PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. O ^ o ^ PEOCEEDINGS OP THE EOYAL SOCIETY OF EDINBUEGH. VOL. XXXV. NOVEMBER, 1914 to JULY 1915. / V EDINBUEGH: FEINTED BY NEILL AND COMPANY, LIMITED, MDC CCCXV, CONTENTS. 1. Opening Address by tlie President, November 2, 1914, . 2. The Baleen Whales of the South Atlantic. By Sir William Turner, Emeritus Professor of Anatomy, K.C.B., F.E.S., D.C.L. Issued separately December 4, 1914, .......... 3. The Optical Rotation and Cryoscopic Behaviour of Sugars dissolved in (a) Forma- mide, (6) Water. By John Edwin Mackenzie and Sudhamoy Ghosh, M.Sc. (Research Student, University of Edinburgh). Issued separately February 2, 1915, . . ' . 4. Studies on Periodicity in Plant Growth. Part II. : Correlation in Root and Shoot Growth. By Rosalind Crosse, B.Sc., Carnegie Research Fellow, 1912-14. (With Two Plates.) Issued separately February 24, 1915, . 5. Properties of the Determinant of an Orthogonal Substitution. By Sir Thomas Muir, G.M.G., LL.D., F..RS. Issued separately EMbruary 24, 1915, . 6. EArmulse and Scheme of Calculation for the Development of a Function of Two Variables in Spherical Harmonics. By Professor J. Bauschinger, Strassburg. Translated and communicated hy The General Secretary, Dr C. G. Knott. Issued separately March 16, 1915, 7. On an Integral-Equation whose Solutions are the Functions of Lame. By Professor E. T. Whittaker, F.R.S. Issued separately March 16, 1915, 8. Regeneration of the Legs of Decapod Crustacea from the Preformed Breaking Plane. By J. Herbert Paul, M.A., B.Sc., Barbour Research Scholar, Physio- logical Department, Glasgow University. (With Four Plates.) Communicated hy Professor D. Noel Paton. Issued separately April 6, 1915, . 9. On the Resistance experienced by a Body moving in a Fluid. By H. Levy, M. A., B.Sc., 1851 Exhibition Research Scholar of the University of Edinburgh. Communicated hy The General Secretary. Issued separately April 8, 1915, 10. Fossil Micro-organisms from the Jurassic and Cretaceous Rocks of Great Britain. By David Ellis, Ph.D., D.Sc, Royal Technical College, Glasgow. (With Two Plates.) Issued separately April 27, 1915, . . . . . 11. The Reaction between Sodamide and Hydrogen. By F. D. Miles, B.Sc., A.R.C.S. Communicated hy Principal A. P. Laurie, D.Sc. Issued separately April 27, 1915, .......... 12. On the Electrical Conductivity of Aqueous Hydrochloric Acid, saturated with Sodium Chloride ; and on a new form of Conductivity Cell. By F. D. Miles, B.Sc., A.R.C.S. Communicated hy Principal A. P. Laurie, D.Sc. Issued separately April 27, 1915, . . PAGE 1 11 22 46 54 63 70 78 95 110 134 138 VI Contents. 13. The Reflective Power of Pigments in the Ultraviolet. By Charles Cochrane, M.A., B.Sc., Assistant to the Professor of Natural Philosophy in the University of Glasgow. Communicated by Dr R. A. Houstoun. Issued separately May 21, 1915, .......... 14. The Theory of the Gyroscope. By Professor H. Lamb, F.R.S. Issued separately May 25, 1915, ......... 15. The Densities and Degrees of Dissociation of the Saturated Vapours of the Ammonium Halides. By Professor Alexander Smith and Robert H. Lom- bard. Issued separately May 22, 1915, ..... 16. On a Modification of Pelouze’s Method for determining Nitrates. By Professor E. A. Letts and Florence W. Rea. Issued separately June 24, 1915, . 17. Quaternion Investigation of the Commutative Law for Homogeneous Strains. By Frank L. Hitchcock. Communicated by Dr C. G. Knott, General Secretary. Issued separately July 8, 1915, . 18. On the Functions which are represented by the Expansions of the Interpolation- Theory. By Professor E. T. Whittaker, F.R.S. Issued separately July 13, 1915, .......... 19. On the Composition of Milk as affected by Increase of the Amount of Calcium Phosphate in the Rations of Cows. By A. Lauder, D.Sc., and T. W. Fagan, M.A. Issued separately September 21, 1915, ..... 20. On a See-Saw of Barometric Pressure, Temperature, and Wind Velocity between the Weddell Sea and the Ross Sea. By R. C. Mossman. Issued separately September 21, 1915, ........ 21. The Magnetic Quality of Iron and Steel as affected by Transverse Pressure. By Win. J. Walker, B.Sc. Communicated by Professor W. Peddie. Issued separately December 3, 1915, . 22. The Interaction of Methylene Iodide and Silver Nitrate. By Professor C. R. Marshall and Elizabeth Gilchrist, M.A., B.Sc. Issued separately December 3, 1915, .......... 23. A Comparative Study of the Reflexes of Autotomy in Decapod Crustacea. By J. Herbert Paul, M.A., B.Sc. (From the Physiological Department of the University of Glasgow, and the Marine Laboratories at Millport and Culler- coats.) Communicated, by Professor Noel Paton. Issued separately December 4, 1915, .......... 24. Chalk Boulders from Aberdeen and Fragments of Chalk from the Sea Floor off the Scottish Coast. By the late William Hill, of Hitchin, F.G.S. Com- municated by Professor D’Arcy W. Thompson. Issued separately December 14, 1915, .......... 25. Notes on the Structure of the Chalk occurring in the West of Scotland. By the late William Hill, of Hitchin, F.G.S. Communicated by Professor D’Arcy W. Thompson. Issued separately December 14, 1915, . . , . Obituary Notice — Sir John Murray, K.C.B., LL.D., Ph.D., D.Sc., F.R.S., etc.. PAGE 146 153 162 168 170 181 195 203 217 227 232 263 297 305 Contents. vii PAGE Appendix — Laws of the Society, . . . . . , . .321 The Keith, Makdougall-Brisbane, Neill, and Gunning Victoria Jubilee Prizes, . 326 Resolutions of Council in regard to the mode of awarding Prizes, . . 328 Awards of the Keith, Makdougall-Brisbane, Neill, and Gunning Victoria Jubilee Prizes, .......... 329 Proceedings of the Statutory General Meeting, October 1914, . . . 334 Proceedings of the Ordinary Meetings, Session 1914-1915, . . . 335 Proceedings of the Statutory General Meeting, October 1915, . . . 340 Accounts of the Society, Session 1914-1915, ..... 342 The Council of the Society at January 1916, . . . . . 348 Alphabetical List of the Ordinary Fellows of the Society at January 1916, . 349 List of Honorary Fellows of the Society at January 1916, . . . 366 List of Ordinary Fellows of the Society elected during Session 1914-1915, . 368 Honorary Fellows and Ordinary Fellows deceased and resigned during Session 1914-1915, 368 List of Library Exchanges, ........ 369 List of Periodicals purchased by the Society, ..... 393 Additions to Library during 1915, by Gift or Purchase, .... 397 Index, ........... 399 List of Papers published in the “Transactions” during Session 1914-15, . 402 PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SESSION 1914-15. Part 1.1 VOL. XXXV. [Pp. 1-112. CONTENTS. NO. PAGE I. Opening Address by the President, November 2, 1914, . 1 II. The Baleen Whales of the South Atlantic. By Sir William Turner, Emeritus Professor of Anatomy, K.C.B., F.B.S., D.C.L., . . . . . . . II {Issued separately December 4, 1914.) III. The Optical Rotation and Cryoscopic Behaviour of Sugars dissolved in (a) Formamide, (h) Water. By John Edwin Mackenzie and Sudhamoy Ghosh, M.Sc. (Research Student, University of Edinburgh), . . .22 {Issued separately February 2, 1915.) IV. Studies on Periodicity in Plant Growth. Part II : Correlation in Root and Shoot Growth. By Rosalind Crosse, B.Sc., Carnegie Research Fellow, 1912-14. (With Two Plates), 46 {Issued separately February 24, 1915.) V. Properties of the Determinant of an Orthogonal Substitution. By Thomas Muir, LL.D., ..... {Issued separately February 24, 1915.) VI. Formulae and Scheme of Calculation for the Development of a Function of Two Variables in Spherical Harmonics. By Professor T. Bauschinger, Strassburg. Translated and communicated by The General Secretary, Dr C. G. Knott, 54 63 {Issued separately March 16, 1915.) \_Continued on page iv of Cover. EDINBURGH: Published by ROBERT GRANT & SON, 107 Princes Street, and WILLIAMS & NORGATE, 14 Henrietta Street, Covent GARDEiiyAr.o^«Er^ MDCCCCXV. Price Seven Shillings. V RDEJi.y--4r,O^P^.---~- ^ may 5 1915 REGULATIONS REGARDING THE PUBLICATION OF PAPERS IN THE PROCEEDINGS AND TRANSACTIONS OF THE SOCIETY. The Council beg to direct the attention of authors of communications to the Society to the following Regulations, which have been drawn up in order to accelerate the publication of the Proceedings and Transactions, and to utilise as widely and as fairly as possible the funds which the Society devotes to the publication of Scientific and Literary Researches. 1. Manuscript of Papers. — As soon as any paper has been passed for publication, either in its original or in any altered form, and has been made ready for publication by the author, it is sent to the printer. 2. Method of Publication. — As soon as the final revise of a Trans- actions paper has been returned, or as soon as the sheet in which the last part of a Proceedings paper appears is ready for press, a certain number of separate copies or reprints, in covers bearing the title of the paper and the name of the authoi, are printed off and placed on sale. The date of such separate publication will be printed on each paper. 3. Additions to a Paper after it has been finally handed in for publication, if accepted by the Council, will be treated and dated as separate communications, and may, or may not, be printed immediately after the original paper. 4. Brief Abstracts of Transactions Papers will be published in the Proceedings, provided they are sent along with the original paper. 5 Special Discussion of Papers accepted for Publication. — Where a paper has been accepted for publication, the Council may, with the consent of the author, select this paper for Special Discussion. In the case of such papers advanced proofs will be sent to the members of the Society desiring copies, and copies will be supplied to the author for dis- tribution. A paper selected for Special Discussion will be marked with an asterisk (^) and placed fii*st on the Billet for the day of reading. Any following papers for that day may be adjourned or held as read if the discussion prevents their being read. 6. Communications not submitted for Publication, such as Demonstrations of Experiments, Statement of Scientific Problems, etc., may be received by the Council, and may also be selected for Special Discussion. The Council does not undertake to publish any notice of such communications in the Proceedings or Transactions of the Society. [Continued on page iii of Cover PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. VOL. XXXV. 1914-15. I. — Opening Address by the President, November 2, 1914. Gentlemen, — Before calling for the communications indicated on the billet, 1 may be permitted to give a short summary of the Society’s work during the session which has closed. At the opening meeting, it will be remembered, a bust of Lord Kelvin was presented to the Society by Lady Kelvin. Professor Crum Brown made the presentation in the name of Lady Kelvin, and the President, Sir William Turner, received the bust in the name of the Society. During the session 42 communications were read — 2 of these being of the nature of addresses. The communications on the biological side of science might be classified as follows : — Anatomy, 3 ; anthropology, 3 ; bacteriology, 1 ; botany, 1 ; medicine, 1 ; palaeontology, 3 ; pharmacology, 2 ; zoology, 8 — in all, 22. Those on the physical or non -biological side might be classified as follows : — Chemistry, 1 ; engineering, 2 ; geology, 3 ; mathe- matics, 6 ; experimental physics, 8 — in all, 18. Two prizes were awarded by the Council : the Keith prize to Mr James Russell for researches in magnetism, and the Neill prize to Dr W. S. Bruce for the scientific results of the Scotia expedition. The membership of the Society has been increased during the year by the election of nineteen ordinary fellows ; but we have lost by death fifteen fellows, of whom seven were honorary and eight were ordinary. The names of the former are so well known that it will suffice to indicate very briefly the nature of the scientific work they accomplished : — Alfred Russel Wallace, O.M., LL.D., F.R.S., who died on 7th November 1913 at 90 years of age, was a great biologist of the older type. He was VOL. XXXV. 1 2 Proceedings of the Royal Society of Edinburgh. [Sess. an independent discoverer of the theory of natural selection, and was a conspicuous upholder of what he regarded as true Darwinism.” His books on the geographical distribution of animals have been a great stimulus to many a travelling naturalist. To the end he retained the keenest interest in all the problems of biology. He was elected an Honorary Fellow of our Society in 1910. Sir Robert S. Ball, LL.D., F.R.S., who died on 26th November 1913, was a distinguished mathematician and astronomer. His “ Treatise on the Theory of Screws ” is an extremely elegant mathematical treatment of the rotation of rigid bodies, and his elementary work on “ Experimental Mechanics ” gave a great impetus to the teaching of mechanics by means of apparatus and not simply in terms of mathematical formulae. He held in succession the Professorship of Astronomy in the University of Dublin and the Lowndean Professorship of Astronomy at Cambridge. He was much interested in stellar parallax, and while in charge of Dunsink Observatory gave much time to the observation of stars. For some years he was very active as a popular lecturer and writer of astronomical books. He was elected an Honorary Fellow of our Society in 1889. Sir David Gill, K.C.B., LL.D., F.R.S., was born in Aberdeen in June 1843, and was educated at Dollar Academy and at the University of Aberdeen. He was early attracted to the study of astronomy, and while still a young man carried out observations for finding the correct time at Aberdeen. As Superintendent of Lord Lindsay’s private observatory at Dunecht, David Gill organised an expedition to Mauritius to view the transit of Venus in 1874. The experience in this work suggested to him the utilising of observations of the minor planets and of Mars for the purpose of determining the solar parallax. In 1879 he was appointed Her Majesty’s astronomer at the Cape of Good Hope, and at once proceeded to observe several minor planets, from the observations of which he deduced the total distance of the sun to within one-tenth per cent. Sir David Gill took a leading part in advocating the advantages of photography for the cataloguing of stars, and also did valuable work in connection with geodetic surveys. He retired from the office of astronomer at the Cape in 1907. He was President of the British Association in 1907-8, and of the Royal Astronomical Association from 1909 to 1911. He was elected an Honorary Fellow of our Society in 1892. After serious illness for some months he died on 26th January 1914. 3 1914-15.] Opening Address by the President. Albert C. L, G. Gunther, M.D., Ph.D., F.R.S., for many years keeper of the zoological department of the British Museum, died on 1st February 1914, at the age of 84. He was a Prussian by birth, and graduated in Science and Medicine at Tubingen. A full biographical notice from the pen of Professor MTntosh will soon be published in our Proceedings, so that it is not necessary at this time to give a detailed account of his valuable labours in systematic zoology. He was elected an Honorary Fellow of our Society in 1895. Col. Alexander Ross Clarke, C.B., R.E., F.R.S., who died on 11th February 1914, at 85 years of age, was one of the foremost geodesists of our time. He was commissioned second lieutenant in the corps of Royal Engineers in 1847, and was appointed to the Ordnance Survey in 1850. For thirty-one years his energies were devoted to the work of the Survey. In 1858 he pub- lished the final results of the Triangulation of the United Kingdom, and gave his first investigation as to the figure of the earth. In I860 he published an account of the comparison of the standards of length of various countries, and added a further discussion as to the shape of the earth. His work on geodesy, which appeared in 1880, has been translated into several languages. He was elected an Honorary Fellow of our Society in 1892. For the foregoing notices I am obliged to our Secretary, Dr Knott. Eduard Suess, the son of a German wool-merchant, domiciled in Eng- land, was born in London on 20th August 1831. Two or three years later the family left for Prague, and subsequently removed to Vienna. At the early age of 20, young Suess was appointed an assistant in the Imperial Museum of that city, where he devoted himself to the study of palaeontology with such zeal and ability that he became, in 1857, at the age of 26, extra- ordinary professor in the University. He had now found his metier, and ten years later he entered on the full professorship of geology — a post which he held for thirty-four years, retiring as emeritus professor in 1901. His success as a teacher is vouched for by the large number of his pupils who have subsequently risen to distinction in every department of geological research. Suess became well known to his countrymen not only as a teacher of geology, but as an able and energetic politician. In 1862, while still a young professor, he was much interested in the question of a pure water supply for Vienna, and was induced to enter the Municipal Council, that his fellow-citizens might get the benefit of his advice on this im- portant question. He then boldly advocated the introduction of the pure water of the Alps by means of an aqueduct, some 110 kilometres in length 4 Proceedings of the Royal Society of Edinburgh. [Sess. — a scheme which was realised in 1873. Having made his mark in the Municipal Council and gained the confidence of the citizens, he was subsequently chosen by them as one of the parliamentary representatives, and for over thirty years remained a powerful leader of the liberal party in the Austrian Parliament. His political labours do not seem to have interfered with his geological work, which is represented by an astonishing number of memoirs and books. One of the latter, dealing with the origin of the Alps, published in 1875, is especially worthy of note for its grasp of detail and its suggestive generalisations. Ten years later appeared the first volume of his famous Antlitz der Erde — a work on which he laboured until nearly the close of his life, the fourth volume having been completed in 1910. This monumental book will undoubtedly take a foremost place amongst geological classics. It represents the labours of a long life, and is remarkable for its masterly resume of all that had hitherto been ascer- tained as to the geological structure of every land. His knowledge of the literature of the subject was indeed unique, and the lucidity with which he marshals his evidence is admirable. But what constitutes the chief glory of the Antlitz is the magnificent sweep of its generalisations. We may not always agree with his conclusions, but their suggestiveness is un- deniable— and one may safely say that in all time coming his work will be a source of inspiration to every earnest student of geology. It is pleasant to know that the value of Suess’s labours was abundantly recognised in his lifetime by all civilised countries. Learned societies everywhere vied with each other in showering honours upon him. He was elected an Honorary Fellow of the Royal Society of London, and in 1903 was awarded its highest distinction — the Copley Medal. He became an Honorary Fellow of our Society in 1905. He died on 26th April 1914. For the following notice I am indebted to Professor Sampson, Royal Observatory : — George William Hill was one of the most celebrated mathematicians of the past generation. His most original work relates to the theory of the moon’s motion. Long as this problem has been handled, it has always presented features that baffled analysis, significant as they are of the general problem of Three Bodies. If this problem is now gradually taking a more lucid shape, the credit is largely due to Hill, in whose works, as Poincare remarked, ‘‘ il esb permis d’apercevoir le gerrne de la plupart des progres que la Science a fait depuis,” — though we cannot adopt this judgment without recalling the achievement of Darwin in the same field. Besides great force and originality. Hill’s work is marked by extreme 5 1914-15.] Opening Address by the President. perseverance and perfection of form. The greatest single completed monument of astronomical labour is his application and development of Hansen’s method to the theory of Jupiter and Saturn, to which he devoted the whole of twenty years. The importance of Hill’s work has been freely recognised by learned bodies for many years back. He was elected an Honorary Fellow of our Society in 1908. He was also a Foreign Member of the Royal Society of London, which conferred the Copley Medal upon him in 1909, a correspondent of the Paris Academy of Sciences, and an Honorary Sc.D. of Cambridge. His personal tastes were modest and retiring. He spent thirty years of his life in the obscure position of assistant computer of the American Ephemeris and Nautical Almanac. Leaving this on the completion of his work on Jupiter and Saturn, he withdrew to a farm which he had inherited from his father, at West Nyack, twenty-live miles from New York. He was appointed to a professorship at Columbia University, but held it only for a short period. His scientific productiveness continued to the end of his life. He was born in New York on 3rd March 1838, studied at Rutger’s College, New Brunswick, in 1855, joined the staff of the American Ephemeris in 1861, and died in May 1914, at the age of 76. Capt. George J. Johnstone was born at Dunnet, Caithness, on 12th March 1852. He was for many years the Marine Superintendent in Calcutta of the British India Steam Navigation Company, and after his retirement in 1907 he settled in Edinburgh. He was highly qualified as a nautical expert, having a practical experience of all the engineering questions which have to do with ship construction. He became a Fellow of our Society in 1902, and was a member of the Institute of Naval Architects and of the Institute of Engineers and Ship- builders of Scotland. He also held His Majesty’s commission as Lieutenant in the Royal Navy Reserve. He died on 26th December 1913. James Macdonald, born in 1852, in the parish of Glenrinnes in Banffshire, was one of a family, several of whom distinguished themselves in agricultural journalism. He himself had a thorough knowledge of practical farming, and was a conscientious student of the sciences more intimately associated with agriculture. He w^as for several years the 6 Proceedings of the Royal Society of Edinburgh. [Sess. agricultural representative of the Scotsman in the North of Scotland, and afterwards became editor of agricultural journals in various parts of the United Kingdom. In 1893 he became Secretary of the Highland and Agricultural Society, and thereafter his aim was to make the Society as prosperous and efficient as possible. He travelled extensively in the United States and Canada and on the Continent of Europe, and in his book on Food from the Far W est he gave the results of his investigations in the North American Continent. The work with which his name will be chiefly associated is his edition of Stephens’ Book of the Farm, many chapters of which — especially those on cattle feeding, stock breeding and rearing — were completely re-written by him. Mr Macdonald was at the very centre of all the recent movements for the development of agricultural education. He became a Fellow of the Royal Society in 1894. On account of failing health he resigned his Secretaryship of the Highland and Agricultural Society in February 1912, and died on 11th November 1913. Prof. John Gibson, Ph.D., was born in Edinburgh in 1855, and educated at the Edinburgh Academy. He studied chemistry at Heidelberg under Bunsen, shortly afterwards returned to Edinburgh, and in 1879 was appointed assistant to Professor Crum Brown. In 1892 he became Professor of Chemistry at the Heriot-Watt College, and continued to conduct this growing department of chemical teaching and research till his death. He communicated a series of papers to our Proceedings, chiefly on electrical conductivity of saline solutions, and his analysis of manganese nodules,” carried out for the Challenger Expedition, is a valuable analytical research. He was a profound student of German literature, especially of the works of Goethe. He became a Fellow of our Society in 1877, and served two terms on the Council. After a year or two of failing health, he died on 2nd January 1914. Robert Traill Omond, LL.D., was born in Edinburgh in 1858, and educated at the Collegiate School and Edinburgh University. He was chiefly interested in physical science, and was closely associated with Professor Tait in various investigations, notably in the experiments on the compression of liquids, which arose out of the examinations of the 7 1914-15.] Opening Address by the President. errors of the Challenger deep-sea thermometers. Mr Omond was also a very keen student of geology. In 1883 he was appointed Superintendent of the newly erected observatory on the summit of Ben Nevis, and for the remainder of his life he was occupied in the work of the observatory. After eight years of devoted service both on the summit and at the low- level observatory, Mr Omond’s health became so impaired that he was compelled to give up the work of observation. He returned to Edinburgh, and as Honorary Superintendent of the Ben Nevis Observatory continued to control the work and to discuss the observations that had accumulated. First in collaboration with Dr Buchan and then by himself he prepared for the press all the observations made at Ben Nevis and Fort William; these were in due course published in four quarto volumes by our Society. Mr Omond contributed several papers to our Society, the more important being descriptions and discussions of glories, halos, and coronse as seen from the observatory. He was elected a Fellow in 1884; was awarded the Keith prize for the biennial period 1889--91, and served on the Council from 1901 to 1904. In 1903 he became Honorary Secretary of the Scottish Meteorological Society, and the Journal of that Society contains several important papers written by him. In July 1913 he received the honorary degree of LL.D. of the Uni- versity of Edinburgh. Although hampered in his latter years by a malady brought on during his Ben Nevis experiences, Mr Omond retained to the end his cheerful and genial disposition ; his humour was inimitable. During the last year or two several attacks of influenza seriously impaired his physical strength, but he continued in full mental activity until a few weeks before his death, which took place on 28th January 1914. The foregoing notices of Ordinary Fellows have been prepared by our Secretary. Sir John Murray, K.C.B., LL.D., F.R.S., was born in Ontario, Canada, in 1841, and came to Scotland in 1858. From his earliest years he had evinced a strong predilection for natural science, and ten years after his arrival here he took the opportunity of visiting Spitzbergen and the Arctic regions as a naturalist on board a whaler. The experience thus gained in marine investigations, together with certain research work he had conducted in Professor Tait’s physical laboratory, led to his appointment on the scientific staff of the Challenger Expedition. As might have been expected, the four years of that epoch-making expedition determined what 8 Proceedings of the Royal Society of Edinburgh. [Sess. his life’s work should be. So highly were his services as assistant naturalist valued, that on the retirement of Sir Wyville Thomson in 1881, he became Director and Editor of the Challenger publications, which, on their comple- tion in fifty volumes, he truthfully characterised as forming “ the greatest advance in the knowledge of our planet since the celebrated geographical discoveries of the fifteenth and sixteenth centuries.” It is with the splendid results obtained by this great national expedition that Sir John Murray’s name will always be associated. His labours in connection with the Challenger Expedition, however, did not absorb all his energies. To him and his friend Mr Frederick Pullar we are indebted for the initiation of a most important work — the Bathymetrical Survey of the Scottish Fresh- water Lakes — a work which was carried to a successful conclusion under the direction of Sir John Murray and Mr Laurence Pullar. An important side issue of this Survey was the observation of seiches in the Scottish lochs, the results of which were given in a series of papers by the late Professor Chrystal and Dr E. M. Wedderburn. Sir John’s continued interest in oceanographical research was shown by his establish- ment of marine laboratories on the Firth of Forth and at Millport on the Firth of Clyde, while only a year or two ago he financed the deep-sea expedition of the Michael Bars in the Atlantic, the direction of which he shared with Dr Johan Hjort — the results being published in 1912 in a volume entitled The Deaths of the Ocean. His enthusiasm for the cause of research was further evidenced b}^ his powerful support of an Antarctic Expedition, the subsequent inception of which by the British Government undoubtedly owed much to his strenuous advocacy. Nor was his sym- pathetic interest confined to such research ; he was always ready to throw himself into every movement that had for its object the advancement of knowledge in any department of science that seemed to him likely to advance the welfare of mankind. He was, for example, a devoted member of the Scottish Meteorological Society, and shared in the foundation of the Ben Nevis Observatory, which, until it closed, found in him a zealous supporter. He likewise rendered important services to the Royal Scottish Geographical Society, of which he was President for five years, and during his connection with which he was a frequent contributor to the Scottish Geographical Magazine. His tragic death on 16th March was a great shock to all his friends, and was everywhere recognised as a public loss. Although he had attained the threescore years and ten, he was still full of vitality — buoyant and hopeful as ever, and looking forward with eagerness to further research, which he would doubtless have accomplished had life been spared. In 9 1914-15.] Opening Address by the President. him a strongly marked personality has been removed, but not before he had established his reputation as the foremost oceanographer of his day. An excellent observer and a diligent student of the work of others, he was specially distinguished as a bold and brilliant generaliser. Many of his novel views and theories, it is true, have been keenly controverted, but their suggestiveness cannot be denied, and they have undoubtedly stimu- lated and inspired scientific research in many directions. Sir John Murray became a member of this Society in 1877. He served on the Council for three terms, was Secretary to the ordinary meetings for nine years, and Vice-President for two terms. The notices I shall now read are also prepared by Dr Knott : — John W. Inglis, M.Inst.C.E., was born in 1838, and at the age of 23 went to India as a Civil Engineer. As a volunteer in the artillery he served in the Indian Mutiny. He was engaged in various engineering works in the province of Oudh, and was student at Lucknow till 1865. He then proceeded to Fyzabad and did much important work in the building of bridges and the making of roads throughout the district. Latterly he was employed in various divisions of the Lower Ganges Canal. Since his retirement in 1880 he settled in Edinburgh and was fre- quently seen at our ordinary meetings. He died on I7th March 1914. David Patrick, M.A., LL.D., was born in Lochwinnoch, Ayrshire, in 1849, and was educated at the Ayr Academy and the University of Edinburgh. With the intention of entering the Church he studied at the New College, and gained the Cunningham Fellowship at the close of his four years’ course. He subsequently studied theology at Tubingen, Berlin, Leipzig, and Gottingen. He then determined on a literary career. He was introduced to encyclopaedical work as one of the staff who assisted Dr J. M. Ross of the Edinburgh High School in producing the Globe Encyclopcedia. After a few years he entered the publishing house of Messrs W. & R. Chambers as assistant to Dr Findlater in the Literary Department, and ultimately became head of the literary staff. He was editor of the revised edition of Chambers’s Encyclojorndia which appeared between 1888 and 1892 ; brought out a completely new issue of Chambers s Cyclopcedia of English Literature (1901-3), and also edited a small bio- graphical dictionary in 1897. His duties as editor and part author of these important works brought him into touch with the best literary life of our country. In spite of these absorbing literary activities he retained his keen interest in theo- 10 Proceedings of the Royal Society of Edinburgh. [Sess. logical and ecclesiastical studies, and in 1907 he translated for the Scottish History Society the Statutes of the Scottish Church from 1225 to 1559. Dr Patrick was a man of immense information, both in literature and in human affairs. He had remarkable conversational powers and was a keen observer of men and things. Not only had he met most of the great men of our day, but he was able, apparently without effort, to retain the clearest memory of their characteristics. After some months of impaired health, he died on 23rd March 1914. John S. Mackay, M.A., LL.D., for many years Mathematical Master at the Edinburgh Academy, was born in 1843 at Auchencairn, and received his early education at Perth Academy. He studied both at St Andrews and Edinburgh, and originally intended to enter the Church. He retired from liis post in the Edinburgh Academy in 1904 after thirty-eight years’ service. His interest lay mainly in the region of pure geometry, and most of his papers are published in the Proceedings of the Edinburgh Mathematical Society. He was a recognised authority on Greek mathematics. He edited the well-known Elements of Euclid, and communicated various articles to the Encyclopcedia Britannica and Chamhers s Encyclopcedia. He was also a member of the Permanent International Commission for Mathematical Bibliography. He became a Fellow of the Society in 1882, served twice on the Council, and was a useful memher in the Library Committee. He died on 26th March 1914. A fuller notice of his career has been prepared by George Philip, M.A., D.Sc., and has been published in the Proceedings. 1914-15.] The Baleen Whales of the South Atlantic, 11 II. — The Baleen Whales of the South Atlantic. By Sir William Turner, Emeritus Professor of Anatomy, K.C.B., F.R.S., D.C.L. (MS. received October 26, 1914. Read November 2, 1914.) Whaling companies have for some years successfully conducted a whale fishery off the shores of the South Shetlands, Graham Land, South Orkneys, and South Georgia, where the waters of the Antarctic mingle with the South Atlantic Ocean. A year ago Mr G. Millen Coughtrey, a former student of the University, an employe of the New Whaling Company of Leith, Messrs Salvesen & Co., kindly presented to me specimens from this southern latitude, which have been of value and interest in extending our knowledge of the Cetacea frequenting these seas. In a memoir communicated to the Society in December of that year * I described from these specimens the external Auditory Meatus and its plug of wax, also the Tympano-petrous bones in several species of Cetacea, which, when compared with the corresponding bones in the Anatomical Museum of the University, were identified as from the Blue Whale, Balamoptera sibbaldi, the Sye Whale, Balcenoptera borealis, the common Rorqual, Balcenoptera musculus, and the Humpbacked Whale, Megaptera boops (longimana). It was clear, therefore, that these well-known Northern species were also denizens of the South Atlantic.]- In September of this year Mr Coughtrey added to the collection by kindly presenting specimens obtained from whales captured off the South Shetlands and Graham Land during the fishing season 1 9 13-14, which have further extended our knowledge of the species of Cetacea that frequent the Southern Ocean. This collection, in addition to examples from B. sibbaldi, B. borealis, and Megaptera boops, contained a tympano-petrous bone of the South Atlantic Right Whale, also a tympanic bone and foetus * Proc. Roy. Soc. Edin., vol. xxxiv. p. 10, Dec, 1, 1913. t In a recently published memoir Mr Theodore E, Salvesen has described the Whale Fisheries of the Falkland Islands and Dependencies. He enumerates Megaptera, the three species of Balgenoptera referred to in the text, and the Southern Right Whale, Balcena australis, baleen whales captured by the whalers. He estimates that nearly 11,000 animals were killed during the season, November 1, 1912, to April 30, 1913. He gives the approximate value of the whalebone and oil from each species respectively, that of the fresh flesh as food, and of the whale guano as a manure. The gross value of these products was about £1,350,000. See Report on Scie7itific Results of Scottish National Antarctic Expedition, vol. xix.. May 12, 1914. 12 Proceedings of the Royal Society of Edinburgh. [Sess. of a Balsenoptera, which I have identified as similar in character to B. rostrata of the North Atlantic. BAL.ENOPTERA ROSTRATA. This species, known to fishermen as the Lesser Piked Rorqual, is the smallest and most frequent of the baleen whales stranded on the coast of Scotland.* It has not been, I believe up to now, recognised by zoologists as a species frequenting the South Atlantic. Mr Coughtrey, however, informed me that the whaling seamen engaged in the South Shetlands and Graham Land fishing are acquainted with a small baleen whale called by them Minim, which contrasted strongly in its dimensions with the Blue Whale, Sye Whale and Humpback. Its relatively small size, the thinness of its coat of blubber, and the short whalebone made it of so little commercial value that it was seldom captured. During the last whaling season one was shot, and a right adult tympanic bone, along with a well- grown fcetus, was preserved by Mr Coughtrey. From the study of these specimens I regard this cetacean as the species Balcenoptera rostrata. Tympanic Bone. The small size of this bone in rostrata at once distinguished it from the large tympanies of the other Balmnopteridse. I have carefully compared the South Atlantic specimen with the tympanies of this species from the North Atlantic in the Anatomical Museum. Length. Breadth. Height. B. rostrata — South Atlantic Elie, Firth of Forth 1? 55 -5 • • Burntisland, „ „ . . Alloa ,, ,, (young) . 3 '3 in., 85 mm. 87 „ 87 „ 85 „ 81 „ 2 in., 50 mm. 45 „ 46 ,, 44 „ 2’2 in., 56 mm. 55 „ 56 „ 56 „ 1 The South Atlantic specimen closely corresponded in dimensions to the tympanic bones of rostrata captured in the Firth of Forth, the somewhat greater breadth being due to the outer surface being a little more convex in the Southern specimen than in those from the North Atlantic. The configuration of the outer and inner surfaces of the tympanic, the appear- ance of the shallow inferior keel, the sharp ridge of the anterior border, the blunt posterior border, the sinuous character of the upper border * See my memoir on the Lesser Rorqual in Proc. Roy. Soc. Edin., vol. xix., 1892, in which several specimens are described. 13 1914-15.] The Baleen Whales of the South Atlantic. from which the lip-like process projected, the great tympanic cleft with its comparatively shallow Eustachian notch, proclaimed the South Atlantic Fig. 1. — Outer Surface of Left Tympanic, Balcenoptera rostrata, from Elie, Firth of Forth. Reduced in size. A, anterior, P, posterior border. specimen to be identical with that of the well - known Lesser Piked Balaenoptera which frequents the Scottish seas. It will be noted that in all the specimens measured in the Table the height of the tympanic, taken from the keel below to the superior border immediately in front of the lip-like process, was distinctly greater than 14 Proceedings of the Koyal Society of Edinburgh. [Sess. the greatest breadth, a character which I have elsewhere noted as to be recognised in B. rostrata* Foetus. Mr Coughtrey had fortunately secured the foetus of a Minka Whale which he had removed from the mother, shot during the late whaling season. The length of the latter was not measured, though it had possibly been about 16 feet.f The fcDetus was preserved in spirit and soldered up in a tin. It arrived in good order, and the cuticle was almost intact. From its length along the curve of the back, 64 cm. (2 ft. 1 in.), in relation to the size of the mother it was evidently well grown. The maximum girth was at the head, behind which the body diminished in girth to the constricted region in front of the tail. The principal dimensions are given in the Table : — From Dimensions of Fcetus. tip of beak along dorsal curve to mid notch of tail Inches. 25 Centimetres. 64 same to axilla ....... 7 18 ?5 „ to eyeball ....... 4 10 55 ,, to front of blowholes ..... 2*9 7*5 55 „ to angle of mouth 4-3 11 55 „ to anterior border of dorsal fin . 17*3 44 5^ „ to flange of tail ...... 22-8 58 „ to attachment of pectoral limb . 7 18 55 tip of mandible to umbilicus .... 11-8 30 51 umbilicus to genital orifice .... 3*5 9*2 55 „ to anus ...... 4-3 11 Girth around summit of head ..... 13-7 35 55 in front of pectoral limb ..... 12-8 32*5 55 at umbilicus ....... 11*4 29 55 in front of dorsal fin 8-2 21 55 at root of tail . . . . . . 2-7 7 The summit of the Head had a low boss-like prominence, in front of which the dorsum sloped downwards and forwards to the tip of the beak, also outwards to each lateral border, which formed a straight line from the base of the beak to its pointed tip. Immediately in front of the promin- ence, but on a lower plane, two narrow slit-like Blowholes, 1*5 cm. long, were situated ; they were separated by a shallow median furrow and converged at their anterior ends, but did not communicate with each other. On the dorsum of the Beak a distinct median ridge was present which subsided near the tip. On each side of the ridge the surface was flattened and directed outwards to the straight lateral border of the beak. In * Marine Mammals in the Anatomical Museum^ University of Edinburgh, p. 18, 1912. t Well-grown specimens of B. rostrata from 134 feet and upwards have been recorded. I described an adult female 28 feet 4 inches, the articulated skeleton of which is in the Anatomical Museum of the University. See Proc. Roy. Soc. Edin., vol. xix., 1892. 1914-15.] The Baleen Whales of the South Atlantic. 15 general form the outline of the beak was triangular ; the base was 8 5 cm. broad when measured in a straight line, but 11 cm. across^the median ridge on the dorsum ; the apex was vertically flattened. Over a dozen short, delicate Hairs formed a scanty beard at the tip of the lower jaw; a few scattered hairs were seen at the margins of the beak, also immediately below the lower lip and on each side of the anterior nares.^' The Dorsal Fin projected from the mid-line of the back vertically above the genital opening. It was only 2 cm. (f in.) high, and its base of attachment was 3'7 cm. Its shape was falciform, the colour grey on the surfaces, black on the convex anterior border. Fig. 3. — Profile of Head with Pectoral Fin of Foetus of Baloenoptera rostrata. Reduced. The Tail was horizontal. Its posterior border was divided by a mesial notch into two symmetrical lobes, each of which had a thickened anterior border and a sharp posterior border, and ended in a somewhat pointed tip : the breadth between the opposite tips was 15*5 cm. (6 in.). The Ventral aspect was for the most part either convex or flattened; but from the anus to the tail the sides were laterally compressed, and a mesial ridge was produced both ventrally and dorsally. The skin of the ventral surface of the mouth, throat, and as far back as the pectoral limbs presented numerous shallow furrows and ridges placed antero- posteriorly ; they were the rudimentary representatives of the remarkable tegumentary folds which form so striking a character in the Rorquals. * Arnold Japlia has figured (Spengel’s Zoolog. Jahrh., xxxii., 1911) hairs on the chin, lower jaw and upper jaw of foetus of B. rostrata. W. B. Benham had previously described about 30 hairs on the chin and jaws of a young B. rostrata {Trans. New Zealand Inst., 1901). 16 Proceedings of the Royal Society of Edinburgh. [Sess. The Navel string had been torn across at the umbilicus and a few coils of intestine protruded through the aperture in the wall. The Genital opening was an antero-posterior slit, 5 mm. long. The Anal orifice, about 2 cm. behind the genital opening, was nearly circular, and admitted only a small probe. The Orbit was situated immediately above the angle of the mouth. The eyelids were thin folds, and as the palpebral fissure, directed antero- posteriorly, was narrow, only a small part of the eyeball was visible. The orifice of the Auditory Meatus was not seen, but a shallow pit, 15 mm. behind the palpebral fissure, might indicate its position, though it would not admit a hair bristle. The Buccal opening was 12 cm. (4'7 in.) long and 8 cm. (3T in.) wide at the angles. Narrow rudimentary folds represented the upper and lower lips. The Palate formed an elongated triangle ; it was grooved mesially and the mucous membrane at the sides of the groove was thick and some- what succulent. The Baleen plates had not as yet formed, and except faint transverse markings on the surface of the mucous membrane immediately behind the anterior end of the palate, no indications of the transverse folds of membrane, in connection with which the baleen plates are developed, could be seen. The Tongue was well formed and had a distinct dorsal median furrow, which widened into a fossa near the tip. It was movable within the mouth, for 2‘5 cm. at the anterior end ; the circumference of this part was surrounded by mucous membrane, which formed a shallow fraenum continuous with the membranous covering of the floor of the mouth. The sides of the tongue were also free, and at the part where the mucous coverino- was reflected on to the floor a well-marked raised band was present. The mucous lining of the floor of the mouth and of the sides of the tongue was grey, that of the dorsum linguae was greyish black and with distinct papillae. The Bucco-pharyngeal opening scarcely admitted the tip of the little finger. The Pectoral limb was narrow and short in relation to the size of the foetus, its length was 9 cm. (3'5 in.), the greatest breadth 2*8 cm. (1 in.), the surfaces were flattened ; the posterior border was faintly convex, the anterior slightly concavo-convex, but in the outer third of the limb they approximated so that the tip assumed a lance-shaped form. Colour. — As the cuticle was in place on the head and on a large part of the body, the natural colour of the foetus had doubtless been preserved. The prominence on the summit of the head and the dorsum of the body were black. At one spot the cuticle was loose and could be raised from the 17 1914-15.] The Baleen Whales of the South Atlantic. cutis, when its deep surface showed the rich black rete Malpighi, which contrasted with the pink cutis. The dorsal fin and the dorsal mesial ridge were greyish black, but the dorsum of the tad was quite black. The dorsum of the beak was dark grey, which was modified to light grey at the border of the beak, the upper lip and around the orbit. On the sides of the body the cuticle was translucent and colourless, and the vascular cutis subjacent to it modified the tint of the skin to a greyish pink. The larger part of the ventral aspect had a similar colour, but the lower lips and the skin covering the mandible were greyish like the upper lips. The sides and ventral ridge of the compressed body in front of the tail were greyish and the cuticle was not pigmented. The ventral surface of the tail was greyish pink. The dorsum of the pectoral limb was grey interspersed with black streaks and spots. A greyish white band marked the anterior border and part of the dorsum, where it joined the side of the body. The ventral surface of the limb was grey. The characteristic furrows on the ventral surface, though shallow, proclaimed the foetus to be a Rorqual of the genus Balmnoptera. The form and relative size of the pectoral limb, the position of the dorsal fin vertically above the genital opening, the triangular beak with its straight lateral borders are characters present in Balcenoptera rostrata. The boss- like prominence on the summit of the head of the foetus, which Mr Coughtrey had also noticed in the parent animal, is a character which has been figured in the North Atlantic B. rostrata and strengthens the identi- fication of the species.* The tympanic bone from the adult was without question that of rostrata. The testimony of these specimens established, therefore, this species as frequenting the South Atlantic. The collection included several triangular plates of Whalebone, which varied in length from 11 to inches, and in greatest breadth from 5 to 2 1 inches. The colour pattern was uniform : the outer half was black, inclining to dark grey near the middle of the plate ; the inner half was white with a slight yellow tint. The bristly hairs from the inner edge were white and delicate in texture. If this whalebone had belonged to the Minka Whale, it differed in colour from the baleen of the Northern B. rostrata, which is uniformly white or yellowish white. On the other hand, it approximated to the baleen of the Sye Whale, B. borealis, which is * In the presence of a low boss-like prominence on the top of the head, in the position of the dorsal fin, and in the form of the pectoral limb the foetus closely corresponds with the figure of a B. rostrata 15 ft. 4 in. long, in F. W. True’s great memoir on the Whalebone Whales of the North Atlantic, Smithsonian Contributions, Washington, 1904. VOL. XXXV. 2 18 Proceedings of the Eoyal Society of Edinburgh. [Sess. black with white or grey stripes in its inner part, so that I am disposed to regard it as belonging to the Sye Whale. Bal^na australis. A tympano-petrous bone of the Southern Bight Whale, B. australis, was obtained by Mr Coughtrey from a specimen shot in the Schollert Channel, Belgic Strait, Graham Land, in March 1914. The animal was a female, with blades of whalebone 7 feet long. I have measured the tympanic bones and append a Table in which the dimensions are given, along with those of other specimens of B. australis \ also those of the Eight Whale of the North Atlantic, Balcena hiscayensis. These bones are in the Anatomical Museum of the University. Dimensions of Tympanic Bones. Length. Breadth. Height. Balcena australis — Belgic Strait, Graham Land, 1914 Te Awite, New Zealand Balcena hiscayensis — St Kilda, 1910 .... Tarbert, Harris, 1912 . ?> 55 ... 4’7 in., 120 mm. 126 „ 124 „ 127 „ 129 „ 128 „ 3d in., 81 mm. 75 „ 73 „ 90 „ 88 „ 93 „ 4 in., 104 mm. 105 „ 109 „ 113 „ 112 „ 113 „ In my memoir on the Eight Whale of the North Atlantic, Balcena biscayensis* I discussed the question of the relation between B. hiscayensis and B. australis, and came to the conclusion that there was no structural reason why the Eight Whale of the North and South Atlantic should not be regarded as the same species, for difference in habitat did not necessarily imply specific difference. From a comparison of the measurements of the tympanic bones in the Table it will be seen that whilst the specimens from the Eight Whale of the North Atlantic were a little larger than those from the Eight Whale of the South Atlantic, probably derived from older animals, the length, breadth, and height corresponded in their relative proportions ; the height in each case also much exceeded the breadth, owing to the strong keel on the inferior aspect of the bone. They corresponded also in their general configuration. In each bone the outer surface in its upper part had two definite convexities separated by a wide, deep, oblique groove, whilst the * Trans. Roy. Soc. Edin., vol. xlviii. p. 889, 1913, and Marine Mammals in Anatomical Museum of University, 1912. 19 1914-15.] The Baleen Whales of the South Atlantic. lower part formed a broad, shallow, concave surface which sloped down- wards to the strong keel. The upper border of the outer surface formed the sinuous outer edge of the tympanic cleft and a strong lip-like mallear process, I, projected from this border. The inner surface was roughened Fig. 4. — Right Tympano-petrous, Balcena australis. Natural size. A, anterior, P, posterior border of tympanic ; I, lip-like process for mallear attachment ; L, labyrinthine, PR, pre-otic, OP, opisthotic divisions of petrous at their junction with the peduncles ; M, head of malleus ; S, stapes ; Au, opening into tympanic cavity closed in living head at deep end of auditory meatus by membrana tympani, in proximity to the keel, but immediately below its upper border it was moderately convex and striated, where it formed the inner edge of the tympanic cleft, which was relatively thin as it turned into the tympanic cavity. This border was mostly horizontal, but anteriorly it formed a deep Eustachian notch. 20 Proceedings of the Eoyal Society of Edinburgh. [Sess. In the specimen from Belgic Strait the tympanic ossicles, malleus and stapes had been preserved, and the malleus was fused by a pair of processes parallel to each other with the lip-like process on the sinuous border of the tympanic cleft. The Petrous bone consisted of the Labyrinthine, Pre-otic and Opisthotic parts. The Labyrinthine was locked between the pre-otic and opisthotic divisions. Its upper surface was rough for articulation with the basis cranii; the under surface showed a smooth convexity directed to the tympanic bulla and cleft ; it formed the inner wall of the tympanic cavity, in which was a deep fossa ovalis, with the stapes attached to the fenestra ovalis. The inner end of the labyrinthine projected to the cranial cavity and contained large canals and foramina for the passage of the divisions of the auditory nerve and blood-vessels. The Pre-otic was a rough mass of bone 17*8 cm. (7 in.) in its longest diameter ; the outer end tapered to a point, the inner end was blunted. The Opisthotic was a flattened plate 18 cm. in length, and 12 cm. (4'7 in.) broad at its labyrinthine attachment, whilst it narrowed posteriorly to a pointed process. These divisions were fused by peduncles to the tympanic bone : the anterior peduncle connected the pre-otic to the sinuous border of the tympanic cleft in front of the lip-like process ; the posterior peduncle con- nected the opisthotic to the posterior end of this border, and was separated from the lip-like process by a gap, which corresponded with the deep end of the external auditory meatus and the membrana tympani in the living animal. The pre-otic and opisthotic had strong articulations with the basis cranii. Their general form and relations corresponded in the three specimens of B. australis, though the opisthotic in those from New Zealand was more massive, but not so wide as that from Graham Land. The opisthotic in Balsena, when removed in its entirety from the skull, was much shorter than in the larger species of Balmnoptera, in which I have seen it to attain a length of 43 cm. (17 in.) and to be of the almost uniform breadth of 13 cm. in the greater part of its length.* The specimens in the Anatomical Museum, as well as those recently presented by Mr Millen Coughtrey, warrant the statement that the follow- ing species of Baleen Whales are to be found in the South Atlantic : — The Balmnopteridse — Megaptera hoops (longimana), Balmnoptera sihhaldi, borealis, rostrata, also B. musculus. The Right Whale, Balcena australis, has been associated with the South Atlantic since its recognition by Desmoulins in 1822. * See my memoir on the Auditory Organ in the Cetacea, and compare B. australis with the petrous hone in Balsenoptera, Proc. Roy. Soc. Edin., vol. xxxiv. p. 10, 1913. 1914-15.] The Baleen Whales of the South Atlantic. 21 The comparison of the tympano-petrous bones from the Balsenopteridse in the South Atlantic with those from animals captured in the North Atlantic warrants the statement, that differences do not exist between them which can be regarded as specific, notwithstanding that their habitats are so widely separated. Similarly, the smaller Right Whale, Baloena australis, which frequents the temperate waters of the South Atlantic, so closely resembles the corresponding Right Whale, Balcena biscayensis, of the North Atlantic, that they are obviously the same species.* On the other hand, the larger Greenland Right Whale of the Arctic Ocean, Balcena mysticetus, so far as we at present know, has no representative in the Antarctic. * See my memoir on Balcena biscayensis in Trans. Roy. Soc. Edin., vol. xlviii., 1913. {Issued separately December 4, 1914.) 22 Proceedings of the Royal Society of Edinburgh. [Sess. III. — The Optical Rotation and Cryoscopic Behaviour of Sugars dissolved in (a) Formamide, (6) Water. By John Edwin Mackenzie and Sudhamoy Ghosh, M.Sc. (Research Student, University of Edinburgh). (MS. received September 22, 1914. Eead November 2, 1914.) THEORETICAL. The optical rotation of a solution of sucrose in water was first measured by Biot {Mem., 1819, ii, 41) in 1819. He introduced the term “optical saccharimetry ” for the method of estimation of sugar by measurement of its optical rotation. In 1846, Dubrunfaut {Ann. Chim. Phys., 1846, xviii, 99) observed that the specific rotation of a freshly prepared aqueous solution of glucose decreased from an initial value of about +110° to a constant value of +52°. The initial value being approximately double the constant value, he called the phenomenon “ bi-rotation.” This term proved unsuitable in the case of other substances where a similar change of rotation took place, the initial and final values being rarely in the proportion of 2:1; hence the expression “ multi-rotation ” came into use. A better term is that introduced by Lowry {Chem. Soc. J., 1899, Ixxv, 212), viz., “ mutarotation,” which is now in general use to indicate the change in rotation of a solution from its initial to its constant value at the same temperature. Mutarotation is a characteristic property of the sugars which display reducing properties, and of many optically active substances which occur in tautomeric or iso- dynamic forms. In the case of the sugars many theories of the mechanism of the change have been proposed. Some of these theories have had to be laid aside owing to the isolation of distinct modifications of the same sugar. Thus in the case of glucose two forms are now known, the one showing an initial rotation [a]|°=+110°, the other [a]D®=+19°, and both becoming constant with [a]|^=+52°. The former is the ordinary glucose, which was known to Saussure {Bulletin de Pharm., 1814, 6, 502) ; the latter was discovered by Tanret {Bull. Soc. Chim., 1896, [III], 15, 195). The existence of two modifications of the same sugar led Lowry to advance the view that the mutarotation of glucose is caused by a balanced action between the highest and lowest rotating forms — a-glucose^^8-glucose. 1914-15.] The Optical Rotation of Sugars. 23 The so-called y-oxidic constitution offers a reasonable explanation of the differences between the two forms of sugars — e.g., for glucose, HO . C . H H . C . OH /\ /\ / \ / \ H . C . OH \ H . , C . OH \ 1 0 and 1 0 HO . C . H / HO , . C . H / \ / \ / \/ \/ HC HC 1 1 H . C . OH 1 H . C . OH i CH2OH CHgOH Of the theories advanced to explain the mechanism of the change from the a- to the modification, only one or two need be mentioned. The first, that of Lowry {Chem. Soc. J., 1903, Ixxxiii, 1314), supposes the y-oxidic ring to break up with formation of aldehydrol or aldehyde hydrate thus — HO C . H +11,0 CH(OH), 1 -H^O H . C . OH 1 - (0H0H)2 0 ^ (CH0H)2 \ (CHOH)j 1 -HgO 1 -f-H20 CH^^ CHOH CH-- 1 1 CHOH 1 CHOH 1 CHOH 1 j CHgOH j CH2OH 1 CH2OH 0 the addition and splitting off of water taking place, so that both modifica- tions may be formed. The second, that of E. F. Armstrong {Chem. Soc. J., 1903, Ixxxiii, 1305), supposes the y-oxidic ring to remain unbroken, but that water becomes attached to the y-oxidic oxygen and thereafter is separated in different ways giving the a- and /3- forms respectively. The formation of an oxonium compound is possible, but problematical, in the case of the sugars {cf. Mackenzie, Sugars, pp. 128-131). Both these hypotheses assume the presence of water in the solution, and indeed the majority of the measurements of the mutarotation of sugars has been carried out in aqueous solution. Methyl and ethyl alcohols and acetone were not available as solvents owing to the very small solubility of most of the sugars in these liquids. Using mixtures of the alcohol or of acetone with water as solvent, the rate of mutarotation was diminished, an argument used in support of the theory that the mutarotation 24 Proceedings of the Eoyal Society of Edinburgh. [Sess. was dependent on the presence of hydroxyl groups (Trey, Zeitsch. phys. Chem., 1903, xlvi, 620). Perhaps the strongest argument in favour of this theory is the fact that the presence of traces of caustic alkali or ammonia causes extremely rapid mutarotation, the rotation becoming constant almost immediately (Lowry, loc. cit). On the other hand, the non-electrolytic nature of aqueous solutions of sugars would appear to militate against this hydroxyl theory. Further, the fact that mutarotation takes place in non-hydroxylic solvents such as pyridine is remarkable. Pyridine appears to have been used first by Behrend and Roth {Annalen, 1904, 331, 359) as a solvent for glucose. They found an initial rotation [a] + 138'88° which became constant after twenty- four hours with [a] d= -f 70'89^. Subsequently they showed the formation of an addition compound of glucose with pyridine, Cj2H220;^^, C^H^N, which decomposed on heating or on standing over sulphuric acid (Annalen, 1910, 377, 220). Similar measurements with a solution of galactose in pyridine were made by Heikel (Annalen, 1904, 338, 71). Subsequently Grossmann and Bloch (Zeitsch. Ver. dent. Znckerind., 1912, 62, 19) made comparison of the mutarotations of xylose, rhamnose, galactose, glucose, fructose, sucrose, lactose, maltose and raffinose in aqueous, pyridine, and formic acid solu- tions respectively. They found that mutarotation took place more slowly in pyridine than in water solution, but in the same direction. On the other hand, the direction of mutarotation in formic acid is the reverse of that in water solution, and mutarotation is shown by non-reducing sugars such as sucrose and raffinose, which do not exhibit the pheno- menon in water or pyridine solution. Grossmann and Bloch suppose that in formic acid solution the higher sugars are hydrolysed and con- verted into formates of the simpler sugars. It seems probable that this would take place in the case of all the sugars, and consequently the changes of rotation are due not to isodynamic change but to the formation of these formates. The experiments with pyridine as solvent suggest that the hydration theory of the mechanism of mutarotation is untenable. If similar results were obtainable with other non-aqueous solvents, some new theory must be forthcoming. The cryoscopic experiments of Walden on the molecular weight of starch, using formamide as solvent, were extended by the present authors to the sugars, most of which are sufficiently soluble in it to allow of measurements of molecular weight and of specific rotation. As it was of importance to know that each sugar dissolved in formamide in the mono- molecular state, the molecular weight was determined by the cryoscopic 25 1914-15.] The Optical Rotation of Sugars. method, and the data obtained proved this to be the case. Apparently no such determinations of molecular weights were made by the above men- tioned investigators of mutarotation in pyridine and formic acid solution ; and, though there is no reason to suspect that the molecular weights in pyridine solution are abnormal, there is much reason to expect that in formic acid solution complicated changes take place, and that the data obtainable from cryoscopic or ebullioscopic measurements would give evidence of such changes. The mutarotation experiments in formamide solution gave results com- parable to those obtained in aqueous solution, though the rate of muta- rotation was slower in the former than in the latter solution. The mutarotations in pyridine solution as obtained by Grossmann and Bloch are inserted for the sake of comparison. EXPERIMENTAL. Formamide. The formamide used was supplied by C. A. F. Kahlbaum and was purified by careful fractional distillation under diminished pressure. The dehydra- tion by means of anhydrous sodium sulphate previous to distillation under diminished pressure, as recommended by Walden (Zeitsch. phys. Chem., 1903, xlvi, 145), was not found to offer any advantage over direct distillation. Formamide distils at 99-100"’ under 11 mm. pressure, using a fine capillary air inlet. Walden mentions the melting-point as + 2*1° and the conductivity *25 = 4-7 X 10“^, and our experiments confirm these numbers, our data being, melting-point -f-2-l° and x^^ = S'2 x 10“^ The cryoscopic constant used — 38'5 — was that of Bruni and Trovanelli (Gazz. chim., 1904, 343, 350). Water. The distilled water of the laboratory was used. Cryoscopic Apparatus. The ordinary Beckmann freezing-point apparatus was used, the thermometer being graduated in 0’02° and read with the help of a lens, so that the limit of error in reading was approximately 0'01°. To prevent access of moist air, dry air was bubbled through the side tube, escaping through the small glass tube in which the stirrer moved. 26 Proceedings of the Eoyal Society of Edinburgh. [Sess. The Polarimeter. The polarimeter was a Landolt-Lippich triple-field instrument, graduated in 0*01°, supplied by Schmidt & Haensch. A sodium flame produced by a Meker burner heating fused sodium chloride contained in a circular platinum gutter was the source of light. In the first experiments unj acketed tubes were used and the atmospheric temperature of the dark chamber kept as constant as possible. For comparison the rotations at a series of different tempera- tures were made, using a tube enclosed in an asbestos-covered box filled with water, which could be heated or cooled as required. The tubes and other vessels with which the solutions came in contact had been washed repeatedly with distilled water before use to remove alkali from the surface of the glass. In later experiments a jacketed 2-dcm. tube provided with a thermo- meter immersed in the solution was used. The Sugars. The sugars used in the following experiments were obtained from C. A. F. Kahlbaum. Further purification of such forms as were obtain- able in sufficient quantities was effected by crystallisation from aqueous or aqueous-alcoholic solutions. The measurement of the specific rotation of these optically active forms is practically the only method of testing their purity. In such cases as that of lactose, where well-defined crystals of each modification are obtainable, the specific-gravity determination affords valuable confirmation. The melting-points of sugars are so in- definite as to be of little value, generally speaking. Some difficulty was at first experienced in dehydrating sugars owing to their decomposition on long-continued heating at 105° or even lower. Eventually a drying apparatus arranged in the following manner was found to give good results. The finely divided sugar was placed in a copper-foil boat about 5 in. long by J in. deep and J in. broad, and the boat inserted into a tube B, which is sealed on to a drying tube A, filled with phosphorus pentoxide and having an air inlet regulated by a screw clip. The other end of B is provided with a rubber stopper, through which passes the end of a second drying tube C, which leads to a mercury pump by means of which a pressure of from 1 to 2 mm. could be maintained for hours. As a rule the tube B was kept at ordinary room temperature for one or two hours, and then gradually heated by means of a steam jacket to near 100° until constant weight w^as attained. In this manner most of the adherent moisture and some hydrate water were expelled at room temperature and the remainder at the higher temperature without decomposition. 1914-15.] Tlie Optical Eotation of Sugars. 27 Prepaeation of Sugar Solutions. The sugar, after drying to constant weight, was again finely powdered — this being done in a large desiccating case provided with openings for the hands — weighed in a tube, and emptied into a dry 10-c.c. or 25-c.c. glass- stoppered fiask, and the solvent added and the whole vigorously shaken till solution was complete. In some cases the solution had to be filtered to remove particles of fibre, which caused opacity of the solution. The first measurements of the rotation were made as soon as solution was complete, the time being taken from the instant when the sugar came in contact with the solvent. ^-^-Arabinose. The arabinose was dried at 105® till of constant weight. It was perfectly colourless, and melted at 151° (uncor.). Cryoscopic measurements gave the following data : — Solvent. Concentration per 100 grams of solvent. Mol. weight found. Mol. weight calcu- lated, CjH^oOs- Water 1-23 148*4 150 2-28 149*0 55 Formamide 0-39 153*0 J? 0-77 144*7 ?? 0-66 158*5 1-22 155*7 V 28 Proceedings of the Koyal Society of Edinburgh. [Sess. The polarimetric results were as follows : — Solvent . . 1 1 Water. W ater. Formamide. Graph . . j X + Concentration grams in 100 c.c. solution. 1 2-606 4-512 2-3984 Time. Time. Hi?. Time. [-fl 64 min. + 172-68° 9 min. + 167-98° 10 min. + 185-75° 10 165-39 124 55 158-80 16 55 184*49 12 161-55 15“ 55 154-03 23 55 183-87 19 150-99 18 55 149*38 26 55 183-04 25 ?? 142-36 22 55 143-73 29 55 182-83 33 134-69 27 55 137-85 33 55 181-58 40 55 128-93 32 55 133*20 39 55 180-54 54 55 121-26 39 55 127*66 46 55 179-08 58 55 119-15 44 55 124*33 53 55 177-41 1 hr. 19 55 113-01 50 55 121-12 1 hr. 1 55 175-53 1 „ 30 55 110-91 57 55 118-13 1 55 10 55 173*45 1 „ 50 55 108-98 i: hr. 5 55 115-02 1 55 26 55 170-32 2 „ 56 55 106-48 1 5) 15 55 112-36 1 55 46 55 166-78 3 „ 13 55 105-91 1 28 55 110-04 2 55 4 55 163-03 4 „ 16 55 105-91 1 31 55 109-70 2 55 34 55 158-65 22 „ 30 55 + 105-91 1 5) 46 55 107-93 3 55 155-31 2 5) 5 55 106-82 3 55 56 55 148-93 K = 0-0134. 3 7 55 105-82 4 55 41 55 143-64 Calc, initial raln = 4 J5 30 55 105-82 5 55 16 55 140-30 CO 00 + 8. 5 •>•) 15 55 105-82 6 55 3 55 136-34 Extrapolated initial 24 55 + 105-82 23 55 44 55 117-16 1 Wd = + 186°. 25 5? 16 55 117-16 26 55 46 55 116-53 !30 55 16 55 116-53 i47 55 31 55 116-32 52 55 46 55 116-32 i74 55 31 55 + 116-32 K = 0-00154. Calc, initial [a]}J = + 189-5°. Extrapolated initial [g]lf=+189°. As will be seen from the graphs (figs. 1 and 2), the initial specific rotation obtained by extrapolation is about +186° for water, whereas the value obtained for it, using Levy’s formula (Zeitsch. ]pliysikal. Chem., 1895, xvii, 301), where and are times from moment of solution till polarimetric readings were made, and are the actual polarimetric readings at times \ and and

