of Thingvallavatn and Myvatn. 1113 they belong to the bottom flora and have been carried away accidentally by the rivulets or the waves. Sphcerocystis schroeteri, Chodat. — This widely distributed plankton-alga is found in most of the samples ; it seems to have its max. in the summer (June) and the autumn (October). Most of the specimens agree well with the figures, p. 64 and p. 115, in Chodat’s paper (1902). Oocystis crassa, Wittr. — Following Sphcerocystis in its periodicity a species of Oocystis occurs. It .is very difficult to identify the species within this genus, in which the number of species has augmented greatly during the last few years, especially by descriptions of new forms by W. West and G. S. West and E. Lemmermann. The latter author has given a key to the plankton species of Oocystis (1904 a, pp. 106-108). G. S. West has recently (1904, p. 227) figured several species, and Chodat (1902, pp. 189-191) has enumerated the Switzerland species. These three authors do not quite agree in their views of the definition and limits of the species. Lemmermann has created a new genus Oocystella , differing from Oocystis only by the existence of pyrenoids and the substellate chloroplasts, but West as well as Chodat admit the existence of pyre- noids in species of Oocystis ; it seems therefore unnecessary to have this separate genus. The species from Thingvallavatn has one pyre- noid in each chloroplast ; the chloroplasts are two or four in each cell, often tetrahedrally arranged ; the cells are four (rarely two) in a globular mucilage ; their shape is ellipsoid or ovate with subacute apices; length 22-26 g, breadth 16-20 /x. In my note (1904, p. 235) on phytoplankton from a lake in South Iceland, I have drawn a figure of an Oocystis which is the same as the Thingvallavatn form;* the specimen drawn shows two chloroplasts in each cell, and the cells are not as subacute as in our form ; the pyrenoids are not visible. Of the Thingvallavatn form I have drawn a specimen with pyrenoids in the four chloroplasts (PI. I. fig. 8) ; this drawing comes near to G. S. West’s figure (1904, p. 227, fig. 97 D) of O. crassa , Wittr., but these latter have eight chloroplasts. It is upon this figure that I base my determination of the form, as the description given by V. Wittrock (1880) is very short and with- * I have named it O. lacustris, Chod. (?), which is evidently incorrect. 1114 Proceedings of Royal Society of Edinburgh. [sess. out any figure. Chodat has emended the diagnosis of the species (1902, p. 189), but he does not mention the pyrenoids, while these are present in West’s drawing. Bacillariace^:. Asterionella formosa, Hassall. — The Asterionella , which inhabits Thing vallavatn, is rather short and robust, thus representing the typical A . formosa. Fragilaria. — With regard to the species of Fragilaria , my determinations may he insufficient ; this genus is a very difficult one. No doubt the species are connected with each other without distinct limits. The easiest discernible form is Fragilaria crotonensis , (Edw.) Kitton, distinguished by the intervals between the cells ; it is not common in Thingvallavatn, and occurs only in the summer and autumn. The commonest Fragilaria in the plankton is a small bottom form, F. construens, (Ehbg.) Grun., of which I have given a figure of a filament in my previously quoted paper (1904. p 232, fig. 3). Very near to it, and mostly distin- guished from it by the denser striae, is F. capucina , Desmaz, which also often is present in the samples. The last, again, goes over into the F. virescens. It seems to me as if the limit between F. construens , F. binodis, (Ehbg.) Grun., and F. capucina is not clear, and I fear that my identifications of these two species may have been arbitrary. Synedra. — Besides S. ulna, (Nitzsch) Ehbg., another or several other species occur in the samples ; they are smaller, narrower, and slenderer, but they vary much in length and breadth. Most of these individuals are 70-150 g long and 2-4*5 g broad ; they agree well with the figures by Yan Heurck (1880-1881, pi. xxxix. fig. 6) of S. delicatissima, W. Sm., v. mesoleja, Grun., but this form is very near to S. radians , W. Sm. (Yan Heurck, l. c. pi. xxxix. fig. 11). I take all these species as forms of S. acus, Kiitz., and name our form S. acus, f. delicatissima, (W. Sm.) Grun. The specimens have in most cases been found one by one, but occasion- ally 2, 4, 6 or a still greater number of individuals were arranged in a radiate manner, thus forming stellate colonies, probably an adaptation for the limnetic life (see PI. II. figs. 16, 17).* Also * Cp. the colony of S. radians, by W. Smith, 1853, pi. xi. fig. 89. 1904-5.] The Plankton of Thingvallavatn and Myvatn. 1115 typical S. acus occur, but rarely, in the samples ; the specimens observed measured 120-150 g in length, and about 6 g in breadth. Gyclotella comta, (Ehbg.) Kiitz. — In some of the samples a little Cyclotella has been found (PI. I. figs. 9, 10). Its diameter is 7-17 /a; it is very difficult to observe any heterogeneousness amongst the marginal radiating striae, but perhaps some of them are more distinct than the others. Supposing this, and counting upon the fact that the frustules are not undulated, I take it as a small form of G. comta. The cells always occur separately. I have seen a single specimen of which one valve was of ordinary shape, the other semi-globular ; this specimen is purely one daughter-cell of an auxospore, the semi-globular valve being the half part of the auxospore wall. The Melosirce play an important part in the plankton of Thing- vallavatn. Several species have been found, but only two of these are true plankton forms and have a distinct max. in which they are the predominant forms. Two species occur more acci- dentally ; of these M. varians, Ag., has been observed in most of the samples, but it was always rare and often the specimens were empty ; thus we are right in taking it as a stranger, its home being at the shores. Also M. arenaria, Moore, has only been found in a few specimens, and without doubt it acts just as the foregoing species ; also of this species some of the specimens observed were dead. With regard to the other species the matter is different. They are true plankton forms, which have been found in all the samples ; they are not rare in July 1902, but since then their number decreases rapidly, so that they have become very rare in the late summer months, when the tp. is above 9 ’5° ; in the autumn they begin to grow better, when the tp. sinks below 8°, but it is not before it has gone down to 5° that they really begin to develop. We now see that they are predominant in the winter, attaining their max. in March-April at a tp. of l°-2\ The coarser of the two species begins to be numerous in November-February, and attains its max. in March-April; while the slenderer grows a little less intensely in the beginning and has its max. in April-May. As it is very difficult to determine the Melosira species, I have 1116 Proceedings of Royal Society of Edinburgh. [sess. sent some samples and slides to Dr Otto Muller of Berlin, who has worked especially with this genus (1903, 1904). He has been so kind as to name the coarser species M. islandica , O. Muller, n. sp., and the narrower one “ M. italica, Ktitz., f. tenuis and f. tenuissima , with forms which pass into M. crenulata, Ktitz.” The M. islandica is most nearly allied to M. granulata, from which, according to his letter, it differs in the shape of the pores, in the absence of marginal teeth of the valves, and in the form of the so-called “ mutation.” Dr Muller will examine the species more thoroughly and publish the results later on in a separate paper. In a letter he tells me that the interesting facts of the different development of the pores in the two halves of a cell, or in the different cells of a chain, as well as in the different chains of a sample — a fact which he explains as mutation in the sense of H. de Yries — also occurs in the species from Thingvallavatn. He has given an interesting paper on this subject (1903), and he will now take also the two Icelandic forms into the examination. Dr Wesenberg-Lund and I are very happy to have obtained help from such an authority with regard to Diatoms as Dr Muller, and we desire to express to him, here, our best thanks for his kindness. Dr Midler will probably treat the question of the auxospore forma- tion from a more systematical point of view, but here I only intend to give a description of the development of this propagation method. In M. islandica I have found numerous chains wdtli auxospores, and thus I have been able to follow their formation rather well. The drawings in PI. I. figs. 1-7 will show some of the successive stages. The formation begins in the same manner as the ordinary cell-division : a cell in the chain prolongs itself by moving the connecting parts apart from each other, the plasma becomes con- centrated in the new-formed, thin- walled part of the cell, swells up and forms a sphere. At that time the cell bursts, because the cohesion between its two halves is diminished by the formation of the globular body ; we therefore always find the auxospore at the end of a chain, and often the chains have an auxospore at each end. At first the auxospore has no siliceous wall ; it increases until it reaches it legal dimension, then it produces a rather thick siliceous wall with a very low connecting part consisting of one 1904-5.] The Plankton of Thingvallavatn and Myvatn. 1117 (later on of two) thickened rings placed parallel to the valve faces,* as shown in fig. 3. At the same time we generally notice that the cell of the chain next to the auxospore-forming cell is in bipartition ; it has reached the prolongation stage. When the auxospore is fully developed, it almost immediately undergoes a division : between the half-globular valves a cylindrical part appears (fig. 4) and new flat valves are formed (figs. 5, 6). We now get a two-cellular chain, of which each cell has one globular and one flat valve. Contemporaneously with this process the above- mentioned next placed cell has finished its bipartition and has begun a new division. The auxospore chain continues its divisions in the ordinary manner (cf. Otto Mliller, 1883); often many- celled chains (fig. 7) with the auxospore valves at the ends have been found. The thickness of these chains is about 2-3 times that of the ordinary ones. The auxospores are often cohering to the ordinary chains until the auxospores become two-cellular, hut rarely later. The auxospore formation must begin rather suddenly ; in the sample of 14th December, no auxospores have been observed, while in that of 23rd January these are numerously observed and some of them already consist of two cells. In the sample of 18th February many-cellular auxospore chains occur, and such is also the case in the following samples. They do not become rare before May-June. Also in M. italica I have found auxospores ; but only rarely, and not at different stages; they occur in both samples from June 1903. They are rather like those of the foregoing species, as will be shown by my figures (PL II. figs. 6-8), but there are some differences. ' They are globular, and appear in the same manner in a prolongated ordinary cell, but while the cell in M. islandica soon bursts, it is not so in M. italica ; on the other hand, the neighbour cells have often disappeared, the individual then only consisting of a much prolongated empty cell with a globular auxo- spore placed in the thin- walled part nearest to one of the valves. A further distinction from the above-mentioned species is the connecting ring, which is not always parallel to the valve faces, but often more or less oblique. As I have seen only the unicellular * Holmboe (1900) has, p. 17, mentioned such auxospores in M. granulata, and given figures of them (figs. 2 and 3). 1118 Proceedings of Royal Society of Edinburgh. [sess. stage of the auxospores, I am unable to say anything of the further development ; worthy of notice is the fact that they appear much later in the year than the auxospores of the other species. A phenomenon in the plankton Melosirce , which is rather inter- esting, is that the chains are curved , generally so much so that they form a spiral or corkscrew. In my note on phytoplankton from an Icelandic lake (1904, p. 233), I have mentioned the same pheno- menon from a lake at Heidi in Myrdalur (South Iceland), and have given two drawings to illustrate it (figs. 4 and 5). The species which is so curved has been defined by me as M. granulata , f. curvata , Grun., but Dr 0. Muller, who has seen the plankton sample, tells me that it is better to name it M. italica. In Thingvallavatn the M. italica is straight or only a little curved, while the M. islandica is often curved in the same manner as the form from Heidi. My drawings of parts of auxospore-bearing chains will give an idea of the degree of curvature ; the longer chains form often a corkscrew. There is no doubt that this cur- vature, as pointed out by me (1904, p. 233), must be regarded as an adaptation to the limnetic existence ; it is evident that the power of floating must thus be augmented. It is curious that the curved Melosirce are so seldom mentioned in the plankton litera- ture, although the Melosirce are very commonly found in the plankton of lakes in many different countries, and generally play a predominant part in the composition of the plankton where they occur. In a paper by E. Lemmermann (1904 b, p. 17) we find the following remarks concerning the evolution of new plankton forms : “ As the first influential factor, I take, naturally, the movement of the water ; it causes, e.g., the different curvatures of the Melosira forms. It is very rare to find quite straight chains in the plankton ; generally the stronger of them are more or less semicircularly curved, the weaker ones often being spirally twisted” (cf. also E. Lemmermann, 1903, p. 92). If we add to this that H. Yolk (1903, p. 133) in a table notes a curved Melosira as rarely occurring in a single sample, I have mentioned all which I have succeeded in finding on that question.* * O. Muller (1895) has, according to information given me by Mr Lemmer- mann, mentioned the curved Melosirce, but the paper has not been accessible to me. 1904-5.] The Plankton of Thingvallavatn and Myvatn. 1119 From the remarks of Lemmermann, it seems as if the pheno- menon is a very common one ; hut if we consult the numerous photographs by Wesenberg-Lund (1904), we always will find the Melosirce, straight. Dr Wesenberg-Lund also tells me that such is the case in the Danish lakes. E. Lemmermann very likely is right in taking the movement of the water as the cause, but we have herein no explanation of the fact that the phenomenon is common in Iceland, hut does not exist in Denmark. We want here the experiment, and it cannot he very difficult to make it, if one has plankton with Melosirce at his disposal. Until that has been done, we must content ourselves by affirming the probability of the curvature being an adaptation for floating, but we are not able to explain anything of the cause which has produced it. Rhizosolenia. — In many of the samples I have found the peculiar fresh-water Rhizosolenias, but only in the two samples from June 1903 did they become rather abundant. The identifi- cation of the species is not easy ; at first I thought that all the specimens belonged to one species, which must be a form of R. eriensis, and that the individuals varied greatly in size and shape. But on a closer examination of many specimens, I became convinced of the existence of two species or races. I shall here give some figures representing the results of measurements of 14 specimens (in //,). It will be seen that the breadth of the cell Table I. Indi- viduals. No. Length of the Cell. Length of the Cell without Setae. Length of the Setae. Breadth of the Cell. 1 174 134 20 + 20 8-5 2 104 68 20 + 16 7‘5 3 110 74 18 + 18 10 4 184 136 24 + 24 10 5 132 98 18 + 16 8 6 160 122 20 + 18 8 7 180 136 20 + 24 11 8 120 84 20 + 16 4 9 120 90 16 + 14 5-5 10 160 120 22 + 20 7 11 148 110 20 + 18 4 12 112 76 20 + 16 45 13 100 70 16 + 14 4-5 14 134 94 20 + 20 5 1120 Proceedings of Royal Society of Edinburgh. [sess. varies greatly in the different individuals, the narrower ones measuring from 4 to 7 /x, the broader ones from 7 '5 to 11 g, but no relation seems to exist between the breadth of a cell and its length ; there are broad and long, broad and short, narrow and long, and also narrow and short individuals ; perhaps the broad individuals generally are a little longer than the narrow ones. Nor does any clear difference express itself between the broad and the narrow ones as regards the length of the setee. But never- theless do the broad individuals differ from the narrow ones in small morphological characters as well as in the breadth, which will he seen if we compare the drawings of some specimens (PI. II. figs. 1-5). In the broad specimens an undulation of the cell contour near the basis of the setae indicates the place of the seta of the neighbour cell, while in the narrow specimens the cell contour is not undulated, hut has only a double outline, i.e., the cell has a furrow, in which the seta of the neighbour cell fits in. Further, the narrow specimens are cylindric, the broad ones are applanated; a specimen, which was 11 g broad at the one axis, measured only 4 g at the other. Many of the narrow specimens are somewhat curved, while the broad ones always are straight. By all this I think we must conclude that the broad specimens belong to one race or species, the narrow ones to another. In all the samples in which Rhizosolenice have been observed, some specimens have been measured with regard to the breadth of the cell. It was a priori possible that the two races were different forms of one season-dimorphic species ; if so, we must have found samples in which only one of the forms occurred, other samples in which the one form was rare, the other common, etc.,* but this does not seem to be the case, as both races were present in about the same quantity in the samples in which a larger number of specimens has been met with, as will be seen from the following text-table II. In the first sample (14th July 1902) I did not succeed in finding the broad race, nor did I see more than three individuals of the narrow ones. In the samples from the early spring of 1903, very few specimens were seen, and the greater part of these were of the broad race ; but as the number is so small, I dare not draw any conclusions based on observations of as few specimens as these. * Cf. Schroter, C. , and Vogler, P. (1901), 1904-5. j The Plankton of Thingvallavatn and Myvatn. 1121 Table II. Date of the Sample. Narrow Race. Broad Race. Number. Per cent. Number. Per cent. 1902, July 14 3 100 1903, Feb. 18 4 40 6 60 ,, March 31 2 20 8 80 ,, April 16 3 23 10 77 „ ,, 30 15 60 10 40 ,, May 11 10 33 20 67 „ „ 31 10 50 10 50 ,, June 15 48 48 52 52 „ „ 30 20 51 19 49 Total 115 135 The measurements in Table I. have been taken from specimens lying in the preserving fluid, and after treatment with methyl- violet ; the breadth of the cell varies then from 4 to 1 1 p. In the same manner the 100 specimens in Table III. have been measured, hut as the measurements of Rhizosolenias hitherto published by different authors generally have been made in dried specimens, I have also, for easier comparison, measured 100 specimens of the same sample (15th June 1903) in dried condition (Table IV.). The figures 4-16 represent the breadth of the cell in p, and each point denotes a specimen ; to the right the number of specimens have been summed up. In this way we get two curves, which tell us several things. Table III. Table IV. Breadth of the Cell (p), 100 Breadth of the Cell (p), 100 non-dried Specimens. dried Specimens. 4 17 4. ... 3 5 16 5. 7 6 11 6. 10 7 6 7 11 8 23 8. 1 7 9. . 11 9. Q 10 8 10 o 7 11 6 11 10 12. . . 2 12 13 7 14. ... 3 15. . 1 16. . 1 PROC. ROY. SOC. EDIN. — YOL. XXV. 71 1122 Proceedings of Royal Society of Edinburgh. [sess. Both curves have two climaxes, which become an important support for our opinion that there are two races. The comparison of the two tables shows further that the drying of specimens causes the climax of the narrow race to be transferred from 4-5 y to 8 y, and that of the broad race from 8 to 12 y* It is natural that the narrow race has changed a little less than the broad one, because the change occurring is that of a cylinder being flattened, and this effect must be greater in a large cylinder than in a smaller one. The effect of drying may also more directly be made out. Some of the broader specimens contain resting spores which are much more strongly silicified than the other part of the cell, and therefore they do not become flattened in any mentionable degree. In two specimens the figures were : breadth of the cells, 1 4 y and 11 y, breadth of the corresponding spores respectively, 11 y and 8 *5 y ; the difference is then 3- 2-5 y, that is, 1 y less than the comparison of the tables gives us, but it must be remembered that also the spore becomes a little flattened. The result arrived at through all these reflections is, that the narrow race, which has its normal breadth at about 4 y. must be reckoned as about 8 y broad, if we want to compare our figures with the measurements of other authors ; regarding the broad race the figure is, instead of 8 y7 about 12 y. To make these figures as exact as possible, I have measured specimens from all the samples in dried condition ; the above Table II. gives the number of specimens measured in each sample, and in this table the distinction between the narrow and the broad race has been determined according to the above reflection and to the following Table V., in which the breadth of 250 specimens is represented. * An ocularmicrometer, in which each space between two lines corresponds to 4 /x, has been used for the measurements ; this may explain the curious fact that Table III. is one-sided, then the specimens, which really are 3 /x broad, may easily be taken as 4 ^ broad. ] 904-5.] The Plankton of Thingvallavatn and Myvatn. 1123 Table Y. Breadth of the Gell (/a), 250 dried Specimens. 4 6 5 16 6 24 7 26 8 . . 43 9 13 10 21 11 23 12 43 13 18 14 10 15 5 16. . . 2 The shape of this curve is exactly like that of Table IV., the same two climaxes of 8 jul and of 12 /x exist here, also the same extremes of 4 /a and of 16 p. As mentioned above, the broad race bears resting spores , while I have not been able to discover any spore-bearing specimen of the narrow race. The spores occur only in the samples from June 1903. My drawings (PI. II. figs. 2, 3) will give the shape of such a resting spore seen from the broad as well as from the narrow side ; they have one convex and one concave valve, and are much more silicious than the other part of the cell ; the whole plasmatic content of the cell is concentrated in the spore, in which the nucleus and the chromatophore substance is easily shown. The spore-bearing specimens vary in breadth from 9 to 16 fx (in dried condition), 11 to 13 g being the ordinary figures. If we wish to consult papers dealing with the fresh-water Rhizo- solenias, we will find many notices scattered in different publications. The first-described species is R. eriensis , H. L. Smith, found in the large North- American lakes and later also registered from Europe (Italy, Switzerland, Germany, Finland, Sweden, and Scotland), but always only in a single or in few lakes in each country. To this species, of which two varieties have been proposed, I should refer the broad race from Thingvallavatn. Different drawings of this species exist. A drawing which comes near to the Thing- vallavatn form has been published by O. Zacharias (1898. p. 716; 1899, p. 85). He gives some measurements which do not differ much from those of the Icelandic form, the most striking divergence being the length of the setae. Also Bruno 1124 Proceedings of Royal Society of Edinburgh. [sess. Schroder (1898, p. 529) has measured a form of R. erie7tsis, Avhich he found near Breslau ; this form is shorter than ours. K. M. Levander* (1904) has recently written a little paper on the Rhizosolenias of Finland ; he has found R. eriensis in two lakes, and has had specimens from Lake Erie for comparison ; his drawings of the Finland as well as of the Erie forms agree well with my drawings. Table YI. Saxony. Breslau. Finland (Keitele). Finland (Valijarvi). Iceland (Thirigvalla- vatn). Canada. Recorded by, O. Zacharias B. Schroder Levander Levander Ostenfeld Levander M M M- V- Length of the setae, 20-40 18-7-25-5 24 40 14-24 25-40 Length of the cell without setae, 30-64 30-57 8 52 80 68-136 70 1 Breadth of the cell, 6-10 9-4-15-3 11 12 8-16 12-20 In Table YI. I have placed the different measurements together ; it will be seen that the Icelandic form is somewhat longer than the others, but has shorter setae. The narrow race seems also to have been found by 0. Zacharias, and his drawing and notes are published as quoted above. In 1898 he has named it R. paludosa, Zacharias, but in 1899, p. 87, he has taken it as a variety of R. longiseta, Zacharias, formerly described by him. From this species it differs by the much shorter setae, the curved shape and the more distinct structure ; the cells with setae are 100 to 120 g long, and 8 to 12 g broad, while the setae are about 40 p. The typical R. longiseta , Zacharias, has a length of 160 p (without setae) and the setae measure about 180 to 200 p. By these figures it becomes evident that there is a great difference between the type and the variety, and if we take the narrow Icelandic form as belonging to the variety, the difference will be still greater. Although the above-mentioned measure- ments of the Icelandic form in some ways differ from Zacharias’ figures of his R. paludosa , I have found it better to register my * I have taken the figures of the Erie form in my Table YI. from the drawing on his plate i. 1904-5.] The Plankton of Thingvallavatn and Myvatn. 1125 form under his name ; his drawing is very like mine, and the lengths and the breadths of the cells are about the same, but the Saxonian R. paludosa has longer setae. Perhaps we should do better in making a new species, but at present I do not intend to do so. No doubt there are many races of fresh-water Rhizoso- lenias connected with each other, so that they form a series, of which the extremes are the broad R. eriensis with short setae and the narrow R. minima , Levander, 1901, with very long setae. There are two ways to go : either take all the races as one species or separate them ; whether the one or the other way is correct, is at present impossible to decide. The simultaneous occurrence of two forms in a sample may be used as an argument against as well as in favour of both contentions. We do not know anything of auxospores in the fresh-water Rhizosolenias, but if such things exist (which is not at all unlikely, as several of the marine Rhizo- solenias have been found with auxospores) we therein perhaps may find the explanation of their peculiar occurrence in apparently distinct but nearly allied races. It seems rather peculiar that both species in Thingvallavatn occur also in the winter samples, although they have their maxima in June. Nearly all the previous records of Rhizosolenias belong to the summer, only by Wesenberg-Lund (1904) we find records of R. longiseta from every month of the year (p. 68). This circum- stance is probably partly due to the fact that most of the plankton investigations have been made in the summer, and partly on account of the very thin and small Rhizosolenias having been over- looked when they were not present in large quantities. The fresh-water Rhizosolenias have a very wide distribution ; the most common form is R. longiseta , Zach. Of R. eriensis we have records from Canada (Lake Erie), Finland (two lakes), Germany (two lakes), Sweden (one lake), Scotland (two lakes), Switzerland (two lakes), and Italy. Worthy of notice is the very scattered occurrence. Concerning R. paludosa, Zach., the records are scarcer ; besides Germany, we have more or less reliable statements from Scotland (Loch Shin), Denmark (Soro lake), and Finland (Yalijarvi). At last we must remember the most delicate form, R. minima , Levander, found in the bay of Wiborg (Finland), together with Altheya and other fresh-water forms. 