5 36*02 K = 0*0188. 4 55 59 55 34*90 Calc, initial ral?? = 5 55 19 55 33*42 + 90*31°. 5 55 35 55 32*67 Extrapolated + 90°. 1 — 1 s II 24 47 55 55 42 34 55 55 25*25 + 25*12 Constant K = ( 3*00306. Calc, . initial 1 HS’= + 109*39°. Extrapolated II + 109°. * initial^ +117*39°, maximum 122*07°, constant + 40*63°. Specific Rotation. 1914-15.] The Optical Eotation of Sugars. 31 a-C?-GLUCOSE. Glucose (Kahlbaum) was recrystallised three times from 90 per cent, alcohol solution. It was powdered and then dried at 105° till of constant weight. Extremely accurate cryoscopic measurements of glucose in water having been made by several investigators (Loomis, Zeitsch. physikal. Chem., 1901, xxxvii, 407), it was not considered necessary to repeat them. The data obtained in formamide solution were : — 32 Proceedings of the Royal Society of Edinburgh. [Sess. Concentration per 100 grams solvent. Mol. weight found. Mol. weight calcu- lated for CgHigOg. 0-35 183-0 180-0 0-43 185-8 0-959 177-6 9) 1-453 172-2 99 2-926 172-0 99 The polarimetric figures {cf. figs. 5 and 6) given for water solution corre- spond closely with those of Parcus and Tollens (Annalen, 1890, 257, 164). The figures for pyridine solution are those of Grossmann and Bloch (loc. cit.). Solvent Water. Pyrid iiie G. and B. Formamide. Graph X 0 4- Concentration grams in 100 c.c. solution. ) 9-097. 0-5625. 2-5144. Time r i2o L^Jd. Time. r i20 L^Jred. Time 7 min. 4-102-34° 10 min. 4-151-11° 17 : mill. 4-119-91° 10 9 9 101-07 20 99 145-78 29 99 118-32 14 99 98-31 30 99 142-23 37 99 116-93 23 99 93-00 60 99 133-33 40 99 116-33 30 99 88-75 120 99 127-11 41 99 114-94 39 99 84-29 180 99 122-66 1 hr. , 7 99 112-35 50 99 79-83 1 day 97-77 1 99 17 99 110-76 1 hr. 0 99 75-80 2 days 87-15 1 99 30 99 109-17 1 „ 11 99 72-61 3 99 80-00 1 99 44 99 106-98 1 „ 21 99 69-64 4 99 78-04 2 99 7 99 104-00 1 „ 31 99 67-10 5 99 75-56 2 99 37 99 100-62 1 „ 43 99 65-19 6 99 4- 75-56 3 99 50 99 94-06 1 „ 59 99 62-64 3 99 54 99 93-66 2 „ 12 99 60-73 4 99 13 99 91-67 3 „ 32 99 55-63 4 99 37 99 89-69 4 „ 3 99 54-78 5 99 87-88 4 „ 43 99 53-72 5 99 20 99 86-10 5 „ 25 99 53-08 5 99 48 99 83-90 24 „ 4- 52-23 23 99 46 99 60-85 24 99 20 99 60-64 K = 0-00627. 24 99 46 99 60-24 Calc, initial 1 — I II 25 99 15 99 59-65 + 108- 5°. 71 99 15 99 57-27 Extrapolated initial 73 99 15 99 + 57-27 Hd = -fl08°. K = 0-001091. Calc. initial II 122-7°. Initial [o' ]d from curve — 4-122-5°. Specific notation. 1914-15.] The Optical Kotation of Sugars. 33 Fig. 6. — a-c^-Glucose. Time in hours. VOL. XXXV. 3 34 Proceedings of the Eoyal Society of Edinburgh. [Sess. a-d-GALACTOSE. The powdered galactose was dried in vacuo at 100° till of constant weight. It melted at 155-157'" and dissolved in water, forming a colour- less solution. The cryoscopic determinations in water and in formamide solutions gave the following figures : — Solvent. Concentration per 100 grams solvent. Mol. weight found. Mol. weight calculated. Water 1-01 171-4 180 5? 2-07 179-5 Formamide 0-415 164-7 55 ?? 0-57 164-4 ?? ?? 0-738 159-6 ?5 0-77 159-6 5? 1-05 161-3 ?5 The polarimetric results are tabulated below (c/. figs. 7 and 8). A second series of readings in water solution proved to be practically concordant with that given. 1914-15.] The Optical Rotation of Sugars. 35 Solvent Water. Pyridine G. and B. Formamide. Graph X © + Concentration grams in 100 } 2-1752 2-0128 c.c. solution. Time. Time. — O 03 CM - Tilin'. 6 mill. + 136-30° 23 min. + 120-98° 18 min. + 152-77" 8 „ 134-24 30 „ 112-34 31 „ 150-53 11 „ 132-40 45 „ 106-17 53 „ 147-80 15 „ 130-10 60 „ 102-47 1 hr. 8 „ 145-81 IH „ 128-49 90 „ 100-00 1 „ 24 „ 144-07 21 „ 127-34 120 „ 97-50 1 „ 48 „ 142-09 25 „ 125-50 180 „ 93-88 2 „ 15 „ 139-35 28 „ 124-12 240 „ 91-31 2 „ 30 „ 137-86 33 „ 122-51 1 day 74-04 2 „ 41 ,, 136-62 38 „ 120-90 2 days 55-53 3 „ 48 „ 131-65 43 „ 119-07 3 „ 46-94 4 „ 22 „ 129-17 48 117-23 4 „ + 46-96 4 „ 53 „ 126-68 53 „ 11608 Constant 5 „ 40 „ 124-69 58 „ 114-70 23 „ 19 93-64 1 hr. 3 „ 112-86 24 „ 1 „ 93-15 1 n 8 „ 111-71 24 „ 39 „ 92-65 1 „ 16 „ 109-87 25 „ 17 „ 92-15 1 „ 26 „ 107-11 25 „ 53 „ 91-91 1 „ 37 „ 105-05 27 „ 52 „ 90-66 1 „ 48 „ 102-75 28 „ 45 „ 90-17 1 „ 58 „ 100-91 47 „ 8 „ 86-44 2 „ 13 „ 98-42 49 „ 5 „ 85-94 2 „ 28 „ 95-85 52 „ 85-94 2 „ 46 „ 94-24 53 „ 30 „ 85-45 3 „ 46 „ 88-95 4th day + 85-45 4 „ 24 „ 86-19 4 „ 53 „ 84-82 Fall in [aj^ for 1° C. 5 „ 23 „ 83-67 -0-34°. 5 „ 33 „ 82-75 Final = + 84-94°. 24 „ 23 „ 79-30 48 „ + 79-30 K = 0-000843. Fall in [a]^ Calc, initial Wl? = for 1° C. + 154-5°. -0-23°. From curve = = +155". Final = +77-57°. K = 0-00479. Calc, initial 1 =■ + 139-29°. Initial from curve = + 139°. 1 Specific Rotation. 36 Proceedings of the Royal Society of Edinburgh. [S Dess. Fig. 8. — a-c?-Galactose, 1914-15.] The Optical Rotation of Sugars. 37 (i-MANNOSE. The mannose was finely powdered and heated to 105° till of constant weight. It was perfectly colourless and melted at 129-132°. The cryoscopic measurements, using formamide as solvent, were as follows : — Concentration per ' 100 grains of solvent. Mol. weight found. Mol. weight calculated. 0-706 187-5 180-0 1-42 191-8 ?? 2-25 182-7 5? The following polarirnetric results (cf. figs. 9 and 10) were obtained Solvent Water. Formamide. Graph X + Concentration grams in 100 > 2-8128. 2-02 72. c.c. solution. Time. r i2o Hd. Time. r 120 Wd. 10 min. - 3-91° 7 min. - 25-16° 22 „ + 2-13 11 „ 22-70 28 „ + 7-64 18 „ 21-43 32 „ 10-84 24 „ 20-22 38 „ 11-02 35 „ 18-24 71 „ 13-83 45 „ 15-30 80 ., 14-22 2 hr. 6 „ 5-42 93 „ 14 22 2 „ 12 „ 2-46 19 hr. 30 „ + 14-40 2 „ 33 „ ! 1-72 19 „ 45 ,, Constant 2 „ 49 „ 1 - 0-49 20 „ 3 „ 1 + *0-98 3 „ 13 „ 1 + 1-97 K = 0-0273. 3 „ 32 „ 2-95 Calc, initial [»]!?= 4 „ 3 „ ! 5-67 -19-9°. 21 „ 52 „ + 11-84 Extrapolated - 20-0°. [»]!?= 23 „ Constant K = 0-000326. Calc, initial ■ [“]”= - 26-9°. Extrapolated - 26-0°. 38 Proceedings of the Royal Society of Edinburgh. [Sess. c?-Frixtose. Powdered fructose was dried at room temperature in vacuo till of constant weight. As in the case of glucose, it was not considered necessary to make cryoscopic measurements of fructose in water. The following figures were obtained in formamide solution : — Concentration per 100 grams solvent. Mol. weight found. Mol. weight calcu- lated for C(,Hj20g. 0-483 186 180 0-64 183-1 0-915 180-8 1-33 181-3 1-78 171-4 99 39 1914-15.] The Optical Eotation of Sugars. The polarimetric results (cf. figs. 11 and 12) are given in the following table, in which Grossmann and Bloch’s figures for mutarotation in pyridine solution are for red light. Their comparison between aqueous and pyridine solutions shows a much greater change in the latter than in the former solution. For water, [aJJd eight minutes after solution is —85°, and when constant —74°; whereas for pyridine, fifteen minutes after solution is —115°, and when constant —25°. Solvent Water.* Pyridine G. and B. Formamide. Graph X 0 + Concentration i grams in 100 > 9-9870. 0-9997. 2-2600. c.c. solution. Time. Time. r 1 20 Lajred. Time. r 120 6 min. - 104-02° 15 min. -115-03° 17 min. - 139-60° 55 102-29 20 5, 11003 21 „ 136-94 74 55 100-56 30 „ 105-03 24 „ 135-39 8 55 98-84 45 „ 101-03 29 „ 133-62 9 5, 97-96 60 „ 98-02 35 ,5 I 130-97 10 „ 97-44 90 „ 93-02 45 „ 127-65 15 „ 93-80 120 „ 89-02 57 „ 123-89 20 „ 92-76 150 „ 85-02 1 hr. 7 „ 121-45 25 „ 92-42 180 5, 80-02 1 5, 18 „ 119-24 35 „ 92-09 240 „ 22 hrs. 72-02 1 „ 29 5, 117-25 4| hrs. 92-09 25-0 1 5, 40 „ 115-93 48 „ - 92-09 48 „ - 25-0 1 5, 54 ,5 114-38 2 ,5 3 ,5 113-49 3 55 8 „ 110-61 3 ,5 42 5, 109-51 24 5, 1 - 109-51 K - 0-00839. Calc, initial [«]d = -151-76°. Extrapolated initial [«]»=- 151”. * Tollens and Parens (Annalen, 1890, 257, 166). 40 Proceedings of the Royal Society of Edinburgh. [Sess. Fig. 12.— c?-Fructose. 1914-15.] The Optical Kotation of Sugars. 41 a-LACTOSE. This sugar was recrystallised twice from aqueous solution. Some difficulty was experienced in obtaining it in the anhydrous state, but this was overcome by means of the drying apparatus mentioned above. The temperature was ultimately raised to 130° before constant weight was obtained. The cryoscopic measurement of ct-lactose in aqueous solution was not repeated, having been done previously with great accuracy (Loomis, Zeitsch. physikal. Ghem., 1901, xxxvii, 407). The slow rate of solution of lactose in formamide, owing to the formation of gummy masses, vitiated the results of some experiments. The following figures are typical of an experiment in which solution took place rapidly : — Concentration per 100 grams solvent. Mol. weight found. Mol. weight calcu- lated for Cj2ll22f^ll- 1*783 326*8 342 The specific rotations as observed in water and in formamide solutions are given below (c/. figs. 13 and 14). Grossmann and Bloch state that lactose is only soluble in pyridine to the extent of about one per cent., and that they were unable to obtain exact readings, but found [aj^ed initial — 4-20*52°, and constant =4-31*5°; a reversal of the direction of tlie mutarotations in water and in formamide. The small initial value is probably due to incomplete solution of the lactose. [Table. 42 Proceedings of the Royal Society of Edinburgh. [Sess. Solvent . . * Water. Formamide. Graph X + Concentration grams in 100 } 2*3164. 2*2756. c.c, solution. Time. Time. 1 7 min. + 83-75° 48 min. + 81*29° ^ j) 82*88 52 „ 81*07 14 „ 81-80 1 hr. 22 „ 79*97 20 „ 80*29 1 „ 52 „ 7y*53 27 „ 79*22 3 „ 15 „ 77*34 1 33 „ 78-14 3 „ 55 „ 76*46 1 36 „ 77*70 4 „ 28 „ 76*02 43 „ 75*98 5 „ 15 „ 74*92 52 „ 74*68 22 „ 24 „ 61*74 1 hr. 1 „ 73*39 23 „ 55 „ 60*86 1 „ 12 „ 71*87 25 „ 55 „ 59*98 1 ,, 26 „ 70*36 27 „ 47 „ 59 40 1 „ 36 „ 69*29 28 „ 30 „ 58*44 2 „ 3 „ 66*43 29 „ 20 „ 55*44 3 „ 5 „ 62*38 46 „ 20 „ 54*05 3 „ 47 „ 60*00 52 „ 25 „ 53*17 4 5) 42 ,, 58*71 3 days 51*85 4 „ 49 „ 58*28 5 „ 51*41 5 „ 20 „ 57*41 5 „ + 51*19 24 „ 29 „ + 55*25 Constant Constant K = 0 000387. K = 0*00378. Calc, initial Hd = Calc, initial Wlf- + 82*39°. + 84*4°. Extrapolated initial Extrapolated initial r«llf=+83\ [a]t^= + 85' 1 [ot]i) ill water solution decreases 0’08 for each 1° C. rise in temperature from 10° to 25°; hence [aj^o constant = +54*77°. Specific Rotation. 1914-15.] The Optical Rotation of Sugars. 43 /3-Lactose. This sugar was prepared by the method of Hudson (^7. Amer. Chem. Soc., 1908, XXX, 960). The crushed crystals were found to have density L600 at IS"", whereas ordinary lactose, the a-form, has density 1‘534. 44 Proceedings of the Royal Society of Edinburgh. [Sess. The following molecular weights were found in aqueous solution : — Concentration per 100 grams solvent. Mol. weight found. Mol. weight calcu- lated for C]^2H22^11- 1-35 342-4 342 2-28 342-1 2-56 337-5 2-58 348-5 55 3-61 341-1 55 4*74 341-1 55 In formamide solution the numbers were — 1-235 324 342 2-46 327 55 The specific rotations {cf. figs. 13 and 14) are given in the following table — Solvent Water. Formamide. | Graph 0 Concentration grams in 100 [ 2-752. 1-8544. c.c. solution. ) 1 Time. Time. [4U. 1 4 min. + 36-33° 45 min. + 29-65° 9 55 37-06 53 55 29-65 1 55 37-24 1 hr. 15 „ 30-19 i 14 „ 37-42 1 „ 32 ,5 30-46 ! 23 „ 38-51 1 „ 49 55 30-73 ' 26 „ 38-88 2 „ 5 55 31-27 ' 34 „ 39-42 3 „ 7 55 32-62 i 37 „ 39-78 3 5, 58 ,5 32-89 : 45 „ 41-06 4 5, 33 5, 33-43 55 „ 41-78 5 5> 5 5, 34-24 1 hr. 5 „ 42-58 5 55 33 55 34-78 1 55 16 „ 43-75 23 5 5 5 55 44-48 1 55 ^9 5, 45-60 25 55 7 55 44-75 2 „ 3 „ 46-87 27 5, 37 5, 45-83 3 „ 2 „ 49-60 28 55 42 5, 46-37 3 „ 5 „ 49-78 29 55 20 55 46-37 3 „ 31 „ 50-87 47 5, 15 5, 49-34 4 „ 51-59 50 55 10 5, 49-88 : 4 „ 37 „ 52-32 52 55 13 5, 50-15 1 5 ,j 5 j, 52-87 3 days 50-69 1 9 55 3/ 55 53-05 5 „ 4- 51-22 22 55 55 ,5 -f 55-23 Constant Constant K = 0-0004. K = 0-00297. Calc, initial ra]D = Calc, initial F all! = 4-29-11°. -1-35-97°. Extrapolated initial Extrapolated initial [<.K=+29-5°. [“]d = +36°. 45 1914-15.] The Optical Eotation of Sugars. {Cf. figs. 14 and 15). [ajc in water decreases 0-08° for each 1° rise in temperature from 10° to 25°; hence [0]^*^ = 54*99°. The corresponding values in formamide solution are 0*07° ; 4-50*98°. It will be observed that the equilibrium solution in both the water and the formamide solution is the same starting from either the a- or the /3- modification of lactose. The results obtained prove conclusively that mutarotation takes place in non-aqueous solutions of sugars with a velocity comparable with, though not so great as, that in aqueous solutions. This is seen most readily on inspection of the curves, though it must be noted that the curves in the case of pyridine solutions as given by Grossmann and Bloch are for red light and not for the sodium flame. The velocity of mutarotation for the two kinds of light does not apparently differ to any great extent, so that for comparison the curves for red light have only to be moved parallel to themselves (G. and B., loc. cit). It is the pleasant duty of the first-named author to acknowledge grate- fully a grant from the Moray Bequest Fund for the purchase of the polari- meter used in the above experiments. Chemistry Department, Univeksity of Edinburgh. (Issued separately February 2, 1915.) 46 Proceedings of the Royal Society of Edinburgh. [Sess. IV. — Studies on Periodicity in Plant Growth. Part II : Correla- tion in Root and Shoot Growth. By Rosalind Crosse, B.Sc., Carnegie Research Fellow, 1912-14. (With Two Plates.) (MS. received July 2, 1914. Read February 1, 1915.) Part I of this work on Growth Periodicity {Proc. Roy. Soc. Edin., vol. xxxiii. Part I (No. 8), p. 85) dealt with the occurrence of a four-day periodicity in plant organs and with rhythm in roots. With reference to the latter, the following conclusions were deduced from various observations made up to that time : — 1. “ Roots exhibit a periodicity under ordinary conditions of environ- ment which differs from that of shoots. 2. “ Owing to correlation, the root periodicity is affected by changes in the root rhythm, but to what extent has yet to be determined.” Since then, numerous experiments have been performed to find out whether any correlation exists between the growth of the root and the shoot, and if so, the nature of such a correlation. As far as I know, very little has been done in this connection. Kny {Annals of Botany, 1894, vol. vii, pp. 265 et seq.; 1901, xv, p. 613) concludes, by a method of amputation, that no correlation exists between root and shoot growth ; while Hering (Jahr. f. wiss. Bot, 1896, xxix, p. 132) has criticised Kny’s results on technical grounds. The immediate purposes of this work were to find the correlation between the root and shoot growth, and to verify the presence of a root periodicity. There is every reason to believe that the root periodicity already referred to is very like that of the stem — contrary to the conclusion o^iven above. Methods. A detailed account of the automatic precision apparatus used, and the methods employed during this investigation, has already been given in Part I (loc. cit, p. 90). Vida f aha seedlings have been used throughout, because of their plentiful reserve supply and strong roots and shoots. It is thus possible to compare the results of different experiments with one another. The records of the growth of the roots and shoots were taken simul- 47 1914-15.] Studies on Periodicity in Plant Growth. taneously on the same drum, and the experiments carried out within a temperature of 19°-23° C., while the limits of the humidity were 40-65 per cent. The external light conditions were varied for the different experiments as follows : — 1. Normal Conditions : i.e. the root and shoot under natural conditions — the root in the dark and the shoot in intermittent light and darkness. 2. Intermittent Conditions : i.e. the root under abnormal conditions — both root and shoot in intermittent light and darkness. 3. All-Dark Conditions : i.e. the shoot under abnormal conditions — both root and shoot in continuous darkness. 4. All-Light Conditions : i.e. the root and shoot under abnormal con- ditions— both in the light during the day and in electric light during the night. {Note. — Two electric lights, one of 50 and the other of 25 candle-power, were used at night, giving a diffuse light.) The hours of light and darkness were calculated from the natural periods of day and night at the season of the year, and not from an artificial 12-hours day and 12 -hours night used by Sachs and Barenetzsky in their experiments on periodicity. One set of experiments was carried on during the winter months of February, March, and November, when the relative amounts of light and darkness occurring is 10:14, 12:12, and 9:15 hours respectively ; a second series during the summer, in May, June, and July, when the proportion of light to darkness is about 18:6 hours. Many duplicates were performed to get reliable results. Results. The auxanometer curves were divided into two-hourly intervals, the growth measured in millimetres, and the figures obtained plotted in graph form. From these figures were calculated the actual amounts of growth per day for the shoot and root under the four different conditions, and the amounts of growth in each during the day and night periods respectively. From the latter can be calculated the mean hourly growth during the day and night in root and shoot, and also the linear growth coefficients — i.e. the increment of growth of a unit of length in unit time — for each under all the conditions. The linear growth coefficient of an organ depends upon 48 Proceedings of the Koyal Society of Edinburgh. [Sess. the length of the growing region, and can be calculated from the following formula : — L Q. Q _ Amount of growth in x time Length of growing region in millimetres x time in minutes" As there appeared to be some doubt that the length of the growing region in roots and shoots was a constant factor, the growing regions for both organs were measured daily under all four conditions of light and darkness, both in winter and summer, to find whether they varied under the different conditions. It was found that they did vary, so that no constant factor could be used for root and shoot. The divisions had to be made for the above formula with factors varying with each condition and with the season of the year. Correlation in the Growth Rate. The following table, giving the mean results of several experiments, shows the amounts of growth per hour in millimetres of roots and shoots for day and night during the winter and summer seasons, under the four conditions of light and darkness, with the varying lengths of the growing regions in each (G.R.) — as well as the linear growth coefficients calculated from these by the formula : — Table I. Amount of Growth per Hour. Linear Growth Coefficients. Root. Shoot. Root. Shoot. Day. Night. G.R. Day. Night. G.R. Day. Night. Day. Night. Winter — Normal •36 •39 8-5 •48 1 •66 40 •0007 •00076 •0002 •00026 Intermittent •27 •51 8-5 •39 •59 ! 45 •0005 •0010 •00014 •00021 Dark . •42 •7 9-0 I-I 1-47 40 •00076 •0013 •00045 •00056 Light . •28 •43 8-0 •56 •83 40 •00058 •00087 •0002 •0003 Summer — Normal •46 •57 8-5 •8 •97 50 •00085 •0011 •00026 •0003 Intermittent •36 •45 8-5 •9 I-Ol ! 55 •0007 •0008 •00025 •00028 Dark . •42 •49 9-0 1-47 1-37 40 •0007 •00085 •00059 •00055 Light . •59 •49 8-0 •74 •89 ’ 50 •0012 •0010 •00023 •00029 These linear growth coefficients can be compared, showing in Table II the relation between the root and shoot growth in the day and night 49 1914-15.] Studies on Periodicity in Plant Growtli. periods, under all four conditions, and in Table III the relative amounts of growth during the day and night periods in root and shoot respectively, under all the conditions. Table II. Winter. Summer. Day. Night. Day. Night. Root : Shoot. Root ; Shoot. Root : Shoot. Root ; Shoot. Normal ' 3-5 : 1 3 : 1 3-2 : 1 3-6 : 1 {a) Intermittent 3-7 : 1 5 : 1 2-8 ; 1 2-8 : 1 {b) Dark . 1-6 : 1 2-3 ; 1 IT ; 1 1-5 : 1 (c) Light . 2-5 : 1 2-6 : 1 5-2 : 1 3-3 : 1 General Results from Table II. 1. Under ordinary conditions the root always grows more quickly than the shoot by day or night. 2. Change of external conditions, such as — {a) Exposing the whole plant, root and shoot, to alternate light and darkness ; (h) Keeping the whole organism in continuous darkness, i.e. the case of etiolated plants ; (c) Keeping the whole plant in continuous illumination, but not of uniform intensity, substituting electric light during the night, affects this rate ratio, but never reverses it. 3. Illumination accelerates the root rate the converse of the shoot rate. 4. The rate ratios are affected by the natural seasonal changes — summer and winter. The relative rate is influenced by the seasonal change under {a), being increased in winter but lowered in summer. The relative growth rates tend more nearly to equality in etiolated plants (6), the root, however, still keeping the lead. This is due, of course, to the increased growth of the shoot when the relative discrepancy is made up. Under the converse conditions of constant illumination (c) the relative rates of root and shoot are diminished compared with the normal, except during the long summer day, when the ratio is very much increased, just as during the long winter night under (a), when it is also very much VOL. XXXV. " 4 50 Proceedings of the Royal Society of Edinburgh. [Sess. increased, but for exactly opposite reasons. In the former the growth of the shoot is restricted by prolonged illumination, in the latter the growth of the root is stimulated by illumination, and the after-effect of the preceding illumination is seen in the increased ratio during the night. In (c), during the winter, the ratio is reduced because the shoot growth is not so much retarded by the short period of daylight, and the longer night period of weaker electric light is not sufficient to retard its swing, while it is not strong enough to stimulate the root appreciably. It there- fore compares with the normal conditions in the summer. Table III. Winter. Summer. Root. Shoot. Root. Shoot. Day : Night. Day : Night. Day : Night. Day : Night. Normal DO ; DOS 1-0 : D3 1-0 : D29 DO : 1T5 {a) Intermittent 1-0 : D92 DO : D5 1-0 : 1T4 DO : 1T2 (6) Dark . 1-0 : D71 10 : D24 DO : D21 DO : -93 (c) Light . DO : D5 DO : 1-43 DO : -82 1*0 : D26 General Results from Table III. In root and shoot respectively, the night rate is greater than the day rate under ordinary conditions, both in winter, when there is a long night, and in summer, when the night is short. This holds even when the conditions are changed as already formulated. Two exceptions only are noted when the ratios tend to equality : (1) in the etiolated stem during the summer, where the shoot is under uniform external conditions of darkness ; and (2) in the root under the converse conditions — constant illumination in the summer, when the electric light during the night gives a weaker growth for the root than the stronger light in the daytime. Correlation in Growth Rhythm. Two main views can be held with regard to growth periodicity in plants — either that it is autonomic, that is, due to internal changes inherent in the plant (but moulded by external conditions), or that it is an induced phenomenon. The former was upheld by Sachs, who regarded the appearance of periodicity in shoots of Brassica rapa produced from the tuber in darkness 51 1914-15.] Studies on Periodicity in Plant Growth. as an evidence of its autonomic nature ; while Barenetzsky took the latter view because he found the periodicity disappeared in two shoots, after three and fourteen days respectively, in continuous darkness. He ex- plained the appearance of the periodicity in Brassica shoots as a pheno- menon of correlation, the tendency to periodicity being transferred from the tuber to the stem as an after-effect. The results of this research support Sachs’ view that there is an autonomic growth rhythm in all higher plants. This may occur in some lower plant forms as a primitive rhythm. Roots, being under more uniform conditions than stems, might be expected to show a rhythm most nearly approximated to this primitive type, due to internal causes, but modified by correlation with the shoot. If both root and shoot of a plant grown from seed in continuous uniform conditions show periodicity after a considerable time, we are justified in considering this periodicity autonomic, even though the first few days’ rhythm may be an after-effect transferred from the seed to the new plant. Also the shoot rhythm of a plant grown from the seed in the dark would tend to revert to the rhythm of the root after the after-effect of the light and darkness period has passed off. It is therefore possible that when grown in continuous darkness some kind of adjustment will take place between the root and shoot rhythms — we should expect the shoot rhythm first to alter considerably, being under abnormal conditions, while the root periodicity will also alter in correlation with that of the stem, and both will tend to produce a fundamental rhythm which will be present after a considerable time in the dark, being due to internal causes. In the same way, if a plant is grown in continuous light we should expect a change to take place in the rhythm. The root is now under abnormal conditions — in continuous light — and may be expected to respond first to the altered conditions, while the shoot will also alter to adjust its rhythm to the new external light conditions and the correlation with the altered root periodicity. That these changes take place is clearly seen from a study of the graphs of the growth measurements taken two-hourly under the various conditions of light and darkness already mentioned (Plates I and II, figs. I, 2, 3, and 4). The time of the maximum changes under the various conditions of light and darkness, and its variation, provide an easy method of noting the change from the normal in the periodicity of both roots and shoots when grown in continuous light or continuous darkness or other conditions. 52 Proceedings of the Eoyal Society of Edinburgh. [Sess. In the winter, in February and March, when the light and darkness are approximately equal periods, under the normal conditions, the maximum of the shoot occurs in the early morning, 5 a.m.-7 a.m., while that of the root is much the same — the range being greater, extending back to mid- night and on towards mid-day. Under the intermittent light conditions the shoot is very much the same as under normal conditions, though there is an occasional earlier maximum in the evening, and in the root a change to an earlier maximum between 8 p.m. and midnight. It may be this change in the root — due to being in the light during the daytime — which affects the shoot rhythm. When grown in continuous darkness, the early morning maximum gradually gives place to a much earlier one, about fourteen hours or more earlier, occurring during the early afternoon, and often followed by a secondary maximum during the early morning, 5 a.m.-7 a.m., as though an attempt were being made to revert to former maximum. This earlier maximum in the darkness is evidently due to the previous long period of exposure to the dark stimulating the shoot. The same thing is seen in the root, though there is evidence to show that the change takes place first of all in the shoot, and is followed by a change in the root to an earlier evening maximum followed by a secondary maximum as in the shoot. A daily periodicity is still evident in the Bean root after seventeen days’ and in the shoot after nineteen days’ continuous darkness. Under the continuous ligiit conditions, a change also takes place, the usual normal early morning maximum giving place to an earlier one, though not so early as in the dark — in this case about eight hours earlier. It occurs first in the root, being the organ most affected by the strange conditions, and is followed by the shoot. Periodicity was still evident in the Bean root after eleven days’ and in the shoot after nineteen days’ continuous illumination. In this case the light at night was diffuse and probably favourable to growth. Seasonal changes affect the maximum growth. In the summer : — (a) The normal maximum is earlier than in winter — because at this time the amount of light to darkness is 18 : 6 hours, only about one- third the amount of darkness present in February and March, so that there is a quicker rise to a maximum after the very short period of stimulation. (b) The maxima are more variable than in the winter. The root maximum also varies more, but is usually from midnight to 5 a.m. P7 [Vol. XXXV, h IT 1 r r- — !, • r- . i ... — y . — — •‘v! _ 1 i^. — w ■M p.‘.jv.vj 1 ; ■■'1 ; ill •:i: 0 ' — tHt* •... f.. I rv lx _j I' ■ ( . f .. — , .r i fet-w: _>., .-. M — JiW , , -i -. B sUi? mm •• ■ r • v.i'-w - T m 3 7 // / ■T" 9 d / 3 E>" 7 7 hr 1- f}T 7 — 1 i fc 7- 7^ j 9 I r*.*!*’ 1 r~t‘ _ . •• ^ r* ••*j» , — "7 'v — Iv ■|V:v; §**V 1 - ...■ • •: — y^{ W: -4- -- ->-r 1 • : T7 T 1 L 5- 7 ? f 3 7 9 fi ( 3 7 7 u 3 5* r «; V /Jr 5, 7^ r~ r?. f U R( [Vol. XXXV. Ptoc. Roy. Soc. b'dhi.] ^Vol. XXXV. Rosalinii Cue 53 1914-15.] Studies on Periodicity in Plant Growth. (c) The same peculiarities are seen in the organs in continuous darkness or lisrht as in the winter months. o General Results. 1. The root and shoot rhythms are correlated, and vary together with changing conditions. 2. No evidence is obtained of any sign of the disappearance of the periodicity under uniform conditions whether of light or darkness — an argument in favour of the autonomic nature of the phenomenon. {Issued separately February 24, 1915.) 54 Proceedings of the Koyal Society of Edinburgh. [Sess. V. — Properties of the Determinant of an Orthogonal Substitution. By Thomas Muir, LL.D. (MS. received October 21, 1914. Read November 16, 1914.) (1) If we seek to extend the definition of an orthogonant by making the square of each row equal to o- instead of 1, this fixed quantity will naturally be found to appear in the statement of almost all the properties of the determinant in question. It is therefore convenient and appropriate to call it the base of the orthogonant, and to speak of an orthogonant to the base a- or an orthogonant of base cr. It is a simple matter to ascertain what modifications are necessary in the statement of the known properties of the ordinary orthogonant to make them applicable to the extended definition. (2) The following additional theorems, which concern the effect of the substitution of a row for a column, need only be enunciated : they are deductions from more general propositions which have been established elsewhere ; — If the h^^ column of an orthogonant to the base a be deleted, and the p''* row be inserted in its place, the resulting determinant is equal to (rowp . colj,). (I) The determinant got by deleting the h^'* column of an orthogonant and inserting the p^^ row is equal to that got by deleting the p''" row and inserting the h^'* column. (II) If any column of an orthogonant to the base a- be multiplied by each row, the sum of the squares of the resulting products is cr^. (HI) The sum of the squares of the n determinants formed from any orthogonant of base a- by interchanging its h^^' column with all its rows in succession is equal to (t”. (I^) (3) If we proceed to the substitution of two rows for two columns, the following are the corresponding results : — If the h^^ and k^^ columns of an orthogonant to the base cr be deleted, and the p^^' and q^^ rows be inserted in their places, the resulting deter- minant is equal to roWp cob rowg cob (!') 1914-15.] The Determinant of an Orthogonal Substitution. 55 The determinant got by deleting the h^^' and columns of an ortho- gonant and inserting the and rows is equal to that got by deleting the and rows and inserting the and columns. (II') If any pair of columns of an orthogonant to the base cr be multiplied by each pair of rows, the sum of the squares of the resulting products is (III') The sum of the squares of the Jn(n— 1) determinants formed from an orthogonant of base a by interchanging a fixed pair of columns with every possible pair of rows is (IT') In proving these it is readily seen that there exists a corresponding set of theorems for the case where the number of substituted rows is three or more, the proofs being only a little more troublesome to exhibit. (4) Connected with any 7?.-line determinant there are n entities which have not received as yet sufficient attention from students, namely, the sums of the coaxial minors of like order ; and as in the study of ortho- gonants these sums become more than ordinarily prominent, it is con- venient to have a short notation for them. Let us therefore denote the sum of the r-line coaxial minors of a determinant by Saxm,. ; so that, for example, in the case of the determinant | afpgd^ | we shall have Saxnij = + ^3 + ^^4 > Saxiri2 = I \ + | ] -1- . . . . + | \ , Saxnig = I | + . . . . + \h^cgl^ \ , Saxm^ = I \ . (5) If each element of any determinant be multiplied by its conjugate element, — or, what comes to the same thing, if each row of any determinant be multiplied by the corresponding column, — the sum of the resulting products is Saxm^^ — 2Saxm2 . (V) Taking the determinant | af^cgd^ \ , the sum of the products in question is evidently af + -1- 2agCj + -f- hf + “t" 4- ef + 2c^c?3 + df, and the simultaneous addition and subtraction of ^af)^ + 2ajCg -f 2a^cC 4- 262^3 + ^ + 2cgri4 56 Proceedings of the Poyal Society of Edinburgh. [Sess. gives “1“ ^3 1 + I ^1^3 1 + . . . . + 1 1^ , as desired. (6) In an n-line orthogonant of base a- the sum of the coaxial minors of the order hears to the sum of those of the (n — order the ratio 1 ; Or, in symbols, Saxm^_,. = or=”~’'SaxTn^ . (VI) This follows from the relation which exists between complementary minors of an orthogonant. When n is 6 the examples are Saxnig = cr® Saxnig = o-^ . Saxnij Saxm^ = or . Saxm2 . (7) If the rows and columns of an orthogonant of base a- be denoted by ^ 1 ’ ^2 ’ • • • • 5 n 5 Cl , C2 , . , C,„ , and the rows and columns of its adjugate be denoted by then j ’ • • • • 5 , 2(K.iCi = O'” ^(Saxnii^ - 2Saxni2) . For, since any element of the adjugate is equal to a,,, it follows that and therefore ■h-rsh-sr ^ • ^rs^sr 5 2EA = whence with the help of (V) the desired result is obtained. (VII) (8) The sum of the n determinants formable from an n-line ortho- gonant of base cr by deleting a column and inserting the corresponding row is equal to cr=”~^(Saxm2 “ 2Saxnii) . (^Iff ) By (I) the sum in question is ^^n-i(roWj.coli + row2.col2 +.... + row„.col„) , to which, again, it is only further necessary to apply (V). 1914-15.] The Determinant of an Orthogonal Substitution. 57 (9) The duplicant of a three-line orthogonant whose base is cr is equal to 2o-V-Saxmi)2. (IX) The duplicant 2ai + ag + ‘^(^2 /^3 72 a.3+7l ^3 + 72 % of any three-line determinant | I known to be 2{|«,^27sI +2»-A}' consequently, if the determinant be an orthogonant whose base is a, the duplicant is which by (V) is equal to and by (VI) is equal to 2|o-t -1- o-hSaxm^^ - 2Saxni2)| , !|ot2 + o-TSaxnij^ _ 2cr=Saxmj)| , ^.e. ^.e. 2|o-t - o-^Saxm^j- 2(rTo-* - Saxm^)2 . (10) The sum of the two-line coaxial minors of the duplicant of an n-line orthogonant whose base is 2 + Cg + + 62 + Cg -1- , and I I = Cr^ y Consequently the sum of the fifteen coaxial minors in question is then o-(Saxmi2 _ ^ (XIII) (12) The sum of the three-line eoaxial minors of the duplicant of a four-line orthogonant of base a- is equal to 2Saxmj(Saxm2 - 2cr) . (XIV) If the orthogonant be | 1 ? fbe first of the coaxial minors in question is + f^i 0-3 + 7i + 2^2 A + 72 I “3 + 7l /^3 + 72 ^73 j and the three others are got by performing simultaneously the cyclical substitutions 1,2,3, 4 2,3, 4, 1 o — an operation which we may denote by S. Now, by the theory of duplicants the said leading coaxial minor is equal to 2 I «i^273 I + 5 ^1 j 7i ^ ! /^27s 1 5 ■“ 1 /^lys I > I /^i72 1 ) + ^(^2 j ^2 ’ 72 ^ “ 1 “-273 I ’ 1 ®'-i73 1 ’ “ I ®'i72 1 ) + 2(ttg } /I3 5 73 ) ! «-2/^3 ! » “ I I > 1 ^1/^2 i ) i consequently the sum of this and the three others is I ®"i/^273 I + ^2 I 73^4 I + I /^2^4 ! + I ^73 I )} - |a2( 1 a284 I + I tt2yg | )| -22{a3(|a3bl + |a3/?2l)} “2{'"4(|a473l + l“4/^2l)}- 60 Proceedings of the Royal Society of Edinburgh. [Sess. Here the first double cyclical sum is recognised to be 2Saxm3 ; the second = 2^^ -la^iSaxing — j 1 ~ 1 “■i73 i ~ I ^1^4 1 )j" = 2Saxmj . Saxni2 - ^2 + 73 + ^4) ~ + ®-37i + ‘^4^i)| = 2Saxmj . Saxiri2 - 2 |g-i^Saxm^ - a^(roWj.cob)| ; = - 2^ jas^Saxm^ - a3(roWj.col3)| ; the third the fourth and the fifth = - 2^|a^2gaxnij - a^irow^.cob)! . Summing these five expressions and noting that o - 2 ^ ^2 ^ _ ScrSaxnij , and that 2^ |aj(roWj.cob) + a2(roWj.col2) + a2(roWj.col3) + a4(roWj.cob)| O = 22(a^roWj2 + a2row^.row2 + a3roWprow3 + a^row^.row^), o = 22airoWi2^ = 2Saxm^ . cr , we obtain the total 2Saxni3+ 2Saxnij.Saxm2 - ScrSaxm^ + 2o-Saxm^ , which, since Saxm3 = crSaxm^^ , is equal to 2SaxnijSaxm2 - 4o-Saxnq , as desired. (13) The sum of the six determinants formahle from a four-line orthogonant of base a- by deleting a pair of columns and inserting in their places the corresponding rows is equal to Saxni2^ - 2crSaxm^2 + 2 {2 I “1/^2 I } - {i l‘l ""i73 1} + ^2, {I H ^i72 i} 5 f J 11^172 ii<^i72 n- 73^^ 12 And as the first part of this is the square of Saxm2 , and the part to be subtracted is double the sum of the two-line coaxial minors of the second compound of | I ’ fbe result desired is reached with the help of (XIII). (14) The dwplicant of a four -line orthogonant of base a- is equal to (Saxnig - 2o-)2. (XYI) The duplicant of any four-line determinant | known to be 2 I 1234 1 -1-22 I 1234'! and therefore, if the determinant be an orthogonant whose base is cr, the duplicant is by (VIII) and (XV) equal to 2(7^ -f 2a-(Saxmj2 - 2Saxni2) + (Saxni2^ — 2crSaxm4^ -1- 2cr^) , i.e. fSaxnig^ - 4orSaxni2 + 4or^. (15) The sum of the coaxial minors of every order in the case of 2ttj ^2 /^] «3 + 7i a4-f3i «2 + ft 2/^2 A's + 72 /^4 + ^2 «3 + 7i /^3 + 72 273 74 -<-^3 A + ^2 74 + ^3 2S4 62 Proceedings of the Eoyal Society of Edinburgh. [Sess. the duplicant of the orthogonant | \ of base cr, is equal to (Saxni2 - 2o- + Saxnii +1)2-1. (XVII) From (XVI) the sum of those of the 4th order = Saxni22 - 4(rSaxm2 + ; from (XIV) the sum of those of the 3rd order = 2Saxm^ . Saxra2 - IcrSaxm^ ; from (X) the sum of those of the 2nd order = Saxnij2 + 2Saxm2 - 4cr ; and by inspection the sum of those of the 1st order = 2Saxiiij . It is readily verified that the total of these four expressions is as stated. (16) There is no corresponding theorem in the case of the duplicant of the three-line orthogonant, the total in question then being 2o-^(Saxm^2 _ 2o-^Saxmj + a) + Saxm^2 + 2Saxni2 - 3o- + 2Saxrn^ , which in its simplest form is (2(t^ + l)Saxni]2 + (2 + 2o-- - 4cr)Saxm3^ + (2o-t - 3(t). In the case of the duplicant of the orthogonant | \ we have 2ttj + f^i — 4a^y52 2a2/?j (Sf = («1 + + 2 I tti^2 I -o-f- jSf = (ttj + |32)2 - 2o- + 2o- and = Saxnij2 . 2a^ + 2y^2 = 2Saxnq ; so that the sum of the coaxial minors of every order is (Saxni2 + 1)2 - 1 . There is a probability, therefore, that the theorem of the preceding para- graph can be extended to all determinants of even order. Capetown, S.A., September 1914. {Issued separately February 24, 1915.) 1914-15.] Spherical Harmonic Computation. 63 VI. — Formulae and Scheme of Calculation for the Development of a Function of Two Variables in Spherical Harmonics. By Professor T. Bauschinger, Strassburg. Translated and com- municated by The General Secretary, Dr C. G. Knott. (MS. received December 7, 1914. Read January 18, 1915.) (This paper was read at the Napier Tercentenary Celebration on July 27, 1914. The Council, on the suggestion of the Napier Committee, have much pleasure in making it accessible in the Society’s Proceedings.) When a function has been expressed as a series of spherical harmonics with constant coefficients, the determination of these coefficients from given values of the function is in the general case one of the most complicated operations which can be set before the calculator. Since Gauss first carried out these operations in a calculation of this kind,* * * §' efibrts have not been wanting to simplify them and make their frequent application possible. The most successful of all in this respect was Franz Neumann,]- who showed that by a suitable choice of the argument the calculation could be materially shortened. For the application of Neumann’s method H. Seeligerj arranged the constant coefficients in tables, and thereby made the calculations so easy and so obvious that even a non-scientific calculator can carry it out. I would now show that some further steps may be taken in this direction, with the advantage that in addition to a further shortening of the calculation the whole process can be carried out by one operation on the calculating machine, since only sums of products have to be formed. [The given values § of the function /(/x , 0), where cos~V( = ^) is l^he polar distance and 0 the longitude, are supposed distributed over a spherical surface, such as the earth’s, and the function itself is expressed as /(/*,<#>)= 2 "'Y” o * Burckbardt, Oszillierende Funktionen, pp. 384 ff. t Astronomische Nachrichten, Bd. xvi, p. 313 (1838). I Silzungsberichte der Konig. layer. Ahademie der Wissenschaften Miinchen : Math.-phys. Classe, Band xx, p. 499 (1891). § The part in square brackets has been added by the translator, so as to make the notations immediately intelligible to the reader. 64 Proceedings of the Poyal Society of Edinburgh. [Sess. where Y” is the spherical surface harmonic of degree n and is of the general form i — n i = 0 where A and B are the 2U+1 arbitrary constants to be determined, and where t nM = V-l - ’ P'" being the zonal spherical harmonic of degree n of one variable. In Frank Neumann’s method 2^(p + l) values of the function are taken, namely. Ah , 0) , ... . , (‘ip - 1) f(p, , 0) , ,^y ... . .f{p, , {ip - 1).^) ./V.+1 , 0) , , {ip - 1)^) where /xi . . . /x^+i are the (p + 1) roots of the equation P^+V) = 0. For each root the values of C and S are defined by v^2'p-l = 2 where is unity, except when i = 0 or p, when the value is 2. If now we write it may be shown that the constants A and B are determined by the values given in (I) below.] Take then the expressions for the constants sought, namely, X=j0+1 Ant= 2 ^ni{P\)Ci{f^x) X = l • (1) In Professor J. (not ‘‘ T.”) Bauschinger’s paper on Calculation by Spherical Harmonics (Proc. vol. xxxv, p. 64), the following correction should be made ; Third equation from bottom on p. 64 should read a-^ being given by the solution of the equations + . . . + — a\ (X = 0 , 1 , 2 j 3 . . . ^), 1914-15.] Spherical Harmonic Computation. 65 and combine the known coefficients in the C and S with the % when we obtain A=p + 1 v = 2p-l X = 1 v = 0 A=p+1 v = 2p-l B»<= 2 Z A = 1 1^ = 0 / i7T\ •/( 7T \ P*’ v; / ^7^\ •/( ^ 7T \ (2) In every case the 2p(p + l) coefficients and (of the latter p + 1 are ah initio equal to zero) are tabulated for each combination n, i, and the operation to be carried out with the calculating machine is then continued quite simply so that each of the given values of the function is multiplied with the corresponding G and H respectively, and the sums of all products taken. After determination of the and the interpolation formula for the function f{juL, + (P22B22+ .... +P^2Bij2) siu 2^ + ^ cos (3) where the associated spherical harmonics P are functions of the powers of sin^ and cos^( = ya). For convenience of application, the expressions within the brackets in (3) require to be changed into rows which are developed in sines and cosines of multiples of 0 ; that is, the arrangement takes the form / (0, 4>) = (ttoo + 0-10 cos ^ 4- Ooo cos 2^ + . . . . 4- Opo cos pO) 4- (oii sin 0 4- ogi sin 2^4- +0.^1 sin pO) cos 4- (fSii sin 0 + /321 sin 2^4- + Ppi sin j;(9) sin cf> 4" (oq2 4“ 0^2 cos 0 + 0.22 COS 2^4".... 4" 0.^,2 cos pO^ cos 2(f> + (/?02 + /di2 cos 0 4- ^22 cos 2^4-.... + (ip2 cos p6) sin 2(^ + The second step to be made in preparing once for all for the carrying out of the calculations is that, instead of the above-named tables for the G„^ and H„i, similar tables may be immediately constructed for the calcula- tion of the a^i and This is easily possible, since the a^i, /3ni are simple known functions of A„^ and VOL. XXXV. 5 66 Proceedings of the Eoyal Society of Edinburgh. [Sess. The ani and /3ni are then obtained as sums of the 2^9 (p + 1) products, of which the one factor 1 and the other factor stands in the table. Such a table possesses the advantage that a glance enables us to recognise and calculate the influence of a change of a given value of the function f(^fj.x, upon the coefficients a and ^ ; for if gniw is the value in the table for an% which corresponds to X, v, and A/a^ the known change, then will gnixvVfw be the corresponding change of anh and . P even jcOS *<^>1^. the change of the function f{0, (p). In practical work the direct use of the table is not to be recommended, for, although the mode of calculation is indeed very clear, the number of products to be formed is great. It is possible also to supply a much simpler procedure, since the tabulated values of each are for the greater part zero, or equal, or equal and opposite. We have now left a few of the different coefficients v^hich are to be multiplied by constantly recurring combinations of /^/xx, These latter are made up solely out of the sums and differences of the/^/xx, without factors, and are quickly formed by calculation with the hand ; all further working is best done with the machine. In practice the calculator will mostly be concerned with developments up to the fourth order of spherical harmonics, and only in exceptional cases will be compelled to go as far as the sixth order. I here restrict myself therefore to the communication of the formulae and numbers for the case p = 4>; their deduction may be left out, as it is quite simple. In accordance with the theory, we must take as given values of the function the points of section of the meridian 4> = 0% 45°, 90' . . . 315' with the parallels whose polar distances are ^1= 154 58 57-6 ^0= 122 34 46-2 ^3= 90 0 0-0 57 25 13-8 2b 1 2-4, forty values in all. 1914-15.] Spherical Harmonic Computation. 67 I represent them shortly in the following way ; f{0\, j/45°) = Xv 1 , 2 , 3, 4, 5 !/=:(), 1, 2, 3, 4, 5, 6, 7 The coefficients a, /5 are then expressed by the interpolation formula f(0 , 4>) = COS 0 + tt20 COS 2S + ag^ COS 30 + cos 40 4- (ttjj sin 0 + a^i sin 20 + ag^ sin 30 + sin 40) cos 4> + (jdii sin 0 + fSoi sin 20 + pg^ sin 30 + ^4^ sin 40) sin 4- (aQ2 + aj2 cos 0 -t- a22 COS 20 + ag2 COS 3$ + COS 40) COS 2 4 (/di3 sin 0 + ^23 sin 20 + sin 30 + sin 40) sin 3<^ 4- (ttQ4 + tt24 cos 20 + tt44 cos 40) COS 40 In the first place, all the combinations of the given values of the function are to be calculated. They are shown in Table A, being represented by the symbols [l]i j [^]i 5 [^]i [^^]i [1]2J2]2,[3]2 [15^ [IhHSJsJSjg [15]g This table gives at the same time an appropriate scheme for carrying out the calculation. The first column contains the forty values of the function arranged in the most convenient order ; the other columns explain themselves. It will be seen that numbers which are to be added or subtracted stand directly under one another. For these simple opera- tions controls are hardly necessary, and are indeed furnished by the mode of their summation. The same process repeats itself constantly so as to become strongly impressed on the memory. The a and 8 follow as sums of products, with constant factors, of the numbers just determined. These products are given in Table B. It is there evident that for the finding of the thirty coefficients a, (8 (six of which are immediately expressible in terms of the others), ninety-two products are necessary. Since these can be immediately formed and summed by means of the calculating machine, a further control other than is furnished in the usual way by the working of the machine is superfluous. In the second table, for simplification of the numbers the first factors with their tenfold totals are set down ; compensation is effected most simply by dividing the values of the function by ten before using them, whereby as a rule a desirable homogeneity in the whole set of numbers is brought about. 68 Proceedings of the Koyal Society of Edinburgh. [Sess. Table A. a _o ’■4J First Second Differ- i Successive Successive O Sum. Sums and Differences. Differences and Sums. ence. 10 14 10 + 14 10-14 (10+14) + (12 + 16) (10 + 14)1 . -(12 + 16)/ -"1 (10- 14) = C4 (12-16) = d4 12 16 50 12 + 16 12-16 50 + 54 50-54 (50 + 54) i (50 + 54)1 , (50-54) = C5 (52-56) = d5 54 + (52 + 56) f- ^5 -(52 + 56)/ (7i + (75 = [5]i 52 52 + 56 52-56 ^1 + ^5 = m, + = ci + c, = [3], 56 n. Ci-C5 = [4L ^1 — 11 11 + 15 11-15 (11 + 15)' \ (11 + 15)1 -f -(13 + 17)i -•'1 (11-15)^ 15 + (13 + 17). \ + (13-17)/ "^1 -(13-17) ) 13 17 51 55 13 + 17 13-17 51 + 55 51-55 (51+55) + (53 + 57) h ^5 (51 + 55)1 , -(53 + 57)/ (51-55) ( _ + (53-57) ( (51-55)) ^ -(53-57) ) 53 53 + 57 53-57 ^1 + ^5 = Pi A +/,=[+ 9i+9^ = [^]i hi + h^ = [ll]i K-h=mi 57 2m /.-A = [8]i 9i-95 = [^0\ mi+^i = [13Ji mi-j?i = [15] 1 ni + gi-[14Ji 20 24 20+24 20-24 (20 + 24)' + (22 + 26). :«2 (20 + 24) 1 -(22 + 26) J ~ 2 (20-24)-C2 (22-26) = d2 22 22 + 26 22-26 26 40 44 40 + 44 40-44 (40 + 44)' + (42 + 46) ■a^ (40 + 44)1 ^ -(42 + 46)/ (40_44) = C4 (42-46) = d4 42 42 + 46 42-46 U2 + = TUo {h2 + b,) = [ll (C2 + C4) = [3]2 <^2 + <74= [5]2 46 (Xo - U4 = (62 -64) = [2/2 (Cg — C4) = [4]2 <^2-^4 = W2 21 21 + 25 21-25 (21+25) - P (21+25)'! (21-25) ) _ (21-25)) , 25 + (23 + 27), / -H -(23 + 27)/ -^2 + (23-27)) -(23-27) i 2 23 27 41 45 23 + 27 23-27 41 + 45 41 -45 (41+45) + (43 + 47) (41+45)1 -(43 + 45)) -^4 + (43-47)) ^4 (41-45)) - (43 - 47) ) 4 43 47 43 + 47 43-47 e-2 + ^4 = e.2-e^ = ■-P2 ■Pi /2+/4 = m2 /2-/4 = [8]-2 92 + 9iH^]2 5'2-S'4 = [10J2 h2+h=[n\ ^2 - ^4~[l^]2 ^2 + 7^2== '13' 2 d5“ 2 + ^2 = d4' 2 30 30 + 34 30-34 (30 + 34)\ (30 + 34)1 (30-34) = C3 (32-36) = dg 34 + (32 + 36) ) ~ -(32 + 36) 1 “3 32 32 + 36 32-36 36 31 31+35 31 - 35 (31+35)\ (31 + 35)/ . -(33 + 37) ) “-^3 (31-35) ( _ + (33-37) ) ^3 (31-35)) ^ -(33-37) i “^^3 35 + (33 + 37) J " 33 33 + 37 33-37 ^3 + ^3 = [ 3 ^3 = PL ^3 ~ [^]3 ^3 ~ [ 5 Is 37 ^3 ~ ^3 ~ [ Is y3=[p3 93 — A-3 = [10]3 69 1914-15.] Spherical Harmonic Computation. Table B. (The first factors are set down with their tenfold totals.) +0-3296[13p -0*5973[14Ji a,o= +0*5087[13]i + 0-1444[13]2 -0T555[14]2 ” -0’3628[13]2 + 0-3021[13]3 ^ -0'2917[13]3 a3,= -0-3246[14h +0-179iri3l. + 0-5462[14]2 - 0-5072[13]2 + 0-6562[13]3 aii= +0-3155[3], + 0'2231[ll]i + 0-8306[3]2 + 0-6873[11]„ + 0-8333[3]3 + 0-5893[11]” /3,i= +0-3155[5]i + 0-2231[9]i + 0-8306[5l2 + 0-5873[9]2 + 0-8333[5]3 + 0-5893[9]3 a,j= -0-6449[4]j-0-4560[12], -0-9328[4]2-0-5887[12]2 ^21= -0'6449[6], -0-4660[10]i -0-9328[6]2- 0-5887[10]2 agi= +0-6382[3]j + 0-4513[11]i + 0 3720[3]2 + 0-2630[11]2 - 1'1667[3]3“-0-8250[11]3 ^3,= +0-6382[5]i + 0'4513[9]i + 0-3720[5]2 + 0-2630[9]2 -M667[5j3-0-8260[9]3 a„= -0-7675[4]j -0-5427[12], + 0-6482[4]2 + 0-4584[12]2 ^^2= -0-7675[6]j-0-5427[10]i + 0-6482[6]2 + 0'4584[10]2 +0-1823[l]j + 0-6289[1]2 + 0-2917[1J2 ;8„2=+0-1823[7], + 0-6289[7]2 + 0-2917[7]” ' a,„= -0-1575[2l. - 0-7506[2],2 /3,2= - 0-1575[8]i - 0'7506[8]2 a22=+0-1272[l]3 - 0-0907[1]2 - 1-1667[1]3 ^22=+0 1272[7]2 -0-0907[7]2 - 1-1667[7]3 “32 = ~ “l2 ^42= “(«02 + «22) /^32 ~ “ /^12 /^42 ~ " ^^02 ^^22) aj3= +0-0368[3]j-0-0260[ll]i + 0-5872[3]2-0-4152[11]2 + M667[3]“-0-8250[11]3 ^j3= -0'0368[6]i + 00260[91i -0-5872[5]2 + 0-4152[9]2 - 1-1667|5]3 + 0-8250[9]3 «23= - 0 0997[4]i + 0-0706[12]i -0-9487[4].2 + 0'6710[12]2 /S23= +0-0997[6]i-0-0706[10]i + 0'9487[6]2-0-6710[10]2 “33 = ” i“l3 “43 = “ 2“23 A33 = “ ?/^13 /^43 = “ 2/^23 “04= +0-0044[15]i 0^4= - f -a;,, + 0-1392[15]2 + 0-3281[15]3 a„=+J.a„, {Issued separately March, 16, 1915.) 70 Proceedings of the Eoyal Society of Edinburgh. [Sess. VII.— On an Integral-Equation whose Solutions are the Functions of Lam4. By Professor E. T. Whittaker, F.R.S. (MS. received December 7, 1914. Read December 7, 1914.) § I. Object of Paper.— TYiq chief object of the present paper is to establish the followino^ theorem : The functions of Lame [that is to say, the doubly -periodic solutions of the differential equation sn^ x + K)y'\ . . . • (1) are the solutions of the homogeneous integral-equation y{x) = \ I idn X dn s + k cosh rj cnx C7is + kk! sinh t] snx sn s)”^(s) ds , (2) Jo where rj denotes an arbitrary constant. It will be found that this result plays much the same part in the theory of Lame’s functions as the theorem P = constant X j - 1 coss}”cos wsJs . . • (3) does in the theory of Legendre’s functions, or the theorem 1 r — — / cos {ns - X sin s)ds . . . . (4) 7T 7c does in the theory of Bessel’s functions : or (to take a case in which the analogy is still more marked) as the integral-equation y(x)=^XrV^^^^^^^^y(s)ds ..... (5) Jo does in the theory of the Mathieu or elliptic-cylinder functions. It will be shown, in fact (§ 5 infra), that (5) is a limiting case of (2), while (4) may be regarded as a limiting case of (5) and also as a limiting case of (3). It will be noticed that the integrals occurring in (3) and (4) are ordinary definite integrals which do not involve the Pi” or the under the integral sign : whereas (2) and (5) are integral-equations, that is to say, the function y occurs both on the left-hand side and also under the integral sign. This 71 1914-15.] Integral-Equations and Lame’s Functions. is an instance of a general theorem, which I propose to establish in another paper, namely, that integral-equations play the same part in relation to differential equations with four regular singularities that ordinary definite integrals do in relation to differential equations with three regular singularities.* It may be remarked that the differential equation (1) has Lame’s functions for its solutions when the parameter A has certain special values : but unless A has one of these special values, the solution of the differential equation (1) is not doubly-periodic, and consequently is not one of the Lame’s functions required in Applied Mathematics. The integral-equation (2), on the other hand, does not involve the parameter A at all : and its solutions are Lame’s functions and no others. § 2. Proof of the Theorem. — In order to establish the result (2), we shall require two curious properties of the expression dnx dns + k cosh r] cnx cns + kk' sinh t] snx sns . This expression we shall denote by U. In the first place, we have dHJ_dfV dx'^ ds'^ = - k'^ dn s dn X (I - 2 sn- x) - k cosh y) cn s cnx {\ -2 k^ sn^ x) - kk' sinh yj sn s sn x {1 - 2k^^ sn^ x) - [ - k^ dn s dn x {\ - 2 sn^ s) - k cosh -q cns cnx - 21^^ sn‘^ x) - kk' sinh -q sn s sn x — 2k‘^ sn‘^ s)] = 2{sn‘^ X - sn^ s) {k^ dn s dnx -k- k^ cosh 'q cns cnx + k^k' sinh y] sns sn x) — 2k!^{sn'^x-sn‘^s)\] ........... (6) In the second place, we have /^Y _ /auy \^X ) \06* / — iy — W" snx cnx dn s — k cosh q dnx snx cns + kk' sinh q cn x dn x sn sf — { — k^ sn s cn s dnx - k cosh q dns sns cnx + kk' sinh q cns dns sn xf. * Lame’s differential equation (1) when expressed in algebraic form has four regular singularities. Mathieu’s differential equation ^ + {a + cos2 = 0 , dx^ when expressed in algebraic form has two regular singularities and one irregular singularity, which latter may be regarded as formed by the confluence of two other regular singularities, making four in all. Legendre’s differential equation has three regular singularities : and Bessel’s equation is a confluent form of Legendre’s. 72 Proceedings of the Eojal Society of Edinburgh. [Sess. Writing for snx, for sns, etc., this becomes /0UY puy V^/ + cosh^ y^{s^d^c<^ - s^d^Jc^) + ^'2 sinh^ i]{c^d-^si^ - c^d.,^s-^) + cosh y] c^d-^c^dj^s-^ - H- 2A:^ k' sinh 77 s^d-^s^d^{s-^ - .s^^) + k' cosh 77 sinh 77 ~ = ^2/, 2_ 2) pi -A:2(9,2 + ;/) + ^4 ,^2,^2 _ /,'2 ,^2 ,^2 + B COsh2 77 { 1 - ( 9^2 + + 9,2 ^’^2 + /^'2 9,2 } + 2^ cosh 77 c-^d-^c^d^ + 2k k' sinh 77 s-^d-^s^d^ + 2^2 Qosl, yj ginh 77 9,C,92Cg_ = U2 P) With the help of the two properties (6) and (7) it is an easy matter to establish the result (2). In fact, if we write 1 = ds 6^.2 r^iS. U«2/(s) J 0 odic soluti = [n{n + \)k‘^ sn^ s + A]y where y{s) denotes a doubly-periodic solution of the equation d‘^y (8) we have ^21 dx^ '4K =ri >i{n + 1)F 9?z2ir + A}I «-2/9U\2 dx Using (6) and (7), the right-hand side becomes n(n + 1)Zj2 s^2 xV'^ ~ AU* wU” M + 2k‘^{sn^ X - sn^ s)J] +n{n-\)\'J n{n + 1)^2 g^2 X U'^ — AU”" | y(s) ds. ') + k?{sn^ X - 97^2 s)XJ2 I ds J y{s) ds, or ri"”' -10^U , , 1MT..-2/3UV 0?+”(”-i)U" w - n{n + 1)7:2 or by (8) f{ ds^ j or kr ds J’ (79, which is zero, since and y{s) have the period 4K. 73 1914-15.] Integral-Equations and Lame’s Functions. The integral I, therefore, satisfies the differential equation (1): and it is a doubly-periodic function of x. But any douhly-periodic function of x satisfying equation (1) must be a constant multiple of the Lame’s function y{x), which corresponds to the particular value of A concerned : and thus we have the required result .4K ll{x) = A. I TJ'^y{s) ds . •'0 § 3. A Definite Case worked out directly. — It is somewhat surprising to find how much difficulty is attached to the verification of even the simplest particular cases of this theorem by direct integration. As an example, let us take n — 2, in which case one of Lame’s functions is y{x) = srd x — t where t = 71 - ^2 + ^4} . This function is the doubly-periodic solution of the equation where A = -2{l-hA:2- + . In this case we have to consider the integral ,-4K / {dn X dns + k cosh y cn x cns + kk' sinh rj snx sn sY{k^ sn^ s -t) ds . Jo We can omit terms of the (expanded) integrand which are odd functions of s, since these give zero when integrated between 0 and 4K : and we can also omit the term which contains dn s cns multiplied by a function of sn s, as this is the perfect differential of a doubly-periodic function and therefore vanishes when integrated over this range. Thus the integral may be written (arranging the integrand according to powers of sn s) riK I { (d7i^ X + Id cosh2 y crd x) + sn'^ s{ - k‘^ drd x — k^ cosh^ rj crd x + Idk'd sinh2 rj srd x) } {Id srd s-t) ds . Now we have —{sn s cn s dn ds l-2(l+A;2)s7^2s+3A;2s7^4s, and therefore if the integrals yK .4K I ds and / sn‘^s ds '0 Jo are denoted by I and J respectively, we have •4K 1 74 Proceedings of the Poyal Society of Edinburgh. [Sess. Substituting these values for the integrals, and rearranging, the integral becomes I r{ - t{\ + COsh2 rj) + 1{Z;2 + cosh^ rj)} 1 L + x{ - cosh2 y{) + k^ - k^ cosh2 ^'2 cosh2 rj + k^ k'^)]\ + J r {( - ^ + I + W){ - COsh2 yj) + F(1 + A'2 COsh2 ^)} + sn^ x[{ - t + |A’2)(A:‘^ + A;2 cosh2 yj + k^ k'^ cosli^ yj -k'^ k'^) + k\ -k‘^-k‘^ cosh2 ry) } _ The coefficient of k^l cosh^ t] is + J + - \k'^) sn^ X . But since t is a root of the quadratic 3^2- 2^(1 +F) + A:2 = 0, we have t-\- \k'^ _ t’ and therefore the terms which involve I cosh- rj may be put in the form (A;2 sn^x-t) x a quantity which does not involve x . Consider next the term^s which involve I but do not involve rj. They are (omitting the factor I) -t + JA^2 4- 8n^ x{tk‘^ - + \k^^ k'‘^) . But again from the quadratic 32^2 - 2^(1 + ^.2,^0 we see that ^A;2-1A:4 + 1A:2A^2 -t + \Jc^ t ’ and therefore the terms which involve I but do not involve rj can be put in the form (A;2 sn^ X -t) x a quantity which does not involve x . A similar method shows that the terms which involve J can likewise be put in the form (^2 sn^x-t) X a quantity which does not involve x ; and therefore, finally, the entire integral can be put in this form, which is the required result. The above analysis shows that to verify the theorem by direct integra- tion, even in the simple case of ?i = 2, is a somewhat difficult task, requiring the use of the recurrence-formulae between the integrals of elliptic functions, and also a considerable amount of algebraical work connected with the quantity t. 75 1914-15.] Integral-Equations and Lame’s Functions. § 4. Extension of the Theorem. — It will be seen that the proof in § 2 makes no use of the fact that the range of integration is from 0 to 4K beyond the inference that the values of U and y{s) are the same at the end of the range of integration as at the beginning. The theorem may there- fore be stated in the following extended form : The functions of Lame are the solutions of the homogeneous integral- equation yix) = A I {dn x dns -{■ h cosh rj cnx cns + kk' sinh rj sn x sn sf y{s) ds , Jc where C denotes a path of integration beginning at any point in the plane of the complex variable s, and ending at the same point or any other point of the plane which is congruent with it. Of course, the path must not pass through any of the poles of the functions sn, cn, dn, which are at the points congruent with s = iK'. In particular, we can take the range to be the straight line from s = K to s = K -h 4iK'. Thus rVi+UK' y{x) = A / {dn x dns + k cosh t] cnx cns + k k' sinh t] snx sn s)^ y{s) ds . Jk Writing s = K-f-f, x = K-\-z, and making the corresponding change in the differential equation, we have the result that (k' + kk' cosh 7] snz snt -l- k sinh rj cn z cn ty dn^ z dn^ t u{t) d,t is an integral-equation satisfied by the doubly -periodic solutions of the equation d‘^u dz^ = I n{n -f- cn^z dn^ z It might be expected that an interesting particular case of the general theorem would be obtained by supposing the path of integration to be a simple closed contour enclosing one of the poles of the integrand, in which case the Lame’s function of x would be expressed as a constant multiple of the residue of the integrand at this pole. A closer examination shows, however, that the residues at the poles are zero, so that this proposal leads to no result. § 5. Derivation of the Integral-Equation whose Sohitions are the Functions of Mathieu. — We shall now show how the integral-equation for the Mathieu or elliptic-cylinder functions, which was obtained by the present writer in 1903, can be obtained as a special case of the integral- equation whose solutions are the functions of Lame. 76 Proceedings of the Eoyal Society of Edinburgh. [Sess. The differential equation for the Mathieu functions may be written + (9) and may be derived as a limiting form of Lame’s equation (1), by making k tend to zero while at the same time n tends to infinity in such a way that the product nk is equal to the finite quantity /x. The integral-equation which we have obtained for the Lame functions now becomes I jtx , . I ^ y(x) = XJ j dnx dns + ~ (cosh y cn x cns + k! siiih y sn x sn s) y(s) ds , and when k tends to zero dn s tends to unity, while sn s tends to sin s and cn s tends to cos s. Thus y{x) = A|'|l + ^(co.h y COS X cos s + sinh y sin x sin s) | y(s) ds . When n tends to infinity this becomes y{x)==\re>^^^oshr,coszcoss + smhr,smxsms)^^^^ _ Jo and this is the most general form of the integral-equation satisfied by the function of Mathieu. As was remarked in § 1, the well-known trigonometrical definite-integral for the Bessel functions is a limiting case of this latter integral-equation. In order to obtain it, we shall first take a new independent variable ^ = ZjLl COS X in Mathieu’s differential equation (9), when the equation (9) becomes d^y d.y dl + 1 + 9 , y IX- + r).y = o (11) and the integral-equation (10) becomes (taking y to be zero) ,-2t7 y(x) = X . . (12) We can now convert the differential equation (11) into Bessel’s differential equation by making ju tend to zero while keeping ^ finite : in order to make the resemblance to the ordinary form of Bessel’s equation complete, we write —n^ in place of the constant A. Thus y(os) becomes the Bessel function Jn(0- 2/(®) becomes the solution of the equation 77 1914-15.] Integral-Equations and Lame’s Functions. into which Mathieu’s differential equation transforms when fj. is put zero, that is, the equation ^ + nhj = 0, as- so y{s) = cos ns. Equation (12) thus becomes Jo - iC cos s 7 e cos ns as which will be recognised as one form of the trigonometrical integral for the Bessel functions. {Issued separately March 16, 1915.) 78 Proceedings of the Eoyal Society of Edinburgh. [Sess. VIII.— Regeneration of the Legs of Decapod Crustacea from the Preformed Breaking Plane. By J. Herbert Paul, M.A., B.Sc., Barbour Research Scholar, Physiological Department, Glasgow University. (With Four Plates.) Communicated hy Professor D. Noel Paton. (MS. received December 4, 1914. Read December 21, 1914.) CONTENTS. PAGE Introduction .......... 78 Historical . . ....... 79 Methods and Material ........ 81 Observations .......... 82 1. The Provisions for Loss of the Limb ...... 82 2. Papilla-formation ........ 84 3. The Changes at Moulting ....... 88 Discussion .......... 89 Summary ......... 91 Bibliography .......... 92 Description of Plates ........ 93 Introduction. The observations recorded in the following pages are the result of work continuously prosecuted from March 1913 until the date of writing (November 1914). Several series of observations have been carried out under strict experimental conditions, and many observations have been made on decapods taken from the trawl and shore. At the same time I have been able to take note of the regenerative processes in the large numbers of captive Crustacea in the tanks at the Marine Biological Station, Millport, where the work has been largely carried out. The object for present publication is to make a general statement of the results up to the time of writing. While these agree in most respects with work of the same nature carried out by previous observers, many phenomena hitherto unnoticed have been recorded. These are of distinct interest and must be taken into account in discussion of the physiological and developmental problems connected with limb regeneration which I hope later to take up. The work was first suggested by Prof. Noel Paton, in whose department all the histological work and some of the experiments were carried out. I have to thank him sincerely for his sympathy and encouragement. To the staff at the Marine Biological Station, Millport, especially to Mr Elmhirst, 79 1914-15.] Regeneration of the Legs of Decapods. my thanks are also due for sound practical aid,"*^ Dr J. F. Geramill supplied me with references to literature on the subject, and I have to acknowledge my gratitude to him on that account. I have also to thank him for facilities for working in the Embryological Laboratory, Glasgow University. Historical. For more than two centuries regeneration of limbs in decapod crus- taceans has drawn the attention of biologists. While a great deal of information has been obtained regarding the conditions and extent of reproduction, the veil of mystery hangs as darkly over many points connected with it as over most vital phenomena. Reaumur (1) (1712) first described the regeneration of legs in crabs, lobsters, and crayfish, though Du Tertre had drawn attention to it as early as 1654. The following extract from the work of Reaumur is quoted by Herrick (2) : “ I took several from which I broke off a leg ; placed them in one of the covered boats which fishermen call ‘ boutiques,’ in which they keep fish alive. As I did not allow them any food, I had reason to suppose that a reproduction would occur in them like that which I had attempted to prove. My expectation was not in vain. At the end of some months I saw, and this wfithout surprise, since I had expected it, — I saw, I say, new legs which took the place of the old ones which I had removed ; except in size they were exactly like them : they had the same form in all their parts, the same joints, the same movements.” Reaumur explained the phenomenon by postulating the presence of eggs or limb-germs scattered throughout the appendage, showing that when the leg was lost the nutriment which normally went to the whole limb was now supplied to the egg, development thus taking place. Bonnet in 1775 used the same theory to explain the regeneration of new heads and tails in Lumbriculus. In 1871 Chantran (3) pointed out that regeneration in Crustacea varies according to season. He indicated (which Reaumur failed to do) that moults must intervene during the period of regeneration in order that perfect limbs may be formed. Herrick (2), writing in 1895, mentions the work of Brooks (12) (1887), and describes the process of regeneration in lobsters. He indicates the relation- ship between the age of the individual and the power of regeneration, and also takes note of the fact that the rate of growth varies much at different times within the moulting period. * Mr J. Peden carefully recorded dates of moulting in my absence and fed the animals regularly. I am therefore indebted to him. 80 Proceedings of the Royal Society of Edinburgh. [Sess. In 1898 (4) Morgan published the first of a series of papers on regenera- tion in the hermit crab (Eupagarus longicarpus). He first showed that power of regeneration is not related to liability to injury, and in a second paper demonstrated that, though regeneration takes place normally from a preformed breaking plane, nevertheless it can occur central and distal to this point. Steele (5) in 1904 published the results of work extending over several years. The observations were made on the regenerative process in the crayfish. A full description of the natural conditions influencing the rate and extent of reproduction of limbs is given, but the larger part of the paper is concerned with regeneration of optic peduncles, following on the work of Herbst. Cheliped regeneration is mentioned in the course of the work, but no details are given, and very little minute structure is described. In 1904 Reed (6) studied the regeneration of the first leg in crayfish, and pointed out that the new musculature for the limb is derived from the epidermis at the point of breakage. This demonstration of the fact that tissues of the same order can regenerate from different primary layers of the embryo brought the work into line with what had been seen in the regenerating head of Lumbriculus ; for here tissue derived from ectoderm in normal development regenerates from endoderm of the alimentary canal. The work of Reed differed from that which preceded, in that an attempt was made to discover the exact nature of the cellular change. Previous workers had confined themselves mainly to microscopic observations of the phenomena. Miss Reed, on the other hand, is concerned with minute structure, and on this account has probably failed to take note of several facts which are of great physiological importance. Observations on these points, when related to what is revealed by microscopic examina- tion, throw much light on such problems as the intimate nature of muscle contraction, or the functional relationship of the various parts of the contractile unit. For example, she does not mention the great changes which take place in the newly formed fibres on the occurrence of moulting, when the preformed limb increases in size fivefold almost immediately. Nor is any note made of the coming of function in the new muscle or the appearance of cross striations in the fibres. Emmel (7) in 1910 wrote an account of observations he had made on the regenerative processes in young lobsters. He described a valve mechanism for the stopping of haemorrhage at the breaking joint of the cheliped. One the same in principle but different in detail is present in the hermit crab, and the present writer studied it before he was aware of or had 81 1914-15.] Regeneration of the Legs of Decapods. access to the work of Emmel. The information, however, is useful for comparative purposes. Emmel went a step further than Reed when he described in detail the morphological side of the replacement of muscle. Many other workers have given attention to limb regeneration in Crustacea, but their results are of interest more from a morphological point of view than from a physiological one, and it is of the latter that this paper attempts to treat. They include Ost (8), Zeleny (9), and Haseman (10). Methods. The observations recorded here were made upon decapod crustaceans because this group shows limb regeneration in its highest development. Homarus vulgaris (the common lobster), Eupagurus bernhardus (the hermit crab), and Carcinus moenas (shore crab) were taken as species typifying the process. On the first a straight papilla is grown on the old stump. It is invested by a chitinous coating, and is almost a perfect miniature of the normal limb (figs. 14 and 16). The hermit crab, on the other hand, grows a curved papilla much more stout in proportion to size than the lost appendage. In the last-named species the new limb-bud is completely folded in and enclosed in a chitinous envelope. In every case, as will hereafter be described, the bud suddenly expands to become a limb of almost normal size when moulting occurs. In the case of the lobster the chelipeds were damaged and subsequently autotomised between the first and second joints by the animals themselves. The walking legs were either removed directly by the scissors or by autotomy at the second joint. Separate tanks were provided for each lobster, and the animals were fed weekly throughout the period of regeneration. Hermit crabs were treated in two ways. Firstly, a series of globes were fitted up with siphon tubes and a continuous circuit kept up through them. The crabs, thus isolated, were fed weekly. The second method employed also kept the crabs under a continuous circuit, but the animals were not fed at all during the period of regeneration. Air-tight bottles with inlet and outlet tubes passing through rubber corks were connected up in series, and in each a crab removed from its whelk shell was placed. Confusion on the occurrence of moulting was thus avoided. Legs were damaged and autotomised by the animals at the breaking plane. Shore crabs required less careful treatment, and on this account were placed in a common tank, operated on at one time, and removed at definite intervals. In addition to those decapods of which the limbs were regenerated VOL. XXXV. 6 82 Proceedings of the Pojal Society of Edinburgh. [Sess. under experimental conditions, many hundreds regenerating in the natural habitat were examined. These were taken in the trawl, collected on the shore, or captured by creels at different seasons of the year. Crabs re- generating in the common tanks at the laboratory were also continually watched, and it was in these that many of the processes which occur at moulting were observed. Fixation of tissue at first gave difficulty, disintegration taking place when ordinary fluids were used. It was found that fixing solutions must be strong to give good results, and the greatest success was obtained by use of the following : — Pure formaline . . . . .25 per cent. Saturated solution of picric acid . 35 „ „ 90 per cent, alcohol . . . . . 40 „ „ The whole crab was fixed, for it was found that parts of the body collapsed if removed. Tissues were decalcified in phloroglucin-nitric acid solution, then carefully orientated, and embedded in paraffin. Complete serial sections were cut and stained on the slide with hmmalum, and also with eosin as counter-stain. Certain parts of the tissue were reconstructed by ordinary methods after examination of the series. Observations. 1. The Provisions for Loss of the Limb. — Blood circulation in a crus- tacean limb differs from that in the higher animals. Arteries bringing blood from the heart penetrate to the distal extremity and end there. There are no definite veins, and the fluid travels backwards in the shell- like limb, bathing the bands of muscle and connective tissues. If such a leg be crushed, broken open, or cut across, the animal runs a great risk of losing all its blood ; for, as an additional danger to its broad blood- channels, the crab has a hard integument which cannot contract to prevent haemorrhage. Both of the above factors would therefore tend to make fatal haemorrhage the common lot of the crab, but another process has been evolved to prevent this. This is the process of autotomy or self-amputa- tion. Autotomy is a reflex action resulting from nocuous stimulation of the nerve to the limb. Frederique (13) first pointed out that the contraction at the extensor muscle of the basi-ischium (second limb segment) and the contact of the leg with a point of resistance produced amputation at a preformed breaking plane or joint at the base of the limb. The references to autotomy in this paper are only made so that the regenerative process may be described ah initio, for this process virtually begins immediately 83 1914-15.] Kegeneration of the Legs of Decapods. after autotomy has occurred. Regeneration after autotomy at the breaking plane is also the process as it occurs in nature, though, as Morgan pointed out, new growth can take place from any point if certain precautions be taken to prevent removal of the limb at the breaking plane, and if life be preserved in the animal. Most decapods have at the base of their more vulnerable limbs this breaking joint, and here a membrane composed of two flaps stretches across the limb cavity. Through a foramen in this structure the nerve and vessel pass, and when the limb is autotomised these retract. Most writers say that a blood-clot then forms in the foramen and haemorrhage thus ceases (14), but my observations have led me to believe that in the majority of decapods, at least, such is not the case. In the hermit crab, for example, a beautifully arranged valve mechanism exists, and this, coming into action whenever autotomy has occurred, prevents the loss of even one drop of blood. Tait (15) in a recent paper failed to find any relation between the ease and frequency of autotomy in decapod crustaceans and the degree of development of clot-formation in the blood ; it may turn out, however, that there is a relationship quite different from what he imagined, and that the valve-mechanism now to be described is developed inversely as the clotting power of the blood. The epidermis of decapods consists of a single layer of columnar cells. On the outer side this secretes chitin and lime-salts, and so the shell is formed. At the breaking plane these outer hard layers are discontinuous in the greater part of the circumference of the leg, and the epidermis is modified. The bodies of the cells are greatly elongated and their pro- cesses seem to stretch inwards, joining with those of the opposite side (fig. 1). In short, they seem to be modified into connective-tissue fibres which mat together and form a diaphragm. Many writers on the subject have spoken of the epidermis being invaginated to form the diaphragm, and many have refrained from describing it altogether. From my own observations both in the developing and in the regenerating leg, I am led to the conclusion that the diaphragm is formed as described above, and corresponds with the “ collonades de soutien” described by Vitzou (16) in decapods. The following remarks on structure refer to Eupagurus, for in this species the mechanisms are most highly developed, and preparation of the tissue is most easy. The artery passes through a simple foramen in the diaphragm, which it completely fills, but not so the nerve. The latter has a funnel- like prolongation of the diaphragm fitting loosely round it, and passing back- wards and through this the venous blood from the limb must return, since 84 Proceedings of the Koyal Society of Edinburgh. [Sess. there is no other opening (fig. 2). The two foramina lie very close together, and in Eu'pagurns are placed dorsally and internally on the diaphragm as seen after autotomy. Before describing the physiology of these structures a word must be said of the relative positions of nerve and vessel behind the diaphragm. The nerve is dorsal and internal to the vessel, and at the breaking plane lies almost upon the upper wall of the basi-ischium or second limb segment. A short distance proximal to its passage through the diaphragm the artery gives off about half a dozen small branches which run obliquely to the ventral wall of the limb, some passing through the epidermis to its outer side but running beneath the basement-membrane and the outer chitinous coating. Another set passes upwards, and is similarly distributed (fig. 3). Immediately after autotomy the crab extends the stump, and the diaphragm, now laid bare, faces dorsally. This condition lasts for forty- eight hours at most, and is caused by continued contraction of the extensor muscle of the basi-ischium. No blood is lost through the foramen, and this is probably accounted for by the fact that the part of the artery distal to the branches mentioned above is occluded. The diaphragm then bulges slightly, and in a period of weeks or days, according to circumstances mentioned below, a papilla or limb-bud grows out from it. The conditions immediately behind the diaphragm a few minutes after autotomy have been deduced from serial sections of the parts. The artery retracts and its torn end dilates, forming a little aneurism filled with plasma and lined with blood cells (fig. 3). The nerve also retracts slightly and the funnel- like flaps of the diaphragm are forced out over it owing to the great decrease of pressure on the outer side of the membrane. Meeting together, the flaps at once stop bleeding (fig. 4). The capillary branches running from the artery to the epidermis at once become dilated. Blood is extravasated from some into the dermis, and this, forcing the diaphragm outwards at various points, helps the action of the general venous pressure in closing the valve. A most im- portant point at this stage is seen in the extravasation of blood on the outer side of the epidermis. This causes the single layer of columnar cells to be detached at its ends and to curve inwards on the surface of the limb- stump beneath the diaphragm. The regenerative process now begins by the proliferation of cells of this layer from its free edges (fig. 5). 2. Pa'pilla Formation. — By the fifth day a single sheet of cells has grown from the edges, and this approaches the foramen from all sides (fig. 6). Before this layer is complete, however, it is of great interest to find that provision is already being made for subsequent accidents by the 85 1914-15.] Regeneration of the Legs of Decapods. formation of a new valvular diaphragm exactly the same in type and origin as that which has so recently saved the blood of the animal, and which now, with disintegrating blood corpuscles adhering to it, is still covering the new proliferating layer. Epiderm cells at the edge of the stump are sending processes across the limb-cavity which fuse. Only a few nuclei are seen, and the whole mass is plicated as if allowance were being made for expansion. On the twelfth day this new diaphragm is almost completely formed. It then consists of a wavy band of clear material with a definite outer and inner border. From the ventral side of the limb it arises from epiderm cells there, and passes upwards towards the nerve. Reaching this structure it turns inward along its course and takes part in the funnel formation before mentioned. On the dorsal side the cell processes do not run down to the nerve, but form a layer covering the more central epiderm of the stump, and thus running parallel to but at some distance from the nerve, form the upper part of the funnel (fig. 7). The functional significance of this layer will be discussed later. It is perhaps of importance to note at this point that a new diaphragm, the possession of which is necessary for the continued safety of the crab, is the first structure to be laid down. Haseman (10), writing on direction of differentiation in regenerating appendages of crustaceans, maintains that in the cheliped of the hermit crab the distal portion is the first to be laid down and differentiated. He says that since the claw portion is the most important part of the leg, it is probably on this account that it is re-formed first in the new appendage. The observations made were macroscopic only, and therefore Haseman has come to a conclusion which the facts at present stated refute. The cheliped of the hermit crab, like the other legs, is differentiated from the base outwards, and the process begins at the new diaphragm. When the single layer of epidermis proliferated over the stump is com- plete, there is a virtual cavity formed between it and the new diaphragm. Into this the nerve and blood-vessel are destined to pass, and within it also new muscle will be laid down. No cells come into the cavity except those of the blood, and all the tissues for the new limb are derived from the epidermis lining the space on the distal side. The old diaphragm, which has performed its work and is shrivelled and brown, now peels off, leaving bare the newly formed layer of cells across the stump. These are seen to have preserved at least this part of their original functional activity that they secrete a thin layer of chitin on their outer edges. Soon the layer thus laid over the cut end of the limb-stump is several cells thick, and 86 Proceedings of the Royal Society of Edinburgh. [Sess. mitotic figures are present. The thickening is most marked in the centre, and it presents the appearance of a raised disc. By the twelfth day the cavity between the new diaphragm and the layer proliferated across the stump has changed its character. It is now dilated and the outer layer is bulging (fig. 8). The inside of the hemisphere so formed is invariably found after fixation filled with clear coagulated plasma. At the upper free border of the ventral flap of the diaphragm the nerve is found to be growing into the cavity, as is also the artery, though it may be here mentioned that the latter passes in at a later date than the former. The nerve, which from the beginning had its end in contact with the central part of the new stump-membrane, retains itself in this condition, and as the cavity increases in length it proliferates, sending out cell-chains which run in various directions. Some form a lining on the inside of the new epidermis, and others pass directly into the extreme tip of the new papilla, which is now the main centre of growth. Reed (6) holds that cells bud off from the main ectoderm and, passing to the free nerve-end, are added on to it, and in this way the nerve increases in length and comes to lie in the cavity. I am unable to agree with this, however, and from my observations am convinced that the nerve follows by its cell-chains the centre of proliferation with which it is always in contact. Further evidence is that any injury to the papilla, either by cutting or puncturing, is always responded to by violent movement on the part of the crab. This would indicate that in its new member sensory innervation seems to be as complete as in the other legs. Such a condition exists from the beginning of growth, and cannot therefore be explained by a secondary junction, as Reed seeks to prove. At the centre of proliferation at the tip of the papilla, mitotic figures can be seen scattered along the outer parts of the cavity wall, and they are most abundant at the tip. Here proliferation of two kinds occurs. Many cells remain in the wall after division, and take up their places as part of the epidermis. Others are seen in little groups or nests of five or six. These groups pass into the cavity free from the walls and come to lie in masses (fig. 9). The pink-staining cytoplasm of each group becomes collected in the centre, and fusion of the cells seems to take place, the nuclei lying on the outside edge of the mass. As the growing point recedes from the base, these cell-masses are deposited across the cavity, and later become differ- entiated into muscular tissue. By the twentieth day (in crabs inhabiting ordinary periwinkle shells) constrictions can be seen on the outer side of the papilla, and the segmented form thus presented imitates, in a way, the normal limb. Microscopic 87 1914-15.] Eegeneration of the Legs of Decapods. examination shows that the following changes are taking place ; — At certain points an invagination of epidermis appears. The outer cells continue to secrete chitin, and so a plate is formed down the middle of the invagination. This splits and a constriction appears on the outer side. At the extreme tip of the invagination a double row of cells can often be seen pushing into the muscle-masses. These cells also form a chitinous plate between them, and so the large tendon is formed. This plate is attached at the point of constriction, and in the fully formed leg comes to be placed at the end of the synovial membrane of the joint, into which the constricted part of the papilla develops. Thus the papilla increases in length, and at the full period of its growth (which varies with the age of the crab) it is only about one-fifth of the size it assumes immediately after moulting takes place. All the parts are laid down compactly, and the epidermis is several cells thick. The muscle- masses have developed into fibres, and the nerve is connected with each one of these. A few words may be said here on the muscle-differentiation, but these must necessarily be brief, as the subject is one which will receive special treatment in a later publication. The cell-nests mentioned above come together and form a plasmodial mass. The large nuclei then form up into parallel lines with cytoplasm between each pair. Very soon this material shows longitudinal striation, and later it takes the appearance of a bundle of hyaline tubes running between rows of nuclei (fig. 10). In mature papillm these tubes show cross striation, and a Dobie’s line is visible between the dim bands (fig. 11). They may now be identified with the fibrillse of the adult muscle. In transverse section a ring of nuclei is seen to enclose the bundle of fibrillse, but the outstanding difference between this young muscle fibre and the normal one is the absence of interstitial substance or sarcoplasm. A net- work of connective tissue fits loosely round the whole, and this represents the sarcolemma. Its origin can also be traced to the epidermis (fig. 12). To summarise, the appearances of papillae immediately before moulting are as follows : — In the lobster papilla, which may be regarded as the least perfected one, the miniature limb is straight and is almost a proportionate model of the normal appendage. It has no functional activity, no calcareous coating like the rest of the shell, and is covered by a thin layer of chitin. On section it shows an epidermis beneath the chitin coat, composed of several layers of cells. Nerve and vessel are present, and these pass to the muscle- masses. Muscle fibril! 96 are striated and enclosed in bundles 88 Proceedings of the Royal Society of Edinburgh. [Sess. by a layer of muscle-corpuscles. Outside these is a sarcolemma of connective tissue with few nuclei. Everything is compact, and there is very little space left within the papilla. The hermit crab has a papilla which, on maturing, is found to be curved. It is smaller in proportion to the post-exuviate size than that of the lobster, but the epidermis and muscle present the same appearances, being several cells thick, and striated, respectively. In the crab, papilla formation is most perfect, and in the case of walking legs the new member is folded on itself three times inside a tough, chitinous envelope. The epidermis, again, is composed of several layers of cells, and the muscle-fibres in it are striated like those in the normal leg, with Dobie’s lines visible. The outer wall of the papilla has pigment, but no calcareous deposit. 3. The Changes at Moulting. — I have only once seen the act of moulting taking place, and that was in the case of a shore crab. The process has been seen before in a large decapod (17), but no one has recorded a case of moulting in which a papilla enlarged to form a normal leg. The crab was fixed within ten minutes (fig. 16), and shows the shell with its empty papilla-envelopes, and the new legs on the crab itself. The carapace split along its posterior margin, and one after another the legs were withdrawn. What surprised me very much was that the new legs were drawn out of the old shell exactly as they are in the photograph, i.e. about normal size. There was no gradual swelling or blowing out. Whereas the other legs were velvety to the touch, normally pigmented, and functional, the new ones were pale in colour, waving about in the currents created by other limb- and body-movements, and absolutely devoid of spontaneous movement. I had previously considered, like other observers, that the great increase in size would take a few hours to occur, as I had not previously seen a crab nearer the actual moulting time than at most three hours, but my fortunate experience proved to me conclusively that increase is immediate. The examination of serial sections of the newly expanded limbs shows exactly what has happened. The epidermis is now composed of a single layer of columnar cells. Muscle-fibres are attached to this and stretched between the tendon-plates before mentioned and the wall of the limb. They are much thinner than those seen in a mature papilla, and the nuclei are not so plentifully scattered beneath the sarcolemma. In 89 1914-15.] Eegeneration of the Legs of Decapods. short, the fibres show signs of stretching. There is much plasma now present in spaces between the muscle-bundles, and this covers the larger part of the surface shown in section. The vessel and nerve, also much stretched, have the same relative positions as they had in the papilla, but the new diaphragm is changed. The upper flap, which before ran parallel to the epidermis of the stump, is now turned down towards the nerve, and its lower part forms a portion of the funnel-like sheath before mentioned. From these appearances we may conclude that the following has happened : — Release of the papilla from its envelope exposes a surface less resistant to the blood-pressure than that of any other part of the body. The result, of course, is that expansion of the epidermis takes place forthwith, and the layer previously several cells thick is now reduced to one cell in thickness. Another factor may help in the process, and this is the change taking place at the diaphragm. The dorsal free flap was seen before moulting to be lying parallel to the epidermis and leaving a considerable space for the return of venous blood between it and the nerve. When the papilla loses its tough envelope, the great difference in pressure between the blood within and the surrounding medium causes this part of the diaphragm to be forced against the nerve, so preventing the return of venous blood. The thick-walled artery, however, containing fluid at a still higher pressure, continues to pump its blood into the limb-cavity, and thus swelling out occurs till the much-folded epidermis has become sufficiently tense to raise the pressure within the new leg and cause partial opening of the valve, so establishing a return of the venous blood. This probably would only take a minute to happen, and this time corresponds with what is actually occupied in enlargement at the moult. To confirm the above I took a crab ready for moulting, with papillae fully formed. By careful dissection the envelope was removed without much damage to the epidermis, and at once the leg assumed the size in which it is found immediately after moulting. Discussioj^. In the above descriptive account several points are worthy of discussion. The first of these is the outward form of the papilla. The formation of a papilla is itself a beautiful adaptation to the requirements of these higher decapods. In other animal groups where regeneration of the appendages or parts of the body takes place, the growth is graded in time till a more or less complete part is formed. Examples of such a process are seen in the regenerating ray of a starfish or in larval 90 Proceedings of the Royal Society of Edinburgh. [Sess. amphibians replacing a lost leg. The typical decapods selected for the present work would be handicapped by such a limb, and the fact that they can lay a leg down in miniature and expand it only when it is practically ready for use must be a considerable advantage to them. The papilla, too, has very complete sensory innervation, and this must provide for its careful protection by the crab. It is devoid of the calcareous coating which covers other parts of the body, and so is able to increase in size, unlike the animal as a whole. Even as the form of this miniature limb suits the general requirements of these decapods, so is the form of the papilla itself modified to meet the needs of each species. The lobster in nature is practically always under water. When removed from its element its straight papillae droop and tumble about like paralysed limbs (fig. 16) ; below water they stand out under cover of the other legs and seem to be perfectly well supported by their own rigidity. The shore crab, on the other hand, is usually living in air half its time. In it the papilla is compactly rolled up within a tough envelope, and quite firm in air or water. The hermit crab is intermediate between the other two forms both in its life-habits and in the shape of its papillae. The perfection of papilla formation also varies directly as the frequency of injury. In the shore crab 50 per cent, of individuals are regenerating in the spring of the year, whereas in the lobster regeneration of limbs is only found to the extent of 2 per cent, or 3 per cent. The second point of note in the regenerative process is that it goes on at the expense of the body, and, as was the case with my experiments on Eupagurus, in the entire absence of food. This is very like what happens in the growth of a malignant tumour in the higher animals, and I have often seen the analogy carried so far that the crab dies when the process has been completed. This points to an influence in the cells them- selves towards multiplication, rather than to a local nutritional stimulus to division, as many have sought to prove. The experiments also show, as those of previous workers have shown, that the rate of regeneration decreases as the animal becomes older. In short, it is dependent on the frequency of moulting, which decreases with age, and it is most marked in the period leading up to moulting. Thirdly, the problems connected with the advent of function in the new muscles have yet to be attacked. It may be here noted, however, that though the fibrillse of the new fibre are anatomically complete, function does not come till several days after moulting has occurred. Its first appearance is seen in rhythmic movements of the limb, as if only a few of the stimuli per second passing down the nerve actually caused muscular 91 1914-15.] Regeneration of the Legs of Decapods. contraction. The presence of abundant sarcoplasm is also lacking in the new fibres. It is hoped that by microchemical and other methods some light may be thrown on this phenomenon and on the very much broader problem of the intimate nature of muscle-contraction. Summary. (1) Homarus vulgaris, Engyagurns hernhardus, and Carcinus moenas all form limb-buds or papillse in the process of limb regeneration. These are covered by a chitinous envelope, and the observations here recorded show that their outer form and size are adaptations to the requirements of the animal. That of the lobster is straight, that of the hermit crab curved, while the shore crab has a papilla which may be folded on itself three times inside the envelope. (2) Valvular action of the diaphragm at the breaking plane plays a greater part in the stopping of haemorrhage after self-amputation than clotting, and the dilatation of small vessels which pass beneath the epidermis detaches a layer of cells. This layer of epidermis proliferates from its free edges to form the new limb. (3) A new diaphragm is the first structure laid down, and differentiation takes place from the base outwards. Muscle arises at the growing tip from cells proliferated from the old epidermis (an ectodermal structure), and the nerve grows outwards from the torn end by cell proliferation. (4) Muscle-fibres are anatomically complete immediately before moult- ing. The fibrillse are cross-striated and enclosed in a sarcolemrna, but full functional activity does not come till several days after moulting, beginning with slow rhythmic movements. Sarcoplasm seems to be less plentiful than in the normal fibre. (5) When moulting occurs the papilla is at once expanded to several times its previous size by valvular action, and the epidermis, previously composed of several layers of cells, now thins to a single layer, as is seen in the normal limb. The expenses of this research were defrayed by a grant from the Carnegie Trust. 92 Proceedings of the Royal Society of Edinburgh. [Sess. BIBLIOGRAPHY. (1) Reaumur, “ Sur les di verses reproductions qui se font dans les ecrevisses, les omars, les crabes, etc., et entre autres sur celles de leurs jambes et de leurs ecailles,” Mem. de VAcad. Roy. des Sc., 1712. (2) Herrick, F. H., “The American Lobster,” U.S. Fish Commission, 1895. (3) Chantran, “Experiences sur la regeneration des yeux cliez les ecrevisses,” Gompt. rendu, Ixxvii. (4) Morgan, T. H., “ Regeneration and Liability to Injury,” Zool. Bull., i, 1898. Morgan, T. H., “Further Experiments on Regeneration of the Appendages of the Hermit Crab,” Anat. Anz., xvii, 1900. Morgan, T. H., Regeneration, The Macmillan Co., 1901. (5) Steele, M. L, “Regeneration of Crayfish Appendages,” University of Missouri Studies, Yo. 4, 1904. (6) Reed, M. A., “ Regeneration of the First Leg of the Crayfish,” Arch./. Entio., T. xviii, 1904. (7) Emmel, V. E., “ Dififerentiation of Tissues in the Regenerating Crustacean Limb,” Amer. Jour. Anat., vol. x, 1910. (8) OsT, J., “Zur Kenntnis der Regeneration der Extremitaten bei den Arthropoden,” Arch. f. Entw., T. xxii, 1906. (9) Zbleny, C., “The Direction of Differentiation in Development,” Arch, f, Entw., T. xxiii, 1907. (10) Haseman, J. D., “Direction of Differentiation in Development,” /. Entw., T. xxiv, 1907. (11) CooDSiR, H. D. S., “A Short Account of the Mode of Reproduction of Lost Parts in the Crustacea,” Ann. Mag. Nat. Hist., xiii, 1844. (12) Brooks, G., “Notes on the Reproduction of Lost Parts in the Lobster {Homarus vulgaris),’’^ Proc. Roy. Physical Soc., Edin., cxvi, 1887. (13) Frederique, L., “Nouvelles recherches sur Tautotomie chez le crabe,” Archives de Biol., t. xii, 1892. (14) Pearson, J., L.M.B.G. Alemoir on Cancer, 1907. (15) Tait, j., “Types of Crustacean Blood Coagulation,” Jour. M.B.A., vol. ix. No. 2. (16) ViTZOU, A. N., “Recherches sur la structure et la formation des teguments chez les crustaces decapodes,” Arch, de Zool. exper. et general, t. x, 1882. (17) Taylor, J. A., “The Casting or Moulting of the Lobster,” Report of N ortlvamJerland Sea Fisheries Committee, 1911. 1914-15.] Regeneration of the Legs of Decapods. 93 DESCRIPTION OF PLATES. Plate I. Fig. 1, Longitudinal section through the region of the breaking plane of the hermit crab’s leg, photo, x 50 diars., showing how the diaphragm stretches across the limb cavity before autotomy. This section is not through the region of the foramen, and therefore the diaphragm stretches completely from epidermis of one side to epidermis of the other. Diaphragm formed by the union of cell processes from the epidermis of either side {d). Cells of the epidermis with processes running into the limb cavity (e). Chitinous and calcified layers outside the epidermis (c). Fig. 2. Longitudinal section through basi-ischium of normal limb at the region of the breaking plane, photo, x 50 diars., showing the lower flap of diaphragm {d) passing upwards to the nerve {n) and turning inwards along its course, forming a sheath or funnel (/). Fig. 3. Longitudinal section through the limb-stump of a hermit crab two minutes after autotomy, photo, x 66 diars., showing anatomy of structures behind the diaphragm {d). Retracted artery dilated with blood serum {a). Extravasated blood behind the diaphragm (h). Branch in longitudinal section showing bifurca- tion (h Is). Smaller branches, cut obliquely {h os). The same in transverse section now at the region of the epidermis (e), and passing beneath it {h ts). Fig. 4. Longitudinal section of limb-stump fifteen minutes after autotomy, X 66 diars. The nerve (n) has now retracted from the funnel which it occupied. The flaps of diaphragm (/' and /") forming this, are forced together at (v) by extravasation of blood (5), from the artery, and by disturbance of the balance of pressure in the region of the diaphragm. This valvular mechanism prevents loss of blood when autotomy occurs. Plate II. Fig. 5. Longitudinal section of limb-stump fifteen minutes after autotomy, from the same series as section in fig. 4, x 66 diars. The pressure in branches from the artery shown in fig. 3 (6 ts) has been raised, and blood is extravasated outside the epidermis (b), and beneath the chitinous and calcified layers {i). The epidermis (e) is now hanging free in the cavity of the stump, and the end of the layer thus freed grows over the stump. Fig. 6. Longitudinal section through a limb-stump five days after autotomy, X 50 diars., showing the beginning of regeneration. The free layer of epidermis (fig. 5, e), has sent out a chain of cells from either side (P and 1"). These are beneath the old diaphragm (d), and the crust of blood-clot formed outside it. Fig. 7. Longitudinal section through limb-stump twelve days after autotomy, X 66 diars. The new layer (1) is now complete, and the old shrivelled diaphragm (d) is seen outside it ready to be cast off. (d') is the upper flap of the new diaphragm growing backwards, parallel to the epidermis. The lower flap (d") grows upwards to the nerve which is not seen in this section, and forms the new nerve foramen (nf). A virtual limb-cavity (yc) is thus formed between the layer of cells (1) and the new diaphragm, and this expands gradually to form the hollow papilla. 94 Proceedings of the Eoyal Society of Edinburgh. [Sess. Fig. 8. Section cut longitudinally through a young papilla of about fourteen days’ growth, X 50 diars. The cavity (vc) has increased, and the nerve {n) is seen sending out fibres to the growing tip {gt). An invagination of the outer chitinous coat at {{) shows the beginning of segmentation and tendon formation. Plate III. Fig. 9. Longitudinal section of a papilla of about three weeks’ growth, x 50 diars. Segmentation is now advanced, and constrictions (c' and e”) represent the joints of the future limb. Cells budded off from the epidermis at the growing tip have come to lie within the cavity as muscle-masses (mm), and the nerve is seen running upwards {n). Fig. 10. Section through muscle-mass, showing embryonic fibres in longitudinal section, x 300 diars. The nuclei of cells of the muscle-masses have lined up outside the fused cytoplasm (n), and longitudinal striation indicates the formation of fibrillse {fih). {t) is the tendon of attachment for the new fibres. Fig. 11. This photograph is one of the same field as fig. 10, but the focus is altered to show cross striation in the young fibrillm (/). Fig. 12. Transverse section through a fully developed muscle-mass, x 300 diars. The new muscle-fibres, cut transversely, show nuclei outside {n), and fibrillae as dots within them (/). The loose investment of connective tissue, which, after moulting, fits tightly round the fibres, represents the new sarcolemma (sar). It will be noticed that it has no nuclei. Plate IV. Fig. 13. The lobster in this photograph autotomised its right cheliped and two first walking legs on 16th April 1914. By the middle of August of the same year it presented the appearance shown in the photo ; i.e. papillae had grown out from the bases of the lost legs. These are marked {jp), (p), and (p"). Fig. 14. This photograph represents the appearance of the same lobster as that shown in fig. 13, immediately after it had moulted (1st September 1914). (ch), (wlr), and (ivll), are the regenerated appendages expanded from the papillae (^), (p), (p"), respectively, in fig. 13. Fig. 15. These outline drawings represent in life size the lost cheliped and the regenerations of the lobster shown in figs. 13 and 14. (P) is the papilla, (R) the regenerated limb after moulting, and (N) the lost limb. Fig. 16. These photographs show the shore crab with its empty shell referred to in part third of the observations. In A, the shell, pieces of black paper have been placed behind the empty papillae-envelopes. The latter are marked (a), (b), (c), and (d). When moulting occurred the papillae were immediately expanded, and {a'), {b'), (c ), and (d') in B are the new limbs thus formed. (Issued separately April 6, 1915.) Proc. Roy. Soc. Edin. Legs of Decapod Crustacea Vol. XXXV. Plate I. 1. J Herbert Paul M'Farlane ^ErsWue. Lith Edin Vo!. XXXV. Proc. Roy. Soc. Edin. Lp:gs of Decapod Crustacea — Plate II. i Vol. XXXV. Proc. Roy. Soc. Edin. ]jEgs of Decapod Crustacea — Plate III. / Sar J Herbert Paul MTarlane &.Erskine L;th E8in. Vo!. XXXV. Proc. Roy. Soc. Edin. Legs of Decapod Crustacea — Plate IV. J- Herbert Paul. 15. M'Farlane S-Erskiue. Lith Edin, 191 4-15. J Resistance to Motion of a Body in a Fluid. 95 IX. — On the Resistance experienced by a Body moving in a Fluid. By H. Levy, M.A., B.Sc., 1851 Exhibition Research Scholar of the University of Edinburgh. Communicated by The General Secretary. (MS. received January 11, 1915. Read March 1, 1915.) A NECESSARY condition in any hydrodynamical problem is that the pressure exerted by the fluid at any point must always be positive, and be given by p = c-pvy2 (1) C being a constant determined by the boundary conditions of the problem, V the velocity, and p the density of the fluid, provided there are no external forces involved. Should the velocity at any point, however, be so great that the expression C — pf^/2 becomes negative, the problem in this respect at least loses its validity as an approximation to actual fact. Now it can easily be shown that, in any form of potential streaming about a body with sharp edges, the velocity at the sharp edges becomes infinite, and the pressure therefore negative. The equations of motion of the fluid having been obtained on the assumption of continuity of motion, this suggests at once that some form of discontinuity of the fluid probably exists near the sharp edges.'* The assumption adopted f has therefore been to suppose that from each of the sharp edges of the moving body AB (fig. 1), a surface AC and BD divides the fluid into two separate and distinct regions, the shaded portion representing a region of constant pressure, known as the “ dead water.” The pressures being constant along the stream lines AC and BD, it follows from equation (1) that the velocity must also be constant there. It is assumed that the motion is steady. How it arose does not concern us for the moment. In the case where the rigid boundaries are straight, all the circumstances of the motion may be derived with comparative ease by methods of conformal representation.^ For the mere construction of such problems, however, we can reverse * Enunciated by Stokes, “ On the Critical Values of the Sums of Periodic Series,” Trans. Carnb. Phil. Soc., vol. viii. t Helmholtz, “Uber diskontinuierliche Eliissigkeitsbewegungen,” Berlin. Monatsherichte, 1868. i E.g. Lamb’s Hydrodynamics, p. 86. 96 Proceedings of the Eoyal Society of Edinburgh. [Sess. the process and find the fluid motion which has a given free surface, that is to say, a given surface along which the pressure and velocity are constant. We proceed as follows ; — z = x + iy ....... (2) m = j ds(cos 0 + i sin 0) = jdsd^ . . , . . . . (4) c If the constant in (1) be made Po~\-p/^, where is the constant pressure along the free stream line, we may write the velocity = 1 ds (5) .'. (p = s ii (p = 0 when s = 0. Hence, if ^ = 0 be the free stream line whose intrinsic equation is F(6‘, d) = 0, we have merely to substitute for s. It follows, therefore, that z = jdtvd® (6) ®) = 0 (7) where w = (j) -\- iyfr , and @ = complex parameter, represents a fluid motion with E(s, 0) = 0 as the equation to the free surface. Any one of the other stream lines may then be taken as one of the rigid boundaries. Some very interesting problems of the motion of a fluid against a fixed obstacle 97 1914-15.] Resistance to Motion of a Body in a Fluid. can then be constructed by choosing as the fixed boundary that one at a point on which the modulus of is zero, that is to say, where ctz the velocity is zero, so that the stream divides at this point. Against the kind of motion we have here supposed to exist, and to remain steady, may be levelled some very serious criticisms. A free surface is equivalent to a vortex sheet, and is therefore essentially unstable. As a result of any slight disturbance, it tends to roll itself up at points and finally to break up into a series of isolated vortices (fig. 2). There is another objection. Behind the moving body an infinite mass of dead water is dragged, a state of affairs with no counterpart whatsoever in actual fact. The pressure in this dead-water region being constant, we have also lacking the suction effect which is so noticeable behind a body in motion. As a result, the expression for the resistance, calculated on the foregoing assumptions, does not agree at all closely with measurements obtained. In a paper ^ by Lord Kelvin on the formation of coreless vortices by the motion of a solid through an inviscid incompressible fluid, a suggestion was thrown out which Von Karman f has made the basis of a theory of the motion of a body through a fluid in the case of vanishingly small viscosity. Suppose the body, a cylinder, has been in steady motion from * Proc. Roy. Soc., Feb. 3, 1887 ; Phil. Mag., xxiii, 1887, p. 255 ; Math, and Phys. Papers, vol. iv, p. 149. t “ Fliissigkeits und Luftwiderstand,” Phys. Zeitschrift, xiii, 1912. VOL. XXXV. 7 98 Proceedings of the Koyal Society of Edinburgh. [Sess. an infinite distance, Von Karman suggests that the solution of the problem lies in determining the stable arrangement of the rectilinear vortices set up behind the body in rows extending off to infinity. For our purpose it will be sufficient to admit the motion of a system of vortices as stable, if, when they are slightly displaced from their positions of steady motion, the displacements do not increase indefinitely with the time. If the original displacements be preserved, then the arrangement has neutral stability.^' As a first condition the motion of the vortices must be steady, and if there is no arrangement in which the vortices set up behind the body can move forward steadily, then there can be no possible steady motion of the body. For example, by simple considerations it can easily Fig. 3. be seen that no odd number of rows of an infinite number of vortices can move forward parallel to their length so as always to retain the same geometrical arrangement. There cannot, therefore, be any steady motion of a body having such a shape as to throw off an odd number of rows of vortices. In the same way there is no steady motion of four infinite rows of vortices, so that, on Von Karman’s theory, there could not be any steady motion of two cylinders moving along parallel lines, or of a cylinder moving parallel to a plane (see fig. 3), the two cylinders being sucked together in the former case, and in the latter, the cylinder being sucked into the plane. Cylinder in an Infinite Fluid. The simplest but at the same time the most searching problem of this nature is that of the steady rectilinear motion of a cylinder in an infinite * For a more rigorous definition of stability, see one given by Prof. Love in Proc. London Math. Soc., xxxiii, p. 325 (1901). 99 1914-15.] Resistance to Motion of a Body in a Fluid. fluid. The body in its motion continually throws off vortices along two lines trailing behind it, parallel to the direction of motion, and our problem is to determine the arrangement giving both steady and stable motion of the vortices. I propose to discuss the stability of the vortices at a great distance behind the moving body, so that, instead of dealing with two semi- infinite rows, we may, following Von Karman, suppose the vortices extend to infinity in both directions, and our problem reduces to discussing the stability of two infinite rows of vortices. There are evidently only two possible arrangements such that the vortices move forward steadily, (a) and (b) (see fig. 4). (ou) f -- (-&) 5 J7 P ■ ^ - Fig. 4. That (a) is probably an unstable arrangement is indicated a priori from the fact that, if we increase the distance between a pair, all the vortices behind will at once tend to shrink and shoot through those in front. A simple proof may, however, easily be given as follows : — Suppose the origin of co-ordinates be so chosen that the vortices are situated at the points {^l , and where ^ and q are all integers between -1- oo and — oo , and suppose the vortex g = 0 is displaced to the point ^^0 , ^ -f 71^ where and are small. If -f f and — f be the strengths of the vortices in the first and second rows respectively, the component velocities of the displaced vortex are given by 100 Proceedings of the Royal Society of Edinburgh. [Sess. h_ fh , \ h {h ^ \ 2 + 00 "2“l2 + ’'d 27T _ ^ C ~ - ^o)‘^ + V ^j(p^ - 4)^ + (^ + Vo)^ -00 +00 -00 = Z / - Ho + 00 -GO + Z 2M^qP + ^ h2_p2l2 (7^2 + pH^f ^ // 1 V 1 + ^2^2 + _^(;,2 + ^2^2;>2j ’ (8) on neglecting terms of the second order in and and equating P to zero. In the same way - —V. 7T 1^, = Z' -2, Pl-io + CO 2 00 r+oo 1+A qrqV\ ^ r t ^ ~ 2az»7jp n ~ “ ^"(FTioW “ (F++W J L/j2 + J)2/2 ’«(7i2 H- y2;2)2 (/j2 ^ y2;2)2 = fo /I -pH-i (9) If the whole fluid be given a velocity ^ 772 ^2 parallel to X in the negative direction, we may omit that term in equation (8), and substituting di. d and for and respectively, these equations become dt dt where and 0 s 1 11 5S; 1"^ . ■ (10) ^ Ao = aA . . , ( dt • (11) ' 1 W"" -t- p’-'>f I— 1 d% o?i\ *2“4^2fo- , . (13) dt^ ^ 4+^" ■ • (14) Since a cannot vanish,^ these equations imply that no matter what relations exist between h and I, and tend to increase exponentially * From equations (66) and (70) in Appendix it is easily found that a= — ^ Z2 sinh2 101 1914-15.] Resistance to Motion of a Body in a Fluid. with the time, and therefore, according to our criterion for stability, such an arrangement of vortices is unstable. Following immediately upon the displacement of g = 0, of course, the remaining vortices in the two rows proceed to displace themselves also from their positions of steady motion, and react slightly differently upon the motion of the vortex q = 0. But these disturbances and consequent reactions are evidently all of the second order at least, and therefore need not be considered in comparison with first order quantities. As a mere proof of instability, the displacement of a single vortex from its steady position is evidently a sufficient test, but in the case of a stable arrangement the disturbance would require to be perfectly general. If there is a stable distribution of two infinite rows of vortices — and it is not a priori evident that there must be — it must be the arrangement (5), fig. 4. Von Karman asserts that this is so. Taking the origin of co-ordinates (see fig. 5) midway between the vortices p = 0 and q — 0 when in the position of steady motion, suppose the vortices are each given small displacements to the q^^^ vortex on the one row, and {^pr]p) to the on the other row. The co-ordinates of the vortices at time t = 0 will then be given by ^q~ 9.^ — + pi h h 2+"^^ lip We proceed to consider the motion of the vortices ^ = 0, p = 0, whose co-ordinates we call ' I , h Vo - 2 . r I p 4 + = h , and 102 Proceedings of the Poyal Society of Edinburgh, and component velocities respectively. [Sess. and (Vo) 27T _1 + 00 - V yf 7^(+- ■^(y + {yp- -y,r 27T , 1 O / -V' Vq - Vo + 00 Vp - ?/o' + (x„ -00 ' ® — XqY + [t/q -y,y 7^(+- -y,'r + 00 — v' Xq - Xq + 00 V 0 |isj» 1 ^ (^3 -00 ^ 2 — XqY+ {Uq ■ -Vaf - ^af + (%. - y^f (15) (16) (17) (18) Inserting the values for , Xq , , etc., in these equations, and neglecting terms of higher order than the first in the ^’s and /;’s, we obtain + y“o=2/l 5 + 2g- 1 % ^[^2(j_i)2 + /,2p +2.% ,,, V + V - - 2/ - ^ [^^(2 - 4)'^ + ^ \n'i - hf + ^>^] ^ **0 ~ fc + 00 72/ P(g-i)ii-;>^ -« j,2Z2 + “ _ 1)2 _ ;j2 %n 00 +00 (19) 1 -00 nq-hf-h^ (3g-l)^, (20) 2:r A 4“" + + + '^0 +co,yi _ Z.rpri, + i^2 + ;,2i2 ^ z. ^[<2(^ + 1)2 + A2] + 00 z+ 4 f“^/2(j, + i)2 + /j2]2 ^[i2(^ + |)2+;,2]2 .00 L ■ z,/ J _oo ^2^2 _ (p + 4)+-A^ 4(2/>+l) 1X272 J. 7.212 “Z. -CO + GO [(p + J)2p + ft2]2 [(p + 1)2^2 + /,2J: (21) 7?p(2j>+l) f; + » <;2(j, + J))2_;j2 ^P^(P + 4>+/<^? + 00 ,^3 7+.-1 • (22) 00 g2^2 J The whole system of vortices when in their position of steady motion moves forward with a velocity h :^Z2(jP + 1)2 + /72 . (23) 103 1914-15.] Resistance to Motion of a Body in a Fluid, as is easily seen by putting ~ iq ~ Vp ~ V7 ~ We will suppose that the axes of co-ordinates move with the system, so that we may write for u. and w/ , and ^ , for r. and v' , ^ and — ‘'0 > dt ^0 ’ dt dt respectively, neglecting the above infinite series in the expressions for and . We have not as yet supposed the f s and ^’s connected by any definite law. If, however, we suppose & = Vp = V,^ (24) 4 = Vq = 'n(f^ (25) where P and Q are for the moment arbitrary functions of and q respect- ively, then the positions of the vortices will be assigned when we fix the functions P and Q, for all positive and negative integral values of and q. Equations (19) to (22) now become : — A%+B'f; + cv . . ■ ■ (26) • • (27) -|f= . . • • (28) • • (29) + ^ ■ ■ . (30) ^ W(p + i)^ + ^ • • (31) (2i^ + l)P ^WiP+hf+h-^Y ■ ■ ■ • • (32) (2g-l)Q ^[i^ci-w+n ■ ■ ■ . . (33) “ ^[PYp+w+h-^r ■ ■ ■ ■ . (34) . . (35) 104 Proceedings of the 'Royal Society of Edinburgh. [Sess. So far the only restriction that must be imposed upon P and Q is that for p = 0 q = 0, P = Q = 1 in order that ~ for q) = 0 and for ^ = 0. We may suppose, in order to solve equations (26) to (35), that rjq, t , rjQ increase with the time as where a = ~ • From (26) to (29) 27T the equation for X is obtained as -X -A -B' -C' -A -X -C' -B' -B C -X A' C B A' -X which, when expanded, becomes - A2(A2 + A'2 + 2BB' - 2CC') + A^A'^ + B^B'2 + C^C'^ + B2C'2 + B'2C2 - 2 AA'CC' - 2AA'BB' = 0 (37) The arrangement of vortices will be stable, provided that for arbitrarily assigned functions P and Q, and for some definite relation between h and I, all the values of \ obtained from equation (22) are either purely imaginary or else complex and such that does not increase indefinitely with the time. As a particular case, suppose that merely the vortex corresponding to y) = 0 is displaced, all the others being undisturbed. Q then is everywhere zero, and P also, except for p = 0. In this case hi 2 * B B' = 0 C = - + /i^ - - w W' C' = 0 The equation for X then becomes X4-2A2X2 + A4 = 0 X= + A twice . (38) (39) (40) (41) (42) (43) (44) A being real, it follows that this arrangement of vortices is also unstable for this disturbance unless A = 0 when the equilibrium is neutral. Now the two series in (38) when summed become Z2 cosh2 llTT ZP T . (45) 1914-15.] Eesistance to Motion of a Body in a Fluid. 105 and therefore for ^^ = cosh~^^3 (46) the equilibrium is neutral for this disturbance. Since the stable arrangement must be so for every displacement that can be given to it, condition (46) must necessarily be satisfied. We may therefore now proceed to impress other disturbances upon the vortices on this assumption. Suppose none of the vortices are displaced except the two corresponding to ^ = 0 and q = 0. P and Q are then zero except for these values of p and q, when they are both unity. In this case we find ■ • (47) • • (48) C--C'-- * . • (49) and equations (12) to (15) now become 27t _ ' ji n ' ■ • (BO) ^ ' 4- Br? ' ~ ^ dt~ • ■ • (51) 27t d^^ _ Cr) . (52) 2^ dvo p ( dt~ • . ■ (53) Hence ■■ 47t2^ ^ " 47tV^’^_^,2V • • (54) and similar equations for the other co-ordinates. Equation (54) shows at once that this arrangement of vortices with the relation ~ = = cosh ^ ^3 is stable for this special disturbance. Consider a slightly more general type of disturbance by assuming P cos (2/. + !)(/) cos • • (55) ^ cos (2g'+ l)<^' cos . (56) 106 Proceedings of the Royal Society of Edinburgh. [Sess. where (p and p' are for the moment quite arbitrary, except that they must not be chosen in the region of The various coefficients in equations (30) to (35) now reduce to _ 1)2 _ 7^2 /COS (2p +!)(/>- COS (/) ^ ~ir+ ^ ^ • A' = etc. B =0 = B' r = _ V i cos (2p + !)(/) ^ [l^(p + J)’^ + cos p (57) (58) and the equation for X becomes X4-X2(A2 + A'2-2CC') + A2A'2 + C2C'2-2AA'CC' = 0 . . (59) and therefore ±2A = A-A'± x/(A + A'}2_4C0' .... (60) Now . . , _ ^/COS (279 + 1)(^ _ ”^/COS (2^' - ~ p)H^ cos p ^ cfP cos p' ^ ^ cos 2pp ^ ^ cos 2qp' = - 7t) - P'{p' - 7t)] = + (^1)* It is evident that a first condition for stability must he that the real part in the expression for X, viz. A — A', must vanish, but this involves or p = p' p-\- p' = 7T (62) No matter, therefore, what relation exists between h and I, this arrange- ment is not stable for all disturbances of the type (55) and (56). Further, suppose the vortices in the g-row be not disturbed, so that Q = 0, and those in the y>-row be displaced in any arbitrary manner, then B' = C'-0 and the equation for X becomes X4-X2(A2+ A'2)+A2A'2 = 0 X= ± A ( X = ± A I (63) * See equation (67) in Appendix. 107 1914-15.] Resistance to Motion of a Body in a Fluid. Using the relation ^ = cosh~^ ^3 in (30) and (31), A and A' become V/2 -oo-^ + GO p a=2:A and therefore from (63) A' = 0 + 00 , p (64) and the motion is seen to be unstable for all disturbances given by P except those for which + CO p -CO for example when P is an odd function of p, in which case the equilibrium is neutral. By subjecting the system to a particularly simple disturbance we have found that j = cosh ^3 is a necessary condition for stability, but that even when this condition is satisfied the arrangement does not remain stable to more general types of disturbances. Contrary, therefore, to Von Karman’s conclusions, there is no com- pletely stable arrangement of the vortices created behind the moving body. They persist in the arrangement (h) for some time after creation and for a very short distance behind the moving body, but they finally break up and diffuse through the fluid as vorticity generally. This is no doubt the real explanation of the photographs taken by Von Karman and Rubach,^ showing the formation of half a dozen vortices in each row in arrangement (b) behind the moving body. The problem is evidently much more compli- cated than Von Karman’s theory suggests. It would seem that for a short distance behind the moving body a free surface is momentarily set up, but that in consequence of its instability it immediately breaks up and gives rise to the series of vortices. For a short time these persist, but finally they also break up as indicated, and the difficulties of the problem only commence. I desire to express my gratitude to Professor A. E. H. Love for his helpful and instructive criticism during the progress of this investigation. Appendix. In the foreofoing discussion the sums of certain Series which occurred o o were assumed to be known. These series may be simply and quickly summed in the following manner. * Phys. Zeitsch., Bd. xiii, 1912. 108 Proceedings of the Koyal Society of Edinburgh. [Sess. Expanding cosh a{x — ir) as a Fourier Series in the region 0<^r<27r, we easily obtain cosh a{x — 7t) = sinh air The limiting case where gives 00 2 -1 CO -1 1 ^ cos nx cos nx _{x- 7t)2 4 "6 • (65) • (66) + GO ••• 2 /cos {2n+ 1)(^ cos ^ + CO 2 cos (2n - 1)(^' 11^ cos 0' _t^/cos27^<^ ^^/cos2w(^' ^i^/sin 2w. Proc. Roy. Soc. Edin. Vol. XXXIV. Ellis: - Fossil Micro-organisms — Plate II. 5. X 250 7. X 250 8. X 400 M'Farlane ikErsIane. Ltth Edin. 1914-15. 1 Fossil Micro-organisms. 133 DESCRIPTION OF PLATES. Plate I. Fig. 1, X 800. Hyphse of Phycomycites Frodinghamii (Ellis). Photographed from section of Frodingham Ironstone. Hyphae were enclosed in fossilised organic fragments, and encrusted with ferric oxide. Frodingham Ironstone belongs to the upper part of the Lower Lias, a, Hypha. Fig. 2, X 250. Phycomycites Frodinghamii (Ellis). Interior of fossilised organic fragment in Frodingham Ironstone. Shows hyphse and also a good specimen of those irregular swellings that are characteristic of this organism, a, Swellings on hypha ; h, at this point a branch hypha arises ; c, hyphee scattered in matrix. Fig. 3, X 250. Phycomycites Frodinghamii (Ellis). Interior of fossilised organic fragment in Frodingham Ironstone, a, A sporangium-bearing hypha ; 6, mature sporangium ; c, young sporangium. Fig. 4, X 250. Two sporangia of Phycomycites Frodinghamii. Interior of fossilised organic fragment in Frodingham Ironstone. In the sporangium to the right in the figure, 6, a spore, a, is seen partially extended from the sporangium. The sporangium was evidently crushed during the process of preparation of the slide with the result that one of its four spores had become exposed. Plate II. Fig. 5, X 250. Section of calcareous oolitic stone from island of Raasay (N.W. Scotland). Shows fragment of organic remains which had been ravaged by the attacks of a fungus. Fungus is provisionally named Paleeomyces a. a, Hyphse ; h, remains of host. Fig. 6, X 27. Dunliath ferruginous limestone. a is an organic fragment which, unlike the neighbouring oolites, is only incompletely rounded. This fragment is full of the remains of a small micro-organism. For details see text. Organism is named Actinomyces a. Fig. 7. Dunliath ferruginous limestone. Shows the spot marked a in fig. 6 magnified 250 times, so as to render visible the hyphse of the micro-organism which has been named Actinomyces a. The hyphse are the small dark short lines which relieve the whiteness of the central part of the photograph. 1, Calcite matrix ; 2, remains of animal cells ; 3, other hyphse not further investigated. Fig. 8. Section of a nodule from the base of the Gault (Folkestone). x 400. In section the stone is seen to be cellular in composition, the cells being very minute. The walls of the cells are reddish brown, due to the large percentage of ferric oxide. The cavities of the cells are very minute and are in the majority of cases filled with air. In some, however, as in the plate shown, the cavity was filled with organic fragments. The bacteria are found in the latter, a, Walls; b, cavity filled with organic fragment. The rods pointing in all directions are the remains of the bacteria which lived in the organic remains. Organic fragments of all sizes are common throughout the nodule. {Issued separately April 27, 1915.) 134 Proceedings of the Royal Society of Edinburgh. [Sess. XI. — The Reaction between Sodamide and Hydrogen. By F. D. Miles, B.Sc., A.R.C.S. Communicated by Principal A. P. Laurie, D.Sc. (MS. received January 16, 1915. Read March 1, 1915.) In some experiments on sodamide carried out at 200°, in which an attempt was made to use hydrogen as an indifferent atmosphere, it was found that a slow but constant evolution of ammonia took place. The sodamide being isolated from the glass tube in which it was heated, by silver foil, the formation of ammonia could not be due to a reaction between the glass and the sodamide. Titherley, who investigated the alkali amides, noticed the use of hydrogen as an indifferent gas and concluded that it had no considerable action on sodamide at 300° C. He states : ‘‘ In one experiment a weighed quantity, 0'8791 gram, was prepared in a platinum-lined stopcock tube and heated at various temperatures during known intervals of time. The experiment was conducted at the ordinary pressure in an atmosphere of puriffed dry hydrogen. On keeping the amide at a temperature of 300- 350° for one hour, only 0'8 c.c. of gas was evolved, the sodamide remaining unchanged. Even when heated at 450° the decomposition was scarcely appreciable, gas being evolved extremely slowly, in an hour only 8T c.c. being given off* ; the gas consisted chieffy of ammonia, with a little hydrogen and nitrogen.”^ This small quantity of gas corresponds to a decomposition of only 0'09 per cent. Titherley explained its evolution by the volatilisation of sodamide on to the glass and the ensuing reaction. Preliminary experiments proved that if 0‘3 gram of sodamide were heated in a stream of pure hydrogen, 30 c.c. or more of ammonia could be obtained in an hour, even at 230°, and that a white crystalline deposit sublimed on to the cooler parts of the tube. On plunging the boat con- taining the sodamide into water a copious evolution took place of a gas which proved to be hydrogen. This result could be explained if sodamide decomposed on simple heating with formation of ammonia. Such an explanation was shown to be untenable by heating pure sodamide, obtained by a method to be described later, in a current of pure nitrogen at 250°. No ammonia was given off*. In addition, it has been shown by Titherley that the amide does not decompose * Trans. Ghem. Soc., 1897, vol. Ixv, p. 509. 1914-15.] The Eeaction between Sodamide and Hydrogen. 135 appreciably in a vacuous tube at temperatures between 200° and 300°.* It is therefore clear that hydrogen is not without action on sodamide, if the gas be passed continuously over the solid. Only one explanation of this fact seemed reasonable — that the sodamide was being converted into sodium hydride by the action of the hydrogen, according to the equation NaNHg + H2 = NaH + NH3. Since Moissan discovered that sodium, heated in hydrogen at 340°, forms the hydride, which is volatile at that temperature, and is, moreover, soluble in excess of the unchanged metal,f the explanation suggested became a probable one, and experiments were made to test it. At first it was attempted to employ the commercial sodamide ; but as this material always contains some sodium hydrate and cannot be trans- ferred from one vessel to another without reacting with atmospheric moisture, its use was abandoned. The small quantities of sodamide required were accordingly synthesised from pure sodium and pure ammonia. The loss of weight on heating each one of these samples in hydrogen was noted. It was then treated with water, and a measurement made of the hydrogen evolved. If formation of hydride has occurred, for every 1 5 ’02 grams which the sodamide loses in weight, 22’4 litres of hydrogen should be evolved, according to the equation NaH-f-H20 = .^W0-^H2 on treating the product with water. To deprive the amide of nitrogen completely was not found possible, but this is immaterial, since the pre- sence of unchangred sodamide does not affect either estimation. An attempt was made to estimate the ammonia given off on heating in hydrogen, and to compare its amount with that of the hydrogen evolved on adding water. Although one result obtained in this way is given, the method was abandoned. A large reacting mass of hydrogen is required and the absorption of the greatly diluted ammonia becomes very difficult. The reactions were carried out in a specially made glass tube, about ten inches in length, and three-quarters of an inch in bore. It was lined on the inside with a thick roll of silver foil. In order to allow of the in- sertion of a silver boat, a ground-in stopper was fitted to one end of the tube. Leading tubes with stopcocks were fitted to the stopper and to the unstoppered end of the tube. The tube containing the roll of foil and the boat could be heated in an air-bath, with the ends projecting, and could be suspended from the arm of a balance and weighed. * Loc. cit, p. 508. t Oomptes Rendus, 1902, vol. cxxxiv, p. 71. 136 Proceedings of the Eoyal Society of Edinburgh. [Sess. Pure hydrogen was made by the action of sodium hydroxide solution on aluminium foil, and was purified by passing over sulphuric acid and then over pieces of bright sodium. Ammonia was made by dropping the concen- trated aqueous solution on to sticks of sodium hydroxide, and was purified by passing over solid potassium hydroxide and then over clean sodium. In making an experiment the tube was filled with hydrogen and weighed. A piece of clean sodium, purified by melting under paraffin wax, and kept under light petroleum, was then quickly put into the boat, which was at once replaced in the tube. A current of hydrogen was then passed through, with gentle heating, to remove the petroleum. The tube was again weighed. The weight of sodium having been obtained, ammonia was allowed to ffow through, the tube being heated to 200°. The issuing hydrogen was collected in a Schiff nitrometer fflled with 20 per cent, hydrochloric acid. When hydrogen no longer came off, the tube was cooled, the ammonia was displaced by hydrogen, and the tube was weighed. The change in weight showed the conversion of the sodium to sodamide to be complete. The reaction tube was then heated and the pure hydrogen passed through it. A deposit of the finely crystalline hydride slowly appeared on the inside of the cool ends of the tube. After about one and a half hours the evolution of ammonia became very slow. At this stage, though it was evident that the reaction had affected only 25 per cent, or less of the sodamide, the tube was cooled, fflled with hydrogen, and weighed. In order to measure the hydrogen evolved by the action of water, the tube was evacuated by a Topler pump and connected by one of its leading tubes to a Hempel burette filled with dilute sulphuric acid. By dipping the other leading tube into a beaker of dilute acid and opening the stop- cock, acid was also drawn up into the reaction tube. The ammonia evolved was absorbed by the acid, and the hydrogen was drawn over into the burette and measured. The results are given below : — Tempera- ture. Weight of Sodium. Soda- mide formed. Sodamide calculated. Loss of weight in Hydrogen. Hydrogen evolved on action of water. Hydrogen calculated from loss of weight. Ammonia evolved on passing Hydrogen. 240°-250° • 341 gm. (from stock) 41 c.c. 44 c.c. 245°-250° •2676 gm. •4520 „ •4541 •0251 34-8 37-5 250”-260° •3010 „ •5085 „ •5108 •0376 57-2 56-1 245“-250° •2551 „ •4344 „ •4330 •0300 44-0 44-8 1914-15.] The Keaction between Sodamide and Hydrogen. 137 The last column but one gives the volumes of hydrogen which should be liberated on adding water. They are calculated from the loss of weight which occurs to the amide when it is heated in hydrogen, on the assumption that a loss of weight of 15 ‘02 grams will correspond to the evolution of a gram molecule of hydrogen. The last column but two gives the observed values. The agreement between the two series is in accord with the assumed reaction. It is notable that though the metallic amides have received considerable attention, no case of the conversion of a simple amide into a hydride has been noted. The amides and imide of lithium have been fully investigated by Dafert and Miklauz.^ The only reaction of any one ,of these sub- stances which resembles the present one, is that between lithium imide and hydrogen, at 450°. Trilithiurnamide is formed : — * 2H2 4- 3Li2NH = 2Li3NH2 + NH3. The same observers state that the formation of tribariumamide occurs when hydrogen is passed over barium nitride. This reaction is always accompanied by an evolution of nitrogen, and they suggest that the pro- duction of this gas is due to conversion of the tribariumamide into barium hydride,! according to the equation Ba3(NH2)2 + H2 = 3BaH2 + ^2. Summary. When sodamide is heated in a stream of hydrogen at temperatures between 200° and 300°, partial formation of sodium hydride occurs, ammonia being evolved. The equation NaNH2 -1- H2 = NaH -1- NH3 has been shown to hold. This conversion into a hydride has not been shown to occur in the case of any other simple metallic amide. * Dafert and Miklauz, Monatshefte, 1912, xxxiii, 66. t Ihid.^ 1913, xxxiv, 1708. Heriot-Watt College, Edinburgh. {Issued separately April 27, 1915.) 138 Proceedings of the Koyal Society of Edinburgh. [Sess. XII. — On the Electrical Conductivity of Aqueous Hydrochloric Acid, saturated with Sodium Chloride; and on a new form of Conductivity Cell. By F. D. Miles, B.Sc., A.R.C.S. Com- municated by Principal A. P. Laurie, D.Sc. (MS. received January 16, 1915. Read March 1, 1915.) The objects of this communication are to give the results of determinations of the electrical conductivity and composition of a range of aqueous solutions of hydrochloric acid saturated with sodium chloride at 18° C., and to describe a form of conductivity cell which has been found of great use for solutions which are saturated or contain a volatile solvent. The specific conductivity of the aqueous solution of any one of the strongly ionised mineral acids attains to and then decreases from a maximum, as the concentration is increased. From a study of the changes in electrical conductivity which accompany chemical changes in homo- geneous systems, the late Professor John Gibson was led to the general- isation that “ Homogeneous chemical systems which undergo change, either of themselves or under the influence of the electro-magnetic vibrations which we call Might,’ change so that their specific electrical conductivity is increased, unless when coerced in the opposite direction by stronger chemical affinities.” * In the communication referred to, several examples were noted of a ver}^ interesting type of system to which this general statement was found to apply. In these examples a relatively large mass of an aqueous solution of a mineral acid was the main constituent, and there was also present in each case a relatively small mass of some reagent which could undergo a chemical change either with the acid or with the water. It was found that the initiation and continuance of such a chemical change was de- termined by the concentration of the acid being greater or less than the concentration at which the conductivity of the solution was a maximum. An acid of lower concentration than this, tended, therefore, to become stronger, and vice versa, the system gaining in conductivity in each case. It is evident from these, and from other facts, that some change in the constitution of mineral acid solutions may reasonably be looked for, which, though not sharply coincident with the attainment of maximum conductivity, * Trans. Roy. Soc. Edin., xlviii, p. 130. 1914-15.] Conductivity of Salt- saturated Hydrochloric Acid. 189 is most clearly marked in the region of that point. Taking hydrochloric acid as an example, it is notable that “ maximal ” {circa 20 per cent.) acid is the least concentrated solution which has a marked odour and is not hygroscopic. It is also curious that the constant boiling mixture has at atmospheric pressure a concentration of 20 ’2 per cent. In view of these considerations, any observations on the attainment of maximum conductivity in solutions of strong electrolytes are of interest. The measurements to be described were made at the suggestion of the late Professor John Gibson, to ascertain where the maximum would occur in salt-saturated hydrochloric acid. The thermostat and electrical apparatus used were those described by J. and G. E. Gibson in these Proceedings.^ With these it was found possible to maintain the temperature constant to C. and to measure the conductivity with an accuracy much higher than the immediate purpose required. The hydrochloric acid and sodium chloride were Merck’s guaranteed reagents. The acid solutions were jipproximately adjusted to the strength required by means of a hydrometer and were put into stoppered bottles with a large excess of the pure salt. The stoppers were tied down and sealed with paraffin wax. After remaining for several days fixed to the revolving wheel of a thermostat kept at 18°, they were transferred to a submerged wire grating in the large thermostat already mentioned. The measurement of the conductivity of such solutions as these presents considerable difficulties. With the open form of cell, closed only by lids, or with a dipping electrode in a test-tube, any volatile constituent escapes — in this case the hydrogen chloride — and constant readings cannot be obtained. Also, in transferring the solution from the containing vessel to the cell, a pipette is usually necessary, and in the pipette a saturated solution is very apt to deposit the dissolved substance. Even if this does not occur, change of concentration from the same cause or by evaporation will probably occur while the cell is being washed out with the solution. After several attempts to secure concordant readings with some of the ordinary types of cell, a pattern was devised (fig. 1) which was found free from their defects and is otherwise considerably more convenient in use. The cell consists of two electrode compartments connected, in the case of the pattern used for these highly conducting solutions, by three inches of glass tube of one-eighth inch bore. The electrodes are sealed into narrow glass tubes c and c by means of blue enamel glass. Thick platinum wire, * Proc. Roy. Soc. Edin., xxx, p. 254. 140 Proceedings of the Royal Society of Edinburgh. [Sess. wound in the form of a cone, makes the best electrode. Discs of platinum plate, welded to stout wire stems, should not be employed, because electrodes of this form were found to be liable to slight deflection by the incoming stream of liquid. In one case an error of one part in four hundred was traced to this cause. Connection with the electrodes is made by running in mercury and inserting copper wires. If a little paraffin is melted and allowed to solidify above the mercury, the connections become permanent, and the cell may be turned upside down without their being disturbed. In order to fill the cell with a given solution, a length of fine-bored glass tube, bearing a right-angled bend, is attached to a by a rubber tube, so that the vertical part dips into the bottle of solution. Suction is applied to h by means of a length of thin rubber tubing, so that the solution passes through aa' into the cell. A clip on the suction tube may be used to prevent the solution running out again. To have h' connected to the upper electrode compartment as high as possible is important, in order to avoid the inclusion of air when the liquid is made to rise through the cell. 1914-15.] Conductivity of Salt-saturated Hydrochloric Acid. 141 This cell may be filled and washed out while in the bath, and need seldom be removed. The liquid in entering it passes through only a short length of tube, and has very small opportunity to cool. It is very light in construction, and even when filled with liquid colder than the surrounding water reaches a constant conductance in from twenty to thirty seconds. The constant of the cell used for these measurements was about 170. The exact figure was found to remain constant within the limits of the error of measurement for many weeks. It was determined at intervals by means of a sodium chloride solution saturated at 18° (K^go = 0‘216I). By slightly modifying the design, other cells having a constant of from 2'0 to 3*0 were constructed. They differed from the one illustrated in having no central narrow tube. The leading tubes and electrodes were all sealed into the same compartment, so that the latter were from IJ to 2J inches apart These cells were found useful for aqueous solution of strong electrolytes of about decinormal strength and proved specially convenient for work with decinormal solutions of salts in mixtures of alcohol and water. In case the liquid in the cell is required for chemical analysis it can be easily blown out, without removing the cell from the bath, into a weighing bottle. This was done in the present case for the estimation of the salt. The solution was washed into a platinum dish, evaporated, and the salt residue was weighed after heating to dull redness. Samples were also taken in the same way for estimation of their acid contents. After weighing, they were diluted with water, and a known fraction was titrated with decinormal potassium hydroxide, using phenol- phthalein, and boiling during titration. The potash solution had been titrated against a solution of pure hydrochloric acid. The acid had in turn been standardised by a solution of silver nitrate prepared from pure silver, using the Gay-Lussac method of dropping the acid into the silver nitrate solution until no further cloudiness appeared. The temperature of the solutions was kept as nearly constant as possible and all measuring apparatus was standardised. The results obtained are given in the table. R is the resistance in ohms used to balance the cell so that the point of balance was nearly in the centre of the slide wire. is the specific conductivity at 18°, in reciprocal ohms. Column III gives the percentage of hydrogen chloride, and Column IV the percentage of salt, found by analysis in each of the solutions used. The figures in Column V were calculated from those in Columns III and IV. They give the percentages of hydrogen chloride in those solutions 142 Proceedings of the Royal Society of Edinburgh. [Sess. of the acid in water, from which, by saturation with salt, the solution investigated may be supposed to be derived. I. II. III. IV. V. Per cent. HCI Per cent. NaCl HCI X 100 X\. IV 18°. in mixture. in mixture. HCI + H2O. 240 •6650 15-26 5-98 16-23 220 •6941 17-14 4-39 17-93 •7161 19-36 2-90 19-94 •7226 20-58 2-23 21-05 55 •7246 21-50 1-85 21-90 55 •7235 22-50 1-45 22 84 55 •7196 23-83 MO 24-00 5? •6979 26-61 0-60 26-77 The figures in Columns IV and V are given in graphical form by the broken curve in fig. 2. Determinations of the solubility of sodium chloride in aqueous hydrochloric acid of the same range of concentration have been made by Engel at 0° and by Irvine Masson f at 30°. The lower unbroken curve of fig. 2 is plotted from the results of conductivity measurements given in Column II, and the calculated con- centrations of hydrogen chloride given in Column V. The relation between conductivity and concentration in the case of aqueous hydrochloric acid is shown by the uppermost curve. For this the data are given by Kohlrausch.+ Only five of Kohlrausch’s figures are useful here, and two of them represent interpolated values, but they are ample for a general comparison. This comparison can readily be made by noting that any vertical line in fig. 2 will cut the curves in three points wliich represent respectively, beginning with the uppermost, (I) the conductivity of a solution of hydrogen chloride ; (2) the conductivity of the same solution after saturation with salt ; (3) the percentage of salt in the same solution after saturation. It is evident that the infiuence of the salt is to lower the conductivity over the range investigated. With higher concentrations of acid, owing to the falling off of the solubility of the salt, its diminishing effect on the conductivity becomes less and less marked. With low concentrations of acid, however, this need not be the case. Since a solution containing no acid but saturated with salt has a considerable conductivity, it follows that the upper curve, in descending to the origin, must cut the lower curve. * Bull. Soc. Chiw., (2) 45, 654. f Trans. Chem. Soc., 99, 1911, 1132. J Leitvermogen der Electrolyte, 1898, p. 154. 1914-15.] Conductivity of Salt-saturated Hydrochloric Acid. 143 In other words, at a certain concentration not far from 5 per cent., a solution of hydrogen chloride may be saturated with salt without the conductivity of the solution being affected. The maximum of conductivity is stated by Kohlrausch to occur in aqueous hydrochloric acid at about 18 per cent., but full and accurate determinations of the conductivities of this acid communicated to this Society by Professor J. Gibson, but as yet unpublished, show the maximum to occur very close to 19T per cent. In a salt-saturated solution the maximum occurs at a higher concentration, very nearly 21 ’9 per cent. 16 18 20 22 24 26 28 30 Fig. 2. according to fig. 2, or 21 ’5 per cent, if the concentration of hydrogen chloride be considered in relation to the total weight of solution. It has been seen that, under certain conditions, the initiation of a chemical change by a mineral acid may be determined by the concentration of the acid being greater or less than the concentration of the acid which has maximum conductivity. As regards the occurrence of certain chemical changes in which hydrochloric acid may play a part, the acid containing 19T per cent, of hydrogen chloride is of critical concentration. It is interesting to find out, if possible, whether the critical concentration in the case of the salt-saturated hydrochloric acid is also the same as that of the solution having maximum conductivity. 144 Proceedings of the Royal Society of Edinburgh. [Sess. Among the changes described by J. Gibson as being subject to this influence, that of the colour of cobalt chloride * seemed to give opportunity for a test which would be roughly quantitative. Acids of various concen- tration were made up and saturated with salt at room temperature in clear glass bottles, each containing 60 c.c. of acid. To each, 0T5 c.c. of a saturated solution of cobalt chloride was added and the mixture was shaken. By analysis of the solution it was found that an acid of 19*8 per cent, would, after saturation with salt, just tinge the pink colour of the cobalt salt with a faint shade of purple. An acid of 21*2 per cent, was just able, after saturation, to change the colour to blue green. Since J. Gibson (loc. cit.) found that in solutions containing no salt the first purple change took place at a concentration of 18*2 per cent., it is apparent that the critical point, so far as the behaviour to cobalt chloride is concerned, has shifted through an interval of 1*6 per cent. The point of maximum conductivity in the acid medium has, however, been moved over a range of 21*9 — 19*1 = 2*8 per cent. The difference between this and the other figure is rather large. Difficulty of determining the maxima accurately may account for the difference to a small extent, but in any case the fact that the movement of the critical point is in the same direction as the movement of the point of maximum conductivity is significant. On the other hand, it is difficult to see how, in view of these results, the colour change in cobalt chloride can be due to dehydration by the acid. A solution containing 18*2 per cent, of hydrogen chloride is capable of producing the colour change in its first stage. If dehydration were the explanation, saturating this solution with salt might reasonably be expected to increase the dehydrating action, and to render the colour change more marked. After saturation with salt, however, the acid of 18*2 per cent, has no effect at all on the colour. In order to produce an effect, a more concentrated acid must be employed. Summary. (1) Determinations have been made, at 18” C., of: — {a) the specific electrical conductivity, (h) the percentage composition by weight, of a series of mixtures made by saturating, with sodium chloride, solutions of hydrochloric acid containing from 16 to 27 per cent, of hydrogen chloride. (2) Within this range of concentration the salt-saturated acid has lower specific conductivity than the aqueous solution of hydrogen chloride alone, from which it may be supposed to be derived. Of the salt-saturated acid * Trans., loc. cit., p. 125. y 1914-15.] Conductivity of Salt-saturated Hydrochloric Acid. 145 mixtures, that one has maximum conductivity which could be prepared by adding salt to hydrochloric acid containing 21 '9 per cent, of hydrogen chloride. Of solutions of hydrogen chloride alone, in water, that containing 19’1 per cent, hydrogen chloride has maximum conductivity. (3) The critical concentration of hydrogen chloride at which hydro- chloric acid is able to afiect the colour of cobalt chloride is changed, in the same sense as the concentration of hydrogen chloride corresponding to maximum conductivity is changed, by saturating the solution with salt. (4) A new form of conductivity cell is described. It is specially suitable for solutions which are saturated with dissolved solid, or contain a volatile solvent. Heriot-Watt College, Edinburgh. (Issued separately April 27, 1915.) VOL. XXXV. 10 146 Proceedings of the Royal Society of Edinburgh. [Sess. XIII. — The Reflective Power of Pigments in the Ultraviolet. By Charles Cochrane, M.A., B.Sc., Assistant to the Professor of Natural Philosophy in the University of Glasgow. Communicated by Dr R. A. Houstoun. (MS, received January 25, 1915. Read March 15, 1915.) The eye is sensitive only to light of wave-length 7600 to 4000 A.U. With the ordinary dry photographic plate and glass lenses we can get an effect down to wave-length 3300 A.U. ; with the same plate and quartz lenses we can get an effect from a wave-length as short as 2000 A.U. The gelatine of the plate absorbs the wave-lengths immediately above this limit, and their effect is very faint. A camera fitted with a quartz lens can take a picture in which all the wave-lengths down to 2000 A.U. produce their share, and hence can extend the range of the eye another octave, but the disadvantage of this picture is that it integrates all the different colours. We cannot, for example, tell whether a mark is due to light of wave-length 3500 A.U. or 2500 A.U. Such a picture makes the ultraviolet appear the same as the visible would appear to a man with monochromatic vision. All the detail due to variety and wealth of colour is lost. Now if we could photograph the same objects in succession with monochromatic light of wave-length say 3500 A.U, 3000 A.U., 2500 A.U., and 2000 A.U, it is possible that a great amount of new detail might be obtained of the utmost value to science. It was with the purpose of obtaining monochromatic photographs in the ultraviolet that the present research was undertaken. Former investigations of this kind have been confined to a single region of the ultraviolet spectrum. Thin films of silver are opaque to visible and to the greater part of ultraviolet light but comparatively transparent to rays of wave-length 3160 A.U. to 3260 A.U. ; this was first observed by Foucault, and has been utilised by different physicists. By using a silvered quartz objective, R. W. Wood* was enabled to obtain photographs which were produced solely by these rays and which can be termed monochromatic. White paper still appeared white in these photographs, but powdered zinc oxide and Chinese white paint — whose essential constituent is zinc oxide — appeared black. Michaud and Tristan j* extended this investigation to a large number of organic and inorganic salts and to a series of flowers of all colours. The white inorganic salts, bismuth nitrate and cerium carbonate,, * Smithsonian Institution Annual Report, 1911, p. 155. t Arch, des Sc. p>hys. et nat, xxxiii, p. 498 (1912) ; ibid., xxxvii, p. 47 (1914). 1914-15.] Reflective Power of Pigments in the Ultraviolet. 147 also appeared black, and zinc carbonate greyish. Schweinfurth green (cupric aceto-arsenite) and copper carbonate were equally darker than in visible light, and dark and black inorganic salts had in general the same appearance as in visible light. Of the organic salts the alkaloids showed many inexplicable differences in behaviour towards these rays. Ninety flowers were photographed, and all except the yellow ones appeared uniformly black. The yellow flowers could be divided into two classes : those in one class followed the general law and absorbed these rays strongly,, those in the other class almost completely reflected them. Michaud and Tristan term the latter “ultraviolet flowers,” and suggest that they will form four or five per cent, of a random choice of flowers of all colours. For the present work a Thorn ton-Pickard Imperial camera was used,, fitted by R. and J. Beck, Ltd., with a quartz lens system of two components, which is similar in shape and arrangement to a rapid rectilinear lens. Each component has a focal length of 30 cms. and an aperture of 2*2 cms. The camera is of the triple-extension type, with a total extension of 38 cms.^ and carries quarter-plates. A maximum magnification of 1'6 can be obtained with the double lens, or 0’3 if only one component is used. The method naturally occurring to me for obtaining monochromatic pictures in the ultraviolet was to use colour filters ; these in general allow of reasonably short exposures in the visible spectrum. However, with the exception of the silver film already referred to, there are as yet no mono- chromatic filters known suitable for the ultraviolet. A few preliminary experiments were made with a silver film deposited on the surface of a quartz plate. It tarnished rapidly and had some small holes which trans- mitted white light. It is possible that by combining special sources of illumination with suitable absorbing solutions a series of monochromatic pictures may be obtained, but after some preliminary work it was resolved to leave the investigation of this matter to a future research. The next method tried was to place the objects under investigation in a darkened room and illuminate them with ultraviolet light from a mono- chromatic illuminator; the constant deviation nickel-mirror spectroscope already described in these Proceedings * was used. The source of light was an iron arc placed on a ledge outside the window and suitably enclosed to prevent extinction by wind. The light was admitted to the slit of the spectroscope through a hole in a shutter. The plate carrier of the spectro- scope was replaced by an adjustable slit, by means of which a beam of light of any desired width could be transmitted. The wave-length of the trans- mitted light was varied by rotation of the focussing mirror, and could be * R. A. Hoiistoim, Proc. Roy. Soc. Edin., xxxii, p. 40 (1912), 148 Proceedings of the Royal Society of Edinburgh. [Sess. determined from the reading of the micrometer screw. All adjustments were made for the middle of the ultraviolet. A very steady arc was obtained with a positive electrode of 11 mm. diameter, and negative electrode of 8 mm. diameter on a voltage of 145 volts with 15 ohms ballast resistance, an inductance consisting of one of the coils of a large electro-magnet being placed in series with the arc Kayser * recommends for the iron arc poles of 10 to 15 mm. diameter with a current of 10 to 15 amperes, while Pfund f recommends 3*5 amperes on a 2 20- volt circuit with a positive electrode 12 mm. and negative electrode 6 mm. in diameter. It is interesting to note that Nutting J obtained a good ultraviolet spectrum for photographic purposes by using a spark source between terminals of an alloy of two parts of aluminium to one part of zinc; a large capacity was placed in parallel with the spark to make the spectrum continuous. While this arrangement gave a fairly strong beam of ultraviolet light, it was found necessary to purify it by resolving the incident radiation by means of an objective quartz prism ; only the ultraviolet was then allowed to enter the spectroscope. The intensity of illumination, however, when the beam was projected on an object of any considerable size was small, and very long exposures were required. The apparatus was therefore modified and the scope of the investigation limited to examining the appearance of different pigments and salts in ultraviolet light. This paper contains the results obtained for a number of pigments of various colours. Instead of illuminating these with mono- chromatic light, the whole iron arc spectrum as reflected diffusely from them was photographed and compared with the spectrum reflected from a selected piece of white cardboard. The usual method for producing a spectrum was employed ; a plan of the essentials is shown in the figure. The source S was the iron arc placed outside the window as before. A Cornu prism of 4’6 cms. side and 4‘0 cms. height was mounted on a levelling table B along with two quartz lenses of 2'7 cms. aperture and of 22*9 cms. and 49*8 cms. focal length respectively, the prism being set for minimum deviation of wave-length 308 micromillimetres. The slit A in the window shutter was 2*0 cms. high and 0*5 mm. wide. Its spectrum lies practically in a single plane CD. Winsor and Newton’s oil colours were used. They were laid thickly on narrow strips of wood by means of a palette knife ; the oil was absorbed by the wood, leaving a hard even layer of pigment. The painted strip was * Handhuch der Spectroscopie, vol. i, p. 916. t Astroph. Jr., xxvii, p. 296 (1908). f Pliys. Rev., xiii, p. 193 (1901), 1914-15.] Reflective Power of Pigments in the Ultraviolet. 149' mounted in the focal plane CD between the comparison piece of cardboard and a similar piece on which a reference scale had been inscribed in Indian ink. The spectrum of the slit was sufficiently high to fall partly on all three, and was photographed by the quartz lens camera E at a distance of 35 cms. ; the camera was so placed as to receive only diffusely reflected light. With an aperture of F 16 two exposures of ten minutes each were made for each pigment, one giving the near half of the ultraviolet in focus, the other the further half. During the latter exposure the visible and -S near ultraviolet regions were screened off'. Two pictures were taken on each plate, the unexposed half of the plate being protected from stray light by a screen placed within the dark slide. The exposures were made in groups of four, the two exposures for each pigment being made on different plates. Thus each plate contained two images in focus for the same part of the spectrum but for different pigments. The relative densities of the images produced by the light reflected from the pigments and from the cardboard respectively were estimated visually at selected points of the spectrum. As the method of visual observation is liable to considerable error, the determinations were standardised at first by means of blackened comparison strips of different densities. These were prepared by fogging photographic plates, and the fraction of light transmitted by each was carefully measured. They were 150 Proceedings of the Royal Society of Edinburgh. [Sess. placed in turn over the less dense of two images under observation until one was found which made the images appear of equal density. The fraction of light transmitted by the strip gave the relative density of the two images. After a time the visual estimations were found sufficiently reliable, and the use of the comparison strips was dispensed with. Care has to be observed in making photometric comparisons by means of photography. Strictly speaking, the relative densities of the images produced by independent sources is an accurate measure of the relative intensities of the sources only when images of equal density are produced simultaneously on adjacent portions of the same plate by sources of the same wave-length. The numbers tabulated below can therefore be regarded as approximations only, and are intended to indicate the order of magni- tude rather than the actual values of the respective relative reflecting powers. Relative Reflective Powers for Ultraviolet Light. Wave-length in Micromillimetres. 445. 388. 322. 274. 240. White cardboard 1-00 LOO LOO LOO LOO Flake white LOO •70 •20 •81 L40 Cremnitz white ..... 103 LOO L08 1-23 2 03 Silver white 1-00 LOO 1-00 1-05 1-15 Zinc white ...... LOO •99 •89 L20 L85 Chinese white 1-00 •93 •34 •14 •02 Pale chrome yellow .... •36 •38 •35 ■84 L16 Naples yellow, French ... •70 •80 •78 LIO L40 Yellow lake ...... •00 •11 •09 •22 2-48 Yellow ochre ...... •26 •33 •21 •88 L13 Transparent gold ochre .... •36 •45 1-18 1-20 2-45 Crimson lake •00 •01 •02 •05 •10 Yermilion •18 •32 •16 •99 •99 Light red ...... •31 •36 •34 •58 •82 Indian red ...... •50 •53 •72 1-00 L30 Venetian red ...... •41 •50 •70 1-23 L25 Chrome green, No. 3 •16 •39 •58 1-00 3-93 Cinnabar green (deep) .... •29 •36 •39 •99 2-43 Emerald green •15 •25 •13 •86 LIO Cobalt blue •02 •01 •01 •20 •68 Prussian blue •00 •00 •00 ■00 •00 Antwerp blue ...... •04 •11 •02 •18 100 Indigo ...... •18 •26 •26 •93 3-33 Burnt sienna ...... •20 •30 •20 •80 115 Vandyke brown ..... •58 •68 •73 •85 LOO Brown ochre •45 •58 •69 LIO 4-23 Raw umber ...... •29 •38 •50 1-28 3-38 Bone brown ...... •49 •53 •67 LOO L13 Lamp black ...... •44 •50 •56 LOO L98 Ivory black . •27 •51 •62 •84 L78 Blue black ...... •45 •53 •70 LOO L33 Payne’s gray ...... •13 •26 •20 •56 •94 Charcoal gray •31 •38 •38 •51 •58 Davy’s gray •40 •48 ! •53 1 •86 •95 1914-15.] Reflective Power of Pigments in the Ultraviolet. 151 With cardboard used as a standard a considerable increase in the values obtained for most of the pigments takes place towards the extreme ultra- violet end of the iron arc spectrum. As this might simply be due to a falling off of the absolute reflective power of cardboard, it was thought advisable to compare the latter with ground quartz in the same manner. The quartz was backed by black velvet, which was found to reflect practically no light diffusely from the spectrum, in order to prevent reflection at the second surface, and gave the following results : — Wave-length in Micromillimetres. 445. 388. 322. ^ 274. 240. White cardboard 1-00 100 1-00 ]-00 100 Ground quartz ..... •09 •10 •12 •13 •13 Quartz exerts no selective reflection in this region of the spectrum, so that its reflective power will vary uniformly throughout, and will probably be somewhat greater the shorter the wave-length. It is likely, therefore, that the white cardboard has a more or less constant reflective power at all the points examined. Even if this were not so, the decrease in reflective power of the cardboard in the extreme ultraviolet as compared with quartz is not of itself sufficiently great to account wholly for the increase observed in the case of many of the pigments. There is thus evidence of selective reflection on the part of the latter in that region. Further observation would be valuable in the extreme ultraviolet with a more extended spectrum — for example, Nutting’s spark spectrum, which extended to the aluminium line of wave-length 1850 A.U. Messrs Winsor and Newton, Ltd., have kindly supplied me with notes on the chemical composition of the pigments. These bring out some striking anomalies. Flake white, though similar chemically to Cremnitz white and silver white, shows a drop in reflective power as compared with them in the middle of the ultraviolet. Chinese white, a dense variety of zinc oxide used only in water colour, is an exception to the rule that the relative reflecting power increases towards the extreme ultraviolet, while zinc white, which is also composed of zinc oxide, obeys that rule. And though the essential constituent of light red, Indian red, and Venetian red is in each case sesquioxide of iron, the first of these pigments has a lower reflecting power throughout the ultraviolet than the other two, whose values are very similar. The black pigments examined, which are carbon blacks obtained by different processes, reflect a considerable proportion of ultraviolet light. 152 Proceedings of the Royal Society of Edinburgh. [Sess. No attempt can yet be made to interpret the results in the light of chemical constitution. The preparation of compounds for use as pigments may produce complex conditions of which we are unaware, and it will be necessary for comparison to determine the diffuse reflective powers of the same compounds in their chemically pure state. It is in any case unlikely that the problem of the interpretation of reflection spectra will be any simpler than that of absorption spectra, and the exhaustive investigation of numerous series of compounds will probably be required before any satisfactory theory can be suggested which will fit the observed facts. I am indebted to Dr R. A. Houstoun for advice during the progress of the foregoing investigation, which was carried through during my tenure of the Houldsworth Research Studentship in the University of Glasgow. {Issued separately May 21, 1915.) 1914-15.] The Theory of the Gyroscope. 153 XIV. — The Theory of the Gyroscope. By Professor H. Lamb, F.R.S. (MS. received March 13, 1915. Read May 3, 1915.) The object of this note is to obtain briefly the intrinsic equations of motion of a gyroscope, and to show how they lead immediately to the solution of a number of problems. So much has been written on the subject of the gyroscope that these equations are hardly likely to be new^ but I do not remember to have met with them in their explicit form. Apart from their use as a basis for calculation, they have a simple interpretation which enables us to foresee the general character of the motion in cases where the actual calculation would be difficult. 1. It is assumed that two of the principal moments of inertia at the “ flxed point” (0) are equal, and the three moments are accordingly denoted as usual by A, A, C. We may also denote by C one of the two points in which the axis of symmetry meets a unit sphere having its centre at 0. For definiteness we choose that point of the pair which is such that the angular velocity {n) about the axis OC shall be right-handed. This point C may be called the pole of the gyrostat, and it is with its path that we are concerned. c Fig. 1. We draw from C, on the unit sphere, a quadrant CA tangential to the path and in the direction of motion, and a quadrant CB at right angles. 154 Proceedings of the Royal Society of Edinburgh. [Sess. so that OA, OB, OC (in this order) shall form a right-handed system. We distinguish the positions of the corresponding lines after an interval St by OA', OB', OC'.* If V be the velocity of the pole along its path, and (5^ fhe angle between the projections on the tangent plane to the sphere of two consecutive tangent lines to the path, we have CC' = r8j^, AC'A' = 8x (1) At the instant t the component rotations about OA, OB, OC are 0, v, n respectively, and the components of angular momentum are accordingly 0, Av, Cn . . . . . • (2) In the time St these are altered to 0, A(v-\-Sv), C(n + Sn) . . . • (3) about OA', OB', OC', and therefore to - AvSx + CrivSt, A{v -f Sv), C{n + dn) . . . • (I) about OA, OB, OC, terms of the second order being neglected. If, as we will suppose, the external forces have zero moment about the axis of symmetry, they may be replaced by two forces P, Q acting at C along the tangents to the arcs CA, CB respectively, i.e. along and at right angles to the path of C. P is, in fact, the moment of the external forces about OB, and — Q that about OA. Hence, equating the increments of angular momentum to —QSt, VSt, 0 respectively, we find A«| = Q + C«., a| = P (5) with n = const. These are the equations which I take leave to call “ intrinsic,” as involving no arbitrary lines or planes of reference. Tlie expressions dv/dt and vd^ldt are the accelerations of the pole C along and at right angles to its path on the sphere. If we put n = 0 we have as a particular case the equations of motion of a particle on a spherical surface, and we infer that the motion of the pole C in the present case will be exactly the same as that of such a particle, of mass A, under the same forces P, Q, provided we introduce in addition a fictitious deviating force Onv acting always towards the left of the path, as viewed from without the sphere. j* This statement includes the old rule about hurrying on the precession,” but is more precise and of more general application, and at least equally simple. The examples which follow are intended mainly to illustrate its convenience. * The figure is simplified by the assumption that C' may be taken to lie in CA. The error thus involved, and in the consequent positions of A', B', is of the second order, and so does not affect the final results. t There is also an obvious interpretation of (5) in terms of the two-dimensional dynamics of a particle ; but this is, as a rule, less convenient for our purpose. 155 1914-15.] The Theory of the Gyroscope. 2. In cases of “ precessional ” motion, the pole C describes a circle on the unit sphere with constant angular velocity If 0 be the angular radius of this circle, the acceleration of C towards its centre is t;Vsin 0, and the component at right angles to the path, in the tangent plane, is therefore cot 0. Hence, if there are no external forces, cot 0 = Cnv, or, since v — sin 0 v/y , i/r = Cn/(A cos 0) . . . . . • (6) which is the ordinary formula for the free “ Eulerian nutation.” The same formula applies to the ‘‘rapid” precession of a top whose velocity of spin is very great, gravity being in this case relatively unim- portant. In the case of the “ slow ” precession we may ignore the acceleration, which involves the square of v, and equate the deviating force Cnv, or Cn sin 0 to the effective component of gravity, viz. ALgh sin 0 in the ordinary notation. Thus ij/ = Mgh/Cn ...... (7) The exact condition for steady motion, including both cases, is obviously Av^cot^= - sin ^ -H Cwv . . . . • (S) or A sin ^ cos ^ = - Mp'/i sin ^ -1- Ctz sin ^ . . . • (9) The small oscillations of a rapidly spinning top about a state of precessional motion are also easily investigated. Suppose, for instance, that the pole C is initially at rest. It will at once begin to descend, but the deviating force which is quickly called into play will deflect it continually to the left, so that it presently turns upwards again, describing a sort of cycloidal curve. When the undulations are small the circumstances are very closely analogous to the case of a particle moving in a plane under two forces, one of which is constant in magnitude and direction, whilst the other is at right angles to the path and varies as the velocity.* The equations of motion in such a case are of the forms i/=f+/3x (10) whence x = ct + a sin /3t, y — a cos (St . . . . (11) if the origins of x, y, t be suitably adjusted. The path is therefore a trochoid, the period of oscillation about the uniform rectilinear motion being * This case occurs in Hydrodynamics, in the motion of a cylinder with cyclic irrotational motion about it, and subject to a constant force such as gra\dty. Again, in Electricity we have the case of an electron moving in a field where the electric and magnetic forces are uniform and at right angles to one another. 156 Proceedings of the Poyal Society of Edinburgh. [Sess, 27t/^. In the case of the top we have and the period is therefore A 27t C w (12) in agreement with the usual more elaborate theory. 3. The deviating force Cnv, being proportional to and at right angles to the velocity, is easily resolved into components in any system of co- ordinates. Thus, to obtain the general equations of motion of a solid of revolution in terms of the usual spherical polar co-ordinates 6, \jr, we note that since the components of the velocity v in and perpendicular to the plane of (9 are 0 and sin 6 \jr respectively, those of deviating force will be — Cn sin 0 yjr and Cnd. Hence, assuming the known expressions for the accelerations of a point in spherical polars, we have at once A((9 - ij/^ sin 0 cos B)= — On\p sin 0 ® j I (13) where 0, 'P are the moments of the external forces tending to increase 0 and respectively. The theory of the nearly vertical top, which is a little troublesome to deal with on the basis of equations such as (13), is easily treated directly If X, y be the projections of the unit vector OC on fixed horizontal rect- angular axes through O, the components of deviating force will be whence - Cny, Cnx, Kx= - Qny + Ai) = Gnx + lAghy . . . (14) If we put z = x-\-iy, these may be combined into the single equation Az - iCnz - M.ghz = 0 ..... (15) ^ ^ . . . . . (16) oy^lOnjA, v = lJ{CV-iAMgh) . . . . (17) the solution of which is where and the (complex) constants H, K are arbitrary. This represents motion in an elliptic orbit which revolves about the origin with the angular velocity 00, the period in the ellipse being 27t/i/. Before leaving the ordinary top we may recall the familiar experiment where a projecting material axis, or stem, is observed to follow the wind- ings of a metal arc or wire brought into contact with it. The friction of the wire causes the cylindrical stem to roll along the arc, and the deviating force called into play tends to maintain the contact (see fig. 2). 157 1914-15.] The Theory of the Gyroscope. The “rising” of a top due to excentric friction at the pivot is also readily accounted for by the action of the deviating force. / 4. In an experiment devised by Foucault, the axis OC of the gyroscope is restrained to move in a horizontal plane, but is otherwise free. The earth’s angular velocity (co) may be resolved into co sin X about the vertical and o) cos X about the N. and S. line, where X is the latitude. If (p be the angle which OC makes to the E. of N., the latter component gives to C a velocity o) cos X sin (p downwards, and so calls into play a deviating force Cncio cos X sin (p in the horizontal plane, tending to diminish (p. Meantime the N. and S. line is rotating about the vertical with the angular velocity (iOsinX. We have then A— - o)t sin X) = - CncD cos X sin