1126 Proceedings of Royal Society of Edinburgh. [sess. Flagellate. Mallomonas. — In the two samples from June 1903 I have observed a few specimens of a small Mallomonas , but as I have seen only so few individuals, I have not succeeded in discerning distinctly the shape of the scales and cannot with certainty identify the species. I have drawn two figures (Pl. II. figs. 9-10), the one showing a specimen with resting spore, hut without setae ; the other represents an ordinary cell with setae only in the antapical (or apical?) part, perhaps also the resting part of the cell has been covered with setae, now fallen off. As far as I have been able to notice, the scales are round, but they may also have been transversely ovate, the setae are hardly visible, but I cannot tell whether they are smooth or denticulate. The dimensions (length 28 g, breadth 18/r) agree very well with those of M. longiseta , Lemm.,* of which no figure exists ; it has denticulate setae, which cover the entire cell, and ovate scales. Owing to these insufficient notices, I have preferred not to name the form specifically, hoping that future investigations may decide the question. Peridiniales. Peridinium. — The only f species of Peridinium which has been found in the samples is a rather interesting form ; it occurs in the samples from 1903, and has its maximum in February-March, when it constitutes a great part of the phytoplankton. In the Plate I have given drawings of specimens at different stages. In February and March nearly all the individuals are cells without any wall, but embedded in a wide gelatinous envelope (see PI. I. fig. 11). In the cell a large nucleus is shown partly covered by large refractive granules (see PI. I. figs. 11-12). The vegetative multiplication occurs by ordinary cell-division, and different stages of the division are often seen, by which it is easily observed that the division takes place at a right angle to the longitudinal axis of the cell (PI. I. fig. 13). In this stage of development it is impossible to identify the organism with any degree of exactness, * See the key of the genus by E. Lemmermann (1904, pp. 117-118). f In the sample from 30th June I found one single specimen of a little Peridinian which I was unable to define. 1904-5.] The Plankton of Thingvallavatn and Myvatn. 1127 but it seems most natural to place it in the genus Gymnodinium. Together with these Gymnodinium-like cells a few specimens of a true Peridinium have been found, and these become more frequent in the samples from April, when the Gymnodinium-like cells decrease in number. From the similarity of the contents in the Peridinium (PI. I. fig. 18) and of the naked cells, as well as from a few specimens of the Peridinium in which the cell-contents are breaking out (PI. I. fig. 19), it will be evident that we have two stages of one and the same organism. The cell-wall is rather thin, and it is difficult to discern the plates, but after treatment with iodine-zinc-chloride the wall becomes reddish-violet and the sutures to a certain degree visible. The arrangement of the plates (PI. II. fig. 18) of the apical limb is about the same as in P. umbonatum, Stein, but I have been unable to see the plates of the antapical one, so the placing of our organism in the genus Peridinium consequently is based on analogy. Around the antapical part of the longitudinal furrow three small spines occur ; they are merely prominent membranous prolongations of the sutures (PL II. fig. 18); the middle one is the most prominent; it is linear when seen in a ventral view, but triangular when seen in more dorsal view. These three spines distinguish our species from the P. umbonatum , Stein, to which it is nearly allied. In the literature I have found a short description of a Peridinium aciculiferum named by E. Lemmermann (1900, p. 28), which agrees very well with our species, but as I did not dare to run the risk of identifying the two forms merely on the basis of but such a short description without any drawing, I asked Mr Lemmermann for a drawing or a sample containing his species. He has been so kind as to send me a drawing as well as a sample, for which I am much indebted to him, and after examina- tion of the latter I do not hesitate to take my form as identical with his species, and consequently I name it P aciculiferum , Lemm. Perhaps the spines in his form are a little longer, and more prominent. He writes that his species, which has been found in a lake in the neighbourhood of Berlin, has numerous, discoid, brown chromatophores ; the above-mentioned refractive bodies are perhaps chromatophores, but it is impossible to decide on the question when having only preserved material at hand. 1128 Proceedings of Royal Society of Edinburgh. [sess. When the number of our species in May begins to decrease, a number of thick-walled cysts appear, one of which I have drawn on PL I. fig. 20 ; the cell-wall consists of cellulose, like the wall of the Peridinium ; the cell-content contains starch and is rather condensed, but a nucleus of the ordinary Peridinian shape is clearly shown. I suppose that these cysts represent the resting stage of the Peridiniums. In June our species has become very rare, only some empty scales of the Peridinium stage and some cysts having been found. I presume that most of the cysts have dropped to the bottom. Then probably the life cycle of the species is as follows : in the summer and autumn the cysts rest in the bottom mud, then in January-Pebruary they rise in the plankton developed in the Gymnodinium stage and embedded in a large jelly ; the cells divide repeatedly in Pebruary-March, and in April form the Peridinium stage with cell-walls consisting of plates. Prom this stage we must imagine the cysts developing in such a manner that the cell-contents of the Peridiniums go back from the inner side of the cell-wall, and then secrete the new, thick homogeneous cell- wall, thus forming the cysts which sink from the plankton to the bottom. Length of the Peridinium, 35-40 g ; breadth, ab. 30 g. Lemmer- mann says (1900, p. 28) 32-42 g broad and 41-51 g long : thus his forms seems to be a little larger than the Thingvallavatn form In a later paper (1903, p. 109) he mentions our species as occurring in the months February to April, and quotes (pp. 86- 90) the following tp. figures of the water, observed when the samples were taken, viz., 4‘25°, 2,9°, 6'5°, 4*8°, 8*5° and 12-1°. These figures correspond rather well to the tps. of the Thing- vallavatn, varying from 1° to 8 ‘5° in February- June. We accordingly must take our species as a cold-water Peridinium. ( c ) Zooplankton. By C. Wesenberg-Lund. Heliozoa. Acanthocystis aculeata , Hertwig and Lesser. During the time from 31st March to 30th April I have found in the samples a small Heliozoan ; it was always rare, being 1904-5.] The Plankton of Tliingvallavatn and Myvatn. 1129 most common on 16th and 30th April. As my knowledge of the Heliozoa is but slight, and as the animal was badly preserved, I sent it to Dr Penard, who kindly wrote me that, according to his opinion, it was an Acanthocystis aeuleata, but a somewhat smaller specimen than those which he had examined in the Swiss lakes, for instance, in Lake Geneva. Infusoria.. Front onia, Ehrbg. In the sample of 16 th April I found a very peculiar body, which at first sight caused me a good deal of trouble ; it was a brown sack generally c. 200 g long and 50 p broad ; it was quite filled with long Melosira chains in numbers of 3-7, and the chains often stuck out either at the one end or the other; near the centre I always found a black body, and the surface of the creature was covered with fine granulations. I had never before in a plankton sample seen anything like this creature, and was hardly sure of having an animal before me. Dr Penard, who kindly also examined this body, told me that it must be an Infusorian, and Dr Roux, to whom he showed it, supposed it to be a Front.onia. I wish to offer both gentlemen my most cordial thanks for their kind determination of the animal. It is the first time we have met wdtli an Infusorian of this group as a plankton organism ; as far as I remember, I have never seen such a one living so exclusively on another organism and, so to say, preying upon Melosira and solely upon this single organism. Rotifera. Polyarthra platyptera, Ehrbg. P. platyptera is perennial, although it has not been found in a few of the early spring samples. The variety euryptera has not been found. P. platyptera has a great max. (14th July) ; at that time some individuals with male eggs have been proved ; the dark-spined winter eggs are by no means rare, especially in the autumn and winter samples. 1130 Proceedings of Royal Society of Edinburgh. [sess. Synch ceta neglecta , Zaeh. It is a well-known fact that the different species of the genus Synchceta can hardly he distinguished by means of preserved material ; when the water with the living animals is immediately poured out into glasses containing concentrated formaline, it some- times happens that the animals do not pull in their wheel organ. In the samples I have found a few specimens with protruded wheel organ ; on the basis of these samples I suppose that the species in the pelagic region of the lake is S. neglecta (Zach.). It is doubt- less perennial, and its max. seems to occur at a low tp. Ploesoma lenticulare , Herrick. In the two samples of 15th and 30th September I have found a species of Ploesoma . The animal was rare ; the lorica of the animal lacked the fluffy tissue characteristic of the two species P. Hudson i (Imh.) and P. molle (Kellicott.) It differed from the easily recognisable P. triacanthum (Bergend.). Still, I am not sure whether I had the P. lenticulare (Herrick) or P. truncatum (Levander) to deal with, as all of the animals were greatly contracted. In all the samples from August to September I found the limnetic egg characterised by a great hyaline space between the very small yolk mass and the egg-shell. Asplanchna priodonta, Gosse. This species has occurred in very few samples at different times of the year. I believe it to be perennial, but it seems rare in the , pelagic region of the lake. Anur cea cochlearis , Gosse. The species is found in all the samples and is therefore un- doubtedly perennial; I have not observed any strongly marked max. The number of specimens is never great ; perhaps a small max. may be pointed out for October and November. All the individuals belong to the well-marked hyaline, long-spined lake form. 1904-5.] The Plankton of Thingvallavatn and Myvatn. 1131 Notholca longispina , Kell. N. longispina of the Thingvalla lake differs slightly from most specimens of southern countries, the posterior spine is not straight or only slightly arched, hut shows a very remarkable upward curve. It is perennial, and seems to carry its eggs all the year round ; strongly marked max. and min. have not been pointed out, but it seems to me that it has been most common in winter. Notholca striata , O.F.M. Only a very few specimens of N. striata have been found ; just as with us, it appears in the winter months and disappears in early spring. Gonochilus unicornis , Rousselet. The first individuals were found on 30th August, the last on 23rd January. I have not b^en able to find a single individual from January to August. In the samples the colonies have all been broken up and only single individuals were found. Except Ploesoma lenticulare , all the Rotifers mentioned above belong to the common, widely spread stock of cosmopolitan plankton organisms which have been found in every locality where plank- ton explorations have been carried on. Their existence on the Kolgujev island has also been pointed out by Skorikow (1904, p. 209), and on the Murman coast by Levander (1901, p. 1.) It is strange that only so few of these species have been mentioned by Bergendal (1892) from Greenland, which has been better explored as regards its Rotifer fauna than any other arctic country. According to my opinion, this stock of cosmopolitan plankton Rotifers may also be found in Greenland. The reason why Prof. Bergendal has only met with such a few species in his explorations of the pelagic region of the greater lakes, is most likely because he could not make use of a plankton net, the plankton explora- tions in fresh water at that time (1890) being anything but methodically carried on. 1132 Proceedings of Royal Society of Edinburgh. [sess. Among the cosmopolitan stock of plankton Rotifers from greater lakes, I also reckon Anurcea aculeata and Triarthra longiseta, which have not been found in Thingvallavatn. This stock then consists of the following species : Polyarthra platyptera , SyncJiceta sp., Asplanchna priodonta , Anurcea cochlearis, Anurcea aculeata , Notholca longispina, Conochilus unicornis , and Triarthra longiseta. Skorikow (1904, p. 209) has pointed out that all the species from the lakes on Kolgujev have also been found in the alpine lakes of Switzerland. Skorikow’s point of view in this regard is expressed as follows (p. 212): “Ein Ubereinstimmen der ark- tischen und alpinen Fauna ist gewiss nichts Neues, aber eine so vollstandige Identitat wie in diesem Falle, meine ich, verdient einige Aufmerksamkeit ; besonders ist dies hinsichtlich der Rota- torien interessant weil man sie in schon iibertriebenen Mass als untauglich fur geographische Z we eke ansah.” According to my opinion, Skorikow takes a wrong view of the result of the exploration. Nowadays we have found in every thoroughly explored lake with a well-defined limnetic region the above-mentioned stock of Rotifers ; it belongs by no means only to the arctic and alpine lakes, but quite as well to all lakes situated between the arctic and the central European highlands. So that when we may show “vollstandige Identitat” in the plankton Rotifers of the arctic and the alpine lakes, this is, geo- graphically speaking, by no means noteworthy ; on the other hand, and from a biological point of view, it becomes of interest that the association of Rotifers living under arctic conditions remains the same everywhere ; in the shallower, and in summer much warmer, lowland lakes this association also exists, but is here mixed up with all the monocyclic summer Rotifers which, in order to exist, require a tp. of between 16° and 20° C. It may be that the Rotifers at some future time may become instrumental in furthering geographical studies far beyond those we at present dream of. Still, I feel convinced that the way in which so many naturalists, from observations based upon a few samples collected in out-of-the-way places of the globe, often think fit to lay down laws for the distribution of the associations, or to subvert results that have been arrived at by others, is not much to the purpose. 1904-5.] The Plankton of Thingvallavatn and Myvatn. 1133 Cladocera. Daphnia longispina, O.F.M. With regard to the longispine group of the genus Daphnia , I have in my plankton work (1904) followed Lilljeborg (1900), who refers all the longispine Daphnids to the two species D. hyalina (Leyd.) and D. longispina (O.F.M. ). Still, I supposed these two species to be only one, of which the hyaline group, at any rate in our country, mainly consists of plankton organisms in the greater lakes, the longispine group belonging chiefly to the central parts of ponds and smaller lakes ; for want of time I was prevented from studying the smaller lakes more closely, and did not venture at that stage of my explorations to refer all longispine Daphnids to one species only. Later on Sars (1903, p. 8) has united the two species, and Ekman (1904, p. 17) likewise. The form which occurs in the Tliingvallavatn proves to belong to the microcephala galeata group (Ekman, p. 123). In early spring we only find forms which undoubtedly are identic with the microcephala forms ; Ekman also classifies these as spring forms. In Thingvallavatn the species never develop into the galeata forms, which often occur in Sweden as well as in our country. In the summer and fall the individuals may most probably be referred to the form obtusifrons , yet differing from this by a more acute rostrum and a greater bend in the ventral edge of the head. On 14th July we only find young parthenogenetic mothers, some of them with 2 to 3 eggs (fig. 1) ; from 31st July males and females with ephippia (fig. 2) occur in all the samples till 15th September ; the joint number of individuals is very small. On 15th September D. longispina is common; most of the animals are parthenogenetic females with few (2-3) eggs ; ephippial females do not occur, but some males with faintly developed first pair of antennae. On 30th September D. longispina is very common, and many of the females have ephippia again ; besides, we find many quite young females without eggs of any kind (fig. 3) ; the males are now common. On 15th October D. longispina is remarkably rare ; young females without ephippia and young males occur. From 31st October to 14th December D . longispina 1134 Proceedings of Royal Society of Edinburgh. [sess. is the main form in the plankton samples. On 31st October several females have ephippia, yet the greater part have none ; the males appear in countless numbers and are now fully developed ; even now we find no more young animals. On 16th November the Fig. 1. — 14th July, young female, two eggs. Fig. 2.— 31st July, female with ephippium. Fig. 3. — 30th Sep- tember, young female. Fig. 4. — 14th December, big female with ephippium. Fig. 5. — 14th December, small female with ephippium. ephippia of most of the females are more or less conspicuous, but very few have eggs in them. On 30th November all the females have ephippia and in most of them are eggs ; the number of males is decreasing. On 14th December only females with ephippia or barren females occur; males are wholly wanting. On 23rd January the number of D. longispina is but small and consists only of females. D. longispina is wanting in all the samples 1904-5.] The Plankto7i of Thingvalla.vatn and Myvatn. 1135 from 23rd January till 31st May, when the first very slender young ones may be noticed ; these occur also in the last samples, 15tli and 30th June. In D . longispina of the Thingvallavatn we only find a very slight seasonal variation. The microcephala forms, which occur in May, and probably disappear in July-August, are very much alike throughout the period, but they differ some- what from forms which occur during August- January and which, as stated above, may be considered as obtusifrons forms. The drawings will show the main differences, especially with regard to the shape of the head. I have not been able to point out any seasonal variations as to the obtusifrons form. Only in December it may be noted that the ephippial females occur in two sizes, the one is c. 2-3 mm., the other only 1'2 to 1*5 mm., the former has a short spine, the latter commonly a much longer one (figs. 4 and 5). From the facts stated above, we may gather that the life cycle of D. longispina lasts at least from the end of May to February. Still, I think it very probable that some animals — the young ones of the last autumn’s brood — here as in Danish lakes survive in deep water and propagate in spring. How large. a percentage of the total number of D. longispina in the lake the stock of these females amounts to, and how many of these individuals are derived from ephippia, we are unable to decide. With regard to the number of generations and broods, I have arrived at the following conclusions. At the end of July and in August we find males and females with ephippia, but after the 15th September no ephippial females, but only young animals with 2 to 3 parthenogenetic eggs and a few not quite developed males, occur. As we again find on 30th September ephippial females and numerous males, I cannot see but that D. longispina in the Thingvallavatn may be regarded as dicyclical. Moreover, when taking into consideration that during the time in which the first sexual period appears we first (July) find females with 2 to 3 eggs and later on males and females with ephippia, I conclude that the spring generation to begin with will propagate parthenogenetically, thus producing males and females, but in all probability only one or two broods ; afterwards it will produce ephippia and then disappear (September). 1136 Proceedings of Royal Society of Edinburgh. [sess. The second generation will produce two parthenogenetic broods and then ephippia. The first of these broods will also, to begin with, propagate parthenogenetically (August-September), and later on sexually (October-December) ; the second one only sexually (November-December). The first of these broods lives from July to December, and is in December represented by large females with ephippia and short spines ; the second brood, which lives from September-October to December, is in December represented by the small-sized, loug-spined, ephippial females. With regard to the above given details, there is especially one doubtful point. I have not been able to decide whether the first generation totally disappears in the latter part of August, or whether some of its members live on and assume the aspect of the obtusifrons generation ; according to my knowledge of the cycle in the Danish lakes, I feel inclined to consider the first view as the correct one. Copepoda. Diaptomus minutus, Lilljeb. The Diaptomus species of the Thingvallavatn is the easily recognisable D. minutus (Lilljeborg). It is described by Lilljeborg from Greenland and Newfoundland ; it is mentioned by Marsh (1893, p. 199) from Green lake, North America. In a subsequent paper (1897, p. 8) Marsh describes it as the commonest of all Diaptomidae appearing in samples collected in the great American lakes. Richard and De Gueme (1889, p. 632) states that it has been found in Greenland near Tasersuak. The species of the Thing- vallavatn has already some time ago been determined as D. minutus by the same authors. On 14th July D. minutus occurs in enormous numbers, but only as young ones. On 31st July I found many males with spermato- phores within their bodies ; the abdomen of the females is quite straight and the oviducts hardly noticeable ; some females have 2 to 3 eggs. From 14th August till 15th September the sexual period is at its max. Males and females are nearly equal in number ; the males all have spermatophores in their bodies, and the females often carry a cluster of 4 to 5. The egg-sacks never contain more than 4 1904-5.] The Plankton of Thingvallavatn and Myvatn. 1137 eggs and later in the period only 2 to 3. The oviducts are very conspicuous, and present dark tubes containing unripe eggs. The abdomen of the females is strongly curved and often, owing to pressure of the egg-sack, bent upwards at a right angle with the cephalosome. Yery often I have found females with remnants of an earlier egg-sack attached to the abdomen, at the same time having oviducts filled with unripe eggs. By this we learn that a female may produce more than one brood. From 30th September to 16th November the species gradually disappears. On 15th October the oviducts contain no more unripe eggs, and females with egg-sacks are rare. The va-sa efferentia of the male have no spermatophores ; a few males were found on 16th November but no females with eggs. The last individuals are observed on 23rd January, when the species totally disappears, new individuals again appearing in spring 1 904. As far as I have been able to make out, D. minutus has only one kind of egg, and I have never seen any egg beyond the gastrula stage. With regard to the colour, we find two kinds of eggs, one being red and uncleft, the other gray and cleft to the gastrula stage. First I supposed the shell of the former, which is of a yellow colour, to be a little thicker than the hyaline shell of the gray eggs, but later I found intermediate stages between these. Furthermore, as I have never found nauplii in the time from 14th July 1903 to 16th April 1904, I suppose that all of the eggs are resting eggs. Ekman (1904, p. 103) arrives at the same result with regard to the eggs of D. laciniatus , denticornis , and laliceps. Owing to the quality of the material it is impossible to give a correct conspectus of the life cycle of D. minutus ; in this respect it is most unfortunate that the collections have not been carried on after 30th June 1903, when the nauplii had begun to appear. I feel inclined to believe that the species has only one generation, which is hatched in April-May and dies out in January. This generation is derived from resting eggs which have hibernated in deep water either on the bottom or suspended in the water. My interpretation of the life cycle may perhaps be correct, inas- much as Marsh, in 1897 as well as in 1903 (p. 22), after a most PROC. ROY. SOC. EDIN. — YOL. XXY. 72 1138 Proceedings of Royal Society of Edinburgh. [sess. thorough exploration, has given a rather similar sketch of the life cycle of D. minutus in Green lake and in Lake Winebago. According to Marsh, D. minutus occurs there from July to December; the great max. occurs about the 1st of August, but it also has another but smaller max. in October ; the species is rare in winter and spring. Cyclops strenuus, Fischer. The Cyclops species of the pelagic region of the Thingvallavatn is C. strenuus (Fischer), and not C. scut if er (G. 0. Sars), to which result Richard (1892, p. 310) already has arrived. The species appears in the forma vernalis , Lilljeb. (1901, p 47), which, accord- ing to Ekman (1904, p. 30), also is characteristic for the North Swedish alpine region. As far as my experience goes, it has no conspicuous seasonal variations in the Thingvallavatn. On 14th July the species is rare, and only a few young unripe animals are found ; on 31st July the number of animals is enormous, but all are quite young. In all the following samples till 30th September, its occurrence is rare, after that the species again becomes common ; ripe males and a few females with eggs appear ; the number increases steadily until 23rd January, when the species attains the main form and occurs in enormous numbers. All the females carry eggs, and males may be noticed in all the samples, but become rare in January. Then C. strenuus disappears entirely, and is not seen again until 16 th April. In all the following samples till 30th June we find the number of individuals in- creasing. In May we only observe nauplii or very young animals ; they become very numerous in June. From the above statements it is impossible to arrive at any con- clusion as to the propagation of C. strenuus in the Thingvallavatn. The very small number of individuals at 14th July, the enormous quantities at 31st July, and the almost total disappearance from 31st July to 30th September, clearly show that the samples by no means verify the existing facts. We are only able to note that from 14th July to 30tli September 1902, as well as from 16th April to 30th June 1903, no ripe males or females with eggs appear. During this period we only find nauplii or half-grown 1934-5.] The Plankton of Thingvallavatn and Myvatn. 1139 broods; the sexual period does not begin till the last days of September, and continues till January. The number of eggs in every egg-sack at 30th September is about 4, in October-November 6-7, but in December- January it diminishes again (2-3). I suppose that further explorations will show that the limnetic region of the Thingvallavatn contains several other plankton Crustacea .than those mentioned in this paper. It must be kept in mind that all the samples are surface samples, and I consider it most probable that different species, especially Bythotrephes , may be found in deeper waters. Richard and De Guerne men- tion, as stated above, different bottom and shore species, among which we also find Bosmina arctica (B. obtusirostris). This species may be considered a plankton as well as a shore organism. I only wish to emphasise that none of my numerous plankton samples ever contained a single B. arctica. III. MYVATN. By C. Wesenberg-Lund. 1. General Remarks. Myvatn is situated in the northern part of Iceland, in latitude 65° 33' N., 292 m. above sea-level, and is'nearly 27 square kiloms. in extent. The lake has been formed in down-sunken parts of enormous lava torrents. The bottom consists almost entirely of lava, and is nearly everywhere surrounded by widely extending lava grounds. Along the shores, and forming islets in the lake itself, the lava is congealed in very peculiar and fantastic columns. The lake is situated in a volcanic area, which even now-a-days may be considered extremely active. Upon the east side of the lake very many solfatares occur. According to Thoroddsen, the ground is here actually seething with hot vapours, and it is dangerous to walk upon it; little hillocks of sulphur are very common and alternate with pools of mud, which incessantly boil and bubble, while ejecting bluish-black clay mud. The surrounding country, especially the northern and eastern part, is extremely void of water, as all the rain is absorbed by the porous volcanic soil. It seems as if the water, partly through 1140 Proceedings of Royal Society of Edinburgh. [sess. subterranean channels, is conducted to the lake, which is mainly nourished in this manner. Especially the eastern side of the lake has very many hays, and in the lake itself we find many (c. 100) inlets, for instance, the wood-covered Sluttness and Geitey ; many of the inlets are craters. The small Geitey, although measuring hut 14 kiloms., has no less than 10 craters ; the highest of these is 70 feet above the level of the lake. Many of the craters are now filled with water, and present themselves as circular, quiet crater lakes. The vegetation around the lake, upon the inlets and in the lake itself, is extremely rich. There exists a list of plants gathered near and in Myvatn by Gronlund (1890, p. 107), to which paper I refer. The islands are often covered with birch, sorb, and willows, the stems of the birch being 12-14 feet high, or with Angelica and other plants. In the lake itself we find Myriophyllum , Potamogeton, Hip- puris , etc., in great abundance. Nostoc is further, according to Soemundsson and Thoroddsen, abundant, forming huge masses near the shores. Myvatn is an extremely shallow lake ; the oars will 1904-5.] The Plankton of Tliingvallavatn and Myvatn. 1141 always reach the bottom in great parts of it, the greatest depth being only 2-3 m. It must he emphasised that during the great volcanic eruption in 1729 the lava ran into the lake ; the greater part of this became exsiccated, and people thus laboured under the impression that the water burned like oil. Great quantities of the water were trans- formed into vapour, and all living organisms probably became extinct. The shape of the lake was altered, islands arose, and in other localities the water inundated the meadows and old islands disappeared. At the present moment animal life is extremely rich. The fine mud, which covers the lava bottom, is filled by myriads of larvae of gnats, especially Chironomus and other diptera ; at certain seasons the water teems with enormous quantities of the skins of the pupa and dense clouds of gnats arise. From these clouds the lake has derived its name, Myvatn signifying the lake of gnats. These gnats have never to my knowledge been scientifically studied. Some of my samples contain nothing but skins of Chironomus pupae, but undoubtedly stinging gnats ( Culex , Simulium) may also be found in or near the lake. All travellers have pointed out how difficult the sojourn is near or on the lake in hot summer days on account of the mosquitoes, which attack people as well as horses. In shallower bays, especially in those in which the water is tepid owing to hot springs near the shore, a great many molluscs, •especially Limncea , Succinea, and Planorbis, are found. Myvatn is an extremely fine trout lake, the trout being present in enormous quantities. The same is also the case with Thing- vallavatn. One of those peculiarities, which makes Myvatn an extremely interesting locality, is the innumerable masses of birds, especially ducks, which breed on its shores or along the inlets ; various travellers and naturalists have given extensive reports with regard to this bird life. The temperature of Myvatn is quite different from that of Thing- vallavatn ; still, it must be remembered that the observations made in the two lakes unfortunately do not date from the same year. The lake is icebound until 28th May, then the tp. in only 6 weeks reaches its max., 121° C. (15th July). This tp. we also find 1142 Proceedings of Royal Society of Edinburgh. [sess. on 1st August, but as early as 15th August it has gone down to 8°. On 18th September it further falls to 6°, and then rises a little (on 1st October it is 7° C.) ; but then it falls rapidly, and on 24th October the lake is already icebound. It was frozen over the rest of the year, with the exception of a short period from 7th to 10th November, in which the lake was again open, but at the time when these observations were finished (2nd April) it was not once open. Hence we learn that the lake, in the year when the investigations were carried on, was only free from ice 152 days (£) of the year, being icebound 213 days (f). Further, we see that the water of the lake follows the variations in the tp. of the air extremely quickly, owing to which the lake is able to reach the relatively high tp. of 12’ C. in a period of but 45 days. Owing to the hot springs, the tp. in the bays of the lake may often rise to 15°-20° C. (Thoroddsen) at an air tp. of only 10° C. Monthly Mean tp. of the Air at Ahureyvi and Modrudalur. 1903-1904. Akureyri. Modrudalur. i March, -4*1 ... April, - 0*8 - 27 May, 47 3-3 June, 9-6 77 July, ... 9-8 August, . 5 6 3-3 1 September, 6-9 4 3 October, . 0-5 -1*1 November, -1-6 -6-3 December, -0’4 -3'6 January, -2-3 -6-3 February, -2-9 -6-9 March, -2*3 -6-6 2. Plankton. It is the first time a regular plankton exploration has been* established in a lake which is ice-covered for more than seven months, and it must, according to my opinion, be of great interest to receive some information concerning the plankton of such a lake. Owing to the nature of the lake in question, the results of the 1904-5.] The Plankton of Thingvallavatn and Myvatn. 1143 exploration mast unfortunately — when taken as a paradigm to a sub-arctic lake — be used with great caution. This will best be understood when remembering that all animal life in the lake is, according to all accounts thereof, only 120 years old, and when keeping in mind the extremely volcanic area in which the lake is situated. The most conspicuous fact with regard to the plankton of Myvatn is the non-existence of phytoplankton. Of the Myxo- phycern I have only noted some few individuals of the genus Anaboena , and this only in a single sample (15th July 1903) and at the highest tp. of the water. Not a single plankton Diatom is pound, nor any plankton Chlorophycese ; the plankton of Myvatn is almost wholly zooplankton. While the lake was ice-covered I ordered the samples taken from a hole in the ice. In these samples I have found the cosmopolitan perennial Eotifer fauna as mentioned above, as well as some bottom Crustacea shown in the plankton table. Of course the number of animals in these vertical samples, taken in a water column of only a few feet, is very small ; yet the samples clearly show that in winter all life, even in as cold a lake as this, is by no means wholly wanting. Still, I presume that the plankton life in winter is greatly reduced, and that it only flourishes during a period of 4 \ months, for instance in 1904 from 28th May to 24th October. The plankton consists almost solely of Rotifera and Crustacea. The Rotifer fauna is probably extremely rich. Among the plants contained in the samples I have found many bottom and shore Rotifers ; in as shallow a lake as Myvatn, and one which is to such a degree covered with vegetation, no limit between a limnetic and a littoral region can be said to exist. Besides, we find in the samples the entire stock of cosmopolitan perennial Rotifers, but none of the periodical summer forms appear. I have only found well-marked max. and sexual period for Gonochilus and for A-splanchna priodonta, both at the highest tp. of the water (15th July). Also with us these Rotifers reach their max. at tp. 12°, but as our lakes reach this tp. twice in the year, in May and in September-October, they are dicylic with us. The Crustacea fauna I also suppose to be very rich. I found in the samples many bottom and shore animals, for instance, Macrothrix 1144 Proceedings of Royal Society of Edinburgh. [sess. hirsuticornis, Alona sp., Acroperus leucocephalus , Chydorus sphcericus, and several species of Cyclops. Of these bottom forms the sample of 18th September contains C. sphcericus in great numbers, as well as many Macrothrix hirsuticornis. Of the genus Bosmina only B. obtusirostris appears in May and June, but only a very few individuals of this species may be found. Of plankton Crustacea Myvatn has only one species, Daphnia longispina, which in its short lifetime fills the water with huge masses. I have tried to give its life-history in the following pages. Most of the samples contain a lot of detritus, and the samples of 16th June and 1st July contain hardly anything but empty skins of pupae of Chironomus, which colour the samples black. If this sample gives a true picture of the limnetic region of the lake, it must at that time have been teeming with pupa skins, and the great swarm must have been hatched by this time. Owing to the absolute absence of all phytoplankton, the zooplankton is almost wholly reduced to depend upon detritus for its main sustenance. It is most interesting to see how the genus Diaptomus , which in a far greater degree than all other plankton Crustacea exist upon phytoplankton and more especially upon Diatoms, is wholly wanting, and that among the plankton Crustacea the main form of the plankton is also here a Daphnia , which is everywhere known to feed upon detritus. Without any attempt at generalising, I still suppose we may conclude that further investigations probably will prove the phytoplankton of the arctic lakes to play by no means the prominent part in the composition of the plankton as in lakes of the temperate zone. 3. The life cycle of Daphnia longispina , O.F.M. D. longispina in Myvatn presents but a very slight seasonal variation. All the individuals from May to June belong to the typical microcephala form ; later on the head becomes a, little higher, and its ventral edge is curved slightly more inward ; further, the rostrum is more prominent. All in all, the head is highest in those females which only propagate sexually, and lower in those which only propagate partlienogenetically. On 30th May we only find a few quite young ones ; on 16th June 1904-5.] The Plankton of Thingvallavatn and Myvatn. 1145 we see the first parthenogenetie females containing 30-40 eggs (fig. 1) ; and on 1st July besides those a few young ones derived from ephippia or from parthenogenetie females. On 15th July we find many young small-sized animals, males and females (figs. 2 and 3), but only a few of the latter have eggs (2-3) and no ephippia ; further, we find some females of larger size, all with eggs (often 12) (fig. 4). In all these samples the number of D . longispina has only been small; on 15th July we find for the first time the two sizes of females which now will be found in all the following samples. The small females are only c. T5 mm., the large c. 2*5 mm. in length. On 1st and 15th August the number of animals is suddenly enormous ; most of them are young animals, males and females (fig. 5), of which a few have ephippia (fig. 7). The large females from 1 5th July are now almost all barren ; but on 15th August I have found a few with ephippia ; a great many newly hatched young ones appear. On 1st September we find almost only animals of the smaller size, some of them with ephippia ; males are rare. Of the large females I have only found but few and barren individuals. On 18th September a great many of the small-sized females (fig. 10) have ephippia (fig. 8), but these are only half-developed and with- out lodges ; the males are rather common, and so are also the young ones. The large females are again very common and contain 8-10 eggs (fig. 9). On 1st October the smaller-sized ones commonly have fully- developed ephippia ; still I noticed a few without these. A few 1146 Proceedings of Royal Society of Edinburgh. [sess. of these females contained 4-5 parthenogenetic eggs ; young ones are still rather common, and so are the males and the big females con- taining 8-12 eggs. On 16th October almost all the small-sized Fig. 4. — 15th July, big female, eight young ones. Fig. 5. — 1st August, young female. females have ephippia, the males are rare and there is very little brood ; the large females are still rather common and contain 7 -9 eggs. The above-mentioned facts may, I think, best be explained as follows : As the number of animals to be found on 30th May,, only two days after the ice has broken up, is extremely small and continues so the whole of June, I suppose that almost all the individuals of the lake have hibernated in ephippia. As the 1904-5.] The Plankton of Thingvallavatn and Myvatn. 1147 sample of 16th October, only eight days before the lake is frozen over,, contains numerous animals, many of these with parthenogenetic eggs or with young ones in the incubating part of the carapace, I cannot believe that the Daphnids should die immediately after the lake becomes frozen over, even though the sample of 31st October does not contain i a single individual. Perhaps a few individuals will hibernate, but all in all I suppose that hiber- nating females here in Myvatn only play a very inconspicuous role in the whole life cycle of D. longispina. My opinion with regard to the cycles may be expressed as follows : Fig. 8. — 18th Septem- ber, small female with ephippinm. Fig. 9. — 18th Septem- ber, big female with twelve eggs. Fig. 10.— 18th Septem- ber, young female. From 15th July to 16th October the females of D. longisjpina always appear in two different and well-marked sizes ; the one is c. P5 mm., the other 2-5 mm.; between these two sizes I only have found (16th October) a few intermediate stages. The small females rarely have parthenogenetic eggs, and perhaps already, a fortnight after they have become full-grown, they carry ephippia ; the size of the males agrees with that of these females. The large females propagate only parthenogenetically, only in one sample (15th August) we find a few with ephippia. I received the impression that almost all parthenogenetic propagation is restricted to those large females, and that the small females mainly are sexual ones, which in 1148 Proceedings of Royal Society of Edinburgh, [sess. case of fecundation will get resting eggs, but otherwise commonly will remain barren. With regard to the derivation of these large females I think it most probable that they are derived immediately from the ephippia which in spring and during the few summer months will be hatched at quite different periods. If this holds good, the life cycle of the large females is as follows : The individuals hatched in spring produce a very large brood (c. 40 eggs), and later on broods of some 6-12 eggs. How many broods they produce I don’t know, but undoubtedly more than one. I have found females with big young ones in the incubatory part of the carapace, and with more than twenty dark eggs in the oviduct well separated from each other. How long the large females live is not known, but on 1st August I have found many with only one or two very large young ones (fig. 6) in the incubatory part, and these were always males. In the same sample were many barren females, and on 1st September almost all had disappeared ; the few I saw were all barren. On the other hand, large females with many eggs become common again, as stated above, at 18th September as well as in the following samples. As I have not myself made the collections, I will not draw the very obvious conclusion which the sample of 1st Septem- ber might occasion, but shall restrict myself to the above-cited results, which may be arrived at through direct study of the sample. My opinion of the life cycle may shortly be expressed as follows : During the time from May to November, the ephippia in different numbers will be hatched and the young ones — the first generation — very quickly grow out to large females, which commonly only propagate parthenogenetically, producing an un- known number of broods. The young ones — the second generation — derived from these females are males or sexual females, which pair and which ordinarily only produce resting eggs. D. longispina is in Myvatti jnonocyclic. To the above I shall add the following remarks : In two of the Danish lakes, the lakes of Yiborg and Hald, D. longispina appears in races very like the race of Myvatn. In the lake of Yiborg we also find the above-mentioned great females characterised by their 1904-5.] The Plankton of Tlmigvallavatn and Myvatn. 1149 enormous prolificness, and which I have never seen with ephippia. In the second part of my plankton work I shall further treat of the propagation of the species in these two lakes. As far as I know, this is the first time that attempts have been made to determine the life cycle of a Daphnid in a special locality by means of regular fortnightly collections of plankton material. Of course I do not expect the above sketch of the life cycle of D. longispina in Thingvallavatn and Myvatn to be exact, especially as I have not myself gathered the samples. Further, it must be remembered that even if we suppose it to be reliable with regard to this particular year, the development of the organisms may in other years take a quite different course. Light, tp., and the settlement of ephippia, which depend on the direction and the force of wind at the moment of settlement, undoubtedly exercise their influence upon the course of the cycle. These pages must not be expected to present more than an outline sketch of my subject to the reader; further explorations must test its correctness. When comparing the results of the investigations into the life- cycle of D. longispina in Thingvallavatn with that in Myvatn, we find these very different. In Thingvallavatn D. longispina may be regarded as dicyclic, in Myvatn it is monocyclic. As I have never had any living material, nor collected the samples myself, I do not wish the results to be regarded as conclusive. Besides, if this is the case, it becomes quite plain that D. longispina in Thing- vallavatn, which in 1902-1903 seems never to have been frozen over, might be dicyclic and in Myvatn only monocyclic. I suppose that the last autumn brood hibernates in deep water and propagates in spring in Thingvallavatn as well as in our own lakes, and that the ephippia on the whole play but an inconspicuous part with regard to preserving the species in the lake. On the other hand, I should think that almost the whole stock of D. longispina in Myvatn is hatched from ephippia, and that the hibernating parthenogenetic females here only play a minor part i^- the whole life-cycle of the species. I venture to express this idea, because it agrees with the results of my explorations in Danish lakes, accord- ing to which the ephippial eggs of the plankton species of the genus Daphnia do not play a prominent part in regard to the life 1150 Proceedings of Royal Society of Edinburgh. [sess. cycle of the species, especially in the larger and deeper lakes ; they only become of consequence in shallow and warm lakes or in ponds. I think it very probable that the first of the two generations in Thingvallavatn belongs to the form microcephala, the second to the obtusifrons. The question arising with regard to the degree in which the different generations vary according to tp. is of the greatest moment with regard to the understanding of the seasonal variations, but it is also extremely difficult to deal with. I have studied this problem upon our own plankton organisms for quite a while, and a full account will be given of this in the second part of my plankton work. With regard to the question in the Icelandic lakes I have of course formed some opinions, but as these have not been tested by means of more thorough-going explorations in the Danish lakes, they are of no value, and will therefore not be mentioned here. It will then be seen that the life cycle of D. longispina in Thingavallvatn is [in accordance with the cycle which Zschokke (1892) has found in the Swiss alpine lakes, whereas that of D. longi- spina in Myvatn corresponds with what I have found in Greenland (1895) and Ekman (1904) in the sub-arctic alpine lakes in Sweden. The exploration has further confirmed the supposition first set forth by me, and later on confirmed by Ekman, that otherwise polycyclical Cladocera nearer the poles will become monocyclic, the autumn sexual period being omitted, and that the parthenogenetic propagation here is of inferior significance when compared to the sexual one. Ekman (1904, p. 94) maintains, contrary to my observations with regard to the Cladocera of Greenland, that the number of partheno- genetic eggs in an alpine or arctic country is by no means less than in a lowland country, but even greater. I daresay that Ekman, generally speaking, is quite right ; still, I must emphasise the fact that the number of eggs which I have found in the Thingvallavatn samples has never exceeded 4 and has often numbered only 2 or 3. With regard to the number of eggs in Myvatn, I refer to the fact stated above : it is very high in spring, but by no means greater than may, for instance, occur in Danish lakes at the same time of the year. I suppose that, taken all in all, the number of eggs to be noted is about the same all the year round as in Danish lakes. 1904-5.] The Plankton of Thingvallavatn and Myvatn. 1151 Ekman (1904, p. 88) states that in the first summer months he has occasionally found numerous males, which he supposes to have been derived from ephippial eggs. Hot all of the females were outgrown, and none of them had eggs. He points out that the observations are of interest, because we would then here have the only known example, according to which males had been produced from ephippial eggs. Till more thorough explorations have been carried on, I think it safer to suppose that these males as a first brood have been derived from the females hatched from the ephippia. IY. COMMON RESULTS. Lastly, we shall shortly draw attention to the following results of the exploration. As compared with the Danish explorations, it will readily be seen how much these have been promoted and sup- ported by this little investigation. 1. In Myvatn no phytoplankton has been found at all. In Thingvallavatn we have not found any plankton Myxophycese; when we add hereto that none of the rather few samples from higher latitudes, which have as yet been studied, record Myxo- phycese, we may conclude that the Myxophycese do not play any conspicuous part in the plankton of more northerly situated lakes. When taking into consideration the explorations from Switzerland, Germany, and Denmark, we must suppose that the low tp. (below c. 12° C.) and the clear water, poor in organic matter, most probably form the greatest hindrances to the progress of the Myxophycese towards the poles. Eurther explorations may show whether the plankton Oscillatoria and Lyngbya are found further north than the other Myxophycese ; then their max. may lie at a tp. which arctic or sub-arctic lakes, at least for a short time of the year, may also arrive at. 2. The Diatoms constitute the main part of the phytoplankton of northern lakes. In Thingvallavatn the Melosiroe and Asterionella formosa are the main forms ; they have in temperate regions their max. at a tp. of 4°-10°, which is in accordance with their occurrence in Iceland. On the other hand, Fragilaria crotonensis , whose max. lies at tp. 16°, occurs only in a few specimens and at the highest 1152 Proceedings of Royal Society of Edinburgh. [sess. tp., and consequently does not play any important part in the plankton. The occurrence of two Rhizosolenice in nearly all the months of the year, although only fairly common in June (tp. 7°-8-5°), is very interesting and indicates probably, as several other facts do, that Thingvallavatn by no means may be regarded as an arctic lake. It is only a northern lake in want of the higher summer tp. ; it differs considerably from a true arctic lake in only being ice-covered for a short time, and even this does not occur every year. The same difference must also be remembered when comparing it to alpine lakes. Corresponding hereto we do not find in Thingvallavatn the large quantities of Cyclotella which occur, e.g., in Switzerland. If we compare our results concerning Diatoms with the few statements from arctic lakes, we find that in Greenland, at c. 71° lat. N. (Vanhoffen, 1897), in Bear Isle (Lagerheim, 1900), and in Lule Lappmark (A. Cleve, 1899), the plankton Diatoms do not play any prominent part in the plankton, the phytoplankton being very poor. The fact is worth noticing, that these statements are based on samples collected in very small lakes or, more correctly, in ponds (except those from Lule Lappmark). We think that the large quantities of Melosira and Asterionella in Thingvallavatn show how nearly allied its plankton is to that of north-western Europe. Besides the above-mentioned forms, several other Diatoms occur regularly in the plankton of Thing- vallavatn, viz., Fragilaria construens , F. capucina , Synedra acus , and S. ulna. These forms are not of as typical a limnetic character as the others ; we presume that their home is the shores of the lake, from whence they are driven into the open lake by winds and waves. On account of the low tp. they are able to float for rather a long time. The papers by Lagerheim (1900) and Ostenfeld (1904) mention such tycholimnetic forms, which with higher tp. probably quickly would sink to the bottom. 3. As might be expected, the limnetic Chlorophycese are not abundant in Thingvallavatn ; the main form is Sphcerocystis , the same which predominates in alpine lakes and which is probably very common all over the Central European plain. In Thingvalla- vatn its max. occurs at 7° C. ; with regard to its max. in other lakes we have no exact information. The rather common 1904-5.] The Plankton of Thingvallavatn and Myvatn. 1153 occurrence of different Desmids in the limnetic region of Thing- vallavatn is quite in accordance with the explorations of the lakes of the Faeroe islands, hut particularly with those of Scotland. In the lakes of the most western part of the European Highlands, Scotland, Faeroes, Iceland (with regard to Norway nothing at all is known) there seems to exist a peculiar semi-limnetic flora of Desmids, which in the other parts of Europe is only represented by one or two species ( Staurastrum gracile , S. paradoxum). With regard to their occurrence in Scotland, Wesenberg-Lund (1905) has supposed that their very peculiar occurrence may he accounted for by the fact that these Desmids originally are derived .from, and also nowadays are recruited from, the rich Desmid flora living in the almost always mist-wrapped moist moss carpets which cover the precipitous sides of the hills, where streamlets feed the rivers and from whence the Desmids, especially in spring, are carried out with the rapidly flowing waters into the limnetic region of the lakes ( cf . p. 1158). Probably this supposition will also hold good as to the occurrence of Desmids in the limnetic region of the lakes in the above- mentioned localities, although the hills around Thingvallavatn are not precipitous. 4. With regard to the Peridinians we particularly note the total absence of Ceratium hirundinella. In accordance with explorations in more southern countries, this was only what might he expected, the max. of C. hirundinella lying at a tp. which the Icelandic lakes rarely attain. Besides, we refer to the remarks about the Euflagellata. 5. The absence of Dinobryon is more striking. We are in- clined to suppose the absence of this genus in the Thingvallavatn to be only accidental ; probably Dinobryon is one of the main forms in arctic and northern lakes. 6. The total absence of Tintinnidium and Codonella, whose max. occurs at a relatively low tp., is rather remarkable. 7. The plankton Rotifers belong chiefly to the cosmopolitan perennial stock, whose members in more southern countries are poly- or di-cyclical, with max. at c. 12° C. in spring and in autumn. According to observations from Myvatn, it seems as if the group in the more northern lakes is monocyclical, with the max. PROC. ROY. SOC. EDIN. — YOL. XXV. 73 July 1902 -June 1903. -Plankton from TImigvallavatn, South Iceland. 