= 0 (19) where, as is easily seen, A must be taken to include the moment of inertia of the frame of the gyroscope about the vertical through O. For a small oscillation about the N. and S. direction the period is 277 ^ (-20) In the “ gyrostatic compass ” the frame of the gyroscope is suspended by a wire, or floats on mercury, so that the axis OC has two degrees of freedom, horizontal and vertical. The theory is therefore modified. If 0 be the inclination of OC below the horizontal plane, which we will suppose small, the vertical velocity of C is cos X sin 0 + d, and we have therefore, for the horizontal motion, A^ = - Cw(to COS X sin (^ + C • • • • (21) Again, owing to the horizontal motion Of the two values of o-^, one is greater than the greater, and the other is less than the smaller, of the two quantities and (C^io; cos X)/A. In practice n is very great compared with _p or co, and the two roots are cr2 = C%VAB and o-^ = ^ . . . (25) \^7l approximately. The former corresponds to a very rapid vibration, which is quickly checked by friction, and makes = (26) nearly. The second and more important root gives a slow oscillation in which n iCno- j iwcosX. ^ = 9^ ^ ar (27> The period {^iTjcr) of this slow oscillation is in practice about 70 minutes,, and the ratio of 0 to 0 is therefore small. 5. In the Schlick contrivance for steadying the rolling of a ship, a fly- wheel maintained in rapid rotation is carried by a frame which can swing about an axis at right angles to the medial plane of the vessel. The axis of the flywheel itself moves in this plane, and its standard position is upright, this being the position of stable equilibrium when the ship is at rest and there is no rotation, the frame being weighted with this object- The swinging of the frame about the transverse axis is resisted by frictional brakes. Briefly the principle of the contrivance is that the rolling of the ship produces a deviation of the axis of the flywheel in the medial plane,, and a consequent absorption of energy by friction, which means so much lost to the rolling vessel. If the angular displacements are small the equations of motion of the frame are obtained by a slight modification of the equations (14) relating ta * So that 27t/^ is the period of oscillation when n - 0. 159 1914-15.] The Theory of the Gyroscope. the nearly vertical top. If x, y denote small rotations about transverse and longitudinal axes respectively, we have x= -p^x - fSy - kx, y== l3x + Y . . . . (28) where /3( = Cn/A) represents the gyroscopic effect, k is the coefficient of damping, and 2irlp is the period of oscillation of the frame in the absence of friction and rotation. The symbol Y is written for N/A, where N is the couple exerted on the frame as the ship rolls. If we are to write down the equation of rotation of the vessel itself about the longitudinal axis, Y could be eliminated, and we might proceed to the consideration of the free and forced oscillations. The discussion is, however, very complicated,^ the equation for the free periods, for example, being of the fourth degree. The subject can, however, be illustrated to a certain extent by examining the effect on the flywheel of a prescribed oscillation of the ship, and the consequent absorption of energy. This is a comparatively simple matter. Assuming^, then, .... (29) . . . . (30) we have whence In real form we have y = (o-^ — ikp — "t" g^x^fSo. .... (3) * A general law for commutation of matrices is given by H. Taber, Am. Acad. Proc.y 1891, 26, 64-66, but the result is ill adapted to physical interpretation. Several elegant examples are given by Gibbs, in the language of dyadics {Scientific Papers, ii, p. 63), but the discussion is not completed so as to cover all cases. C. J. Joly, in his Manual of Quaternions, gives the rule : Two linear vector functions are commutative when, and only when, they have the same axes. This rule holds whenever both strains have three distinct axes, but is otherwise insufficient, as exemplified in the text, t Kelland and Tait, Pntroduction to Quaternions, chap. x. 1914-15.] The Commutative Law for Homogeneous Strains. 171 If p be distinct from the other axes, at least two of the coefficients x^, x^, x.^ must be different from zero. Suppose x-^ and x^ not zero. Equating coefficients of /3-^ and /S^ in (2) and (3), we have g-^ equal to g^. The strain in the plane of and is therefore a uniform dilation, and every vector in that plane is an axis. 2. Strains of the general type, having three, and only three, distinct axes, have been clearly described.* They may always be written in the form (2). If we multiply both sides of (1) by take the scalar part of the product, we find (I) __ and similarly x - We may, if we prefer, replace these scalar products of three vectors by the determinant of their components along axes of co-ordinates. The case of imaginary values for a pair of g's has also been sufficiently treated.f 3. To obtain the most general strain with a double axis, let cp convert /3 into g^ and into Suppose ^ to be a double root of Hamilton’s symbolic cubic,J that is, (5) identically. In consequence, (0 is annulled hy {(p — g-^). What is the same thing, {(p — gYp is a vector parallel to /5p or else null. Moreover, {(p—gYp is linear in p. In any case, therefore, we must have {cp-gy^p = (3^SXp, (6) where A is some constant vector (perhaps null), because any scalar linear in p can be written SAp. By similar reasoning, {P = 9P + c/3Spf3^p -H c^/B^SafSp, • (13) (14) which may be taken as a normal form for a linear vector function having hut two distinct axes, one of these being a double axis, corresponding to a double root of the cubic in (p. It is worthy of note that, so long as /5 and a determine a fixed plane, we may alter a in any manner in that plane without altering (p, the constant c satisfying the equation pa = ga + ..... (15) 4. The chief peculiarity of the strain defined by (14) is its effect upon vectors in the plane of a and (3. It is evident that any vector in that plane undergoes stretching proportional to the factor g, and is further altered by addition of a component parallel to /3. The effect of repeated operation with upon all vectors in this plane is therefore continued progress toward the direction /5. No such phenomenon can occur when the strain is of the general type. For convenience I shall speak of a plane of vectors affected in this manner by a strain ^ as a precessive plane ; and (p may be said to be precessive with respect to that plane. For a precessive plane to exist, it is necessary that four vectors a, ^ (pa, whatever, g being any root of the cubic, because the corresponding axis is reduced to zero by cp—g.) In the present case, by (18), the repeated operation (0 — pf)2 reduces every vector to the direction y. Therefore the axis lies in the plane of {

p = gp + c^Sf^yp + C-^ySyap . . . . (24) is a normal form for a linear vector function having all its axes coincident. Since the only limitation imposed upon has been the coincidence of roots of the symbolic cubic, we may infer that (24) contains, implicitly, seven scalar constants : the axis counts as two, the root g as one ; the precessive plane must contain the axis, but its aspect is otherwise arbitrary, and its angle with a fixed plane through the axis may be taken as a fourth scalar ; if we choose /3 as a unit vector making a fixed angle with the axis, and a a unit vector at right angles to the axis, the constants c and c^ are arbitrary; and, finally, the angle between a and ^ may count as the seventh scalar. To illustrate this strain by a physical example, let us suppose, as before, that a parallelepiped stands on a level table. Take ^ and y along the horizontal edges, and a along the non-horizontal edges. Apply in succession the two shears, ifp = p + a^S/3yp and a>p = p + a^ySyap, . . . (25) which by compounding give ^p = coi/^p = p -f- (a/3 + aajySa/3y)S/3yp + a^ySyap, . . . (26) which is in the form (24). If we wish to obtain the most general strain 1914-15.] The Commutative Law for Homogeneous Strains. 175 of the type, we may follow i/r and w with a uniform dilation g, equal to the root of the cubic. (The root of the cubic for (26) is equal to unity.) It may be noticed that the and oo of (25) differ from \fr and ^ of Art. 4 in not being commutative. For if/dip = p + a^^ySyap a/3S/3yp, .... (27) which, however, is also of the type under discussion, having y for its only axis, with (py = y. 6. It remains to consider strains with an infinite number of axes. A necessary condition for indeterminateness of axes is the identical vanishing of the product (

P = 9P + y^^P^ (28) where y is the axis of g-^, and X is some constant vector (perhaps null). We may take (28) as a normal form for a linear vector function having an infinite number of axes. Any direction perpendicular to X is evidently an axis. There can, by the form of the expressions involved, be no other axis except y ; so that in case SXy = 0 all the axes are in one plane. If SXy = 0 and g = 1, the strain reduces to a shear. 7. To sum up the discussion of homogeneous strains : Any linear vector function, hence a fortiori any homogeneous strain, may be expressed by one of these four normal forms : — I. y>p . S/3^/?2/?3 = + ,72^2^/^3/^iP 9z(^fi*(^i(^2Pi where g^, g^, g^ are unequal roots of the 0-cubic. II. (f)p = gp + cf3Sl3/3^p + cfifiafSp, where g is a double root of the cubic, and may vanish. It is assumed c and do not vanish. Sa^p = 0 defines a precessive plane for this form of (p, not containing III. a = 0{aa) = aOa, because scalars are commutative. But if 0 and 6 are commutative, d0a = 0da. Equating values of d0a, we have ea = cf>(xa + tj^ + z[3^), by (30), = %a + c'/3) + yy^ + 2^ift, by (14) and (13). If we now compare values of (pOa, we find, from the terms in a, an identity ; the terms in ^ give cx = ch, and, as c is, by hypothesis, different from zero, we must have x — h; the terms in /3^ give gz = g^z, and as, by hypothesis, g is different from g-^, we must have z = 0. Accordingly y is arbitrary. But the conditions z = 0, x = h (31) are precisely the conditions that the precessive plane of (p should also be precessive for 0. We have therefore the rule: Two strains of class II are commutative when, and only when, they have the same axes and the same precessive plane. If we assume cp of class II, conditions (29) and (31) determine the most general form of d commutative with 6a = 0(fia, if the strains are to be commutative, = 0{ga + c'[3), by (24), letting c =cSaj3y, = g{x^a + + z^y) + c\lll5 + zy\ by the conditions already proved for 0^, Again, cfiOa = (f>{x-^a + y-^/3 + Z^y) = x^(ga + c'/?) + ?j^{g(3 + c^y) + z^gy, by (24). By comparison of coefficients, Xi = h, cyy^^cz. ..... (35) These conditions serve to determine Oa in part, if we suppose d/3 previously determined by the assignment of values to h and to 0, but they leave the y-component of da wholly arbitrary. We have, therefore, the rule : Two strains of class III are commutative when, and only when, they have the same axis and the same precessive plane, and satisfy the condition If we assume

)p = 0, ..... (40) whence one way of finding a value of r, if a- is homogeneous, is to find an integrable Odp with

(” -1)334 + (n + lMn-l)(«-2)gy^ (2) which is supposed (when it converges) to represent /((X -P where n can have any value. It is obvious, however, that there is no reason a 'priori why this expansion should represent f{x) in preference to any other function of the set cotabular with f{x)\ and thus two questions arise, namely : — (1) Which one of the functions of the cotabular set is represented by the expansion (2)? (2) Given any one function f(x) belonging to the cotabular set, is it possible to construct from f(x), by analytical processes, that function of the cotabular set which is represented by the expansion (2) t These questions are answered in the present paper. It is, in fact, shown that there is a certain function belonging to the cotabular set which is represented by the expansion (2). This function is named the cardinal function of the set, and its properties are investigated. A formula is given by which the cardinal function may be constructed when any one function of the cotabular set is known. § 2. Removal of singularities from a function, by substituting a cotabidar function for it We shall first show that x/’f(x) has a singularity at a point c, we can find a function cotabular with f(x) which has no singularity at c. For suppose first that the singularity is a simple pole, so that f{x) becomes infinite in the same way as r X - c near the point c. Then the function r sin 7t{x - a) /(*)- {x — c) sin ^ w is cotabular with fix), since the factor sin ^ vanishes at all the 183 1914-15.] Expansions of the Interpolation-Theory. places a, a + w, a — iv, etc. : and this function has no singularity at c, since the infinite part of the term . Trix — a) r sin — ^ ^ {x - c) sin -(c - a) exactly neutralises the infinite part of f{x). Moreover, this term does not introduce any fresh singularity in the finite part of the ic-plane, and does not cause the new function to become infinite even at x = co so long as x is real. This establishes the result for the case when the singularity is a simple pole. When it is a pole of higher order, or an essential singularity, we can make use of the known result that the part of the expansion of f{x) which becomes infinite near this singularity may be expressed in the form f/(zyh 27ri I Z — X Jy where y denotes a small circle enclosing the singularity c. Now this can be neutralised by a term f{z)dz 1 . 7t(x - a) — . sm ^ ' 2tvi w I {z — x) sin '{z - a) ’ and as this term contains sin as a factor, it vanishes when the . . Hence in this w argument has any of the values a, a-\-w, a — w, u + 2w, case also we can write down a function, namely, f{z)dz + sm ■(x — a) \-ni {z - x) sin 7t{z - a) ’ which is cotabular with f{x) but has no singularity at the point x = c. By repeated application of this process we can remove all the singu- larities of f(x) in the finite part of the plane, and obtain a function which is cotabular with f(x), and which does not become infinite except for values of x whose imaginary part is infinite. § 3. Removal of rapid oscillations from a function, by substituting a cotabular function for it. Having replaced the original function fix) by a cotabular function of the kind just described, we shall now suppose the latter function to be analysed into periodic constituents by Fourier’s integral-theorem (or, in 184 Proceedings of the Koyal Society of Edinburgh. [Sess. a particular case, Fourier’s series) just as radiation is analysed by the spectroscope. Consider first a single one of these periodic constituents, say A sin Xx , where A and X are constants. We can without loss of generality suppose X to be positive. The period of this term is 27t/X. We shall now show that if this period is less than 2w, then an expression can he found which is cotahular with the given term and which has a period greater than 2w. For, e.g., if the period lies between 2w and 2^^;/3, so that X lies between Trjw and SttIw, the function A sin has the same values as AsinXcc when x = a, a + w, a — w, a + 2w, etc.: and since X lies between tt/'u; and Sirlw, we see that (X — 27tIw) lies between — irlw and tt/'Iu, so the period of this new term is greater than 2w. Similarly if the period of the given term lies between 2w/S and 2w'5, so that X lies between Stt/w and birlw, then the function is cotabular with A sin Xx and has a period greater than 2w. Other possibilities can be treated in the same way, and the theorem stated is thus established. We are thus led to the idea that if a function is given which can be analysed by Fourier’s integral-theorem (or Fourier’s series) into periodic constituents, then we can find another function which is cotabular with it and which has no constituents of period less than 2w. That is to say, we can replace the given function hy a cotabular function in such a way as to remove all the rapid oscillations from it. § 4. Introduction of the cardinal function. We shall now carry out what has been indicated in the preceding article, namely, to analyse a given function into a number (generally an infinite number) of periodic constituents, then to replace the short-period components by long-period components which are cotabular with them, and finally to synthetise all the components into a new function. It will be shown later that this new function, which will be called the cardinal function, has certain remarkable properties. Let/(cc) be the given function, from which all infinities except for 1914-15.] Expansions of the Interpolation-Theory. 185 imaginary infinite values of the argument are supposed to have been removed already by the method of § 2. Let g{x, k) denote the function —J /(/x) J 6 cos X{x - fx)dX . Here k denotes a positive constant, introduced for the purpose of securing convergence in the following developments. Break up the range of integration in g{x, k), thus — g(x, k) = — ^00 77 StT StT ^ /»- 1 W 1 w 1 w + + + — Jo — IV w e cos X{x - ix)dX . The first partial integral consists of terms whose period in x is greater than 2w, the second partial integral consists of terms whose periods are between 2w and f n;, and so on. Replace every periodic term whose period is less than 2w by the corresponding cotabular term whose period is greater than 2w, as explained in the preceding article. We thus obtain an expression which we shall denote by G(x, k), where 7T7-00 W ^-Kk e cos {X(x — fx)}dX I. + e ^cos I X{x - [X) + —(a - /x) | o'A. ~ w + ^(^^«’)cos| - /x) + — (a - /x) | (iX + Summing the series of exponentials and cosines, we have ,5 . , ^irk w smn cos ^ - Afc w I X{x - /x) I - sin I X{x - ft) j> sill j — (a - /x) j- - 7T W cosh ‘hrk dX cos — (a - ix) w Performing the integration with respect to X, this gives X) = 27TZ d(xf{p) sin - (a; - /X - ik) cos - ft - ik) sir -(x- ul + ik) cos - (a - ft + ik) 10^ w IV w (x- jjL- ik) sin ^ (a - ft - ik) {x- jx + ik) sin — (a - ft + ik) Now if we evaluate the integral ^iri -(x-fj.-ik) COS —(a - ft - ik) dfxf{fX); w ft - ik sin —(a-fx- ik) %(! 186 Proceedings of the Koyal Society of Edinburgh. [Sess. where k is positive, by Cauchy’s Theorem of Residues, taking as contour the real axis of /x together with an infinite semicircle below the real axis, we obtain for it the value in r=-co -a - rw) w Similarly if we evaluate the integral X IX m sin — (a - tx- ik) IV taking as contour the real axis of /x together with an infinite semicircle above the real axis, we obtain for it the value zero, since the integrand has no poles inside this contour. Subtracting the latter result from the former, we have t//x/(/x) sm—{x-fx-ik) cos— {a- IX- ik) _ ^ ^^(x-a-rw) x-ix — ik • 7T / X / \ ^ sin — {a - IX- ik) “ — (x -a- riv) w iV Similarly we have 2TTi sin — (x-fx + ik) cos — (a-ix + ik) p , , ,, X 10^ ^ ^ ^ ’ 1 ^f{a^-riv-^ik).e ^-{x-a~rw) (lixflix)- X fx + ik] sin — (a - /X + ^’A:) — (x - a - riv) w and thus we obtain G(x,k)^^ iTT In f(a + 7nv - ik) . - f(a + rw + ik) . e : 2i—(x — a- riv) w so that |lim jfc_^o k) = 00 f{a + 7'w) sin — {x - a — rw) •?oo ^ — (x -a- rw) w Now (a{x, k) is the function which was formed from g(x,k) by replacing all the short-period terms by the corresponding cotabular long-period terms: and (as in Poisson’s discussion of Fourier’s integral) we have /(o;) = lim&^oP'(a;, k) . Hence we infer that the expression 00 E r= — 01 f{a + rw) sin —{x -a - rw) —ix -a- riv) w (3) 1914-15.] Expansions of the Interpolation-Theory. 187 or ^sin + 7T w x-a-rw (4) represents a function which is cotabular with the given function f(x), hut which has no periodic constituents of period less than 2w. Now, in order to construct the expression (3) or (4), we do not need to know anything about f{x) except its YdluQS, f{a), f{a-\-w), f{a — w), etc., at the tabulated values of the argument. These values, however, are not peculiar to f{x), but are common to the whole set of cotabular functions. It follows that we arrive at the same expression (3) whatever function f(x) of the cotabular set we start from. The expression (3) is therefore an invariantive function of the cotabular set : and it may be regarded as the simplest function belonging to the set. We shall call it the cardinal FUNCTION of the set. § 5. Examples of the determination of a cardinal function. We shall now work out two examples in order to show how in any given case the cardinal function may be obtained from the formula (4). Example 1. — Suppose that the given tabular values of the function f{x) are as follows : — /(o)=o, /(i)=-i, /(2)=i, /(3)=-i /{„)=oyi, Th /(-i)=i, /(-2)=-i, /(-3)=i — /(-„)=uyA\ — To The corresponding cardinal function is, by formula (4), 1 . - sin 77X 7T 1111 -1 ^r-l'^2(x-2)'^3(a:-3) ■^4(^-4)'^ ' ' ' ' 1111 x+l 2(x + 2) 3{x + S) 4.{x + i)^ ' ■ ■ or, summing the series, or sin ttxV r'( 1 -x) V'{x +1)1 ~ 7TX Lr(i-4” r(ic + i)J or sin ttx d , sin ttx — log TTX dX TTX or cos TTX sin TTX TTX^ X 188 Proceedings of the Royal Society of Edinburgh. [Sess. This is the required cardinal function. It is the only analytic function having the above tabular values which has no singularities in the finite part of the ^c-plane and no oscillations of period less than 2. Example 2. — Suppose that the given tabular values of the function f{x) are as follows : — f{a) = 0, J\a + w) = \, f{a+‘ho) = l, /{a + 3w?) = 0, /(a + 4?(;) = - 1, .... f{a -w)= - 1, /(a - 2tv) = - 1, f{a - Siv) = 0, f(a - 4:iv) = 1, . . . . , so that by (4) the cardinal function is in this case sin I - - a) I r ^ ^ ^ ) \_x- a + iv X- a + 10 x -a- 1 1 2io X- a + 2io x-a- iiv + 1 a; - a + x - a-bw J Now remembering that cot {x - a - to) 3iv 3w 3w I 1 7T ] X - a 1 1 1 + ^ + w X- a + 2io x-a - ^'10 x-a-\-biv + i- no ) and 7t{x -a + io) _3io { 1 7T 1 a? cot 3w 1 1 + a + w X - a + 4:10 x- a-2w x - a + 7io 1 X - a-bio + } we see that this cardinal function is * / -(a; - a) I 1 . -sm , Trix-a + w) , irix-a-w) cot - cot ^ ^ - ' 3io ow or 1 . 7t{x - a) . 2tt — o sm sm S to 3 , . 7t(x - a + to) . 7t(x - a- w) ^ sm 5 sm ^ 3to 6w so, making use of the identity sin 3x = - 4 sin x sin sin (^x " ^ > we obtain the cardinal function corresponding to the above tabular values in the simple form 2 , '7t{x - a) sm — 5 • J3 It will be noticed that in Example 1 the tabular values of the function tend to the limit zero for infinite values of the argument, whereas in Example 2 they do not tend to the limit zero. * It is not in general permissible to alter the order of the terms in a conditionally convergent series : but it may readily be proved that in the present case the value of the sum is not altered by the particular rearrangement which is made. 1914-15.] Expansions of the Interpolation-Theory. 189 § 6. Direct proof of the properties of the cardinal function. Let C(x) denote the cardinal function associated with a given function f(x), so that f{a + 7'iv) sin I ~{x- a- w) I ( w ) C(x)=2 ~ {X- a — rtv) Then we can prove the characteristic properties of this function directly. 1°. C(x) is cotabular with f(x). sin I — — a — rw) i ( w ) For the expression — a — rw) has the value unity when IV x->{a-{-rw), and has the value zero when x has any other one of the values a, a-{-w, a — w, a-\-2w, . . . From this it follows at once that C{a + nv)=/{a + rw) (r = 0, ±1, ±2, ±3, . . . .), which establishes the property of cotabularity. 2°. C(x) has no singularities in the finite part of the x-plane. For a singularity at any point would give rise to a failure of con- vergence of the series (3) at that point : but its convergence, for the class of functions f(x) considered, can readily be deduced from its mode of origin as a sum of residues. 3°. When C(x) is analysed into periodic constituents by Fourier's integral-theorem, all constituents of period less than 2w are absent. For if we resolve the function sm w ) (5) (where c denotes any constant) into periodic constituents by Fourier’s integral-theorem, we have -{x - c) i ^ sin I -(/X - c) I cos | \{x - /x) | dX I (7/x — -{x - c) -{[X - c) writing y for 7t(m - w w , = —^\ dX sin y cos \Xx — Xc dy Xiv y 190 Proceedings of the Poyal Society of Edinburgh. [Sess. Now it is well known that is zero when k>l\ and sin y cos ky > y dy sin y sin ky y dy is always zero. Hence in the above repeated integral the first integration gives a zero result so long as \w > ir ; that is to say, there are in the expression (5) no constituents of the type cos {\{x — iul)} for which \w>7r, and for which therefore the period is less than 2w. The theorem being thus seen to be true for every single term of the series (3), is consequently true for the cardinal function as a whole. We may remark in passing that it is possible to construct an infinite number of functions cotabular with f(x) by means of series more or less resembling the series (3) : for instance, the function sin— (x -a- rw) n w r 1 1 where c denotes any real positive constant, and m and n denote any positive integers, is a function cotabular with f(x). But this function does not possess the property characteristic of the cardinal function, namely, that periodic constituents of period less than 2w are absent. Such functions are, however, all of them solutions of the problem “ To find an analytical expression for a function when we know the values which it has for the values a, a-fw, a — w, a + 2w ... of its argument ” ; which is essentially the fundamental problem of the theory of interpolation. § 7. Solution of the questions proposed m § 1. We are now in a position to answer the first of the questions proposed in § 1, as to which of the functions of the cotabular set is represented by the expansion /u -t + 9T— oYo + 31 67 i + 4! The answer is that this expansion represents the cardinal function. This we shall now prove. 1914-15.] Expansions of the Interpolation-Theory. 191 Consider the algebraical identity 1 + nw + n{n — \)w‘^ z- a-nw z - a {z- a){z - a-w) {z-a + w){z - a)(z -a-w) (n + l)n{n — \ )w^ + + {z - a + tc){z - a){z - a - w){z - a - 2io) n{ii^ - - 2^) ... . - (r - l)^}(w - {z — a){{z-aY-iv‘^)[(z-aY‘-2‘^w^) .... [{z - - rhv‘^} 7^(7^2- 12)(^2_22) .... (n2 - r2)w;2-+i {z - a){{z - ay - w‘^) .... [{z - ay - rhv'^]{z - a - nio) Let f{x) be the given function, and let C(x) be the corresponding cardinal function. Multiply the identity (6) throughout by (z), and integrate Ztt'I with respect to 2; round any simple contour y which encloses all the points a, a-\-w, a — w, a-\- 2w, . . . . , a -f- rw, a — rw, a + nw. Now we have 1 i C{z)dz ' y ^ ±.f 27rijy z- a-nw Q{z)dz ■ibT- ^Trijy C(z)dz z - a 2lw^ {z — a){z — a- w) C{z)dz 27^^ jy {z-a-\- iv){z - a){z -a-w) Thus the equation (6) becomes C(« + nw) =/„ + «8/i + = C(a + nw) = C(a)=/„ = C(a + w) - C(a) =/, -/, = 8/j = 8%, etc. 3! ?^(?^2 - 12)(?^2 - 22) .... {n^^ - {r - \)‘^]{n - + 2H ^ + -f — ^7^^ Jy (z — 7^(7^2 - 12)(^2 _ 22) . (?^2 - 27rijy (z - a) {(z - a)^ - .... {(z - a)^ - rVj(z - a ~ nw) We have now to investigate the value of the last term in the right-hand side as r increases indefinitely. Since C(z) has no singularity in the finite part of the plane, we are free to extend the contour as much as we like. We can suppose it to be a circle of very large radius, whose centre is at a + nw. Now the integrand, apart from the factor C(0) z— a— nw may be written n\ 1 r 22 1 - i 1 _ i i I I V IV ) \ \‘^W^ J I 22^(;2 j • ' ' ■ [ {z - a) 2 192 Proceedings of the Eoyal Society of Edinburgh. [Sess. and when r increases indefinitely this tends to the value sin TTfi . 7r(z — a) sin — ^ - lu so that the integral to be studied is essentially r C(z)dz sin 7T?z 7r(z - a) Iz - a — 7UV) sin - Jy w . (8) The question as to whether this integral tends to zero or not depends fundamentally on whether C{z) becomes infinite to a lower or higher order than sin when the imaginary part of 2; tends to infinity. Now a simple periodic function like sin \z becomes infinite to the same order as e^y, where y denotes the modulus of the imaginary part of 2:: and we have seen that the distinguishing property of the cardinal function C(z) is that the periodic constituents into which it can be analysed all have periods greater than 2w : so, combining these statements, we see that C(^) becomes infinite to an order less than , whereas sin — — becomes infinite to IV Ly. the order 6^ Thus the factor sin •(^ - 0^) w of the integrand tends to zero when the imaginary part of 2; tends to dz either positive or negative infinity : and as the other factor may be written idO, where 0 denotes the vectional angle of the point 2; measured from the origin a + tiw, we see by a proof of the kind usual in analysis that the integral (8) vanishes.^ The equation (7) now becomes C(a + nw) =/o + 7^S/x + n{n-\) {n+l)n(n-\) 2 ! 3 ! + + ad. inf., which shows that the function rejpresented by the expansion is the cardinal function of the cotabular set which is associated with the given function f(x).f * The manner in which the characteristic properties of the cardinal-function are required in order to ensure the vanishing of this remainder-term is v^ery remarkable. t It should be noted that the interpolation-expansion considered is a “central- difference ” formula, i.e. it makes use of all the tabulated values of f{x) both above and ]93 1914-15.] Expansions of the Interpolation-Theory. The first question proposed in § 1 is thus answered ; and the answer to the second question follows from it, since we have seen in §§ 4-5 how the cardinal function may be constructed analytically. § 8. Conclusion. The cardinal function may be regarded from many different points of view. We defined it originally as that (unique) function of the cotabular set which has no singularities in the finite part of the plane and no constituents whose period is less than twice the tabular interval w. But the result of § 7 shows that it might be defined as the sum of the central- difference expansion formed with the given set of tabular values : or (what amounts ultimately to the same thing) it might be defined as the limit, when r->oo, of that polynomial in x of degree 2r which has the values /q, /^, f^, /_2, when the argument has the values a, a + ia, a — w, . . . . , a-{-rw, a — riu respectively. When we regard it from this latter point of view, we see the underlying reason for the absence of singularities in the finite part of the plane and of short-period oscillations. The introduction of the cardinal function seems to necessitate some reconstruction of ideas in the general theory of the representation of an arbitrary function by a series of given polynomials, say f(x) ^ cIqPq(x) -1- aii?i(ir) + ^ ad inf. Our ideas on the subject of these expansions have hitherto been based chiefly on the study of the two best-known cases, namely, Taylor’s expansion f{x) = aQ-\- afx - a) + afx - a)‘^ + af^x- aY + . ... , and the expansion in terms of Legendre functions f{x) = af?fx) + a^fx) + afdfx)+ .... Now it so happens that in both these special cases the roots of the given polynomials are either all concentrated in a single point (as in Taylor’s expansion) or else everywhere-dense on a finite segment of the real axis (as in the Legendre case, the roots of P,i(^r) when n~^cc being everywhere- below a. In the case of an interpolation-formula such as Newton’s, namely, f{a + nw)=fQ + nfi + n(n-l) 2 ! n(n-l)in-^) use is made only of the tabulated values of f(x) for the values a, a + w, a + 2w, .... of the argument, and no use is made of the tabulated values of f(x) for the values a — w, a — 2w, a — 3w, .... of the argument ; in such cases a wholly different theorem holds, which I hope to give in a later paper. VOL. XXXV. 13 194 Proceedings of the Royal Society of Edinburgh. [Sess. dense on the segment of the real axis between —1 and +1). In such cases the coefficients a^, a2, .... of the expansion can be determined in terms of f{x), and there is no doubt as to what function is represented by the expansion so long as it converges — there is nothing analogous to the property of cotabularity. When, however, the roots of the polynomials, instead of being everywhere-dense on a segment, are distributed discretely over the whole infinite length of the real axis of x (as is the case in the expansion /o + i + - 1) _^(w+l)n(n-l) 2! ^8% + ^ 3! where the polynomials are 1, n, n(n—l), (n-i-l)n(n — 1), etc.), it seems probable that a property analogous to cotabularity will come into evidence, and the theory of the expansion will depend essentially on a “ cardinal function ” analogous to that introduced above. The results of the present paper suggest another development. For long past the applied mathematicians have complained that Pure Mathematics is daily becoming more complicated and harder to understand. This complaint refers chiefiy to the increased rigour with which the theories of Analysis are now expounded, and which is closely connected with the extension of knowledge regarding discontinuities, singularities, and other phenomena of which the older mathematics took no account. Indeed, the modern Theory of Functions of a Real Variable is concerned largely with cases in which the distribution of fluctuations and singularities transcends all intuitive or geometrical representation. It seems possible that some of the difficulties of such cases might be avoided by the introduction of a function analogous to the “ cardinal function ” of the present paper, which would be simpler than the function under discussion, but would be equal to it for an infinite number of values of the variable, and could be substituted for it in all practical and some theoretical investigations. {Issued separately July 13, 1915.) 1914-15.] Influence of Feeding on Composition of Milk. 195 XIX. — On the Composition of Milk as affected by Increase of the Amount of Calcium Phosphate in the Rations of Cows. By A. Lauder, D.Sc., and T. W. Fagan, M.A. (MS. received May 11, 1915. Read June 21, 1915.) The various factors which are supposed to influence the composition of milk have already been the subject of numerous investigations. The general result of these has been to show that within very wide limits the com- position of milk is very little affected by the nature of the food supplied. As regards the mineral constituents the results of some of the investi- gations are rather conflicting, and while there is a general consensus of opinion that the composition and amount of the mineral constituents are independent of the food-supply, certain investigators claim to have been able to increase both the calcium and phosphoric acid in the milk by slight amounts. Duclaux'*^' in 1893 investigated the preparation of the so-called ‘‘phos- phate milk,” in which the phosphates are supposed to have been in- creased by feeding calcium phosphate to the cows. He found, however, no more than the normal percentage of phosphates in milk obtained in this way. Somewhat later J. Neumann]* investigated the same question, and came to the conclusion that he had been able to increase both the calcium and the phosphoric acid. He suggests that the negative results obtained by other workers are due to their not having continued the experiment long enough, as the results became apparent only after three or four weeks. His average figures are ; — CaO. P2O5. Without calcium phosphate . . 0T479 0T960 With „ „ . . 0T592 0-2132 The differences are slight, and, as will be seen later, appear to be within the limits of natural variation. He concludes, however, that the production of the so-called phosphate milk by special feeding is im- possible. In 1894 H. WeiskeJ attacked a somewhat different side of the problem. * Ann. Inst. Pastern^ 1893, 2-17 ; Chem. Soc. Jour.., Ixiv (1893), ii, 582. t Milch Zez7.,xxii, 701-704 ; Ghem. Soc. Jour., 1894, ii, 246. I Landw. Versuchs-Stat., 1894, xlv, 242-245 ; Chem. Soc. Jour., Ixviii (1895), ii, 121. 196 Proceedings of the Royal Society of Edinburgh. [Sess. He. investigated the effect of adding calcium phosphate to the milk fed to calves. He found, contrary to the earlier work of Neumann,* that the calcium phosphate had no injurious action, and that it even appeared doubtful if it had any efiect at all. The influence of the addition of various salts to fodder on the com- position and yield of the milk produced was further studied by Von Wendt. j* The salts experimented with were sodium chloride, calcium carbonate, sodium phosphate, magnesium bromide, calcium glycero-phos- phate, and calcium hydrogen phosphate, and he concluded that none of these salts influenced the composition of the milk in any deflnite way. Calcium hydrogen phosphate, however, was considered to increase the yield and generally to a slight extent the amount of calcium. In 1911 Fingerlingf tried the effect of food deficient in calcium and phosphoric acid on the secretion of milk. When these are deficient in food they are, for some time, provided by the organism without diminish- ing the activity of the milk glands. He concludes that the percentages of calcium and phosphorus in milk are only slightly affected by deficient feeding, and tend to increase rather than diminish. For the present investigation six cows of the dairy shorthorn breed were selected, as nearly equal as possible in regard to age and period of lactation. They were then divided into two lots of three each. The yield of milk given by each cow was determined at every milking by weighing. Weekly samples of the milk of each cow were also taken for analysis, and the percentages of phosphoric acid, ash, fat, and “ solids not fat” determined. The experiment was commenced on 10th December, and for flve weeks all the cows were fed alike and received the followinp; ration : — O 75 lb. turnips. 4 „ Bombay cotton cake. 1 „ bran. 8 „ hay. Straw {ad lib.). The mineral matter in this ration, exclusive of the straw, contained about *5 lb. of calcium phosphate. The analyses made during this preliminary period (Tables I and II) showed that the percentage of phosphoric acid and mineral matter in the milk of each cow was relatively constant, although there were slight * J. Landw., 1894, xlii, 33. t Ghem. Gentr., 1908, ii, 1881 ; Ghem. Soc. Jour., xcvi (1909), ii, 164. ; Landw. Versuchs-Stat., 1911, Ixxv, 1 ; Ghem. Soc. Jour., c (1911), ii, 510. 197 1914-15.] Influence of Feeding on Composition of Milk. differences in the amount when one cow was compared with another. The percentage of fat, as is usually the case, showed more variation (Table III). Lot I was kept on the same ration during the whole period of the experiment. On 15th January the feeding of calcium phosphate to the cows in Lot II was commenced, the quantities added to the ration of each cow being as follows : — For the first 3 days: 2 oz. per day. „ „ next 4 „ 4 „ „ j j 5 j 7 ,, b ,, ,, ,, 21 8 The addition of calcium phosphate was then stopped and the original ration continued for other two weeks. An examination of the percentages of phosphoric acid found shows that the addition of calcium phosphate has not increased the amount of phosphoric acid in the milk. There is practically no change, and the results vary less than those obtained from Lot I, where the cows were on the same ration all the time. Since the cows were receiving calcium phosphate over a period of five weeks, Neumann’s criticism that the negative result is due to the experiment not being continued sufficiently long is inapplicable in this case. The increase in the amount of phos- phoric acid (•0172) which he claims to have effected appears to be well within the ordinary limits of variation. In the same way an examination of the percentages of fat, ash, and “solids not fat” obtained (Tables II, III, and IV) does not indicate that the extra calcium phosphate fed to Lot II has had any effect on the amount of these substances secreted. Finally, no definite effect on the yield can be observed. The investigation was carried out at Bangour Village Farm, and we have to express our indebtedness to the Edinburgh District Board of Control for providing the facilities for the work. [Table I 198 Proceedings of the Royal Society of Edinburgh. [Sess. Table I. Showing the Percentage of Phosphoric Acid (P2O5) in the Milk. Lot I. (No Phosphate.) t Cow 1. Cow 2. Cow 3. Date. Notes. 1 1 A.M. P.M. A.M. P.M. A.M. P.M. Dec. 10 0*26 0-24 0-25 0-23 0-24 0-24 i 1 M 17 0-28 0-24 0-24 0-23 0*21 0-24 [ Preliminary I period. Jan. 7 0 25 0-26 0-23 0*23 0-21 0-25 1 14 0-27 0-27 0-24 0*24 0-23 0-22 Average 0-26 025 0-24 0-23 0-22 0-24 j Jan. 21 0-27 0-27 0*24 0-24 0-25 0-27 28 0-29 0-29 0-26 0-26 0-27 027 Feb. 4 0-28 0-28 0-23 0-29 0-26 0-26 - Middle period. 1 ?? 11 0*30 0-29 0-26 0-21 0-28 0-20 1 18 0-29 0-29 0-25 0*24 0-26 0-26 Average 0-29 0-28 0-25 0-25 0-26 0-25 Feb. 25 0-29 0-29 0-24 0-25 0-25 0-25 1 1 1 Mar. 4 0-29 0-29 0-23 0-24 0-27 0-26 1 1 End period. Average 0-29 029 023 0-24 026 0*25 J Lot II. (With Phosphate.) Date. Cow 4. Cow 5. Cow 6. Notes. A.M. P.M. A.M. P.M. A.M. P.M. Dec. 10 0-22 0T9 0-33 0-28 0-25 1 17 0-20 0-20 0-28 0-27 0-23 0-21 T) V • Jan. 7 0-19 0-19 0-25 0-26 0-22 0-22 1 1 X rBliniiiiary 14 0-22 0-21 0-26 0-29 0-22 0-26 1 j period. Average 0-21 0-20 0-28 0-27 0-23 023 J 1 Jan. 21 0-22 0-22 0*28 0-27 0-22 0-22 28 0-22 0-23 0 29 0-26 0-22 0-22 Feb. 4 0-20 0-22 0-27 0-26 0-24 0-24 With additional 11 0-21 0-19 0 29 0-30 0-24 0-23 phosphate. 18 0-21 0-21 0-28 0-29 0-22 0-22 Average 0-21 0-21 0-28 0-27 023 0-23 j Feb. 25 0-22 0-21 0-28 n-28 0-23 0-22 Mar. 4 0-20 0-23 0-27 0-29 0-23 0-22 ^ Jliiici psriocl Average 0-21 0-22 0-27 0-28 0-23 0-22 JJllUOJJXiClLCy. 1914-15.] Influence of Feeding on Composition of Milk. 199 Table II. Showing Percentage of Ash in the Milk. Lot I. (No Phosphate.) Cow 1. Cow 2. Cow 3. Date. Notes. A.M. P.M. A.M. P.M. A.M. P.M. Jan. 7 „ 14 Average Jan. 21 „ 28 Feb. 4 » 11 „ 18 Average Feb. 25 Mar. 4 Average 0-77 0-75 076 0-84 0*79 0*77 0-81 0-80 0-80 079 0-80 079 0-82 0-82 0-84 0-83 0-85 0-83 0-87 077 082 070 071 070 0-85 071 072 073 075 074 073 073 079 072 073 074 074 074 073 073 073 074 070 072 074 072 075 075 078 0 75 078 077 0 77 07*7 074 074 076 073 075 073 075 074 1 Preliminary ^ period. 1 Middle period. End period. Lot II. (With Phosphate.) Cow 4. Cow 5, Cow 6. Date. Notes, A.M. P.M. A.M. P.M. A.M. P.M. Jan. 7 „ 14 075 073 077 077 0-69 1 Preliminary C period. Average 0-74 077 0-69 Jan. 21 073 07*6 0*81 076 0-69 0-67 „ 28 073 076 074 077 0-66 074 Feb. 4 071 071 079 0-82 071 0 71 W'ith additional „ 11 071 077 0-85 0-87 071 072 phosphate. „ 18 073 074 077 0-80 072 071 Average 072 0 75 079 0-80 070 071 Feb. 25 074 074 0-81 0-80 0-69 070 f End period r (no phosphate). Mar. 4 073 075 0-81 0-81 0-68 0-69 Average 073 074 0-81 0-80 0-68 0-69 200 Proceedings of the Royal Society of Edinburgh. [Sess. Table III. Showing Percentage of Fat in the Milk. Lot I. (No Phosphate.) Date. Cow 1. Cow 2. Cow 3. A.M. P.M. A.M. P.M. A.M. P.M. Dec. 10 3-60 4-30 3-40 4*00 3*20 4*30 17 3-70 4-00 3*90 4*20 3*00 4*70 Jan. 7 3-90 3-80 3*35 3*50 3*50 3*00 55 14 4-50 3-50 4*25 3*60 3*30 4*10 Average 3-90 3-90 3*72 382 3*25 402 Jan. 21 4-70 3*70 4*50 3-00 3*70 3*30 55 28 4-35 3*80 3*70 3*30 3*20 3*00 Feb. 4 4-20 3*40 4-60 4-70 3*60 2*70 55 11 4T0 3*50 3-55 3-50 3*30 3*10 55 18 3-90 4-00 3*65 2*90 3-35 3*45 Average 4-25 3-68 4*00 3-48 3*43 311 Feb. 25 4T0 4*00 4*10 3*90 3*30 4*00 Mar. 4 3-90 4-25 3*45 3*75 3*50 3*70 Average 400 417 3-77 3*82 3*40 3-85 Notes. Preliminary period. V Middle period. End period. Lot it. (With Phosphate.) Cow 4. Cow 5. Cow 6. Date. Notes. A.M. P.M. A.M. P.M. A.M. P.M. Dec. 10 » n Jan. 7 » 14 Average Jan, 21 „ 28 Feb. 4 » 11 „ 18 Average Feb. 25 Mar. 4 Average 3*00 3*20 3-00 3-60 3*20 3*20 3*30 3*05 3*15 3*00 314 3*40 2*75 3*07 3*00 3*15 3*10 3*00 3*06 2- 90 2*95 3*10 2*85 3- 20 300 2*90 3*10 300 4*00 3*90 3*00 2*40 3*32 3*70 3*60 3-00 3*20 3*40 3-38 2*65 2*80 2*72 4*70 3-80 1*80 3*80 3*52 3*40 4*00 1 2*90 4*00 3*30 3*52 3*60 3*60 3*60 3-90 3*20 2*60 3*45 3*29 2*30 2*30 1*90 2*95 2*30 2-35 2*60 3*10 2*85 400 2*50 3-25 2*95 317 3-80 3*25 3*35 3*10 2-30 316 2*40 3*10 2-75 ] Preliminary j' period. With additional 1 phosphate. ■ End period ^ (no phosphate). 1914-15.] Influence of Feeding on Composition of Milk. 201 Table IV. Showing Percentage of “Solids not Fat” in the Milk. Lot I. (No Phosphate.) Cow 1. Cow 2. Cow 3. Date. Notes. A.M. P.M. A.xM. P.M. A.M. P.M. Jan. 7 n 14 8-93 9*02 9-00 8*75 8*77 8*84 9*02 8*92 9*11 > i Preliminary period. Average 8-97 9-ob 8*76 8-84 8*97 9ii Jan. 21 9-32 9-34 9*07 9*37 9*18 9*35 A „ 28 9-21 9*43 8-91 9*23 9*25 9*39 Feb. 4 „ 11 8-95 9*02 9*32 9*32 8*64 9*37 9*09 9*47 9*53 9*57 9*23 9*64 - Middle period. „ 18 9-01 9*19 8*97 9*05 9*23 9*19 Average 910 9*32 8*99 9*24 9*35 9*36 Feb. 25 9-04 9*21 8*94 9*15 9*27 9*04 ) Mar. 4 9-34 9'31 9*36 9*34 9*47 9*51 i - End period. Average 919 9*26 915 9*24 9*37 9*27 Lot II. (With Phosphate.) Cow 4. Cow 5. Cow 6. j 1 Date. 1 Notes. A.M. P.M. A.M. P.M. A.M. P.M. Jan. 7 „ 14 8*37 8*54 8*34 9*42 9*50 8*88 9*56 8*80 8*40 ) Preliminary period. Average 8*45 8*34 9*46 8*88 918 8-40 i Jan. 21 8*61 8*72 9*28 9*38 8*89 8*62 „ 28 8*43 8*77 8*92 9*13 8*60 8*41 Feb. 4 8*35 8*47 8*97 9*34 8*71 8*73 With additional „ 11 „ 18 8*62 8*80 8*99 9*21 8*73 8*61 phosphate. Average 8 50 8*69 9*04 9*26 8*73 8*59 Feb. 25 909 9*12 9*57 9*46 9*33 9*77 i End period (no phosphate). Mar. 4 Average 8*79 8*94 8*93 9*02 9*55 9*56 9*38 9*42 8*55 8*94 8*76 9-26 202 Proceedings of the Poyal Society of Edinburgh. [Sess. Table V. Showing the Yield of Milk (in lbs.) per Week for each Cow. Week Ending Lot I. (No Phosphate.) Lot II. (With Phosphate.) Notes. Cow 1. Cow 2. Cow 3. Cow 4. Cow 5. Cow 6. Dec. 13 2390 255-25 218-5 300-5 211-5 3470 5 j 20 244-0 265-5 218-0 298-5 208-75 347-5 55 27 236-0 261-0 215-0 288-0 207-0 339-0 • Jan. 3 216-0 243-5 201-5 285-0 189-5 318-5 PreJiniinary 5? 10 219-0 226-0 205-5 280-0 184-5 306-5 period. 17 226-0 243-5 213-0 288-0 187-5 296-0 Average 2300 249-1 211-9 290-0 198-75 325-7 > Jan. 24 214-0 235-0 206-0 300-0 188-0 293-25 A 55 31 215-5 229-5 203-0 302-0 175-5 284-5 Feb. 7 216-5 215-5 196-0 295-5 168-5 276-0 cl d. 1 L 1 0 ri 3, 1 55 14 203-5 220-5 202-0 296-5 156-0 277-0 •- to T nf TT 55 21 208-0 218-0 202-5 294-5 153-0 273-5 IjOL 1 L. Average 211-5 223-7 201-9 297-7 168-2 280-85 Feb. 28 201-0 219-5 196-0 294-5 153-0 2600 ) 1? A -A Mar. 7 200-5 215-0 196-0 296-0 136-5 242-0 f Jhnci p6rioQ. Average 200-7 217-25 196-0 295-25 144-75 2510 ^ ^Tio pldospld^tc^. Chemistry Department, College of Agriculture, Edinburgh, 3Iay 10, 191 {Issued separately September 27, 1915.) 1914-15.] Meteorological See-Saw over Antarctic Seas. 203 XX.— On a See-Saw of Barometric Pressure, Temperature, and Wind Velocity between the Weddell Sea and the Ross Sea. By R, 0. Mossman. (MS. received May 28, 1915. Read June 28, 1915.) In the course of a large inquiry on the inter-relations between the meteoro- logical conditions in Antarctica and the Southern Ocean, on the one hand, and those prevailing in the southern continents, more especially South America, on the other, there has come to light an interesting see-saw between the barometric pressure, air temperature, and wind velocity in the Weddell and the Ross Seas. The above inquiry, which I hope to lay before this Society shortly, refers to the eight-year period 1902-09 ; and since the present paper deals with the years 1902, 1903, 1911, and 1912, I have thought it better to make it the subject of a separate communica- tion. The positions of these stations and others where observations have been made are shown on the accompanying map, for which I am indebted to Dr H. R. Mill. The figures within the rings give the number of years covered by the records at the various places. The data for the Ross Sea are derived from Scott’s two expeditions * which wintered in M‘Murdo Sound, and those for the Weddell Sea are based on the observations initiated by the Scottish National Antarctic Expedition at Laurie Island, South Orkneys, and carried on since February 1904 under the direction of the Argentine Meteorological Office. As the observations at the South Orkneys did not begin tiil March 1903, the data available from the neighbouring station occupied by the Nordenskjold Expedition at Snow Hill, Graham’s Land, have been laid under contribution. Fortunately the two series overlap during eight months, and it has thus been possible to interpolate values by differential methods, and fill in the deficiencies that exist for the period March 1902 to March 1903 covered by the M‘Murdo Sound observations. This applies to temperature and wind data, the mean monthly pressures during the above period having been measured off* the monthly isobaric charts given in the Meteorologischer Atlas, Deutsche Sildpolar Exioedition, 1901-03, by Drs Meinardus and Mecking.]- The following are the posi- * The data derived from Shackleton’s Expedition of 1908-09 are not yet available, except provisional temperature means, t Berlin, 1911. 204 Proceedings of the Royal Society of Edinburgh. [Sess. tions of the stations and the periods covered by the various observations utilised : — Station. Lat. Long. Period. M‘Murdo Sound ^ . . . M‘Murdo Sound t . . . Laurie Island, South Orkneys Snow Hill, Graham’s Land § 77° 5L 77 38 60 44 64 22 166° 45' E. 166 24 E. 44 39 W. 57 0 W. Feb. 1902-Feb. 1904. Jan. 19il-Dec. 1912. Apr. 1903-Feb. 1904, 1911, 1912. Apr. 1902-Nov. 1903. METEOROLOGICAL RECORDS IN SOUTH POLAR REGIONS. The data are discussed in three-monthly groups corresponding to the four seasons in temperate latitudes. Had monthly means been used, it would have considerably increased the scope of the inquiry without adding * National Antarctic Ex'pedition^ 1901-04: Meteorology^ part i, p. 408. t Simpson, Quart. Jour. Roy. Met. Soc., vol. xl, p. 222. t Scotia" Reports.) vol. ii, Physics] Anales de la Oficina Meteorologica Argentina, Tomo xvi. Data for 1911 and 1912 in manuscript. § Wiss. Ergehnisse dtr Schwedischen Siidpolar Expedition, 1901-03, Band ii, pp. 353, 355. 1914-15.] Meteorological See-Saw over Antarctic Seas. 205 much to its interest. The mean seasonal values for M‘Murdo Sound and Laurie Island, South Orkneys, are as follows : — ______ Months. Barometer, Mean corrected to 0° C., Sea-Level, and I. at. 4y. Temperature in Degrees Centigrade. Wind Velocity, Metres per Second. M‘Murdo Sound. South Orkneys. M^Murdo Sound. South Orkneys. M‘Murdo Sound. South Orkneys. Evange- lists’ Island. 1 (Beaufort.) Dec., Jan., Feb. Mar., ApL, May June, July, Aug. Sept., Oct., Nov. mm. 745-6 44-7 40- 7 41- 9 mm. 744-5 43- 2 44- 0 42-3 - 6-1 -20-7 -25-6 -18-5 - 0-4 - 4-5 - 10-0 - 5-1 5- 5 7-1 7-4 6- 2 1 4-3 i 4-8 6-6 ' 4-9 6-4 4-8 4-9 4-7 The salient features of the see-saw are shown in Table I, in which the departures from the normals in the barometric pressure, temperature, and wind velocity are given for each seasonal three-monthly group. Baro- metric pressure is given in millimetres, temperature in centigrade, and wind velocity in metres per second. The mean wind velocity on the Beaufort scale as recorded at Evangelists’ Island at the Pacific entrance to the Straits of Magellan (lat. 52° 24' S., long. 75° 06' W.) is also shown. Records from this station are of particular interest owing to its position, about midway between the South Pacific high-pressure area and the Bellingshausen Sea low-pressure area. As we have shown,^ there exists over the South Pacific a well-marked see-saw of pressure, temperature, and wind velocity just as marked — even more so, in some respects — as the one existing between the Weddell Sea and Ross Sea areas. Every confidence attaches to the uniformity of the wind data, since the observations throughout the four years under review were made by the same observer, Sehor Eduardo Williams, keeper of the light- house, in what is one of the most inclement regions on the surface of the globe. The hours of observation were 8 a.m., 2 p.m., and 9 p.m. during the seasons of 1902, 1903, and 1904, and 7 a.m., 2 p.m., and 9 p.m. during 1911 and 1912.t * “ Meteorology in Weddell Quadrant during 1909,” Scot. Geog. Jour., vol. xxvi, p. 413. t Data till February 1904 from tlie Anuario del Servicio Meteorologico de la Direccion del Territorio Maritimo, 1902, 1903, and 1904, and for 1911 and 1912 from the Anuario Meteoro- logico de Chile, by Dr Walter Knoclie, Director. [Table I 206 Proceedings of the Poyal Society of Edinburgh. [Sess. Table I. — Showing the Departures from the Normal of Barometric Pressure, Temperature, and Wind Velocity at M‘Murdo Sound (1) and Laurie Island, South Orkneys (2). Wind Velocity on Beaufort Scale is given for Evan- gelists’ Island (3). Pressure. mm. Temperature in Degrees Centigrade. Wind Velocity, Metres per Second. Summer: Dec., Jan., Feb. (0 (2) (1) (2) (1) (2) (3) 1902-03 + 1-7 -1*2 -0*5 -0*8 -2*0 4-0*2 -1*1 1903-04 -3*4 -2*2 4-lT 4-0-5 - 1*9 4-0*5 -0*1 1910-11* . -3-9 4-0*5 4-0*6 -0*1 -b2*4 -0*6 + 0*1 1911-12 4-5*5 4-3*1 -1*3 4-0*4 4-1*4 -0*2 -80*9 Autumn : Mar., April, May. 1902 . 4-2*2 -1*1 4-0*8 4-1*2 -1*4 4-1*7 -0*8 1903 . 4-1*0 -1*0 -3*3 -0*7 -2*6 4-1*8 -0*6 1911 . -0*9 4-6*4 4-2*1 4-0*5 + 0-8 -1*7 -80*9 1912 . -2*4 -4*2 4-0*5 - 1*0 -h3*3 -1*6 -80*5 Winter : June, July, Aug. 1902 . 4-1*2 -2*1 4-0*3 -2*8 -2*3 4-2*6 -1*1 1903 . -F3*9 -0*5 -1*7 4-0*4 -2*8 4-0*3 -0*5 1911 . -1*0 4-lT -2*5 4-3*3 -0*2 - 1*4 4-1*2 1912 . -4*0 4-1-6 4-4*0 - 1*1 -F5*4 - 1*5 4-0*2 Spring : Sept., Oct., Nov. 1902 . 4-4*0 -1*3 -0*9 -1*6 -2*1 4-1*6 -1*2 1903 . -5*4 4-1*2 -1*1 4-0*2 - 1*2 -0*3 -0*1 1911 . -0*1 4-2*2 -0*5 4-1*1 4-1*0 -0*6 4-0*1 1912 . 4-1*4 -1*9 4-2*5 4-0*3 4-2*5 -0*5 4-1*3 A study of these numbers seems to establish the existence of a pro- nounced see-saw in the case of barometric pressure and wind velocity at all seasons of the year. In the sixteen seasons discussed there are only three instances in which as regards barometric pressure the deviation from the normal is characterised in the two cases by the same sign, viz. the summers of 1903-04 and 1911-12, and the autumn of 1912. Again, only in the winter of 1911 and the spring of 1903 is the sign of the departures of the wind velocity from the normal the same at these two widely separated stations. As regards temperature the results, except for the winter period, are indefinite ; during this season, however, the contrast between the two regions is strongly marked. The comparative failure in the pressure see-saw in summer is doubtless due to the relatively feeble Antarctic circulation then prevailing, there being at this time a levelling-up * For pressure and wind velocity the values refer only to the months of January and February 1911. For temperature, December 1910 at Cape Evans has been interpolated. 207 1914-15.] Meteorological See-Saw over Antarctic Seas. process due to the great transference of air from lower latitudes to the Antarctic Continent. It must be kept in mind that neither Laurie Island nor M‘Murdo Sound are situated in “action centres.” The Weddell Sea barometric minimum is located some 300 miles to the south of the South Orkneys and the Ross Sea minimum to the east-north-east of MMurdo Sound.^ What we are really discussing is therefore a somewhat modified result of the changes taking place, on the one hand, in the adjacent foci of cyclonic activity, and on the other in the conditions on the great Antarctic plateau — doubtless the controlling factor. As regards Laurie Island, the advance or retreat of the anticyclonic area that normally covers the south of Graham’s Land is also a prominent factor, more especially during late spring and early summer. It will be noted that the seasonal variations of wind force at Evangelists’ Island are in remarkable agreement with those recorded at M'Murdo Sound, since the signs differ in only one season, viz. the winter of 1911, while they are the reverse of those at Laurie Island except in the spring of 1903. As there is an agreement between the departures from the normal in pressure temperature and wind velocity at Laurie Island and on the west coast of Graham’s Land,f it follows that the Antarctic circulation in the South Pacific in high latitudes (63°-70° S.) must be in harmony with that in the Weddell Sea in similar latitudes. This indicates that the atmo- spheric circulation in the Bellingshausen Sea at least as far west as 100° W. long, is controlled, as is the circulation in the Weddell Sea as far east as the Greenwich meridian, by the conditions prevailing over the south of Graham’s Land and the continental area located to the south-west and * The mean wind at Cape Evans and Framheim during the period under review was about E.S.E., and at Cape Adare S.E. At Framheim (see Birkeland, “Remarks on the Meteorological Observations,” Appendix II of The South Pole, by Roald Amundsen, vol. ii, pp. 372-94, London, 1912) the percentage frequency for the period April 1911 to January 1912 was as follows : — N. N.E. E. S.E. S. S.W. W. N.W. Calm. 2 8 32 7 12 14 2 1 22 The percentage frequency was thus 7 with northerly winds, 40 with easterly, 22 with southerly, and 9 with westerly, calms being apparently much more frequent than at Cape Evans or Cape Adare. As, however, the winds at the two last-named stations were largely affected by local conditions, the results “ must be considered in the light of information which will be given in the discussion which is at present being written” (see Simpson, Quart. Jour. Boy. Met. Soc., vol. xl, pp. 224 and 226). For this reason it is unsafe to attempt to lay down the precise position occupied by the centre of the Ross Sea barometric minimum, which, doubtless, is subject, as are other “ action-centres,” to considerable variations from one year or season to another. t Scot. Geog. Jour., vol. xxvi, p. 413. 208 Proceedings of the Royal Society of Edinburgh. [Sess. south-east respectively. The Ross Sea area is under the influence of other action-centres already referred to, and in addition the cyclonic area to the south of the Indian Ocean probably forms part of the great cyclonic system which dominates conditions in M‘Murdo Sound. In discussing the M‘Murdo Sound data we must bear in mind that the climatic features of that region as regards temperature and wind velocity differ in a marked degree from those of contiguous places. A brief passing reference to these is desirable in the present instance, based on the syn- chronous data from April to December I9II at Framheim (lat. 78° 38' S., long. 163° 37' W.) and at Cape Adare (lat. 71° 18' S., long. 170° 9' E.). It is unnecessary to go into details, since a comprehensive memoir based on a very large mass of data is in course of preparation by Dr Simpson, F.R.S., Meteorologist to the British Antarctic Expedition of 19 10-13. The mean values of pressure temperature and wind velocity at the above three stations for the periods April to December I9II, April to September 1 91 1 (the winter season), and October to December, are given in the following table : — Barometer, Mean corrected to 0° C., Sea- Level, and Lat. 45°. Temperature in Degrees Centigrade. Wind Velocity. Metres per Second. Cape Fram- Cape Cape Fram- Cape Cape Fram- Cape Evans. lieim. Adare. Evans. heim. Adare. Evans. heim. Adare. mm. mm. mm. April-Dee. 743-1 738-7 740-9 -21-0 - 28°-8 -17-3 6-9 3-5 3-9 April-Sept. 741-2 736-1 738-6 -25-5 -35-7 -21-4 6-8 3-1 4-3 Oct.-Dec. . 746-8 743-9 745-4 - 12-0 -14-8 - 9-1 7-3 4-5 3-2 Hence it will be seen that in the nine months under review the mean pressure at Framheim was 4*4 mm. lower than at Cape Evans, the mean temperature 7°‘8 lower, and the mean wind velocity only half that recorded at the adjacent station. In winter (that is, from April to September) the contrast is most pronounced, the pressure at Framheim being 5T mm, lower, the temperature I0°*2 lower than at Cape Evans, and the wind velocity less than half. The maximum temperature difference, I5°*0, was reached in August ; and in this month the wind velocity was 7*4 m.p.s at Cape Evans and only 3T m.p.s at Framheim, while the pressure at the latter station was the lower by 5’8 mm. From October to December the differences between the two stations were less marked, the pressure at Framheim being the lower by 2‘9 mm. and the temperature lower by 2°-8, also the relative lightness of the winds at the barrier station was less pronounced than 209 1914-15.] Meteorological See-Saw over Antarctic Seas. during the winter season. For the three months ending January 1912 the levelling-up process became more pronounced, pressure being only 1*7 mm. lower at Framheim than at Cape Evans, and temperature 2°’5 lower. Pressure at Cape Adare was on the mean of the whole period (April to December) 2'2 mm. higher than at Framheim, temperature 11°‘5 higher, and the wind velocity 0*4 m.p.s. greater ; but from October to December the winds were lighter than on the barrier. Compared with the temperature at Cape Adare, some 380 miles to the north, the Cape Evans temperature is relatively high, the thermal gradient being only at the rate of 0°*7 C. per degree of latitude, while, as compared with Amundsen’s station, only 53 miles to the south and some 400 miles to the east, the excessive warming effect is remarkable. This is obviously due (1) to the Fohn effect caused by the suck-out and descent of the air from the mountainous Victoria Land, (2) to the effect of the lower pressure to the north-eastward over the Ross Sea (most pro- nounced in winter), and (3) partly to the greater frequency of calms at Amundsen’s station. (See footnote on page 207.) The fact that rises of temperature at Cape Evans were frequently accompanied by snow does not dispose of our view that dynamic heating was responsible for the relative warmth noted under these conditions. For it has been shown that under suitable topographical surroundings an appreciable warming effect is set up in rainy or snowy weather, due to the presence of mountainous areas over which the moisture-laden winds had previously passed.* This effect at MAIurdo Sound varies greatly from one year to another and was most marked in the period May to August of 191*2, when the mean pressure was 3‘6 mrn. under the four years’ normal for these months, the mean temperature 3°'7 higher, and the mean wind move- ment nearly double the average, blowing with a velocity of 12*4 m.p.s. or 5*0 m.p.s. above the average. The normal seasonal variations of pressure, temperature, and wind velocity from three regions where the available data are sufficient to give fair monthly means are shown in Table II. The means are based on four years’ data from M'Murdo Sound, nearly twelve years’ data from the South Orkneys, and a composite series from the west coast of Graham’s Land derived from Charcot’s two expeditions to that region, supplemented by the data from the Belgica records, covering three years in all. The wind velocity is not given for the latter series, since the data are not homogeneous. Looking at the tabulated values which give for each month the departures from the annual mean for each of the three elements, we observe that there are marked variations between the three localities. * “ The Meteorology of Glen Nevis,” Trans. Roy. Soc. Edin.., vol. xliv, pp. 652, 653. VOL. XXXV. 14 Table II. — Showing the Mean Barometric Pressure, Temperature, and Wind Velocity, and the Monthly Departures from THE Annual Means at M‘Murdo Sound, the South Orkneys, and the West Coast of Graham’s Land, with the adjacent Bellingshausen Sea. Barometer, Mean Corrected to 0° C,, Sea-Level, and Lat. dS*". 210 Proceedings of the Koyal Society of Edinburgh, [Sess, . GJ r-l V 6 p pi c5 S CO P dh P P 6 6 6 o; d ^ rH 1 1 1 . O 05 00 00 lO 00 w ^ p p V 9 9 V o> p g G cb o g »o P r-l lb P 6 P 6 6 6 P P P P P + + + 1 1 1 + + + + i 1 . 05 CO CD 05 lO CO p p P r-H p p CD O f> g lb >-H lb Gq Gq P 6 Gq Gq P P 6 6 6 6 6 6 S ^ ^ ^ I— 1 + 1 + 1 1 1 + + + + 1 . »0 00 CO X- Gq P T P X- CO Gq V 9 Gq lo g cb CO P 00 o o 6 P 6 6 P 6 6 6 6 6 6 o b CO 1 1 + 1 1 1 1 1 + + 1 + . GQ CD O -f' x^ P r" P p p jp *P 6 rH IH p , g cb P CO 6 6 6 6 6 6 P P P 6 6 6 6 6 CU b ^ Gq m b 1 + 1 1 1 1 1 1 1 1 1 + . CD CO Gq lo X- p p p p p p p p CD Gq g 05 cb Gq CO Gq r-H 6 6 P 6 6 P P P 6 6 6 b CO ^ Gq <1 1 + 1 1 1 1 till + + . CD 05 05 CD X- 00 lO CD p p p p p p p o Gq g 6 lb »b Gq .-H P 6 P 6 P oo P- 6 6 P 6 b Gq l-H rH rH t + + 1 1 1 1 1 1 1 + 1 . ri 05 r^H P 00 r-H 00 p ^ p P rH O CO g cj cb »b r-l Gq rH 6 6 P P P 6 P P 6 P 6 g Gq rH s ' 1 i i b S3 a 1 1 1 1 6 b g + 1 . CD 00 05 ^ CD 00 P P V p p p p 8 rH CD fS 05 lO Gq g GJ so lb ^ ^ 6 6 rH P 6 P GT 6 6 6 P 6 6 le 1 1 + 1 1 1 1 i 1 1 t-l 05 + ±_ ; . Gq CO § p o p o5 V 6 V ^ ^ p p ^ V 9 b Gq CD g CO P b cb P Gq o 6 6 P b P 6 P P O CO CD b 6 6 pin b ^ ^ ^ ■+H cC Gq - 'rtl r:tH ^ lO p ot^ O CD r- CD CD * ' CQ m ' ■ CO CO ’ cw CO " 02 CO . S . s .a ^ . b b a + o o M‘Miirdo Sound South Orkneys West coast Graha Land, and Belli hausen Sea M‘Murdo Sound South Orkneys West coast Graha Land, and Belli hausen Sea M‘Murdo Sound South Orkneys West coast Graha Land, and Belli hausen Sea M‘Murdo Sound Do. do. * South Orkneys West coast Graha Land, and Belli hausen Sea M‘Murdo Sound South Orkneys M‘Murdo Sound South Orkneys * Five years, including means of Shackleton’s British Antarctic Expedition, 1908-09, taken from a diagram facing p. 386, vol. ii of The Heart of the Antarctic, London, 1909. 211 1914-15.] Meteorological See-Saw over Antarctic Seas. At M‘Murdo Sound pressure is above the mean from November to April, reaching the annual maximum in December, and during the months May to October it is below the average, reaching the minimum in October. At the South Orkneys there is a pronounced maximum in June, July, and August when pressure at M‘Murdo Sound is at its seasonal minimum ; and there is a secondary maximum in December. The period of mini- mum pressure embraces the five months January to May ; in October also the pressure is slightly below the normal, and the most prominent minimum occurs in November. In the South Pacific area represented by the French and Belgian data, the maximum for the year, as at the other two stations, falls in December, and the minimum — which is very pronounced — from February to April. As at the South Orkneys, pressure is in excess of the normal in June and July. In summer — November to January — the departure is in harmony with that at M‘Murdo Sound. The temperature values show that the mean is above the annual average from November to March at M'Murdo Sound, from October to March in the South Pacific area, and from October to April at the South Orkneys, the prolongation of the warm period at this station being due to the absence of ice in the seas surrounding these islands until well on in autumn. At M‘Murdo Sound, as already pointed out, the values from April to September show little variation, due to the causes referred to. Temperature rises sharply in November, and continues rising into December, when the annual maximum is reached. An appreciable fall occurs in February, and in March and April continental conditions are asserting themselves, only to be checked in May. At the South Orkneys the maximum, as is usually the case at island stations, occurs in February, and there is only a slight fall in March. The wind velocity is at its annual minimum in summer — November to January — both at the South Orkneys and at M‘Murdo Sound. At the former station there is a distinct double period with maxima at the equinoxes and minima at the solstices. The maximum at M‘Murdo Sound is reached in March and the minimum in January, but the stormy period here begins in February and terminates in August, whereas at the South Orkneys September has the highest mean velocity of the year, and October is also a stormy month. It is not necessary to amplify details, since the general features of Antarctic meteorology have been already treated in papers published some years ago. The additional material since accumu- lated does not modify to any appreciable extent the conclusions then arrived at. 212 Proceedings of the Royal Society of Edinburgh. [Sess. Correlations with M^Murdo Sound. Dr Simpson, F.R.S., at the Australian Meeting of the British Association, drew attention to the existence of a large negative correlation between the barometric pressure at Cape Evans and pressure in Tasmania and Australia.* We have extended the inquiry to New Zealand and some other places in the South American area, with the object of bringing the M‘Murdo Sound data into association with those of other regions which have formed the subject of special investigation for the period December 1901 to November 1909. In this way some glimpses have been obtained of the relations between pressure and temperature in the Ross Sea and other regions. For pressure we have taken seasonal values for the four years utilised in connection with the South Orkney data, while for temperature we have supplemented Captain Scott’s data by a fifth year derived from Shackleton’s 1908-09 expedition. The following are the more striking seasonal contrasts obtained, the values for the respective seasons being referred to a four years’ mean for pressure, and a five years’ mean for temperature. In treat- ing the data from New Zealand and the Straits of Magellan we have taken the means of the departures for several stations, the departures from the normal for individual seasons being all of the same sign in both these two regional groups. The data are tabulated in Table III. Pressure. In summer the pressure departures at MAIurdo Sound are of the same sign as at Perth (West Australia) and at Point Galera on the Chilian coast, and the reverse of those at New Zealand and the Straits of Magellan. At the South Orkneys, as already pointed out, the negative correlation is weak. In autumn the negative correlation with New Zealand and Magellan Straits is again strongly marked, and this prevails on the Atlantic coast of South America up to the latitude of Monte Video. The correlation with the South Orkneys fails in the autumn of 1912. In winter the contrast between M‘Murdo Sound and the South Orkneys, Magellan Straits, and the Atlantic coast of South America is strongly marked, and extends over the South Atlantic as far north as St Helena. The correlation with New Zealand is relatively weak. At Suva, Fiji, the pressure departures are in harmony ,with those at MAIurdo Sound. In spring the negative correlation with New Zealand and the South * Discussion on Antarctic Meteorology opened by G. C. SimjDson, D.Sc., Brit. Ass. Rep., Australia, 1914, p. 302. 1914-15.] Meteorological See-Saw over Antarctic Seas. 213 Orkneys is again prominent, but there is no relation with Magellan Straits and the Atlantic coast. Table III. — Pressure Departures from Seasonal Nohmal at jVPMurdo Sound AND OTHER PLACES. Station or Area. Lat. S. Long. 1902- 1903. 1903- 1904. 1910- 1911. 1911- 1912. Mean at Sea- Level and Lat. 45°. Summer. mm. mm. mm. mm. mm. M‘Murdo Sound 77 44 166 34 E. -fl-7 -3-4 -3-D 4-5-5 745-6 South Orkneys 60 44 44 39 W. - 1-2 -2-2 4-0-5 4-3-1 44-5 Perth (W. Australia) 31 57 115 45 E. -fO-8 -0-7 -0-2 4-0-1 60-2 New Zealand* 43 16 172 14 E. -0-2 4-0-4 4-3-1 -3-3 58-8 Magellan Straits t . 52 39 71 28 W. -1-2 4-1-2 4-1-1 -1-1 50-1 Point Galera . 40 01 73 44 W. -f 1-0 -0-1 -1-0 4-0-2 61-8 Autumn. 1 M‘Murdo Sound 77 44 166 34 E. 4-2-2 4-1-0 -0-9 -2-4 44-7 South Orkneys 60 44 44 39 W. - 1-1 - 1-0 4- 6-4 -4-2 43-2 New Zealand . 43 16 172 14 E. -2-2 -0-2 4-2-1 4-0-3 61-0 Magellan Straits 52 39 71 28 W. - L5 -2-5 4-2-5 4-1-5 50-5 Bahia Blanca . 38 43 62 17 W. - 1-4 0-0 4-0-3 4-1-2 60-8 Monte Video . 34 52 58 32 W. -0-8 -0-2 4-0-8 -80-4 60-2 W inter. M‘Murdo Sound 77 44 166 34 E. 4- 1-2 4-3-9 -1-0 -4-0 40-7 South Orkneys 60 44 44 39 W. -2-1 -0-5 4-1-1 4-1-6 44-0 New Zealand . 43 16 172 14 E. 4-1-8 - 1-2 -0-3 -0-2 61-4 Suva, Fiji 18 08 178 26 E. -hO-5 4-0-4 -0-2 -0-7 61-1 Point Galera . 40 01 73 44 W. -1-1 -0-6 -f 1-4 4-0-2 62-7 Magellan Straits 52 39 71 28 W. -0-5 -2-4 -81-5 -81-6 51-4 Bahia Blanca . 38 43 62 17 W. -1-3 - 1-0 4-0-4 4-1-7 62-5 Monte Video . 34 52 58 32 W. -0-7 0-0 4-0-6 4-0-3 62-0 St Helena 15 57 5 40 W. -0-7 -0-5 4-0-9 -8 0-3 12-2 f Spring. M‘Murdo Sound 77 44 166 34 E. 4-4-0 -5-4 -0-1 4-1-4 41-9 South Orkneys 60 44 44 39 W. - 1-3 4-1-2 4-2-2 -1-9 42-3 New Zealand . 43 16 172 14 E. - 1-5 4-4-9 - 0'5 -2-9 57-8 Magellan Straits 52 39 71 28 W. -10 - 1-2 4-3-3 - 1-1 51-7 Temperature. A few temperature resemblances and contrasts which have come to light may be briefly summarised. In summer the departures of tempera- ture from the five years’ normal at MAlurdo Sound are the same as those at the South Orkneys, New Zealand, Perth (West Australia), and Rio Gallegos in Patagonia, and the reverse of those at Sydney (N.S.W.) and * Mean of Wellington, Hokitika, Lincoln, and Dunedin. t Mean of Diingeness, Punta Arenas, and Evangelists’ Island. X Mean at station -level, 619 metres above sea. 214 Proceedings of the Royal Society of Edinburgh. [Sess. St Helena. The following are the particulars, the means and departures being given in Centigrade : — Station or Area. Lat. S. Long. 1902- 1903. 1903- 1904. 1908- 1909. 1910- 1911. 1911- 1912. Mean. M‘Murdo Sound . 77 44 166° 34 E. -1°0 4-0°6 4-2°0 o 4-01 o - 1-8 o -5-6 South Orkneys . 60 44 44 39 W. -0-9 4-0-4 4-0-7 -0-2 4-0-3 -0-3 New Zealand* . 42 18 173 25 E. -1-0 4-1-3 4-0-1 4-0-8 -1-2 15-2 Perth (West Australia) 31 57 115 45 E. -0-3 4-0-2 4-0-6 -0-4 -0-2 22-7 Rio Gallegos 51 53 68 59 W. -0-7 -FO-3 4-0-5 -0-1 -0-1 13-2 St Helena . 15 57 5 40 W. + 0*8 -1-1 -0-6 -0-2 4-0-9 17-5 Sydney 33 52 152 11 E. 4-0 5 -0-7 -0-2 -0-3 4-0-6 21-8 During the first three seasons the agreement is good for all the stations, but in the summer of 1910-11 (December 1 910 interpolated for M‘Murdo Sound) the signs differ at the South Orkneys, Perth, and Rio Gallegos, and a divergence also occurs in the summer of 1911-12 at the South Orkneys. There is little doubt, however, that cold summers at M‘Murdo Sound are associated with cold summers in New Zealand and the far South Atlantic, and with warmth in New South Wales and the region of the south-east trades, as shown by the St Helena record. Mild summers at M‘Murdo Sound show a similar relation with those in New Zealand and the far South Atlantic, and the reverse at Sydney and at St Helena. In autumn and winter the relation between the temperature at MAIurdo Sound and that at other regions is not on the whole very definite. When the data are obtained from a short term of years, it is obvious that an exceptional season at M‘Murdo Sound — such, for example, as the autumn of 1903 or the winter of 1912 — must strongly affect the sign of the de- partures from the short-period averages. In lower latitudes, where condi- tions are much more equable from one season to another, this disturbing factor does not exist. There is little doubt, however, that in autumn, as in summer, the temperature variations at New Zealand and Sydney are strongly influenced by Antarctic conditions. In winter no connection can be traced between the conditions at the places examined and at M‘Murdo Sound, if we except a well-marked positive correlation with Santiago de Chile and a negative correlation with Perth (West Australia) and the South Orkneys. In spring the Antarctic influence becomes more prominent, since a well-pronounced negative correlation is shown between M'Murdo Sound on the one hand, and Hobart (Tasmania), Adelaide, Punta Arenas, and Rio de Janeiro on the other. The following are the values : — * Mean of six stations, viz. Auckland, Wellington, Hokitika, Lincoln, Dunedin, and the Chatham Islands, 1914-15.] Meteorological See-Saw over Antarctic Seas. 215 Station. Lat. S. Long. 1902. 