1154 Proceedings of Royal Society of Edinburgh. SESS. o CO > CM Lp 00 IT IT rr IT c rr 8 + + '£ ^ + £ + £ ^ O + + + io VI. 00 i>- £ • h ^ ^ o S S ? c rr r 4- rr • o+ + + t—( CO > O b JL, . . Jh ?H ?H . . ?H *H fH ^ O + + £h + + • U f-l 't 1 s' 2p 00 U0 rr rr rr rr rr cc c r cc c IT rr i o ! CO uo ?p rH °h' 1 ■'•&&&&•• o ?h ?h • Sh H • . . O O ^ fn u O *4 ?H CO B CO to r rr rr rr rr rr C r r rr rr <© y o • ° • 1-1 M ° ^ Sh..,£h,.. i Sh H ^ ® t* h . S-l • ■ & • -SB •& • §•&•**••& -«J|§3 CO • o * O " 1 (N 1— 1 tH 03 | * * h S ^ ‘ + ■ s - + o- • 14. XII. 2°. 5°. . . &H PH &H . U U 0._1_ S-. S-* 1 «SH+ ■ '^^TU ■ • S' *' b i • § •+ • ’■* & • •£ + « • . s' b b i •& •&* + * • § - -fc*K • -C + ® • • rH lj kC o * co n q o fc & & & + o h ■ o • t ■ * S & • & B h -% v* c, • 2 Xj °« £ + « + ^ & ’£ -\- ■ ~~ ’£ ■ ’£ • + - • S ^ oi oo Ph.Sh^, !SL(# f-| ?H ?H ^ *H r rH ?H * ?H * Jh kD ^ o tp rH HH 1-1 00 o g « b 10 > g .« H <>a rH ! " £ ^ ^ : ■•■■6 s £ ' M P H C» * • • S S • ' • ++8 £ + k a * * z++ ■ z . ~ o £ 08 oa , 2 pa g -rS c/2 O H r+ § 2 3 S go- 's «.a- m c ^ a pa & --O' - - ^ ■ 8 oil O 02 1904-5.] The Plankton of Thingvallavatn and Myvatn. 1155 *h &H r rr r r | ccc u U f-* • ‘ h h * * ccc + J-t Ph • * (h Ph • ‘ rr ccc + h ^ • • • • + o u u n • • H Si £ • • -S + f-t * U + • H h + ■ ■ ■ & + cc * • + * • ^ fH ^ • O • • • • u • • o ?H S-l • * ?H ^ • • + + • -++^ h rr rr ccc • ■++ •+' ccc ccc g g 8^o + n • •++ • * ccc + ccc H • • • n H • + ccc c cc £ • • • H h • + c cc cc *-» * £ • H ^ o o .. « o ° £ + £ • u u • + c ccc r S ■ • • ^ tl • + O O ^ rr IT . r rr r ccc S • • • • r cc ccc O - - ® ^ B ‘ ‘ h o ri I O 1 5 ^ § ; Jlrk ; - ^ «i a> o J H „ co u (S; qj 3 _oo s' ^ ® c/T c ® o I 3® rt Ij 8 3^S g| O-g g s cs^q v ~ r-! O cc U -J CO ^4 ^ 2 7 2 <1374 s2 2 oW&BO § Pn xn ft -2 <1 £i o O ft 23 W CO g gft e,' § g 03 s 2 ’Sb’3 e fiS July 1902 -June 1903 . -Plankton from Thingmllamtn, South Iceland. Proceedings of Royal Society of Fdinburgh. [skss. 1 1904-5.] The Plankton of Thingvallavatn and Myvatn. 1155 April \§QZ- April 1904. — Plankton from My vain. North Iceland. Proceedings of Royal Society , of Edinburgh. April \§Q3- April 1904. — Plankton from My vain, North Iceland. 1156 Proceedings of Poyal Society of Edinburgh. [sess. ©i > - !>■’ rH d iO | < - no £ CO M c M « CO s • (H • E • • rl ^ 00 N 29 co" co + • + . . o > V i— i i 2 6 .CO ' g ef-& 5 CO _ •S O CO ft Jj 3 .2 m 2 boS c §3 8 88 £§■ — „ a 5 o >5 CO C P-| ^ ^ 1904-5.] The Plankton of Thingvallavatn and Myvatn. 1157 occurring at midsummer time at the same tp. (12° C.) as in the southern ones. 8. Ekman (1904, p. 68) has, with regard to its Crustacea, ad- joined Iceland as an appendix to the sub-region Greenland, which is a part of his boreo-glacial region. The reason for so doing he declares principally to he the common occurrence of Diaptomus minutus , hitherto not found outside of North America and Greenland. Nothing in the present little exploration is in contradiction to Ekman’s point of view7. All plankton Crustacea hitherto found belong to the common boreo-subglacial society pointed out by Ekman. Owing to incomplete explorations of the island we have missed different species, especially Bythotrephes. Further ex- plorations will undoubtedly also bring to light more species of Diaptomus and Cyclops. It must be hoped that the great collections from c. 60 localities made by Mr Soemundsson may find their adapter. It must be noted that, in Iceland as well as in almost all other parts of the boreo-subglacial region, all the plankton Crustacea, which are characteristic for the limnetic region of the more southern lowland lakes (Ekman), are missing. 9. With regard to the life cycle of the Daphnids, I refer to p. 1149. The explorations have confirmed the fact that the other- wise polycyclical Cladocera will be monocyclical nearer the poles, the autumn sexual period being precluded ; in more northern latitudes the parthenogenetic propagation is of inferior significance in comparison to the sexual one. 10. From Ekman’s explorations in the Sarek, James Murray’s and my own in Scotland, and the present report from Iceland, added to the numerous explorations in Central European lowland lakes, we may presume that the great seasonal variations of the plankton organisms are restricted to the lowland lakes with their high summer tp. They are wanting in all those lakes whose summer tp. never rises above 12°, the very tp. at which the variations begin in the lakes of the Central European plain. As a general result of the exploration, we wish to draw attention to the following conclusions: We think it probable that the plankton of the arctic lakes, to a much greater degree than in more southern countries, mainly consists of zooplankton, and that 1158 Proceedings of Royal Society of Edinburgh. [sess. the phytoplankton, especially in summer time, only plays an in- significant part in those lakes ; hence the main nutriment of the zooplankton for a long time of the year mainly consists of detritus. The phytoplankton of arctic and sub-arctic lakes consists in all probability mainly of algse with yellowish or yellowish-brown chromatophores ; algse with green or blue-green chromatophores are almost entirely wanting. As exceptions from this common rule we only mention Sjohcerocystis, the semi-limnetic Desmids and a few rare Chlorophycese. It is a well-known fact that, in the arctic, antarctic, and cold temperate seas, the Phseophycese are the pre- dominating algse (see e.g., Schimper, 1898, p. 832); also with regard to the marine phytoplankton, so the Diatoms with their yellow-brown chromatophores play the greatest part in the colder seas (see e.g., Schiitt, 1893, p. 26). None of these facts can be explained by us. Further explora- tions may probably show whether the optima of assimilation for yellow-brown coloured chromatophores commonly lie at a lower tp. than those of the green or blue-green chromatophores. We are quite aware that these assertions are as yet only proble- matic; still, we do not hesitate to set them forth here, thinking that they might be of use as working theories for further explora- tions carried on in higher latitudes than at this time has been possible. Note received October 3, 1905 After our paper had gone to press, I received from Professor W. West, F.L.S., and Professor G. S. West, M.A., F.L.S., their paper : A Further Contribution to the Fresh-water Plankton of the Scottish Lochs {Trans. Roy. Soc. Edin., 1905, p. 477). As the said paper essentially touches on the same subjects as my paper : A Comparative Study of the Lakes of Scotland and Denmark ( Proceed . Roy. Soc. Edin., vol. xxv., 1905, p. 401), and the present paper, I take the liberty here shortly to mention some points in the same. In the summary the authors write : — 1. “ The quantity of plankton is relatively small at any time and scarce affects the colour of the water. It exhibits 1904-5.] The Plankton of Thingvallavatn and Myvatn. 1159 little periodicity, the seasonal variations being slight. This absence of any marked variation in character is to be attributed to the relatively slight changes in the temperature of the surface waters at different seasons.” 6. “ The Desmids were doubtless originally derived from the pools and bays of the mountains, and only those species have flourished which found the conditions most suitable for their existence as pelagic organisms.” 7. “There is no very obvious maximum development of Diatoms, and some of the larger species of the JSTavicu- loidese and Surirelloidese have firmly established them- selves.” 8. “The proportion of Myxophycese is relatively small, and species of Oscillatoria, Lyngbya, and other genera are somewhat scarce.” 1 am glad to see that in all these points we are of quite the same opinion. I take the liberty to point out that I in my paper, see especially pp. 423, 426, 427, 430-31, have expressed quite the same suppositions. This the authors seem quite to have overlooked. Also with regard to the derivation of the rich Desmid flora we are mainly in full accordance. Pre- viously to the authors’ statement, I had pointed out (p. 430), that the plankton Desmids must have been originally derived from tarns and moors on the hill-tops , and that the Scottish lakes (p. 431), unlike most other larger lakes , present one of those great life- conditions which so many of the Desmids seem to require , viz., peaty water rich in humic acid, ( cf . Summary, point 4, by Messrs West). Besides, the authors add the very important fact that the Desmids oive their existence * (p. 515) to the Older Palaeozoan and Pre-Cambrian formation. On the other hand, when the authors (p. 512) maintain that I was of opinion that many of the Conjugates adopt a pelagic life as soon as they arrive in the lakes from the peat moors, and, contrary to me, set forth that the plankton Desmids have existed under these pelagic conditions for a very long time, the authors have totally misunderstood me. In p. 430 I have written that the Desmids were originally derived from the tarns and pools, and (p. 431) that the home of the Desmids is the sides of the * An expression which I do not find very clear. 1160 Proceedings of Royal Society of Edinburgh. [sess. kills, and that some of those forms tohich, according to their primeval structure , were best adapted to plankton-life, are now in fact, under the new conditions, about to develop processes. I have of course meant that the adaptation has been going on for immense spaces of time, and is going on to this day ; that many of the Desmids have existed under these pelagic conditions for a great length of time is a matter of course which I did not think necessary to point out especially, and which I never have denied. On the other hand, I suppose that the authors will hardly deny that the adaptation continually takes place up to this very day ; so that also on this point the suppositions of the authors are not at variance with mine. Besides, the very thorough study of the plankton Desmids by the English authors has greatly augmented our knowledge of the extremely interesting subject : the plankton Desmids of the Scottish and probably also the Icelandic loch? ; all in all, I cannot hut see that they support the correctness of my suppositions set forth on p. 431. I am fully convinced that it is an exaggeration to say (Messrs West, p. 477) that the lochs of the west and north-west of Scotland were probably richer as regards the phytoplankton than any lakes previously examined, and it is not in accordance with facts that the Danish plankton is relatively much poorer in Chlorophyceae, especially Conjugates (Messrs West, p. 514). Only with regard to the Desmids these two sentences are fully correct. The plankton in the lakes of the northern part of the Central European plain is much richer with regard to the number of species as well as to the masses in which the species appear. Especially with regard to Chlorophycese our plankton flora, the Desmids always excepted, is much richer than the Scottish lakes. As my knowledge of the Scottish lakes of course could only he very furtive, I have in my paper only set forth the results of the explorations as mere suppositions. Several of those suppositions, viz., the relatively small quantity of plankton, the slight perio- dicity, the slight seasonal variations, the absence of well-marked maximum development of Diatoms, the scarceness of Myxophycese, especially Oscillatoria, Lyngbya, the English authors now regard as a “summary” of our knowledge of the phytoplankton. This may he so ; still, I feel inclined to pronounce that in my opinion the two authors have by no means grounded these suppositions 1904-5.] The Plankton of Thingvallavatn and Myvatn. 1161 more substantially than I have been able to do. It is necessary to bear in mind that all the samples which the authors have used for their investigations only have been collected in July-September (Messrs West, p. 477). Without regular fortnightly or monthly explorations of the lakes, it is quite impossible to obtain a well-founded idea with regard to most of these points, and such regular explorations in the Scottish lakes are as yet only a desideratum ; at all events, nothing has been published upon this point. In particular, it must be noted that the great maxima of Diatoms are always to be found in spring and in autumn, and that the maxima of Oscillatoria and Lyngbya, especially the latter, in our lakes are often extremely short and therefore only traceable by means of very thorough explorations. C. W.-L. List op Literature. 1892. Bergendal (D.), “Beitrage zur Rotatorienfauna Gron- lands,” Lunds Universitets Aarsskrift, xxviii. p. 1. 1897. Borge (0.), Botaniska Notiser, p. 211 : “ Algologiska Notiser. Siisswasserplankton aus der Insel Mull.” 1900. Borge (0.), “Schwedisches Siisswasserplankton,” ibid., p. 1. 1902. Brehm (Y.), “ Zusammensetzung, Verteilung und Perio- dicitat des Zooplankton im Achensee,” Zeit. d. Ferdinandeums, iii. F., Innsbruck, xlvi. p. 1. 1898. Borgesen (F.), “Nogle Ferskvandsalger fra Island,” Botanisk Tidsskrift , xxii. p. 131. 1902. Borgesen (F.) and Ostenfeld (C. H.), “Phytoplankton of Lakes in the Faeroes,” Botany of Faeroes , Kobenhavn, ii. p. 613. 1902. Chodat (R.), Algues vertes de la Suisse, Bern. 1899. Cleve (A.), “Notes on the Plankton of some Lakes in Lule Lappmark, Sweden,” Oevers. af Kgl. Svenska Vetensk. Akad. Forhandl., No. 8, p. 825. 1889. De Guerne (J.) and Richard (J.), “ Sur la faune des eaux douces du Greenland,” Comp. Rend., cviii. p. 630. 1162 Proceedings of Royal Society of Edinburgh. [sess. 1892. De Guerne (J.), “ Sur la faune des eanx douces de l’Islande,” ibid., cxiv. p. 310. 1904. Ekman (S.), “Die Phyllopoden, Cladocera und frei- lebende Copepoden der nord-schwedischen Hochgebirge,” Zool. Jahrb. xxi., Abth. Systematik, p. 1. 1902. Fritsch (F. E.), “Preliminary Reports on the Phyto- plankton of the Thames,” Annals of Botany , xvi. p. 1 . 1905. Fritsch (F. E.), “ The Plankton on some English Rivers,” ibid., xix. p. 163. 1890. Gronlund, “ Karakteristik af Plantevaeksten paa Island,” Naturhist. Forenings Festskrift , p. 107. 1904. Hlava (S.), “Monografie Celedi Melicertidse,” Archiv der Natunv. Landesdurchforschung von Bohmen, xiii. , No. 2. 1900. Holmboe (J.), “ Undersdgelser over norske Ferskvands- di atomer, ” A rchiv for Mathem. og Nature. Christiania, xxi., No. 8,p. 1. 1900. Huitfeldt Kaas, “ Die limnetischen Peridineen in norwe- gischen Binnenseen, 1900,” Vidensk. Selskab. Skr., No. 2. 1890. Johnstrup (F.), “Om de vulkanske Udbrnd og Solfata- rerne i den norddstlige Del af Island,” Naturhist. Forenings Festskrift, p. 147. 1857. Kruper (T.), Der Myvatn und seine Umgebung, Nau- mannia, vii. p. 33. 1900. Lagerheim (G.), “ Beitrage zur Flora der Bareninsel,” Bih. til Kongl. Svenska Vetensk. Akad. Handl., xxvi., Ap. III. No. 11, p. 1. 1898. Lauterborn (R.), “ Ueber die zyklische Fortpflaiizung limnetischer Rotatorien,” Biolog. Centralbl., xviii. p. 173. 1900. Lemmermann (E.), “ Beitrage zur Kenntniss der Plankton- algen,” iii., Berichte der Deutsche botan. Gesellsch., xviii. p. 24. 1903. Lemmermann (E.), “ Brandenburgische Algen. II.: Das Phytoplankton des Miiggelsees,” Zeitsch.f. Fischerei, ix. p. 73. 1904a. Lemmermann (E.), “Das Plankton swedischer Ge- wasser,” Arkiv f. Botanik, ii. 2, Stockholm, pp. 1-209. 19045. Lemmermann (E.), ‘‘Beitrage zur Kenntniss der Plank- tonalgen,” xvii., Ber. Deutsche botan. Gesellsch., xxii. p. 17. 1901. Levander (K. M.), “Beitrage zur Fauna und Algenflora der siissen Gewasser an der Murmanktiste,” Ada Societas pro Fauna et Flora Fennica, xx., No. 8, p. 1. 1904-5.] The Plankton of Thingvallavatn and' Myvatn. 1163 1904. Levander (K. M.), “Zur Kenntniss der Rhizosolenien Finlands,” Meddelanden af Societas pro Fauna et Flora Fennica, xxx. p. 115. 1900. Lilljeborg (W.), Gladocera Sueciae , Upsala. 1901. Lilljeborg (W.), “Bidrag til en Ofversigt af de inom Sverige iagttagna Arterna af Slagtet Cyclops ,” Kongl. Svenska Vetensk. Akad. Handl ., xxxv., No. 4, p. 1. 1893. Marsh (C. D.), “ On the Cyclopidse and Calanidie of Cen- tral Wisconsin,” Wise. Acad. Sci., Arts, and Letters , ix. p. 189. 1897. Marsh (C. D.), “Cyclopidae and Calanidse of Lake St Clair,” Bulletin Michigan Fish Commission, No. 5, p. 1. 1903. Marsh (C. D.), “The Plankton of Lake Winnebago and Green Lake,” Wisconsin Geol. and Nat. Hist. Survey Bulletin, $o. 12, p. 1. 1901. Marsson (M.), “ Zur Kenntniss der Planktonverhdltnisse einiger Geivdsser der Umgebung von Berlin ,” Forschungsber aus der biol. Station zu Plon, viii. p. 86. 1883. Muller (O.), “Die Zellhaut und die Gesetze der Zell- theilungsfolge von Melosira arenaria , Moore,” Jahrbucher f. iviss. Botanik., xiv. p. 231. 1903. Muller (O.), “ Sprungweise Mutation bei Melosiren,” Ber. d. Deut. bot. Gesellsch., xxi. p. 326. 1904. Muller (O.) “ Bacillariaceen aus dem Nyassalande,” etc., Englers botan. Jahrb. xxxiv., p. 256. 1903. Ostenfeld (C. H.), “ Studies on Phytoplankton. I. : Notes on Phytoplankton of two Lakes in Eastern Norway,” Bot. Tidskr . Kobenhavn , xxv. p. 235. 1904. Ostenfeld (C. H.), “Studies on Phytoplankton. II. : A Sample from a Lake in Iceland. III. : Phytoplankton from some Tarns near Thorshavn (Stromo in the Faeroes),” Bot. Tidskr., xxvi. p. 231. 1902. Ostwald (W.), “Zur Theorie des Planktons,” Biolog. Centralbl., xxii. p. 596. 1904. Penard (E.), Les Heliozoaires. Geneve, 1904. 1902. Rousselet (C.), “The genus Synchseta .” Jour n. Roy al Micros. Soc., p. 269. 1901. Roux (J.), Faune Infusorienne des eaux stagnantes des environs de Geneve , Geneve. 1164 Proceedings of Boy al Society of Edinburgh. [SESS. 1861. Sars (G. 0.), “0m de i Omegnen af Christiania forekom- mende Cladocerer,” Videnskabsselsk. Forhandl. Christiania , p. 144 og 250. 1901. Sars (G. 0.), Crustacea of Norway , Christiania, vol. iv. 1903. Sars (G. 0.), “On the Crustacean Fauna of Central Asia. II. : Cladocera,” Annuaire du Musee Zool. Acad. Imp. St Peters- hour g, viii. p. 1. 1898. Schimper (A.), Pfianzengeographie , Jena. 1874-1903. Schmidt (A.), Atlas der Diatomaceenkunde , Leipzig. 1898. Schroder (B.), “ Planktologische Mitteilungen,” Bioiog. Centralbl ., xviii. p. 525. 1901. Schroeter (C.) and Vogler (P.), Variationsstatistische Untersuchung liber Fragilaria crotonensis (Edw.) Kitton, Vierteljahrsschrift der naturf. Gesell. in Zurich , xlvi. p. 185. 1904. Skorikow, “ Beitrag zur Planktonfauna arktischer Seen,” Zool. Anz., p. 209. 1853. Smith (W.), A Synopsis of the British Diatomacese, vol. i., London. 1904. Steuer(A.), “ Die Entomostracenfauna der ‘altenDonau’ bei Wien,” Zoolog. Jalirb. Jena , xv., H. 1, p. 1. 1900. Scemundsson (B.), Fiskirannsoknir , 1899: “Andvari,” xxv. p. 36. 1901. Scemundsson (B.), Fiskirannsoknir , 1900: ibid. xxvi. p. 53. 1904. Scemundsson (B .), Thingvallasben, Geografisk Tidsskrift , xvii. p. 175. 1887. Thinemann (F.) and Gunther, Reise im Norden Europas vorziiglich in Island , Leipzig. 1878. Thoroddsen (T.), “Et Besbg ved Myvatn paa Island,” Geografisk Tidsskrift , ii. p. 116. 1884. Thoroddsen (T.), “En Undersdgelse 1882 i det bstlige Island,” ibid., vii. p. 95. 1905. Thoroddsen (T.), “Lavaorkner og Yulkaner fra Islands Hdgland,” ibid., xviii. p. 26. 1897. Vanhoffen (E.), “ Die Fauna und Flora Gronlands,” Gronlands- Expedition der Gesellsch. f. Erdkunde zu Berlin, 1891 — 93, vol. ii. p. 159. 1880-81. Van Heurch (H.), Synopsis des Diatomees de Bel- gique, Anvers. 1904-5.] The Plankton of Thingvallavatn and Myvatn. 1165 1903. Yolk (R.), “ Allgemeines iiber die biologischen Yerhalt- nisse der Elbe bei Hamburg,” Jahresber. d. Hamburg- Wissensch. Anstalten, xix. p. 65. 1898. Weber (E.), “Faune rotatorienne du bassin du Leman, ” Rev. suisse Zool. Geneve , v. p. 264. 1876-79. Weismann (A.), Beitrage zur Naturgeschichte der Daphnoiden , Leipzig. 1895. Wesenberg-Lund (C.), “ Gronlands Ferskvandsentomo- straca,” Meddelelser fra naturh. Foren ., Kbbenhavn, p. 82. 1900. Wesenberg-Lund (C.), “Yon dem Abhangigkeitsver- haltnis zwiscben dem Bau der Planktonorganismen und dem spezifischen Gewicbt des Stisswassers,” Biolog. Gentralbl., xx. pp. 606 and 644. 1904. Wesenberg-Lund (C.), “ Studier over de danske Sbers Plankton,” Spec. Bel. Kobenhavn. 1905. Wesenberg-Lund (C.), “A Comparative Study of the Lakes of Scotland and Denmark,” Proc. Roy. Soc. Fdin., vol. xxv. p. 401. 1902. West (W.) and West (G. S.), “A Contribution to the Fresh-water Algae of the North of Ireland,” Trans. Roy. Irish Acad., xxxii. 1903. West (W.) and West (G. S.), “Scottish Fresh-water Plankton,” Journ. Linnean Soc., Bot., xxxv. p. 519. 1904. West (G. S.), A Treatise on the British Fresh-water Algae , Cambridge, 1904. 1879. Wille (N.), “ Eerskvandsalger fra Novaja Semlja, etc.,” Of vers. Kongl. Svenska Vet. Akad. Forh., 1879, No. 5. 1880. Wittrock (Y.) and Nordstedt (O.), Algae aquae dulcis excicc. pr. Scandinaviae , No. 355. 1898. Zacharias (O.), “ Ueber einige interessante Funde im Plankton sachsischer Fischteiche,” Biolog. Centralbl., xviii. p. 714. 1899. Zacharias (O.), “Zur Kenntniss des Planktons sach- sischer Fischteiche,” Forschungsber. aus der biolog. Station zu Plon , vii. p. 78. 1892. Zschokke (F.)., “ Die Fortpflanzungsthatigkeit der Clado- ceren der Hochgebirgseen,” Festschrift zum siebenzigsten Geburts- tage Rudolf Leuckarts, Leipzig. 1166 Proceedings of Royal Society of Edinburgh. [sess. 1900. Zschokke (F.), “Die Tierwelt der Hochgebirgseen,” Denkschr. d. Schweiz, naturf. Ges. Zurich , xxxvii. p. 1. 1904. Zykoff (W.), “ Zur Crustaceen fauna der Insel Kolgujev,” Zoolog. Anzeiger, xxviii. p. 337. Explanation of Plate I. Figs. 1-7. Melosira islandica, O. Muller, n. sp. : — 1-5. Chains showing the successive stages of the auxospore formation. 6. Two-celled auxospore chain. 7. Eight-celled auxospore chain. Fig. 8. Oocystis crassa, Wittr., forma. Figs. 9-10. Cyclotella comta, Kiitz. ; a small and a large cell, valvar view. Figs. 11-20. Peridinium aciculif erum, Lemmerm. : — 11. A cell in Gymnodinium stage with mucilaginous en- velope. 12. Another Gymnodinium cell with large oil drops. 13. The formation of two daughter cells. Here and in fig. 12 the envelope has been omitted. 14-15. A specimen in two views. 16. Another specimen in dorsal view. 17. Side view. 18. Ventral view. 19. A specimen of which the contents are bursting. 20. Resting cyst. The microscope used is Zeiss’s large microscope (Stand la), with compensating eye-pieces and apochromatic objectives. The figures are drawn with Abbe’s camera (No. 44a). The magnifications are as follows Figs. 1-7, 11-20, objective 1*25 x 2*5 mm. Comp, ocular, 8 (Water immersion.) Fig. 8, objective 0‘95 x 4-0 mm. Comp, ocular, . . 8 Figs. 9-10, objective P40x2‘0 mm. Comp, ocular, . 8 (Oil immersion.) Vol. XXV. OSTENFELD and WESENBERG - LUND ICELANDIC PLANKTON. Plate I. Os tenfeld , del. M^Farlane U Ers3iiTie, Lith_ EcUn.7 Vol. XXV. Proc. Roy. Soc. Edin. OSTENFELD and WESENBERG — LUND : ICELANDIC PLANKTON. Plate II. Ostenfeld, del. M'Fa.-rls.-nc Etlrat j C. H. Osteneeld and Dr C. Wesenberg-Lund. 1904-5.] The Plankton of Thmgvallavatn and Myvatn. 1167 Explanation of Plate II. Figs. 1-3. Rhizosolenia eriensis, H. L. Smith : — 1. Large cell, with the plasma concentrated near the one end, where the rest from the last division is seen. 2. Part of a cell with resting spore. 3. Resting spore of another cell, seen from the narrow side. Figs. 4-5. Rhizosolenia paludosa, 0. Zacharias : — 4. A whole cell. 5. Newly finished cell-division, the two daughter cells cohering. Figs. 6-8. Melosira italica, Kiitz. ; parts of different chains with auxospores. Figs. 9-10. Mallomonas sp. : — 9. Vegetative cell with setae. 10. Spore-bearing cell without setae. Fig. 11. Cosmarium phaseolus, Breb. ; the same cell in front and in vertical view. „ 12. Staurastrum pelagicum , West and G. S. W. ; in front and in vertical view. ,, 13. Staurastrum brevispinum, Breb.; in front and in vertical view. ,, 14. Staurastrum paradoxum, Meyen, forma; in front and in vertical view. ,, 15. Staurastrum Bieneanum , Rabenh., forma; in front and in vertical view. Figs. 16-17. Stellate colonies of Synedra acus, Kiitz., var. delica- tissima, (W. Sm.) Grun. ? Fig. 18. Peridinium aciculiferum , Lemmerm. ; cell in ventral view, showing the arrangement of the plates ; under- neath the three prominent ridges (forming the spines) seen from the antapex. The magnifications are as follows : — Figs. 1—5, 8, 18, objective P25 x 2*5 mm. Comp, ocular, 8 (Water immersion.) „ 6, 7, 9-15, objective 0'95 x 4*0 mm. Comp, ocular, 8 , 16,17, ,, 0'65x8'0 mm. „ 8 ( Issued separately , January 5, 1906.) Meetings of the Royal Society — Session 1903-1904. The 121st Session. General Statutory Meeting. Election of Office-Bearers, p. I. FIRST ORDINARY MEETING. Monday , '2nd November 1903. The Hon. Lord M‘Laren, LL.D., Vice-President, in the Chair. The following Communications were read : — 1. The People of the Faroes. By Nelson Annandale, B.A. (Oxon.). Communicated by Professor D. J. Cunningham, F.R.S. pp. 2-24. 2. Theorem regarding the Orthogonal Transformation of a Quadric. By Thomas Muir, LL.D. pp. 168-172. 3. The Theory of General Determinants in the Historical Order of Development up to 1846. By Thomas Muir, LL.D. pp. 61-91. 4. The Theory of Continuants in the Historical Order of its Develop- ment up to 1870. By Thomas Muir, LL.D. pp. 129-159. Dr James Johnston Dobbie, Director of the Museum of Science and Art, was balloted for, and declared duly elected a Fellow of the Society. SECOND ORDINARY MEETING. Monday , l Qth November 1903. Sir John Murray, K.C.B., Vice-President, in the Chair. Mr Robert A. Robertson and Dr Thomas Nicol Johnston were admitted Fellows of the Society. The following Communications were read : — 1. On the Bathymetrical Survey of Scottish Fresh-water Lochs : — (i a ) Bathymetrical Survey of Loch Ness. By T. N. Johnston, M.B., C.M., and R. C. Marshall, M.A. (b) On the Seiches observed in Loch Ness. By Mr E. M. Wedderburn. Communicated by Prof. Chrystal. pp. 25-26. 1903-4.] Meetings of the Society . 1169 (c) On the Temperature Observations made in Loch Ness. By E. R. Watson, B.A., B.Sc. Communicated by Sir John Murray. 2. On Generalised Functions of Legendre and Bessel. By the Rev. F. H. Jackson, H.M.S. Irresistible. Communicated by Dr W. Peddie. Trans., vol. 41, pp. 1-28. FIRST SPECIAL MEETING. Monday , 23 rd November 1903. The Rev. Professor Flint, D.D., Vice-President, in the Chair. At the request of the Council, Dr Robert Munro gave an Address on “ Man as Artist and Sportsman in the Palaeolithic Period,” ( With Lantern Illustrations.) pp. 92-128. THIRD ORDINARY MEETING. Monday , 7 tli December 1903. Dr Robert Munro, Vice-President, in the Chair. The Keith Prize for 1899-1901 was presented to Dr Hugh Marshall for his discovery of the Persulphates, and for his communications on the properties and reactions of these salts, published in the Proceedings of the Society. The Chairman, on presenting the Prize, read the following statement : — Persulphuric anhydride was discovered in 1877 by Berthelot, but all efforts to obtain persulphates from it were fruitless, and it was even asserted, from a theoretical point of view, that per- sulphates were incapable of existence. When Dr Marshall in 1891 first obtained persulphates by the electrolysis of the acid sulphates, they formed a group of salts quite unique in character and constitution. Since that time the percarbonates (a perfectly analogous series of salts) have been prepared in 1896 by Constam and von Hansen, by means of an analogous method. Persulphates are now made on a manufacturing scale, and have taken a place as practically useful substances, being employed both in the laboratory and chemical works. PROC. ROY. SOC. EDIN. — VOL. XXV. 74 1170 Proceedings of Royal Society of Edinburgh. [sess. Among the interesting reactions discovered by Dr Marshall may be mentioned the ready solubility of metals, such as copper and silver, without evolution of gas, in solutions of persulphates, an action which has found an application in photography ; also the action of silver salts on solution of ammonium persulphate, in which ammonia is directly oxidised to nitric acid at the ordinary temperature. The oxidising action of persulphates has also been made use of in the preparation of some artificial dye-stuffs and in bleaching. The Makdougall-Brisbane Prize for 1900-1902 was presented to Dr Arthur T. Masterman for his paper entitled “ The Early Development of Cribrella ocidata (Forbes), with remarks on Ecliinoderm Development,” printed in Yol. XL. of the Trans- actions of the Society. The Chairman, on presenting the prize, said : — The observations given in Dr Masterman’s paper provide many new data for the discussion of the vexed question of the hom- ologies of the various coelomic cavities present in Echinoderms. Briefly his observations on the development of Cribrella oculata may be summed up as follows : — At the close of segmentation of the egg a solid morula of cells is produced, from which a blastula is formed by a process peculiar to Cribrella , which Dr Masterman has termed egression. Gastrulation follows, and later the archenteron divides into mesenteron, anterior coelom and posterior coelom. The anterior coelom becomes sub-divided into four portions — the hydrocoel, the epigastric coelom, the central coelom and the pre-oral coelom — the fate of each of which has been carefully traced. One of the most important points in the paper is the weight of evidence accumulated to prove the homology of the hydrocoel and epigastric coelom as left and right portions of the anterior enterocoelomic punches. The central coelom becomes the dorsal sac or cardiac vesicle, and the pre-oral coelom remains, in fact, as the axial sinus. The right and left posterior coeloms fuse to form the hypogastric coelom. In addition to these most important observations on the fate of the coelomic cavities, Dr Masterman has worked out many other interesting points in the development ; he has determined the relation of the planes of 1903-4.] Meetings of the Society. 117] the larva to those of the adult, and he has instituted striking comparisons between some of the developmental stages of Cribrella and of Balanoglossus leading to useful generalisations on the phyletic history of Echinoderms, The following Communications were read : — 1. The Bull Trout of the Tay and of Tweed. By W. L. C alder wood. pp. 27-38. 2. Field Evidence relating to the Modes of Occurrence of Intrusive Bocks. By J. G. Goodchild, F.G.S. Communicated by Dr R. H. Traquair. {With Lantern Illustrations.) pp. 197-226. Dr Ernest George Coker, Dr Alfred Charles Coles, and Mr Frederick T. G. Horday, F.R.C.V.S., were balloted for, and declared duly elected Fellows of the Society. FOURTH ORDINARY MEETING. Monday , 2\st December 1903. The Rev. Professor Flint, D.D., Vice-President, in the Chair. The following Communications were read : — 1. The Relative Efficiency of Certain Methods of performing Artificial Respiration in Man. By Professor E. A. Schafer, F.R.S. pp. 39-50. 2. Physico-Chemical Investigations in the Amide Group. By Charles E. Fawsitt, Ph.D. Communicated by Professor Crum Brown, pp. 51-60. 3. Bathymetrical Survey of Scottish Fresh- water Lochs : — Preliminary Note on the Biology of Loch Ness. By Mr James Murray. Com- municated by Sir John Murray, K.C.B. FIFTH ORDINARY MEETING. Monday , 4 tli January 1904. The Rev. Professor Duns, D.D., Vice-President, in the Chair. The following Communications were read : — 1. On the Origin of the Epiphysis Cerebri as a Bilateral Structure in the Chick. By John Cameron, M.B., M.R.C.S. Eng., University of St Andrews. Communicated by Dr W. G. Aitchison Robertson, pp. 160-167. 1172 Proceedings of Royal Society of Edinburgh. [sess. 2. On a Multi-Metre Resistance Bridge. By Professor A. Crichton Mitchell. 3. Certain Fundamental Power Series and their Differential Equations. By the Rev. F. H. Jackson. Communicated by Dr W. Peddie. Trans., vol. 41, pp. 29-39. 4. Additional Note on Generalised Functions of Bessels and Legendre. By the Rev. F. H. Jackson. Communicated by Dr. W. Peddie. Trans., vol. 41, pp. 1-28. Dr W. Leslie Mackenzie, Mr William Charles Smith, K.C., Mr Charles B. Boog Watson, Dr William Gibson Wedder- spoon, Mr Alexander Scott Ireland, and Dr Charles Stewart Lowson were balloted for, and declared duly elected Fellows of the Society. SIXTH ORDINARY MEETING. Monday, 1 8th January 1904. Dr Robert Munro, Vice-President, in the Chair. Professor J. Graham Kerr, and Messrs C. B. Boog Watson, Andrew Fuller Hargreaves, and A. Scott Ireland were admitted Fellows of the Society. The following Communications ivere read : — 1. On some Points in the Early Development of Motor Nerve Trunks and Myotonies in Lepidosiren paradoxa (Fitz.). By Professor J. Graham Kerr, M.A. ( With Lantern Illustrations .) Trans., vol. 41, pp. 119-128. 2. Histology of the Blood in Lepidosiren paradoxa : Part I. Structure of the Resting and Dividing Corpuscles. By Dr T. H. Bryce, M.A. ( With Lantern Illustrations .) Trans., vol. 41, pp. 291-310. 3. On the Development of Xenopus. By Edward J. Bles, B.A., B.Sc., University of Glasgow. Communicated by Professor J. Graham Kerr. ( With Lantern Illustrations.) Trans., vol. 41, pp. 729-821. SECOND SPECIAL MEETING. Monday, 2hth January 1904. The Rev. Professor Flint, D.D., Vice-President, in the Chair. At the request of the Council, Dr Charles Sarolea, Lecturer on French Language, Literature, and Romance Philology, in the University of Edinburgh, gave an Address on “ A New Interpretation of the Essays of Montaigne.” 1903-4.] Meetings of the Society. 1173 SEVENTH ORDINARY MEETING. Monday, \st February 1903. The Rt. Hon. Lord Kelvin, G.C.V.O., President, in the Chair. The following Communications were read : 1. On Deep-water Two-dimensional Waves produced by any given Initiating Disturbance. By the President, pp. 185-190. 2. On the Relation of Visual Efficiency to Visual Acuity : a con- sideration of the data for determining, in general, the relative loss of efficiency caused by accidents which lead to different degrees of inter- ference with sight. By Dr George A. Berry. Mr Erskine Beveridge, Mr Edward J. Bles, Mr Charles Duff Campbell, Mr William Brown Dunlop, Mr Norman Hay Forbes, Mr Thomas W. Stewart, Mr James Wallace Peck, and Mr Joseph Riley Ratcliffe were balloted for, and declared duly elected Fellows of the Society. THIRD SPECIAL MEETING. Monday, 8th February 1904. Dr Robert Munro, Vice-President, in the Chair. The following Communication was read : — “Heredity and the Cause of Variation.” By Dr John Beard. Communicated by Professor J. Cossar Ewart, F.R.S. ( With Lantern Illustrations.) EIGHTH ORDINARY MEETING. Monday, 15 th February 1904. Dr John Horne, F.R.S., in the Chair. The following Communications were read : — 1. The Glacial Deposits of Northern Pembrokeshire. By T. J. Jehu, M.D., M.A., Lecturer in Geology in the University of St Andrews. Communicated by Professor Geikie. Trans., vol. 41, pp. 53-87. 3. Ocean Temperatures and Solar Radiation. By Dr C. G. Knott. pp. 173-184. 1174 Proceedings of Royal Society of Edinburgh. [sess* NINTH ORDINARY MEETING. Monday , 1th March 1904. Professor Geikie, LL.D., Vice-President, in the Chair. The following Communications were read : — Communications on the Establishment of a Research Institute. The need of such an Institute as an aid to — 1. Biological Research. By Sir Thomas Gibson Carmichael* Bart., Professor Cossar Ewart, Professor Schafer, and F. H. A. Marshall, Esq. 2. Pharmacological and Pathological Research. By Sir Thomas R. Fraser and Dr Ford Robertson. Mr John Cuthbertson, Mr R. B. Young, Dr James Haig Ferguson, and Mr E. M. Horsburgh were balloted for, and declared duly elected Fellows of the Society. TENTH ORDINARY MEETING. Monday , 21s^ March 1904. The Rev. Professor Flint, Vice-President, in the Chair. Dr James Haig Ferguson was admitted a Fellow of the Society. The following Communications were read : — 1. On a Differentiating Machine. By J. R. Erskine-Murray, D.Sc.,. pp. 277-280. 2. Spectroscopic Observations of the Rotation of the Sun. By Dr J. Halm, Assistant Astronomer, Royal Observatory, Edinburgh. Com- municated by the Astronomer-Royal for Scotland. Trans., vol. 41, pp. 89-104. 3. The Viscosity of Aqueous Solutions of Chlorides, Bromides, and Iodides. By W. W. Taylor, D.Sc., and Clerk Ranken, B.Sc. Com- municated by Professor A. Crum Brown, pp. 231-241. 4. Note on the Standard of Relative Viscosity and on “ Negative Viscosity.” By W. W. Taylor, D.Sc. Communicated by Professor A. Crum Brown, pp. 227-230. 5. The Action of Chloroform on the Heart and Arteries. By Professor E. A. Schafer, F.R.S., and H. J. Scharlieb, C.M.G., M.D. ( With Lantern Illustrations.) Trans., vol. 41, pp. 311-341. 6. On the Thermal Expansion of Dilute Solutions of certain Hydroxides. By G. A. Carse, M.A., B.Sc. Communicated by Pro- fessor J. G. MacGregor, pp. 281-291. 1903-4.] Meetings of the Society. 1175 7. An Analytical Theory of the Equilibrium of an Isotropic Elastic Plate. By John Dougall, M.A. Communicated by Professor G. A. Gibson. Trans., vol. 41, pp. 129-228. 8. Theorem relating to a Generalisation of the Bessel Function. By the Rev. F. H. Jackson. Communicated by Dr Wm. Peddie. Trans., vol. 41, pj3. 105-118. FOURTH SPECIAL MEETING. Monday, 28 th March 1904. Professor Geikie, LL.D., Vice-President, in the Chair. At the request of the Council, Mr Robert Kidston, F.R.S., gave an Address on “ Certain Points in the Structure and Affinities of Carboniferous Ferns, Fern-like Plants and Cordaites.” ( With Lantern Illus- trations.) ELEVENTH ORDINARY MEETING. Monday, 2?id May 1904. Professor Geikie, LL.D., Vice-President, in the Chair. Dr W. Leslie Mackenzie was admitted a Fellow of the Society. The following Communications were read : — 1. On the date of Upheaval which caused the Twenty -five feet Raised Beaches in Central Scotland. By Dr Robert Munro. pp. 242-272. 2. Exhibition of Remains of Bos taurus, var. primigenius (Great Extinct Ox), and Bangifer tarandus (Reindeer), from Dundas Castle, near Dal- meny. By Dr R. H. Traquair, F.R.S. 3. Note on the Determination of the Rate of Convective Loss of Heat from a Surface exposed to a Current of Air. By Professor A. Crichton Mitchell. Mr Wm. Muirhead Baxter, Mr Walter George Burnett Dickinson^ Mr James Robert Milne, Dr Walter Colquhoun, M'r R. T. A. Innes, and Dr Wm. Elder were balloted for, and declared duly elected Fellows of the Society. 1176 Proceedings of Royal Society of Edinburgh. [sess. TWELFTH ORDINARY MEETING. Monday , 1 6th May 1904. Sir John Murray, K.C.B., Vice-President, in the Chair. Dr Erskine Beveridge, Mr W. Muirhead Baxter, and Mr James Robert Milne were admitted Fellows of the Society. The following Communication was read : — A Cosmic Theory of the Diurnal and Long-Periodic Changes of Terrestrial Magnetism and their possible Connection with Seismic Phenomena and the Displacements of the Earth’s Axis of Rotation. By Dr J. Halm, Assistant Astronomer, Royal Observatory, Edinburgh. Communicated by the Astronomer-Royal for Scotland. ( With Lantern Illustrations.) THIRTEENTH ORDINARY MEETING. Monday , 6th June 1904. The Rev. Professor Duns, Vice-President, in the Chair. The following Communications were read : — 1. Obituary Notice of Dr Charles Catty. By Professor W. C. M‘Intosh, F.R.S. pp. 1228-1234. 2. On the Measurement of Stress by Thermal Methods : an Account of some Experiments on the Influence of Stress on the Thermal Expansion of Metals. By E. G. Coker, M.A., D.Sc., Assistant Professor of Civil Engineering, M‘Gill University, Montreal. Trans., vol. 41, pp. 229-250. 3. On the Spectrum of Nova Persei and the Structure of its Bands, as photographed at Glasgow. By Professor L. Becker. Trans., vol. 41, pp. 251-290. 4. Note on Astronomical Seeing. By Dr J. Halm, Assistant Astronomer, Royal Observatory, Edinburgh. Communicated by 'the . Astronomer-Royal for Scotland, pp. 458-462. Dr Donald James Mackintosh and Mr William Macdonald were balloted for, and declared duly elected Fellows of the Society. 1903-4.] Meetings of the Society. 1177 FOURTEENTH ORDINARY MEETING. Monday , '2 Otli June 1904. The Hon. Lord M‘Laren, LL.D., Vice-President, in the Chair. The following Communications were read : — 1. On the Front and Rear of a Free Procession of Waves in Deep Water. By the Rt. Hon. Lord Kelvin, G.C.V.O., President, pp. 311-327. 2. Observations on some Aged Specimens of Sagartia troglodytes , and on the Duration of Life in Ccelenterates. By J. H. Ashworth, D.Sc., and Nelson Annandale, B.A. pp. 295-310. 3. Effect of Transverse Magnetisation on the Resistance of Nickel Wire at High Temperatures. By Dr C. G. Knott, pp. 292-294. {Abstract.) 4. Note on a New Form of Juxtapositer, to bring together the two beams of light used in spectrophotometry, and for other purposes. By J. R. Milne, B.Sc. {The Apparatus was exhibited.) pp. 355-363. FIFTEENTH ORDINARY MEETING. Monday , 4 tli July 1904. Professor Geikie, LL.D., Vice-President, in the Chair. Dr Walter Colquhoun was admitted a Fellow of the Society. The following Communications were read : — 1. Obituary Notice of Professor W. His, Honorary Fellow. By Professor D. J. Cunningham, pp. 1235-1240. 2. On the Structure of the Series of Line-Spectra. By Dr J. Halm, Assistant Astronomer, Royal Observatory. Communicated by the Astronomer-Royal for Scotland. Trans., vol. 41, pp. 551-598. 3. A New Form of Spectrophotometer. By J. R. Milne, B.Sc. {The Apparatus was exhibited.) pp. 338-354. 4. The Complete Solution of the Differential Equation of J[n]. By the Rev. F. H. Jackson. Communicated by Dr W. Peddie. pp. 273-276. Mr John Edwards, Mr J. A. Macdonald, Mr John W. Tait, Dr James Barr, and Mr Edwin O. Sachs were balloted for, and declared duly elected Fellows of the Society. 1178 Proceedings of Royal Society of Edinburgh. SIXTEENTH AND LAST ORDINARY MEETING. Monday , 18 th July 1904. Sir Jolm Murray, K.C.B., Vice-President, in the Chair. Mr J. A. Macdonald, Mr John W. Tait, and Dr James Barr were admitted Fellows of the Society. The following Communications were read : — 1. On the Histology of the Blood of the Larva of Lepidosiren parctdoxa. Part II. Histogenesis. By Dr T. H. Bryce. Trans., vol. 41, pp. 435-467. ( With Lantern Illustrations.) 2. Notes on Experiments in Spectrophotography. By J. R. Milne, B.Sc. 3. Note on the Molecular Condition of Nickel (and Iron) Demag- netized by Decreasing Reversals. By James Russell, pp. 309-310. 4. Some Results in the Mathematical Theory of Seiches. By Pro- fessor Chrystal. pp. 328-337. It was proposed from the Chair by Sir John Murray, seconded by Dr Buchan, and carried unanimously : — (1) That Law IX. be amended so as to read as follows : — “Candidates for admission as Ordinary Fellows shall make an “application in writing, and shall produce along with it a “certificate of recommendation to the purport below,* signed “by at least/owr Ordinary Fellows, two of whom shall certify “ their recommendation from personal knowledge. This re- commendation shall be delivered to the Secretary, and by “ him laid before the Council, and shall be exhibited publicly “ in the Society’s Rooms for one month, after which it shall be “considered by the Council. If the Candidate be approved “ by the Council, notice of the day fixed for the election shall “ be given in the circulars of at least two ordinary Meetings of “ the Society.” (2) That Law XIII. be amended so as to read as follows : — “The election of Ordinary Fellows shall take place only at one “Afternoon Ordinary Meeting of each month during the “Session. The election shall be by ballot, and shall be “determined by a majority of at least two-thirds of the votes, “ provided twenty -four Fellows be present and vote.” * “ A. B. , a gentleman well versed in Science {or Polite Literature > as the case may he), being to our knowledge desirous of becoming a Fellow of the Royal Society of Edinburgh, we hereby recommend him as deserving of that honour, and as likely to prove a useful and valuable Member.” Meetings of the Royal Society — Session 1904-1 905* The 122nd Session. GENERAL STATUTORY MEETING. Monday , 24 th October 1904. The following Council were elected : — President. The Right Hon. Lord Kelvin, G.C.Y.O., F.R.S. Vice-Presidents. Prof. James Geikie, LL.D., E.R.S. The Hon. Lord M‘Laren, LL.D. The Rev. Professor Flint, D.D. Robert Munro, M.A., M.D., LL.D. Sir John Murray, K.C.B., LL.D., F.R.S. Ramsay H. Traquair, M.D., LL.D., F.R.S. General Secretary — Professor George Chrystal, LL.D. Secretaries to Ordinary Meetings. Professor Crum Brown, F.R.S. Professor D. J. Cunningham, M.D., LL.D., F.R.S. Treasurer — Philip R. D. Maclagan, F.F.A. Curator of Library and Museum — Alexander Buchan, M.A., LL.D., F.R.S. Ordinary Members of Council. John Horne, LL.D., F.R.S. C. G. Knott, D.Sc. Professor Ralph Stockman, M.D., F.R.C.P.E. Professor James Walker, D.Sc., Ph.D., F.R.S. Professor Andrew Gray, M.A., LL.D., F.R.S. Robert Kidston, F.R.S., F.G.S. Dr D. Noel Paton, F.R.C.P.E. Professor John Chiene, C.B., M.D., LL.D. Professor J. Graham Kerr, M.A. William Peddie, D.Sc. Leonard Dobbin, Ph.D. Professor J. C. Ewart, M.D., F.R.S. 1180 Proceedings of Royal Society of Edinburgh. [sess. FIRST ORDINARY MEETING. Monday , 7th November .1904. The Hon. Lord M£Laren, LL.D., Vice-President, in the Chair. The following Communications were read : — 1. On Professor Seeliger’s Theory of Temporary Stars. By Dr J. Halm, Assistant Astronomer, Royal Observatory, Edinburgh. Com- municated by the Astronomer-Royal for Scotland, pp. 513-552. 2. The Sum of the Signed Primary Minors of a Determinant. By Dr Thomas Muir. pp. 372-382. 3. Continuants resolvable into Linear Factors. By the Same. 'Trans., vol. 41, pp. 343-358. 4. The Three-line Determinants of a Six-by-Three Array. By the Same. pp. 364-371. SECOND ORDINARY MEETING. Monday, 21 st November 1904. The Hon. Lord McLaren, LL.D., Vice-President, in the Chair. The following Communications were read : — 1. A Laboratory Apparatus for Measuring the Lateral Strains in Tension and Compression Members, with some Applications to the Measurement of the Elastic Constants of Metals. By Professor E. G. Coker, M.A., D.Sc. pp. 452-457. 2. A Possible Explanation of the Formation of the Moon. By George Romanes, Esq., C.E. Communicated by Dr C. G. Knott. ( With Lantern Illustrations.) pp. 471-479. Mr George Alexander Carse, Mr Wm. Anderson, F.G.S., and Dr Jacob E. Halm were balloted for, and declared duly elected Fellows of the Society. THIRD ORDINARY MEETING. Monday, 5th December 1904. Dr R. H. Traquair, F.R.S., Vice-President, in the Chair. The Chairman intimated to the Society that the following had been proposed by the Council for Ballot on 9th January 1905 : — As British Honorary Fellows. Alfred Newton, M.A., F.R.S., Professor of Zoology and Com- parative Anatomy in the University of Cambridge. 1181 1904-5.] Meetings of the Society. Joseph John Thomson, D.Sc., LL.D., F.R.S., Cavendish Professor of Experimental Physics, University of Cambridge. Sir William Ramsay, K.C.B., LL.D., E.R.S., Professor of Chemistry in the University College, London. ^4s Foreign Honorary Fellows. Moritz Cantor, Hon. Professor of Mathematics, University of Heidelberg. Wilhelm Wundt, Professor of Philosophy, University of Leipzig. Wilhelm Waldeyer, Professor of Anatomy, University of Berlin. Eduard Pfluger, Professor of Physiology, University of Bonn. Eduard Suess, Em. Professor of Geology, University of Vienna. Paul Ehrlich, Director of the Institute for Experimental Therapeutics, Erankfurt-a-M. Waldemar Chr. Brogger, Professor of Mineralogy and Palaeon- tology, University of Christiania. Paul Heinrich Groth, Professor of Mineralogy in the University of Munich. The following Communications were read : — 1. The Igneous Geology of the Bathgate and Linlithgow Hills. By J. D. Falconer, M.A., B.Sc. Communicated by Professor Geikie. Trans., vol. 41, pp. 359-366. 2. The Effect of Simultaneous Removal of Thymus and Spleen in Young Guinea-pigs. By Dr D. Noel Paton and Alexander Goodall. pp. 389-391. 3. Crystallographical Notes. By Dr Hugh Marshall, F.R.S. pp. 383-388. FOURTH ORDINARY MEETING. Monday, 19 tli December 1904. Sir John Murray, K.C.B., LL.D., Vice-President, in the Chair. Mr George Alexander Carse was admitted a Fellow of the Society. The following Communications were read : — 1. The Lower Devonian Fishes of Gemiinden. Supplement. By R. H. Traquair, M.D., LL.D., F.R.S. ( With Lantern Illustrations.) Trans., vol. 41, pp. 469-475. 2. A Specimen of the Salmon in the Smolt to Grilse Stage. By W. L. Calderwood, Esq. ( The Specimen was exhibited.) pp. 395-400. 1182 Proceedings of Royal Society of Edinburgh. [sess. 3. Networks of the Plane in Absolute Geometry. By Duncan M. Y. Sommerville, M.A., B.Sc., University of St Andrews. Communicated by Professor P. R. Scott Lang. ( With Lantern Illustrations.) Trans., vol. 41, pp. 725-747. ( Abstract , pp. 392-394.) Mr David Corrie, F.C.S., Mr Wm. Alex. Francis Balfour Browne, M.A., and Dr David Lawson were balloted for, and declared duly elected Fellows of the Society. FIFTH ORDINARY MEETING. Monday , 9th January 1905. Professor Geikie, LL.D., D.C.L., Vice-President, in the Chair. The Gunning Victoria Jubilee Prize for 1900-1904 was presented to Sir James Dewar, LL.D., D.Sc., F.R.S., etc., for his Researches on the Liquefaction of Gases, extending over the last quarter of a century, and on the Chemical and Physical Properties of Substances at Low Temperatures, his earliest papers being published in the Transactions and Proceedings of the Society. The Chairman, on presenting the Prize, said : — In 1867 Mr James Dewar read a paper to this Society on the oxidation of Phenol to Oxalic Acid. This, his first contribution to the Chemistry of the Aromatic Compounds, was followed by a more important one on the oxidation of Picoline, first given by him to the British Association in 1868, and in a fuller form to this Society in 1870. In this he proposed a graphic formula for Pyridine which expresses the relation now universally recognised between the constitution of Benzene and that of Pyridine. Dewar’s experiments on the liquefaction of gases extend over the last quarter of a century, and have culminated in the produc- tion of liquid and solid Hydrogen in large quantities, so that as thirty-five years ago he studied the chemical and physical properties of Hydrogenium solidified in Palladium, he has now given us the properties of the solid element Hydrogen itself. Having thus in his hands the means of preparing large quantities of liquefied gases, and having devised most ingenious arrangements for keeping these 1904-5.] Meetings of the Society. 1183 very volatile liquids for a long time with only a small loss from evaporation, he made good use of the opportunity for examining the chemical and physical properties of substances at extremely low temperatures. The results of these enquiries are of the highest interest and importance. For this long series of investiga- tions in Chemistry and PhysicsJ characterised by ingenuity, skill, and perseverance, and crowned with success, the Council has awarded to Sir James Dewar the Gunning Victoria Jubilee Prize. The Chairman, on presenting the Keith Prize to Sir William Turner, K.C.B., LL.D., F.R.S., etc,, said: — The Keith Prize for 1901-1903 has been awarded to Sir William Turner for his Memoir entitled “A Contribution to the Craniology of the People of Scotland,” published in the Trans- actions - of the Society, and for his “ Contributions to the Craniology of the People of the Empire of India,” Parts I., II., likewise published in the Transactions of the Society. These memoirs, important as they are, form a comparatively small part of the work which Sir William Turner has done in the field of Physical Anthropology. More especially should notice he taken of the two elaborate reports which he published on the Crania and other bones of the Human Skeleton which were collected by the Challenger Expedition. These Reports are not only valuable on account of the information which they convey regarding the physical characters of many races of mankind, but also because they establish methods of craniological and antliropo- metrical research which have very generally been accepted in this country by workers in the same field. Four great leaders have been chiefly instrumental in developing that branch of Science which has received the name of Physical Anthropology — Broca in France, Huxley and Flower in England, Turner in Scotland. The Chairman, on presenting the Makdougall-Brisbane Prize to the General Secretary for transmission to Mr John Dougall, said : — The Makdougall-Brisbane Prize for 1902-1904 has been awarded to Mr John Dougall, M.A., for his Paper on “An 1184 Proceedings of Royal Society of Edinburgh. [sess. Analytical Theory of the Equilibrium of an Isotropic Elastic Plate,” published in the Transactions of the Society. The problem of the deformation of an isotropic elastic plate under given forces has occupied the attention of mathematicians from the time of Lame. The solution given by Lame himself is merely formal ; the integrals by which that solution is expressed are not only very complicated, hut are not convergent, and they do not lead to the approximate theory. In his memoir Mr Dougall makes a new departure and develops a method that has important applications in other branches of applied mathematics. By an exceedingly skilful use of Cauchy’s theory of contour integration certain integrals, which in Lame’s solution are not convergent, are transformed into highly convergent series, and the modifications which are necessary to secure convergence lead at once to the most significant terms of the solution. The theorem of Betti is applied to develop a method, analogous to the method of Green’s function in the theory of the potential, by which the properties of the solution for a finite plate can be deduced from that for an infinite plate, and here as elsewhere throughout the memoir numerous results are obtained which have great value both for pure and for applied mathematics. The memoir confirms the ordinary approximate theory, but extends it in various directions ; for example, the edge conditions given by Kirchhoff in correction of Poisson are found directly from the mathematical investigation, without the aid of any special physical hypothesis, and are carried to a higher degree of approximation than by Kirchhoff himself. The memoir contains much acute analysis, and strikes out a new method of treating the problems of mathematical physics that seems likely to be of great value in future investigations. The Chairman, on presenting the Neill Prize for 1901-1904 to Professor Graham Kerr, said : — The Neill Prize for the period 1901-1904 has been awarded to Professor John Graham Kerr, M.A., for his Researches on Lepidosiren paradoxa, published in the Philosophical Transactions of the Royal Society, London. This work includes an account of the embryological material 1904-5.] Meetings of the So'ciety. 1185 collected during an expedition specially organised for the purpose to the Grand Chaco of South America in the years 1896-1897. The general biology and habits of Lepidosiren are described, the external features of development are fully dealt with, and in a discussion of the general hearings of the phenomena considered, reference is made to, amongst other things, the relations of the protosoma to the body of the vertebrate ; to the origin of the spiral valve ; and to the morphological significance of the external gills which it is suggested are the persisting representatives of the organs from which the limbs of vertebrates have been evolved. The following Communications were read : — 1. Sequel to a Paper, “On Charcoal Vacua,” by Professors Tait and Dewar, read before the Society in 1875. By Sir James Dewar, LL.D., D.Sc., F.R.S. {Illustrated by means of experiments with liquid air.) 2. The Theory of Continuants in the Historical Order of Develop- ment up to 1880. By Thomas Muir, LL.D. pp. 648-679. The following were balloted for, and declared duly elected : — As British Honorary Fellows. Alfred Uewton, M.A., F.R.S., Professor of Zoology and Com- parative Anatomy in the University of Cambridge. Joseph John Thomson, D.Sc., LL.D., F.R.S. , Cavendish Professor of Experimental Physics, University of Cambridge. Sir William Ramsay, K.C.B., LL.D., F.R.S., Professor of Chemistry in the University College, London. As Foreign Honorary Felloios. Moritz Cantor, Hon. Professor of Mathematics, University of Heidelberg. Wilhelm Wundt, Professor of Philosophy, University of Leipzig. Wilhelm Waldeyer, Professor of Anatomy, University of Berlin. Eduard Pfluger, Professor of Physiology, University of Bonn. Eduard Suess, Em. Professor of Geology, University of Vienna. Paul Ehrlich, Director of the Institute for Experimental Therapeutics, Frankfurt-a-M. Waldemar Chr. Brogger, Professor of Mineralogy and Palae- ontology, University of Christiania. Paul Heinrich Groth, Professor of Mineralogy in the University of Munich. PROC. ROY. SOC. EDIN. — YOL. XXY. 75 1186 Proceedings of Royal Society of Edinburgh. [sess. SIXTH ORDINARY MEETING. Monday , 23 rd January 1905. I)r R. H. Traquair, F.R.S., Vice-President, in the Chair. The following Communications were read : — 1. On the Canal Ship Waves. By the Rt. Hon. Lord Kelvin, G.C.V.O., President, pp. 562-587. 