1903. 1908. 1911. 1912. Mean. M‘Murdo Sound . 77° 44 163° 34'e. 0 -P6 -1°'8 + 3°-0 -P2 o + 1-8 - 1°7-8 Hobart 42 53 147 20 E. + 0*1 + 1*6 -0-1 + 0-1 -0-6 12-5 Adelaide 34 56 138 35 E. -t-0‘9 + 0-4 -0-7 -1-0-3 -1-0 17-2 Punta Arenas 53 10 70 54 W. + 0*4 + 0-4 -1-5 + 0-7 -0*1 6*0 Kio de Janeiro 22 55 43 10 W. -1-0-3 + 0A -0-1 + 0-2 -0-8 22-1 Owing to the shortness of the period available one cannot utilise the MMurdo Sound seasonal data as an index of what will occur later in other localities. The contrast between the temperature conditions there in summer and those which hold in autumn at Adelaide, Perth, Curityba, Rio de Janeiro, and St Helena is, however, so remarkable as to be worth drawing attention to. Station. Lat. Long. 1903. 1904. 1909. 1911. 1912. Mean. Summer. M‘Murdo Sound . 77° 44 166° 34 E. O - 1-0 + 0°-6 + 2°0 + 0°1 - 1-8 o -5-6 Autumn. Adelaide 34 56 138 35 E. -f-0'7 -0-4 -0-2 -0-4 + 0-4 17-5 Perth .... 31 57 115 45 E. + 1-1 - 1-1 -0-5 -0-5 -f-0’8 18-7 Curityba 25 26 49 16 W. + 0-9 0-0 -0-6 -0-8 + 0-7 16-8 Rio de Janeiro . 22 55 43 low. + 0-2 -0-3 -0-1 -0-3 + 0-4 23’3 St Helena . 15 57 5 40 W. + 0*7 -0-1 -0-8 -0-1 + 0-4 18-3 Thus cool summers at M‘Murdo Sound were followed by warm autumns at Adelaide and Perth, and also in the south of Brazil and in the south- east trade-wind region of the South Atlantic, while mild summers at M‘Murdo Sound were followed by cool autumns in the regions specified. The connection between MMurdo Sound and the region of the south-east trades of the South Atlantic may not at first sight appear very obvious. We have, however, seen that a see-saw exists between the Weddell and the Ross Seas, more especially as regards barometric pressure and wind force. A further connection is found between the wind force at the South Orkneys and the mean temperature at St Helena. For Laurie Island we have wind data based on hourly observations since June 1903.^ Dealing only with the complete annual values since 1904, and bloxaming these in continuous three-year groups, we find that there has been a progressive diminution in the wind velocity from the first three-year group, 1904-06, down to the * Davis, Anales de la Oficina Meteorologica Argentina, Tomo xvii ; Glima de las Isles Orcadas del Sud, Secimda Parte, p. 137, Buenos Aires, 1913. Data from 1911-14 kindly sent by Dr Davis in manuscript. 216 Proceedings of the Koyal Society of Edinburgh. [Sess. last, which covers the period 1912-14, and that this has been associated with a progressive rise in the mean annual temperature of St Helena similarly bloxamed since the three-year group 1906-08.*' The values in metres per second of mean wind velocity at the South Orkneys, and the air temperatures at St Helena are as follows: — Period .... 1904- 1906. 1905- 1907. 1906- 1908. 1907- 1909. 1908- 1910. 1909- 1911. 1910- 1912. 1911- 1913. 1912- 1914. Wind velocity. South Orkneys 6-9 6-3 5-5 5-3 5-2 5*0 4-7 4-7 4-5 Temperature, St Helena 0° F. 61T 61-2 60-6 60-7 60-9 61-3 61*7 62-4 62-7 The wind velocity thus shows a steady diminution throughout, and this is associated since 1906-08 with a rise in the St Helena mean annual temperature. The wind velocity at the South Orkneys was thus a third less in the last group of years than in the first, while the St Helena tem- perature increased 2°T during the period 1906-08 to 1912-14. There is no doubt that in the Antarctic circulation there will occur from one year to another, or even between groups of years, certain great changes which must profoundly modify conditions in lower latitudes. At M‘Murdo Sound the mean wind velocity during Scott’s first expedition (1902-04) was only half that recorded during the second expedition (1911-12). In the Weddell sea area, as shown by the data from the South Orkneys and Snow Hill, storms were frequent and violent from 1902-06, while from 1907-14 few storms have been experienced. There is steadily growing evidence regarding the important relations that exist between Antarctic conditions and those in lower latitudes, but the discussion is hampered by the sporadic manner in which the circum- polar material accumulates. In general the data refer to relatively short periods covered by expeditions, working as a rule in widely separate reofions. The establishment of fixed observatories in high southern latitudes would certainly lead to many practical results of the first im- portance, especially in the direction of utilising the material as an aid to long-range weather forecasting in Australia, South America, and South Africa ; but for this we should require synchronous data extending over many years from several typically Antarctic stations. * Data to 1908 from The Trade Winds of the South Atlantic, M.O. 203, supplemented by later data, kindly forwarded by Sir Napier Shaw, F.K.S. {Issued separately September 27, 1915.) 1914-15.] Magnetic Quality and Transverse Pressure. 217 XXI. — The Magnetic Quality of Iron and Steel as affected by Transverse Pressure. By Wm. J. Walker, B.Sc. Communi- cated by Professor W. Peddie. (MS. received April 14, 1915, Kead June 28, 1915.) It has been thought advisable to place the following qualitative results on record owing mainly to their general interest and to the unavoidable interruption of the experiments. The experiments were carried out in order to determine the effect of transverse pressure on the magnetic induction in a piece of iron or steel. Apparatus Used in the Experiments. This is shown in fig. 1. The ballistic method of induction measurement was adopted, and the apparatus, from the figure, will be seen to afford exceptional facility for the investigation. The cast-iron piece C was made a very close fit in the main cast-iron block D. The coil E is placed in the gap in this block so that its centre lies in line with the centre of the hole in the casting through which the test piece is inserted. It will be seen that in this way the necessary condition of endlessness in the iron circuit 218 Proceedings of the Royal Society of Edinburgh. [Sess. is obtained. The wooden pieces GG carry both the primary and secondary coil terminals P and S. There were 4600 turns of No. 30 wire on the secondary circuit with a resistance of 117’4 ohms, while the primary circuit consisted of 120 turns of No. 17 wire with a resistance of *262 ohm. Galvanometer. This was of the d’Arsonval type. The resistance of its coils, found by Mauce’s method, was 10*92 ohms. Test Pieces. All the test pieces were turned down to a diameter of 2 cm. They were each slightly more than 20 cm. long, with a length of 6*5 cm. in the centre which was filed square. When in position in the apparatus this square part was wholly within the coil E. Method of Conducting Experiments. The induction curve for the iron or steel test piece was first obtained with the piece in its normal condition. It was then taken out of the apparatus, and its dimensions taken. It was next demagnetised, and then compressed to 5 tons per square inch. This was carried out in a 50-ton Wicksteed testing machine in the Mechanical Engineering Laboratory. Pieces of cast iron AA as shown in fig. 2 were made to fit over the square part of the test piece. Pressure was then applied by the machine in the direction indicated by the arrowheads. It will be seen that this method of applying the pressure leaves two of the sides of the square part free to expand laterally. The effect of this is shown in fig. 2 by the two shapes of these free faces before and after compression. The measurements of dimensions given were all taken at the centre, i.e. where the bulging is greatest. After this compression to 5 tons per square inch, the dimensions were again taken, the piece was inserted into the apparatus, demagnetised, and its induction curve then obtained as before. It was again demag- netised, taken out of the apparatus, and compressed to 10 tons per square inch, and so on as before. This was continued till the specimen broke or became too distorted to enter the coil. Method of Demagnetisation of the Pieces. Demagnetisation was necessary to ensure that the tests would be reliable, and was carried out both before and after compression, since it is well Deflections 1914-15.] Magnetic Quality and Transverse Pressure. 219 Fig. 2. Amperes Fig. 3. 220 Proceedings of the Royal Society of Edinburgh. [Sess. known that the application of stress often changes the magnetic condition of a metal. The method of demagnetising was a novel one, and consisted in connecting the primary coil to an alternator running at 500 revolutions per minute. The current was adjusted till it was slightly above the current to be employed in the test. The alternator was a very free-running machine. On breaking the field switch, its speed and current decreased together slowly. The eftectiveness of this method of demagnetisation was proved by means of a very delicate galvanometer, hardly a trace of deflec- tion beino; obtainable. Specimens Tested. Three different specimens were tested : one each of cast iron, soft wrought iron, and mild steel. Experimental Data and Results. The cast-iron piece was tested first. At 5 tons per square inch its induction curve was practically^ the same as at no compression. At 10 tons per square inch, however, a distinct lowering of the curve at all points occurred. At 15 tons per square inch the specimen broke. This was seen to be due to the shearing action of the two compression blocks AA (fig. 2). In the next tests the corners of these blocks were rounded over in order to minimise this shearing action. The curves for this test are shown in fig. 3, and the figures are given in Table I. No reliability can be placed upon this test, since in all likelihood the sudden chano;e in the induction was due to a split developing in the piece. This is indicated by its giving way at such a low pressure as 15 tons per square inch. The piece of mild steel was next tested, and then the wrought-iron piece. Both gave good readings up to 50 tons per square inch in each case. The figures of these tests are given in Tables II and III, and the induction curves in figs. 4 and 5. From the nature of the curves in these two cases it was seen that the greatest change in induction with compression took place first at the low currents and then later at the high currents. That is, in pass- ing from curves I to lY and I to VI in figs. 4 and 5 respectively, the induction changes are not regular. Had they been regular the various curves would have been similar. Owing to this the curves showing the relation between compression and induction are drawn and shown in figs. 6 and 7. Taking fig. 6 first, which gives the relation for the wrought-iron piece, 1914-15.] Magnetic Quality and Transverse Pressure. 221 Amperes Amperes Fig. 4. Fig. 5, 222 Proceedings of the Koval Society of Edinburgh. [Sess. it will be noticed that the induction changes become more rapid the higher the compression, but that this becomes less and less pronounced as the current is increased. This is shown by the decrease in the slopes of the curves on proceeding from IV to I. The same thing is noticeable in the curves of fig. 7, but here another feature requires to be noted. After compressing to 40 tons per square inch, and the induction curve obtained, it was noticed that this curve had higher inductions in the initial stages than the curve obtained after a compression of 35 tons per square inch. In other words, the curves crossed, this occurring at a current of 3'5 amperes. After 45 tons per square inch, this efiect was still present but to a lesser degree, the two curves crossing at a current of 2'85 amperes. Then at 50 tons per square inch the effect was absent. The result of this is shown in the curves of fig. 7. From these it would seem that the irregularity of the curves becomes less at the high currents. This would seem to indicate that some change of structure is taking place in the metal which can be observed at the low- current values, but which becomes masked by the effect of the higher currents. It will be seen from the figures given in Tables II and III for the dimensions of the pieces after the various compressions that the deforma- tions are fairly regular. The cross-sectional area of the pieces in all cases is practically constant, as obtained from the product of the two dimensions. It will be noticed also that the deformations increase as the load increases. The reason for this is as follows. At all the compression values, when the particular load had been applied to the test piece, it was necessary to wait until the pointer on the compression machine became steady, i.e. until plastic flow of the material had stopped. At the higher values 45 and 50 tons per square inch this plastic flow lasted quite an appreciable time, and this accounts for the increase of deformation with increment of load. In other words, the higher the load, the longer the duration of the period of plastic flow. In figs. 8 and 9 the curves are shown giving the relationship between induction and deformation. The same remarks apply here as in the case of the curves in figs. 6 and 7 showing the relationship between induction and load. Here the irregularity before referred to is still more pronounced. Generally speaking, increase of deformation decreases the induction except at the points previously indicated. It may be stated here that there is very slight probability of this irregularity being due to any errors of observation. All the induction curves were obtained from at least four separate series of figures, in some cases six, and in no case was there any 1914-15.] Magnetic Quality and Transverse Pressure. 223 'll ^ I I M I.Ll 1 i I il I 1 1 IdlLl I 1 1 I M I M M I IJJ LI 1 M N 1 I M I I M I 1 mlJ q ■'t 6d. No. XVII, . Price 8d. No. XVIII, . ” 11 lOd. No. XIX, . 11 6d. No. XX, • 11 lOd. No. XXI, . • 11 8d. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SESSION 1914-15. Part III.] VOL. XXXV. [Pp. 225-402, CONTENTS. NO. PAGE XXII. The Interaction of Methylene Iodide and Silver Nitrate. By Professor C. R. Marshall and Elizabeth Gilchrist, M.A., B.Sc.,. ...... 227 {Issued separately December 3, 1915.) XXIII. A Comparative Study of the Reflexes of Autotomy in Decapod Crustacea. By J. Herbert Paul, M.A., B.Sc. (From the Physiological Department of the University of Glasgow, and the Marine Laboratories at Millport and Cullercoats.) Communicated by Professor Noel Paton, ....... 232 (Issued separately December 4, 1915.) XXIV. Chalk Boulders from Aberdeen and Fragments of Chalk from the Sea Floor off the Scottish Coast. By the late William Hill, of Hitchin, F.G.S. Communicated by Professor D’Arcy W. Thompson, . . . 263 (Issued separately December 14, 1915.) XXV. Notes on the Structure of the Chalk occurring in the West of Scotland. By the late William Hill, of Hitchin, F.G.S. Communicated by Professor D’Arcy W. Thompson, ...... 297 (Issued separately December 14, 1915.) Obituary Notice — Sir John Murray, K.C.B., LL.D., Ph.D., D.Sc., F.R.S., etc., . 305 [^Continued on page iv of Cover. EDINBURGH : Published by ROBERT GRANT & SON, 107 Princes Street, and WILLIAMS & NORGATE, 14 Henrietta Street, Covent Garden, London. MDCCCCXV. Price Seven Shillings, REGULATIONS REGARDING THE PUBLICATION OF PAPERS IN THE PROCEEDINGS AND TRANSACTIONS OF THE SOCIETY. The Council beg to direct the attention of authors of communications to the Society to the following Regulations, which have been drawn up in order to accelerate the publication of the Proceedings and Transactions, and to utilise as widely and as fairly as possible the funds which the Society devotes to the publication of Scientific and Literary Researches. 1. Manuscript of Papers. — As soon as any paper has been passed for publication, either in its original or in any altered form, and has been made ready for publication by the author, it is sent to the printer. 2. 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In the case of such papers advanced proofs will be sent to the members of the Society desiring copies, and copies will be supplied to the author for dis- tribution. A paper selected for Special Discussion will be marked with an asterisk (^) and placed first on the Billet for the day of reading. Any following papers for that day may be adjourned or held as read if the discussion prevents their being read. 6. Communications not submitted for Publication, such as Demonstrations of Experiments, Statement of Scientific Problems, etc., may be received by the Council, and may also be selected for Special Discussion. The Council does not undertake to publish any notice of such communications in the Proceedings or Transactions of the Society. [Continued on page iii of Cover. 225 1914-15.] Magnetic Quality and Transverse Pressure. appreciable difference between these. Demagnetisation was also carried out between each of these various readings. There is a possibility, of course, that the irregularity was due to the development of a small cavity in the interior of the test piece, which cavity became closed up on further compression. The probability of this is rather remote, however. In conclusion, the author desires to express his thanks to Professor Peddie for much encouragement and advice given during the course of the work. Table I. — Cast Iron. Dimensions = 13*908 mm. x 13*413 mm. Compression, Box Resistance tons per Deflections. Differences. in Secondary- Amperes. square inch. Circuit. Right. Left. 27-4 21*8 5*6 f •44 29-8 19*5 10*3 •83 32*5 17*0 15*5 1-54 34-3 15*4 18*9 2-11 0 35- 5 36- 6 14*4 13*2 21*1 23-4 500,000 ohms o o 37-5 12*4 25*1 4*01 38-2 11*8 26*4 4*69 40-6 10*6 30*0 6*00 41*2 10*2 31*0 6*64 41*3 9*0 32*3 \ 7*33 Dimensions = 14'576 x 12‘800 mm. r 26-5 22*8 3*7 ~\ *63 28-4 21*1 7*3 *97 31-0 19*0 12*0 1*65 330 17*3 15*7 2*24 34-6 16*1 18*5 2*83 10 36-3 14*8 21*5 500,000 3*75 37-0 14*3 22*7 ohms 4 17 37-7 13*7 24*0 4*70 38-4 13*0 25*4 5*23 38-9 12*5 26*4 5*75 39-5 11*6 27*9 6*53 40-2 10*8 29*4 7*40 y VOL. XXXV. 15 226 Proceedings of the Eoyal Society of Edinburgh. [Sess. Table II. — Mild Steel. Box Eesistance in Secondary Circuit = 1,000,000 ohms. Compression, \ tons per sq. in. / ‘ ’ 0. 25. 35. 40. 45. 50. Diff. Amps. Diff. Amps. Diff. Amps, Diff. Amps. Diff Amps. Diff Amps. 6*7 •33 13*5 1*00 10*6 *8 8*0 •55 7*7 *55 2*8 •28 16*5 *80 19*2 2*00 16*5 1*78 16*8 1*42 16*2 1*50 10*9 *83 18*5 1*08 21*3 2*93 19*3 2*59 19*9 2*44 19*5 2*53 15*6 1*58 19*9 1*43 22*3 3*71 20*9 3*20 21*2 3*37 20*9 3*45 18*8 2*63 21*0 1*90 23*5 4*90 22*1 3*98 22*1 4*22 21*9 4*40 20*4 3*79 21*6 2*46 24*1 5*74 22*7 4*76 22*9 5*07 22*7 5*23 21*4 4*63 22*4 3*17 24*6 6*70 23*3 5*50 23*5 5*83 23*2 6*22 21*8 5*42 23*1 3*78 25*0 7*29 23*7 6*06 23*7 6*50 23*7 7*23 22*4 6*47 23*3 23*7 24*3 24*7 25*1 25*5 4*03 4*69 5*32 6*06 6*72 7*41 24*2 24*5 6*66 7*20 24*1 7*03 22*9 7*25 Original dimensions = 13*81 x 13*685 mm. Dimensions after 25 tons per sq. in. compression = 14*5 x 13*09 „ „ 35 „ „ „ =14*95x12*70 „ „ 40 „ „ „ =15*83x11*92 „ „ 45 „ „ „ = 1 7*04 X 11*15 „ ,, 50 „ „ ,, =18*30x10*41 Table III. — Soft Wrought Iron. Box Eesistance = 1,000,000 ohms. Compression, \ tons per sq. in. / * * 0. 20. 30. 40. 50. Diff. Amps. Diff Amps. Diff. Amps. Diff. Amps. Diff Amps. 1*3 *16 1*4 *11 1*8 *18 1*7 •15 2*0 *20 8*7 *48 5*5 *34 5*6 *33 5*9 •41 9*5 *66 17*4 *90 11*5 *67 14*0 *86 13*6 *95 15*0 1*40 19*6 1*30 16*3 1*17 19*0 1*47 17*7 1*60 17*0 2*05 20*6 1*65 20*2 1*90 20*3 2*03 19*8 2*32 19*0 3*10 21*3 2*31 21*2 2*60 21*2 2*67 21*0 3*00 20*0 3*90 21*9 2*92 22*1 3*70 22*0 3*33 22*0 3*80 20*9 4*60 22*5 3*42 22*7 3*75 22*6 3*93 22*6 4*50 21*5 5*80 22*9 3*70 23*2 4*42 22*9 4*32 23*1 5*21 22*0 6*80 23*2 4*24 23*6 4*95 23-3 4*78 23*5 5*85 22*5 7*65 23*9 5*37 23*8 5*53 23*7 5*52 23*9 6*65 24*4 5*99 24*3 6*37 24*3 6*39 24*6 7*66 25*0 7*13 24*9 7*40 24*45 6*86 25*2 7*65 24*6 7*23 Original dimensions = 13*56 x 14*63 Dimensions after 20 tons per sq. in. compression = 13*97 x 14*07 „ „ 30 „ „ „ =14*48x13*55 „ „ 40 „ „ „ =15*50x12*75 „ „ 50 „ „ „ =16*80x11*75 mm. 55 55 55 55 {Issued separately December 3, 1915.) 1914-15.] Interaction of Methylene Iodide and Silver Nitrate. 227 XXII. — The Interaction of Methylene Iodide and Silver Nitrate. By Professor 0. R. Marshall and Elizabeth Gilchrist, M.A., B.Sc. (MS. received July 5, 1915. Eead July 5, 1915.) In the course of some experiments, designed to prepare methylene nitrate, an interesting reaction between methylene iodide and silver nitrate in alcoholic solution was observed. When approximately an equimolecular quantity of methylene iodide is added to a saturated solution of silver nitrate in methyl or ethyl alcohol, glistening white crystals quickly^ begin to appear and soon form a bulky precipitate. Scholl and Steinkopf {Ber., xxxix, p. 4397, 1906) obtained a similar crystalline precipitate on dropping 6*7 gms. methylene iodide into a solution of 8‘5 gms. silver nitrate in 17 gms. water, constantly stirred and kept cool with ice. The crystals were washed with anhydrous acetone and afterwards with anhydrous ether. The yield was 10 gms. The determination of the carbon, hydrogen, and silver suggested the formula AgN03.CH2l2. The compound had a slight methylene iodide odour, decomposed slowly and became yellowish at ordinary temperatures, melted with decomposition at 80°-81° C., and was immediately decomposed by water and more slowly by alcohol with formation of silver iodide. It was not further examined. Donnan and Potts {Journ. Chem. Soc., XCVII, ii, p. 1895, 1910) made a few experiments to determine the velocity co- efficient of the reaction between methylene iodide and silver nitrate in alcoholic solution, which will be referred to later. The substance obtained by us appears to be the same compound as that described by Scholl and Steinkopf. The crystals are colourless when pure and become yellowish and finally greyish or greenish grey on the surface when exposed to light. They have a faint odour of methylene iodide. If left exposed to air in the dark the compound is largely converted into a mixture of silver iodide and silver nitrate, the proportions varying with the conditions of exposure. If exposed in thin layers more nitrate is formed ; if exposed in bulk the iodide preponderates. When heated, the crystals decompose at 79°-80° C. with evolution of iodine and nitrous fumes. Heated in a dry test-tube, nitrous fumes seem to come off first, but if warmed under a layer of xylol or liquid paraffin the liquid becomes violet and nitrous fumes do not appear until the temperature is further raised. 228 Proceedings of the Poyal Society of Edinburgh. [Sess. Preparation. — Different proportions of silver nitrate and methylene iodide yielded the same product, although with excess of methylene iodide in bulk a solid yellowish substance or mixture was also formed which was not further examined. It was converted into the colour- less double compound on the addition of alcoholic silver nitrate solu- tion. With a decinormal solution of silver nitrate the yield of AgN03.CH2l2 was, with molecular quantities, 75 per cent, of the theoretical ; with two molecular quantities of silver nitrate it was 90 per cent., and with two molecular quantities of methylene iodide 100 per cent, of the theoretical. To obtain the compound in a pure form it is necessary to use an alcoholic solution of silver nitrate not less than decinormal in strength. With a fortieth normal solution none of the compound is precipitated, but the solution becomes opalescent owing to the formation of silver iodide. With a twentieth normal solution crystals of the double compound begin to be deposited in about two minutes, but they increase in number rela- tively slowly, and a small quantity of silver iodide is soon formed, so that the product is liable to become impure. Some silver iodide is eventually formed when saturated solutions of silver nitrate are employed, but the stronger the silver nitrate the later it is in appearing. The substance is most conveniently prepared by adding pure methylene iodide to a saturated solution of silver nitrate in alcohol, filtering in two or three minutes^ washing the crystals rapidly with absolute alcohol followed by anhydrous ether, pressing between filter paper and drying in an incubator at 38° C. So prepared the product retains a small amount of alcohol, which com- bustion shows to be about 4 per cent, of the weight of the compound. The alcohol is dissipated by placing the substance in an evacuated desiccator left in the dark for three days. Longer retention is inadvisable owing to the gradual evolution of CH^Ig. The following analytical results were obtained : — 0'2845 gm. gave 0*0285 gm. CO.2 and 0’0152 gm. H2O. C= 2*73. H = 0*59. 0*4173 gm. „ 11-8C.C. Isk ^ N=3*50. 2*3079 gms. ,, 0*570 gm. Ag. Ag = 24*7. 8*5629 gms. ,, 4*914 gms. I. 1 = 57*4. AgN03.CH2l2 requires 0 = 2*74; H = 0*46; N = 3*20; Ag = 24*7; 1 = 57*7. The substance is moderately soluble in absolute ethyl alcohol — 100 gms. dissolve 1*7 gms. at room temperature (16°-18° C.) — but it gradually undergoes decomposition in it and cannot be recrystallised from it. Of the solvents we have tried for recrystallisation absolute methyl 1914-15.] Interaction of Methylene Iodide and Silver Nitrate. 229 alcohol gave the purest product, but it also was contaminated with silver iodide. The substance is best kept in an alcoholic solution of silver nitrate. It is insoluble in benzene and paraffins and is almost insoluble in ether. Effect of Water. — On addition of water the compound moderately rapidly decomposes; the crystals lose their crystalline form and become yellowish, and the supernatant fluid becomes acid. When 8’562 gms. was heated with 150 c.c. water under a reflux condenser for one hour, 3*800 gms. silver iodide was recovered. The supernatant liquid was 0075 normal acid, and contained 0*618 gm. silver nitrate. The acidity was mainly due to nitric acid. Formic acid was present in much smaller amount, and there was a questionable trace of oxalic acid. On distillation the liquid yielded a small quantity of a colourless oily substance which was proved to be methylene iodide. This substance was also isolated from the mixture in the distilling flask, but owing to difficulties in separation the amount could not be quantitatively estimated. The decomposition appears to vary somewhat with the conditions of the experiment. For- maldehyde is at first formed, and the earlier part of the reaction may probably be expressed as — SAgNOg . CH2I2 + H2O = 2AgI + AgNOg + 2HNOg + 2CH2I2 + HCOH. Effect of Caustic Alkali. — The action of an aqueous solution of caustic alkali was similar to that of water except that a large proportion of the precipitate formed consisted of silver hydroxide. When boiled for an hour with 10 per cent, aqueous potash 14*8 per cent, of the silver appeared as silver hydroxide and 9*5 per cent, as silver iodide. Effect of Potassium Cyanide. — When the substance was treated with twice the molecular quantity of potassium cyanide in aqueous solution, the mixture separated into two layers, an upper aqueous layer of solution of silver potassium cyanide and a lower layer of methylene iodide. The quantity of methylene iodide recovered was 58*3 per cent, (theoretical yield = 61*1 per cent.). The silver in the aqueous layer was estimated, after previous boiling with nitric acid, by Volhard’s method, and was found to be 22*4 per cent, (theoretical yield = 24*7 per cent.). A small quantity of insoluble residue, too small for further examination, accounted for the slight difference between the actual and theoretical yields. Discussion. — There seems little doubt that the substance is an unstable additive compound of molecular proportions of silver nitrate and methylene iodide. The compound is interesting because the two neighbouring iodo- 230 Proceedings of the Royal Society of Edinburgh. [Sess. methanes — methyl iodide and iodoform — do not seem to form such combina- tions. When methyl iodide or iodoform, in bulk or in solution, is added to an alcoholic solution of silver nitrate, a precipitate forms as in the case of methylene iodide, but it is amorphous and consists of silver iodide. With methyl iodide Fanto {Monatsli., xxiv, 477, 1903), using special pre- cautions, appears to have obtained a crystalline compound (AgN03)2 . Agl. Donnan and his collaborators, like ourselves, only obtained silver iodide from the action of methyl iodide or iodoform on alcoholic silver nitrate solutions. Burke and Donnan {Journ. Chem. Soc., Ixxxv, p. 569, 1904), and Donnan and Potts (loc. cit), determined the velocity coefficients for methyl iodide and silver nitrate, and iodoform and silver nitrate in alcoholic solution. The last-named observers also made a few experiments with methylene iodide and silver nitrate under similar conditions. They found that the velocity coefficient is about one hundred times smaller than the corresponding coefficient for iodoform ; and since the velocity coefficient for iodoform is only about eight times smaller than the velocity coefficient for methyl iodide, they conclude that “ in point of reactivity with silver nitrate, methylene iodide does not therefore occupy a position intermediate between methyl iodide and iodoform, but is characterised by a very great sluggishness.” The experiments were made at 25° C., and the reaction velocities were determined by estimating the amount of silver salt in solution by the thiocyanate method. We have repeated some of Donnan and Potts’ experiments and can corroborate their facts, but in view of the formation of a double compound of silver nitrate and methylene iodide, which is moderately soluble in alcohol and only gradually decomposes in it, and the silver of which can be estimated by the thiocyanate method, it is questionable if the results obtained are strictly comparable with those got from methyl iodide and iodoform. The dilutions employed by them are not given, but were probably not greater than N/25, giving N/50 when the two solutions were mixed. The solubility of the double compound at 25° C. is N/25 5 or 2*2 grns. in 100 gms. of ethyl alcohol. It is, however, difficult to say whether this compound exists as such in solution. Its silver can be precipitated by thiocyanate, which shows that some of the silver exists in solution as free silver ions. Its electrical conductivity in absolute alcohol does not differ materially from that of a corresponding solution of silver nitrate — the molecular conductivity of a N/25’5 solution of the double compound in absolute ethyl alcohol being 1'68 x 10“^, and of a N/25'6 solution of silver nitrate in absolute ethyl alcohol 1'6I x 10“^. When equal volumes of N/20 silver nitrate and N/20 methylene iodide 1914-15.] Interaction of Methylene Iodide and Silver Nitrate. 231 are mixed the electrical conductivity is the same as that of N/40 silver nitrate, and it does not begin to change until silver iodide commences to form; and on adding methylene iodide to N/18*5 silver nitrate the conductivity does not change until the double compound begins to crystallise out. It would therefore seem that if AgN03.CH2l2 exists in solution in any large proportion the ionisation is practically the same as that of silver nitrate. {Issued separately December 3, 1915.) 232 Proceedings of the Royal Society of Edinburgh. [Sess. XXIII. — A Comparative Study of the Reflexes of Autotomy in Decapod Crustacea. By J. Herbert Paul, M.A., B.Sc. (From the Physiological Department of the University of Glasgow, and the Marine Laboratories at Millport and Cullercoats.) Communi- cated by Professor Noel Paton. (MS. received May 19, 1915. Eead June 21, 1915.) CONTENTS. Introduction . Descriptive Parts- The Prawn The Lobster The Crayfish Hermit Crabs Galatheids The Shore Crab The Edible Crab The Spider Crab The Swimmer Crab. Discussion and Summary — The Nature of the Keflex . Degeneration in Reaction Type Theories of Autotomy Bibliography . Macrura Anomura . Brachyura PAGE 232 234 245 250 259 260 261 262 Introduction. The self -amputation of limbs, or autotomy, as it has been called, is a remarkable example of one of the provisions which marine animals have for their survival in the struggle for existence. Many species, especially members of the decapod Crustacea, have the power of leaving a leg in the grasp of an enemy and escaping to the shelter of a kindly rock. Autotomy also occurs very markedly in some echinoderms. Without at this point attempting to discuss the nature of autotomy, some of its benefits to the animal may here be noted. Since the process is found in all its degrees of development in decapods, the remarks here specially refer to that group. The group, in addition, presents admirable material for a comparative study, because of the great variety of conditions under which individual members live. Autotomy is a reflex act, simple in some cases and highly complex in others, and it is the result of nocuous stimulation of the limb. There is a definite breaking-plane or joint at the base of the appendage, and it is here that autotomic rupture always takes place. Observation shows that 233 1914-15.] The Eeflexes of Autotomy in Decapods. regeneration occurs very much more easily from the region of the breaking- plane than from any other level. Morgan (1) has pointed out this fact in his experiments on hermit-crabs, though at the same time he indicates that slower and less perfect regeneration is possible from all levels, both above and below the breaking-plane. In typical regeneration a lirnh-bud is first formed, many times smaller than the normal leg. In this papilla, as it is called, differentiation goes on, and all the parts are laid down in miniature. On the occurrence of moulting, sudden increase of blood- pressure causes great expansion of the miniature limb, and in a few days the leg is ready for service with its fellows. Calcium salts are deposited in its integument at the same rate as in the rest of the hard integument ; and after the new muscles have gone through certain chemical changes, only slight difference of size enables an observer to distinguish it from the other legs. The small size of the regenerating appendage during the period in which it is functionless and tender is a marked benefit to the animal, for further damage is less likely to happen to the papilla than it would to a leg regenerating at once to normal size. One other benefit comes to the animal by its sacrifice, and this is as vital to the welfare of the crab as escape from enemies — fatal haemorrhage is prevented. The crustacean blood circulation in a limb differs from that seen in the higher animals. Blood passes by means of arteries to the distal end, but the venous channels do not confine it to such strict limits. They are broad sinuses occupying all the limb space not filled by muscle or dermis. Thus crushing of the shell-like limb causes the crab to run a grave risk of death by haemorrhage. But provision is made for this con- tingency. At the breaking-plane a diaphragm or “ membrane obturatrice ” (Fredericq (2) ) stretches across the lumen of the limb, and a foramen in this gives passage to the nerve and artery. This diaphragm consists of two flaps, and when autotomy occurs these are forced together by relative change of pressure on the outer side. They therefore act as a venous- valve, and the moment autotomy takes place bleeding is stopped. The mechanism is fully described in the case of the hermit crab in a previous paper by the writer (15). Both this valvular mechanism and the power of autotomy are very well developed in the shore-crab {Garcinus moenas (Penn.)). This animal uses them to good purpose, for, living on the shore between tide marks, and usually on stony ground, it is subject to the danger of crushing from movement of the stones by violent seas. So much is this the case, that after the winter storms fifty per cent, of the crabs collected are found to have autotomised one or more limbs. 234 Proceedings of the Koyal Society of Edinburgh. [Sess. The benefits accruing from autotomy being so evident, it remains, therefore, to find by comparative study how the process may have been evolved, and what are its essential features. Examination of different species of decapods by different persons has produced a good deal of literature on the subject. It is very noticeable, too, how each author con- tradicts on fundamental points those who have gone before him, simply because he has studied a different animal, and because a particular feature of the process in his type may be more developed than others, and so overshadow them. The older biologists {e.g. Reaumur (3), 1712) noticed that if a crab’s leg were cut off outside the breaking-plane at the base, it was subsequently thrown off by the animal at the breaking-plane. The same was recorded by many observers of the first part of the nineteenth century, including Faxon (4), McCulloch (5), and Heinehen (6), but it was only when Fredericq (2) took up the question at the end of the ’eighties that new light was thrown on the subject. The result of his work was that in Garcinus moenas autotomy was shown to be the result of reflex contrac- tion of a definite muscle which came to be called the “ autotom iste ” or “ Brechmuskel.” The reflex-arc involved had its centre in the ganglionic mass of the thorax, and acted independently of the cephalic ganglia. The necessary stimulation could be provided by burning, cutting, crushing, or electrically stimulating any distal segment of the leg except the last one. Autotomy could also be produced by central stimulation. Fredericq’s conclusions regarding the reflex in Garcinus have been applied to other species without allowance having been made for differences of form and conditions, and a certain amount of confusion has arisen. Among recent writers are Morgan (1), Reed (7), Steele (8), Przibram (9), Pieron (10), and Drzewina (11). The results of these workers will be discussed under the parts of this paper dealing with the special animals on which the work was done. Section I. MACRURA. Suborder Nat anti A. The Prawn. Of this group I have examined only one species — the prawn, Leander squilla (Lin.). This animal, in relation to its size, is one of the fast- swimming decapods. Its tail fin and abdominal muscles are well developed, and by violent contractions of the latter it makes rapid backward move- ment. The walking-legs are very like those of the lobster, but there are 235 1914-15.] The Eeflexes of Autotomy in Decapods. no heavy chelate claws like those possessed by the latter. The prawn has therefore very little provision for defence. The limbs have six segments, and the first and second pairs of each side are pincered. In prawns collected from the contents of a trawl, very few are found which have lost a leg. In those which I have seen short of limbs, the break has always taken place at the free joint between the second and third segments. The following observations were made on the results of mutilation : — (a) When any part of the limb distal to the second segment is sharply cut across by scissors, the prawn (under water) immediately shoots back- wards on account of a violent swimming movement or flap of its powerful tail. When it comes to rest it is found that the stump is rigidly extended Fig. 1. — The leg of the prawn, showing how the sound joint next to the cut end is sharply flexed, and haemorrhage prevented. owing to violent contraction of the extensor muscle of the second limb- segment. This condition lasts for about thirty seconds, and the limb is then flexed inwards to the jaws. Here it is subjected to violent pulling for several minutes, but soon the animal quietens. The limb then takes up its normal walking position, with this exception, however, that the next sound joint is sharply flexed (fig. I). This sequence of events follows every instance of quick and clean cutting across one of the distal segments, with almost always the same time [relations. Prawns treated in this manner never cast off the stump of the limb, even after many weeks, and, as a rule, the sharp flexion at the next sound joint to the cut surface has disappeared in twenty-four hours. (6) When clumsy scissors are employed in mutilating, which cannot be disengaged from the leg before the violent tail movement takes place, the leg, from the third segment distally, is thrown off' as the animal escapes. The break is found to be identical with that seen in prawns taken from the sea with a leg missing (fig. 2). 236 Proceedings of the Koyal Society of Edinburgh. [Sess. (c) To follow further the indications of the nature of what we must regard as normal autotomy in the prawn (namely, division of the leg between the second and third limb-segments), an individual may be fixed in a hardening fluid with some of the legs fully extended at the|second Fig. 2. — The leg of the prawn, showing the position of the first three limb-segments when division is taking place. articulation, and others fully flexed. It is then found that the application of almost equal pulling forces at the ends of the limbs causes rupture at the junction of body and first segment in the first case, but rupture between the second and third segments in the second case (fig. 3). In the former Fig. 3. — The prawm. 1 is the plane of division when the leg is fully flexed ; 2, when it is fully extended. The arrow indicates the direction of traction. the leg pulls with it all the muscles which find attachment to the body skeleton, and leaves a large wound ; in the latter the break is almost clean, and the rupture-surface comparatively small. The following conclusions on the nature of autotomy in this decapod may therefore be drawn from the above experiments : — (I) Since autotomy does not follow quick and clean cutting across a limb, evasion is its chief purpose. 237 1914-15.] The Reflexes of Autotomy in Decapods. (2) Extension of the leg at the second joint moves the point of least resistance to traction from the first joint to the second. By this means a smaller wound is secured and the probability of fatal hsemorrhage prevented. (3) When the source of mutilation is quickly removed from the leg, autotomy does not occur, but the prawn is seen to tear violently at the stump with its jaws, and later to flex the next sound joint. Thus excessive bleeding is prevented. (4) As far as can be judged, there is a constant time relation between the various reactions — extension, tail-flapping, attempts at “ autophagie ” (or tearing with the jaws), and flexion. Suborder Reptantia. The Lobster. The common lobster, Astacus gammarus (Lin.) = (Homarus vulgaris (Edw.)) is a very good example of this section, and a detailed description will be given of autotomy as it occurs in the walking-legs, because the animal is large, and a very suitable subject in which to record the times of the various reflexes. The process shows many characteristics similar to those present in the prawn, and, so far as autotomy is concerned, is a stage higher than the crayfish {Astacus), which forms a link between prawn and higher palinuran. The common method of lobster capture is the setting of creels or pots, and it is found that the percentage of individuals captured short of limbs is very small. Herrick (12) records that out of 725 lobsters caught at Woods Holl in December and January 1893-1894, 7 per cent, had lost one or both claws. He gives no figures regarding the loss of walking-legs, but I can state from experience that it is much less, probably between 3 per cent, and 4 per cent. It is a significant fact that if lobsters are captured and put in one tank, fightinggoes on amongst them till the majority have lost both chelipeds. The loss in walking-legs is not so great, for these are well protected by the large overhanging chelae. The greatest danger lobsters run of losing limbs is probably due, therefore, to members of their own family. In examination of many hundreds, very few are found which have lost a leg at any other point than the breaking-plane in the case of the chelipeds, and the region of the joint between the second and third limb-segments in the walking-legs. Mutilation of limbs by various methods produced the following results : — (1) If a cheliped or a walking-leg be crushed by strong pincers and held, the limb first becomes extended. Immediately afterwards several powerful 238 Proceedings of the Royal Society of Edinburgh. [Sess. flaps of the tail cause the limb to break off at its base, and the lobster escapes. (2) If a sharp cut be made across a walking-leg and the animal at once released, the leg becomes extended for a few seconds, and the lobster shoots backwards by flaps of its tail. After a definite time (usually about fifteen seconds), the stump is flexed inwards to the middle line and violently pulled forwards by the chelate walking-legs and the maxillipeds. In a few cases removal of the remaining part of the leg at the second joint takes place, but as a rule the cut end heals up in a few days and the part is retained. If a lobster which has not autotomously removed a stump be kept over the moulting period, that leg does not regenerate, while those which have been thrown off at the base are replaced. In order to study further the points revealed by the above observations, the structure of the basal segments of the walking-leg must be examined. The second segment (fig. 4, (2)) consists of a hollow triangular pyramid hinged at two of its basal points on to the first segment. Yentrally a flexor muscle has its tendon attached to the lower border, while dorsally an extensor from the rounded edge (which represents two sides of the pyramid base) passes into the cavity of the first segment (fig. 5, e). The inner side of the dorsal wall of the second segment gives attachment to a muscle of which the tendon is inserted on the ventral edge of the third segment. This muscle (fig. 6, a) by its position may be regarded as a flexor ; but since movement at the joint between the second and third segments is very limited, it probably does ilot function as such. The third segment articulates with the second by a hinge joint, and at the point of attachment of the muscle described above (figs. 4 and 5, /) a furrow begins at its lower edge and passes round the greater part of the lower edo^e of the segment at a distance of about one millimetre from the edge. After autotomy at the second joint, a ring of calcareous material corresponding to the part of segment three below the groove, / is found attached to the stump (fig. 9, h). The muscle a is contracted, and thus the ring is pulled into the cavity of the second segment. The division of the limb has thus taken place along the groove at the base of the third segment, and, where that groove ended, along the arthrodial membrane joining segments two and three (figs. 7 and 8). The factors controlling autotomy of the walking-leg were further investigated, with the following results : — (I) Division of the extensor muscle of the second segment prevents autotomy occurring. 1914-15.] The Eeflexes of Autotomj in Decapods. 239 Figs. 4, 5, and 6, These figures show the normal position of the basal segments of a lobster’s walking-leg with the muscle attachments, e is the extensor of the second segment, a the autotomiser, and /the breaking-furrow. 240 Proceedings of the Royal Society of Edinburgh. [Sess. (2) Division of the flexor muscle of the third (the one attached to the ring which actually breaks off) has the same effect. (3) Cutting of the nerve-cord to the tail also prevents it. (4) Cutting of the nerve to the limb as it leaves the gangliated cord prevents it. (5) Division of the ventral nerve-cord above the segment from which Stages in autotomy of a lobster’s walking-leg. a is the autotomising muscle, h the detached ring of the third limb-segment, and /the breaking- furrow. Fig. 10. — Contractions of the extensor muscle of the second limb-segment produced by single induced shock. Time in secs. the limb is innervated makes autotomy more easy {i.e. removal of cephalic influence). The process can be further studied as follows : — The tendon of the extensor of the second segment is cut and its end attached to a heart lever, the lobster being placed on its back on a frog-board. A record of the contraction when the limb is stimulated by induced faradic current shows a latent period of T4 seconds and presents the appearance shown in fig. 10. The tail, or properly speaking the abdomen, which flaps violently after each cut or electrical stimulation, can also be connected up to a lever, and a record of its contraction made along with the contraction of the extensor 241 1914-15.] The Keflexes of Autotomy in Decapods. of the second segment. A definite time relation of about three seconds exists between the two events (fig. 11). Fig. 11. — A, tail contractions ; B, contraction of extensor of second segment. Time in seconds. This trace is only meant to indicate the time relations of reflexes. The curves on B occurring simultaneously to those on A are due to inertia.. Electrical stimulation of the cut end of the limb produces the same result as cutting, but tail-flapping does not always follow. Fig. 12. — Compared with fig. 10, this contraction is much greater in extent and duration. It occurred when the nerve segment was isolated. When the segment of the nervous system innervating the limb is isolated from those above and below, the extent of contraction of the extensor of the second segment increases (fig. 12), and the time of con- traction is prolonged. VOL. XXXV. 16 242 Proceedings of the Royal Society of Edinburgh. [Sess. When the cut end of the limb is continuously stimulated by rapidly interrupted induced shocks (Neef s hammer), contractions of the extensor muscle last several seconds and are repeated after a definite period. This also happens when the nerve segment is isolated. In some cases a peculiar rhythmic contraction of the extensor of the second segment may be recorded when electrical stimulation is used (figs. 13 and 14). Owing to the inaccessibility of the tendon of the flexor of the third segment, the time of its contraction and its latent period cannot be recorded. Fig. 13. — Rhythmic contractions of the extensor of the second segment. (The speed of drum same as in fig. 12.) Fig. 14. — The same with slower drum. but I believe that it contracts after the extensor of the second segment and before tail-flapping begins. Study of muscle-contraction in the case of chelipeds is also prevented by the overhanging carapace, but, as the mechanism is very much the same as that found in the higher Brachyura, detailed examination is unnecessary. This point, however, may be mentioned: the break which takes place after autotomy occurs at a definite groove in the basi-ischium or second limb-segment. This segment is probably the product of fusion of two parts, represented in the walking-legs by the second and third segments. The break is clean as a knife-cut, and involves calcareous material at all points. This stands in marked contrast to what is seen in the case of the walking-legs, where the ring of cut surface is partly calcareous and partly membraneous. Of great importance, too, is the fact that after 243 1914-15.] The Reflexes of Autotomy in Decapods. autotomy the remaining part of the leg is rigidly extended much beyond that degree of extension which it could obtain if the whole of the chela were present (fig. 15). The following conclusions can be drawn from the above study of the processes of autotomy in the lobster : — In the walking-legs there is a distinct advance on what was found in the prawn. In both the second limb-segment is sharply extended, but in the latter a new element is added. The break, instead of wholly involving a tough membraneous structure, is partly through brittle calcareous matter. This, of course, is due to contraction of the flexor of the third segment, and an indrawing of the ring of integument central to the groove described above. Regarding the limb-segment as a rigid cylinder, it is Fig. 15. — Basal parts of the chelipeds showing breaking-furrow in the right chela and stump extended after autotomy on the left. B.f., breaking-plane. easily seen that the combined result of contraction of the two muscles is to make the region of the groove the weakest part. If, therefore, the traction set up by tail-flapping cannot be resisted, breaking must occur at the groove. The graphic recording of m usd e-contraction has established the fact that a definite time-relation exists between the different parts of the reflex. The reflex is plurisegmental, for autotomy does not occur when the nerve connection to the tail is severed. If the influence of upper neurons be removed, the reflexes are more powerful. This demonstrates that even in an animal with so little cerebral development as the lobster the inhibitory action of the upper ganglia is manifest. Evasion of an enemy would seem to be the most powerful factor in the production of autotomy in the lobster, for it is necessary that the walking- leg be held in order that amputation may be effected. The movements of retreat suggested by tail-flapping also make it highly probable that escape is the real purpose. In the prawn, if the limb was not held after mutilation. 244 Proceedings of the Eoyal Society of Edinburgh. [Sess. attempts at removal by the maxillipeds and other legs followed the retreat of the animal. The same has been described in the lobster, and it is pointed out, in addition, that the chelate walking-legs can often be seen to remove a damaged limb at the proper breaking level. The Crayfish. In structure the fresh-water crayfish (Astacus fiuviatilis (Fabr.)) closely resembles the lobster. The animal could not be studied in its natural habitat, and the conclusions drawn are from laboratory observations only. The crayfish behaves in almost a similar manner to the lobster when its limbs are mutilated. Autotomy of all legs at the base may occur. There is this difference, however : the chelipeds are abandoned on a very much weaker stimulation, in comparison to size, than in the lobster. On the other hand, walking-legs are autotomised much less readily. In a paper on regeneration of the first leg in crayfish, Reed (7) points out the necessity of holding a mutilated walking-leg in order that the animal may autotomise, but she mentions nothing about the tail-flappings At the same time she states that rupture occurs at the “ free joint between the second and third segments of the limb,” implying that only a tearing of synovial membrane occurs. I examined the stump of a walking-leg after self-amputation, and found the same half-ring of calcified material carried away from the third segment as in the lobster. As the flexor muscle remains firmly contracted, the ring is drawn into the cavity of the second segment, and may be so sunken in the soft tissues that it cannot be seen. Although no tracings have been taken, there is little doubt but that^ as in the lobster, a definite time-relation exists between the various muscle contractions. First, the limb is extended at the second joint; then the flexor of the third segment, which weakens this segment in the region of its base, contracts. These movements are quickly succeeded by rapid tail-flapping and autotomy at the weakest point, i.e. the groove in the third segment. If no resistance be offered to the walking-leg, and if the scissors be quickly disengaged, tearing movements of the other legs and jaws occur markedly. The chelipeds, also, can very effectively pull off a damaged walking-leg if they are able to get hold of it. This form of removal has reached a high degree of development in the hermit crab, and it will bo discussed fully at a later point. 1914-15.] The Reflexes of Autotomy in Decapods. 245 Section II. ANOMURA. Subsection I. Pagurids. Hermit Grabs. The Pagurids are lobster-like decapods characterised by shelter adapta- tion. The abdomen has become soft, and the posterior appendages have diminished in size, and act merely as a means of bracing the animal against the inner walls of its borrowed home. The most usual form of shelter taken by these animals is an empty whelk-shell, but one individual (Pylocheles) is found in Indian waters inhabiting the hollow inside of little pieces of water-logged bamboo. Whenever danger threatens a Pagurid it at once retires to the shelter of its shell by contraction of the thick abdominal muscles which grip the inner part of the spirals. This retiral is produced in very much the same manner as the back-swimming of the Palinura and Natan tia by tail-flapping. The type chosen for observation was Eupagurus bernhardus (Lin.), or the “ soldier hermit.” This animal is very plentifully got in trawling below tide marks, and it gets its martial name from its fierce method of attacking its neighbours and brothers. Hermit crabs, however, do very little real damage to one another. It is a rare occurrence to find one autotomised claw in a tank where upwards of fifty have been confined for several weeks. Loss of appendages in the natural habitat seems to be even more rare, and the number found regenerating is probably always under I per cent. It is interesting, therefore, to find that both autotomy and regeneration take place readily. It was found that if a chela or walking-leg be seized quickly and violently with forceps, the animal immediately withdraws to its shell and almost simultaneously the limb breaks off at a groove in the basi-ischium or second segment. The changes which take place in the basal muscles cannot be observed, for this part of the crab is hidden beneath the shell. After the leg has been autotomised it is found, on removing the animal from its shell, that the stump is firmly extended. If the tendon of the extensor be disconnected from its attachment at the base of the second segment, autotomy cannot occur. Whatever else happens at the time of injury, the extensor contracts violently, and remains contracted after the leg has been thrown off. In cases where the cut across a limb was quickly made and the stump freed, it was found, again, that the crab shot backwards into its shell. After a few minutes it emerged, and the damaged leg was seen to drop 246 Proceedings of the Royal Society of Edinburgh. [Sess. away, having been divided, as before, at the breaking-plane in the basi- ischium, but retained in its position relatively to the animal on account of the tight packing and folding of legs within the mouth of the shell. On account of the small size of the crab, and the covering afforded to the basal limb-segments by the shell, I was unable to study the process of autotomy by graphic methods under normal conditions. It was found, however, that when the shell was broken away over the tail, and the nerve-segments of the particular limbs operated on separated from those nerve-segments above and below in the gangliated chain, autotomy took place. Under normal conditions, therefore, the reflex of autotomy in the hermit crab is unisegfinental. This is a distinct advance on the condition found in the Macrura, for there it was found that the reflex involved the nerve-segment controlling the damaged limb, and the ganglia and arcs of the abdominal region also. It is practically an unknown thing to find a hermit crab without a shell. The animal, during its growth, has to change shells periodically, but it takes very great care to find a suitable new home before it leaves the old one. It places the new one close up against the mouth of the one it is about to discard, and those who have seen the changing report that it only occupies a portion of a minute. Autotomy is therefore occurring under abnormal conditions when it happens in a crab removed from its shell ; but it is a most surprising thing to find to what extent the reaction of the animal to injury varies. Instead of extending its limb or contracting its tail, the hermit crab promptly plucks oft" the stump of a damaged leg with its chelipeds. The reaction is deliberate and purposeful. Division always takes place at the breaking-plane, and the profuse hsemorrhage is at once stopped by closure of the valve which is formed by flaps of the membrane obturatrice.” But the influence of the cerebral ganglia does not in the least affect the reaction. Division of the nerve-cord below the level of injury is likewise without effect. It was stated that no marked extension of the leg can be noticed ; but if the extensor muscle of the second segment be connected up to a heart lever, it is found to contract vigorously when the limb is cut, burned, or crushed, or when the cut end is stimulated by a faradic current. The latent period is about one-tenth of a second, and the period of re- laxation is about fifty times as long as the period of contraction. This contraction will not take place if the nerve trunk of the segment be divided as it leaves the central nerve mass. It is, therefore, a reflex. Since no marked extension of the limb can be observed, there must be a flexor antagonism to this extensor contraction, but no details of such could be 247 1914-15.] The Eeflexes of Autotomy in Decapods. worked out. The corabined result of these reflex contractions must be to weaken the leg at the region of the breaking-plane, and so to facilitate removal by plucking on the part of the chelipeds. If any one of the muscles be divided, autotomy cannot take place. It is thus seen that, when the hermit crab is removed from its shell, the normal unisegmental reflex is not sufficient to produce autotomy. It must be reinforced by spread to other segments, and participation of effector organs belonging to these. Something may be said of the nature of this spread. Firstly, if one cheliped be damaged it is promptly plucked off by its fellow of the opposite side, only a few seconds intervening between the times of injury and of autotomy. The movement is always well aimed. In the second place, if the next pereipod be damaged, the aim is not so good, and it may take the chelipeds almost half a minute to seize and remove the offending stump. Sometimes it seizes the wrong leg and pulls violently at it, but removal never results, probably because the unisegmental reflex contraction of the basal muscles has not taken place, and therefore instability at the breaking- plane has not been produced in this sound limb. If, thirdly, the seat of injury be in a limb innervated by a segment of the nervous system still further removed, quite a time may elapse before the leg can be plucked off, and many attempts on sound legs may have been made during this time. The speed and degree of certainty of autotomy, therefore, vary inversely as the distance of the innervation centre of the injured limb from the region of the chelipeds. Another point indicating the faulty means of connection between different levels of the nervous system is seen in the behaviour of the damaged leg. When the chelipeds seem to be doing their utmost to get hold of the stump, this part is calmly going on with its rhythmic walk- ing movements, and instead of bending up to meet the chelipeds it always seems to be in the process of retreat when the claws are about to seize it. These plucking movements of the hermit crab have been mentioned by Morgan (1) in one of his papers ; but as his observations do not agree with those described above, some discussion is necessary. He, in the first place, takes no account of the fact that the crab is in a most abnormal condition when it is autotomising outside its natural shelter. I have shown that the reflex removal of damaged limbs is unisegmental in normal circum- stances, but that reinforcements by arcs of other levels is necessary when the crab is removed from its shell. There is no need, therefore, to invoke complex instinct when dealing with the matter. Furthermore, Morgan states that plucking only takes place in those cases where there is a definite breaking-plane at the base of the injured 248 Proceedings of the Royal Society of Edinburgh. [Sess. limb, and when the injury is distal to the breaking-plane, suggesting that it does not occur when, for example, the diminished legs are cut, because it could serve no useful purpose. I find that in all the Pagurids which I have examined a definite plucking of a damaged fourth leg occurs after injury, and in this limb there is no breaking-plane. In addition, I find that in every case in which the eyestalks have been cut through, the chelipeds rise and tear at the seat of injury. At a later point “plucking” is discussed in relation to other acts of autotomy, and I hope to be able to show that in the Pagurid it is a return to an ancestral reaction type, which occurs when abnormal conditions arise. One other observation on autotomy in the hermit crab is of great importance. It was found that if the extensor of the second limb-segment of a cheliped be cut (this destroys the unisegmental mechanism which weakens the breaking-plane), and if the limb be damaged lower down, the stump is gradually picked away by the other sound cheliped. The process usually takes about a day to perform, but when it is complete the stump has been nicely dressed off down to the level of the breaking- plane. A large percentage of crabs die from haemorrhage before the process is complete, but in those in which it is carried out successfully regeneration takes place in the same manner as it does after autotomy. This “Autophagie” (Przibram) is a reaction of still lower type, and it occurs when all the mechanisms of autotomy have been disorganised. The above description of autotomy in the hermit crab shows the pro- found influence of environment on the animal. From a highly specialised type of reflex which is unisegmental, a plurisegmental one involving plucking movements can be produced by removing the animal from its shell. Autophagy after mutilation is a process which takes some time to perform, but it is the next reaction of the animal when all mechanisms of autotomy have been disorganised. Subsection 2. Galatheids. It is somewhat unfortunate that the majority of Galatheids found in the Clyde are too small for the anatomical study of the mechanisms of autotomy and for the analysis of autotomy reflexes by ordinary physio- logical methods, because in this group limbs seem to be abandoned on the slightest provocation and with the least difficulty. A consideration of certain phenomena to be seen in them leads to the form found in the Brachyura or “true” crabs. On this account it must now be studied. The Galatheids are lobster-like animals, but the abdomen is turned in loosely on the ventral part of the thorax, and by its rapid flapping move- 249 1914-15.] The Keflexes of Autotomy in Decapods. merits is a very effective swimming organ. The two types examined most carefully were G. squamifera, Leach, and G. dispersa, Bate. These are found on the shore usually clinging to the underside of stones. In spite of the fact that autotomy occurs very readily, the percentage of Galatheids taken short of legs is comparatively small, probably between 5 per cent, and 10 per cent. The first observations made on autotomy are usually the result of accident, for in shore collecting nearly every Galatheid picked up by a cheliped or walking-leg promptly abandons the leg and drops back into the weed. One would be very much inclined to give the animal credit for deciding that it would be better to escape without a leg than be taken. So much is this the case that Pieron (10) recently, in describing a similar form of autotomy in Grapsus, calls it psychic. The evidence tends to show that no decapod limb is abandoned except as the result of some stimulus received in that limb, which is nocuous to the animal. This is indicated by the fact that the ordinary porcelain crab (Porcellana platycheles), when suspended by the hydroid which grows on its claws, will not autotomise. If it is picked up on the beach by the fingers, ever so lightly applied, autotomy almost invariably happens if a leg be held. It is not clear whether pressure or whether the heat of the fingers is the nocuous stimulus. In any case it rarely happens in the laboratory (where the heat of air and wafer must be nearer that of the body). M. Pieron records the same fact for Grapsus. If limbs are sharply cut by scissors, the Galatheid has usually shot backwards by tail movement before the scissors are disengaged, and the limb is broken off at the breaking-plane. If the cut be clean enough, however, the limb is often shot off by the animal in the course of its flight, without touching any point of resistance. At other times it is retained, and may be later plucked off, either by the chelipeds or by the diminished fourth leg, which is usually used for cleaning. The leg is usually markedly extended at the second joint, and, if it is touched by the Anger or forceps, usually snaps off at the breaking-plane. In comparison with the Pagurids, it may be said that the local weakening of the limb at the breaking-plane by segmental reflex muscular contraction is very much more marked. Escape seems to be the chief purpose of autotomy in the Galatheids, for movements of flight always accompany self -amputation. In the Brachyura, which are studied in the next section, stoppage of haemorrhage seems to be the main purpose, for usually the animal does not attempt to fly from the source of danger. 250 Proceedings of the Royal Society of Edinburgh. [Sess. Section III. BRACHYURA. The True Crabs. The Brachyura represent the most highly specialised form of Crustacea. Swimming habits have practically been abandoned, and the diminished abdomen is permanently turned under the thorax. Armouring is usually fairly heavy, and the crab sees a fight to a finish instead of escaping at the expense of a leg. The most easily procurable types in the Clyde are Garcinus moenas (Penn.) (the green shore crab). Cancer pagurus, Lin. (the edible crab), Portunus puber (Lin.) (the swimmer crab), Hyas araneus (Lin.) (the spider crab), and Inachus dorsettensis (Penn.) (the slender spider). It was on the first four types that the majority of the observations were made, but the more rare forms were also examined. Garcinus mcrnas may be got beneath almost every weed-covered stone on a rocky shore, and is remarkable for the extent to which it loses its legs. The following tables show the percentage : — Crabs collected at Cullercoats, Northumberland, January 1915. Number, Carapace. Number with Legs Missing. Per cent. Total Loss of Legs. Average Loss per Crab. 37 cm. ov^er 5^ 18 48-6 36 2 29 over 4 7 24-1 9 1*2 40 under 4 9 22-5 10 IT Crabs collected at Lion Rock, Cumbrae, March 1913. Number. Carapace. Number with Legs Missing. 1 1 Per cent. ' 1 cm. 22 4i-3i 11 50 26 14 3J-2* 21-3 6 4 23 28 13 2‘'-ll 0 0 The above crabs were collected from rocky shores, and the liability to injury is seen to vary directly with the size, loss of limbs being present in about 50 per cent, of crabs three years old and upwards. If collections are made on sandy beaches at the same season of the 1914-15.] The Reflexes of Autotomy in Decapods. 251 year, the percentage is found to be much lower, and rarely goes above 30 per cent. In the summer of 1914 (August) collections were made again at Lion Rock, Cumbrae, and it was found that the percentage of crabs showing signs of having lost legs was in all cases below 35 per cent, (for three- year-olds). There are, therefore, two factors at work in causing autotomy : one is the nature of the shore, and the other is the season of the year. The storms of winter doubtless cause great movement of stones under which the crabs live, and thus limbs must be liable to crushing. On sandy shores there will, of course, be very much less danger. The moulting season is in early summer, and by August limbs lost during the winter have regenerated. Shore crabs live peaceably together even though fifty of various sizes are kept in one tank. Only one autotomised leg may be found in weeks. In the natural state, therefore, the chief producer of autotomy in Carcinus is crushing by movement of stones. Thus self-amputation is more a provision for stoppage of haemorrhage than for escape, for it allows the valvular mechanism at the breaking-plane to close. The same applies to the other Brachyura, but in these the loss of limbs is not so great, for they are not permanent shore-dwellers. Cancer, Hyas, and Fortunus show a 10 per cent, figure for loss of limbs. In a typical crab autotomy is purely a unisegmental reflex. Only in one form does plucking with the chelae ever take place (in the spider crabs), and this is due to the lack of carapace overhanging the basal parts of the limb, which is essential for the process. In Cancer, Carcinus, and Fortunus, after a limb is crushed or cut across it immediately extends violently at the second joint, and, coming in contact with the carapace, snaps cleanly across at the breaking-plane in the basi-ischium. In Fortunus, however, autotomy may occur without the limb coming in contact with external resistance. This resembles the condition found in Galatheids. A crab will keep on autotomising limbs as they are cut, till none are left, and may not move more than half a yard from the spot on which it received its first cut. If a cut leg of Carcinus comes in contact, during extension, with a resistant body before it reaches the carapace, e.g. the finger of the operator, division takes place at the breaking-plane, just as it does when the limb is extended quite against the body of the animal. In all cases a point of resistance for the distal part of the limb is necessary. The same is necessary in the case of Cancer. In Hyas, however, a difference is some- 252 Proceedings of the Royal Society of Edinburgh. [Sess. times seen. The crab is a very slow animal in its movements, and, if it has not succeeded in autotomising a damaged leg after about a minute, it begins slowly to pluck at it, just as the hermit crab does. The structure of the basal limb-segments in all the Brachyura is almost uniform. The second segment (basi-ischium) is divided by a furrow at the breaking-plane into two parts. It is connected by muscles to the first segment and to the body wall, the short extensor and the short fiexor moving it on the first segment, and the long extensor and long flexor V- Fig. 17. Figs. 16 and 17 show the arrangement of tendons and muscles at the limb-base in Carcinus mcenas. (Fig. 17 is after Fredericq. ) B.p., breaking-plane ; s.f., short flexor ; l.f., long flexor ; s.e., short extensor ; l.e., long extensor ; d., diaphragm. joining it to the body. The bellies of these last muscles pass through the cavity of the first segment. Figs. 16 and|17 show this arrangement from the lateral aspect, and looking through the limb-cavities, respectively. As the tendon attachments of the extensor muscles are of great im- portance in the later description of the process of autotomy. they must be described in some detail. Looking at the upper division of arthrodial membrane of the articulation between the second and third limb-segments, we see the tendons shining through in the region of their attachment to the lower edge of the basi- ischium. The long extensor is attached anteriorly and the short posteriorly. If a knife is passed between the tendon heads of the muscles it will be found that if the handle is turned towards the head region of the crab 253 1914-15.] The Reflexes of Autotomy in Decapods. it cuts through tough material till it reaches the breaking-furrow, when it is stopped. There is thus a junction in the ring of calcified material at an angle to a line of radius (figs. 18 and 19). The physiological processes connected with autotomy in Brachyura have been studied principally by Fredericq and Demoor (13). The former used Carcinus moenas in his experiments, and the following are his findings : — (1) The leg of a dead crab resists a force of to 5 kgms. applied i Fig. 18. These figures show the structure of the basi-ischium in Cancer. B.p., breaking- plane ; l.e., long extensor ; a, joint in the lower ring (basium). along the axis of the leg, and when rupture takes place it occurs at the junction between body and first segment, leaving a large wound. (2) When a leg is injured the long extensor of the second segment con- tracts violently, and the leg is pulled upwards till its distal part reaches the overhanging carapace. The long extensor continues to contract, and the leg divides at the groove in the basi-ischium (the point of least resistance) (fig. 20). (3) In all cases Fredericq afilrms that a point d’appui is necessary, and this may be the overhanging carapace or the finger of the operator. (4) Integrity of the long extensor of the second limb-segment is the sole condition for the performance of autotomy, for breaking occurs when 254 Proceedings of the Royal Society of Edinburgh. [Sess. all other muscles to the second segment are cut, except when the leg is forcibly extended at the second joint. Fredericq draws his conclusions without taking this last fact into consideration. Demoor examined the process in Portunus and contradicted Fredericq. An external point d’appui, he says, is not necessary ; and autotomy at the breaking-plane probably takes place by the torsion of the '' partie caduqne’' of the leg on the basal part, the forces meeting at the breaking-plane, which is the locus of least resistance. He advances this view only as a theory, and at the same time points out that the reflex mechanism cannot be of such a simple nature as Fredericq would endeavour to show. It must, he says, be a highly complex reaction, involving to some degree most of the basal muscles of the leg. With this statement he finished his account of the subject, and since then no one has again taken it up. Fig. 20 (After Fredericq). — Explanation in text, c., carapace; h., body; l.e., long extensor. In the course of the present experiments, the movements of the long and short extensors were studied by means of graphical records of their contractions. Firstly, the combined tendons of the long and short extensors were attached to a heart lever and the cut end of the limb was stimulated by single induced shocks. The following were the results (see figs. 21, 22, 23, and 24). The traces show that there are two elements in the curve. The tendons of the long and short extensors were therefore isolated, and when this was done properly the following were the results. The flexor of the second segment was also attached to the lever, and it was found that it too contracted after a longer latent period than the two extensors. (Carcinus was used in this experiment.) (Fig. 25.) This demonstrated that the short extensor, contracted along with the “muscle disjoncteur” of Fredericq and with the flexor, probably played an important and independent part in autotomy. 19 14-1 5.] The Reflexes of Autotomy in Decapods. 