2. A Comparative Study of the Lakes of Scotland and Denmark. By Dr C. Wesenberg-Lund. Communicated by Sir John Murray, K.C.B., P.R.S. pp. 401-448. 3. On a New Family and Twelve New Species of Rotifera of the order Bdelloida, collected by the Lake Survey. By James Murray, Esq. Communicated by Sir John Murray, K.C.B., F.R.S. Trans., vol. 41, pp. 367-384. 4. Variations in the Crystallisation of Potassium Hydrogen Succinate due to the presence of other metallic compounds in the solution. (Pre- liminary Notice.) By Alexander T. Cameron, M.A. Communicated by Dr Hugh Marshall, F.R.S. pp. 449-451. 5. Continuants whose main Diagonal is Univarial. By Thomas Muir, LL.D. pp. 507-512. 6. The Eliminant of a set of General Ternary Quadrics. By the Same. 'Trans ., vol. 41, pp. 387-397. Mr William Anderson, M.A., Dr John Cameron, the Rev. Wm. Galloway Donaldson, Professor Hector Munro Macdonald, F.R.S., Mr Archibald Milne, M.A., Mr C. II. Miller-Milne, M.A., Mr Peter Pinkerton, ALA., Mr George Romanes, and Mr Alexander Thoms were balloted for, and declared duly elected Fellows of the Society. SEVENTH ORDINARY MEETING. Monday , (5th February 1905. Dr R. H. Traquair, F.R.S. , Adce-President, in the Chair. Dr John Cameron and Air R. George Romanes were admitted Fellows of the Society. The following Communications were read : — 1. On Penella : a Crustacean Parasitic on the Finner Whale ( Balce - noptera musculus). By Sir William Turner, K.C.B., LL.D. ( With Lantern Illustrations.) Trans., vol. 41, pp. 409-434. ( Abstract , p. 480.) 1904-5.] Meetings of the Society. 1187 2. The Ontogeny of the Neuron in Vertebrates : a Cytological Study of the Embryonic Nucleus. By John Cameron, M.D., St Andrews. ( With Lantern Illustrations.) EIGHTH ORDINARY MEETING. Monday , 20 th February 1905. Sir John Murray, K.C.B., F.R.S., Vice-President, in the Chair. Mr Archibald Milne was admitted a Fellow of the Society. The following Communications were read : — 1. On the Graptolite-bearing Rocks of the South Orkney Islands. By J. Harvey Pirie, B.Sc., M.B., Scottish National Antarctic Expedi- tion. Communicated by Dr John Horne, F.R.S. ( With Lantern Illustrations .) pp. 463-470. 2. Palaeontology of the Upper Old Red Sandstone of the Moray Firth Area. By Dr R. H. Traquair, F.R.S. ( With Lantern Illustrations.) 3. The Constitution of Complex Salts. I. Derivatives of the Sesqui- ■ oxides. By Alexander T. Cameron, M.A. Communicated by Dr Hugh Marshall, F.R.S. (With Lantern Illustrations.) pp. 722-737. 4. Theorems relating to a Generalisation of Bessel’s Function, II. By the Rev. F. H. Jackson. Communicated by Dr W. Peddie. Trans ., vol. 41, pp. 399-408. Captain William Alfred Pallin, F.R.C.V.S., Professor John Walter Gregory, F.R.S., Dr Wm. Colin Mackenzie, Mr Robert Blyth Greig, Mr Harold William Swithinbank, and Dr Arthur Logan Turner were balloted for, and declared duly elected Fellows of the Society. NINTH ORDINARY MEETING, Monday , 6 th March 1905. Dr Robert Munro, Vice-President, in the Chair. The following Communications were read : — 1. A Study of Three Vegetarian Diets. By Drs Noel Paton and J. C. Dunlop. (With Lantern Illustrations.) pp. 498-506. 2. A Further Contribution to the' Fresh-water Plankton of the Scottish 1188 Proceedings of Royal Society of Edinburgh. [sess. Lochs. By W. West, F.L.S., and G. S. West, M.A., F.L.S. Com- municated by Professor I. B. Balfour, F.R.S. Trans ., vol. 41, pp. 477-518. 3. On the Sarcodina of Loch Ness. By Dr E. Penard. Communi- cated by Sir John Murray, K.C.B. pp. 593-608. 4. On some Rhizopods and Heliozoa from Loch Ness. By James Murray, Esq. Communicated by Sir John Murray, K.C.B. pp. 609-615. FIRST SPECIAL MEETING. Monday , 13th March 1905. Dr Munro, Vice-President, in the Chair. At the request of the Council, Dr W. Leslie Mackenzie,, Medical Member of the Local Government Board for Scotland,, gave an Address on “ The Medical Examination and Supervision of Schools and School Children. ” ( With Lantern Illustrations.) TENTH ORDINARY MEETING. Monday , 20 th March 1905. Sir John Murray, K.C.B., F.R.S., Vice-President, in the Chair. The following Communications were read : — 1. Some Suggestions on the Nebular Hypothesis. By Dr J. Halm., pp. 553-561. 2. The Diameters of Twisted Threads, with an Account of the History of the Mathematical Setting of Cloths. By Thomas Oliver, B.Sc. Communicated by Dr C. G. Knott, pp. 481-497. 3. On Two Liquid States of Sulphur Sa and S/n and their Transition Points. By Professor Alexander Smith, pp. 588-589. 4. The Nature of Amorphous Sulphur, and Contributions to the Study of the Influence of Foreign Bodies on the Phenomena of Suj)er- cooling observed when Melted Sulphur is suddenly chilled. By Pro- fessor Alexander Smith, pp. 590-592. 5. Some Further Results in the Mathematical Theory of Seiches. By- Professor Chrystal. pp. 637-647. 1904-5.] Meetings of the Society. 1189 SECOND SPECIAL MEETING. Monday , 27 th March 1905. Dr R. H. Traquair, F.R.S., Vice-President, in the Chair. At the request of the Council, Dr Thomas Oliver, Professor of Physiology in the University of Durham College of Medicine, Newcastle-upon-Tyne, gave an Address on “Ankylostomiasis, or the Miner’s Worm Disease.” ( With Lantern Illustrations.) pp. 813-826. ELEVENTH ORDINARY MEETING. Monday , ls£ May 1905. Professor Geikie, LL.D., Vice-President, in the Chair. The following Communications were read : — 1. On the Internal Structure of Sigillaria elegans of Brongniart’s “ Histoire des Vegetaux fossiles.” By Robert Kidston, F.L.S., F.G.S. (With Lantern Illustrations.) Trans ., vol. 41, pp. 533-550. 2. Note on the Rainfall on the Drainage Area of the Talla Reservoir. By B. Hall Blyth, Memb. Inst. C.E., and W. A. Tait, Memb. Inst. C.E. pp. 616-629. 3. Remarks on the Rainfall Records in the Talla Drainage Area during the years 1896 to 1902. By P. D. Donald, Assoc. Memb. Inst. C.E. Communicated by W. A. Tait, Memb. Inst. C.E. pp. 630-636. 4. Variant Forms of Vanishing Aggregates of Minors of Axisy na- me trie Determinants. By Professor W. H. Metzler. pp. 717-721. It was proposed by Dr Horne, seconded by Dr Noel Paton; and carried : “ That from the beginning of next Session onward, all the Ordinary Meetings of the Society be held at 4.30 p.m., except four, to be held in the evening at 8 o’clock, viz. : — the first Meeting in November, in January, in March, and in June.” TWELFTH ORDINARY MEETING. Monday , 15 th May 1905. Sir John Murray, K.C.B., F.R.S., Vice-President, in the Chair. The following Communications were read : — 1. A Form of Bolometer adapted for Physiological Investigations. By Dr Walter Colquhoun. pp. 827-830. 1190 Proceedings of Royal Society of Edinburgh. [sess^ 2. Magnetic Quality of a Boscovicliian Assemblage of Molecular Magnets. {Illustrated.) By Dr Wm. Peddie. pp. 1025-1059. 3. Suggestions towards a Theory of Electricity based on the Bubble Atom. By Mr John Fraser, late Ordnance Survey. Communicated by Dr Wm. Peddie. pp. 680-716. 4. The Nudibranchiata of the Scottish National Antarctic Expedition. By Sir Charles Eliot, K.C.M.G. Communicated by Sir John Murray, K.C.B. Trans ., vol. 41, pp. 519-532. Mr James Campbell Dewar, C.A., and Mr George William Jones, M.A., were balloted for, and declared duly elected Fellows of the Society. THIRTEENTH ORDINARY MEETING. Monday , 5 th June 1905. Professor Geikie, LL.D., Vice-President, in the Chair. Dr Donald James Mackintosh, M.V.O., was admitted a Fellow of the Society. The following Communications were read : — 1. The Distribution of the Nerve Cells in the Intermedio-Lateral Tract of the Dorso-Lumbar Region of the Human Spinal Cord. By Alexander Bruce, M.A., M.D. {With Lantern Illustrations.) Trans. , vol. 45. 2. The Tardigrada of the Scottish Lochs. By James Murray, Esq. Communicated by Sir John Murray, K.C.B. Trans. , vol. 41, pp. 677-698. 3. Report on the Medusae found in the Firth of Clyde (1901-1902). By Edward T. Browne, B.A., Zoological Research Laboratory,. University College, London. Communicated by Sir John Murray,. K.C.B. pp. 738-778. 4. Notes on the Pelagic Fauna of the Firth of Clyde. By the Same. Communicated by Sir John Murray, K.C.B. pp. 779-791. 5. Report on the Free-swimming Crustacea found in the Firth of Clyde (1901-1902). By Thomas Scott, LL.D., F.L.S. Communicated by Sir John Murray, K.C.B. pp. 792-805. 6. On a new Method of Preparing Esters. By W. W. Taylor, M.A.,, D.Sc. Communicated by Professor Crum Brown, pp. 831-834. 7. Vanishing Aggregates of Determinant Minors. By Professor W. H. Metzler. pp. 853-861. 1904-5.] Meetings of the Society. 1191 THIRD SPECIAL MEETING. Wednesday , 1 4dh June 1905. Sir John Murray, Iv.C.B., E.R.S., Vice-President, in the Chair. At the request of the Council, Wilhelm Waldeyer, M.D., LL.D., D.Sc., Professor of Anatomy, University of Berlin, and Permanent Secretary of the Royal Prussian Academy of Sciences, Honorary Fellow of the Royal Society of Edinburgh, gave an Address on “The Present Position of the Neuron Doctrine.” (Illustrated by Specimens.) The Rt. Hon. the Lord Provost, in the name of the Magistrates, Town Council, and Citizens, welcomed Professor Waldeyer to Edinburgh. On the motion of Principal Sir William Turner, seconded by Professor M ‘Kendrick, and unanimously approved, the Chairman conveyed to Professor Waldeyer the cordial thanks of the Society for his able and interesting address. FOURTEENTH ORDINARY MEETING. Monday , \Wi June 1905. Dr R. H. Traquair, E.R.S., Vice-President, in the Chair. The following Communications were read : — 1. A Comparative Study of the Dominant Phanerogamic and Higher Cryptogamic Flora of Aquatic Habit. By George West, Esq. Com- municated by Sir John Murray, K.C.B. pp. 966-1024. 2. Les Concretions phosphatees de F Agulhas Bank (Cape of Good Hope), par Dr Leon W. Collet, Assistant de Sir John Murray ; avec une description de la Glauconie qu’elles renferment, par Gabriel W. Lee, B.Sc. Communique par Sir John Murray, K.C.B. pp. 862-893. 3. Note on some of the Magnetic Properties of Demagnetised and Annealed Iron. By James Russell, pp. 849-852. 4. Certain Mathematical Instruments for Graphically Indicating the Direction of Refracted and Reflected Light Rays. By James R. Milne, B.Sc. pp. 806-812. 5. On the Hydrodynamical Theory of Seiches. By Professor Chrystal. Trans., vol. 41, pp. 599-649. 6. On a Group of Linear Differential Equations of the Second Order, including Professor Chrystal’s Seiche -Equations as special cases. By Dr J. Halm. Trans., vol. 41, pp. 651-676. 1192 Proceedings of Royal Society of Edinburgh. [sess. 7. A Monograph on the General Morphology of the Myxinoid Fishes, based on a Study of Myxine. Part I. The Anatomy of the Skeleton. By Frank J. Cole, Esq. Communicated by Dr R. H. Traquair, F.R.S. Trans.j vol. 41, pp. 749-788. Mr George Andrew, M.A., Mr Eorrest-Lightbody, and Dr Thomas Lowe Bunting were balloted for, and declared duly elected Fellows of the Society. FIFTEENTH ORDINARY MEETING. Monday % 3rd July 1905. Professor Geikie, LL.D., Vice-President, in the Chair. The following Communications were read : — 1. The Plant Remains in the Scottish Peat Mosses. Part I. The Scottish Southern Uplands. By Francis J. Lewis, F.L.S., Assistant Lecturer in Botany, University of Liverpool. Communicated by Professor Geikie. Trans., vol. 41, pp. 699-723. 2. Dissociation of the Action of the Auricles and Ventricles. By W. T. Ritchie, M.D., F.R.C.P.E. Communicated by George A. Gibson, M.D., LL.D. pp. 1085-1091. 3. Cape Hunting Dogs {Lycaon pidus ) in the Gardens of the Royal Zoological Society of Ireland. By Professor D. J. Cunningham, F.R.S. {With Lantern Illustrations.) pp. 843-848. 4. The Alcyonarians of the Scottish National Antarctic Expedition. B}^ Professor J. Arthur Thomson, M.A., and James Ritchie, M.A. Trans., vol. 41. 5. The Theory of General Determinants in the Historical Order of Development up to 1852. By Thomas Muir, LL.D. pp. 908-947. 6. On the Action of Radium Bromide on the Electromotive Phenomena of the Eyeball of the Frog. By Professor J. G. M‘Kendrick, M.D., F.R.S., and Walter Cglquhoun, M.A., M.B. pp. 835-842. FOURTH SPECIAL MEETING. Monday, 10 th July 1905. Dr R. H. Traquair, F.R.S. , Vice-President, in the Chair. Dr David Lawson and Mr George Wm. Jones were admitted Fellows of the Society. The following Communications were read : — 1. On the Bathmetry, Deposits, and Temperature of the South-Western Pacific. By Sir John Murray, E.C.B., F.R.S. 1904-5.] Meetings of the Society. 1193 2. The Varying Form of the Stomach in Man and the Anthropoid Ape. By Professor D. J. Cunningham, F.R.S. ( With Lantern Illus- trations.) Trans., vol. 45. 3. Evaporation of Must and other Odorous Substances. By John Aiken, LL.D., F.R.S. pp. 894-902. SIXTEENTH AND LAST ORDINARY MEETING. Monday , 17 th July 1905. The Hon. Lord M‘Laren, LL.D., Vice-President, in the Chair. The following Communications were read : — 1. On Some Points in the Geometry of Reflecting Telescopes, with Graphical Solutions. By Dr James Hunter. 2. Some General Principles of Absorption Spectrophotometry, and a New Instrument. {The Instrument ivas exhibited.) By James R. Milne, B.Sc. 3. Note on some generally accepted views regarding Vision. By Dr Wm. Peddie. pp. 948-951. 4. On the Opacity of Aluminium Foil to the Ions from a Flame. By George A. Carse, M.A., B.Sc. pp. 903-907. 5. On Deep Sea Ship Waves. By the Rt. Hon. Lord Kelvin, President, pp. 1060-1084. 6. On the Periods and Nodes of Seiches of Lochs Earn and Treig. By Professor Chrystal and E. M. Wedderburn. Trans., vol. 41, pp. 823-850. 7. A Regular Fortnightly Exploration of the Plankton of the two Icelandic Lakes, Thingvallavatn and Myvatn. By C. N. Ostenfeld, Esq., and Dr C. Wesenberg-Lund. Communicated by Sir John Murray, K.C.B., F.R.S. pp. 1092-1167. 8. Note on the Boiling Points of Solutions. By S. N. Johnson, B.A. Communicated by Professor J. G. MacGregor, F.R.S. pp. 952-966. 9. The Oxidation of Manganese by Persulphates. By Dr Hugh Marshall, F.R.S. 10. Influence of Cross Magnetization on the Relation between Resist- ance and Magnetization in Nickel. By Dr C. G. Knott. Mr Joseph Henry Carter, F.R.C.V.S., was balloted for, and declared duly elected a Fellow of the Society. A Ballot, proposed by the Council, also took place for the re- admission of Mr A. E. Scougal, H.M.C.I.S., who resigned the Fellowship of the Society in 1899, and Mr Scougal was declared duly re-elected a Fellow of the Society. ( 1194 ) Donations to the Library of the Royal Society from 1904 to 1905. I. Transactions and Proceedings of Learned Societies,, Academies, etc., received by Exchange of Publications, and List of Public Institutions entitled to receive Copies of the Transactions and Proceedings of the Royal Society of Edinburgh. T.P. prefixed to a name indicates that the Institution is entitled to receive Transactions and Proceedings. P. indicates Proceedings. AFRICA (BRITISH CENTRAL). Zomba. — Scientific Department. Meteorological Observations,, 1903-5. — Rainfall Tables, 1903-4. Fol. ( Presented by H.M "... Acting Commissioner and Consul-General.) AMERICA (CENTRAL). Mexico — t.p. Sociedad cientifica “ Antonio Abate.” Memorias. t.p. Observcctorio Meteorologico- Mag netico Central. Boletin Mensuab p. Istituto Geologico. Boletin. p. Academia Mexicana de Ciencias Exactas , Fisicas y Naturales. p. Tacubaya. — Observatorio Astronomico. Annuario. p. Xalapa. — Observatorio Meteorologico Central del Estcido Vera Cruz.. AMERICA (NORTH). (See UNITED STATES and CANADA.) AMERICA (SOUTH). t.p. Buenos Ayres (Argentine Republic). — Museo NacionaL. Anales. — Communicaciones. Cordoba — t.p. Academia Nacional de Ciencias de la BepubUca Argentina. Boletin. t.p. National Observatory. Anales. — Climate of the Argentine Republic. By Walter G. Davis. Fol. 1902. t.p. La Plata (Argentine Republic). — Museo de La Plata. p. Montevideo (Uruguay). — Museo Nacional. Annales (Flora Uruguay). t. p. Para (Brazil). — MuseuParaense de Historia Natural e Ethnographia . Boletin. — Memorias. p. Quito (Ecuador). — Observatorio Astronomico y Meteorologico. Rio de Janeiro (Brazil)— t.p. Observatorio. Annuario. — Boletin Mensal. p. Museu Nacional. Revista (Archivos). 1904-5.] Donations to the Library. 1195 Santiago (Chili) — T.P. Socie'te Scientifique du Chili. Actes. p. Deut schcr Wissenschaftlicher Verein. p. San Salvador. — Observatorio Astronomico y Meteorologico. AUSTRALIA. Adelaide — p. University Library. p. Royal Society of South Australia. Transactions and Proceedings. P. Royal Geographical Society. Proceedings. Observatory. Meteorological Observations, 1900-1. 4to. ( Pre- sented.) Brisbane — p. Royal Society. Transactions. p. Queensland Branch of the Royal Geographical Society of Austral- asia. Queensland Geographical Journal, p. Government Meteorological Office. p. Water Supply Department. North Queensland Ethnography.— Bulletin No. 7. Domestic Implements, Arts, and Manufactures. By W. E. Roth. 4to. 1904. ( Presented by the Home Secretary’s Department.) p. Geelong (Victoria). — Gordon Technical Colleges. Melbourne — t.p. University Library. P. Royal Society of Victoria. Proceedings. Perth, W. A. — p. Geological Survey. Annual Progress Reports. — Maps. Government Statistician’s Office. Monthly Statistical Abstract,. Jan.-Aug. 1905. ( Presented .) Sydney — t.p. University Library. t.p. Department of Mines and Agriculture ( Geological Survey ), N.S.W. Records. — Annual Reports. — Mineral Resources. — Palaeon- tology, No. 10 : A Monograph of the Cretaceous Invertebrate Fauna of N.S.W. By R. Etheridge, jun. — No. 11 : A Mono- graph of the Silurian and Devonian Corals of N.S.W. Pt. 1, By R. Etheridge, jun. 4to. 1904. t.p. Linnean Society of New South Wales. Proceedings. t.p. Royal Society of New South Wales. Journal and Proceedings, p. Australian Museum. Records. — Reports. — Memoirs : No. 4. Scientific Results of the Trawling Expedition of H.M.C.S. Thetis off the Coast of N.S.W. Pts. 6-8, 1904. 8vo. — Catalogues. (Special. No. 1.) Nests and Eggs of Birds found breeding in Australia and Tasmania : North. Pt. 4, 1904. 8vo. Fisheries and Oyster Fisheries of N.S.W. Report for the year 1903. Pt. 1. 4to. (Presented by the N.S.W. Government.) 1196 Proceedings of Royal Society of Edinburgh. [sess. AUSTRIA. Cracow — t.p. Academie des Sciences. Rozprawy Wydzialu matematyczno- przyrodniezego (Proceedings, Math, and Nat. Sciences Cl.). — Rozprawy Wydzialu filologicznego (Proc., Philological Section). — Rozprawy Wydzialu history czno-tilozoficznego (Proc., Hist.-Phil. Section). — Sprawozdanie Komisyi do badania historyi sztuki w Polsce (Proc., Commission on History of Art in Poland). — Sprawozdanie Komisyi fizyjog- raficznej (Proc., Commission on Physiography). — Biblijoteka piserzow polskich (Library of Polish Authors of tbe 16th century). — Geological Atlas of Galicia ; Text, Maps. — Bulletin International. Gratz — t.p. Naturwissenschaftliclier Vereinfiir Steiermark. Mittheilungen. p. Gliemisches Institut der K. K. Universitdt. p. Lemberg. — Socie'te Scientifique de Ghevtchenko. Prague — t.p. K. K. tStermcarte. Magnetische und Meteorologische Beobach- t ungen. t.p. K. Bohmische Gesellschaft. Sitzungsberichte : Math. Naturw. Classe ; Phil.-Hist-Philol. Classe. — Jahresbericht. — And other publications. t.p. Ceskd Akademie Gisare Frantiska Jos fa pro Vedy Slovesnost a Umeni. Almanach. — Vestnik (Proceedings). — Rozpravy (Transactions) : Phil.-Hist. Class ; Math.-Phys. Cl. ; Philol. Cl.— Historicky Archiv. — Bulletin International, Resume des Travaux presentes. — And other publications of the Academy. p. Sarajevo (Bosnia). — The Governor-General of Bosnia-Herzegovina. Ergebnisse der Me teorologischen Beobachtungen. Trieste — p. Societa Adriatica di Scienze Naturali. p. Museo Givico di Storia Naturale. Atti. p. Osservalorio Astronomico-Meteorologico. Rapporto Annuale. Vienna— t.p. Kais. Akademie der Wisse nschaften. Denkschriften : Math.- Naturwissenscliaftliche Classe; Philosophisch - Historische Classe. — Sitzungsberichte der Math.-Naturwissenschaftlichen Classe ; Abtheil. I., II. a, II. b, III. ; Philosoph.-Historische Classe. — Almanach. — Mittheilungen der Erdbeben Commis- sion.— Mittheilungen der Praliistorischen Commission. T.p. K. K. Geologische Beichsanstalt. Abhandlungen. — Jahrbiicher. — V erhandlungen. t.p. 0 ester reichische Gesellschaft fiir Meteor ologie. Meteorologische Zeitschrift. 1904-5.] Donations to the Library. 1197 T.P. P. T.P. T.P. T.P. T.P. T.P. P. Vienna — continued. K. K. Zoologiscli-Botanische Gesellschaft. Verhandlungen. — Ab- kandlungen. K. K. Naturhistorisches Hofmuseum. Annalen. K. K. Central-Anstalt fur Meteorologie und Erdmagnetismus.. Jahrbiicher, Neue Folge. Bde. XXXIX.-XL. 1904-5. 4t Storiche e Filol. Memorie. — Notizie degli Scavi di Antichita. — Rendiconti. t.p. Accademia Ponteficia dei Nuovi Lined. Atti. — Memorie. t.p. R. Comitato Geologico. Memorie descrittive della Carta. Geologica. t.p Societd Italiana d. Scienza ( detta dei XL.). Memorie. p. Sassari. — Istituto Fisiologico clella R. University di Sassari. Studi Sassari. Turin — t.p. Reale Accademia delle Scienze. Memorie. — Atti. Osservatorio della R. University. Osservazioni Meteorologiche. fatte nell’ anno 1904-5. 8vo. ( Presented .) t.p. Venice. — R. Istituto Veneto di Scienze , Letter e, ed Arti. Atti. JAMAICA. p. Kingston. — The Institute of Jamaica. JAPAN. Tokio— t.p. The Imperial University of Toldo ( Teikoku-Daigaku ). College of Science of the University of Toldo. Journal. Medicinische Facultcit cler Kaiserlich - Japanischen Universitat . Mittheilungen. p. Zoological Society. Annotationes Zoologicse Japonenses. p. Asiatic Society. Transactions. p. Deutsche Gesellschaft filr Natur- und Volkerkunde Ostasiens. Mittheilungen. — Geschichte des.Christentums in Japan, von H. Haas. II. 1904. 8vo. Earthquake Investigation Committee. Publications. Nos. 14-21. 1904-5. 8vo. ( Presented .) JAVA. Batavia — T.p. Bataviaasch Genootschap van Kunsten en JVetenschappen. Ver- handelingen. — Tijdschrii't voor Indische Taal-, Land- en Volkenkunde. — Notulen. — Rapporten van de Connnissie in Nederlandsch-Indie voor Oudheidkundig Onderzoek op Java en Madoera. 1901-3. 8vo. t.p. Magnetical and Meteorological Observatory. Observations. — Re- genwaarnemingen in Nederlandsch-Indie. p. Kon. Natuurkundig Vereeniging. Natuurkundig Tijdschrii't voor Nederlandsch-Indie. LUXEMBOURG. p. Luxembourg. — LInstitut Royal Grand-Ducal. Publications. 1904-5.] Donations to the Library. 1211 MAURITIUS. t.p. Royal Alfred Observatory . Annual Reports. — Proceedings and Transactions (N.S.). — Results of Magnetical and Meteoro- logical Observations. 1900-1. 4to. MEXICO. ( See AMERICA, CENTRAL.) MONACO. Monaco. — Muse'e Oceanographique. Bulletins. Nos. 1-52. 8vo. ( Presented .) NATAL. p. Pietermaritzburg-. — Geological Survey of Natal. Annual Reports. — Report on the Mining Industry of Natal. 1902-3. 4to. NETHERLANDS. Amsterdam — t.p. Kon. Akademie van Wetenschappen. Verhandelingen : Afd. Natuurkunde. lste Sectie. 2te Sectie ; Afd. Letterkunde. — Yerslagen en Mededeelingen ; Letterkunde. — Verslagen der Zittingen van de Wis- en Naturkundige Ai'deeling. — Jaarboek. — Proceedings of the Section of Sciences. — Poemata Lati na. t.p. Koninklijk Zoologisch Genootschap. “ Natura Artis Magistral Bijdrage.ii tot de Dierkunde. p. Wiskundig Genootschap. Nieuw Archief voor Wiskunde. — Wis- kundige Opgaven. — Revue Semestrielle des Publications Matheniatiques. p. Delft. — j Ecole Poly technique. t.p. Groningen. — University. Jaarboek. t.p. Haarlem. — Hollandsche Macitschappij der Wetenschappen. Naturkundige Verhandelingen. — Archives Neerlandaises des Sciences Exactes et Naturelles. t.p. Musde Teyler. Archives. t.p. Helder. — Nederlandsche Dierkundige Vereeniging. Tijdschrift. t.p. Leyden. —The University. p. Nijmegen. — Nederlandsche Botanische Vereeniging. Nederlandsch Kruidkundig Archief. — Verslagen en Mededeelingen. — Pro- dromus Florae Batavae. Vol. I. Pars. 3. 1904. 8vo. — Recueil des Travaux Botaniques Neerlandaises. Vol. I. Nos. 1 and 2. Vol. II. 1. 8vo. 1904-5. t.p. Rotterdam. — Bataafsch Genootschap der Proefondervindelijke Wijsbegeerte. Nieuwe Verhandelingen. Utrecht — p. Provinciaal Utrechtsch Genootschap van Kunsten en Wetenschappen. Verslag van de Algenieene Vergaderingen. — Aanteekeningen van de Sectie Vergaderingen. 8vo. 1212 Proceedings of Royal Society of Edinburgh. [sess. Utrecht — continued. Koninklijk Nederlandsch Meteor ologisch Institut. Etudes de Phenomenes de Maree sur les Cotes Neerlandaises. I.— III. 8vo. 1904-5. — Observations Ocean ographiques et Meteoro- logiques dans la Region du Courant de Guinee. (1855-1900.) I. Text. Plates. 4to et Fol. 1904. NEW SOUTH WALES. (See AUSTRALIA.) NEW ZEALAND. Wellington — T.p-. New Zealand Institute. Transactions and Proceedings. — The Art Workmanship of the Maori Race in New Zealand. By A. Hamilton. Pts. 3 and 4. 4to. 1904. p. Polynesian Society. New Zealand Government. Statistics of New Z .aland. 1902-3. 4to. — The New Zealand Official Handbook. 1903-4.— Papers and Reports relating to Minerals and Mining. 1903. 4fo. — Gold Deposits of New Zealand. By Alex M‘Kay. 8vo. 1903. (Presented by the Government.) NORWAY. t.p. Bergen. — Museum. Aarsberetning. — Aarbog. — An Account of the Crustacea of Norway. By G. O. Sars. Yol. Y. 1-10. 1903-4. 8 vo. — Hydrographical and Biological Investigations in Norwegian Fiords. By O. Nordgaard.— The Protist Plankton and the Diatoms in Bottom Samples. By E. Jorgensen. 4to. 1905. Christiania— t.p. K. Norske Frederiks Universitets. Universitets-Program. — Nyt Magazin for Naturviclenskaberne. — Arcliiv for Mathematik og N aturvidenskab. t.p. Meteorological Institute. Jahrbuch. Videnskabs-Selskab. Forhandlinger. — Skrifter (Math. Nat. Kl.) (Presented.) p. Stavanger. — Museum. Aarsberetning. — Aarshefte. t.p. Throndhjem. — Kgl. Norske Videnskabers Selskab. Skrifter. p. Tromso. — Museum. Aarshefter. — Aarsberetning. PORTUGAL. t.p. Coimbra. — University. Annuario. Lisbon — t.p. Academia Peal das Sciencias de Lisboa. t.p. Sociedade de Geographia. QUEENSLAND. (See AUSTRALIA.) 1904-5.] Donations to the Library. 1213 T.P. P. T.P. T.P. T.P. P. T.P. T.P. T.P. T.P. T.P. T.P. P. P. T.P. T.P. T.P. T.P. T.P. T.P. T.P. T.P. P. P. P. P. ROUMANIA. Bucharest — Academia Romana. Analele. — Also Publications relating to the History, etc. of Roumania. Institut Me'te'orologique. Annales. RUSSIA. Dorpat (Jurjew). — University. Inaugural Dissertations. — Acta. Ekatherinebourg. — Socie'te' Ouralienne d’ Amateurs des Sciences Naturelles. Bulletin. Kazan — Imperial University. Uchenuiya Zapiski. Socie'te' Physico-Mathe'matique de Kazan. Bulletin. Kiev. — University. Universitetskiya Isvyaistiya. Moscow — Societe Impe'riale des Naturalistes. Bulletin. L’Observatoire Imperial. Annales. Socie'te' Iwjperiale des Amis IHistoire Naturelle , d1 Anthropologie et $ Ethnographie. Imperial University. Musde Poly technique. Observatoire Magnetique et Me'te'orologique de V Universite Impe'riale. Observations. 1901. 8vo. Odessa. — Societe des Naturalistes de la Nouvelle Russie. Zapiski. Poulkova. — Nicolai Hauptsternwarte. Publications (Serie II.). St Petersburg — Accide'mie Impe'riale des Sciences. Memoires (8e Serie) : Classe Phvs.-Math. ; Classe Hist.-Phil. — Bulletins. — Comptes Rendus des Seances de la Commission Sismique Permanente. Tome II. 1. 1905. 4tc. Comite Ge'ologique. Memoires. — Bulletins. — Explorations Geo- logiques : Region Aurifere d’lenissei, 6-7, de l’Amour, 4, de Lena II. 6. 8vo. Carte Geologique de la Region Aurifere d’lenissei. Imperial University. Scripta Botanica. Fasc. 20, 21, 1902-3. Institut Imperial de Medecine Experiment ale. Archives des Sciences Biologiques. Physicalische Central-Observatorium. Annalen. Physico-Chemical Society of the University of St Petersburg . Journal. Russian Ministry of Marine. Imperial Russian Geographical Society. Russian Society of Naturalists and Physicians. K. Miner alogische Gesellschaft. Verhandlungen (Zapiski). — Materialien zur Geologie Russlands. Societe des Naturalistes ( Section de Geologie et de Mine'ralogie). Travaux et Supplements. 1214 Proceedings of Poyal Society of Edinburgh. [sess. p. p. T.P. P. T.P. T.P. P. P. P. T.P. P. P. T.P. T.P. P. T.P. T.P. T.P. P. T.P. P. T.P. P. P. St Petersburg — continued. Societe Astronomique Russe. Section Geologique du Cabinet de Sa Majeste. Travaux (in Russian). Yol. YI. 1. 1904. 8vo. ( Presented .) Tiflis. — Physikatisches Observatorium. Beobachtungen. SCOTLAND. Aberdeen. — University Library. Berwickshire. — Naturalists' Club. Proceedings. Dundee.— University College Library. Edinburgh — Advocates' Library. Botanical Society. Transactions and Proceedings. Fishery Board for Scotland. Annual Reports. — North Sea Fisheries Investigation Committee. Report on Fishery and Hydrographical Investigations in the North Sea and Adjacent Waters, 1902-3. Geological Society. Transactions. Geological Survey of Scotland. Geology of North Arran, South Bute, and the Cumbraes. By W. Gunn, Sir A. Geikie, and B. W. Peach. 8vo. Glasgow, 1903. — The Tertiary Igneous Rocks of Skye. By A. Harker and C. T. Clough. 8vo. Glasgow, 1904. — The Geology of West Central Skye, with Soay. By C. T. Clough and A. Harker. 8vo. Glasgow, 1904. — The Geolog)7' of the Country round Blair- Atholl, Pitlochry, and Aberfeldy. 8vo. Glasgow, 1905. Maps. {Presented by the Government.) Highland and, Agricultural Society of Scotland. Transactions. Mathematical Society. Proceedings. Pharmaceutical Society. Royal Botanic Garden. Royal College of Physicians. Royal College of Physicians' Laboratory. Reports. Royal Medical Society. Royal Observatory. Royal Physical Society. Proceedings. Royal Scottish Academy. Annual Reports. {Presented.) Royal Scottish Geographical Society. Scottish Geographical Magazine. Royal Scottish Society of Arts. Transactions. Scottish Meteorological Society. J ournal. Scottish Microscopical Society. Proceedings. {Presented.) University Library. Glasgow — Geological Society. Marine Biological Association of the West of Scotland. Annual Reports. 1904-5.] Donations to the Library. 1215 Glasgow — continued. p. Natural History Society. Proceedings. t.p. Royal Philosophical Society. Proceedings. t.p. University. Catalogue of Greek Coins in the Hunterian Collec- tion, University of Glasgow. Yol. III. — Further Asia, Northern Africa, Western Europe. By Geo. Macdonald. 4to. 1905. — Calendar, p. University Observatory. t.p. St Andrews. — University Library. SPAIN. Madrid — t.p. Real Academia de Giencias Exactas , Fisicas y Naturales. Memorias. — Bevista. — Annuario. t.p. Gomision del Mapa Geologico de Espaha. Boletin. — Memorias. p. Vilafranca del Panades (Cataluna). — Observatorio Meteoro- logico. SWEDEN. p. Gothenburg. — Kungl: Vetenskaps- och Vitterhets-Samhdllet. Hand- lingar. t.p. Lund. — University. Acta Universitatis Lundensis (Fysio- grafiska Sallskapets Handlingar. — Theologi. — Medicina). t.p. Stockholm. — Kong. Svenska Vetenskaps- Akademie. Handlingar. — Arkiv for Zoologi. — Arkiv for Matematik, Astronomi och Fysik.— Arkiv for Botanik. — Arkiv for Kemi, Mineralogi ochGeologi. — Meteorologiska Iakttagelser i Sverige. — Astrono- miska Iakttagelser. — Lefnadsteckingar.— Arshok. p. Svenska Sdllskapet for Antropologi och Geografi. Ymer. Upsala — t.p. Kongliga Vetenskaps Societeten {Regia Societas Scientiarum). Nova Acta. t.p. University. Arsskrift. — Inaugural Dissertations (Medical and Scientific).-^Bulletin of the Geological Institution. Observatoire de V Universite. Bulletin Meteorologique Mensuel. SWITZERLAND. t.p. Basle. — Naturforschende Gesellscliaft. Verhandlungen. Bern— t.p. Societe Helvetique des Sciences Naturelles. {Allgemeine Schweizer- ische Gesellschaft fiir die gesammten Naturwissenschaften.) Comptes Rendus. — Actes (Yerliandl ungen); — Nouveaux Memoires. p. Naturforschende Gesellschaft. Mittheilungen. t.p. Geneva. — Societe de Physique et dHistoire Naturelle. Memoires. p. Lausanne. — Societe Vaudoise des Sciences Naturelles. Bulletin. 1216 Proceedings of Poyal Society of Edinburgh. [sess. Neuchatel — t.p. Societe des Sciences Naturelles. Bulletin, p. Societe Neuchdteloise de Geographic. Bulletin. Zurich — t.p. University. t.p. Commission Ceologique Suisse. Beitriige zur geologisclien Karte der Schweiz. t.p. Naturforschende Gesellschaft. Vierteljahrsschrift. p. Schweizerische Botanische Gesellschaft. Berichte (Bulletin). Schweizerische Meteor ologische Central- Anstalt. Annalen fur 1902-3. 4to. {Presented.) TURKEY. p. Constantinople. — Societe Imperiale de Me'decine. Gazette Medicale d’Orient. TRANSVAAL. t.p. Johannesburg. — Transvaal Meteorological Department. Govern- ment Observatory. Reports. TASMANIA. p. Hobart. — Poyal Society of Tasmania. Proceedings. UNITED STATES. Albany — t.p. New York State Library. Annual Reports. State Museum. Annual Reports. — Bulletin, p. Allegheny. — Observatory. Miscellaneous Scientific Papers, p. Annapolis (Maryland). — St John’s College. p. Austin. — Texas Academy of Sciences. Transactions. t.p. Baltimore. — Johns Hopkins University. American Journal of Mathematics. — American Chemical Journal. — American Journal of Philology. — University Studies in Historical and Political Science. — Memoirs from the Biological Laboratory. — University Circulars. Johns Hopkins Hospital. Bulletin, Nos. 149-176. — Reports,. Yols. X. 5-9 ; XI., XII. 1903. {Presented.) t.p. Maryland Geological Survey. Publications. Peabody Institute. Annual Reports, 1903. {Presented.) Berkeley (California) — t.p. University of California. Registers and Annual Reports. — University Chronicle. — Reports of Agricultural College. Agricultural Experiment Station. Bulletin Circulars. — Bulletin of the Geological Department. — Publications (Zoology, Botany). — And miscellaneous pamphlets. 1904-5.] Donations to the Library. 1217 Boston — t.p. The Bowclitch Library. t.p. Boston Society .of Natural History. Memoirs. — Proceedings. — Occasional Papers. No. VII. Fauna of New Zealand. 8vo. t.p. American Academy of Arts and Sciences. Memoirs. — Proceedings, p. Buffalo. — -Society of Natural Sciences. Bulletin. California. ( See San Francisco, Sacramento, Berkeley,, Mount Hamilton, and Mount Wilson.) Cambridge — t.p. Harvard University . Harvard College. Museum of Comparative Zoology. Memoirs. — Bulletins. — Annual Reports. T.P. Astronomical Observatory. Annals.— Annual Reports, p. The Editor, American Naturalist. p. Chapel Hill (North Carolina). — E. Mitchell Scientific Society . Journal. Chicago — t.p. Field Columbian Museum. Publications : Geological Series ; Botanical Series ; Zoological Series ; Anthropological Series. — Annual Reports. t.p. Chicago Observatory . p. University of Chicago. Decennial Publications. 1st Series. Vols. I.-X. 4to. 1903. t.p. Yerlces Observatory (University of Chicago). Publications. Vol. II. — Bulletin. — Reports. p. Academy of Sciences. Bulletins.— Bulletins of the Natural History Survey. Cincinnati — p. Observatory. Publications.— (No. 15) Catalogue of 4280 Stars for the Epoch 1900. 4to. 1905. p. Society of Natural History. Journal, p. Ohio Mechanics' Institute. University. Bulletins. — University Studies. — University Record. (Presented.) t.p. Cleveland (Ohio). — The Geological Society of America. Bulletins. t.p. Clinton (low a).- —Litchfield Observatory , Hamilton College. Colorado Springs.— Colorado College. Colorado College Studies. Vol. XI., pp. 54-190. 8vo. (Presented.) Columbia (Missouri; — University of Missouri. University of Missouri Studies. Vol. I. Vol II., Nos. 1-5. 1903-4.— Bulletin. Vol. V., Nos. 4, 5, 11. 1904. 8vo. (Presented.) Laws Observatory (University of Missouri). Bulletins, Nos. 2-5. 1904-5. 4to. (Presented.) p. Connecticut. — Connecticut Academy of Arts and Sciences . Transactions. p. Davenport. — Academy of Natural Sciences. Proceedings, p. Denver (Colorado). — Scientific Society of Colorado. Proceedings. PKOC. EOY. SOC. EDIN. — VOL. XXV. 77 1218 Proceedings of Royal Society of Edinburgh. [sess. t.p. Des Moines (Iowa). — Iowa Academy of Sciences. t.p. Granville (Ohio). — Denison University and Scientific Association . Bulletin of the Scientific Laboratories. p. Indianopolis. — Indiana Academy of Sciences. Proceedings. Iowa City — P. Geological Survey. Annual Reports. P. State University . Laboratories of Natural History. Bulletins. Iowa. ( See Des Moines.) Ithaca (N.Y.)— p. The Editor, Physical Review. (Cornell University.) P. The Editors, Journal of Physical Chemistry. (Cornell Uni- versity.) t.p. Lawrence (Kansas). — University of Kansas. Science Bulletin (University Quarterly). p. Lincoln (Nebraska). — The University of Nebraska. Agricultural Experiment Station. Bulletins. — Annual Reports. Madison — t.p. Wisconsin University. Washburn Observatory. Observations. P. Wisconsin Academy of Sciences, Arts, and Letters. Transactions. P. Geological and Natural History Survey. Bulletins. {Economic Series.) P. Massachusetts. — Tufts College Library. P. Meriden (Conn.). — Meriden Scientific Association. Minneapolis (Minn.) — P. Geological and Natural History Survey of Minnesota. P. Botanical Survey. Minnesota Botanical Studies. — Minnesota Plant Diseases. 8vo. 1905. Missouri. {See St Louis, Rolla, and Columbia.) p. Mount Hamilton (California). — Lick Observatory. Publications. Yol. YI. (Meridian Circle Observations : Tucker). — Bulletin. t.p. Mount Wilson (California). — Solar Observatory of the Carnegie Institution. Contributions. t.p. Newhaven (Conn.) — Yale College. Astronomical Observatory of Yale University. Transactions. — Reports, p. New Orleans. — Academy of Sciences. New York — t.p. American Mathematical Society. Bulletins. — Transactions, p. American Museum of Natural History. Bulletin. — Memoirs. — American Museum Journal. — Annual Reports, p. American Geographical Society. Bulletin, p. American Institute of Electrical Engineers. Transactions. New York. {See also Albany.) Philadelphia — T.p. American Philosophical Society for Promoting Useful Knowledge. Proceedings. — Transactions. t.p. Academy of Natural Sciences. Proceedings. — Journal. t.p. University of Pennsylvania. Publications : — Philology, Litera- ture, and Archaeology. Political Economy and Public Law. 1904-5.] Donations to the Library. 1219 T.P. P. P. P. P. P. T.P. P. T.P. T.P. P. T.P. P. P. T.P. T.P. T.P. T.P. T.P. T.P. T.P. VT.P. T.P. T.P. T.P. P. P. -P. Philadelphia — continued. History. Mathematics. Astronomy. Contributions from the Zoological Laboratory. Contributions from the Botanical Laboratory. — University Bulletins. — Theses. — Calendar. Geological Survey of Pennsylvania. Wagner Free Institute of Science i, Geographical Club. Bulletin. Commercial Museums. Portland (Maine). — Society of Natural History. Rochester. — Academy of Science. Proceedings. Rolla (Miss.). — Geological Survey of Missouri. Sacramento (California). — State Mining Bureau. Salem. — The Essex Institute. Saint Louis — Academy of Sciences. Transactions. Missouri Botanical Garden. Annual Reports. San Francisco (California). — Academy of Sciences. . Proceedings. 3rd Series (Botany, Geology, Zoology, Matb.-Pli}7s.). — Memoirs. Topeka. — Kansas Academy of Science. Transactions. Trenton. — New Jersey Natural History Society. Washington — U.S. National Academy of Sciences. Memoirs. Bureau of Ethnology. Annual Reports. — Bulletins. U.S. Coast and Geodetic Survey. Annual Reports. U.S. Commission of Fish and Fisheries. Reports. — Bulletins. U.S. Naval Observatory. Reports. — Observations. (N.S.) U.S. Geological Survey. Bulletins. — Annual Reports. — Mono- graphs.— Geologic Atlas of the United States. — Mineral Resources. — Professional Papers. — Water Supply and Irriga- tion Papers. Weather Bureau. {Department of Agriculture.) Monthly Weather Review. — Bulletins. Smithsonian Institution. Miscellaneous Collections. — The same (Quarterly Issue). — Contributions to Knowledge. — Reports. Astrophysical Observatory of the Smithsonian Institution. — The 1900 Solar Eclipse Expedition. By S. P. Langley. 4to. 1904. Surgeon-GeneraVs Office. Index to Catalogue of the Library. 2nd Series. Vols. IX. (L — Lyuri), X. (M — Mriskhovski). 1904-5. Carnegie Institution of Washington. Year-Books. — Publications, Nos. 4, 6, 7, 9-21, 23-31. (See under Donations from Authors.) American Association for the Advancement of Science. Philosophical Society. Bulletin. U.S. National Museum. Bulletins. — Reports. — Proceedings. Department of Agriculture. {Division of Economic Ornithology and 1220 Proceedings of Royal Society of Edinburgh. [sess W ASHINGTON — continued . Mammalogy.) North American Fauna. No. 23. 1904. 8vo. — Bulletins. p. U.S. Patent Office. Washington Academy of Sciences. Proceedings. Vols. IV.-VII., 1904-5. 8vo. {Presented.) U.S. Department of Agriculture. Bulletins. No. 141. — Experi- ments on Losses in Cooking Meat. 1900-3. By H. G. Grindley and T. Mojonnier. No. 149. — Studies of the Food of Maine Lumbermen. By C. P. Wood and E. R. Mansfield. 1904. 8 vo. {Presented.) Bureau of Standards. Department of Commerce and Labour _ Bulletin. Yol. I., 1, 2. 1904-5. 8vo. {Presented.) Wisconsin. {See Madison.) VICTORIA. {See AUSTRALIA.) II. Donations from Authors. Adams (Ephraim Douglass). The Influence of Grenville on Pitt’s Foreign Policy, 1787-98. {Carnegie Inst. Pub., No. 13.) Wash- ington, 1904. 4to. Allen (E. T.). See Day (Arthur L.). Antarctic (Scottish National) Expedition : — Some Results of the Scottish National Antarctic Expedition. By W. S. Bruce, J. H. Harvey Pirie, R. C. Mossman, and R. N. R. Brown. 1905. 8vo. Scotia Collections : — Algse : Gepp (A. and E. S.) and Holmes (E. M.). 1905. 8 vo. The Second Antarctic Expedition. of the Scotia. By J. H. Pirie and R. N. R. Brown. 1905. 8vo. The Botany of the South Orkneys. By R. N. Rudmore Brown, C. H. Wright, and O. V. Darbishire. 1905. 8vo. Outline Map of Laurie Island, South Orkneys, 1903. By W. S. Bruce. 1905. 8vo. Baird (John Wallace). The Color Sensitivity of the Peripheral Retina. {Carnegie Inst. Pub., No. 29.) Washington, 1905. Ballantyne (J. W.). Manual of Antenatal Pathology and Hygiene.. The Foetus. Edinburgh, 1902. 8vo. The same. The Embryo. Edinburgh, 1904. 8vo. Becker (George F.). See Day (Arthur L.). Black (F. A.). Terrestrial Magnetism and its Causes. London, 1905. 8vo. British Offices Life Tables. 1893. An Account of the Principles and Methods adopted in the Compilation of the Data, the Graduation of the Experience, and the Construction of Deduced Tables., 1904-5.] Donations to the Library. 1221 Assured Lives and Life Annuitants. London, 1903. 8vo. {From the Joint Committee on Mortality Investigation of the Institute of Actuaries and Faculty of Actuaries in Scotland.) Brioschi (Francesco). Opere Matematiche. Tomo III. Publicate per cura del Comitato per le Onoranze a Fr. Brioschi. Milano, 1904. 4to. •Castle (W. E.). Heredity of Coat Characters in Guinea^igs and Rabbits. {Carnegie Inst. Pub ., No. 23.) Washington, 1905. 4to. Chaney (H. J.). Memorandum on the Construction and Verification of the new Copy of the Imperial Standard Yard. London, 1905. 4to. {From the Superintendent of Weights and Measures — Standard Department.) Cleve (P. T.). A Treatise on the Phytoplankton of the Atlantic and its Tributaries, and on the Periodical Changes of the Plankton of Skagerak. Upsala, 1897. 4to. {Presented by the University of Upsala. ) Conard (Henry S.). The Water-lilies : A Monograph of the Genus Nymphsea. {Carnegie Inst. Pub., No. 4.) Washington, 1905. 4to. Coville (Frederick Vernon) and MacDougal (Daniel Trembly). Desert Botanical Laboratory of the Carnegie Institution. {Carnegie Inst. Pub., No. 6.) Washington, 1903. 4to. Day (Arthur L.). The Isomorphism and Thermal Properties of the Feldspars. Part I. — Thermal Study, by Arthur L. Day and E. T. Allen. Part II. — Optical Study, by J. P. Iddings. With an Introduction by George F. Becker. {Carnegie Inst. Pub., No. 31.) Washington, 1905. 4to. Dorsey (George A.). Traditions of the Ankara. {Carnegie Inst. Pub., No. 17.) Washington, 1904. 4to. • The Mythology of the Wichita. {Carnegie Inst. Pub., No. 21.) Washington, 1904. 4to. Duerden (J. E.). The Coral Siderastrea Radians and its Postlarval Development. {Carnegie Inst. Pub., No. 20.) Washington, 1904. 4to. Egypt. Results of the Swedish Zoological Expedition to Egypt and the White Nile, 1901, under the direction of L. A. Jagerskiold. Part I. Upsala, 1904. 8vo. {Presented by the University of Upsala.) Endros (Anton). Seeschwankungen, beobachtet am Chiemsee. Traun- stein, 1903. 8vo. Enteman (Wilhelmine M.). Coloration in Polistes. {Carnegie Inst. Pub., No. 19.) Washington, 1904. 4to. Faulds (Henry). Guide to Finger-print Identification. Hanley, 1905. 8vo. Flint (Robert). Philosophy as Scientia Scientiarum. Edinburgh, 1904. 8vo. Flora Batava. 341-348 Afleveringen. {From the Dutch Government.) Fiiedberger and Frohner. Veterinary Pathology. Translated by M. H. Hayes. Ed. by John Dunstan. Vol. II. London, 1905. 8vo. •Galileo. Le Opere di Galileo Galilei. Edizione Nazionale sotto gli 1222 Proceedings of Royal Society of Edinburgh. [sess„. auspicii di sua Maesta il re d’ltalia. Tom. XIY.-XYI. Firenze, 1904-5. 4to. ( From the Minister of Public Instruction of Italy.) Greene wait (Mary H.). Pulse and Rhythm. Philadelphia, 1903.. 8vo. Gulick (Rev. John T.). Evolution, Racial and Habitudinal. ( Carnegie Inst. Pub., No. 25.) Washington, 1905. 4to. Haeckel (Ernst). Kunst Formen der Natur. Lief. 10-11. Leipzig,, 1904. 4to. The Wonders of Life. A Popular Study of Biological Philo- sophy. London, 1904. 8vo. Hahn(Ferd.). Kurukh (Orao) — English Dictionary. Parti. Calcutta,, 1903. 8vo. Hill (George William). The Collected Mathematical Works of. Yol. I. ( Carnegie Inst. Pub., No. 9.) Washington, 1905. 4to. Huygens (Christian). CEuvres Completes. Publiees par la Societe Hollandaise des Sciences. Tome X. Haarlem, 1905. 4to. {Presented by the Society .) Iddings (J. P.). See Day (Arthur L.). Jagerskiold (L. A.). See Egypt. Jennings (Herbert S.). Contributions to the Study of the Behaviour of Lower Organisms. {Carnegie Inst. Pub., No. 16.) Washington, 1904. 4to. Krogh (August). I. — On the Tension of Carbonic Acid in Natural Waters, and especially in the Sea. II. — The abnormal C02 — Percentage in the Air in Greenland, and the General Relations between Atmosphere and Oceanic Carbonic Acid. Copenhagen,. 1904. 8vo. (Reprint from Medd. om Gronland, Yol. XXYI.) Liversidge (A.). Tables for Qualitative Chemical Analysis. Sydney,. 1902. 8vo. Marti (C.). The Weather Forces of the Planetary Atmospheres.. Nidan, 1905. 8vo. MacDougal (D. T.). Mutants and Hybrids of the Oenotheras. Assisted by A. M. Vail, G. H. Shull, and J. K. Small. {Carnegie Inst. Pub.y No. 24.) Washington, 1905. 4to. See Coville (Frederick Yernon). M‘Laughlin (Andrew C.). Report on the Diplomatic Archives of the Department of State, 1789-1840. {Carnegie Inst. Pub., No. 22.). Washington, 1904. 4to. Menteath (R. Stuart). Pyrenean Geology. Part IY. — The Structure of the Pyrenees. Part Y. — Engineering Geology in the Pyrenees. London, 1905. 8vo. Mines. Report of the Royal Commission on the Ventilation and Sani- tation of Mines, Western Australia. Perth, W.A., 1905. 4to. Monaco (S. A. Albert ler, Prince de). Resultats des Campagnes Scientifiques accomplies sur son Yacht. Fasc. XXIII.-XXXI. Monaco, 1904-5. 4to. Morse (Albert Pitts). Researches on North American Acridiidse., {Carnegie Inst. Pub., No. 18.) Washington, 1904. 4to. 1904-5.] Donations to the Library. 1225 Mottier (David M.), Ph.D. Fecundation in Plants. ( Carnegie Inst.. Pub., No. 15.) Washington, 1904. 4to. Newcomb (Simon). A Statistical Inquiry into the Probability of Causes of the Production of Sex in Human Offspring. (Carnegie Inst. Pub., No. 11.) Washington, 1904. 4to. • Contributions to Stellar Statistics : — 1. On the Position of the Galactic and other Principal Planes toward which the Stars tend to crowd. (Carnegie Inst. Pub., No. 10.) Washington, 1904. 4to. Noguchi (Hideyo), M.D. The Action of Snake Venom upon Cold- blooded Animals. (Carnegie Inst. Pub., No. 12.) Washington, 1904. 4to. Norwegian North Polar Expeditions, 1893-1896. Scientific Results.. Ed. by Fridtjof Nansen. Vols. IV., VI. Christiania, 1904-5. 4to. ( From the Council of the Fridtjof Nansen Fund.) Parker (Thomas). The Inch and the Metre. (Copy of Correspondence between Lord Kelvin, Lord Belhaven and Stenton, and Mr Parker.) London, 1903. 8vo. Pumpelly (Raphael). Explorations in Turkestan, with an Account of the Basin of Eastern Persia and Sistan. Expedition of 1903. (Carnegie Inst. Pub., No. 26.) Washington, 1905. 4to. Richards (Theodore William) and Stull (Wilfred Newsome). New Method for Determining Compressibility. (Carnegie Inst. Pub., No. 7.) Washington, 1903. 4to. and Wells (Roger Clark). A Revision of the Atomic Weights of Sodium and Chlorine. (Carnegie Inst. Pub., No. 28.) Washing- ton, 1905. 4to. Sachs (Edwin O.). Modern Opera Houses and Theatres. Examples selected from Playhouses recently erected in Europe, with Descrip- tive Text, a Treatise on Theatre Planning and Construction, etc.. 3 vols. London, 1897-98. Fol. Sawyer (Sir James), M.D. Insomnia : its Causes and Cure. Bir- mingham, 1904. 8 vo. Seler (Eduard). Codex Borgia. Band I. — Eine altmexicanische Bilderschrift der Bibliothek der Congregatio de Propaganda Fide. Berlin, 1901. 4to. (From his Excellency the Duke of Loubai .) Shull (George Harrison). Stages in the Development of Sium Cicutse- folium. (Carnegie Inst. Pub., No. 30.) Washington, 1905. 4to. Shull (G. H.). See MacDougal (D. T.). Small (J. K.). See MacDougal (D. T.). Smith (Edwin F.). Bacteria in relation to Plant Diseases. Vol I. — Methods of Work and General Literature of Bacteriology, exclusive of Plant Diseases. (Carnegie Inst. Pub., No. 27.) Washington,. 1905. 4to. Snell (E. Hugh), Medical Officer of Health of the City of Coventry. Annual Report on the Health of the City, 1903-4. Coventry, 8vo. Stull (Wilfred Newsome). See Richards (Theodore William). Sundbarg (Gustav). Sweden: its People and its Industry. Stockholm,. 1904. 8vo. (Presented by the University of Upsala .) 1224 Proceedings of Royal Society of Edinburgh. [sess. Teixeira (E. Gomes). Obras sobre Mathematical Yol. I. Coimbra, 1904. 4to. ( Presented by the Acad. Polytechnique de Porto.) Thomsen (Julius). Systematisk gennemforte Termokemiske Under- sogelsers numeriske og teoretiske Resultater. Kobenhavn, 3905. 8vo. ( Presented by the Danish Royal Academy of Reviews.) Tyne (Claude Halstead van) and Leland (Waldo Gifford). Guide to the Archives of the Government of the United States in Washing- ton. ( Carnegie Inst. Pub., No. 14.) Washington, 1904. 4to. Yail (A. M.). See MacDougal (D. T.). Ventilation. Report of the Select Committee on Ventilation, appointed by the House of Commons, 1903. London, 1904. 8vo. Wallace (Robert). Argentine Shows and Live Stock. Edinburgh, 1904. 8vo. Walmsley (R. Mullineux). Electricity in the Service of Man. New ed. London, 1905. 8vo. Wells (Roger Clark). See Richards (Theodore William). Williams (Walter). The State of Missouri. Missouri, 1904. 8vo. . III. List of Periodicals and Annual Publications added to the Library by Purchase. Academy. Acta Mathematica. American Journal of Science and Arts. Naturalist. ( Presented .) Journal of Mathematics. ( Presented .) Chemical Journal. {Presented.) Journal of Philology. {Presented.) Anatomischer Anzeiger. Erganzungshefte. Annalen der Chemie (Liebig’s). der Physik. {Presented.) der Physik. ( Bei blatter). {Presented.) Annales de Chimie et de Physique. d’Hygiene Publique et de Medecine Legale. des Sciences Naturelles. Zoologie et Paleontologie. des Sciences Naturelles. Botanique. Annals and Magazine of Natural History (Zoology, Botany, and Geology). of Botany. of Mathematics. Annuaire du Bureau des Longitudes. Anthropologie (L’). Archiv fur Naturgeschichte. for Mathematik og Natnrvidenskab. {Presented.) 1904—5.] Purchases for the Library. 1225 Archives de Biologie. • de Zoologie Experimental^ et Generale. des Sciences Biologiqnes. ( Presented .) des Sciences Physiques et Naturelles. Italiennes de Biologie. Arkiv for Mateniatik, Astronomi och Fysik. ( Presented .) for Kemi, Mineralogi och Geologi. ( Presented .) for Botanik. ( Presented .) for Zoologi. {Presented.) Astronomisclie N achrichten. Astrophysical Journal. Athenaeum. Bibliotheque Universelle et Revue Suisse. Biologisches Central blatt. Blackwood’s Magazine. Bollettino delle Pubblicazioni Italiane. Bookman. Botanische Zeitung. Botanischer Jahresbericlit (Just’s). Botanisches Centralblatt. Beiheft. Buddhism. An Illustrated Quarterly. {Presented.) Bulletin Astronomique. des Sciences Mathematiques. Mensuel de la Societe Astronomique de Paris. de l’lnstitut International de Bibliographic. ■Centralblatt fiir Bakteriologie und Parasitenkunde. fiir Mineralogie, Geologie und Palaeontologie. ■Ciel et Terre. ■Contemporary Review. Dingier’ s Polyteclmisches Journal. Edinburgh Medical Journal. Review. Electrical Engineer. {Presented.) Electrician. {Presented.) English Mechanic and World of Science. Flora. Fortnightly Review. Gazette Medicale d’Orient. {Presented.) Geological Magazine. Gottingsche Gelehrte Anzeigen. Indian Antiquary. Engineering. {Presented.) Interm&liaire (L’) des Mathematiciens. Jalirbiicher fiir Wissenschaftliche Botanik (Pringsheim). Jahresbericht fiber die Fortschritte der Chemie und verwandter Tlieile anderer W issenschaft. Journal de Conch yliologie. 1226 Proceedings of Royal Society of Edinburgh. [.< Journal de Math ematiques Pares et Appliquees. de Pharmacie et de Chimie. des Savants. fiir die Peine und Angewandte Mathematik (Crelle). fiir Praktische Chemie. of Anatomy and Physiology. of Botany. of Malacology. of Pathology and Bacteriology. of Physical Chemistry. {Presented.) Mathematische und Naturwissenschaftliche Berichte aus Ungarn. {Pre- sented.) Mind. Mineralogische und Petrographische Mittheilungen (Tschermak’s). Monist. Nature. {Presented.) (La). • Neues Jahrbuch fiir Mineralogie, Geologie, und Palaeontologie. Beilage. Nineteenth Century. Notes and Queries. Nuova Notarisia (De Toni). Nuovo Cimento ; Giornale di Fisica, Chimica e Storia Naturale. Nyt Magazin for Naturvidenskaberne. Observatory. Petermann’s Mittheilungen aus Justus Perthes’ Geographischer Anstalt*. Philosophical Magazine. (London, Edinburgh, and Dublin.) Physical Review. {Presented.) Quarterly J ournal of Microscopical Science, Quarterly Review. Revue Generale des Sciences Pures et Appliquees. Revue Philosophique de la France et de l’Etranger. Revue Semestirelle des Publications Mathematiques. {Presented.) Politique et Litteraire. (Revue Bleue.) Scientifique. (Revue Rose.) Saturday Review. Science. Science Abstracts. {Presented.) Times. Zeitschrift fur die Naturwissenschaften. fiir Krystallographie und Mineralogie. fiir Wissenschaftliche Zoologie. Zoological Record. Zoologische Jahrbiicher. Abtheilung fiir Anatomie und Ontogenie der Thiere. Abtheilung fiir Systematik, Geographie und Biologie der Thiere. Zoologischer Anzeiger. Jahresbericht. 1904-5.] Purchases for the Library. 1227 New English Dictionary. Ed. by Dr J. A. H. Murray. Thesaurus Linguae Latinae, editus auctoritate et consilio Academiarum quinque Germanicarum, Berolinensis, Gottingensis, Lipsiensis Monacensis, Yindobonensis. Encyclopadie der Mathematischen Wissenschaften. Leipzig. 8vo. Egypt Exploration Fund. Publications. (Archaeological and Annual Reports, Memoirs, Graeco-Roman Branch.) Palaeontographical Society’s Publications. Ray Society’s Publications. Ergebnisse der in dem Atlantischen Ocean yon Mitte Juli bis Anfang November 1889 ausgefuhrten Plankton-Expedition der Humboldt Stiftung. Herausgegeben von Victor Hensen. Fauna und Flora des Golfes von Neapel und der angrenzenden Meeres- Abschnitte. Herausgegeben von der Zoologischen Station zu • Neapel. Manual of Conchology, Structural and Systematic. By Geo. W. Tryon,. continued by Henry A. Pilsbry. International Catalogue of Scientific Literature. Published for the International Council by the Royal Society. London. 8vo. English Catalogue of Books. Monthly Additions to University Library. Edinburgh. 