255 Fig. 22. —Cancer pagurus. Several contractions of combined long and short extensors showing double element. Time xrijfh secs. 256 Proceedings of the Poyal Society of Edinburgh. [Sess. Fig. 24. — Hyas araneus. Single contraction of the combined muscles. Note the long latent period. Time secs. 257, 1914-15.] The Reflexes of A^utotomy in Decapods. It was pointed out that the tendons of the short and long extensors were inserted on the basal ring of the second limb-segment on either side Fig. 25. — Superimposed tracings of contractions of the isolated muscles showing difference in latent period. Time secs. P, short extensor ; A, long extensor ; F, flexors. of a slanting joint (fig. 19). These act in directions shown in fig. 27, and therefore tend to pull the jointed parts of the ring in opposite directions, Fig. 26. Fig. 27. Fig. 28. These diagrams represent changes produced in the basal parts of the limb when the reflex of autotomy occurs. as shown in fig. 26. After autotomy it was found that if the joint A, fig. 28, were cut, the parts of the ring were actually pulled apart, as shown in fig. 26, by the continued contraction of the extensors. Now, if we VOL. XXXV. 17 258 Proceedings of the Eoyal Society of Edinburgh. [Sess. regard the second limb-segment as a rigid cylinder, forces applied at the points of insertion of the extensor muscles, and in the line of their action, must cause great weakening of the cylinder at the region of the breaking-plane. So, if the distal part comes into contact with a resistant point, breaking at that level will be very easily produced, as occurs in Cancer. In Portunus, where the leg may he shot off without meeting a resistant point, the opposing action of the long and short extensors may be so great as actually to cause splitting at the breaking-plane. Fredericq pointed out that autotomy could not occur if the limb were forcibly extended. This position is the only one in which the short extensor cannot act, and Fredericq did not appreciate the fact that its powerlessness was the reason why autotomy could not occur. Recognition of the weakening at the breaking-plane (caused by the Fig. 29. — Explanation in text. opposing action of the extensors at the point of junction in the ischial ring of the second segment), which I have demonstrated, shows that Demoor’s torsion theory is unnecessary. Fredericq and Demoor have criticised one another to no purpose, for they have worked on different animals without making allowance for changed conditions. They both state emphatically that they have not examined one another’s types. To prove my hypothesis that weakening at the breaking-plane, as the result of opposing muscular contraction, is the sine qua non of autotomy, I inserted a knife blade firmly between the two parts of the lower ring, and found that the limb snapped oft at the breaking-plane on the slightest force being applied laterally to the distal part (“ partie caduque ”). When this is not done, no amount of twisting and pulling can accomplish division at the seat of election. Thus, summarising, it can he said that autotomy is a unisegmental reflex in the Brachyura. It is the result of co-ordinate action of the basal muscles of the limb attached to the second segment, and follows weakening of the breaking-plane region. It is most probable that its chief end is to prevent haemorrhage, for division of the leg at the breaking- plane allows the venous valve at that level to close. An external point of 259 1914-15.] The Keflexes of Autotomy in Decapods. resistance is necessary in most forms, but in Portunus and Hyas the leg may snap off at the breaking-plane without having a point d’appui. In Hyas and InacJms plucking by the chelipeds may be the direct cause of autotomy when it is delayed, but the co-operation of the autotomising muscles at the limb-base is necessary. Discussion. The descriptive accounts, in the preceding pages, of autotomy in various decapod forms show that there is much ground for fruitful comparative study, both from morphological and physiological view-points, in this process of self-amputation of limbs. A brief summary of the leading points is given below. It has been recorded by Przibram (9) that if the leg of an amphipod {e.g. Gammarus) be damaged or cut, the animal at once proceeds to bite the stump down to the level of the first segment. This closely resembles the behaviour of the spider {Tarantula), which also bites off a damaged leg down to the coxa at the base (Wagner (14)). In the decapod Crustacea this autophagy does not exist as a normal reaction to injury, but it takes place under certain conditions. The common prawn, when seized violently by a leg, extends the basal segment, and by a violent tail contraction tears the limb off at the free joint between the second and third segments. In the lobster and crayfish the same reaction takes place, but the rupture takes place at the level of a groove in the proximal part of the third segment. Previous to the tail contraction taking place, however, a flexor muscle of the third segment weakens the limb at the level of the groove by pulling inwards one part of the ring of calcareous integument of the third segment central to the groove. There is a definite time- relation between the various elements of the reflex, and autotomy can occur when the nerve cord to the brain is cut. The reflex is plurisegmental, but the part of it vrhich causes weakening of the limb at the breaking- plane is confined to one segment of the nervous system. If the limb be cut cleanly off and immediately freed, movements resembling autophagy in the lower forms result. The limb may be cut off by the chelate walking- legs, and in the case of the crayfish by the chelae themselves. In the hermit crab, the normal process of autotomy is the result of a unisegmental reflex ; but if the crab be removed from its shell, plucking with the chelae is necessary. Thus the change of conditions has necessi- tated the reinforcement of the unisegmental reflex by arcs of higher levels, i.e. the reaction is plurisegmental. If the extensor muscle to the second 260 Proceedings of the Eoyal Society of Edinburgh. [Sess. segment be cut, the crab proceeds to bite the damaged limb down to the level of the breaking-plane in the second segment. Thus, by modifying conditions, we can produce three types of reaction to injury in the hermit crab — autotomy purely local, autotomy involving other levels of the nervous system, and autophagy. In Galatheids autotomy can be performed by muscles at the base of the damaged limb, alone. The reflex is unisegmental, but under changed conditions may be reinforced by arcs of other levels. The Brachyura are the most highly specialised group of decapods, and it is found that in them autotomy is a purely unisegmental reflex. After injury, the extensors of the second segment, acting in opposite directions on the ring of hard integunient central to the breaking-plane, cause weakening of the limb at this point, and division may take place at once, as may be the case in Portunus, or when the distal part of the limb meets an external point of resistance, usually the carapace. There is a definite time-relation between the contractions of the opposing extensors. In Hyas, when no external point of resistance can be found, the animal plucks off the damaged limb with its chelae. This is the only case in which the uni- segmental arc is reinforced from other levels. There is here an assemblage of types in which morphological complexity, as seen in the structure of the breaking-joint, goes hand in hand with physiological specialisation in the local or unisegmental arc. In the lower forms, where rupture occurs at a free joint and is only a tearing of soft tissues, many arcs are involved : in the Brachyura, where slight muscular contraction in certain directions causes profound weakening of the limb at the breaking-joint, only one arc is involved. It is generally held that reactions to nocuous stimuli have remained principally and most powerfully unisegmental in the higher vertebrates, because withdrawal from the source of injury is thus most rapidly effected. In other words, the unisegmental reflex is regarded as the primary one. In these decapods, however, we find that whereas the reaction to damage of a limb involves many levels of the nervous system in lower forms, the reaction is almost always carried by one arc in the more highly specialised forms. Much speculation is possible regarding the degeneration in reaction-type when conditions are altered, and especially on the changes in behaviour of the hermit crab. Are we to regard the plucking movements of the chelae and the occurrence of autophagy as referable back to habits useful to the ancestral stock ? If such is the case, what element in the change of environ- 261 1914-15.] The Eeflexes of Autotomy in Decapods. ment causes the realising of functional capabilities which can have been of no practical value for so long ? Workers in experimental morphology (Entwickelungsmechanik) contend that the fundamental functional characteristics of cells are practically the result of “ hereditary inertia.” Arguing on this basis, therefore, we may conclude that the receiving cell in the unisegmental reflex of autotomy, which normally receives and transmits its impulse to a neuron (efferent) of the same level, is short-circuiting a “ current ” which in the earlier history of the race passed upwards to jaws and chelipeds. The resistance to passage of the impulse must be increased by disorganisation of the lower arc when the reaction-type is changed, as in removal of the hermit from its shell, and the impulse will then travel to higher arcs. On the nature of this increased resistance it would not be safe to speculate at present. Sherrington and others, describing the reflexes of the nervous system, emphasise the purposive nature of the reactions. How, then, are we to regard the reflex abandonment of limbs by these decapods ? In lower forms, evasion of an enemy seems to be the chief end, for movements of flight accompany local changes in the limb muscles. This is the case in the Natan tia and in the Palinura. It also occurs in the Anomura. Another element is seen, however, even in the prawn, for the next sound joint to the cut surface is always sharply flexed or extended, and haemostasis is thus produced (flg. I). Prevention of haemorrhage is also a potent factor in producing autotomy in the Palinura, for at the ‘‘ seat of election ” the animal has better venous valves to prevent loss of blood than at other parts of the limb. In the Brachyura the valves are most highly developed, and, as the causes of loss of limbs in Garcinus were shown to be the stony character of the shore and winter storms, so it may be concluded that auto- tomy normally takes place to stop bleeding. Psychic ” and ‘‘ exuviate ” autotomy have been described by other writers, but the evidence here adduced from many thousands of experiments is that evasion and haemo- stasis are the fundamental ends served by the self-amputation of limbs in decapods. Autotomy, too, is always the outcome of a nocuous stimulus applied to the leg which is abandoned, and it can never be proved to happen in the absence of such. I have pleasure in expressing indebtedness to Professor D. Noel Paton for his continued sympathy and encouragement in the work, and for his sound advice on such parts of it as were carried out in the Physiological Department of Glasgow University. Mr K. Elmhirst, superintendent of the Marine Biological Station, 262 Proceedings of the Royal Society of Edinburgh. [Sess. Millport, provided me with the material required, and aided me very much in points of zoological significance. The work was largely carried out at Millport, and Mr John Peden ably assisted me in making records. My thanks are also due to Dr J. F. Gemmill for kind interest in the work, for suggestions on certain points, and for reading over the manuscript. Professor A. Meek very kindly gave me facilities for working in the Dove Marine Laboratory, Cullercoats, Northumberland, and some of the results are due to observations made there. The expenses of this research were defrayed by a grant from the Carnegie Trust. BIBLIOGRAPHY. (1) Morgan, T. H., “Regeneration and Liability to Injury,” Zool. Bull., 1898. Morgan, T. H., “ Further Experiments on Regeneration of the Appendages of the Hermit-crab,” Anat. Anz., xvii, 1900. Morgan, T. H., Regeneration, The Macmillan Co., 1901. Morgan, T. H., “The Reflexes accompanying Autotomy in the Hermit- crab,” Amer. Jour. Physiology, vol. vi, p. 279. (2) Frbdericq, L., “Nouvelles recherches sur I’autotomie chez le crabe,” Archives de Biol., t. xii, 1892. (3) Reaumur, “ Sur les diverses reproductions qui se font dans les ecrevisses, Jes omars, les crabes, etc., et entre autres sur celles de leurs jambes et de leurs ecailles,” Mem. de V Acad. Roy. des Sc., 1712. (4) Faxon, “ On some Crustacean Deformities,” Bull. Mus. Comp. Zool., Cambridge, viii, 257-74, 1881. (5) M‘Culloch, “ On the Means by which Crabs throw off their Claws,” Quar. Jour, of Sc., Litt., and Arts of Royal Inst., xx, 1826. (6) Heinehen, “Experiments and Observations on the Casting-off and Repro- duction of the Legs in Crabs and Spiders,” Zool. Jour., iv, 422, 1829. (7) Reed, M. A., “Regeneration of the First Leg of the Crayfish,” Arch. f. Entw., t. xviii, 1904. (8) Steele, M. I., “Regeneration of Crayfish Appendages,” University of Missouri Studies, No. 4, 1904. (9) Przibram, Arheiten der zool. Inst. Wien, xi, 163-194, 1899. (10) PiERON, H., Compt. rend. Soc. Biol., May 1907. (11) Drzbwina, a., Compt. rend. Soc. Biol., Nov. 1907. (12) Herrick, F. H., “The American Lobster,” Bull. U.S. Fish. Commission, 1895. (13) Demoor, J., “Manifestations motrices des Crustaces,” Arc/i. de Zool. exp. et gen., 1891, pp. 224-7. (14) Wagner, W., “La regeneration des organes perdu chez les Araignees,” Bull. Soc. Imp. Natur. Moscow, 1887. (15) Paul, J. H., “Regeneration of the Legs of Decapod Crustacea,” Proc. Roy. Soc. Edin., vol. xxxv, 1914. {Issued separately December 4, 1915.) 1914-15.] Chalk Boulders from Aberdeen, etc. 26S XXIV. — Chalk Boulders from Aberdeen and Fragments of Chalk from the Sea Floor off the Scottish Coast. By the late William Hill, of Hitchin, F.G.S. Communicated hy Professor D’Arcy W. Thompson. (MS. received June 12, 1915. Read June 28, 1915.) Introduction. In December 1908 I received from Mr A. Earland a fragment of a rock, believed to be chalk, which had been dredged from the bottom of the North Sea. Mr Earland also informed me that he believed boulders of a similar rock occurred in some profusion near what is known as the Kinnaird Deep, off the northern coast of Aberdeenshire. As a result of our correspondence a little later. Professor D’Arcy Thompson asked me to investigate such boulders as might presumably be chalk, dredged from the northern parts of the North Sea during the operations of the s.s. Goldseeker, a vessel employed by the North Sea Fisheries Commission, and he has kindly permitted me to include a description of the boulders found by the Goldseeker in the details of this paper. In 1904 Dr A. Gibb, of the University of Aberdeen, in a brief notice to the British Association, made known the fact that boulders of chalk occurred in what he regarded as a post-glacial clay at Belhelvie, near Aberdeen. In response to my inquiries. Dr Gibb was so kind as to send me specimens of this chalk. Later in the year I was most kindly invited to join the s.s. Goldseeker when she explored the bottom of the Kinnaird Deep, and I am indebted to Dr Alexander Bowman and his colleagues, the scientific staff of the ship, and also the officers, for their kindliness and courtesy to me on that occasion. Though only five small boulders were obtained, on landing I took the opportunity of visiting the brickworks at Belhelvie myself, accompanied by Dr Bowman, and secured a number of specimens of the chalk which, according to the manager, occurred chiefly in the upper part of the clay. During the summer several pieces of the chalk were picked up by the Goldseeker in various parts of the North Sea, but in one haul just north of the Shetlands (61' 31" N., 2' 20" W.) twenty- six fragments of chalk of varying size were found. All these boulders and fragments of chalk I have examined ; the results I have embodied in this paper. 264 Proceedings of the Royal Society of Edinburgh. [Sess. Rocks of Cretaceous age and apparently in situ have only been found at a few localities on the western coasts of Scotland. The first of these was discovered by Professor J udd ^ at Morvern by the shore of Loch Aline, and also in the Island of Mull. A small patch was discovered by Mr David Tait on the Island of Eigg in the course of his work for the Geological Survey, and another on the Isle of Skye.f In 1898 Messrs Jukes-Browne and Milne, in the Geological Magazine, made a report on the Cretaceous fossils found at Moorseat, Aberdeenshire J — all these will be referred to again in the sequel. In 1908 Mr David Tait § recorded the occurrence of Cretaceous fossils near Leavad, Caithness. The fossils, which include Craspedites, Hamites, and Crioceras, were found in a hard concretionary sandstone which may possibly be in situ.\\ The methods employed in the examination of the boulders were similar to those used by me in the examination of the Chalk of England, which are given at some length in the memoir on the Cretaceous rocks of Britain.^ Many of the boulders, however, contained soluble silica, and it became necessary to estimate the amount. This was done by first pounding some of the chalk (about 10 grams) to a coarse powder, not, however, rubbed to impalpable dust. The powder was treated with a 20 per cent, solution of hydrochloric acid. When effervescence had subsided, the residue was washed with hot water till there was no trace of reaction with nitrate of silver in the filtrate. After being thoroughly dried and weighed, the residue was treated with a 12 J per cent, standardised solution of caustic potash and kept in a water bath just at boiling-point for one hour and a half. The solution containing the residue was then diluted with water to five or six times its bulk, and just acidulated with hydrochloric acid. The liquid was then filtered, and the residue remaining in the filter-paper washed as before, dried, and weighed. The amount of soluble silica was estimated in the difference between the weight of the residue after treat- ment with acid and that after treatment with potash. The question of * “On the Secondary Eocks of Scotland,” Q.J.G.S., vol. xxxiv, 1878, p. 728. t “ The Geology of the Small Isles of Inverness-shire,” Memoir of the Geological Survey (Scotland, sheet 60), 1908, pp. 33-34. I Geological Magazine, Dec, 4, vol, v, 1898, p. 21. § “ On the Occurrence of Cretaceous Fossils in Caithness,” Proc. Edin. Geol. Soc., vol. ix, part 4, 1909, ]d. 318. II This mass of Cretaceous rocks at Leavad has been proved by boring to rest on shelly Eoulder clay. — J. Horne, IF “The Cretaceous Eocks of Britain,” Memoir of the Geological Survey, vol. ii, 1903, p. 499, etc. 265 1914-15.] Chalk Boulders from Aberdeen, etc. what is and what is not to be included as soluble silica is perhaps a debatable one from the point of view of the chemist, and possibly some of the terrigenous matter may have been acted upon in the above process. A friend of acknowledged ability in the analysis of rocks has, however, been good enough to check my work in the case of one specimen ; the result found us in complete agreement. The Boulders from Aberdeen and the Kinnaird Deep. The following is a list of specimens examined, with details of their salient characters. To ensure identification they are numbered as follows: — lA to 9 A are those sent me by Dr Gibb; 1 B to 13 B, those I collected myself at Belhelvie ; and 1 C to 6 C are those dredged by the Goldseeker from the Kinnaird Deep off the north coast of Aberdeen, and 1 G to 22 G those found north of Scotland and in the Faroe Channel. In the table some of these numbers are placed in the first column, the specimens being arranged, with one or two exceptions, according to the amount of residue contained in each after treatment with acid. Following the figures identifying the specimen is a brief description of the macroscopic appearance of the rock. Then follows the percentage dissolved in a 20 per cent, solution of hydrochloric acid, which may fairly be taken to represent the carbonate of lime, plus a little carbonate 1 Insoluble in Acid. Rock. 3 "o <1 •S d 0) Composition of Coarse Residue. o 3 3 w. Per cent 3 m 3 ‘o 3 o ' m O) c 31 C/2 O O Minerals. Max. Size 1 of Grains. Average Size of Grains. Organisms and Other Ingredients. A9 A small rounded fragment of green-grey fri- able rock. None 100 None 40-00 60-00 Quartz, mica, chlorite, zircon. -13 •06 A few residuary casts of spicular canals. Casts of Radio- laria, aggregations of fine siliceous matter. B 1 A subangular boulder of some size. Colour when broken darkish grey, semi-crystalline. 77-06 22-94 21-22 1-72 Quartz, mica, fel- spars, tourma- line, garnet. (Marcasite and iron pyrites. ) •16 •07 Sponge spicules, rod-like lengths, simple Monaxons, and many globate forms. Two casts of Ammodiscus in pyrites. B2 An angular frag- ment of firm white chalk. 55-11 44-89 19-31 25-56 Quartz, mica. (A few glauconitic grains. ) •21 (Sponge spiculesand Radiolaria very abundant.) 266 Proceedings of the Koyal Society of Edinburgh. [Sess. Insoluble in Acid. Rock. 'o n c3 o o:> 0> 3 H3 Composition of Coarse Residue. O) 'o CO Per cent m ’o 'o O "w pc? O) .s ' vx Composition of Coarse Residue. o 'o m Per cent o ‘m Oi O) O) o c/2 c5 O o Minerals. Max. Size of Grains. Average Size of Grains. Organisms and Other Ingredients. B 4 Fragment of a large rounded boulder of grey- ish-white chalk. 94*95 5*04 4*52 •52 Quartz, mica, felspar, tour- maline. *41 *12 Some aggregations of siliceous matter. Few spicules. Fragments of sili- cified vegetable matter. Many arenaeeous Fora- minifera besides siliceous casts. BlOi B 12f Not analysed. kl A rather small sub - angular fragment of rather soft white chalk. 97*58 2*42, 2*16 •26 Quartz, felspar, ' muscovite, bio- tite, chlorite, garnet. (A few grains of glau- conite. ) A few(?) residuary spicular canals in chalcedony. One Radiolarian. Frag- ments of silicified vegetable matter. A5 A small oblong rolled pebble of hard white chalk. 98*68 1*32 1*06 *26 Quartz, felspars, biotite, anatase, zircon. Many minute spheres of pyrites. *30 *12 Two or three spicules. A6 A small sub- angular rolled pebble, chalk hard and white. 98*16 1*81 1*22 *59 Quartz, felspar, muscovite, chlo- rite. *32 *11 A few spicules. Fragments of silicified vegetable matter. Dredged by s.s. Gol 'dseeker. Cl A fragment of greyish - white chalk. 69*50 30*50 8*44 22-04 Quartz, mica. Sponge spicules very abundant. A few Radiolaria. G1 An angular frag- ment of white ehalk, little rolled. 98*50 2*50 1*40 *10, Quartz, a few grains only. *14 RMzammina, Ain- modiscus. Frag- ments of silicified vegetable matter. G3 A small rolled pebble of hard white chalk. 99*20 *798 *780 *018 Quartz, felspar, hornblende, tourmaline. *05 Rhizammina, Am- modiscus. Frag- ments of silicified vegetable matter. G16 A small rolled pebble of hard white chalk. 98*39 1*603 1*542 *061 Quartz (three or four rather large grains, may have re- mained in hol- lows of the pebble). Rhizmnmina'^. Frag- ments of silicified vegetable matter. 269 1914-15.] Chalk Boulders from Aberdeen, etc. of magnesia contained in the rock. The amount insoluble in the acid is then given. This is called the residue, and is separated into two parts by levigation, the fine and coarse residues, and the estimated amount of soluble silica is also given. In the following columns are details of the composition of the coarse residue. These specimens differ from each other in some important particulars, and at the risk of some repetition I feel compelled to describe them fully. Specimens from the Glacial Drift of Aberdeenshire. A 9. — A rounded nodule of greenish-grey friable rock the size of a small potato. Small particles of similar material, sometimes containing small nests of sponge spicules, occur associated with the chalk boulders in the boulder clay. Viewed as a thin section under the microscope with a one-inch objective, this rock was seen to consist of grains with rounded contour, some of them being opaque, while others displayed a green colour. Mineral grains were also abundant, amongst which quartz and mica could be recognised. The remainder was more or less fine inorganic matter which filled the interstices between the grains and slightly separated them. The rock gave no reaction with the 20 per cent, solution of hydro- chloric acid and did not break down without pressure. By levigation rather more than 40 per cent, of the finest matter was removed. The remainder was found to be made up of definite forms and small irregularly shaped masses of dark grey material, grains of glauconite including a few short rod-like lengths, the casts of spicular canals, and mineral grains. Many of the definite forms mentioned above were apparently the casts of some organism. They were cone-shaped and seemed built up of the casts of successive chambers diminishing in size towards the apex of the cone. These casts were sometimes in a greenish mineral akin to glauconite, but not infrequently in grey mud, sufficiently hard to resist considerable pressure with a needle. I believe them to be casts of Kadiolarians, for they closely resemble both in shape and size undoubted casts of those organisms in silica found in other boulders. I have submitted these casts to Dr G. J. Hinde, F.R.S., who says there is a very strong resemblance in general form to genuine Radiolariee and little difference in point of size, so that one can hardly avoid the conclusion that they may be casts of Dictyomitra. Casts in mud and glauconite of other forms occur, probably of Foraminifera, but they give little clue to their identification. The masses of dark grey material in the heavy residue seem to 270 Proceedings of the Royal Society of Edinburgh. [Sess. consist of fine material and sand cemented, probably by the silica of the Radiolaria, and these with the casts are the opaque grains seen in the section. The fine material removed by levigation consisted largely of minute lath-shaped particles, with clearly defined but somewhat broken outline, and very faint double refraction between crossed nicols. The origin and nature of these particles is at present uncertain, though no doubt they are derived from the disintegration of some rock. The remainder of the finer material was amorphous structureless matter, as a whole negative to polarised light. B 1. — Part of a sub-angular boulder of considerable size. When broken, the rock is darkish grey and semi-crystalline in texture. Seen as a thin section it appears to consist chiefiy of well-defined calcitic crystals, probably formed by the conversion of the calcareous portion of the ooze into granular calcite after the deposition of the original material. They mask entirely the terrigenous matter which analysis shows is present in con- siderable quantity, as well as such organisms as may occur. Three or four large fragments of shell can, however, be seen and a few smaller pieces, all having the same structure which, though partially obliterated, is not that of Inoceramus. Opaque grains are scattered throughout. The residue after treatment with acid was large, 22*94 per cent. Of this 1*72 per cent, of coarse material was separated by levigation. Three- fourths of it consisted of short cylinders of minute nodules of silvery mar- casite or brassy-looking pyrites; two casts of Ammodiscus occurred in this material. The residue contained also a few Radiolarians, some sponge spicules, rodlike shafts or simple Monaxons, with few globate dermal spicules of Geodia. There is no silica in the colloid state in this specimen beyond that which can be accounted for by the presence of a few spicules. The proportion of sand grains was not large. The remainder was inorganic matter in an extremely fine state of subdivision, structureless and almost invisible when mounted in balsam, negative with crossed nicols. The behaviour of this material when analysing it, as well as its optical pro- perties, was that of Gault Clay. The specimens which follow all answer to the description of the rock which we know as chalk — that is to say, they consist of Foraminifera, foraminiferal cells, “ spheres,” together with the remains of other organisms, mostly calcareous, embedded in an amorphous calcareous matrix. The word “ cells ” is used hereafter in contradistinction to ‘‘ spheres.” These latter are for the most part round or nearly spherical bodies like 271 1914-15.] Chalk Boulders from Aberdeen, etc. minute shot, though some are ovoid in shape.^ They are especially abundant in the lower part of the Middle Chalk of England, and may be separated in quantity by levigation. The cells ” are usually ovoid, but their outline is irregular, one side being often flattened. They are some- what larger than “spheres,” and measure occasionally as much as 1*8 mm. in their longest diameter. The old definition of the unicellular bodies found in the chalk as “primordial cells of Glohigerina or other Foraminifera ” could be applied perhaps not inaptly to those “ cells.” B 2. — The matrix of this rock is crowded with prisms of Inoceramus shell and sponge spicules. A few well-marked Glohigerina and one or two other species occur together with other foraminiferal cells, some “ spheres,” and Radiolaria. The Inoceramus prisms seem to be of a long narrow type, but the condition of the matrix tends in some degree to obscure their contour and character. Though a large part of the matrix can be seen to consist of minute calcitic particles, the rock is permeated with colloid silica, some of which, especially in the neighbourhood of the spicules, is in a minutely globular form, and the silica in the walls of many of the spicules shows the progress of the molecular change from the amorphous to the globular condition, while in others it has reached the crystalline form of chalcedony. Many of the cells of the Foraminifera are also filled with this mineral. The rock failed to break down in the 20 per cent, solution of hydro- chloric acid, and though a quantity was kept in it for some days, even then all the lime had not been removed. From the residue thus obtained the larger and presumably chalky pieces were separated by sifting, and the remainder was slightly treated with heated caustic potash in the hope of freeing some of the organisms. On attempting to separate the heavy from the lighter portions by levigation, it was found that the heavy part consisted almost entirely of small lumps of white material. Most of these were cavernous and perforated by circular holes, obviously the casts of spicules. On breaking, they were found to consist of the siliceous casts of small Foraminifera, cells, “ spheres,” fragments of spicules and silicihed shell, an occasional Radiolarian, minute spherical bodies or globules of clear silica which sometimes occurred in small aggregations, and irregular masses of amorphous material which, when viewed by direct light, was of a snow- white colour. This amorphous material (the “ ciment ” of M. Cayeux) in which the more definite forms are embedded, when mounted in balsam and viewed with transmitted light, seems to have for its foundation clear structureless * “ The Cretaceous Rocks of Britain,” Mem. of the Geol. Survey., vol. ii, 1903, p. 500. 272 Proceedings of the Royal Society of Edinburgh. [Sess. matter, negative with crossed nicols. Contained within it — or, perhaps more strictly speaking, cemented together by it — are minute particles, and these by interference give it finely granular texture. In some instances the clear matter itself appears to be in the form of minute grains of irregular shape. Foraminiferal cells have become infilled with this material as well as clear silica, and remain in the acid residue as casts. After treat- ment of the acid residue with heated caustic potash, it became evident that the silica contained in this rock had advanced towards crystallisation to a greater degree than could be suspected by the examination of the chalk after the action of acid. Many of the small lumps of the white granular material seemed to be intact, but the colloid silica having been removed, and with it probably a certain amount of terrigenous matter, these masses were now clear and translucent, almost invisible when mounted in balsam and viewed by transmitted light; with crossed nicols they were seen to consist of minutely crystalline chalcedony. A large number of the Foraminifera, cells, shell fragments, Radiolarians, and residuary sponge spicules were also found to be of chalcedony. The white granular material above described clings persistently to the spicules and other organisms contained in the rock, making the investigation of the Microzoa difficult. Only Glohigerina hulloides and Textularia minuta were isolated, though other forms can be seen in the section. The assemblage of spicules was similar to that in the specimen next to be described. A quantity of about 10 grams of fresh material was taken for the determination of the amount of lime and colloid silica by the method already alluded to. Nearly half the acid residue, or 19’31 per cent, of the entire rock, proved to be silica in the colloid state. There seemed but few mineral grains in the final residue, but it was not possible to estimate the quantity of terrigenous matter. A 8. — In this very curious specimen the recognisable elements are in large proportion to the mass of rock, but the facies is difierent from that of the last. There are but few shell fragments; Foraminifera, cells, or “ spheres ” form 35 per cent, of its mass ; sponge spicules and Radiolaria are very abundant. The matrix consists of fine calcareous matter mixed apparently with some terrigenous material ; there seems also to have been a certain amount of secondary crystallisation of the original calcareous ooze after deposition, and this masks to some extent the details in the structure of the more minute particles. When a little fine powder of the rock is examined, one can still recognise amongst it pieces of shell, of Foraminifera, pseudococcoliths, and the like. It is not possible to realise, as in the last specimen, that much colloid silica exists in the matrix ; a few 273 1914-15.] Chalk Boulders from Aberdeen, etc. globules occur, and here and there they can be seen in a few of the spicules. In one of my sections there is, however, a small irregular area permeated with silica in the chalcedonic stage, practically a small immature flint, the organisms contained in the chalk being clearly outlined therein. Viewing the section with crossed nicols, it was at once seen that the whole of the recognisable elements — the Foraminifera, cells, spheres, etc. — were casts or replacements partly in colloid but chiefly in chalcedonic silica. About 150 grams were used in two experiments to test the percentage of lime and colloid silica. In the first of these there were two or three pieces so permeated with chalcedonic silica that they were unaffected by the acid. In the second the whole broke down into a sand, the heavier part, consisting of foraminiferal casts, sponge spicules, and Radiolaria, small masses of white granular material described above, together with comparatively few mineral grains. The casts were partly in colloid and partly in chalcedonic silica, both globular colloid and chalcedonic silica occurring together in the cells of the same cast. Sponge spicules were exceedingly numerous and in great variety of form, many of those described by Dr Hinde in his paper on the Horstead flint ^ being present as well as others that I have not yet seen in published figures. The silica of the walls was in nearly all cases in the chalcedonic stage. Casts of Radiolaria in chalcedonic silica were also abundant, the commonest being a species of Dictyomitra, the shape of these being often identical with those described in B 1. It was evident both in the acid and alkaline residues that this specimen contained more amorphous terrigenous matter than the preceding one, but it was found impossible to estimate the amount in this wreck of silicified organisms. A 3. — A small sub-angular fragment of grey chalk, not hard, mealy to the touch, seems weathered. The matrix of this specimen is crowded with small angular fragments of shell probably derived from Inoceramus, many foraminiferal cells, and some spheres ; there are comparatively few Globigerinee, Textularians, or sponge spicules, but the casts of Radiolaria are a prominent feature throughout the section. The matrix is chiefly calcitic, but there is certainly an admixture of terrigenous matter, the presence of which is seen in the greyish tint of the section. The rock did not break down readily in the acid solution, the matrix being permeated with colloid silica, though it is not optically visible, some of the original lumps of chalk retaining their shape. They broke down, however, on pressure when dried, releasing fragments of spicules, casts of Foraminifera, and Radiolaria. Separation of the coarser * Fossil Sponge Spicules from the Upper Chalky by G. J. Hinde, 8vo, Munich, 1880. VOL. XXXV. 18 274 ProceediDgs of the Royal Society of Edinburgh. [Sess. from the fine matter could not even now be attained, white granular material clinging persistently to the micro-organisms or remaining in small but inseparable particles. After treatment with potash, the lighter part of the residue was found to be lath-shaped particles and amorphous matter, together with minute fragments of chalcedonified organisms. Though it is impossible to estimate the amount, there is no doubt that much of the final residue must be considered as of terrigenous origin. B 13. — This was a large boulder of firm, grey-coloured chalk, and many experiments were made with it. Microscopical examination proved it to be a very shelly chalk similar to the last described, but it contained a greater number of spheres. Though the rock was permeated with soluble silica, the whole of the lime was removed in the acid solution ; small masses, however, remained cemented together which required break- ing. These, as before, were snow-white by direct light and appeared to be of minutely granular or mealy texture. The final residue after treatment with caustic potash was almost entirely terrigenous material with a few fragments of spicules. By taking a little of the residue every few minutes as it was being treated with the potash, it was possible to watch the gradual liberation of the lath-shaped particles from the investing soluble silica as well as the finer inorganic matter. The cementing material (?) appeared to be clear amorphous colloid silica, in this, as in the last specimen, not in a crystalline condition. The white appearance is probably due to the minutely porous condition of the granular material. The heavy residue contained small grains of pale green glauconite ; their proportion was, however, insignificant to the mass of the rock. B 8. — In a section of this specimen small Globigerinse and Textularians are a prominent feature, and there are a few shell fragments, but sponge spicules are abundant, and Radiolaria are scattered through that which looks like the usual calcareous matrix. Analysis again shows that the rock is permeated with soluble silica, and two-thirds of the heavy residue after treatment with acid consisted of white granular material. Sponge spicules constituted the greater part of the remainder of the residue with casts of Foraminifera, cells, Radiolaria, and mineral grains. On treating the acid residue with potash most of the white granular matter was dissolved, though a few fragments remained in which the silica was in minutely crystalline condition. This residue after treatment with the potash consisted, in fact, almost entirely of sponge spicules and casts of Radiolaria in chalcedony, of mineral grains, and a small amount of amorphous terrigenous material. A 2. — Fragment of a boulder. Chalk, white, in part soft, easily broken 275 1914-15.] Chalk Boulders from Aberdeen, etc. on pressure, part hard and splintery. The hard part contained three immature flint nodules, two about as large as a small bean, and one of flattened ovoid shape the size of a small walnut. The matrix is crowded with organisms, chiefly spheres and cells, but many Globigerinse, small Textularians, with several other forms, are present, the whole being estimated to form 65 per cent, of the material, shell fragments 2 per cent. : sponge spicules and Radiolaria occur, but are not common. The results of the analysis of this specimen were peculiar and were repeated several times. In the case of the softer chalk the heavier part of the residue con- sisted chiefly of the white granular material, with a few free spicules and fragments of Hexactinellid sponge mesh, some casts of Foraminifera in amorphous colloid silica, and also casts of Radiolaria. The rock is mainly calcareous, the total residue after the acid being comparatively small — only 3’63 per cent., — and of this nearly two-thirds was found to be soluble silica. In the harder part showing exactly the same constitution the residue was 12 ‘85 per cent., and of this more than eight-tenths was colloid silica, or 10‘75 per cent, of the rock. From the acid residue of the harder part it was clear that silica had infllled a larger proportion of the foraminiferal cells, and that some at least were partly chalcedony. In the final residue after treatment with potash little else remained but the chalcedonic casts of Foraminifera, fragments of spicules, and a general debris of chalcedonic particles with but few mineral grains. It will be noticed that the residues after treatment with acid and alkali closely approximate. B 7. — A smaller boulder roughly rectangular of hard, whitish chalk. The rough surface of this chalk is spotted with dark specks. When the smoothed sides of this block are examined, it will be seen that there are rounded or sub-angular areas, varying greatly in size, slightly lighter in colour than the surrounding material. They are not always well defined, but sometimes blend with the surrounding chalk. The dark specks do not occur in such areas, but a thin line of them often accentuates the division between the lighter and the darker shades. Seen in thin section the recognisable organisms are almost entirely spheres, with a very few cells of Globigerina, together forming 60 per cent, of the mass, the remainder being the fine calcareous paste. The lighter areas can faintly be distinguished by the greater density of the material, but there is practically no difference in the general character of the rock. The dark specks can now be seen to be sand grains of consider- able size, large fragments of Echinoid tests, ossicles or spines, and equally 276 Proceedings of the Royal Society of Edinburgh. [Sess. large pieces of Inoceramus shell, these being embedded in the calcareous matrix above described. The chalk can hardly be called nodular, but I can only conceive this peculiar structure to have been formed by lumps of partly consolidated wet chalk being rolled lightly over sand made up of the above-mentioned materials. The chalk broke down quickly in acid, but a large part of the heavy matter removed by levigation consisted of small masses of the white granular material. Though no spicules or Radiolarians can be seen in the sections, they were numerous in the acid residue, the Radiolarians having the mesh-work of their tests and delicate spines well preserved. Silica had infilled a large number of the “spheres” and cells, casts in silica being very numerous. It will be seen from the table that the sand grains in the coarse residue are exceptionally large, the maximum size being '78 mm. and the average T8 mm. B 3, B 5, B 9, B 11. — These specimens when seen in thin sections re- semble each other in containing the same kind of calcareous organisms, though there is a little variation in their relative abundance. The presence of many Globigerinm and Textularians of small size, with some cells and spheres, is a feature common to all, and in all are sponge spicules and Radiolarians. The heavy residue of B 3 contained a large quantity of white granular material, but the amount in the others was insignificant. The heavy residues of B 5, B 9, and B 11 consisted chiefly of spicules, casts of foraminiferal cells, etc., and mineral grains. All contained Radiolarians, usually well preserved, those of B 11 especially so. The siliceous organisms as a whole were destroyed in heated caustic potash, but a few spicules and casts of Radiolaria in chalcedony occur not infrequently in these and other residues. Of the other specimens, A 4, with a residue of 2'93 per cent., deserves mention. This is a large flattened ice-scratched boulder of hard greyish- white chalk. The rock consists chiefly of amorphous calcareous matter in which a few Foraminifera, shell fragments, and spheres and cells are out- lined. More than a third of the heavy residue consisted of’sponge spicules ; mineral grains form the bulk of the remainder. These were larger and coarser than in many of the other specimens. The residue contained also seven species of Radiolaria, their tests being in a remarkably good state of preservation. None of the white granular material was separated in the heavy residue. A 1, B 4, and B 10 may be considered together. The matrix of these specimens is crowded with “ spheres ” ; there are few Globigerinae or other Foraminifera, while fragments of Inoceramus shell, sometimes rather large 277 1914-15.] Chalk Boulders from Aberdeen, etc. and showing the prismatic structure, are scattered promiscuously through- out. Sponge spicules are rare, and Radiolaria cannot be seen except in B 4. The residue of A 1 consisted chiefly of sand grains, a few spicular fragments, and one well-preserved Badiolarian. That of B 4 consisted chiefly of mineral grains, a few sponge spicules, but Radiolaria were rare. This residue is amongst the few containing grains of glauconite. B 10 has not been analysed. A 7. — In contrast to the last-mentioned specimens this chalk consists chiefly of amorphous calcareous matter with a few small Globigerina0, Textularise, foraminiferal cells, spheres, and shell fragments scattered through it. But both Radiolarians and sponge spicules can be seen. The residue contained spicules the silica in the walls of nearly all of which had reached the chalcedonic stage. There was one Radiolarian also preserved as a chalcedonic cast, the network of siliceous skeleton is obliterated, but the chambers can be distinguished. B 12. — White amorphous calcareous matter forms a large proportion of this chalk ; small Textularians, as well as small Globigerinae, are very numerous ; shell fragments small, not abundant ; sponge spicules occur, but only one Radiolarian can be seen in the section. A 5 and A 6 consist almost entirely of foraminiferal cells, and when compared with A 1 and B 10 are a striking contrast. It will be noted that these are the purest chalks examined from Belhelvie, the insoluble residue being only 1’32 per cent, and 1‘81 per cent, respectively. The residue consisted chiefly of sand grains, with a very few fragments of spicules, but Radiolarians occur in neither of them. The following specimens were dredged by the s.s. Goldseeker from the Kinnaird Deep off the northern coast of Aberdeenshire. They are all rectangular fragments and do not appear to have been rolled, the largest being about 8 J in. x 2 J in. x 1 in. C2, C3, C4, C 5.— These are white, firm, splintery chalks, and are practically identical with A 5 and A 6 of Belhelvie, the recognisable organisms being almost entirely cells and spheres ” more or less thickly crowded together. A few of the same kind of thin, flaky shell fragments occur as in A 5, and here and there a spicule can be seen, but no Radiolaria. These specimens are so honeycombed by boring animals, the holes being filled with mud, that no analysis was attempted. C 1. — Boring animals have shown a nice discrimination and have not attacked this specimen, for it is a siliceous chalk similar to those from Belhelvie. It consists of Foraminifera, cells, spheres, and shell fragments. 278 Proceedings of the Koyal Society of Edinburgh. [Sess. with a large number of sponge spicules and some Radiolaria. The rock is permeated with silica in the amorphous and globular colloid state as well as in the chalcedonic form. As usual, it has filled the foraminiferal cells, though their silicification does not seem so complete as in some examples. The residue after the action of acid consisted of sponge spicules and the white granular material, which, as before, clung to the spicules. C 6. — A small fragment of grey-coloured chalk. It consists almost entirely of spheres and cells, all large in size and bold in outline ; they form about 65 per cent, of the rock. With these are numerous bodies of the same size, slightly elliptical in shape. One end is, however, abruptly truncated, thus giving the organism the shape of a horse-shoe. Were it not for the abundance of these forms, one would consider them to be broken cells or spheres, but their number suggests an organism not yet recognised. I find similar bodies occur in the lower part of the Middle Chalk of England, but they are comparatively rare. From optical observation the matrix seems to contain terrigenous material. I can detect quartz mica and, I think, chlorite in the section, but the grains are very small. I did not see the original specimen ; the section was sent me by Mr Earland already mounted, but a small fragment believed to be the same material was included. On treatment with acid the finer part of the terrigenous material in this was found to consist of lath-shaped particles. The fragment was too small to analyse. The phenomena exhibited by the Belhelvie specimens are such as we should expect to find in dealing with a group of rocks laid down during a period of gradual submergence; and with this fact in mind, though we have no fossils to guide us, it seems possible to follow a sequence of events in their sedimentation and to roughly arrange the boulders in some sort of order. The friable green-grey rock is a purely terrigenous deposit containing much glauconite, and it may be compared with the glauconite sands which are found almost everywhere in the British Islands at the base of true chalk. The presence of Radiolaria, its mineral grains and the lath-shaped form of its finer particles, link it up with the other boulders of the series, and I think it may fairly be regarded as a fragment of the basal bed. Both sand and glauconite grains are of small size — facts which seem to indicate that it was laid down at some distance from land and away from the influence of strong mud-bearing currents. The marl of B I, viewed as a thin section, would hardly be taken as a member of the Cretaceous series, for practically all organisms are 1914-15.] Chalk Boulders from Aberdeeu, etc. 279 obliterated by the recrystallisation of the calcareous matter in the rock ; but treatment with acid discloses Radiolaria spicules of the same species, and mineral grains of the same kind that are found in the other boulders. It contains 22'94 per cent, of terrigenous material and therefore was probably low down in series and its place not far above the Greensand. The average size of the sand grains in both deposits is small, but one would expect that if the terrigenous material was derived from the same land surface, within the same drainage area, and influenced by the same currents, that there would be found a similarity in the finer particles as well as in the mineral grains. This is not the case ; there are no lath-shaped particles in this specimen, and the whole of the lighter portion is in a very fine state of division. I know of no Cretaceous strata in England, except the Gault, in which the terrigenous material is in so fine a condition or exhibits the same physical properties. This curious dis- similarity will be noticed in other specimens, and one might infer that they came from different localities and do not belong to the same succession of beds. It will, however, be noticed that the lath-shaped particles occur in the specimens containing the greater proportions of terrigenous material, and therefore probably the earliest in the series. It seems to me possible that the difference may be due to some alteration in the strength or direction of current action as the land gradually became submerged. The next boulder, B 13, is a true chalk full of small angular fragments of shell probably derived from Inoceramus, Foraminifera, cells, and spheres. Radiolaria and sponge spicules are present and silica in the colloid state distributed through the rock. The quantity of terrigenous material can be fairly estimated, for little else remains after treatment with caustic potash. The amount of this, though only 8T9 per cent., places the specimen after B 1. Here again the greater part of the finest material is in the shape of minute lath-shaped particles. The three specimens B 2, A 8, and A 3, and perhaps also A 2 and B 8, may be grouped together. They all contain Foraminifera, cells, spheres, and shell fragments in greater or less proportions as well as Radiolaria. But three-fourths of the residue of A 8 (40‘58 per cent.) consists of sponge spicules ; they are also equally numerous in B 2. In this specimen silica, probably derived from the spicules, permeates the rock partly in crystalline and partly in minutely globular form. Though spicules are less abundant in A 3, this rock is also permeated with silica, and its position was probablj^ in close proximity to the two previously mentioned. A 2 and A 8 are also siliceous chalks containing spicules and more or less permeated with silica in the colloid state, though in A 2 much of it seems to have 280 Proceedings of the Royal Society of Edinburgh. [Sess. segregated in some small flint nodules. A 3 certainly contains more terrigenous material than the others, but as the whole rock is permeated with silica, and it is necessary to reduce it to powder before an analysis can be made, it is impossible to estimate the quantity, for particles of spicules and silicified calcareous organisms become included in the finer portion when levigation is attempted. But microscopical investigation of the final residue after treatment with potash shows that organic matter is present, the lath-shaped particles occurring plentifully. The next boulder I deal with is B 4. The total residue of this specimen was 5 04 per cent. ; from this ’52 per cent, of coarse material was separated by levigation. There were few spicules in the residue ; such as occurred were chiefly fragments of Hexactinellid mesh of robust type. There were, however, a large number of Foraminifera, chiefly arenaceous forms, with a few Radiolarians (see list), and mineral grains constituted the remainder. The size of these was large when compared with those of other boulders. The finest material consisted largely of lath-shaped particles. Many small fraofments of vegfetable matter were found in the residue. For B 7 I can suggest no relative position with regard to the other boulders. Details of its structure will be found on p. 266. It is a very puzzling specimen. In the other specimens the quantity of terrigenous material is not large ; the presence of quartz, mica, and felspar testifies that the deposit was not free from terrestrial ingredients, but the lightest part is amorphous structureless matter with lath-shaped particles. They are all relatively pure chalks. Though the amount of the residue after treatment with acid is often considerable, this is probably due to the presence of soluble silica derived from siliceous organisms, for all of them except A 5 and 6 contain sponge spicules and Radiolaria. Indeed, the successive decrease in the amount of material insoluble in acid is an indication of the gradual de- crease of the siliceous organisms as well as of terrigenous matter. No attempt has been made to arrive at the percentage of the various ingredi- ents of the coarse residues. In many of them sand grains, spicules, and foraminiferal casts are cemented together by silica in small aggregations which can only be separated by a heated solution of caustic potash. None of the residues can therefore be taken as strictly representing proportions either of organic or terrigenous matter. Fragments of vegetable substance occur in many of these residues. Other fragments of chalk recovered by the s.s. Goldseeker in dredging operations in the North Sea number twenty-four. The largest of these measured 44 in. x 3 in. x I J in., and from this they diminished in size to small 281 1914-15.] Chalk Boulders from Aberdeen, etc. pebbles not larger than a hazel-nut. Three were picked up in the Faroe Channel — one 60' 26" N., 4' 46" W., and one 60' 34" N., 4' 32" W., depth 963 metres, the third on the eastern edge in 778 fathoms, 58' 57" N., 0' 36" W. ; twenty were taken in one haul of the dredge in 61' 31" N., 2' 20" W., in 1400 metres, N.W. of the Shetlands. These last were picked out from a heterogeneous assortment of rocks which came up in the dredge. The identity of those other than chalk has not been ascertained, but some were Jurassic, including oolites. G 3 (61' 31" N., 2' 20" W.). — This specimen is now indurated with finely granular crystalline calcite. As a result, many of the organisms of which the rock is built up are partly obliterated. These were chiefly spheres of small size, some clearly outlined, others only just distinguishable. Amongst them were a very few Globigerinae, Textularians, and Rotaline forms, as well as Inoceramus prisms. Besides these were a number of forms which I have before described as Radiolaria, and I still think they are these organisms, though nothing is left but an outline in calcite clearer and more coarsely granular than the matrix. Fig. 1 in my paper* is the most common, but the outline of the Dictyomitra of the Belhelvie specimens occurs, also others which appear to be spined. The general aspect of the rock is curiously like, almost identical with, that of nodules which I have picked from the Melbourn Rock of Hitchin. Analysis of the specimen proved it to be very pure chalk, with a residue of only '780 per cent. The heavy residue of only ’018 per cent, consisted of minute sand grains, fragments of Rhizammina, Ammodiscus, and some pieces of the same vegetable structure as occurs in the Belhelvie specimens. G 12 (61' 31" N., 2' 20" W.). — Very similar to the last. Spheres rather less abundant, but more clearly marked. Thick-shelled Glohigerina of large size, fragments of Inoceramus shell, many large enough to show their prismatic structure, occur. They are such as may be found in the lower part of the Middle Chalk. A few of the Radiolarian forms can also be seen. G 1 (61' 31" N., 2' 20" W.). — Similar rock in which the organisms, chiefly spheres, are well preserved and fairly numerous, small Globigerinae and Textularians occur. One or two angular prisms of Inoceramus. G9 G 5 G 7 60' 26 G 8 60' 34 61' 21" N., 2' 20" W. Chiefly amorphous calcareous paste. Spheres and cells are scattered evenly through the rock, small Globigerinae and Textulariae occur with a few shell frag- ments. No Radiolaria, spicules rare. * “ Radiolaria in Chalk,” Q.J.G.S., li, 1895, pi. xxii. N., 4' 26" N., 4' 32' W. W. 282 Proceedings of the Royal Society of Edinburgh. [Sess. G 10. — Consists chiefly of amorphous, calcareous matter ; the recognis- able elements form less than 20 per cent, of the rock. There are no cells or spheres, their place being taken by small Textularians and Globigerinm. There are a few shell fragments and spicules, but no Radiolarians. G 11. — Like the last, chiefly amorphous calcareous material, but there are more shell fragments including pieces of Echinoid test. A somewhat different character is given by many minute particles, presumably of shell, in shape suggesting derivation from a small circular form. Two or three large Textularians, besides small ones and small Globigerinse, occur, and one or two other forms. G 13. — A hard splintery chalk crowded with organisms which form 60 per cent, of the rock. These consist of Globigerinae, Textularians, with Foraminiferal cells, spheres, fragments of shell, few of which are those of Inoceramus, but are of diverse structure and outline ; pieces of Echinoid tests and spines and many sponge spicules also occur, their silica replaced by crystalline calcite. There are no Radiolaria. The matrix is indurated with finely granular calcite ; the shapes of all the organisms are clearly outlined, but the tests of the Foraminifera are all very thin. The specimen recalls the structure of chalk rock in its broad features, but there is no glauconite. G 6 and G 14 are two specimens of a type of chalk which differs from any which I have previously examined. Its character is given by the large size and bold outline of the cells and “ spheres,” the latter sometimes measuring T3 mm. in diameter in comparison with ’08 mm. of those of the south. Fragments presumably derived from these tests, for they have a circular outline, are scattered through the matrix (Note Gil). There are many Foraminifera, chiefly Textularian and Rotaline forms; Glohigerina are rare. The larger calcareous fragments include pieces of Echinoid tests, small bits of Bryozoa and of shell, the latter being of ragged irregular outline ; none appear to be derived from Inoceramus. G 2. — Similar rock, though large spheres are not so numerous, hut it contains more shell fragments of ragged outline, thin flaky pieces, and one or two prisms of Inoceramus. A large fragment of a Bryozoan also occurs. These larger elements of the rock are unequally distributed, some parts of the section being crowded with them ; in others the calcareous matrix predominates. G 15 contains shell fragments of the same type, small pieces of Bryozoa, very few large spheres, but many minute Globigerinse and Textularians. G 16. — Shell fragments of the same type but rather larger are very 283 1914-15.] Chalk Boulders from Aberdeen, etc. numerous, one or two small pieces of Bryozoa ; Globigerinse, Textularians, and other forms occur ; the rock also contains sponge spicules, having the silica of their walls replaced by calcite. A few small mineral grains occur throughout the section, but this chalk from ocular observation does not convey the impression that much terrigenous matter is present. Analysis confirms this. The residue contained quartz grains, besides Ammodiscus and fragments of Rhizammina. There were also many pieces of silicified vegetable matter similar to that met with in the specimens from Belhelvie. 21. — Faroe Channel. Two-thirds of the recognisable ingredients are coarse shell fragments, chiefly of the same irregular and ragged type, and large pieces of Bryozoa. There are two or three Textularians, but the few Foraminifera which occur are chiefly Rotaline forms; there are no Globigerinse. Mineral grains are abundant and coarse ; they include quartz and felspars, but mica was not detected. A greenish material allied to glauconite is present ; it has formed within the hollows of shell fragments and foraminiferal cells, but only partially filling them. The matrix of this specimen is coarsely granular calcite. The next four specimens, G 17, 18, 19, and 20, consist entirely of fragments of Bryozoa, and in their general characters bear the closest re- semblance to the Bryozoan limestone of the Upper Senonian of Denmark. The last specimen, which I believe to be a chalk, consists almost entirely of Inoceramus prisms and fragments of shell showing prismatic structure set in a calcareous paste. The prisms are, however, those of the Upper Chalk, long and narrow, retaining their width for about two-thirds of their length, then tapering so irregularly as in some cases to give the appearance of constriction to a blunt point. In their general contour they are less sharply angular than those of the Lower and Middle Chalk. In the section are one or two Globige rinse, one well-marked Rotaline form, and a single- celled Foraminifer. Of this series G I to G 12 (omitting G 6) are chalks differing entirely from the Belhelvie series. They are all very pure chalks ; in one (G 3) analysed 99'2 per cent, was soluble in the acid. The presence of ‘‘ spheres ” and the short broad Inoceramus prisms, together with the larger fragments showing the prismatic structure, the striking similarity of G 3 to nodules of the Melbourn Rock, and of G 12 to the structure of the chalk at the base of the zone of R. Guvieri of the south of England, suggests that the whole of them, though differing slightly from each other, may belong to the Middle Chalk. The presence, in three out of four analyses, of vegetable matter identical with that found in many of the Belhelvie boulders may be taken as evidence of the continuity of the deposit, even 284 Proceedings of the Royal Society of Edinburgh. [Sess. though a different horizon or area of sedimentation is suggested by the structure. G 13 is unlike any other specimen examined. Its structure is not unlike Chalk Rock without glauconite. G 2, 6, 14, 15, 16, 21. — In these specimens one seems again able to trace a successive series of events in the progress of sedimentation. Most of the specimens are small, and there was insufficient material left for analysis after cutting a section. In G 6 and 14 the chalk is of a kind previously unknown to me. From optical observation I think they are pure chalks. A peculiar character is given them by the large size and thickness of the shell of the “ spheres ” and foraminiferal cells, and the few ragged in- determinable shell fragments sparingly scattered through the rock. There are no /'Tiocemmus prisms. In G 2 and 15 the large “spheres” and cells are less numerous, but the same kind of shell fragments increase in quantity ; amongst them are small pieces of Bryozoa. The inequality in the distribution of these fragments suggests current action. In G 16 the same kind of shell fragments are abundant, and a few particles of Bryozoa occur. Globigerinse and Textularise with other Foraminif era are present; some of the tests are large bold forms. Sponge spicules are there also, but their siliceous walls are replaced by calcite. Though analysis shows that no large amount of terrigenous material is present, sand grains can be seen scattered through the deposit, and in the residue were found fragments of vegetable matter identical in structure with that of the Belhelvie boulders. More than two-thirds of the whole rock of G 21 consists of coarse shell fragments of the same ragged indeterminable type ; quite large fragments of Bryozoa are included with them. The Foraminif era, which are numerous, are Rotalian and other forms ; but there are no Globigerinse or Textularise. Mineral grains are large and abundant, quartz and a felspar are certainly present, but no mica can be detected. The impression created by the study of the last six specimens is that they represent a gradual passage from the chalk with large spheres to that containing many shell fragments and mineral grains. G 17, 18, 19, 20 are limestone consisting entirely of the fragments of Bryozoa. They are identical in structure with the Bryozoa limestone in Denmark. Evidence that rocks of Cretaceous age once existed in the north-east of Scotland is being slowly gathered. Mr Tait * has discovered fossils with a Neocomian facies in concretionary masses embedded in sand at Leavad. * “On the Occurrence of Cretaceous Fossils in Caithness,” Proc. Edin. Geol. Soc., vol. ix, part 4, 1909, p. 318. (See footnote, p. 264 of this paper. — J. H.) 285 1914-15.] Chalk Boulders from Aberdeen, etc. The fine-grained sandstone, or gaize, of Moorseat contains fossils which are referred by Mr Jukes-Browne ^ to a ‘'Lower Cretaceous rock, but high in that series, corresponding approximately to the Aptien stage in France, and to the Lower Greensand or Vectian in the Isle of Wight.” Though in neither case have these rocks been proved to be in situ, their occurrence is evidence that members of the Lower Cretaceous series have at one time covered part of the north-east of Scotland. There is yet another source which affords evidence of the occurrence of Cretaceous rocks in Scotland, viz. the flints which are scattered broad- cast on the surface of a large area in Aberdeenshire and the neighbour- ing counties. Dr Gibb kindly sent me a series of these collected in the neighbourhood of Cruden, all of which contained casts of Cretaceous fossils. These have been examined by Mr Jukes-Browne, who sends me the list appended to this paper. Most of them are Upper Chalk forms, but the fact that Inoceramus mytiloides occurs amongst them strengthens the argument below that Middle Chalk may be represented. Thirteen thin sections were cut from these flints to see if any comparison could be made of the chalk in which they were formed and that of the Belhelvie boulders. Examination showed that all were pseudomorphs of calcareous oozes in which varying proportions of Foraminifera, spheres, and shell fragments were the chief ingredients. Though all contained sponge spicules, they were not exceptionally numerous, and there was no evidence that the chalk contained colloid silica in globular form ; it may therefore be inferred that none of the flints originated in a sponge bed. No mineral grains were detected in any of the sections, nor were any Kadiolaria seen. The boulders from Belhelvie may, I think, be taken as evidence of the upward continuation of the Upper Cretaceous series in the north-east of Scotland. Although no fossils have been found in them, the study of the micro- organisms as well as the larger particles of calcareous debris which they contain leaves no doubt that, wdth exception of the two first, they are fragments of the uppermost member of the Cretaceous series, viz. the Chalk. Taken collectively, they show a gradual passage from what is practically a Greensand, consisting entirely of terrigenous material and glauconite, to a pure calcareous ooze. In the twenty-two examined, no two are alike either when viewed as thin sections, or when they are chemically analysed, or when the pro- portional numbers of the various component organisms are compared ; consequently they must represent a very considerable thickness of chalk. * Geological Magazine, Dec. 4, vol. v, 1898, p. 32. 286 Proceedings of the Royal Society of Edinburgh. [Sess. There is nothing in the structure or contents of the glauconite boulder of Belhelvie (A 9) which suggests its connection with the “gaize” of Moorseat, but there is no doubt that it is linked with and must have formed part of the strata from which the other boulders were derived. From the entire absence of calcareous matter, I conclude that it is not a fragment of the glauconite base of the true chalk, but a passage bed, similar in character and position to the glauconite base of the chalk of the west of Scotland (base of bed II of Professor Judd) or of Ireland. In view of the evidence pointing to the possibility that members of the Lower Cretaceous rocks occurred in the north-east of Scotland, it seems possible that it may represent the Upper Greensand or Chloritic Marl. Too much weight must not, however, be given to the lithological character of the deposit without the support of fossils ; the bed may be the homotaxical equivalent of chalk at a higher horizon : in any case it represents an early stage of Cretaceous submergence in the north. I saw no fragments of sandstone associated with the boulders at Belhelvie which might be referred to the estuarine deposits of the west, and therefore I infer that these beds did not occur in the locality from which these boulders were derived. But B I may represent an estuarine mud laid down at a distance from land, and the sponge beds and those containing much terrigenous material might be expected to follow as the natural sequence of events. Though one cannot say at present with what horizon in the English series the beds containing spongarian remains synchronise, they probably held a low stratigraphical position in the Scottish series. My reasons for thinking so are based on the remarks made by Dr Fraser Hume* on the relation of spongarian bands to the adjacent and subjacent strata in the Cretaceous series of Ireland. Dr Hume says, “ Such [spongarian] bands in many cases immediately overlie or are directly connected with beds dis- playing evidence of the commencement of depression, or partial elevation of deep-water beds accompanied by current action.” In support of this he cites the occurrence of sponges in the Plocoscyphia meandrina layer at the base of the Chalk Marl in the South of England, and the Chalk Rock of Devon, Eastbourne, and the Midlands as an instance of the re- appearance of spicules on the elevation of the sea-floor. “ In Antrim the abundance of these glauconite casts of spicules is noticeable as long as the limestones contain small fragments of quartz and other detrital minerals, but the sponges attain their maximum development (forming definite bands) at the point where detrital minerals become rare, and pure * “The Cretaceous Strata of County Antrim,” Q.J.G.S.^ vol. liii, 1897, p. 602. 1914-15.] Chalk Boulders from Aberdeen, etc. 287 white limestone is commencing to be formed.” He believes “the most favourable locality for the formation of the sponge bed appears to be that one where currents are carrying only the very finest particles in sus- pension, the sediment on the ocean-fioor being almost purely calcareous.” In the case of these Scottish chalks we are dealing with submergence : the necessary conditions of sedimentation seem to have been fulfilled and sponge beds have resulted. They may, however, be representatives of the Lower Chalk, a view which finds support in the occurrence of an Holaster allied to Holaster loevis amongst the flint casts picked up at Cruden. Whether the Middle Chalk is represented and whether “ spheres ” have any value from a stratigraphical point of view is an interesting question. A 1, B 4, and B 10 very largely consist of these bodies, and in A 1 they are accompanied by Inoceramus fragments of similar character to those of the lower part of the Middle Chalk. In the South of England they are especially abundant at the base of the Middle Chalk, and this feature is persistent from Devon to Yorkshire. They cease to form an important part of the deposit in the Terebratulina zone, but come again with the Chalk Rock and occur commonly as high as the zone of M. cor- testudinarium. In Dorsetshire and Devonshire they are abundant in that zone. Above this, occurring sporadically, they cease to form an important integral part of the chalk, though with cells they continue to occur. It is possible that the three boulders above mentioned may be Middle Chalk or not higher than the zone of M. cor-testudinarium. The remaining boulders probably belong to the Upper Chalk ; two or three will compare in general character with the chalk represented in the flints. Desiring to compare the structure of the Belhelvie boulders with the Cretaceous rocks found in the west of Scotland, five thin sections and a hand specimen were courteously sent me by Professor W. W. Watts, at the kind request of Professor Judd, from the Royal College of Science, South Kensington ; and my friend Mr Jukes-Browne was able to send me a hand specimen and slides from the glauconite base and the siliceous chalk from Eigg, which had been kindly sent him by Mr Clough, as well as several slides of that found in Skye at Scalpay and Strollamus. The careful study of these much-altered chalks throws, unfortunately, but little light on those occurring in the north-east of Scotland ; this I very much regret, but in the absence of fossil evidence it would be mere speculation to attempt to correlate the siliceous chalk of the west with the boulders found at Belhelvie and off the northern coast of Aberdeenshire. Believing it possible that an examination of the Cretaceous rocks of 288 Proceedings of the Koyal Society of Edinburgh. [Sess. Denmark and Sweden might afford information, I communicated with Professor N. V. Ussing of Copenhagen, and with Professor Holm and Dr E. Erdmann of Stockholm. These gentlemen most courteously sent me specimens from the principal horizons of the chalk in each country, and I desire to express my hearty thanks to them. Dr Smith Woodward, Mr Henry Woods, and Mr Jukes-Browne were also kind enough to send me specimens of Danish Chalk. But none of these will compare with the chalk of Belhelvie. They are all pure chalks laid down under conditions of sedimentation and of life dissimilar to those in the area in which the English Chalk was deposited. Nearly all are characterised by fragments of debris of Bryozoa, by the comparative scarcity of Foraminifera, and by the absence of shell fragments derived from Inoceramus. The chalk of Rtigen and the Upper Senonian of the Isle of Moen approaches most closely in general character to that of England. Thoiigh in both large fragments of Bryozoa occur, they contain also more Foramini- fera, and cells identical with those of A 5 and 6 are abundant. These two boulders are the purest chalks of the Belhelvie series and are probably the highest. That their chief ingredient should be cells similar to those occurring in the Upper Senonian of Riigen and Moen leads one to think that they may be of that horizon. Many of the Belhelvie boulders are ice-scratched, and it may be urged that they have travelled far. But in the brown, tough, unctuous clay in which they occur they are associated with pebbles of other rocks identical with or similar to the rocks of the district, and this, coupled with the fact that the whole series have an intimate connection with each other, makes it probable that they have not been moved a great distance. They could not be English Chalk, for they differ from it in important particulars : (1) in the quality of the arenaceous grains : felspars are more abundant, and the heavy minerals, zircon, rutile, and tourmaline, are less common and more worn ; (2) in the presence of free sponge spicules which yet retain the silica of their walls, though in altered condition ; (3) in the abundance of Radiolaria. Nor does chalk of a similar kind occur in English boulder clays. Mr C. Thompson of Hull was kind enough at my request to collect some thirty- five chalk boulders from the boulder clay of the Lincolnshire and Yorkshire coast ; these I have examined as well as chalk boulders from the clays of my own locality. But I have met with none that resemble either the Belhelvie boulders or the chalk of Sweden or Denmark. Nor can the Scottish boulders be compared with the white chalk of 289 1914-15.] Chalk Boulders from Aberdeen, etc. Antrim and Belfast, for specimens of which I am indebted to Mr C. Tomlinson and Miss Andrews, the President and Secretary of the Belfast Naturalists’ Field Club. The aspect of this rock when viewed as a thin section shows that the sediment accumulated under conditions peculiar to the locality, and not in complete accordance with the chalk of either English or Scottish areas. Mineral grains are here rare; spicules only occur as glauconite casts (?) of the axial canals.^ Ehrenberg, however, seems to have found Radiolaria in it. Whether the boulders have been pushed up by ice from an outcrop beneath the waters of the North Sea, or whether they have been derived from one occurring on the land to the westward, are questions difficult to answer. The general dip of the Mesozoic strata on the east of Sutherland is to the east, and if the land was at a higher elevation than it is at present it is possible that Cretaceous rocks might be exposed. Now that attention has been drawn to the occurrence of chalk boulders at the bottom of the neighbouring sea, further investigation may give us information in this direction. It is also not improbable that beneath the glacial clays which cover so large an area there may remain some fragments of the Cretaceous rocks which sooner or later may be brought to the light of day and help us to determine the extension of the series to the westward. From whatever locality the boulders of Belhelvie were derived, they show that the Cretaceous sea must have extended far to the northward and that in this northern area the deposit assumed characters which distinguish it from the chalk of the south. These characters are probably due partly to geographical position and partly to the physical conditions affecting the sedimentation. The prevalence of felspars and the scarcity of the heavy minerals, as well as the peculiar character of some of the finer material, show that the terrigenous material was derived from a land differently constituted from that which supplied the sand and mud found in the chalk of the south. The absence or com- parative scarcity of certain genera of Foraminifera, such as the Bulimines, Gaudryinas, Tritaxias, and several species of Textularians common in the south, and the incoming of new species not before recorded in the chalk indicate that the change in the character of Microzoa, already fore- shadowed in the investigation of the chalk north of the Wash is continued into this northern area.f * W. F. Hume, “The Cretaceous Strata of County Antrim,” Q.J.G.S., vol. liii, 1897, p. 584. t “The Cretaceous Rocks of Britain,” Memoir of the Geological Survey^ vol. ii, 1903, pp. 286, 309. VOL. XXXV. 19 290 Proceedings of the Royal Society of Edinburgh. [Sess. The presence of well-preserved siliceous organisms, the Radiolaria and sponge spicules, is another distinguishing feature of this chalk. The former probably occurred also in the chalk of the south, and have been found by myself in the meal of flints as low as the zone of R. Cuvieri, and more rarely in shadowy outlines in the chalk itself ; but in some of the Belhelvie boulders they occur in abundance, the delicate network of their tests being often beautifully preserved. It is not improbable that a junction between the eastern and western seas occurred in the early days of the Cretaceous submergence. Mr Jukes-Browne ^ has pointed out that the “height attained by the base of the Greensand in Morvern shows that the Cretaceous sea must have covered considerable areas in Western Scotland,” and, as the lowland district was gradually submerged, a strait would be formed between the Highlands and southern uplands. If that was so, the straits would probably be traversed by currents and the position of the Belhelvie chalks may have been near the eastern entrance and the receiving ground for terrigenous material and vegetable debris. Though one cannot say much with regard to the fragments of chalk gathered from the North Sea, the evidence they give is suggestive. Those found off the north-east coast of Aberdeenshire show distinctly a con- tinuance of the Belhelvie facies, and this with the fact that chalk boulders are washed up along the coast north of Aberdeen lends force to the hypothesis that there may be an outcrop of chalk covered by the waters of the North Sea. But a large proportion of these recovered further north in the neigh- bourhood of the Shetlands and in the Faroe Channel belong to quite another category ; they are pure chalks and must have been laid down in clear water away from the influence of mud-bearing currents. Though two of these contain Radiolaria, these are preserved only in outline by coarser crystals of calcite in a manner similar to those occurring in the chalk of the south. The great similarity in general structure of the fragments G 1, 3, 5, 7, 8, 9, 12 to that of the Middle Chalk of England might suggest derivation from the southward, yet the occurrence of the same vegetable material, which I have never met with in the English Chalk, seems to form a link with the chalk of Belhelvie. G 2, 6, 14, 15, 16, 21 are chalks differently constituted from any I have previously examined. The large size of the spheres and cells, together with the peculiar character of the shell fragments, indicates that they * Building of the British Isles, 3rd ed., 1911, p. 284. 