8vo. [Pre- sented.) Oliver and Boyd’s Edinburgh Almanac. Whitaker’s Almanac. Who’s Who. An Annual Biographical Dictionary. Year-Book of the Scientific and Learned Societies of Great Britain and Ireland. Minerva. Jahrbuch der Gelehrten Welt. Herausgegeben von Dr K, Triibner. Edinburgh and Leith Directory. OBITUARY NOTICES. Dr Charles Henry Gatty, M.A. By W. C. M'Intosh. (Read June 6, 1904.) The subject of this memoir was born on the 6th March 1836, the son of George Gatty, Esq., one of the six clerks in Chancery (an office now abolished), and of Trances, daughter of Henry Jenkin- son Sayer, Esq., a solicitor, and Auditor of the Charterhouse. He was educated at Eton, but for a short time only, as he was a delicate boy, unfitted for the rough life of a public school in those days. He was therefore removed and educated by a private tutor till he entered Trinity College, Cambridge, where he graduated as B.A. in 1859, and as M.A. in 1862. Of an earnest and studious frame of mind, he greatly enjoyed his life at college, where he made some valued friends. He always looked back with pleasure to this part of his career. After taking the B.A. degree he remained at Cambridge about a year studying medicine — not with a view to practising, but simply from his interest in the study of it in connection with zoology and comparative anatomy, as well as botany. After leaving Cambridge he travelled for a few months in the United States of America, a country in which he always felt a great interest, especially in the work of the elder and the younger Agassiz, in that connected with the scientific treatment of the fisheries of their vast shores, and in the general arrangements for the increase and spread of scientific knowledge. He spent the rest of his life for the most part at Eelbridge Place, a beautiful estate near East Grinstead in Sussex. His father died in 1862, but his mother, to whom he was deeply at- tached, and whose remembrances were a source of delight and solace to him to the last, lived till 1876. Her portraits and all that pertained to her seemed ever to awaken fresh interest— just Obituary Notices. 1229 as she herself for so many years had shed a kindly light in his home, had fostered those studies to which by nature he was inclined, and had aided and encouraged him in all his philanthropic work on the estate and in the neighbourhood. To a somewhat delicate physique and sensitive nature such sympathy and support — as could only have been given by his mother — were invaluable, and her death was keenly felt for a long time, whilst everything that reminded him of her was carefully cherished. The property (about 2000 acres) which he inherited is a most charming one — even in the beautiful county of Sussex. Within an easy distance of East Grinstead,* the fine mansion-house (about two hundred years old) is surrounded by fine old oaks, Spanish chest- nuts, sycamores, maples, groups of rare pines and shrubs. From the terrace in front of the house the eye wanders over the extensive park and level landscape to the more distant parts of the estate,, where Hedgecourt (half a mile) and Wire Mill (a mile) ponds are, while all around the rich fields are variegated with woods and clusters of trees. The prolific garden, so nicely sheltered, teemed with rare perennial and other plants, and choice collections of foreign plants occurred in the conservatories. Everything around, indeed, indicated the methodical and orderly habits of the owner, and his love for both plant and animal. In summer, groups of turtledoves, which lived and bred in the oaks near the house, flew from cover to cover and from one tree to another, and their cooing in the early morning, mingled occasionally with that of the cushat and with the notes of the nightingale in the copses and hedgerows, was one of the features most novel to a visitor from the north. In the quiet evenings the shrill note and the tapping sounds of the pied or greater spotted woodpeckers resounded on the terrace. Pheasants abounded in the woods, and from the tufts of grass in the en- closures near the terrace the heads of the leverets now and then were raised. The air indeed was laden with the sounds of life, chiefly from bird and insect, and the whole scene was an ideal one for a naturalist such as Dr Gatty was. Besides, the larger pond The property was originally acquired by Dr Gatty ’s father from one of the daughters and co-heiresses of the last Earl of Liverpool, but formerly belonged to the Evelyn family. 1230 Proceedings of Royal Society of Edinburgh. (Hedgecourt pond, or “Lake Winnipeg” as its owner humorously called it) and the smaller pond gave excellent fishing, and were the resorts of many ducks and other wild-fowl, of which he was very fond, and would never permit to he shot. In the ponds were the usual fishes of the district, viz., pike, perch, tench and bream, and he preferred to retain these rather than introduce more profit- able occupants. While thus enjoying the fascinating and peaceful surroundings •of his country home — loved and esteemed by all connected with it — he conscientiously fulfilled all the duties of a Magistrate for the counties of Surrey and Sussex, and for several years was Chairman of the East Grinstead bench of Magistrates, where he took his seat for the last time about three weeks before his death. He was also for some years a member of the East Grinstead Urban District Council. He was patron of the church, at Eelhridge — which was built and endowed by his father, in place of a private chapel which formerly stood in the grounds of Felbridge Place. He maintained the schools at Felbridge entirely at his own expense, and also to a great extent bore the expenses of the maintenance of divine service — making up whatever the offertories (to which he was the principal contributor) were insufficient to supply. Such, however, was hut one phase of his useful and beneficent life. From his college days he kept in touch with scientific life in London, and he always recalled with satisfaction his visits to the Royal Society — as the guest of an old friend ; and probably his last appearance at a scientific society was at an afternoon meeting of the same body with the writer. He was a Fellow of the Linnean, Geological, Geographical, and Ray Societies (occasionally serving on the council of each), and a member of the Astronomical and Meteorological Societies. He was especially interested in the Ray Society, and it was probably his connection with this body which more particularly drew him to St Andrews, where the early Marine Laboratory had attracted his notice. Nor was this interest in Nature new in his family. His cousin Mrs Alfred Gatty was the charming authoress of the Parables of Nature , and a lady whose love of the subject often brought her to the British Museum in the days of John and Robert Gray, of William Baird and Obituary Notices. 1231 J. Bowerbank (who occasionally worked there). She was the wife of Dr Alfred Gatty, for many years Yicar of Ecclesfield in York- shire. Her daughter, the late Mrs Ewing, was likewise an authoress, having written The Story of a Short Life and other interesting works. Having, after various communications with Principal Donald- son, decided to give <£1000 to encourage marine zoology at St Andrews, Dr Gatty carried out his views in a manner peculiarly his own. Everything about the old wooden laboratory under the Fishery Board for Scotland was carefully examined and the capabilities of the situation understood. He joined the excursion from the Edinburgh meeting (1892) of the British Association next day ; and apparently having thought over what he had seen and heard, he, while examining the marine collection in St Leonards Girls’ School in the afternoon, quietly asked the writer the question, “Will £1000 suffice for the Marine Laboratory ? ” It was explained that it would greatly help in its ■erection. He then asked how much would be necessary for the whole1? A sum of £2000 was mentioned. At once he replied, “ I shall give it.” Thus the intimation which was made public at the luncheon by the University (the cost of which was generously borne by the late Provost Paterson, of K inburn and Langraw), was correctly entered in the evening papers. In writing about his gift shortly after he returned home he says, “I cannot tell you what a pleasure it is to me to be able to do something towards the advancement of Zoology, which has always been my favourite study, and this pleasure has been increased tenfold by the fact that it has brought me into connection with the University of St Andrews.” In the plans of the Laboratory he took a deep interest, and made some improvements, at the suggestion of the writer and the Eev. A. D. Sloan (who had worked at Naples), in regard to increasing space (with additional cost). During the progress of the building, and while sitting on the sand-dunes near it with Prof. Pettigrew and the writer, he thoughtfully said, “ I have given what is required for the erection of the Laboratory, but I have given nothing for the furnishing of it. Can you tell me the sum necessary for this ? ” .A sum of £500 was indicated, and he at once assented 1232 Proceedings of Hoy cd Society of Edinburgh. guaranteeing any excess over this sum should it be requisite, as indeed it eventually was. Thus, in an unostentatious and most kindly way, an Institution — unique of its kind — was erected, fitted by Dr Gatty, and handed over to the University. In his quiet modesty no one thought less of the action than himself. He was satisfied if the study of marine animals and the work of the fisheries could in any way he promoted, and his favourite science generally advanced. Dr Gatty was present at the opening of the Marine Laboratory by Lord Reay, along with a notable band of zoologists and men of science, the Senate of the University, and the public, on the 30th October 1896. Lord Reay, a former Rector of the University, commenced his address by observing, “ It is a pleasant duty which devolves on me to tender to Dr Gatty the sincere thanks not only of the rulers of this ancient seat of learning, but pf all men of science, and of all Scotsmen, for this munificent gift .... Dr Gatty must have felt some difficulty in adjudicat- ing on the multitude of claims which confronted him. There are so many scientific wants, that great discernment is needed in those who wish to benefit their generation. We are doubly grateful to Dr Gatty that he has given a decision in our favour. And I think no assurance is called for that everything will be done by the University to show that it is worthy of so generous a donor. I feel sure that as time goes on the value of this foundation will be enhanced in the eyes of future generations, and that many scientific men from all parts of the world will set out on a pilgrimage to this station, and that tlieir homage to the pious founder will take the form of research.” “How I have no doubt that the best investment for superfluous capital is that chosen by Dr Gatty — the endowment of the Scottish Universities.” “ Dr Gatty has set an example which ought to stimulate those who are in search of employment for capital.” The enthusiasm with which the great assembly received the tribute paid by Lord Reay to Dr Gatty was so great that the occasion must have been a pleasant one for the modest donor, who in subsequent years never ceased to^ be deeply interested in the work of the Laboratory. Even when in search of health in the coast towns of the south, e.g. in Obituary Notices. 1233 Cornwall, the marine fauna and the fisheries of each were carefully contrasted with those of St Andrews, and many interesting observa- tions made. The city in which his generous gift was made was not slow to recognise his high purposes and liberality, for it conferred, in 1896, its freedom on him along with Lord Bute and General Robert Low of Clatto, the former the talented Rector of the University, the latter the distinguished Indian soldier, as indeed his father like- wise was. Dr Gatty also received the degree of LL.D. from the University for his lifelong labours in promoting science, and his special interest in Zoology. For some years his failing health prevented him journeying northward, but he attended the meetings of various societies in London, and kept himself abreast of all that was doing in Zoology. He also took great interest in Meteorology, especially towards the close of his life, when his eyes failed for microscopic work. Every morning he took the readings of his thermometers in the garden, registered the rainfall, read his barometers, and entered all methodically in a weather-chart, which was kept with the greatest accuracy and neatness ; indeed, his caligraphy was at all times a model of exactness. Lately the affection of the heart under which he laboured gave his friends some anxiety, and the end came somewhat suddenly on the 12th December 1903. The University Court, on receipt of the intelligence, entered the following resolution, prepared by Principal Donaldson, in their minutes of date 6th February 1904 : — u The University Court record their great regret at the decease of Dr Gatty, their sense of the great loss the University has sustained thereby, and their high appreciation of Dr Gatty’s acquaintance with and interest in Science, and of the great contribution which he munificently made to the study of it by the establishment of the Gatty Marine Laboratory in this University. The Court desire also to assure his executors that his name will ever be held in affectionate remembrance in St Andrews.” Personally, Dr Gatty was one of the most kindly and considerate men, courteous and self-possessed, ever ready to anticipate the wants of others, and though of a retiring and modest disposition, yet tenacious in his purposes of well-doing. Quiet, studious, and PROC. ROY. SOC. EDIN. — YOL. XXY. 78 1234 Proceedings of Royal Society of Edinburgh. thoughtful, he had many of the habits of Gilbert White in his love and close scrutiny of Nature. He, moreover, was filled with a desire to see its scientific study advancing along modern lines. For this purpose he chose a field in which he himself was deeply interested, and in which he believed that not only the purely scientific aspects of Marine Zoology would make progress, but also that an important branch, viz., the sea-fisheries, so intimately associated with the welfare of the country at large, and of the fishing population in particular, would be advanced.* * I am indebted to C. L. Sayer, Esq. , and G. W. Seymour, Esq. , especially the former, for much information concerning Dr Gatty. Obituary Notices. 1235 Wilhelm His, K. S. Geheimer Rath, Professor of Anatomy, Leipzig, Honorary Fellow of the Royal Society of Edinburgh, 1900-1904. By Professor D. J. Cunningham. (Read July 4, 1904.) Amongst the many remarkable men of science of a remarkable century Professor Wilhelm His will always be given a prominent and honoured place. In almost every branch of anatomy he ha's left his mark, and during the last thirty years no one has done so much to advance our knowledge of that subject. Although a professor in Leipzig, where the best part of his work was accomplished, Germany was merely the country of his adoption. Pie belonged to an old Swiss family, and was born in Basel in 1831. It was there that His received his early education, and it was in the University of that town that he commenced, at the age of eighteen, the study of medicine. His career as a student was marked by a restless desire to profit by the tuition of the great teachers of that time, no matter where they were to be found. Thus in his second year of study we find him at Berne, where he came under the influence of Theile the anatomist and of Valentin the physiologist. In the following year (1850) he went to Berlin, where he had the singular good fortune to have as his teachers Johannes Muller and Robert Remak. There can be no doubt that this formed a crucial point in his career. He was profoundly im- pressed by the manner and method of the teaching of the great comparative anatomist Muller, and it is believed that a lecture which he heard Remak deliver upon the development of glands first stimulated in him that curiosity in regard to development in general which in his after life led to such magnificent results. But his peripatetic pursuit of knowledge did not end in Berlin. In 1852 he went to Wiirtzburg. At that time Virchow was a young professor in this school, and His worked in his laboratory and conducted an investigation the results of which were sub- sequently published. Having completed his studies, he graduated 1236 Proceedings of Boy al Society of Edinburgh. in Basel in 1854 : and after spending some time in Prague, Vienna,, and in the laboratories of Paris, and acting for a short period as a privat docent in his native town, he was called upon, at the age of twenty-six, to succeed Professor Meissner as Professor of Anatomy and Physiology in the University of Basel. In Basel Professor His laboured for fifteen years, and by the- work which he did he very early attracted the attention of those engaged in similar pursuits. In 1872 the chair of Anatomy in Leipzig, which had been previously held by Weber, fell vacant,, and Ludwig, the celebrated Leipzig physiologist, with conspicuous judgment and foresight, recognised in His the proper successor to Weber. There is good ground for the belief that it was mainly through the influence of Ludwig that His was translated to Leipzig. Professor His displayed activity in so many departments of anatomy that it is an exceedingly difficult matter, within reason- able compass, to give anything like an adequate conception of the splendid work which he accomplished. There is no name that is more frequently on the lips of the teaching anatomist of the present day ; there is no one who has exercised a more powerful influence in moulding anatomical thought in almost all branches of that subject. Still, there can be little doubt that it is his embryological work that will produce the most lasting impression. Up to the time when he entered this field of research very little was known regarding the special development of man. Human embryology in its earlier stages was represented in the book of anatomy by a very nearly blank page. What embryology was taught to the student of human anatomy was almost entirely derived from observations conducted on the embryos of the lower animals. Now, with the exception of the few days immediately succeeding the fertilisation of the ovum, we have a very nearly complete- record of the development of man. This we owe to Professor His. Of course, all the work which has led to this result was not done by him alone — other workers have helped in certain departments ; but His was the leading spirit. His not only laid the foundation, but with his own hands reared by far the greater part of the superstructure. His magnificent work, entitled Anatomie men - sclilicher Embryonen , and published in three parts, was completed in 1885. Obituary Notices. 1237 This work is the mine from which anatomists of the present "day have extracted the greater part of their knowledge of human development, and it is from it that they have borrowed the greater part of the embryological illustrations which are used in their text-books. It is difficult to realise the labour and patience required to -successfully carry out investigations into the development of man. Human embryos in the first month — and this is the important month — of development can only be obtained at rare intervals, and as often as not they come into the hands of the investigator in a condition unfit for proper research, and never in the condition in which the embryos of most of the lower animals can be secured. By the most assiduous search after specimens, .and by the elaborate measures undertaken for their preservation, Professor His was enabled to overcome these initial difficulties. But His did not content himself by publishing descriptions and drawings of the human embryo and its different organs : he likewise constructed models of the anatomy of the Embryo at different stages of its growth. These models are singularly beauti- ful. The early human embryo is an exceedingly minute object ; in the middle of the first month of development it measures little more than 2 mm. in length. The skill which Professor His exhibited in the reconstruction and magnification of these small embryos was little short of marvellous. Wherever anatomy is taught these models form a part of the laboratory equipment, and they have proved of the greatest service, not only to the teacher and pupil, but also to all those engaged in embryological research. If we might venture from so much material to select one result obtained by Professor His which at the present moment appears to possess a specially far-reaching significance, we would point to his investigations into the origin of nerve cells and the growth of nerve fibres. This research does not cover a great extent of ground, but even taken by itself it would be sufficient to establish the reputation of Professor His on a lasting and permanent basis. In the early brain and spinal cord the nerve cells assume shape and by a process of migration take up their several positions within the central nervous axis. At first there are no nerve- fibres, so the embryo at this stage has a brain and spinal cord, but 1238 Proceedings of Royal Society of Edinburgh. these are not provided with nerves. The nerve-fibres grow out from the cells and pursue their several paths with the most unerring exactitude towards the elements with which they ultimately become connected. The fibres which form the efferent nerves grow out from the nerve-cells in the brain and cord ; the fibres of the afferent nerves arise from the ganglion cells outside and grow into the brain and cord so as to establish their con- nections with the central nervous axis. This may seem a small point, and yet it forms the embryological basis of our modern conception of the manner in which the nervous system is built up, and also of the manner in which its different units or neurons are connected. But it would be wrong, even in a short notice such as this of necessity is, to omit to refer to the useful work performed by Professor His in the department of topographical anatomy. During the last thirty or forty years our ideas in regard to the form and relations of the different parts of the human body have undergone a complete revolution. Professor His was one of the leading pioneers in bringing about this change. It is not so long ago that the anatomist derived all his information in regard to the topography of the body from dissection alone. No other method was followed ; and when, as in these times, it was not combined with measures for the preservation of the form of the parts under observation, the- amount of information it yielded was limited, and not unfrequently misleading. Sections of the frozen body, introduced by Pirogoff, carried out to such perfection by Braune, and now practised by teachers all over the world, led to a great advance in every department of topographical work. It then became possible to check the results obtained by dissection, and correct many erroneous impressions for which the latter method was responsible. The next step was taken by Professor His, who hardened the viscera in situ by prolonged injection of chromic salts ; and it is no too much to say that the models which he prepared from these specimens, and which are at present used wherever the study of anatomy is pursued, have had a profound effect on anatomical thought and teaching. Recently the method of Pro- fessor His has been brought to a state bordering on perfection by Obituary Notices. 123ff the introduction of formalin as the hardening reagent, and His was not slow to take advantage of this advance. One of his last papers, entitled Studien an gehdrteten Leichen uber Form und Lagerung des menschlichen Magens, deals with observations con- ducted in this manner, and was published as recently as last year. The paper which Professor His wrote upon the skeleton of Johann Sebastian Bach, the distinguished musician, is of such general interest that I may be permitted to allude specially to it. Bach, who died in 1750, at the age of 65, was buried in the churchyard of the Johanniskirehe, but tradition alone pointed to the site of the burial. In 1894, when the new church was in course of erection, it was very naturally considered desirable that the remains should be found, in order that they might be suitably reinterred. A search in the place indicated revealed an oaken coffin containing the skeleton of an aged man. By comparing the skull, which presented some peculiarities — more especially a marked projection of the lower jaw — with portraits of Bach, His was able to identify the skeleton as that of the famous, musician, and he wrote an elaborate memoir on the remains. With much labour he was able to reconstruct from the skull the outline of the head, and he also devoted especial attention to the temporal bones, within which are encased the essential parts of the organ of hearing. There is an impression among certain anatomists who have given attention to the matter that the tympanic membrane of the ear in musicians is set in its bony frame more vertically than in ordinary mortals. His did not find this to be the case with Bach : the angle which the membrane formed Avith the floor of the auditory passage was 42°, whilst the average angle is said to be about 55°. When His became head of the Anatomical Institute in Leipzig,. Wilhelm Braune was appointed Professor of Topographical Anatomy in the same University. The association of these two Avorkers in different departments of the one subject was an ex- tremely happy one. They soon became united by the ties of a Avarm friendship, and it is not surprising that, Avith a combination so strong, it Avas from the Leipzig school that the chief movement took place AAdiich led to so great a change in anatomical thought and method. 1240 Proceedings of Royal Society of Edinburgh. It would hardly be .possible to conceive two men so absolutely different both in temperament and in physical characters as the two Leipzig colleagues : Braune, big, bluff, hearty and almost boisterous in manner; His, tall, spare, and dark, with a sharp sallow face, keen black eyes, and a narrow but good forehead. He was diffident and restrained in manner, and it was only with those whom he knew well that he appeared at his best.* No anatomist of our time has wielded so wide an influence within the limits of his own subject. Students came to his laboratory from all parts of the Continent, from Great Britain, and from America. All who came with the right spirit were made heartily welcome and received every encouragement and help in their work. At the same time, Professor His possessed none of that grace and ease of expression which distinguishes his devoted friend and colleague, Professor Waldeyer of Berlin, none of the impressive lucidity which is characteristic of the teaching of Sir William Turner. Still, he had those qualities which caught the attention and aroused the enthusiasm of his students, and great results followed. Many of his pupils, perhaps chiefly those in America, are now doing excellent work on their own account. He died on the 1st of May last after a painful illness, borne with the most patient fortitude. To the last his mind was in his work. He was deeply interested in the International Committee which had been appointed with the view of organising a combined effort in brain research. He was the chairman of this Committee, and had summoned by his own hand, in April, a meeting to be held in London on the 24th of May. Alas ! he was not there to greet his colleagues. * When Professor His visited Dublin in 1898 he was measured in the Anthropometrical Laboratory of the Anatomical Department. The following ■are the measurements which were obtained : — Stature ........ 1722 mm. Circumference of head ..... 553 Cranial length . . . . . . .197 Cranial breadth 157 Cranial height . . . . . . .140 Cephalic index . . . . . . . 79*7 The average cranial height for adult males in Ireland is somewhere about 131 *3, and for a group of thirty-six anatomists, measured at the same time as Professor His, 133 '4. Abstract of Accounts. 1241 ABSTRACT OF THE ACCOUNTS OF PHILIP ROBERT DALRYMPLE MACLAGAN, ESQ., As Treasurer of the Royal Society of Edinburgh. SESSION 1 904-1905. I. ON ACCOUNT OF THE GENERAL FUND. CHARGE. 1. Arrears of Contributions at 1st October 1904 <£144 18 0 2. Contributions for present Session : — 1. 158 Fellows at £2, 2s. each £331 16 0 134 Fellows at £3, 3s. each 422 2 0 £753 18 0 Add — Contribution of 2 Fellows elected in 1903-1904, whose admission fees were not paid till present session at £3, 3s. each 6 6 0 £760 4 0 Less included in sum received in lieu of future Contributions 2 2 0 £758 2 0 2. Sum received in lieu of future Con- tributions 8 8 0 3. Fees of Admission and Contributions of twenty-one new Resident Fellows at £5, 5s. each 110 5 0 4. Fees of Admission of eight new Non- Resident Fellows at £26, 5s. each 210 0 0 5. Fees of Admission and Composi- tion fee in lieu of future Contribu- tions of one new Resident Fellow 44 2 0 6. 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