291 1914-15.] Chalk Boulders from Aberdeen, etc. were laid down under conditions not at present recognised in any chalk of the British Islands. The fragments of shell are probably derived from Bryozoa, for pieces which can certainly be distinguished as that organism increase at the same time. Like other series which have been described in these pages, they seem to present a sequence, a sequence in which shelly fragments increase and terrigenous matter becomes gradually intermixed with the deposit. The sequence seems continued in a limestone consisting almost entirely of shell fragments, pieces of Bryozoa and Foraminifera (G 21). The Foraminifera are, however, no longer Globigerinse and Textu- larians, but of forms essentially of shallower water type, and there is evidence of much terrigenous material in the shape of large grains. Notwithstanding the dissimilarity in the nature of the deposit, three of these specimens contain the same vegetable material as those of Belhelvie. That amongst these fragments there should occur pieces of chalk consisting entirely of Bryozoan remains seems a fitting end to the sequence. It would be extremely interesting to know if a series of specimens taken at close intervals immediately below the chalk with Bryozoa in Denmark would show anything like the passage above described. If these fragments represent a succession, one could infer from the gradual increase of terrigeneous matter and of Bryozoan fragments a gradual shallowing of the water, and indications of the gradual uplift of the land at the close of the Cretaceous epoch. Linked as they are to the Belhelvie series by the occurrence of the same kind of vegetable remains, a wide door is opened for speculation as to whether the chalk of Scotland may not at one time have continued upwards and have included higher members of the Cretaceous series than have yet been found in England. List of Fossils contained in the Flints from Aberdeenshire. Belemnitella mucronata, Schloth. Inoceramus Giovieri, Sow. Lima cretacea Woods. Pecten cretosus, Defr. „ sexcostata, Woods. Septifer lineatus, Sow. Spondyhbs latus ?, Sow. „ spinosus, Sow. (young). Rliynchonella plicatilis, Sow. „ Reedensis, Eth.). Terehratula carnea, Sow. Scalpellum maximum, Sow. Gidaris sceptrifera, Mant. Gonulus alhogalerus, Leske. Holaster Icevis ? (de Luc). Ecliinocorys scutatus, Leske. Parasmilia centralis, Mant. Goscinopora infundibuliformis, Goldf. Ventriculites deeurrens, T. Smith. „ impressus, T. Smith. „ radiatus, Mant. 292 Proceedings of the Royal Society of Edinburgh. [Sess. The flints were sent to Mr Jukes-Browne, who kindly examined them, and some were eventually sent to Dr Kitchin. They are, as a whole, Upper Chalk forms, with the exception of the Holaster. Of this Dr Kitchin writes — it does not seem to agree with any Holaster planus, — “ The base is too flat and its boundary with the sides too abruptly deflned ; there are also other points of difference — for instance, the depth of the sulcus and the well- defined character of the carinse. I am not inclined to name it definitely.’" Mr Jukes-Browne came to the conclusion that it was probably a well-marked variety of H. Icevis, if not a new species. It must be remembered that the specimen in question is a cast in flint. Thirteen sections were cut from these flints with a view of ascertaining if a comparison could be made between them and any of the Belhelvie specimens. All the sections appeared to be pseudomorphs of the chalk within which they were formed, in some cases showing distinctly the forms of the micro-organisms contained in the rock ; in others such details are less apparent. As a whole they offer little evidence for comparison. In one, however (spine of Gidaris sceptrifera), spheres are well marked and abundant, and the original deposit may perhaps be compared with A 1, B 4, or BIO. The flint with B. mucronata also contains many spheres : these are of large size and suggest comparison with G 6 and 14, specimens found by the Goldseeker north-west of the Shetlands, rather than with any Belhelvie boulder. With two exceptions sponge spicules are not abundant in any of them, though traces occur in all. In one, however (with Spondylus latus), many thin thread-like spicules occur, resembling those of B 9, while the flint itself seems to represent a somewhat similar chalk. In a section cut from one of the Ventriculites — not, however, intersecting the fossil — spicules are more in evidence, two or three large Tetractinellid trisenes are well pre- served, and there are many rod-like lengths. Many of those are only just discernible ; in one part of the section short rows of minute opaque globules seem to indicate the position of their spicular canals. The deposit was probably rich in silica at this point, for in other parts of the section the silica is not in the micro-crystalline condition of ordinary flint, but there is also an area in which it shows the fibrous radiating structure of chalcedony. Calcareous ooze showing Globigerina now silicified has interpenetrated the more siliceous parts. Foraminifera. The following is a list of the Foraminifera found in the boulders of chalk from Belhelvie. I am indebted to Mr A. Earland for their identification. 1914-15.1 Chalk Boulders from Aberdeen, etc. 293 A 2. A3. A 7. A 8. B3. B 4. B5. B9. Psammophaera fusca, Schulze ..... ! X X Hyperammina ramosa, Brady ..... X Reophax guttifera, Brady ...... X ,, scorpiuTus, Montf. ...... X Haplophragmiam glohigeriniforme (Parker and Jones) . X ,, latidorsatum (Bornemann) X Ammodiscus incertus {ddOvb.) ..... X X X X ,, gordialis, Jones and Parker ? X Trochammina ? Tingens,P>r'a.d.j ..... X ,, trullissata, Brady ..... X Thurammina papillata, Brady ..... X Textularia gramen, d’Orb. ...... X ,, agglutinans, d’Orb. ..... X X ,, glohulosa, Ehren. ..... X X ,, minuta, Berth. ...... X ,, conica, d’Orb. ...... X Verneuilina pygmaea ..... X ,, triquetra {M-Viewst.) ..... X X Tritaxia pyramidata, Reuss ..... X Gaudryina suhrotunclata, Schw. ..... X ,, rugosa, d’Orb. ...... X ,, filiformis, Berth. ..... X Biiliinina ohtusa, d’Orb. ...... X X , , ? huchiana, d’Orb. ..... ,, Presli, Reuss ...... X Bolivina punctata, d’Orb. ...... Pleurostomella alterncms, Schw. ..... X ? ,, subnodosa, Reuss ..... X : Lagena glohosa (Montagu) ...... X ,, orbignyana {Segnenzst.) ..... X X ,, (Walker and Jacob) .... X ,, .? Zcews (Montagu) ...... ? ,, ? quadrata Marginulina glabra, d’Orb. ..... X ,, incequalis, Reuss ..... X Flabellina rugosa, d’Orb. ...... X Nodosaria soluta, Reuss ...... X ,5 communis, d’Orb. ..... X Cristellaria rotulata, Lamarck X X X X ,, (Fichtel and Moll) X X ,, cultrata {Jsionti.) ..... X Polymorphina gibba, d’Orb. ..... X ,, communis, d’Orb. ..... X X ,, lactea (Walker and Jacob) X X ,, comprcssa, d’Orb. ..... X Globigerina cretacea, d’Orb. ...... X X X X X X ,, bulloidcs, d’Orb. ..... X ,, cequilatcralis, Brady ..... X Anomalina ammonoides (Reuss) ..... X ,, grrossemgfosa (Giimbel) .... X X X ,, ? complanata, Reuss ..... Truncatulina pygmca, Hantken ..... X X ,, (Walker and Jacob) . X , culter^?. and J.) ..... ,, proccincta (Karr.) ..... X ,, touellcrstorji (Schw.) .... X Pulmnulina truncatulinoides (d’Orb.) .... X X Rotalia exsculpta, Reuss ...... X X ,, Soldanii, d’Orb. . . . . ’ . X X X X Nonionina depressula (Walker and Jacob) X ,, pompilioides {Yichtdi Moll) . I X Of the forms specifically identified in the above list, fifteen species have not been before recorded as occurring in the chalk. On the authority 294 Proceedings of the Poyal Society of Edinburgh. [Sess. of Dr Brady ^ four of these have, however, been found in still older formations : viz. Psammophcera fusca, Hyperammina ramosa, Thuram- mina papillata occur in the Jurassic rocks of Switzerland, and Poly- morphina compressa in the Lias of England. Of the remaining forty-two species all but five occur in the Gault as well as in the Chalk, and all except six are living at the present day. Reophax guttifera is recorded by Dr Brady as an exceedingly rare species ; he describes the test as closely arenaceous : in the two specimens found in B 4 the test is built mainly of sponge spicules. Another species, which unfortunately cannot be identified, has used minute spicules felted together to form a smooth, nearly spherical test. Mr Earland tells me that Reophax guttifera is not uncommon in certain parts of the cold area of the Faroe Channel. He further remarks, “The Ammodisci are very large and fine, larger than any I have seen in the living state. They are like some specimens I have from Oceanic beds of Naparima, Trinidad.” The Lagena Orhignyana “is a typical deep-water specimen; such a wide delicate wing is never seen in those from shallow water.” With regard to Nonionina, Dr Brady f in a footnote refers to the memoir by Reuss on the classifica- tion of the Foraminifera. Reuss states the geological range of this genus as the Silurian formation (?), the Carboniferous limestone, and from the Chalk forwards. Dr Brady remarks that those from the Chalk were probably Pullenia which were included by D’Orbigny, and at that time by Reuss also in the genus Nonionina. At my request, Mr Earland re- examined these specimens and is quite satisfied that his determination is correct. The species recorded in the list have a deep-water facies. Trochammina trullissata, met with in twenty-five localities during the Challenger Expedi- tion, only five of which have depths less than 1500 fathoms. T. ringens, a rarer form, four times met with at depths not less than 1600 fathoms. Verneuilina g>ygnicea, met with in forty-two localities, fourteen of which were above 2000 fathoms, and only eight at less than 1000 fathoms. Pleurostomella subnodosa, nowhere less than 1375 fathoms. Truncatulina pygmea, nowhere less than 1450 fathoms. Rotalia Soldanii, out of sixty localities, six only have a depth of 300 fathoms, thirty-nine above 1000 fathoms, and twelve over 2000 fathoms. Of Nonionina pompilioides Dr Brady remarks, “It is an exclusively deep-water Foraminifer; it occurs in all oceans at depths varying from 1000 to 2750 fathoms.” Truncatulina wuellerstorfi, “ a common constituent of deep-water ooze.” Seven other * “ Challenger ” Reports, vol. ix. t Ihid., vol. ix, p. 725. 295 1914-15.] Chalk Boulders from Aberdeen, etc. species recorded have not been found at less depth than 390 fathoms, and nearly all occur in very deep as well as shallow water. Yet amongst these are Textularia conica, “ living in shallow water amongst the coral reefs of the Tropics,” and Truncatulina 'proecincta, another coral reef species, though it has been found in 225 fathoms. Of Nonionina depressula Dr Brady remarks, “ The home of this species is on bottoms of less than 50 fathoms.” The assemblasre as a whole is characteristic of the chalk north of the o Wash rather than that of southern England.^ Bulimina, Textularia^ Gaudryina, and Tritaxia, the most abundant forms of the south, are rare. The Textularians recorded are very small specimens. Globigerinse are abundant in many specimens of the Belhelvie chalk, and in some of the sections are exceptionally numerous. Ammodiscus incertus also occurs in many of the residues. I am indebted to Mr Herbert H. Thomas for the identification of the mineral grains. Mr Thomas remarks, “ All the quartz of these chalks appears to be primary and contains the usual inclusions of detrital quartz ; there is no evidence of secondary growths. The most striking feature of the residues seems to be the relatively high percentage of felspar and the paucity of some of the heavy minerals such as zircon, rutile, and tourmaline, which are usually common in sedimentary rocks. All the minerals mentioned above have been recorded by Dr Fraser Hume and others from the English Chalk, but Dr Hume states in the case of the * See “ The Cretaceous Rocks of Britain,” Memoir of the Geological Survey, vol. ii, 1903, pp, 286 and 309. 296 Proceedings of the Royal Society of Edinburgh. [Sess. felspars that those noted by him were always much decomposed. Those in the residues under consideration are remarkable for their freshness ; the twinning is clearly visible, and in this they resemble the felspars from the chalk of the north of France described by M. Levy. All the tourmaline occurs as stumpy prisms and is not acicular, as is much of the tourmaline found in other sedimentary rocks. The garnet shows no crystalline form. The hornblende is an actinolitic and not a basaltic variety, as previously described from chalk residues.” The scarcity of glauconite in the residues is remarkable especially in those which contain most terrigenous material. The explanation may be that these chalks were laid down in a considerable depth of water, a fact which the Foraminifera tend to confirm. Fragments of iron oxide, usually so common in the English chalk, are also rare. Minute spherules and cylindrical lengths of iron pyrites and marcasite occur in some profusion in B 5, and a few small spherules in A 5. No attempt was made to estimate the percentage of mineral grains in each residue, but they were more abundant in every specimen than in any English chalk above the zone of Amm. Varians. In size they equalled and sometimes exceeded those found in the most sandy of our chalk marls.* * Mr Hill’s collection lias been presented to the British Museum by Mrs Hill and Mr Arthur Hill. (Issued separately December 14, 1915.) 1914-15.] Structure of the Chalk in the West of Scotland. 297 XXV. — Notes on the Structure of the Chalk occurring in the West of Scotland. By the late William Hill, of Hitchin, F.G.S. Communicated hy Professor D’Arcy W. Thompson. (MS. received June 12, 1915. Bead June 28, 1915.) The general succession of the Cretaceous rocks discovered by Professor Judd on Morvern, along the shores of Loch Aline, Argyllshire, and in the Isle of Mull may be briefly summarised : — I. Sandstone and white marls with plant remains (High Cretaceous or Early Eocene) ... 20 ft. II. White indurated chalk with bands of flints, Belemnitella mucronata and fragments of Inoceramus, some beds of glauconite chalk at the base , . . 10 ft. III. White sandstones without fossils . . 30-100 ft. IV. Glauconite sands passing into dark green glauconite sands or calcareous sandstone, Pecten asper and Exogyra conica ..... 20-60 ft. The lowest bed of glauconite sands (IV), says Professor Judd, ‘‘ unques- tionably represents the Cenomanian or Upper Greensand, and in its mineral characters greatly resembles the equivalent strata in England and Ireland.” * The white sandstones (HI) are regarded as the equivalent of the Middle and Lower Chalk of England ; while the white siliceous chalk with flints, with a bed of nodular and glauconitic limestone at its base, followed by II, are regarded as representing the Upper Chalk zone of B. mucronata. *[* In the “ Geology of the Small Isles of Inverness-shire ” I rocks of Creta- ceous age are thus referred to : “ Bocks of Cretaceous age are represented in Eigg by some two feet of hard white calcareous sandstone . . . underlain by a thin deposit of glauconitic sandy mud of older date.” “ This thin remnant of whitish-calcareous sandstone, with chalky inclusions and siliceous patches and nodules, often of a dark-grey colour, rests upon Oxfordian strata. * “All Cenomanian” — A. J. Jukes-Browne, in litt. after reading the MS. of this paper. t “ Professor Judd, “ On the Secondary Books of Scotland,” vol. xxxiv, 1878, p. 729. f “Geology of the Small Isles of Inverness-shire,” Memoir of the Geol. Survey (Scotland, Sheet 60), 1908, p. 33. 298 Proceedings of the Koyal Society of Edinburgh. [Sess. The rock closely resembles beds of proved Upper Cretaceous age, similarly overlying Oxfordian shales in the south of Scalpay, and at Strollamus and Strathaird in Skye.” Desiring to compare the structure of the Belhelvie boulders with the Cretaceous rocks above mentioned, at the kind request of Professor Judd five thin sections and a hand specimen were courteously sent me by Professor Watts from the School of Science, South Kensington ; and my friend Mr Jukes-Browne was able to send me hand specimens and slides both from the glauconite base and siliceous rock from Eigg, which had been kindly sent by Mr Clough, and several slides of that found in Skye at Scalpay and Strollamus. The sections of the siliceous chalk discovered by Professor J udd have already been described by Professor Rupert Jones in an appendix to Professor Judd’s paper,^' but for purposes of comparison a little more detail may be given of those sent me. To save repetition it may be said that the ground mass of all these specimens is minutely crystalline silica. 0 3. — Siliceous Chalk, Beinn-y-Hattan. Described by Professor Rupert Jones as “ Inoceramus chalk.” This section contains a large number of Inoceramus prisms, the characters of which are fairly well preserved ; as a whole they are similar to those of the Upper Chalk. Though somewhat obscured in the now silicified material of the matrix, it is possible to trace the outlines of F oraminif era ; Glohigerina, Bulimina, Dentalina, and Planorhulina have been recognised by Professor Rupert Jones, but he does not mention sponge spicules which occur in many parts of the section. In my opinion casts of Radiolaria occur also, and I have noticed two well-preserved Xanthidia. It is impossible to estimate the relative proportions of the recognisable organisms of which this rock originally consisted. Shell fragments were the dominating ingredient, with Foraminifera and sponge spicules. There are patches of colloid silica in globular form. In the section from the specimen (O 3) sent me by Professor Watts, the general features are the same. Inoceramus prisms are exceedingly numerous, and there are many Foraminifera. Sponge spicules are also present, but globular colloid silica occurs in great quantity, partly as clear globules and partly opaque. As colloid silica in globular form will be frequently mentioned, it will be well to describe its appearance in the silicified chalks. * “Notes on the Foraminifera and other Organisms in the Chalk of the Hebrides,” Q.J.G.S., vol. xxxiv, 1878, p. 739. 1914-15.] Structure of the Chalk in the West of Scotland. 299 Silica in globular form has been described by Dr G. J. Hinde.* The globules vary much in size, the smallest being only *0014 in diameter. They are translucent by transmitted light and opalescent by reflected light. Evidence that colloid silica in globular form once existed in these chalks is in the multitude of minute bodies which occur through the section. A few are hollow, but most of them have become filled with minute crystals, the nature of which is undetermined. These infilling crystals not infrequently destroy the regular spherical contour, and many of the bodies referred to would hardly be taken to represent an original globule. In Professor Judd’s specimen (O 3) some of the globules of colloid silica occur in their normal glassy condition, and the gradual alterations to the opaque stage can be followed by the eye. 0 5. — Siliceous Chalk, Beinn-y-Hattan. This was originally quite a different deposit from that of 0 3. Globigerina and Textularia, often large bold specimens, with other forms easily distinguished, occur with some regularity all over the section. Many are casts in a now opaque material (? once glauconite). There are few shell fragments or spicules. I am in- clined to think that Radiolaria occur in this section also. R 4. — Gribun, Isle of Mull. The section is for the most part clear silica, but in one portion sponge spicules can be seen thickly packed. It is possible to make out a few Inoceramus prisms and Foraminifera. 0 4. — Beinn-y-Hattan. The clear siliceous matrix is in this section clouded in places with terrigenous streaks which may indicate terrigenous material. Though as a whole more obscured than in the first two sections, Foraminifera and spicules are well shown in places. Long thin prisms of Inoceramus similar to those in 0 3 are present. These forms seem to preserve their identity, whilst other organisms have become obliterated. Small quartz grains are scattered through this section. R 3. — Carsaig, Isle of Mull. The matrix clouded with streaks of fine opaque matter. Few organisms can be made out except small fragments of Inoceramus prisms and a few spicules. Part of some Rotaline form of Foraminifera has been infilled with the opaque matter and is well seen. Viewed with crossed nicols variations in the crystalline texture suggest that the rock was once crowded with organic remains. Large coarse sand grains occur in one part of the section. ' White Limestone, Carsaig, Mull (from Mr Jukes-Browne). This rock appears to have consisted of definite fragments, some of which may have been shell, though their structure is now quite obliterated. There are, * “ Beds on Sponge Remains in the Upper and Lower Greensand,” Phil. Trans. Roy. Soc., clxxvi, 1885 (1886), p>. 426 et seq. 300 Proceedings of the Royal Society of Edinburgh. [Sess. however, indications of sponge spicules. Numbers of small quartz grains are to be seen thickly scattered throughout the section, and the occurrence of opaque spots, blotches, or streaks seems to indicate that fine terrigenous matter occupied the interstices between the fragments. A large part of the finer material seems to have consisted of lath-shaped particles which have preserved this identity notwithstanding the alteration of the rock. Viewed as a whole, there is a curious resemblance in the section to the grey-green friable rock of Belhelvie, but there is no glauconite. These siliceous chalks everywhere overlie beds containing much detrital matter, whether it be the white sandstone or possibly in closer connection with the Greensand, as at Carsaig. As the period was one of submergence, it may be expected that the lower part of the siliceous chalk next above the sands would contain terrigenous matter, and that higher in the series the deposit would become gradually more calcareous. Though I have no accurate knowledge of the stratigraphical position occupied by the specimens from which the thin sections were obtained, yet when this series is reviewed together changes of structure due to different conditions of sedimentation are evident, and there seems to have been a rapid passage from a mud containing much terrigenous material to a comparatively pure calcareous ooze. Thus the white limestone of Carsaig (Mr Clough’s specimen) contains abundant evidence of terrigenous material in the quartz grains scattered throughout it in the lath-shaped particles in the finer part of the deposit. I cannot think that this was ever a chalk in the common acceptation of the term, but was mainly an inorganic deposit, though probably with a con- siderable admixture of calcareous material. In Professor Judd’s sections — O 4, Beinn-y-Hattan, and R 4, Gribun — quartz grains are scattered through the rock, fairly abundant in the former, less so in the latter. Though more obscure than in many examples, both the sections show traces of Foraminifera, shell fragments, and sponge spicules: in one part of the Gribun section spicules are exceptionally numerous. In O 3, Carsaig, and 0 4, Beinn-y-Hattan, which are described by Pro- fessor Rupert Jones as “ Glohigerina chalk,” sand grains are again present mixed with the shell fragments, Foraminifera, and spicules. Fine inorganic matter is not recognisable in these sections, unless a certain dirty streaky appearance is an indication of its presence. The remaining sections give us evidence of terrigenous material. O 2, Carsaig, and O 3*, Beinn-y-Hattan, are described by Professor Rupert Jones as “ Inoceramus chalk,” from the large number of Inoceramus prisms they contain. Professor Rupert Jones makes no mention of sponge 1914-15.] Structure of the Chalk in the West of Scotland. 301 spicules ; but they are present, and the rock must have been once permeated with colloid silica. O 5, Beinn-y-Hattan, seems to have been a purely foraminiferal ooze. There are a few spicules in it, but several species of Foraminifera are clearly, if faintly, outlined in the now siliceous matrix, while not a few are casts in an opaque mineral (? once glauconite). Glohigerina is the predominating form. Thus both at Beinn-y-Hattan and at Carsaig the evidence points to a passage from a deposit containing a proportion of terrigenous matter to a purer calcareous ooze. The whitish calcareous sandstone with chalky inclusions and siliceous patches and nodules of the Isle of Eigg. In the hand specimen it is seen that some of the nodules are bordered by lighter material, suggestive of the rind of flint ; others have no such border. They are distributed irregularly through the sandstone, are of rounded or sub-angular contour, and vary in size from about an inch in the longest diameter to small specks. The material surrounding the nodules is quartz sand, the grains being about I mm. in average size, but some are 5 or 6 mm. and more in greatest length. The material cementing the grains is largely chalcedonic; but calcareous matter is included, for there is a decided reaction with hydro- chloric acid. Some of the nodules give a slight reaction ; in others it is not perceptible. From the hand specimen I had two slices cut, and Mr Jukes-Browne sent me two others (T 4602, T 4603), belonging to the Geological Survey of England, and three small hand specimens were kindly sent me from the same source. T 4603. — This is a section through one of the dark nodules and the sandstone. The ground mass of the nodule is minutely crystalline chalcedony, organisms being vaguely indicated by coarser crystals. Though somewhat obscure, as a whole there is no difficulty in tracing the outline of Foraminifera and foraminiferal cells in all parts of the nodule; they include Glohigerina, Textularia, and two or three Rotaline forms. Inoceramus prisms are fairly common, and there is one fragment showing the prismatic structure of the shell. Sponge spicules are present, but not very numerous. There is evidence that colloid silica in globular form occurred in this nodule. T 4602. — Section through a nodule. The organisms in this section are rather more obscure than in the preceding, but Glohigerina outlined some- times by a brownish filtration occur with some regularity in all parts of it. There are but few Inoceramus prisms : they have merged in the 302 Proceedings of tlie Royal Society of Edinburgh. [Sess. crystalline matrix more than is usually the case. Sponge spicules are common ; portions of their spicular canal are sometimes coloured by the brown infiltration. The whole rock must have been permeated with colloid silica in minutely globular form. 3. — Section through nodule and sandstone from the hand specimen collected by Mr Clough. Inoceramus prisms are the chief ingredient of this rock, the matrix being packed with them. Foraminifera are common ; amongst them are Globigerina, two or three species of Textularia, and several Rotaline forms. Globigerinse do not predominate ; there are as many Textularians. Nearly all are large bold forms, well preserved and distinct in outline. Sponge spicules occur, but not in great numbers, and I am of opinion that more than one Radiolarian occurs in this section. The rock was at one time permeated with colloid silica. 4. — This section is practically a continuation of No. 3 : it is chiefly cut through the sandstone, but includes several specks which can be seen in the rock. These specks are clearly the silicifled fragments of two, if not three, calcareous oozes laid down under different conditions of sedimenta- tion ; though unlike each other, they agree in general structure with the three nodules described above. These fragments of silicifled chalk preserved in the sandstone of Eigg are very similar to those of Argyllshire. One nodule is certainly '‘Ino- ceramus chalk ” (0^ 3, Beinn-y-Hattan). Other nodules are altered siliceo- calcareous oozes, a mixture of Foraminifera, shell fragments, and spicules, often permeated with colloid silica in minutely globular form. The border-line between the nodules and the sandstone is, as a rule, sharply drawn ; but in T 4603 the matrix of the chalk has penetrated and infilled the interstices between the sand grains for some little distance beyond the nodule. From the above it would appear that the whitish calcareous sandstone of Eigg, though occupying a stratigraphical position which enables it to be considered as a representative of the Cretaceous series in the West of Scotland, is in reality a sandstone containing fragments of chalk now silicifled from more than one horizon. Cretaceous limestone from volcanic neck, from Ballymichael, 6 miles S.W. of Brodick Bay, Arran. The ground mass is minutely crystalline chalcedony, but it is full of calcareous particles. The rock contains many shell fragments; the larger ones are practically calcitic crystals showing the cleavage planes, their structure being obliterated. Though a few Ino- ceramus prisms are present, the greater part of these fragments do not suggest derivation from Inoceramus. Many are large angular pieces some- 1914-15.] Structure of the Chalk in the West of Scotland. 303 times with ragged outlines, and from this size they diminish to smaller particles of which the rock is full. Fragments of Bryozoa also occur. Foraminifera, though not abundant, are in some variety. Globigerina, Textularia (two species), several Rotaline forms, and a Nodosarian occur. Sponge spicules are common, their walls are replaced by calcite. Highest Cretaceous limestone, just beneath Eocene beds, Strollamus, Skye. This is a finely granular crystalline limestone in which the forms of all organisms are nearly lost. The angular prisms of Inoceramus can, however, still be traced, and there are a few fragments of Echinoid plates. Here and there the outline of single foraminiferal cells are just discernible. There are no sponge spicules, but in a second section there are traces of two or three. Chert in mudstone overlying Cretaceous limestone, Belach Ban, Scalpay (two specimens). In one of these sections the traces of Foraminifera are rare, but there are a few Inoceramus prisms. Spicules can be seen, though not commonly, but 1 am of opinion that Badiolaria occur. In the other (from the base of the mudstone), while in some parts organisms are obscure, other parts are obviously a pseudomorph of a calcareous ooze. Globigerina, Textularians, Rotaline forms, with cells and spheres are well marked. Some are casts in opaque material. There are but few traces of spicules. Little can be said of the highest Cretaceous limestone of Strollamus, Skye. It is now a finely granular calcite limestone in which are faint traces of Inoceramus prisms, foraminiferal cells, and fragments of Echinoid plates, there being no traces of siliceous organisms or terrigenous material. The section of Cretaceous limestone from a volcanic neck, Brodick Bay, Isle of Arran, seems also a pure chalk. The character of the shell fragments, the presence of Bryozoa, the fact that the walls of the spicules are replaced by calcite, together with the absence of any trace of silica in globular form, or terrigenous material, shows that it must have once been a purely calcareous ooze. Horse-shoe forms occur in this chalk. Both the specimens seem to me to be of a higher horizon than any of those previously described, and they suggest that there may have existed in the West of Scotland Cretaceous strata of greater thickness than any yet discovered. The two specimens of chert from the mudstone and the base of the mudstone at Scalpay yield no evidence of interest ; both doubtless belong to the Cretaceous series. I do not propose to discuss the changes which have taken place in the Cretaceous rocks of the West of Scotland, wrought probably by the heat 304 Proceedings of the Koyal Society of Edinburgh. [Sess. and pressure of the superincumbent basalt. Though the effect of this change has been to convert them either wholly or partially into crystalline silica, and in some of them to obliterate to a great extent the micro- organisms they contain, yet when these can be made out, usually in outline as in many flints, the shell fragments, Foraminifera, and sponge spicules preserve their natural form without sign of distortion. It will be seen from the evidence given in the preceding pages that there appears to be a passage from a terrigenous to a partly calcareous deposit, and in this passage there are stages marked by the abundance of Inoceramus prisms and sponge spicules, culminating in an ooze consisting of the debris of calcareous organisms and Foraminifera. The traces of sponge spicules and colloid silica in globular form in many of the sections of silicifled chalk from Argyllshire and Mull, and in the fragments contained in the white sandstone of Eigg, are evidence that spongarian remains occurred in abundance and that a portion of the strata at least may be regarded as sponge beds. I regret that I cannot say with absolute certainty that Radiolaria exist in these siliceous chalks. I am, however, convinced they are present, and when sufficient material has been examined I believe they will be ultimately identifled. If my reading of the succession is correct, the change from a terrigenous deposit to a calcareous ooze is rapid and possibly indicates current action which probably prevented the accumulation of sediment. The glauconite base of the siliceous chalk would support this theory, and indeed current action is not improbable when we reflect that the siliceous chalk succeeds sandstone believed to be of estuarine origin. In the absence of fossil evidence it would be mere speculation to attempt to correlate the siliceous chalk of the West of Scotland with those they most resemble at Belhelvie. It does not follow that because sponge beds and Inoceramus chalk are represented that they are necessarily on the same horizon ; they can only be regarded as similar phases of sedimentation which are likely to occur not far from the coast of a land undergoing gradual submergence. It is possible that the exposures of the Cretaceous strata in the West of Scotland do not give us the true succession — Professor Judd remarks, in referring to the chalk exposed behind Carsaig House, “ At two separate points I have detected masses of the altered chalk- and flint-beds squeezed out from beneath the mass of superincumbent basalt.” ^ * “The Secondary Rocks of Scotland,” Q.J.G.S., vol. xxxiv, 1878, p. 730. (Issued separately December 14, 1915.) 1914-15. J Obituary Notice. 305 OBITUARY NOTICE. Sir John Murray, K.C.B., LL.D., Ph.D., D.Sc., F.R.S., Knight of the Royal Prussian Order Pour le Merite, Grand Cross of the Royal Norwegian Order of St Olav. By J. Graham Kerr. (Read July 5, 1915.) John Murray was born on March 3, 1841, in the town of Coburg, Ontario, the second son of Robert Murray, accountant, an immigrant from Scotland, and his wife Elizabeth Macfarlane of Coney Hill, Stirlingshire. After spending his boyhood on the plains of Ontario, Murray came at the age of seventeen to relatives in Scotland to complete his education. It was at the period of this first transatlantic voyage that there occurred what were perhaps the first recognisable steps in the scientific career of the great oceanographer, for Murray has told us of the indelible impression produced upon his mind by the great salt rolling sea, so different from the fresh- water lakes which he had hitherto known, and of the fascination which he felt in watching the navigational duties of the officers of the ship as they picked their way across the trackless ocean. And he has told us again how the impressions received during the voyage were deepened when on the west coast of Scotland he watched the rhythmic rising and falling of the tide, like the movements of some great living thing. After some time spent at the Stirling High School,^ Murray proceeded to the University of Edinburgh, where, without working through the regular curriculum for any degree, he received invaluable scientific train- ing under Allman, Goodsir, Turner, Lyon-Playfair, and, above all, Tait, in whose laboratory he spent much time researching in association with a number of men who later became distinguished in very various spheres of activity. Murray’s researches were particularly directed towards thermal conductivity and thermo-electricity, and he was esj^ecially inter- ested in the construction of an electrical thermometer for use in deep-sea work. Apart from his more systematic training in laboratories, Murray gained experience of value for his future work by making a voyage to the * For delightful reminiscences by Murray of his school-days, see “ OM Boys” and dheir Stories of the High School of Stirlmq, collected and edited by J. Lascelles Graham. Stirling, 1900. VOL. XXXV. 20 306 Proceedings of the Royal Society of Edinburgh. [Sess. Arctic regions on board a whaler in 1868, on which occasion he not only collected large numbers of marine organisms, but made many observations in what we should now call oceanography. Murray’s great opportunity came in 1872 when he was appointed to the staff of the Challenger Expedition, that famous expedition, organised in this city, which will probably be for all time recognised as the most important in the history of oceanic exploration. Murray played a large part in the preliminary organising and fitting out as well as in the conduct of tlie expedition. During the four years of the actual voyage he specialised particularly in the collection and study of pelagic organisms and deep-sea deposits, but his greatest work in this connection and the great work’ of his life was after the return of the expedition. Owing to the failing health of Sir Wyville Thomson the main share in organising the working out of the enormous collections fell very soon to Murray, and after Thomson’s death in 1882 he became in name, as he already was in fact, responsible for this side of the work. For nineteen years Murray managed the most remarkable team of scientific workers which was probably ever brought into collaboration. Agassiz, Allman, Buchan, Buchanan, Bergh, Brooks, Carpenter, von Graff*, Gunther, Haddon, Haeckel, K Hertwig, Harmer, Herd man, Huxley, Hubrecht, Kolliker, Moseley, MTntosh, Pelseneer, W. K. Parker, Renard, Sars, Sollas, Schulze, Selenka, Sclater, Tait, Theel, Turner : all these, in addition to other and younger workers, contributed, and contributed of their best, to these wonderful fifty volumes which form not merely the foundation but a great part of the whole edifice of modern oceanography^ One of the most remarkable feats in Murray’s life was surely his management of this great body of workers, differing widely in nationality, in temperament, and in industry : in getting each one of them to carry out investigations of the most arduous kind extending in some cases over many years, and to get his results completed and put into form for publication. The extraordinary driving power which Murray possessed is shown by the carrying of this great work to a triumphant completion, and his ability as a leader of men is testified to by the address, expressive of esteem and friendship, presented to him by his collaborators on its completion. There were other difficulties in Murray’s path besides those naturally inherent to such a work. The Government had behaved with liberality unusual in a British Government in paying the expenses of the actual expedition ; but, in strict accordance with ciistom, difficulties were raised about the expenditure necessary for working out and publishing the results — in other words, about securing that the main expenditure should not have been so much money thrown away. The annual grant was with- 1914-15.] Obituary Notice. 307 drawn in 1889, and it was only after offering to finish the work of publish- ing at his own expense that Murray was able to get a further grant of £1600. As it was, Murray spent a large amount of his own money in completing the undertaking. The completion of the publication of the Challenger Reports did not mean that the great centre for oceanographical research which Murray had created in Edinburgh passed out of existence. Right down to the time of his death Murray’s laboratory, with its skilled staft’, remained open as a centre of active investigation where foreign or British workers were always made welcome, and every facility, including access to the unique collection of oceanic deposits, placed at their disposal. It must not be supposed that Murray’s work was confined to inspiring,, assisting, and organising the activities of other investigators, great and pre-eminent though this work was. He was all the while engaged in active and fruitful research himself, and the three volumes associated specially with his authorship — that on Deep-Sea Deposits, written jointly with Professor Renard, and those which summarise the general scientific results — are amongst the most valuable of the whole series. In these investigations Murray by no means confined himself to data obtained during the actual voyage of the Challenger: with the object of checking and amplifying these, he conducted a number of independent inquiries. In 1880 and 1882 he carried out with Tizard important explorations in the Government surveying ships Knight Errant and Triton. One of the most interesting results of these explorations was the solution of an oceano- graphical puzzle dating from the time of the cruise of the Lightning (1868), when the discovery was made that in the region of ocean com- mencing about 70 geographical miles N.N.W. of Cape Wrath and extend- ing about 85 miles in a north-westerly direction there existed a remarkable sharp line of demarcation between a warmer area (so far as the deeper waters were concerned) to the south-west and a colder area to the north- east. The solution of the puzzle turned out, as suspected by Tizard, to rest on the presence of a submarine ridge running in a north-west and south-east direction, reaching to between 300 and 200 fathoms of the surface, and forming an efficient barrier to the circulation of ocean water below this level. Murray organised an excellent little marine laboratory at Gran ton, and another at Millport. The latter was eventually handed over to a local committee, which later on developed into the Marine Biological Association of the West of Scotland. In connection with this local Scottish work the steam yacht Medusa was built and specially equipped, and on it Murray, 308 Proceedings of the Poyal Society of Edinburgh. [Sess. with the assistance of Mill, Cunningham, and other colleagues, carried out continuous investigations over a period of about eleven years. In this way an immense body of valuable observations was accumulated, some of which were made use of in working out the Challenger results, and published partly in the reports of the expedition, partly elsewhere. Amongst the residuum not immediately published there remained a mass of valuable data regarding the marine fauna of the west of Scotland, the working up of which had been undertaken only a few months before Murray’s death. These data when fully worked out will form a valuable foundation for future work, so it is greatly to be hoped that means will be found to have this done. Murray’s studies upon the mode of formation of coral islands, in which he emphasised the importance of submarine deposits — particularly of the calcareous skeletons of marine animals which are protected from solution by the bottom layer of water becoming saturated with calcium carbonate — in providing the foundations upon which the atoll-forming organisms can proceed to build ; his studies upon rainfall and drainage of continents in their relation to submarine deposits ; and again his studies upon the extent — present and past — of the Antarctic continent, can only be mentioned here, although these are alike of great value in themselves and of still greater value as sources of inspiration of subsequent research on the part of others. Apart from the Challenger Expedition, perhaps the greatest work of Murray’s life was the carrying out of the Murray-Pullar survey of the fresh-water lochs of Scotland, the result of which has been to place Scotland in the same premier position in limnology as it had been placed in as regards oceanography. Murray had endeavoured without success, although backed up by powerful representations from the Royal Societies of London and Edinburgh, to induce the Government to undertake a bathymetrical survey of the fresh-water lochs of Scotland; so in 1898 he commenced the work on his own responsibility, assisted by a young and enthusiastic colleague, Mr Fred Pullar. The survey met an untimely check on the lamentable death of the younger worker by accident in 1901, but was started again in the following year with funds provided by his father, Mr Laurence Pullar, and was prosecuted actively, with the help of a staff of able young assistants, during the following seven years. During that time systematic soundings, with supplementary physical and biological observations, were carried out on no less than 562 separate lochs. The results of the survey were published from time to time by the Royal Geographical Society, and appeared in collected form in 1910 in six large 1914-15.] Obituary Notice. 309 volumes, with numerous charts and other illustrations, forming a contribu- tion to limnology of which Scotland may well be proud, and at the same time a worthy memorial of the able young naturalist who was Murray’s colleague during the earlier stages of the work. The last of Murray’s major works was the Michael Sars expedition tO' the North Atlantic in 1910. This arose out of a visit to Copenhagen in 1909, when he urged upon the International Council for the Exploration of the Sea the desirability of carrying out systematic observations in the North Atlantic with a view to their bearings on the problems of the North Sea. Later on, Murray made a definite offer to pay the expenses of a four months’ expedition on condition that the Norwegian Government lent the Michael Sars and her scientific staff for the purpose. This offer was accepted, and the Michael Sars sailed from Plymouth on April 7, 1910, with Murray on board. The expedition made its way along the western edge of the continental slope to Gibraltar, where valuable studies were made of the great currents which traverse the strait, the ship being anchored in mid-channel by a steel cable, in water of two hundred fathoms. From Gibraltar the expedition worked southwards along the continental edge as far as the Canaries, thence to the Azores, then westwards to the Gulf Stream and northwards to Newfoundland, and finally back across the Atlantic towards Ireland. A call was made at the Clyde, a visit paid to the neighbourhood of Rockall, and finally the concluding observations of the expedition were made in the Faroe-Shetland channel. The Michael Sars had on board her full scientific staff under the leader- ship of Dr J. Hjort ; she was admirably equipped with the necessary scientific apparatus, and, as might have been expected, during the four months of the cruise an immense mass of valuable observations was accumu- lated, together with large collections of marine organisms. Murray gave £500 towards putting these into preliminary order, and now they are being worked up and the results published under the auspices of the Bergen Museum. Of the purely physical observations, mention may be made of the studies of the outflow of warm water of high salinity through the Strait of Gibraltar ; of the very considerable fall in temperature of large masses of the Atlantic water which was found to have taken place since the voyage of the Challenger thirty-seven years earlier ; of the numerous glaciated stones brought up from a depth of 1000 fathoms to the south- west of Ireland ; and of the corroboration of J. Y. Buchanan’s views as to the occurrence of tidal currents, strong enough to wash away the ooze, far out in the open ocean in regions of diminished depth of water : and again, in the realm of pure biology, the obtaining of a number of young, developing 3L0 Proceedings of the Royal Society of Edinburgh. [Sess. individuals of that wonderfully archaic siphonopod Spivula, and of numerous leptocephalus larvm of the common European eel in mid- Atlantic, south of the Azores — an important addition to the data available towards a solution of the problem of the life history of that elusive fish. Much of the most interesting and important work of the expedition bore upon the relations of organisms to physical environmental conditions. Thus, in relation to depth, the Michael Sars results point to the great poverty of life at the extreme depths and to its comparative richness at intermediate depths — in contradiction to commonly held views. Particularly important studies were made bearing on the relationships of pelagic animals to light. The Michael Sars naturalists did not fall into the common blunder of supposing that a deep-sea animal which looks red when drawn up to the surface does so in its native haunts, but fully realised that such animals at the depths in which they live, where no red rays penetrate, have simply a dark appearance like those of their fellows which actually are dark-coloured when seen by ordinary daylight. The upper limit of these dark-coloured and red organisms of deep water was found to vary in level at different latitudes in a manner corresponding to the different depths to which daylight penetrates, being deeper in low latitudes and at a less depth in higher latitudes. Careful measurements were made of the actual depths to which daylight penetrates by exposing sensitive photo- graphic plates submerged at different depths. Apart from the splendid additions to detailed knowledge which the Michael Sars Expedition has produced, a lesson of great general importance for the future of oceanography has been taught, viz. that oceanographical research of the highest class may be carried out even in the deepest and most extensive oceans by means of a vessel no larger than an ordinary o^ood steam trawler.^^ While Murray’s achievements in pure science — the Challenger Expedition, the Scottish Lake Survey, and the Michael Sars Expedition, and the researches centred round them — are what concern us more especially, these by no means exhausted his activities. Of Murray’s achievements outside the realm of pure science there is none of greater interest than that extraordinary by-product of his Challenger work by which he converted an almost unknown and uninhabited tropical island into a busy hive of industry and a valuable centre of commercial activity. The initial discovery was made during the routine examination of oceanic deposits, for amongst a certain series of samples Murray detected a * The Michael Sars measures 125 feet between perpendiculars, is of 226 tons burden, and has engines of 300 horse-power which give her a speed of 10 knots. 1914-15.] Obituary Notice. 311 fragment of phosphatised limestone which appeared to him clearly to be of terrigenous origin. Further inquiry showed that it had come from Christmas Island in the Indian Ocean, and Murray duly followed up the indication so provided that rich phosphatic deposits were to be looked for on that island. After a great deal of trouble, and the application of much pressure, the Government of tlie day was induced to hoist the British flag upon the hitherto derelict island, and thereafter a joint lease of the island was granted to Murray and the late Mr Ross of Cocos Keeling. A company was formed, the immensely valuable deposits of phosphate duly located, the tropical vegetation was opened up, railways, piers, waterworks constructed, and the island became a centre of activity with a population of about 1500 engaged in the main industry of quarrying and shipping phosphate, as well as in subsidiary industries such as the growing of rubber, cotton, hemp, bananas, etc. Naturally, the purely scientific in- vestigation of the island was not neglected. Murray himself made two exploring expeditions thither in 1900 and in 1908, and he also organised and financed two expeditions under the auspices of the British Museum. During these expeditions extensive collections were made by Dr. C. W. Andrews, and the main results of the first expedition were published as A Monograph of Christmas Island by the Trustees of the British Museum (1900). The special interest of this work lies, perhaps, not so much in the fact that it makes known a mass of valuable information about a tropical island of which, hitherto, very little had been known, as in the fact of its being a study of the fauna and flora of an island previously uninhabited by man, but which was about to undergo colonisation. It forms thus a foundation for subsequent investigations, which will be of the greatest interest, into the effects of the presence of man, and animals and plants introduced by him, upon the native fauna and flora. Incidentally Murray in his Christmas Island work has provided a remarkably impressive lesson in regard to the practical value of pure science. The Ruler of our Country — the “ Man in the Street ” — does not realise that all the great achievements in applied science are built upon a foundation of pure science. He does not know that the ships which bring him necessities and luxuries and wealth are enabled to pick their way across the ocean and complete their voyages with regularity through our knowledge of laws which we owe to the labours of pure mathematicians. He is not aware that the successful completion of such an engineering work as the Panama Canal was rendered possible by the results of investi- gations upon parasites of mosquitoes. He has heard the name of Kelvin, and associates it with numerous inventions of practical importance, but he 312 Proceedings of the Royal Society of Edinburgh. [Sessc. is unaware that their invention was rendered possible by a profound grasp of purely scientific principles. While in these days he dare no longer express other than respect for the practical results of science, he as a rule fails completely to appreciate the pure science which has made them possible. The worker at pure science he treats at the most with a good- natured toleration : most likely he looks on the expenses incurred in his investigations as so much money thrown away. Murray’s line of work on submarine deposits he would regard as a particularly good example of such waste of money. And yet these studies led to the discovery and development of the wealth of Christmas Island, and the small fraction of that wealth which went to the British Government, in the form of rents, royalties, and taxes, exceeded within fifteen years the entire cost of the Challenger Expedition and the publication of its results. Murray was an active supporter of various of our Scottish institutions. He acted for a time as scientific member of the Fishery Board. He was the enthusiastic secretary of the committee which got together funds for the erection of a highdevel observatory on Ben Nevis, and remained a director and convener of the Works Committee until the observatory was closed. He was President of the Scottish Natural History Society and of the Royal Scottish Geographical Society. In our own Society he served continuously for about twenty years on the Council, and for a prolonged period acted as one of the Secretaries and as Vice-President. He was one of those who objected most strongly to the eviction of the Society from its old quarters on the Mound. Murray’s achievements as a great man of science won full recognition both at home and abroad. He was created a Knight Commander of the Bath, a foreign Knight of the Prussian Order Pour le Merite, a Knight Grand Cross of the Royal Norwegian Order of St Olav : he was an honor- ary graduate of Edinburgh, Oxford, Harvard, Jena, Geneva, Christiania, Liverpool : he was an honorary member of most of the important scientific societies and academies of the world : and he was the recipient of numerous medals and other distinctions. The end came to his busy and fruitful life on 16th March 1914, when he was instantaneously killed, near Edinburgh, in a motor accident. In connection with this notice I have to record my indebtedness tO' Mr Laurence Pullar for clearing up certain points’ regarding which I was in doubt, and to Mr James Chumley — Murray’s long-time secretary and assistant — for providing the accompanying bibliography. 1914-15.] Obituary Notice. 313 APPENDIX. Publications of the late Sir John Murray. 1876. Preliminary Reports to Professor Wyville Thomson, F.R.S., Director of the Civilian Scientific Staff, on work done on board the Challenger : — (1) Preliminary Report on specimens of the sea-bottoms ob- tained in the soundings, dredgings, and trawlings of H.M.S. Challenger in the years 1873-75, between England and Valparaiso; (2) Preliminary Report on some surface organisms and their relation to ocean deposits ; (3) Preliminary Report on Vertebrates ; Proc. Roy. Soc., voL xxiv, pp. 471-542. 1876. On the distribution of volcanic debris over the floor of the ocean, its character, source, and some of the products of its dis- integration and decomposition : Proc. Roy. Soc. Edin., vol. ix, pp. 247-261. 1877. The cruise of the Challenger, — Two lectures delivered in the Hulme Town Hall, Manchester, December 11 and 18, 1877 : Manchester Science Lectures, 1877, pp. 105-139. 1880. On the structure and origin of coral reefs and islands : Proc. Roy. Soc. Edin., vol. x, pp. 505-518. 1885. Report on the specimens of bottom deposits collected by U.S.S. Blake, 1877 to 1880: Bidl. Mus. Comj^. Zool., vol. xii, pp. 37-61. 1885. The great ocean basins, — Lecture delivered at the Aberdeen meeting of the British Association, and published in Nature, vol. xxxii, pp. 581-584, 611-613. 1886. The physical and biological conditions of the seas and estuaries about North Britain, — Paper read before the Philosophical Society of Glasgow, March 31, 1886, and published in Proc. Phil. Soc. Glasgow, vol. xvii, pp. 306-333. 1886. The exploration of the Antarctic regions : Scot. Geog. Mag., vol. ii, pp. 527-543. 1886. Drainage areas of the continents and their relation to oceanic deposits: Scot. Geog. Mag., vol. ii, pp. 548-555, 1886. Chairman’s opening address to the Royal Society of Edin- burgh, December 6, 1886 : Proc. Roy. Soc. Edin., vol. xiv, pp. 1-20. 314 Proceedings of the Koyal Society of Edinburgh. [Sess. 1887. On the total annual rainfall on the land of the globe, and the relation of rainfall to the annual discharge of rivers, — Paper read before the Royal Society of Edinburgh, January 17, 1887, and published in Scot Geog. Mag., vol. iii, pp. 65-77. 1887, On some recent deep-sea observations in the Indian Ocean : Scot Geog. Mag., vol. iii, pp. 553-561. 1887. On the height of the land and the depth of the ocean, — Paper read before the Royal Society of Edinburgh, December 19, 1887, and published in Scot. Geog. Mag., vol. iv, pp. 1-41, 1888. 1888. Structure, origin, and distribution of coral reefs and islands, — Address to the Royal Institution of Great Britain, March 16, 1888 : Proc. Roy. Inst., vol. xii, pp. 251-262. 1888. On the effects of winds on the distribution of temperature in the sea- and fresh- water lochs of the west of Scotland : Scot. Geog. Mag., vol. iv, pp. 345-365. 1889. On marine deposits in the Indian, Southern, and Antarctic Oceans : Scot. Geog. Mag., vol. v, pp. 405-436. 1890. The Maltese Islands, with special reference to their geological structure : Scot. Geog. Mag., vol. vi, pp. 449-488. 1891. On the temperature of the salt- and fresh- water lochs of the west of Scotland, at different depths and seasons, during the years 1887 and 1888: Proc. Roy. Soc. Eclin.,.Yo\. xviii, pp. 139-228. 1893. The discovery of America by Columbus; the influences which led up to that great event, and its effect on the development of oceanographical knowledge: Scot. Geog. Mag., vol. ix, pp. 561-586. 1893. The renewal of Antarctic exploration, — Paper read before the Royal Geographical Society, November 27, 1893, and published in Geog. Jour., vol. iii, pp. 1-42, 1894 1894. Notes on an important geographical discovery in the Antarctic regions: Scot Geog. Mag., vol. x, pp. 195-199. 1894. The crust of the earth, — Paper read before the Royal Society of Edinburgh, May 21, 1894, and published in abstract in Scot. Geog. Mag., vol. x, pp. 378-379. 1895. A summary of the scientific results obtained at the sounding, dredging, and trawling stations of H.M.S. Challenger ; two volumes, 1627 pages, published by H.M. Government. 1895. The general conditions of existence and distribution of marine organisms : Com23tes-re7idiis cles Seances du 3”'® Gongres inter- national de Zoologie, Leyde, 1895, pp. 99-111. 1914-15.] Obituary Notice. 315 1896. On the deep- and shallow-water marine fauna of the Kerguelen region of the Great Southern Ocean : Trans. Roy. Soc. Edin., vol. xxxviii, pp. 343-500. 1896 Marine orofanisms and the conditions of their environment, — Address to the Royal Institution of Great Britain, February 28, 1896, and published in abstract in Proc. Roy. Inst., vol. xv, pp. 75-77. 1897. Some observations on the temperature of the water of the Scottish fresh-water lochs ; Scot. Geog. Mag., vol. xiii, pp. 1-21. 1897. Balfour Shoal: a submarine elevation in the Coral Sea: Scot. Geog. Mag., vol. xiii, pp. 120-134. 1897. On the distribution of the pelagic Foraminifera at the surface and on the floor of the ocean: Natural Science, vol. xi, pp. 17-27. 1898. The scientific advantages of an Antarctic expedition : Proc. Roy. Soc., vol. Ixii, pp. 424-451. 1898. The Antarctic: a plea for a British Antarctic expedition: Scot. Geog. Mag., vol. xiv, pp. 505-510. 1898. On the annual range of teinperature in the surface waters of the ocean, and its relation to other oceanographical phenomena, — Paper read before the Royal Geographical Society, February 28, 1898, and published in Geog. Jour., vol. xii, pp. 113-137. 1899. On the temperature of the floor of the ocean, and of the surface waters of the ocean: Geog. Jour., vol. xiv, pp. 34-51. 1899. Presidential Address to the Geographical Section of the British Association: ReiJort Brit. As.s., 1899 (Dover), pp. 789-802. 1900. On the deposits of the Black Sea: Scot. Geog. Mag., voJ. xvi, pp. 673- 702. 1901. The South Pole: Quarterly Review, Oct. 1901, pp. 451-473. 1902. Deep-sea deposits and their distribution in the Pacific Ocean, with notes on the samples collected by s.s. Britannia, 1901 : Geog. Jour., vol. xix, pp. 691-711. 1902. Remarks on the deep-sea deposits collected by the U.S.S. Albatross in the Tropical Pacific, 1899-1900 : Mem. Mus. Comp. ZooL, vol. xxvi, pp. 109-111. 1906. On the depth, temperature of the ocean waters, and marine deposits of the south-west Pacific Ocean : Queensland Geog. J our. (Brisbane), vol. xxi, pp. 71-134. 1908. The distribution of organisms in the hydrosphere as affected by varying chemical and physical conditions : Intern. Revue Hydrohiol. und Hydrogr., Bd. i, pp. 10-17. 316 Proceedings of the Royal Society of Edinburgh. [Sess. 1910. The deep sea: Scot. Geog. Mag., vol. xxvi, pp. 617-624. 1910. On the depth and marine deposits of the Indian Ocean, with descrip- tions of the deposit-samples collected by Mr J. Stanley Gardiner in 1905 : Trans. Linn. Soc. Ijond., 2nd ser., Zool., vol. xiii^ pp. 355-396. 1911. Exploring the ocean's floor: Harpers Monthly Mag., March 1911,, pp. 541-550. 1911. Alexander Agassiz: his life and scientific work: Bull. Mus. Comp. Zool., vol. liv, pp. 139-158. 1913. The ocean: a general account of the science of the sea: Home University Library, No. 78, London (Williams & Norgate). In Collaboration. • 1882. John Murray and T. H. Tizard, Exploration of the Faroe Channel during the summer of 1880, in H.M.’s hired ship Knight Errant: Proc. Roy. Soc. Edin., vol. xi, pp. 638-720. 1884. John Murray and A. Renard, On the microscopic characters of volcanic ashes and cosmic dust, and their distribution in deep-sea deposits; Proc. Roy. Soc. Edin., vol. xii, pp. 474-495. 1884. John Murray and A. Renard, On the nomenclature, origin, and dis- tribution of deep-sea deposits : Proc. Roy. Soc. Edin., vol. xii, pp. 495-529. 1885. John Murray, T. H. Tizard, H. N. Moseley, and J. Y. Buchanan, Narrative of the cruise of H.M.S. Challenger, with a general account of the scientific results of the expedition ; two volumes, 1154 pages, published by H.M. Government. 1889. John Murray and R. Irvine, On coral reefs and other carbonate of lime formations in modern seas : Proc. Roy. Soc. Edin., vol. xvii, pp. 79-109. 1891. John Murray and A. Renard, Report on deep-sea deposits based on specimens collected during the voyage of H.M.S. Challenger in the years 1872 to 1876; one volume, 546 pages, published by H.M. Government. 1891. John Murray and R. Irvine, On silica and the siliceous remains of organisms in modern seas : Proc. Roy. Soc. Edin., vol. xviii, pp. 229-250. 1893. John Murray and R. Irvine, On the cliemical changes which take place in the composition of the sea-water associated with Blue Muds on the floor of the ocean : Trans. Roy. Soc. Edin.,. vol. xxxvii, pp. 481-507. 1914-15.] Obituary Notice. 317 1894. John Murray and R. Irvine, On the manganese oxides and manganese nodules in marine deposits : Trans. Roy. Soc. Edin., vol. xxxvii, pp. 721-742. 1898. John Murray and R. E. Peake, On the survey by the s.s. Britannia of the cable route between Bermuda, Turk’s Islands, and Jamaica, with descriptions of the marine deposits brought home : Proc. Roy. Soc. Edin., vol. xxii, pp. 409-429. 1901. John Murray and E. Philippi, Die Grundproben der Valdivia Expedi- tion; Centralhlatt filr Mineralogie, 1901, pp. 525-527. 1901. John Murray and R. E. Peake, On the results of a deep-sea sounding expedition in the North Atlantic during the summer of 1899, with notes on the temperature observations and depths, and a description of the deep-sea deposits in this area : Roy. Geog. Soc. Supplementary Papers, 1901, pp. 1-44. 1900-1. John Murray and F. P. Pullar, A bathymetrical survey of the fresh- water lochs of Scotland, Parts I-III : Geog. Jour., yo\. xv, pp. 309-352; vol. xvii, pp. 273-295. 1903-8. John Murray and L. Pullar, Bathymetrical survey of the fresh- water lochs of Scotland, Parts IV-XIII : Geog. Jour., vols. xxiii- xxxi. 1910. John Murray and L. Pullar, Bathymetrical survey of the Scottish fresh-water lochs : report on the scientific results ; six volumes, Edinburgh {Challenger Office). 1904. John Murray and R. E. Peake, On recent contributions to our knowledge of the floor of the North Atlantic ocean : Extra Publication of the Roy. Geog. Soc., pp. 1-35. 1908. John Murray and E. Philippi, Die Grundproben der Deutschen Tiefsee- Expedition : “ Valdivia'' Reports, Bd. x. Lief. 4, 128 pages. 1909. John Murray and G. W. Lee, The depth and marine deposits of the Pacific: Mem. Mus. Comp. Zool., vol. xxxviii, pp. 1-169. 1912. John Murray and J. Hjort, Tlie depths of the ocean: a general account of the modern science of oceanography, based largely on the scientific researches of the Norwegian steamer Michael Sars in the North Atlantic; one volume, 840 pages (London: Macmillan). i ' . . .• V APPENDIX CONTENTS. PAGE LAWS OF THE SOCIETY . . . . . . .321 THE KEITH, MAKDOUG ALL-BRISBANE, NEILL, AND GUNNING VICTORIA JUBILEE PRIZES ........ 326 RESOLUTIONS OP COUNCIL IN REGARD TO THE MODE OF AWARDING PRIZES . 328 AAVARDS OF THE KEITH, MAKDOUGALL-BRISBANE, NEILL, AND GUNNING VICTORIA JUBILEE PRIZES . . . . . . 329 PROCEEDINGS OF THE STATUTORY GENERAL MEETING, OCTOBER 1914 . 334 PROCEEDINGS OF THE ORDINARY MEETINGS, SESSION 1914-1915 . . 335 PROCEEDINGS OF THE STATUTORY GENERAL MEETING, OCTOBER 1915 . 340 ACCOUNTS OF THE SOCIETY, SESSION 1914-1915 .... 342 THE COUNCIL OF THE SOCIETY AT JANUARY 1916 . . . . 348 ALPHABETICAL LIST OF THE ORDINARY FELLOWS OF THE SOCIETY AT JANUARY 1, 1916 . . . . . . . 349 LIST OF HONORARY FELLOWS OF THE SOCIETY AT JANUARY 1, 1916 . 366 LIST OF ORDINARY FELLOWS OF THE SOCIETY ‘ ELECTED DURING SESSION 1914-1915 ........ 368 ORDINARY FELLOWS DECEASED DURING SESSION 1914-1915 . . 368 FOREIGN HONORARY FELLOWS DECEASED ..... 368 BRITISH HONORARY FELLOW DECEASED . . . . . 368 LIST OF LIBRARY EXCHANGES . . . . . . 369 LIST OF PERIODICALS PURCHASED BY THE SOCIETY . . . 393 ADDITIONS TO LIBRARY DURING 1915, BY GIFT OR PURCHASE . . 397 INDEX ......... 399 LIST OF PAPERS PUBLISHED IN THE “TRANSACTIONS” DURING SESSION 1914-15 ........ 402 Laws of the Society. 321 LAWS OF THE SOCIETY, As revised October 25, 1915. [By the Charter of the Society (printed in the Transactions, vol. vi, p. 5), the Laws cannot be altered, except at a Meeting held one month after that at which the Motion for alteration shall have been proposed.] I. THE ROYAL SOCIETY OF EDINBURGH shall consist of Ordinary and Title. Honorary Fellows, ^ II- Every Ordinary Fellow, within three months after his election, shall pay Two The fees of Guineas as the fee of admission, and Three Guineas as his contribution for the Fef/oSesiding Session in which ne has been elected ; and annually at the commencement of every Scotland. Session, Three Guineas into the hands of the Treasurer. This annual contribution shall continue for ten years after his admission, and it shall be limited to Two Guineas for fifteen years thereafter.* Fellows may compound for these contributions on such terms as the Council may from time to time fix. 111. All Fellows who shall have paid Twenty-five years’ annual contribution shall he Payment to cease after exempted from further payment. 25 years. IV. The fees of admission of an Ordinary Non-Resident Fellow shall he <£26, 5s., Feesofjsron- payable on his admission ; and in case of any Non-Resident Fellow coming to reside ordinary at any time in Scotland, he shall, during each year of his residence, pay the usual annual contribution of £3, 3s., payable by each Resident Fellow ; hut after payment of such annual contribution for eight years, he shall he exempt from any further payment. In the case of any Resident Fellow ceasing to reside in Scotland, and Case of Fellows ... . ° -i becoming Non- Wishing to continue a Fellow of the Society, it shall be in the power of the Council Resident, to determine on what terms, in the circumstances of each case, the privilege of remaining a Fellow of the Society shall he continued to such Fellow while out of Scotland. * A modification of this rule, in certain cases, was agreed to at a Meeting of the Society held on January 3, 1831. At the Meeting of the Society, on January 5, 1857, when the reduction of the Contribu- tions from £3, 3s. to £2, 2s., from the 11th to the 25th year of membership, was adopted, it was resolved that the existing Members shall share in this reduction, so far as regards their future annual Contributions. VOL. XXXV. 21 322 Proceedings of the Poyal Society of Edinburgh. Defaulters. Privileges of Ordinary Fellows. Numbers unlimited, Fellows entitled to Transactions and Pro- ceedings. Mode of Recommending Ordinary Fellows. Form of Recommenda- tion. V. Members failing to pay their contributions for three successive years (due application having been made to them by the Treasurer) shall be reported to the Council, and, if they see fit, shall be declared from that period to be no longer Fellows, and the legal means for recovering such arrears shall be employed. YI. None but Ordinary Fellows shall bear any office in the Society, or vote in the choice of Fellows or Office-Bearers, or interfere in the patrimonial interests of the Society. YU. The number of Ordinary Fellows shall be unlimited. YIII. All Ordinary Fellows of the Society who are not in arrear of their Annual Contributions shall be entitled to receive, gratis, copies of the parts of the Trans- actions of the Society which shall be published subsequent to their admission, upon application, either personally or by an authorised agent, to the Librarian, provided they apply for them within five years of the date of publication of such parts. Copies of the parts of the Proceedings shall be distributed to all Fellows of the Society, by post or otherwise, as soon as may be convenient after publication. IX. Each candidate for admission as an Ordinary Fellow shall be proposed and recommended by at least Ordinary Fellows, two of whom ‘shall certify their recommendation from personal knowledge. This recommendation shall be delivered to the Secretary before the 24th of December of each Session, and, subject to the approval of the Council, shall be exhibited publicly in the Society’s Rooms during the succeeding month of January. All recommendations so exhibited shall be con- sidered by the Council at its first meeting in the month of February, and a list of those approved by the Council for Election shall be issued to the Fellows not later than the 14th of February. X. The recommendation of a Candidate for admission as an Ordinary Fellow shall be in the following terms A. B., a gentleman well versed in Science (or Polite Literature, as the case may be), 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 Fellow. Laws of the Society. 323 XL The Election of Ordinary Eellows shall take place at the first Ordinary Meeting Election of of the Society in March of each Session, and only those candidates approved by the Fellows. Council shall be eligible. The Election shall be by Ballot, and shall be determined by a ma.]ority of two- thirds of those who are present and vote. XII. Honorary Fellows shall not be subject to any contribution. This class shall Honorary consist of persons eminently distinguished for science or literature. Its number and Foreign, shall not exceed Eifty-six, of whom Twenty may be .British subjects, and Thirty-six may be subjects of foreign states. XIII. Personages of Royal Blood may be elected Honorary Fellows, without regard to Royal the limitation of numbers specified in Law XII. Personages. XIV. Honorary Fellows may be proposed by the Council, or by a recommendation (in Recommenda- the form given below*) subscribed by, three Ordinary Fellows; and in case the Fellows. Council shall decline to bring this recommendation before the Society, it shall be competent for the proposers to bring the same before a General Meeting, The election shall be by Ballot, after the proposal has been communicated viva voce from Mode of the Chair at one Meeting, and printed in the circulars for Two Ordinary Meetings of the Society, previous to the day of election. XV. The Ordinary Meetings shall be held on the first and third Mondays of each Ordinary month from Xovember to March, and from May to July, inclusive ; with the exception that when there are five Mondays in January, the Meetings for that month shall be held on its second and fourth Mondays. Regular Minutes shall be kept of the proceedings, and the Secretaries shall do the duty alternately, or accord- ing to such agreement as they may find it convenient to make. * We hereby recommend ^ for the distinction of beinp; made an Honorary Fellow of this Society, declaring that each of us from our own knowledge of his services to {Literature or Science, as the case may he) believe him to be worthy of that honour. (To be signed by three Ordinary Fellows.) To the President and Council of the Royal Society of Edinburgh. 324 Proceedings of the Poyal Society of Edinburgh. The Trans- actions. How Published. The Council. E-etiring Councillors. Election of Office-Bearers. Special Meetings ; how called. Treasurer’s Duties. XVI. The Society shall from time to time publish its Transactions and Proceedings. For this purpose the Council shall select and arrange the papers which they shall deem it expedient to publish in the Transactions of the Society, and shall super- intend the printing of the same. XVII. The Transactions shall be published in parts or Fasciculi at the close of each Session, and the expense shall be defrayed by the Society. XVIII. That there shall be formed a Council, consisting — First, of such gentlemen as may have filled the office of President ; and Secondly, of the following to be annually elected, viz. a President, Six Vice-Presidents (two at least of whom shall be Eesident), Twelve Ordinary Fellows as Councillors, a General Secretary, Two Secretaries to the Ordinary Meetings, a Treasurer, and a Curator of the Museum and Library. The Council shall have power to regulate the private business of the Society. At any Meeting of the Council the Chairman shall have a casting as well as a deliberative vote. XIX. Four Councillors shall go out annually, to be taken according to the order in which they stand on the list of the Council. XX. An Extraordinary Meeting for the election of Office-Bearers shall be held annually on the fourth Monday of October, or on such other lawful day in October as the Council may fix, and each Session of the Society shall be held to begin at the date of the said Extraordinary Meeting. XXL Special Meetings of the Society may be called by the Secretary, by direction of the Council ; or on a requisition signed by six or more Ordinary Fellows. Notice of not less than two days must be given of such Meetings. XXII. The Treasurer shall receive and disburse the money belonging to tine Society, granting the necessary receipts, and collecting the money when due. He shall keep regular accounts of all the cash received and expended, which shall be made up and balanced annually ; and at the Extraordinary Meeting in October, he shall present the accounts for the preceding year, duly audited. At this Meeting, the Treasurer shall also lay before the Council a list of all arrears due above two years, and the Council shall thereupon give such directions as they may deem necessary for recovery thereof. Laws of the Society. 325 XXIII. At the Extraordinary Meeting in October, a professional accountant shall be Auditor, chosen to audit the Treasurer’s accounts for that year, and to give the necessary discharge of his intromissions. XXIV. The General Secretary shall keep Minutes of the Extraordinary Meetings of the General Society, and of the Meetings of the Council, in two distinct books. He shall, under the direction of the Council, conduct the correspondence of the Society, and super- intend its publications. For these purposes he shall, when necessary, employ a clerk, to be paid by the Society. XXV. The Secretaries to the Ordinary Meetings shall keep a regular Minute-book, in Secretaries to which a full account of the proceedings of these Meetings shall be entered ; they Meetings, shall specify all the Donations received, and furnish a list of them, and of the Donors’ names, to the Curator of the Library and Museum ; they shall likewise furnish the Treasurer with notes of all admissions of Ordinary FelloAvs. They shall assist the General Secretary in superintending the publications, and in his absence shall take his duty. XXVI. The Curator of the Museum and Library shall have the custody and charge of Curator of ^ all the Books, Manuscripts, objects of Natural History, Scientific Productions, and Library, other articles of a similar description belonging to the Society ; he shall take an account of these when received, and keep a regular catalogue of the Avhole, which shall lie in the hall, for the inspection of the EelloAvs. XXVII. All articles of the above description shall be open to the inspection of the use of Museum Fellows at the Hall of the Society, at such times and under such regulations as the Council from time to time shall appoint. XXVIII. A Register shall be kept, in which the names of the Fellows shall be enrolled Register Book, at their admission, with the date. XXIX. If, in the opinion of the Council of the Society, the conduct of any Fellow is Power of unbecoming the position of a Member of a learned Society, or is injurious to the character and interests of this Society, the Council may request such Fellow to resign ; and, if he fail to do so within one month of such request being addressed to him, the Council shall call a General Meeting of the Fellows of the Society to consider the matter ; and, if a majority of the Fellows present at such Meeting agree to the expulsion of such Member, he shall be then and there expelled by the declaration of the Chairman of the said Meeting to that effect ; and he shall there- after cease to be a Fellow of the Society, and his name shall be erased from the Roll of Fellows, and he shall forfeit all right or claim in or to the property of the Societ}L 326 Proceedings of the Royal Society of Edinburgh. THE KEITH, MAKDOUGALL-BRISBANE, NEILL, AND GUNNING VICTORIA JUBILEE PRIZES. The above Prizes will be awarded by the Council in the following manner : — I. KEITH PRIZE. The Keith Prize, consisting of a Gold Medal and from £40 to £50 in Money, will be awarded in the Session 1915-1916 for the “ best communication on a scientific subject, communicated,* in the first instance, to the Royal Society during the Sessions 1913-1914 and 1914-1915.” Preference will be given to a paper con- taining a discovery. II. MAKDOUGALL-BRISBANE PRIZE. This Prize is to be awarded biennially by the Council of the Royal Society of Edinburgh to such person, for such purposes, for such objects, and in such manner as shall appear to them the most conducive to the promotion of the interests of science ; with the proviso that the Council shall not be compelled to award the Prize unless there shall be some individual engaged in scientific pursuit, or some paper written on a scientific subject, or some discovery in science made during the biennial period, of sufficient merit or importance in the opinion of the Council to be entitled to the Prize. 1. The Prize, consisting of a Gold Medal and a sum of Money, vdll be awarded at the commencement of the Session 1916-1917, for an Essay or Paper having reference to any branch of scientific inquiry, whether Material or Mental. 2. Competing Essays to be addressed to the Secretary of the Society, and trans- mitted not later than 8th July 1916. 3. The Competition is open to all men of science. 4. The Essays may be either anonymous or otherwise. In the former case, they must be distinguished by mottoes, with corresponding sealed billets, super- scribed with the same motto, and containing the name of the Author. 5. The Council impose no restriction as to the length of the Essays, which may be, at the discretion of the Council, read at the Ordinary Meetings of the Society. * For the purposes of this award the word “ communicated ” shall be understood to mean the date on which the manuscript of a paper is received in its final form for printing, as recorded by the General Secretary or other responsible oflScial. 327 Keith, Brisbane, Neill, and Gunning Prizes. They wish also to leave the property and free disposal of the manuscripts to the Authors ; a copy, however, being deposited in the Archives of the Society, unless the paper shall be published in the Transactions. 6. In awarding the Prize, the Council will also take into consideration any scientilic papers presented* to the Society during the Sessions 1914-15, 1915-16, whether they may have been given in with a view to the prize or not. III. NEILL PKIZE. The Council of the Eoyal Society of Edinburgh having received the bequest of the late Dr Patrick Neill of the sum of £500, for the purpose of “the interest thereof being applied in furnishing a Medal or other reward every second or third year to any distinguished Scottish Naturalist, according as such Medal or reward shall be voted by the Council of the said Society,” hereby intimates 1. The Neill Prize, consisting of a Gold Medal and a sum of Aloney, will be awarded during the Session 1915-1916. 2. The Prize will be given for a Paper of distinguished merit, on a subject of Natural History, by a Scottish Naturalist, which shall have been presented* to the Society during the two years preceding the fourth Monday in October 1915, — or failing presentation of a paper sufficiently meritorious, it will be awarded for a work or publication by some distinguished Scottish Naturalist, on some branch of Natural History, bearing date within five years of the time of award. IV. GUNNING VICTOPIA JUBILEE PRIZE. This Prize, founded in the year 18S7 by Dr R. H. Gunning, is to be awarded quadrennially by the Council of the Royal Society of Edinburgh, in recognition of original work in Physics, Chemistry, or Pure or Applied Mathematics. Evidence of such work may be afforded either by a Paper presented to the Society, or by a Paper on one of the above subjects, or some discovery in them elsewhere communicated or made, which the Council may consider to be deserving of the Prize. The Prize consists of a sum of money, and is open to men of science resident in or connected with* Scotland. The first award was made in the year 1887. In accordance with the wish of the Donor, the Council of the Society may on fit occasions award the Prize for work of a definite kind to be undertaken during the three succeeding years by a scientific man of recognised ability. * For the purposes of this award the word ‘ ‘ presented ” shall be understood to mean the date on which the manuscript of a paper is received in its final form for printing, as recorded by the Genera] Secretary or other responsible official. 328 Proceedings of the Royal Society of Edinburgh. RESOLUTIONS OF COUNCIL IN REGARD TO THE MODE OP AWARDING PRIZES. {See Minutes of Meeting of January 18, 1915.) I. — AVitli regard to the Keith and Makdougall-Brisbane Prizes, which are open to all Sciences, the mode of award will be as follows : — 1. Papers or essays to be considered shall be arranged in two groups, A and B, — Group A to include Astronomy, Chemistry, Mathematics, Metallurgy, Aleteorology and Physics; Group B to include Anatomy, Anthropology^ Botany, Geology, Pathology, Physiology, and Zoology. 2. These two Prizes shall be awarded to each group in alternate biennial periods, provided papers worthy of recommendation have been communicated to the Society. 3. Prior to the adjudication the Council shall appoint, in the first instance, a Committee composed of representatives of the group of Sciences which did not receive the award in the immediately preceding period. The Com- mittee shall consider the Papers which come within their group of Sciences, and report in due course to the Council. 4. In the event of the aforesaid Committee reporting that within their group of subjects there is, in their opinion, no paper worthy of being recommended for the award, the Council, on accepting this report, shall appoint a Committee representative of the alternate group to consider papers coming within their group and to report accordingly. 5. Papers to be considered by the Committees shall fall within the period dating from the last award in groups A and B respectively. II. AVith regard to the Neill Prize, the term “Naturalist” shall be understood to include any student in the Sciences composing group B, namely. Anatomy^ Anthropology, Botany, Geology, Pathology, Physiology, Zoology. Keith, Brisbane, Neill, and Gunning Prizes. 329 AWARDS OF THE KEITH, MAKDOUGALL - BRISBANE, NEILL, AND GUNNING VICTORIA JUBILEE PRIZES. I. KEITH PRIZE. 1st Biennial Period, 1827-29. — Dr Brewster, for his papers “on his Discovery of Two New Immiscible Fluids in the Cavities of certain Minerals,” published in the Transactions of the Society. 2nd Biennial Period, 1829-31. — Dr Brewster, for his paper “on a New Analysis of Solar Light,” published in the Transactions of the Society. 3rd Biennial Period, 1831-33. — Thomas Graham, Esq., for his jiaper “on the Law of the Diffusion of Gases,” ])ublished in the Transactions of the Society. 4th Biennial Period, 1833-35. — Professor J. D. Forbes, for his paper “on the Refraction and Polarization of Heat,” published in the Transactions of the Society. 5th Biennial Period, 1835-37. — John Scott Russell, Esq., for his researches “on Hydro- dynamics,” published in the Transactions of the Society. 6th Biennial Period, 1837-39. — Mr John Shaw, for his experiments “on the Development and Growth of the Salmon,” published in the Transactions of the Society. 7th Biennial Period, 1839-41. — Not awarded. 8th Biennial Period, 1841-1843. — Professor James David Forbes, for his papers “on Glaciers,” published in the Proceedings of the Society. 9th Biennial Period, 1843-45. — Not awarded. 10th Biennial Period, 1845-47. — General Sir Thomas Brisbane, Bart., for the Makerstoun Observations on Magnetic Phenomena, made at his expense, and published in the Trans- actions of the Society. llTH Biennial Period, 1847-49. — Not awarded. 12th Biennial Period, 1849-51. — Professor Kelland, for his papers “on General Differentia- tion, including his more recent Communication on a process of the Differential Calculus, and its application to the solution of certain Differential Equations,” published in the Transac- tions of the Society. 13th Biennial Period, 1851-53. — W, J. Macquorn Rankine, Esq., for his series of papers “on the Mechanical Action of Heat,” published in the Transactions of the Society. 14th Biennial Period, 1853-55. — Dr Thomas Anderson, for his papers “on the Crystalline Constituents of Opium, and on the Products of the Destructive Distillation of Animal Substances,” published in the Transactions of the Society. 15th Biennial Period, 1855-57. — Professor Boole, for his Memoir “on the Application of the Theory of Probabilities to Questions of the Combination of Testimonies and Judgments,” published in the Transactions of the Society. 16th Biennial Period, 1857-59. — Not awarded. 17th Biennial Period, 1859-61. — John Allan Broun, Esq., F.R.S., Director of the Trevandrum Observatory, for his papers “on the Horizontal Force of the Earth’s Magnetism, on the Correction of the Bifilar Magnetometer, and on Terrestrial Magnetism generally,” published in the Transactions of the Society. 18th Biennial Period, 1861-63. — Professor William Thomson, of the University of Glasgow, for his Communication ‘ ‘ on some Kinematical and Dynamical Theorems. ” 19th Biennial Period, 1863-65. — Principal Forbes, St Andrews, for his “Experimental Inquiry into the Laws of Conduction of Heat in Iron Bars,” published in the Transactions of the Society. 20th Biennial Period, 1865-67. — Professor C. Piazzi Smyth, for his paper “on Recent Measures at the Great Pyramid,” published in the Transactions of the Society. 21st Biennial Period, 1867-69. — Professor P. G. Tait, for his paper “on the Rotation of a Rigid Body about a Fixed Point,” published in the Transactions of the Society. 22nd Biennial Period, 1869-71. — Professor Clerk Maxwelf., for his paper “on Figures, Frames, and Diagrams of Forces,” published in the Transactions of the Society. 330 Proceedings of the Eoyal Society of Edinburgh. 23rd Biennial Period, 1871-73. — Professor P. G. Tait, for his paper entitled “First Approxi- mation to a Thermo-electric Diagram,” published in the Transactions of the Society. 24th Biennial Period, 1873-75. — Professor Crum Brown, for his Researches “on the Sense of Rotation, and on the Anatomical Relations of the Semicircular Canals of the Internal Ear.” 25th Biennial Period, 1875-77. — Professor M. Forster Heddle, for his papers “on the Rhombohedral Carbonates,” and “on the Felspars of Scotland,” published in the Transac- tions of the Society. 26th Biennial Period, 1877-79. — Professor H. C. Fleeming Jenkin, for his paper “on the Application of Graphic Methods to the Determination of the Efficiency of Machinery,” published in the Transactions of the Society ; Part II having appeared in the volume for 1877-78. 27'I'h Biennial Period, 1879-81.— Professor George Chrystal, for his paper “on the Differ- ential Telephone,” published in the Transactions of the Society. 28th Biennial Period, 1881-83. — Thomas Muir, Esq., LL.D., for his “Researches into the Theory of Determinants and Continued Fractions,” published in the Proceedings of the Society. 29th Biennial Period, 1883-85.— John Aitken, Esq., for his paper “on the Formation of Small Clear Spaces in Dusty Air,” and for previous papers on Atmospheric Phenomena, published in the Transactions of the Society. 30i'h Biennial Period, 1885-87.— John Young Buchanan, Esq., for a series of communica- tions, extending over several years, on subjects connected with Ocean Circulation, Compressibility of Glass, etc. ; two of which, viz., “On Ice and Brines,” and “On the Distribution of Temperature in the Antarctic Ocean,” have been published in the Proceedings of the Society. 31st Biennial Period, 1887-89. — Professor E. A. Letts, for his papers on the Organic Compounds of Phosphorus, published in the Transactions of the Society. 32nd Biennial Period, 1889-91. — R. T. Omond, Esq., for his contributions to Meteorological Science, many of which are contained in vol. xxxiv. of the Society’s Transactions. 33rd Biennial Period, 1891-93. — Professor Thomas R. Fraser, F.R.S., for his papers on Strophanthus hispiclus, Strophanthin, and Strophanthidin, read to the Society in February and June 1889 and in December 1891, and printed in vols. xxxv, xxxvi, and xxxvii of the Society’s Transactions. 34 i’h Biennial Period, 1893-95. — Dr Cargill G. Knott, for his papers on the Strains produced by IMagnetism in Iron and in Nickel, which have appeared in the Transactions and Proceedings of the Society. 35th Biennial Period, 1895-97. — Dr Thomas Muir, for his continued communications on Determinants and Allied Questions. 36th Biennial Period, 1897-99. — Dr James Burgess, for his paper “on the Definite Integral o ft I with extended Tables of Values,” printed in vol. xxxix of the Transactions 0 of the Society. 37th Biennial Period, 1899-1901. — 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. , 38th Biennial Period, 1901-03.— Sir William Turner, K.C.B., LL.D., F.R.S., etc., for his memoirs entitled “ A Contribution to the Craniology of the People of Scotland,” published in the Transactions 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. ■ 39th Biennial Period, 1903-05. — Thomas H. Bryce, M.A., M.D., for his two papers on “The Histology of the Blood of the Larva of Lepidosiren paradoxa,"” published in the Transactions of the Society within the period. 40th Biennial Period, 1905-07. — Alexander Bruce, M.A., M.D., F.R.C.P.E., for his paper entitled “ Distribution of the Cells in the Intermedio-Lateral Tract of the Spinal Cord,” published in the Transactions of the Society within the period. 41st Biennial Period, 1907-09. — Wheelton Hind, M.D., B.S., F.R.C.S., F.G.S., for a paper published in the Transactions of the Society, “ On the Lamellibranch and Gasteropod Fauna found in the Millstone Grit of Scotland.” 42nd Biennial Period, 1909-11. — Professor Alexander Smith, B.Sc., Ph.D., of New York, for his researches upon “Sulphur” and upon “Vapour Pressure,” appearing in the Proceedings of the Society. 43rd Biennial Period, 1911-1913. — James Russell, Esq., for his series of investigations relating to magnetic phenomena in metals and the molecular theory of magnetism, the results of which have been published in the Proceedings and Transactions of the Society, the last }>aper having been issued within the period. Keith, Brisbane, Neill, and Gunning Prizes. 331 II. MAKDOUG ALL-BRISBANE PRIZE. 1st Biennial Period, 1859. — Sir Roderick Impey Murchison, on account of his Contributions to the Geology of Scotland. 2nd Biennial Period, 1860-62. — AVilliam Seller, M.D. , F.R.C.P.E., for his “ Memoir of the Life and AA^ritings of Dr Robert AAdiytt,” published in the Transactions of the Society, 3rd Biennial Period, 1862-64. — John Denis Macdonald, Esq., R.N., F.R.S., Surgeon of H.M.S. “ Icarus,” for his paper “ on the Representative Relationships of the Fixed and Free Tunicata, regarded as Two Sub-classes of equivalent value ; with some General Remarks on their Morphology,” published in the Transactions of the Society. 4th Biennial Period, 1864-66. — Not awarded. 5th Biennial Period, 1866-68.— Dr Alexander Crum Brown and Dr Thomas Richard Fraser, for their conjoint ]>aper ‘‘on the Connection between Chemical Constitution and Physiological Action,” j)ublished in the Transactions of the Society. 6th Biennial Period, 1868-70. — Not awarded. 7th Biennial Period, 1870-72. — George James Allman, Al.D., F.R.S., Emeritus Professor of • Natural History, for his paper “ on the Homological Relations of the Ccelenterata,” published in the Transactions, which forms a leading chapter of his Monograph of Gymnoblastic or Tubularian Hydroids — since jiublished. 8th Biennial Period, 1872-74. — Professor Listep, for his paper “on the Germ Theory of Putrefaction and the Fermentive Changes,” communicated to the Society, 7th April 1873. 9rii Biennial Period, 1874-76. — Alexander Buchan, A.Al., for his paper “ on the Diurnal Oscillation of the Barometer,” published in the Transactions of the Society, 10th Biennial Period, 1876-78. — Professor Archibald Geikte, for his ])aper “on the Old Red Sandstone of AVestern Europe,” published in the Transactions of the Society. 11th Biennial Period, 1878-80. — Professor Piazzi Smyth, Astronomer-Royal for Scotland, for his paper “on the Solar Sjiectrum in 1877-78, with some Practical Idea of its probable Temperature of Origination,” published in the Transactions of the Society. 12th Biennial Period, 1880-82. — Professor James Geikie, for his “Contributions to the Geology of the North-AVest of Europe,” including his paper “on the Geology of the Faroes,” published in the Transactions of the Society. 13th Biennial Period, 1882-84.— Edward Sang, Esq., LL.D., for his paper “on the Need of Decimal Subdivisions in Astronomy and Navigation, and on Tables requisite therefor,” and generally for his Recalculation of Logarithms both of Numbers and Trigonometrical Ratios, —the former communication being })ublished in the Proceedings of the Society. 14th Biennial Period, 1884-86. — John Murray, Esq., LL.D., for his papers “On the Drainage Areas of Continents, and Ocean Deposits,” “ The Rainfall of the Globe, and Discharge of Rivers,” “ The Height of the Land and Depth of the Ocean,” and “The Distribution of Temperature in the Scottish Lochs as affected by the AVind.” 15th Biennial Period, 1886-88. — Archibald Geikie, Esq., LL.D., for numerous Communica- tions, especially that entitled “ History of Volcanic Action during the Tertiary Period in the British Isles,” published in the Transactions of the Society. 16th ffiENNiAL Period, 1889-90. — Dr Ludwig Becker, for his paper on “ The Solar Spectrum at Aledium and Low Altitudes,” printed in vol. xxxvi. Part I, of the Society’s Transactions. 17th Biennial Period, 1890-92. — Hugh Robert Mill, Esq., D.Sc., for his papers on “The Physical Conditions of the Clyde Sea Area,” Part I being already published in vol. xxxvi of the Society’s Transactions. 18th Biennial Period, 1892-94. — Professor James AA^alker, D.Sc., Ph. D., for his work on Physical Chemistry, jiart of which has been published in the Proceedings of the Society, vol. XX, pp. 255-263. In making this award, the Council took into consideration the work done by Professor AValker along with Professor Crum Brown on the Electrolytic Synthesis of Dibasic Acids, published in the Transactions of the Society. 19th Biennial Period, 1894-96. — Professor John G. M‘Kendrick, for numerous Physiological papers, especially in connection with Sound, many of Avhich have ajipeared in the Society’s publications. 20th Biennial Period, 1896-98. — Dr AVilliam Peddie, for his papers on the Torsional Rigidity of AA^ires. ,21st Biennial Period, 1898-lSOO.— Dr Ramsay H. Traquair, for his paper entitled “ Report on Fossil Fishes collected by the Geological Survey in the Upper Silurian Rocks of Scotland,” printed in vol. xxxix of the Transactions of the Society. 332 Proceedings of the Eoyal Society of Edinburgh. 22nd Biennial Peeiod, 1900-02.— Dr Arthue T. Masteeman, for his paper entitled “The Early Development of Crihrella oculata (Forbes), with remarks on Echinoderm Development,”' printed in vol. xl of the Transactions of the Society. 23ed Biennial Period, 1902-04.— Mr John Dougall, M.A., for his paper on “An Analytical Theory of the Equilibrium of an Isotropic Elastic Plate,” published in vol. xli of the Transactions of the Society. 24th Biennial Period, 1904-06. — Jacob E. Halm, Ph. D., for his two papers entitled “Spectro- scopic Observations of the Rotation of the Sun,” and “ Some Further Results obtained with the Spectroheliometer,” and for other astronomical and mathematical papers published in the Transactions and Proceedings of the Society within the period. 25th Biennial Period, 1906-08. — D. T. Gwynne-Vaughan, M.A., F.L.S., for his papers,. 1st, “On the Fossil Osmundacete,” and 2nd, “ On the Origin of the Adaxially-curved Leaf- trace in the Filicales,” communicated by him conjointly with Dr R. Kidston. 26th Biennial Period, 1908-10. — Ernest MacLagan Wedderburn, M.A., LL.B. , for his series of papers bearing upon “The Temperature Distribution in Fresh-water Lochs,” and especially upon “The 4’emperature Seiche.” 27th Biennial Period, 1910-12. — John Brownlee, M.A., M.D., D.Sc., for his contributions to the Theory of Mendelian Distributions and cognate subjects, })ublished in the Proceedings of the Society within and prior to the prescribed period. 28th Biennial Period, 1912-14. — Professor C. R. Marshall, M.D., M.A., for his studies “On the Pharmacological Action of Tetra-alkyl-ammonium Compounds.” III. THE NEILL PRIZE. 1st Triennial Period, 1856-59. — Dr W. Lauder Lindsay, for his paper “ on the Spermogones and Pycnides of Filamentous, Fruticulose, and Foliaceous Lichens,” published in the Trans- actions of the Society. 2nd Triennial Period, 1859-61. — Robert Kaye Greville, LL.D., for his Contributions to Scottish Natural History, more especially in the department of Cryptogamic Botany, including his recent papers on Diatomacese. 3rd Triennial Period, 1862-65. — Andrew Crombie Ramsay, F.R.S., Professor of Geology in the Government School of Mines, and Local Director of the Geological Survey of Great Britain, for his various works and memoirs ])ublished during the last live years, in which he has applied the large experience acquired by him in the Direction of the arduous work of the Geological Survey of Great Britain to the elucidation of important questions bearing on Geological Science. 4th Triennial Period, 1865-68. — Dr William Carmichael MHntosh, for his paper “on the Structure of the British Nemerteans, and on some New British Annelids,” published in the Transactions of the Society. 5th Triennial Period, 1868-71. — Professor William Turner, for his papers “on the Great Finner Whale ; and on the Gravid Uterus, and the Arrangement of the Foetal Membranes in the Cetacea,” published in the Transactions of the Society. 6th Triennial Period, 1871-74. — Charles William Peach, Esq., for his Contributions to Scottish Zoology and Geology, and for his recent contributions to Fossil Botany. 7th Triennial Period, 1874-77. — Dr Ramsay H. Traquair, for his paper “on the Structure and Affinities of Tristichopterus alcdus (Egerton),” published in the Transactions of the Society, and also for his contributions to the Knowledge of the Structure of Recent and Fossil Fishes. 8th Triennial Period, 1877-80. — John Murray, Esq., for his paper “on the Structure and Origin of Coral Reefs and Islands,” published (in abstract) in the Proceedings of the Society. 9th Triennial Period, 1880-83. — Professor Herdman, for his papers “on the Tunicata,” published in the Proceedings and Transactions of the Society. 10th Triennial Period, 1883-86. —B. N. Peach, Esq., for his Contributions to the Geology and Palseontology of Scotland, published in the Transactions of the Society. 11th Triennial Period, 1886-89. — Robert Kidston, Esq., for his Researches in Fossil Botany, published in the Transactions of the Society. 12th Triennial Period, 1889-92. — John Horne, Esq., F.G.S. , for his Investigations into the Geological Structure and Petrology of the North-West Highlands. 333 Keith, Brisbane, Neill, and Gunning Prizes. 13th Triennial Period, 1892-95. — Robert Irvine, Esq., for his papers on the Action of Organisms in the Secretion of Carbonate of Lime and Silica, and on the solution of these substances in Organic Juices. These are printed in the Soeiety’s Transaetions and Proceedings. 14th Triennial Period, 1895-98. — Professor Cossar Ewart, for his recent Investigations con- nected with Telegony. 15th Triennial Period, 1898-1901. — Dr John S. Flett, for his papers entitled “The Old Red Sandstone of the Orkneys” and “The Trap Dykes of the Orkneys,’* printed in vol. xxxix of the Transactions of the Society. 16th Triennial Period, 1901-04. — Professor J. Graham Kerr, M.A., for his Researches on Lepidosiren paradoxa, published in the Philosophical Transactions of the Royal Society, London. 17th Triennial Period, 1904-07. — Frank J. Cole, B.Sc., for his paper entitled “ A Monograph on the General Morphology of the Myxinoid Fishes, based on a study of Myxine,” published in the Transactions of the Society, regard being also paid to Mr Cole’s other valuable contri- butions to the Anatomy and Morphology of Fishes. 1st Biennial Period, 1907-09. — Francis J. Lewis, M.Sc. , F.L.S., for his papers in the Society’s Transactions “ On the Plant Remains of the Scottish Peat Mosses.” 2nd Biennial Period, 1909-11. — James Murray, Esq., for his paper on “Scottish Rotifers collected by the Lake Survey (Supplement),” and other papers on the “Rotifera” and “ Tardigrada,” which appeared in the Transactions of the Society — (this Prize was awarded after consideration of the papers received within the five years prior to the time of award : see Neill Prize Regulations). 3rd Biennial Period, 1911-13.— Dr W. S. Bruce, in reeognition of the scientific results of his Arctic and Antarctic explorations. lY. GUNNING YICTOKIA JUBILEE PEIZE. 1st Triennial Period, 1884-87. — Sir AAilliam Thomson, Pres. R.S.E., F.R.S., for a remark- able series of papers “on Hydrokinetics,” especially on Waves and Vortiees, whieh have been communicated to the Society. 2nd Triennial Period, 1887-90.— Professor P. G. Tait, Sec. R.S.E., for his work in connection with the “ Challenger” Expedition, and his other Researches in Physical Science. 3rd Triennial Period, 1890-93.— Alexander Buchan, Esq., LL.D., for his varied, extensive, and extremely important Contributions to Meteorology, many of which have appeared in the Society’s Publications. 4th Triennial Period, 1893-96. — John Aitken, Esq., for his brilliant Investigations in Physics, especially in connection with the Formation and Condensation of Aqueous Vapour. 1st Quadrennial Period, 1896-1900. — Dr T. D. Anderson, for his discoveries of New and Variable Stars. ^ND Quadrennial Period, 1900-04. — Sir James Dewar, LL.D., D.C. L., 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. 3rd Quadrennial Period, 1904-08, — Professor George Chrystal, M.A., LL.D,, for a series of papers on “Seiches,” including “The Hydrodynamical Theory and Experimental Investiga- tions of the Seiche Phenomena of Certain Scottish Lakes. ” 4th Quadrennial Period, 1908-12.— Professor J. Norman Collie, Ph.D., F.R.S., for his distinguished contributions to Chemistry, Organic and Inorganic, during twenty-seven years, including his work upon Neon and other rare gases. Professor Collie’s early papers were contributed to the Transactions of the Society. 334 Proceedings of the Royal Society of Edinburgh. [Sess. PROCEEDINGS OF THE STATUTORY GENERAL MEETING Beginning the 132nd Session, 1914-1915. At the Annual Statutory Meeting of the Royal Society of Edinburgh, held in the Society’s Lecture Room, 24 George Street, on Monday, October 26, 1914, at 4.30 p.m., Professor James Geikie, President, in the Chair, the Minutes of the last Statutory Meeting, October 27, 1913, were read, approved, and signed. On the motion of Dr Knott, seconded by Dr Horne, Dr J. R. Milne and Mr A. G. Burgess were appointed Scrutineers, and the ballot for the New Council commenced. The General Secretary announced that the Council had granted leave of absence to Mr G. A. Stewart, Librarian, and Mr W. J. Beaton, Assistant Librarian, so as to enable them to join His Majesty’s forces. The Council had also felt it advisable to close the Society’s Rooms on Saturdays at one o’clock. The Treasurer’s Accounts for the past year, 1913-1914, were submitted. Professor Bower moved the approval of the Treasurer’s Report, and also votes of thanks to the Treasurer and the Auditors, who were reappointed. This was agreed to. The Scrutineers reported that the following Council had been duly elected : — Professor James Geikie, LL.D., D.C.L., F.R.S., F.G.S., President. Professor T. Hudson Beare, M.Inst.C.E., Professor F. 0. Bower, M.A., D.Sc., F.R.S., Professor Sir Thomas R. Fraser, M.D., LL.D,, F.R.C.P.E., F.R.S., Benjamin N. Peach, LL.D., F.R.S., F.G.S., Professor Sir E. A. Schafer, M.R.C.S., LL.D., F.R.S., The Right Hon. Sir J. H. A. Macdonald, K.C.B., P.C., LL.D., D.L., F.R.S., M.Inst.E.E., Cargill G. Knott, D.Sc., General Secretary. Robert Kidston, LL.D., F.R.S., F.G.S., Professor Arthur Robinson, M.D., M.R.C.S., James Currie, M.A., Treasurer. John S. Black, M.A., LL.D., Curator of Library and Museum. Vice- Presidents. \ Secretaries to Ordinary j JMeetings. ORDINARY MEMBERS OF COUNCIL. James Gordon Gray, D.Sc. Professor R. A. Sampson, iM.A,, D.Sc., F.R.S. Professor D’Arcy W. Thompson, C.B., B.A., F L S Professor E. T. Whittaker, Sc.D., F.R.S. Principal A. P. Laurie, M.A., D.Sc. Professor J. Graham Kerr, M.A., F.R.S. Leonard Dobbin, Ph.D. Ernest Maclagan Wedderburn, M.A.,. LL.B. W. B. Blaikie, LL.D. John Horne, LL.D., F.S.S., F.G.S. K. Ste'wart MacDougall, M.A., D.Sc. W. A. Tait. , D.Sc,, M.Inst.C.E. Society’s Representative on I ^ M.Inst.C.E. George Henot s Trust, J ’ 1914-15.] Meetings of the Society. 335 PROCEEDINGS OF THE ORDINARY MEETINGS, Session 1914-1915. FIRST ORDINARY MEETING. Monday, November 2, 1914. Professor James Geikie, LL.D., D.C.L , F.R.S., F.G.S., President, in the Chair, The President opened the Session Avith a Short Summary of Last Session’s Work. The following Communications were read : — 1. The Baleen Whales of the South Atlantic, By Principal Sir William Turner, K.C. B., F.R.S. 2. The Optical Rotation and Cryoseopic Behaviour of Sugars dissolved in {a) Forraamide, {h) Water. By John E. Mackenzie, Ph.D., D.Sc, and Sudhamoy Ghosh, M Sc. Communi- cated by the Secretary, SECOND ORDINARY MEETING. Monday, November 16, 1914. Professor F. 0. Bower, F.R.S., Vice-President, in the Chair. The following Communications were read : — 1. Fossil Micro-organisms from the Jurassic and Cretaceous Rocks of Great Britain. By David Ellis, Ph.D. {IVith Lantern Illustrations.) 2. The Anatomy and Affinity of Deparia Moorei, Hk. By J. M‘Lean Thompson, B.Sc. Communicated by Professor Bower. ( With Lantern Illustrations.) 3. Properties of the Determinant of an Orthogonal Substitution. By Thomas Muir, LL.D., F.R.S. THIRD ORDINARY MEETING. Monday, December 7, 1914. Principal A. P. Laurie, M.A., D.Sc., in the Chair, The following Communications were read : — 1. Obituary Notice of Professor John Gibson, Ph.D, By Principal A. P. Laurie. 2. The Application of Mathematical Methods to Morphology. By Professor D’Arcy W. Thompson, C.B. ( With Lantern Illustrations.) 3. On an Integral -Equation whose Solutions are the Functions of Lame. By Professor E. T. AVhittaker. The following Candidate for Fellowship was balloted for, and declared duly elected : —John Edward Aloysius Steggall, M.A., Professor of Mathematics at University College, Dundee, FOURTH ORDINARY MEETING. Monday, December 21, 1914, Professor Sir Thomas Fraser, F.R.S., Vice-President, in the Chair. The following Communications were read : — 1. The Poisoned Arrows of the Abors and Mishmis of North-East India, and the Com- 336 Proceedings of the Koyal Society of Edinburgh. [Sess. position and Action of their Poisons. By Professor Sir Thomas R. Fraser, F.R.S. {Arrows, Bows, and Quivers ivere exhibited.) 2. Regeneration of the Legs of Decapods from the preformed Breaking Planes. By J. Herbert Paul, M.A., B.Sc. Communicated by Professor D. Noel Paton. ( With Lantern Illustrations.) 3, The Degrees of Dissociation in the Saturated Vapours of the Ammonium Halides. By Professor A. Smith and R. H. Lombard. FIFTH ORDINARY MEETING. Monday, January 18, 1915. Lord Kingsburgh, F. R.S., Vice-President, in the Chair. At the request of the Council the following Address was delivered : — Visit of the|?Bidtish Association to Australia in 1914. {With Lantern Illustrations.) By Professor F. 0. Bower, F.R.S. The following Communication was presented : — Formulse and Scheme of Calculation for the Development of a Function of Two Variables in Spherical Harmonics. By Professor T. Bauschinger, Strassburg. Communicated by the Geheral Secretary. The following Candidates for Fellowship were balloted for and declared duly elected : — Charles Anthony, M.Inst.C.E., M.I.Mech.E., F.R.A.S., etc., Casilla, Correo 149, Bahia Blanca, S.O.S., Argentine; Alfred Archibald Boon, D.Sc., Assistant Professor of Chemistry, Heriot- Watt College, Edinburgh; Lewis P. Orr, F.F.A., Secretary of the Scottish Life Assurance Co., 14 Learmonth Gardens, Edinburgh. Mr Andrew WiLSON;-and Dr Spencer Mort signed the Roll, and were duly admitted as Fellows of the Society. SIXTH ORDINARY MEETING. Monday, February 1, 1915. Professor Sir E. A. Schafer, F.K.S., Vice-President, in the Chair. The following Communications were read : — 1. Studies on Periodicity in Plant Growth. Part II— Correlation in Root and Shoot Growth. By Mrs Rosalind Jones {nee Crosse), B.Sc. Communicated by R. A. Robertson, M.A., B.Sc. 2. The Histology of Disseminated Sclerosis. By Dr James Dawson. Communicated by Dr A. Ninian Bruce. The following Candidates for Fellowship were balloted for, and declared duly elected Raymond Keiller Butchart, B.Sc., Assistant Lecturer in Mathematics, University College, Dundee, 8 Martin Street, Maryfield, Dundee; and Robert Campbell, D.Sc., Lecturer in Petrology, University of Edinburgh, 7 Muirend Avenue, Juniper Green, Edinburgh. Dr A. A. Boon signed the Roll and was duly admitted a Fellow of the Society. SEVENTH ORDINARY MEETING. Monday, February 15, 1915. Dr Peach, F.R.S., Vice-President, in the Chair. The following Communications were read : — 1. Skiagraphic Researches in Teratology. By Dr Harry Rainy and Dr J. W. Ballaniyne. {Illustrated by Lantern and by X-ray ‘photograyhs of abnormal development of bones in the Foetus.) 2. Three connected papers: (1) On Hcemonais laurentii, a representative of a little-known genus of Naididse ; (2) On a Rule of Proportion observed in the Setae of Certain Naididae ; (3) On the Sexual Phase in certain of the Naididae. By Professor J. Stephenson. 3. The Ordovician and Silurian Brachiopoda of the Girvan District. By Dr F. R. C. Reed. Communicated by Dr Horne, F. R.S. 1914-15.] Meetings of the Society. 337 EIGHTH ORDINARY MEETING. Monday^ March 1, 1915. Professor Hudson Beare, Vice-President, in the Chair. The following Communications were read : — 1. On the Motion of a Body in a Fluid. By H. Levy, M, A., B.Sc. Communicated by the General Secretary. 2. On the Electrical Conductivity of Aqueous Hydrochloric Acid, saturated with Sodium Chloride ; and on a new form of Conductivity Cell. By F.D. Miles, B.Sc., A.R. C.S. Communi- cated by Principal Laurie. {Illustrated by Apparatus and Lantern. ) 3. The Reaction between Sodamide and Hydrogen. By F. D. Miles, B.Sc., A.R. C.S. Communicated by Principal Laurie. The following Candidate for Fellowship was balloted for, and declared duly elected : — Walter Leonard Bell, M.D. Edin., F.S.A. Scot., 123 London Road North, Lowestoft, Suffolk. NINTH ORDINARY AIEETING. Monday, March 15, 1915. Professor Bower, F.R.S., Vice-President, in the Chair. The Chairman opened the Meeting with an appreciation of the late President, Professor James Geikie. The following Communications were read : — 1. On the Larvae of Lingula and Pelagodiscus. By Dr J. H. Ashworth. {With Lantern Illustrations.) 2. The Reflective Power of Pigments in the Ultra-Violet. By Charles Cochrane, M. A. , B.Sc. Communicated by Dr R. A. Houstoun. 3. On Archseocyathinee from a Boulder dredged in the Weddell Sea. (Scottish National Antarctic Expedition.) By Dr W. T. Gordon. TENTH ORDINARY AIEETING. Monday, J/ny 3, 1915. Professor Hudson Beare, Vice-President, in the Chair. The following Communications were read : — 1. The Temperatures, Specific Gravities, and Salinities of the Weddell Sea, and of the N. and S. Atlantic Oceans. By Dr W. S. Bruce, Mr A. King, and Mr D. W. Wilton. 2. The Theory of the Gyroscope. By Professor Horace Lamb. 3. The Phenomena of Evaporation and their Bearing on the Kinetic Theory. By Dr H. C. Williamson. The following Candidates for Fellowship were balloted for, and declared duly elected: — Joseph Roberi’ Fraser, Clergyman, U.F. Church Manse, Kinneff, and George Clark Trotter, M.D., Ch.B. (Edin.), D.P.H. (Aberdeen), Medical Officer of Health, Paisley, “Remuera,” Paisley. ELEVENTH ORDINARY MEETING. Monday, June 7, 1915, Professor Sir Thomas R. Fraser, F.R.S.. Vice-President, in the Chaii-. The following Communications were read : — 1. Studies on the Development of the Horse : The Development during the first three weeks. By Professor J. Cossar Ewart, F.R.S. {With Lantern Illustrations.) 2. On the Functions which are represented by the Expansions of the Interpolation Theory. By Professor E. T. Whittaker, F.R.S. ( With Lantern Illustrations.) 3. On a Modification of Pelouze’s Method for determining Nitrates. By Professor A. E. Letts and Miss Florence W. Rea. 4. Quaternion Investigation of the Commutative Law for Homogeneous Strains. By Frank L. Hitchcock. Communicated by the General Secretary. VOL. XXXV. 22 338 Proceedings of tlie Koyal Society of Edinburgh. [Sess. TWELFTH ORDINARY MEETING. Monday, June 21, 1915. Professor Hudson Beare, Yice-President, in the Chair, The Makdougall-Brisbane Prize Award for the biennial period 1912/13-1913/14. The Council of the Royal Society of Edinburgh have awarded the Makdougall- Brisbane Prize- to Professor C. R. Marshall for his studies “On the Pharmacological Action of Tetra-alkyl- aminonium Compounds.” The Prize will be presented at the Ordinary Meeting of July 5, 1915. The following Communications were read ; — 1. On the Composition of Milk as ati'ected by Increase of the Amount of Calcium Phosphate in the Rations of a Cow. By Alexander Lauder, D.Sc., and T. AY. Fagan, M.A. [IVith Lantern Illustrations. ) 2. Comparative Study of Autotomy. By J. Herbert Paul, M.A. , B. Sc. Communicated by Professor Noel Paton. ( With Lantern Illustrations.) 3. A Contribution to the Study of the Scottish Skull. By Matthew Youlg, M.B., Ch.B. Communicated by Professor Bryce. 4. The Development and Morphology of the Sporosacs of Dicoryne, with Description of a new Form. By J, H. Ashworth, D.Sc., and J. Ritchie, M.A. , D.Sc. {With Lantern Illustrations.) The following Candidates for Fellowship were balloted for, and declared duly elected : — James Hermann Rosenthal Kemnal, Managing Director and Engineer-in-Chief of Babcock & AVilcox, Ltd., Kemnal Manor, Chisleburst, Kent, and James Lorrain Smith, Professor of Pathology, University, Edinburgh, 11 Bruntsfield Crescent, Edinburgh. FIRST SPECIAL MEETING. Monday, June 28, 1915. Dr Peach, F.R.S., Yice-President, in the Chair. The Makdougall-Brisbane Prize A’WARD for the biennial period 1912/13-1913/14. The Council of the Royal Society of Edinburgh have awarded the Makdougall-Brisbane Prize to Professor C. R. Marshall for his studies “ On the Pharmacological Action of Tetra-alkyl- ammonium Compounds.” The Prize will be presented at the Ordinary Meeting of July 5, 1915. The following Communications were read : — 1. Six Papers communicated by Professor Gregory : — {a) Contributions to the Geology of Benguella. By Professor J. W. Gregory, F.R.S. (6) Notes on Rocks obtained in Angola by Professor J. AY. Gregory. By G. AY. Tyrrell, A.R.C.S. (c) On some Cretaceous Shells from Angola, Portuguese AA^est Africa. By R. B. Newton. {d) On some Cretaceous Echinoidea from the north of Lobito Bay. By Professor J. AY. Gregory, F.R.S. {e) On some Cephalopoda from Benguella. By G. C. Crick. if) Notes on an Algal Limestone of Angola. By Mrs Margaret F. Romanes. 2 On the Zeolites and Associated Minerals from the Tertiary Lavas around Ben More, Mull. By AAL F. P. M’Lintock, B.Sc. Communicated by Dr J. S. Flett, F.R.S. 3, A See-saw of Barometric Pressure between the AYeddell Sea and the Ross Sea. By R. C. Mossman. 4. The Magnetic Quality of Iron and Steel as affected by Transverse Pressure. By AA^. J. AYalker, B.Sc. Communicated by Professor AY. Peddie, 5 {a) Chalk Boulders from Aberdeen and Fragments of Chalk from the Sea Floor off the Scottish Coast; (&) Notes on the Structure of the Chalk occurring in the Y^est of Scotland. By the late William Hill, Communicated by Professor D’Arcy Thompson. 6. Sponges collected by the Scotia in the Antarctic. Supplementary Note. By Professor E. Topsent. Communicated by Dr W. S. Bruoe. 7. On the Fossil Plants of the Forest of Wyre and Titterston Clee Hills Coalfields. By Dr R. Kidston, F R.S. WTth Remarks on the Geology of the Coalfields by T. C. Cantrill, B.Sc., F. G.S. , and E. Dixon, F.G.S. 1914-15.] Meetings of the Society. 339 THIRTEENTH ORDINARY MEETING. Monday, July 5, 1915. Sir Edward Schafer, LL.D, , F.R.S., Vice-President, in the Chair. The Makdougall-Brisbane Prize Award for the biennial period 1912/13-1913/14. The Council of the Royal Society of Edinburgh have awarded the Makdougall-Brisbane Prize to Professor C. R. Marshall for his studies “On the Pharmacological Action of Tetra-alkyl- ammonium Compounds,” The Prize was presented. The following Communications were read : — 1. Obituary Notice of Sir John Murray. By Professor Graham Kerr, F.R.S. 2. A Contribution to the Craniology of the People of Scotland. Part II. : Prehistoric, Descriptive and Ethnographical. By Sir William Turner, K.C.B., F.R.S. , F.Soc. Ant. Scot. 3. Mallophaga and Ixodidse, Ectoparasites of Birds, from the Scotia Collections (S. N.A.E.). By William Evans, F.F.A. 4. Mathematical Theory of the Harmonic Synthetiser. Part II. By J. R. Milne, D.Sc. ( With Lantern Illustrations.) 5. The Interaction of Methylene Iodide and Silver Nitrate. By Professor C. R, Marshall and Miss Elizabeth Gilchrist, M.A., B.Sc. 6. The Structure and Life History of Braeon hijlohii, a Study in Parasitism. By James W. Munro, B.Sc. Communicated by Dr R. Stewart MacDougall. 7. Lateral Sense Organs of Elasmobranchs, By Augusta Lamont, B.Sc, Communicated by Professor J. C. Ewart. The following Candidate for Fellowship was balloted for, and declared duly elected : — Frederick William Price, M.D., M.R.C.P. Edin., Physician to the Great Northern Hospital, London, 133 Harley Street, London, W. 340 Proceedings of the Royal Society of Edinburgh. [Sess. PROCEEDINGS OF THE STATUTORY GENERAL MEETING, Ending the 132nd Session, 1914-1915. At the Annual Statutory Meeting of the Royal Society of Edinburgh, held in the Society’s Lecture Room, 24 George Street, on Monday, October 25, 1915, at 4.30 p.m. , Professor Hudson Beare, Vice-President, in the Chair, the Minutes of the last Statutory Meeting, October 26, 1914, were read, approved, and signed. The Chairman nominated as Scrutineers of the Voting Papers Professor James Mackinnon and Dr J. G. Gray. The ballot for the Election of Office-Bearers and Members of Council was then taken. The General Secretary announced that Mr G. A. Stewart, Librarian, and Mr W. J. Beaton, Assistant Librarian, were still on service, and that the Council had appointed Miss M. Le Harivel as Temporary Assistant Librarian. In submitting his accounts for the year the Treasurer drew attention to the exceptional conditions under which the Council of the Society had carried on their work and to the manner in which these had influenced the Financial Report. Four hundred pounds of the Society’s funds had been invested in the 4| per cent. War Loan, distributed as follows : — Neill Fund ........ £15 Makdougall-Brisbane Fund ...... 150 Makerstoim Magnetic Meteorological Observation Fund . . 220 Gunning Victoria Jubilee Prize Fund . . . . .15 Professor Crichton MiTCHEr.L moved the adoption of the Treasurer’s Report, and also votes of thanks to the Treasurer and to the Auditors, who were to be reappointed. Dr Knoti' moved and Dr Horne seconded the following changes of Rule, which had been announced at the Ordinary Meeting of July 5 and the Special Meeting of June 28 : — Rule IX. Each candidate for admission as an Ordinary Fellow shall be proposed and recommended by at least four Ordinary Fellows, two of whom shall certify their recommendation from personal knowledge. This recommendation shall be delivered to the Secretary before the 24th of December of each Session, and, subject to the approval of the Council, shall be exhibited publicly in the Society’s Rooms during the succeeding month of January. All recommendations so exhibited shall be considered by the Council at its first meeting in the month of February, and a list of those approved by the Council for Election shall be issued to the Fellows not later than the 14th of February. Rule X. The Recommendation of a Candidate for admission as an Ordinary Fellow shall be in the following terms : — A. B., a gentleman well versed in Science (or Polite Literature, as the case may be), being to our knowledge desirious 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 Fellow. Rule XI. The Election of Ordinary Fellows shall take place at the first Ordinary Meeting of the Society in March of each Session, and only those candidates approved by the Council shall be eligible. Those candidates, and only those, whose election is supported by a majority of two-thirds of those voting shall be deemed elected. These alterations loill necessitate the rearranging and renumbering of the succeeding Rules. These were agreed to unanimously. The Scrutineers reported that the following Council had been duly elected : — John Horne, LL.D. , F.R.S., F.G.S., President. Professor F. 0. Bower, M.A., D.Sc., F.R.S., Professor Sir Thomas R. Fraser, M.D., LL.D., FRCPE FRS Benjamin N. Peach, LL.D., F.R.S., F.G.S. , Professor Sir E. A. Schafer, M.R.C.S., LL.D., F.R.S., The Right Hon. Sir J. H. A. Macdonald, K.C. B., LL.D., D.L., F.R.S., M.I.E.E., Professor R. A. Sampson, M.A., D.Sc., F.R.S. , > Vice-Presidents. 341 1914-15.] Meetings of the Society. Cargill G. Knott, D.Sc., General Secretary. Robkrt Kidston, LL.D. , F. R.S., F.G.S., ) Secretaries to Ordinary Professor Arthur Robinson, M.D., M.R.C.S., [ Meetings. James Currie, M.A., Treasurer. John S. Black, M.A., LL.D., Curator of Library and Museum. ORDINARY MEMBERS OF COUNCIL. Principal A. P. Laurie, M.A., D.Sc. Professor J. Graham Kerr, M.A., F.R.S. Leonard Dobbin, Ph.D. Ernest Maclagan Wedderburn, M.A., LL.B., D.Sc. W. B. Blaikie, LL.D. Principal 0. C. Bradley, M.D., D.Sc. Society’s Representative on \ George Heriot’s Trust, J R. Stewart MacDougall, M.A., D.Sc. W. A. Tait, D.Sc., M.lnst.C.E. J. H. Ashworth, D.Sc. Professor C. G. Barkla, D.Sc., F.R.S. Professor C. R. Marshall, M.A., M.D. Principal A. Crichton Mitchell, D.Sc., Hon. D.Sc. (Geneva). Allan Carter, M.lnst.C.E. Principal Sir William Turner, K.C.B., D.C.L., F.R.S., former President, is a permanent Member of Council. On the motion of Dr J. S. Black, thanks were voted to the Scrutineers. 342 Proceedings of the Royal Society of Edinburgh. [Sess. ABSTRACT V OF THE ACCOUNTS OF JAMES CURRIE, ESQ. As Treasurer of the Royal Society of Edinburgh, SESSION 1914-1915. I. ACCOUNT OF THE GENERAL FUND. CHARGE. 1. Arrears of Contributions at 1st October 1914 as adjusted . 2, Contributions for present Session ; — 1. 151 Fellows at £2, 2s, each . . . . . 120 Fellows at £3, 3s. each ..... Less — Subscriptions for present Session, included in 1914 Accounts as adjusted .... 2. Fees of Admission and Contributions of eight new Resident Fellows at £5, 5s. each ..... 3. Fees of Admission of five new Non-Resident Fellows at £26, 5s. each ........ 3. Contributions for 1915-1916 paid in advance . . . . 4. Interest received — Interest, less Tax £35, 14s. 3 Ad. . . . . . Annuity from Edinburgh and District Water Trust, less Tax £6, Os. 3d. . 5. Transactions and Proceedings sold ...... 6. Annual Grant from Government, , . . . . 7. Income Tax repaid for year to 5th April 1915 . . . . Amount of the Charge . £123 18 0 £317 2 0 378 0 0 £695 2 0 4 4 0 £690 1» 0 42 0 0 131 5 0 864 3 0 4 4 0 £356 12 2 46 9 9 403 1 11 109 13 9 600 0 0 29 4 2 £2134 4 10 DISCHARGE. 1. Taxes, Insurance, Coal and Lighting : — Inhabited House Duty . Insurance Coal, etc., to 14th September 1915 Gas to 10th May 1915 . Electric Light to 1st May 1915 Water 1914-15 .... £43 9 10^ 9 4 7 25 2 6 0 3 6 4 9 Oi 4 4 0 Carry forward £43 9 101 1914-15.] Abstract of Accounts. 343 2. Salahies : — General Secretary, 1913-14 Do. due for 1914-15 Librarian Assistant Librarian Interim Assistant Librarian Office Keeper Treasurer’s Clerk . Brought forward 3. Expenses of Transactions ; — Neill & Co. , Ltd., Printers . . . . . . . Do. Estimated amount due for Printing not delivered .... Do. (for illustrations) .... M'Farlane k Erskine, Lithographers .... Hislop k Day, Engravers . . .... John Fowler & Co., Engravers ...... Xote. — A consideral)le amount of Printing- and Binding of Trans- actions has been postponed, and will form a charge against next year’s Accounts. 4. Expenses of Proceedings : — Neill & Co., Ltd., Printers ....... Do. Estimated amount due for Printing not delivered .... Hislop k Day, Engravers ....... M‘Farlane k Erskine, Lithographers ..... 5. Books, Periodicals, Newspapers, etc. : — Otto Schulze & Co., Booksellers ...... James Thin, do. ...... R. Grant & Son, do. ...... AV. Green k Son, Ltd., do. ...... International Catalogue of Scientific Literature Robertson k Scott, News Agents ...... Egypt Exploration Funds Subscription ..... Ray Society do. ..... Palseontographical Society do. ..... Arthur F. Bird, Bookseller ....... C. Griffin & Co., Ltd. ........ 6. Other Payments : — Neill & Co. , Ltd., Printers ....... E. Sawers, Purveyor ........ S. Duncan, Tailor (uniforms) ..... Roneo, Limited ......... Lantern Exhibitions, etc., at Lectures . . . . . Lindsay, Jamieson & Haldane, C. A., Auditors Post Office Telephone Rent ....... A. Cowan k Sons, Ltd. ........ G. AVaterston k Sons, Ltd. ....... Gillies k AVright, Joiners ....... R. Graham, Slater ...... Subscription to Poincare Memorial ..... Petty Expenses, Postages, Carriage, etc. ..... 7. Interest Paid on Borrowed Money : — Makerstoun Magnetic Meteorological Observation Fund Makdougall-Brisbane Fund . . . . . . . 8. Irrecoverable Arrears of Contributions written off 9. Arrears of Contributions outstanding at 1st October 1915 ; — Present Session ......... Previous Sessions ......... £100 0 0 100 0 0 120 0 0 50 0 0 45 10 0 89 19 0 25 0 0 £166 8 11 255 0 0 5 19 0 18 0 0 41 8 9 5 19 9 £225 5 10 120 0 0 22 1 11 28 17 6 £44 4 5 48 18 3 7 6 4 1 8 6 17 0 0 3 5 0 4 4 0 1 1 0 1 1 0 2 5 6 0 6 4 £65 3 0 26 3 4 4 14 0 29 10 0 10 5 0 6 6 0 10 0 0 5 14 9 6 7 7 32 6 4 6 11 2 I 1 0 79 16 IP £3 10 2 10 0 0 £77 14 0 39 18 0 £43 9 lOi 530 9 0 492 16 5 396 5 3 131 0 4 283 1 9 1 13 10 2 40 19 0 117 12 0 Amount of the Discharge . £2050 1 2 lOH 344 Proceedings of the Royal Society of Edinburgh. [Sess. Amount of the Charge Amount of the Discharge Excess of Receipts over Payments for 1914-1915 . Floatin(; Balance in favour of the Society at 1st October 1914 £2134 4 10 2050 1 2 £84 3 8 22 12 11 Floating Balance in favour of the Society at 1st October 1915 Being — Balance due by Union Bank of Scotland, Ltd,, on Account Current Deduct Loan from the Makerstoun Magnetic Observation Fund ... .... £5 12 Estimated amount due to Neill & Co., Ltd., for printing not delivered .... 375 0 Due to General Secretary . . . . 100 0 Due to Treasurer . . . . . . 37 18 . £106 16 7 £625 6 11 4 0 0 0 — 518 10 4 £106 16 7 II. ACCOUNT OF THE KEITH FUND To Is^ October 1915. CHARGE. 1. Balance due by Union Bank of Scotland, Ltd., on Account Current at 1st October 1914 ............ 2. Interesi' Received On £896, 19s. Id. North British Railway Company 3 per cent. Debenture Stock for year to Whitsunday 1915, less Tax £2, 8s. 3d. . . . _ £24 9 11 On £211, 4s. North British Railway Company 3 per cent. Lien Stock for year to 30th June 1915, less Tax 12s. 4d. . . 5 14 4 3. Income Tax repaid for year to 5th April 1915 DISCHARGE. 1. Balance due by Union Bank of Scotland, Ltd., on Account Current at 1st October 1915 ............ £29 15 6 30 4 3 2 2 6 £62 2 3 £62 2 3 III. ACCOUNT OF THE NEILL FUND To 1st October 1915. CHARGE. 1. Balance due by Union Bank of Scotland, Ltd., on Account Current at 1st October 1914 £33 2 10 2. Interest Received : — On £355 London, Chatham and Dover Railway 4| per cent. Arbitration Debenture Stock for year to 30th June 1915, less Tax £1, 11s. 4d. . . 14 8 2 3. Income Tax repaid for year to 5th April 1915 ....... 148 £48 15 8 DISCHARGE. 1. Investment made : — Purchase Price of £15 four and a half per cent. War Loan, 1925-45 . . . £14 18 5 2. Balance due by Union Bank of Scotland, Ltd., on Account Current at 1st October 1915 33 17 3 £48 15 8 1914-15.] Abstract of Accounts. 345 IV. ACCOUNT OF THE MAKDOUGALL-BRISBANE FUND To 1st October 1915. CHARGE. 1. Balance due by Union Bank of Scotland, Ltd., on Account Current at 1st October 1914 £180 10 9 2. Interest Received : — On £365 Caledonian Railway Company 4 per cent. Consolidated Preference Stock No. 2 for year to 30th June 1915, less Tax£l,8s. 8d £13 3 4 On Daily Balances to 1st October 1914 at Deposit Receipt Rates (transferred from General Fund) . . . . . 10 0 0 23 3 4 3. Income Tax repaid for year to 5th April 1915 ....... 125 £204 16 6 DISCHARGE. 1. Professor C. R. Marshall — Money Portion of Prize 1912-14 .... £14 0 0 2. Alexander Kirkwood & Son, Engravers, for Gold Medal . . . . . 16 0 0 3. Investment made Purchase price of £150 four and a half per cent. AVar Loan, 1925-45 . . 149 4 0 4. Balance due by Union Bank of Scotland, Ltd., on Account Cunent at 1st October 1915 ............ 25 12 6 £204 16 6 V. ACCOUNT OF THE MAKERSTOUN MAGNETIC METEOROLOGICAL OBSERVATION FUND To \st October CHARGE. 1. Balance due by General Fund at 1st October 1914 ...... £220 18 8 2. Interest received on Balances due by General Fund at Deposit Receipt Rates to 1st October 1915 ........... 3 10 2 £224 8 10 DISCHARGE. ‘ 1. Investment made : — Purchase price of £220 four and a half per cent. AYar Loan, 1925-45 , . £218 16 6 2. Balance due by General Fund at 1st October 1915 . . . . . . 5 12 4 £•224 8 10 VI. ACCOUNT OF THE GUNNING VICTORIA JUBILEE PRIZE FUND To 1st October 1915. (Instituted by Dr R. H. Gunning of Edinburgh and Rio de Janeiro.) CHARGE. 1. Balance due by Union Bank of Scotland, Ltd., on Account Current at 1st October 1914 £71 14 2 2. Interest received on £1000 North British Railway Company 3 per cent. Consolidated Lien Stock for year to 30th June 1915, less Tax £2, 18s. 4d, . 27 1 8 3. Income Tax repaid for year to 5th April 1915 ....... 261 £101 1 11 346 Proceedings of the Royal Society of Edinburgh. [Sess. DISCHARGE. 1. Investment made : — Purchase price of £15 four and a half per cent. War Loan, 1925-45 . . . £14 18 4 2. Balance due by Union Bank of Scotland, Ltd., on Account Current at 1st October 1915 ............. 86 3 7 £101 1 11 VII. DR F. R. C. REED’S MEMOIR ON THE BRACHIOPODA OF THE ORDOVICIAN AND SILURIAN ROCKS OF GIRVAN To 1st October 1915. CHARGE. 1. SuBSCEiPTiONs Received : — Mrs Gray ............ £50 0 0 Laurence Pullar, Esq. ........... 50 0 0 Royal Society, London . . . . . . . . 100 0 0 £200 0 0 2. Inteeest Received : — On Deposit Receipts by the Union Bank of Scotland, Ltd., uplifted . . 3 5 4 £203 5 4 DISCHARGE. 1. T. A. Brock, Cambridge, for Drawings (to account) ...... £42 10 6 2. Balance due by the Union Bank of Scotland, Ltd., on Deposit Receipt at 1st October 191.5 ............ 160 14 10 £203 5 4 STATE OF THE FUNDS BELONGING TO THE ROYAL SOCIETY OF EDINBURGH As at 1st October 1915. 1. GENERAL FUND— 1. £2090, 9s. 4d. three per cent. Lien Stock of the North British Railway Company at 7 li per cent. ......... £1494 13 8 2. £8519, 14s. 3d. three per cent. Debenture Stock of do. at 71^ per cent. . 6091 11 11 3. £52, 10s. Annuity of the Edinburgh and District Water Trust, equivalent to £875 at 135 per cent. ......... 1181 5 0 4. £1811 four per cent. Debenture Stock of the Caledonian Railway Company at 98 per cent. ........... 1774 15 7 5. £35 four and a half per cent. Arbitration Debenture Stock of the London, Chatham and DoVer Railway Company at 102| per cent. . . . 35 19 3 6. Arrears of Contributions, as per preceding Abstract of Accounts . . . 117 12 0 £10,695 17 5 Add Floating Balance in favour of the Society, as per preceding Abstract of Accounts ........... 106 16 7 Amount . . £10,802 14 0 Exclusive of Library, Museum, Pictures, etc.. Furniture of the Society’s Rooms at George Street, Edinburgh. 2. KEITH FUND— 1. £896, 19s. Id. three per cent. Debenture Stock of the North British Railway Company at 71| per cent. . . . . . . .£64165 2. £211, 4s. three per cent. Lien Stock of do. at 71^ per cent. . . . 151 0 2 3. Balance due by Union Bank of Scotland, Ltd. , on Account Current . . 62 2 3 £854 8 10 Amount 1914-15.] Abstract of Accounts. 347 3. NEILL FUND— 1. £355 four and a half percent. Arbitration Debenture Stock of the London, Chatham and Dover Railway Company at 102| per cent. . . . £364 15 3 2. £15 four and a half per cent. War Loan, 1925-45, at 97f per cent. . . 14 13 3 3. Balance due by Union Bank of Scotland, Ltd., on Account Current . . 33 17 3 Amount . . . £413 5 9 4. MAKDOUGALL-BRISBANE fund— 1. £365 four per cent. Consolidated Preference Stock No. 2 of the Caledonian Railway Company at 92 per cent. ........ £335 16 0 2. £150 four and a half per cent. War Loan, 1925-45, at 97f per cent. . . 146 12 6 3. Balance due by Union Bank of Scotland, Ltd., on Account Current . . 25 12 6 Amount . . . £508 1 0 5. MAKERSTOUN MAGNETIC METEOROLOGICAL OBSERVATION FUND— 1. £220 four and a half per cent. War Loan, 1925-45, at 97f ]»er cent. . . £215 1 0 2. Balance due by General Fund at 1st October 1915 . . . . . 5 12 4 Amount . . . £220 13 4 6. GUNNING VICTORIA JUBILEE PRIZE FUND— Instituted by Dr Gunning of Edinburgh and Rio de Janeiro — 1. £1000 three per cent. Consolidated Lien Stock of the North British Railway Company at 71^ per cent. ......... £715 0 0 2. £15 four and a half per cent. War Loan, 1925-45, at 97f per cent. . . 14 13 3 3. Balance due by Union Bank of Scotland, Ltd., on Account Current . . 86 3 7 Amount . . . £815 16 10 7. DR F. R. C. REED’S MEMOIR ON THE BRACHIOPODA OF THE ORDOVICIAN AND SILURIAN ROCKS OF GIRVAN— Balance due by Union Bank of Scotland, Ltd., on Deposit Recei[)t . . £160 14 10 Edinburgh, \Qth October 1915. — We have examined the seven preceding Accounts of the Treasurer of the Royal Society of Edinburgh for the Session 1914-1915, and have found them to be correct. The securities of the various Investments at 1st October 1915, as noted in the above Statement of Funds, with the exception of the four and a half per cent. Wai' Loan, 1925-45, have been exhibited to us. LINDSAY, JAMIESON A HALDANE, C.A., A uditors. 348 Proceedings of the Royal Society of Edinburgh. THE COUNCIL OF THE SOCIETY. January 1916. President. JOHN HORNE, LL.D.. F.R.S., F.G.S. Vice-Presidents. FREDERICK 0. BOWER, M.A. , D.Sc., F.R.S., Regius Professor of Botany in the University of Glasgow. Sir THOMAS R. FRASER, M.D., LL.D., Sc.D., F.R.G.P.E., F.R.S., Proiessor of Materia Medica in the University of Edinburgh. BENJAMIN N. PEACH, LL.D., F. R.S., F.G.S., formerly District Superintendent and Acting Palaeontologist of the Geological Survey of Scotland. Sir albert EDWARD SCHAFER, M.R.C.S., LL.D., F.R.S., Professor of Physiology in the University of Edinburgh. The Right Hon. Sir J. H. A. MACDONALD, P.C., K.C., K.O.B., F.R.S., M.Inst.E.E. Professor R. A. SAMPSON, M.A., D.Sc., F.R. S. , Astronomer Royal for Scotland. General Secretary. CARGILL G. KNOTT, D.Sc., Lecturer on Applied Mathematics in the University of Edinburgh. Secretaries to Ordinary Meetings. ROBERT KIDSTON, LL.D., F.R.S., F.G.S. ARTHUR ROBINSON, M.D., M.R.C.S., Professor of Anatomy in the University of Edinburgh. Treasurer. JAMES CURRIE, M.A. Curator of Library and Museum. JOHN SUTHERLAND BLACK, M.A., LL.D. Councillors. A. P. LAURIE, M. A., D.Sc. , Principal of the Heriot-Watt College, Edinburgh. JOHN GRAHAM KERR, M.A., F.R.S., Pro- fessor of Zoology in the University of Glasgow. LEONARD DOBBIN, Ph.D., Lecturer on Chemistry in the University of Edin- burgh. ERNEST MacLAGAN WEDDERBURN, M.A., LL.B., W.S., D.Sc. W. B. BLAIKIE, LL.D. 0. CHARNOCK BRADLEY, M.D., D.Sc., M.R.C. V. S. , Principal of the Royal (Dick) Veterinary College, Edinburgh. R. STEWART MacDOUGALL, M.A., D.Sc., Lecturer on Agricultural Entomology in the University of Edinburgh. W. A. TAIT, D.Sc., M.Inst.C.E. J. H. ASHWORTH, D.Sc., Lecturer on In- vertebrate Zoology in the University of Edinburgh. C. G. BARKLA, D.Sc., F.R.S., Professor of Natural Philosophy in the University of Edinburgh. 0. R. MARSHALL, M.A. , M.D., Professor of Materia Medica and Theurapeutics in the Medical School, Dundee. A. CRICHTON MITCHELL, D.Sc., Hon. D.Sc. (Geneva), formerly Director of Public In- struction in Travancore, India. Principal Sir WILLIAM TURNER, K.C.B., D.C.L., F.R.S., former President, is a permanent Member of Council. Society’s Representative on George Heriot’s Trust. WILLIAM ALLAN CARTER, M.Inst.C.E. Office, Library, etc., 22, 24 George Street, Edinburgh. Tel. No., 2881. Alphabetical List of the Ordinary Fellows of the Society. 349 Date uf Election. 1898 1898 1911 1896 1871 1875 1895 1889 1894 1888 1906 1883 1905 1903 1905 1881 1915 1906 1899 1893 1910 1907 ALPHABETICAL LIST OF THE ORDINARY FELLOWS OF THE SOCIETY, Corrected to January 1, 1916. N.B. — Those marked * are Annual Contributors. B. prefixed to a name indicates that the Fellow has received a Makdougall -Brisbane Medal. K. ,, ,, ,, Keith Medal. N. ,, ,, ,, Neill Medal. V. J. ,, ,, ,, the Gunning Victoria Jubilee Prize. C. ,, , ,, contributed one or more Communications to the Society’s Transactions or Proceedings. C. C. K. V. J. C. c. * Abercromby, the Hon. John, LL.D., 62 Palmerston Place, Edinburgh Adami, Prof. J, G. , M.A., M.D. Cantab., F.R.S. , Professor of Pathology in M‘Gill University, Montreal * Adams, Archibald Campbell, A.M.Inst.Mech.E., A.M.Inst.E.E., Consulting Engineer, 1 Old Smithhills, Paisley * Affleck, Sir Jas. Ormiston, M.D., LL.D., F.R.C.P.E., 38 Heriot Row, Edinburgh Agnew, Sir Stair, K.C.B., M.A., formerly Registrar - General for Scotland, f 22 Buckingham Terrace, Edinburgh 5"i Aitken, John, LL.D., F.R.S,, Ardenlea, Falkirk * Alford, Robert Gervase, M.Inst. C.E., Three Gables, Woodburn Park Road, Tun- bridge Wells, Kent Alison, John, M.A., Head Master, George Watson’s College, Edinburgh Allan, Francis John, M.D., C.M. Edin. , M.O.H. City of Westminster, West- minster City Hall, Charing Cross Road, London Allardice, R. E., M.A., Professor of Mathematics in Stanford University, Palo Alto, Santa Clara Co., California 10 Anderson, Daniel E., M.D., B.A., B.Sc., Green Bank, Merton Lane, Highgate, London, N. Anderson, Sir Robert Rowand, LL.D., 16 Rutland Square, Edinburgh * Anderson, William, M.A. , Head Science Master, George Watson’s College, Edin- burgh, 29 Lutton Place, Edinburgh Anderson-Berry, David, M.D., LL.D., F.R.S. L., M.R.A.S., F.S.A. (Scot.), Versailles, Highgate, London, N. * Andrew, George, M.A. , B.A., H.M.I.S. , Balwherrie, Strathearn Road, Brough ty Ferry 1 5 Anglin, A. H., M.A., LL.D., M.R. I.A., Professor of Mathematics, Queen’s College, Cork Anthony, Charles, M.Inst.C.E., M. Am. Soc. C.E., F.R.San.L, F.R.A.S., F.KMet.S., F.R.M.S., F.C.S., General Manager Water Works Company, Casilla de Correo 149, Bahia Blanca, Argentina Appleton, Colonel Arthur Frederick, F.R.C.V.S., Nylstroom, Smoke Lane, Reigate Appleyard, Janies R., Royal Technical Institute, Salford, Manchester Archer, Walter E., Union Club, Trafalgar Square, London, S.W. 20 Archibald, E. H., B.Sc., Professor of Chemistry, University of British Columbia, Vancouver, Canada * Archibald, James, M.A., Head Master, St Bernard’s School, 1 Leamington Terrace, : Edinburgh Semce on Council, etc. 1882-85, 1886-89, 1891-93, 1895-98. 350 Date of Election. 1911 1907 1896 1877 1905 1892 1902 1889 1886 1883 1903 191-J 1882 1904 1874 1887 1895 1904 1913 1888 1897 1892 1893 1882 1887 1906 1915 i 1900 ! 1887 1893 1897 1904 1880 1907 1884 1897 1904 1898 1894 Proceedings of the Royal Society of Edinburgh. * Ashworth, James Hartley, D.Sc. , Lecturer on Invertebrate Zoology, University of Edinburgh, 4 Cluny Ten-ace, Edinburgh Badre, Muhammad, Ph.D, , Almuneerah, Cairo, Egypt * Baily, Francis Gibson. M.A., M.Inst.E.E., Professor of Electrical Engineering, Heriot-Watt College, Edinburgh, Newbury, Colinton, Midlothian 25 Balfour, I. Bay ley, M.A., Sc.D., M.D., LL.D., F.R.S., F.L.S., King’s Botanist in Scotland, Professor of Botany in the University of Edinburgh and Keeper of the Royal Botanic Garden, Inverleith House, Edinburgh Balfour-Browne, William Alexander Francis, M.A. , Barrister-at-Law, 26 Barton Road, Cambridge * Ballantyne, J. AV., M.D., F.R.C.P.E., 19 Rothesay Terrace, Edinburgh Bannerman, AV. B., C.S.I., I.M.S., M.D,, D.Sc., Surgeon General, Indian Medical Service, Aladras, India Barbour, A. H. F., M.A., M.D., LL.D., F.R.C.P.E., 4 Charlotte Square, Edinburgh 30 Barclay, A. J. Gunion, M.A., 729 Great A\^estern Road, Glasgow Barclay, G. AV. W., IM.A., Raeden House, Aberdeen Bardswell, Noel Dean, ALD., M.R.C.P. Ed. and Lond., King Edward VII. Sana- torium, Alidhurst * Barlda, Charles Glover, D.Sc., F.R.S. , Professor of Natural Philosophy in the University of Edinburgh, Littledene, 34 Priestfield Road, Edinburgh Barnes, Henry, AI. D., LL.D., 6 Portland Square, Carlisle 35 Barr, Sir James, AI.D., LL.D., F.R.C. P. Lond., 72 Rodney Street, Liverpool Barrett, Sir William F., F.R.S., AI.R. LA., formerly Professor of Physics, Royal College of Science, Dublin, 6 De Vesci Terrace, Kingstown, County Dublin Bartholomew, J. G., LL.D., F.R. G.S., The Geographical Institute, Duncan Street, Edinburgh Barton, Edwin H., D.Sc., A. AI.Inst.E.E., F.P.S.L., Professor of Experimental Physics, University College, Nottingham * Baxter, William Aluirhead, Glenalmond, Sciennes Gardens, Edinburgh 40 Beard, Joseph, F.R.C.S. (Edin.), M.R.C.S. (Eng.), L.R.C.P. (Lond.), D.P.H. (Camb.), Aledical Officer of Health and School Aledical Officer, City of Carlisle, 15 Brunswick Street, Carlisle Beare, Thomas Hudson, B.Sc., AI.Inst.C.E., Professor of Engineering in the \ University of Edinburgh (V’ice-President) j * Beattie, John Carruthers, D.Sc., Professor of Physics, South African College, Cape Town Beck, Sir J. H. Aleiting, Kt., AI.D., AI.R.C.P. E. , Drostdy, Tulbagh, Cape Province, South Africa ^''Becker, Ludwig, Ph.D., Regius Professor of Astronomy in the University of Glasgow, The Observatory, Glasgow 45 Beddard, Frank E., ALA. Oxon., F.R.S. , Prosector to the Zoological Society of London, Zoological Society’s Gardens, Regent’s Park, London Begg, Ferdinand Faithfull, 5 AVhittington Avenue, London, E.C. Bell, John Patrick Fair, F.Z.S., Fulforth, AA^itton Gilbert, Durham Bell, Walter Leonard, AI.D. Edin., F.S.A. Scot., 123 London Road, North Lowestoft, Suffolk * Bennett, James Bower, C.E. , 5 Hill Street, Edinburgh 50 Bernard, J. Alackay, ofDunsinnan, B.Sc., Dunsinnan, Perth * Berry, George A., AI.D., C.AL, F.R.C.S., 31 Drumsheugh Gardens, Edinburgh Berry, Richard J. A., AI.D., F.R.C.S.E., Professor of Anatomy in the University of Alelbourne, Victoria, Australia * Beveridge, Erskine, LL.D., St Leonards Hill, Dunfermline j Birch, De Burgh, C.B., AI.D., Professor of Physiology in the University of Leeds, 8 Osborne Terrace, Leeds 55 [ * Black, Frederick Alexander, Solicitor, 59 Academy Street, Inverness | Black, JohnS., ALA., LL.D. (Curator of Library and AIuseum), 6 Oxford I | Terrace, Edinburgh j * Blaikie, AValter Biggar, LL.D., The Loan, Colinton * Bles, Edward J., AI.A., D.Sc., Elterholm, Cambridge Blyth, Benjamin Hall, AI.A., V.P.Inst.C. E., 17 Palmerston Place, Edin- burgh 60 * Bolton, Herbert, AI.Sc., F.G.S., F.Z.S., Director of the Bristol AIuseum and Art Gallery, Bristol ‘ Service on Council, etc. 1912-14, 1915- 1909-12. 1888-91. 1909-12. 1907-1909. V-P 1909-1915. 1891-94. Cur. 1906- 1914- Alphabetical List of the Ordinary Fellov/s of the Society. 351 Date ol' I Klection. ' 1915 1872 C. 1886 1884 1901 1903 1886 1907 1912 1895 C. C, 1893 1901 1907 C. 1864 C. K. B. 1913 1898 1911 1883 1885 1909 1912 1906 1898 1870 1905 1902 1894 C. C. c. B. 0. C. N. K. G. C. K. C. K. 1887 1888 1915 * Boon, Alfred Archibald, D.Sc. , Assistant Professor of Chemistry, Heriot-Watt College, Edinburgh Bottomley, J. Thomson, M.A., D.Sc., LL. D., F.R.S., F. C.S., 13 University Gardens, Glasgow Bower, Frederick 0,, M.A,, D.Sc., F.R.S., F.L.S., Regius Professor of Botany I in the University of Glasgow, 1 St John’s Terrace, Hillhead, Glasgow J (Vice-President) j Bowman, Frederick Hungerford, D.Sc., F.C.S. (bond, and Berk), F.I.C., A.Inst.C.E., A.Inst.M.E., M.Inst.E.F., etc., 4 Albert Square, Manchester 65 Bradbury, J. B., M.D., Downing Professor of Medicine, University of Cambridge * Bradley, 0. Charnock, M.D. , D.Sc., Principal, Royal Dick Veterinary College, Edinburgh Braniwell, Byrom, M.D., F. R.C.P.E., LL.D., 23 Drumsheugh Gardens, Edin- burgh Bramwell, Edwin, M.B., F. R. C.P, E., F.R.C. P. Bond., 24 Walker Street, Edin- burgh Bridger, Adolphus Edward, M.D. (Edin.), F.R.C.P. (Edin.), B.Sc. (Paris), B. L. (Paris), Foley Lodge, Langham Street, London, W. 70 Bright, Charles, M.lnst.C.K, M.Inst.E.E., F.R.A.S., F.G.S., Consulting Engineer to the Commonwealth of Australia, The Grange, Leigh, Kent, and Members’ Mansions, Victoria Street, London, S.AV. Brock, G. Sandison, M.D., 6 Corso d’ltalia, Rome, Italy * Brodie, AV. Brodie, M.B., Thaxted, DunmoAv, Essex Brown, Alexander, M.A., B.Sc., Professor of Applied Mathematics, South African College, Cape Town Brown, Alex. Crum, M.A. , M.D., D.Sc., F.R.C. P.E., LL.D., F.R.S. , Emeritus Professor of Chemistry in the University of Edinburgh, 8 Belgrave Crescent,- Edinburgh 75 * Brown, Alexander Russell, M.A., B.Sc., Lieut. 8th K.O.S.B., Viewhill, Long- riggend, Lanarkshire * Brown, David, F.C.S., F.I.C., J.P., AVillowbrae House, A^^illowbrae Road, j Edinburgh I * Brown, David Rainy, Chemical Manufacturer (J. F. Macfarlan & Co.), I 93 Abbeyhill, Edinburgh I Brown, J. J. Graham, M.D., F.R.C. P.E., 3 Chester Street, Edinburgh Brown, J. Macdonald, M.D., F.R.C.S., 64 Upper Berkeley Street, Portman Square, London, AV. 80 * Brownlee, John, M.A., M.D., D.Sc., Medical Research Committee, Statistical j Department, 34 Guildford Street, Russell Square, London, AA^.C. * Bruce, Alexander ISTinian, D.Sc., M.D. , 8 Ainslie Place, Edinburgh j * Bruce, AVilliam Speirs, LL.D., Director of the Scottish Oceanographical Laboratory, Edinburgh, Antarctica, Joppa, Midlothian * Bryce, T. H., M.A., M.D, (Edin.), Professor of Anatomy in the University of Glasgow, 2 The University, Glasgow Buchanan, John ’Voung, M.A., F.R.S. , 26 ISTorfolk Street, Park Lane, London, AA^. 85 Bunting, Thomas Lowe, M.D., 27 Denton Road, Scotswood, Hewcastle-on-Tyne ■^Burgess, A. G., M.A., Mathematical Master, Edinburgh Ladies’ College, 64 Strathearn Road, Edinburgh * Burgess, James, C.I.E., LL.D., Hon. A.R.I.B.A., F.R.G.S., Hon. M. Imp. Russ. Archseoh Soc., and Amer. Or. Soc., M. Soc. Asiat. de Paris, M.R.A.S., H. Corr. M. Batavian Soc. of Arts and Sciences, and Berlin Soc. Anthrop., H. Assoc. Finno-Ugrian Soc., 22 Seton Place, Edinburgh Burnet, Sir John James, Architect, 18 University Avenue, Hillhead, Glasgow Burns, Rev. T., D.D., F.S.A. Scot., Minister of Lady Glenorchy’s Parish Church, Croston Lodge, Chalmers Crescent, Edinburgh 90 * Butchart, Raymond Keiller, B.Sc., University College, Dundee, 8 Martin Street, Mary field, Dundee Service on Council, etc. 1887-90, 1893-96, 1907-09. V-P 1910- 1907-10, 1915- 1890-93. 1865-68, 1869-72, 1873-75, 1876-78, 1911-13. Sec. 1879-1905 V-P 1905-11. 1909-12. 1911-14. 1878-81, 1884-86. 1895-98. 1899-1902, V-P 1908-14. 352 Date of Election.! 1896 1887 1910 1893 1894 1905 1904 1915 1899 1910 1905 1901 1905 1898 1898 1908 1882 1899 1912 1874 1891 1911 1903 1909 1913 1904 1904 1888 1904 1909 1886 1891 1905 1914 1911 1908 1875 1903 1887 Proceedings of the Eoyal Society of Edinburgh. c. c. c. a- c. c. c. ^ J c. c. * Butters, J. W. , M.A., B.Sc. , Rector of Ardrossan Academy Cadell, Henry Moubray, of Grange, B.Sc., Linlithgow * Calderwood, Rev. Robert Sibbald, Minister of Cambuslang, The Manse, Cambuslang, Lanarkshire Calderwood, W. L., Inspector of Salmon Fisheries of Scotland, South Bank, Canaan Lane, Edinburgh 95 * Cameron, James Angus, M. D., Medical Officer of Health, Firliall, Nairn Cameron, John, M. D. , D.Sc. , M.R. C. S. Eng., Dalhousie University, Halifax, Nova Scotia. * Campbell, Charles Duff, Scottish Liberal Club, Princes Street, Edinburgh * Campbell, Robert, D.Sc., Lecturer in Petrology, University of Edinburgh, 7 Muirend Avenue, Juniper Green, Midlothian * Carlier, Edmund W. W., M. D. , M.Sc., F.E.S., Professor of Physiology, University, Birmingham 100 Carnegie, David, M.Inst.C.E., M.Inst.Mech. E., M.I.S.Inst., 7 Victoria Street, London, S.W. Carse, George Alexander, M. A., D.Sc., Lecturer on Natural Philosophy, University of Edinburgh, 3 Middleby Street, Edinburgh Carslaw, H. S. , M.A., D.Sc., Professor of Mathematics hr the University of Sydney, NeAV South Wales Carter, Joseph Henry, F.R.C.V.S., Stone House, Church Street, Burnley, Lancashire * Carter, Win. Allan, M.Inst.C.E., 32 Great King Street, Edinburgh (Society’s Representative on George Heriot’s Trust) 105 Cams- Wilson, Cecil, F.R.G.S., F.G.S., Waldegrave Park, Strawberry Hill, Middlesex, and Sandacres Lodge, Parkstone-on-Sea, Dorset Cavanagh, Tliomas Francis, M.D., The Hospital, Bella Coola, B.C., Canada Cay, W. Dyce, M.Inst.C.E., 39 Victoria Street, Westminster, London Chatham, James, Actuary, 7 Belgrave Crescent, Edinburgh Chaudhuri, Banawari Lai, B.A.fCah), B.Sc. (Edin.), Assistant Superintendent, Natural History Section, Indian Museum, 120 Lower Circular Road, Calcutta, India 110 Chiene, John, C.B., M.D., LL.D., F.R.C.S.E., Emeritus Professor of Surgery in the University of Edinburgh, Barn ton Avenue, Davidson’s Mains Clark, John B., M.A., Head Master of Heriot’s Hospital School, Lauriston, Garleffin, Craiglea Drive, Edinburgh * Clark, William Inglis, D.Sc., 29 Lauder Eoad, Edinburgh Clarke, William Eagle, F.L.S., Keeper of the Natural History Collections in the Royal Scottish jfluseum, Edinburgh, 35 Braid Road, Edinburgh Clayton, Thomas Morrison, M.D. , D.Hy., B.Sc., D.P.H., Medical Officer of Health, Gateshead, 13 The Crescent, Gateshead-on-Tyne 115 * Cleghorn, Alexander, M.Inst.C.E., Marine Engineer, 14 Hatfield Drive, Kelvinside, Glasgow Coker, Ernest George, M.A., D.Sc., Professor of Mechanical Engineering and Applied Mechanics, University College, Gower Street, London, \V. C. Coles, Alfred Charles, M.D., D.Sc., York House, Poole Road, Bourne- mouth, AV. Collie, John Norman, Ph.D., D.Sc., LL.D., F.E.S., F.C.S., F.I.C., F.R.G.S., Professor of Organic Chemistry in the University College, Gower Street, London * Colquhoun, AA^alter, M.A. , M. B., 18 AA’’almer Crescent, Ibrox, Glasgow 120 * Comrie, Peter, M.A., B.Sc., Head Mathematical Master, Boroughmuir Juuior Student Centre, 1 9 Craighouse Terrace, Edinburgh Connan, Daniel M., M.A. Cooper, Charles A., LL.D., 41 Drumsheugh Gardens, Edinburgh * Corrie, David, F.C.S., Nobel’s Explosives Company, Polmont, Stirlingshire * Coutts, William Barron, M.A., B.Sc., 33 Dalhousie Terrace, Edinburgh 125 * Cowan, Alexander C., Papermaker, Valleyfield House, Penicuik, Midlothian Craig, James Ireland, M.A., ,B.A., Controller of the Department of General Statistics, 14 Abdin Street, Cairo: The Koubbeh Gardens, near Cairo, Egypt Craig, William, M.D. , F.R.C.S. E. , Lecturer on Materia Medica to the College of Surgeons, 71 Bruntsfield Place, Edinburgh Crawford, Lawrence, M.A., D.Sc., Professor of Mathematics in the South African College, Cape Town Crawford, William Caldwell, 1 Lockharton Gardens, Colinton Road, Edin- burgh 130 Service on Council, etc. 1911-14. 1884-86, 1904-06. Date of (Election. 1870 1886 1914 1898 1904 1885 1884 1894 1869 1905’ 1906 1904 1884 1888 1876 1885 1897 1904 1881 1905 1882 1901 1866 1910 1908 1901 1904 1903 1892 1899 1906 1893 1904 1904 1875 1913 1906 1897 1884 Alphabetical List of the Ordinary Fellows of the Society. 140 Peter’s 145 Criclitoii-Browne, Sir Jas., M.D., LL.D. , D.Sc., F.R.S. , Lord Chancellor’s Visitor and Vice-President and Treasurer of the Royal Institution of Great Britain, 45 Hans Place, S.W., and Royal Courts of Justice, Strand, London Groom, Sir John Halliday, M. D., F.R.C.P.E., Professor of Midwifery in the University of Edinhurgh, late President, Royal College of Surgeons, Edin- burgh, 25 Charlotte Square, Edinhurgh Cumniing, Alexander Charles, D.Sc., Lecturer in Chemistry, University, Edin- burgli, 16 Kilmaurs Terrace, Edinburgh * Currie, James, M.A. Cantab. (Treasueee,), Larkfield, Goldenacre, Edin- / burgh \ * Cuthbertson, John, Secretary, West of Scotland Agricultural College, 6 Charles Street, Kilmarnock 135 Daniell, Alfred, M.A., LL.B., D.Sc., Advocate, The Athensemn Club, Pall Mall, London Davy, R. , F. R.C.S. Eng., Consulting Surgeon to Westminster Hospital, Burstone House, Bow, North Devon Denny, Sir Archibald, Bart., LL.D., Cardross Park, Cardross, Dumbarton- shire Dewar, Sir James, Kt., M. A., LL.D., D.C.L., D.Sc., F.R.S. , V.P.C.S., Jacksonian Professor of Natural and Experimental Philosophy in the University of Cambridge, and Fulle.rian Professor of Chemistry at the Royal Institution of Great Britain, London * Dewar, James Campbell, C. A., 27 Douglas Crescent, Edinburgh Dewar, Thomas William, M.D., F.R.C. P., Kincairn, Dunblane Dickinson, Walter George Burnett, F.R.C.V.S., Boston, Lincolnshire Dickson, the Right Hon. Charles Scott, Lord Justice- Clerk, K.C., LL.D., 22 Moray Place, Edinburgh Dickson, Henry Newton, M.A., D.Sc., 160 Castle Hill, Reading Dickson, J. D. Hamilton, M.A. , Senior Fellow and formerly Tutor, St College, Cambridge Dixon, James Main, M.A.., Litt. Hum. Doctor, Professor of English, University of Southern California, Wesley Avenue, Los Angeles, California, U.S.A. * Dobbie, James Bell, F.Z.S. , 12 South Inverleith Avenue, Edinburgh * Dobbie, Sir James Johnston, Kt,, M.A., D.Sc., LL.D., F.R.S., Principal of the Government Laboratories, London, 4 Vicarage Gate, Kensington, London, W. Dobbin, Leonard, Ph, D., Lecturer on Chemistry in the University of Edinburgh 6 AVilton Road, Edinburgh * Donaldson, Rev. Wm. Galloway, F.R.G.S., F.E.I.S., The Manse, Forfar 150 Dott, David B., F. I.C., Memb. Pharm. Soc., Ravenslea, Musselburgh * Douglas, Carstairs Cumming, M.D., D.Sc., Professor of Medical Jurisprudence and Hygiene, Anderson’s College, Glasgow, 2 Royal Crescent, Glasgow Douglas, David, 22 Drummond Place, Edinburgh * Douglas, Loudon MacQueen, Author and Lecturer, 3 Lauder Road, Edinburgh Drinkwater, Harry, M.D., M.R.C.S. (Eng.), F.L.S., Lister House, Wrexham, North AA^ales 155 * Drinkwater, Thomas W., L.R.C.P.E., L.R.C.S.E., Chemical Laboratory, Surgeons’ Hall, Edinburgh * Dunlop, AA^illiam Brown, M.A., 4a St Andrew Square, Edinburgh Dunstan, John, M.R. C.V.S. , Inversnaid, Liskeard, Cornwall Dunstan, M. J. R., M.A., F. I.C., F.C.k, Principal, South-Eastern Agricultural College, Wye, Kent Duthie, George, M.A. , Inspector-General of Education, Salisbury, Rhodesia Dyson, Sir Frank Watson, Kt., ALA., LL.D., F.R.S., Astronomer Royal, Observatory, Greenwich Edington, Alexander, AI. D., Howick, Natal * Edwards, J ohn, 4 Great AVestern Terrace, Kelvinside, Glasgow * Elder, AVilliam, AI.D., F.R.C.P.E., 4 John’s Place, Leith Elliot, Daniel G. , American Aluseum of Natural History, Central Park West, New York, N.Y., U.S.A. 165 * Elliot, George Francis Scott, AI.A. (Cantab.), B.Sc., F.R.G.S., F.L.S., Drumwhill, Alossdale * Ellis, David, D.Sc. , Ph.D., Lecturer in Botany and Bacteriology, Glasgow and AVest of Scotland Technical College, Glasgow * Erskine-AIurray, James Robert, D.Sc., 4 Great Winchester Street, London, E.C. , Evans, AVilliam, F.F.A., 38 Morningside Park, Edinburgh XXV. 160 Royal 353 Service on Council, etc. Treas. 1906- 1872-74. 1905-08. 1904-07, 1913- 1907-10. 23 354 Date of Klection. 1879 1902 1878 1900 1910 1875 1907 1888 1883 1899 1907 1904 1888 1898 1899 1911 1906 1900 1872 1904 1892 1910 1896 1915 1867 1914 1891 1891 1907 1888 1901 1899 1867 1909 1880 Proceedings of the Poyal Society of Edinburgh. Ewart, James Cossar, M.D., F.R.C.S.E., F.R.S., F.Z.S., Regius Professor of T Natural History, University of Edinburgh, Craigybield, Penicuik, Mid-J lotbian 170 ^ Ewen, John Taylor, B.Sc., M.I.Mech.E., H.M. Inspector of Schools, 104 King’s Gate Aberdeen Ewing, Sir James Alfred, K.C.B., M.A., B.Sc., LL.D., M.Inst.C.E., F.R.S., Director of Naval Education, Admiralty, Froghole, Edenbridge, Kent Eyre, John AV. H., M.D. , M.S. (Dunelni), D.P. H. (Camb, ), Guy’s Hospital (Bacteriological Department), London * Fairgrieve, Mungo M'Callum, M. A. (Glasg.), M.A. (Cambridge), Master at the Edinburgh Academy, 37 Queen’s Crescent, Edinburgh Fairley, Thomas, Lecturer on (Jhemistry, 8 Newton Grove, Leeds 175 Falconer, John Downie, M. A., D.Sc., F.G.S., Lecturer on Geography, The University, Glasgow. Fawsitt, Charles A., Coney Park, Bridge of Allan Felkin, Robert W. , M. D., F.R.G.S., 47 Bassett Road, North Kensington, London, W. * Fergus, Andrew Freeland, M.D. , 22 Blythswood Square, Glasgow * Fergus, Edward Oswald, 12 CTairmont Gardens, Glasgow 180 "Ferguson, James Haig, M.D., F.R.C.P.E., F.R.C.S.E., 7 Coates Crescent, Edinburgh Ferguson, John, M.A., LL.D., Professor of Chemistiy in the University of Glasgow, 13 Newton Place, Glasgow * Findlay, John R., M.A. Oxon., 27 Drurasheugh Gardens, Edinburgh * Finlay, David W., B.A., M.D. , LL.D., F.R.C.P., D.P.H., Emeritus Professor of Medicine in the University of Aberdeen, Honorary Physician to His Majesty in Scotland, 23 Dundonald Road, Glasgow, A¥. Fleming, John Arnold, F.C.S., etc.. Pottery Manufacturer, 136 Glebe Street, St Roll ox, Glasgow 185 * Fleming, Robert Alexander, M.A., Al.D., F.R.C.P.E., Assistant Physician, Royal Infirmary, 10 Chester Street, Edinburgh * Flett, John S., M.A., D.Sc., LL.D., F.R.S., Director of the Geological Survey of Scotland, 33 George Square, Edinburgh Forbes, Professor George, M.A., M.Inst.C.E., M.Inst. E.E., F.R.S., F.R.A.S., 11 Little College Street, AA^estminster, S.AA^. Forbes, Norman Hay, F.R.C.S.E., L.R.C.P. Lond., M.R.C.S. Eng., Corres. Memb, Soc. d’Hydrologie medicale de Paris, Druminnor, Church Stretton, Salop * Ford, John Simpson, F.C.S., 4 Nile Grove, Edinburgh 190 * Fraser, Alexander, Actuary, 17 Eildon Street, Edinburgh * Fraser, John, M.B. , F.R.C.P.E., formerly one of H.M. Commissioners in Lunacy for Scotland, 54 Great King Street, Edinburgh * Fraser, Rev. Joseph Robert, U. F. Manse, Kinnetf, Scotland. Fraser, Sir Thomas R., Kt., M.D., LL.D., Sc.D., F.R.C.P.E., F.R.S., Professor of Materia Medica in the University of Edinburgh, Honorary Physician to_ the King in Scotland, 13 Drumsheugh Gardens, Edinburgh. (Yice- President) * Fraser, AVilliam, Managing Director, Neill & Co., Ltd., Printers, 17 Eildon Street, Edinburgh 195 Fullarton, J. H., M.A., D.Sc., 23 Porchester Gardens, London, AV. Fulton, T. A^^emyss, M.D. , Scientific Superintendent, Scottish Fishery Board, 41 Queen’s Road, Aberdeen * Galbraith, Alexander, Superintendent Engineer, Cunard Line, Liverpool, 93 Trinity Road, Bootle, Liverpool Galt, Alexander, D.Sc., Keeper of the Technological Department, Royal Scottish Museum, Edinburgh Ganguli, Sanjiban, M.A. , Principal, Maharaja’s College, and Director of Public Instruction, Jaipur State, Jaipur, India 200 Gatehouse, T. E. , A.M. Inst. C.E., M.Inst.M.E., M. Inst.E.E.. Fairfield, 128 Tulsc Hill, London, S.AV. Gayner, Charles, M.D., F.L.S. * Geddes, Auckland C., M.D., Professor of Anatomy, M‘Gill University, Montreal, Canada Geddes, Patrick, Professor of Botany in University College, Dundee, and Lecturei on Zoology, Ramsay Garden, University Hall, Edinburgh Service on Council etc. 1882-85, 1904-07. V-P 1907-12. 1888-91. 1870-73,. 1877-79, 1883-86,. 1894-97. V-P 1911- Date of Election. J861 1914 1909 1914 1910 1912 1910 1890 1911 1900 1880 1907 1909 1911 1898 1910 1901 1913 1897 1891 1898 1883 1910 1909 1910 1886 1897 1905 1906 1905 1910 1899 1907 1911 Alphabetical List of the Ordinary Fellows of the Society. Geikie, Sir Archibald, O.M., K.C. B,, D.C.L. Oxf. , D.Sc., LL.D,, Pli.D., Late Pres. R. S., Foreign Member of the Reale Accad. Lincei, Rome, of the National Acad, of the United States, of the Academies of Stockholm, Christiania, Gottingen, Corresponding Member of the Institute of France and of the Academies of Berlin, Vienna, Munich, Turin, Belgium, Philadelphia, New York, etc.. Shepherd’s Down, Haslemere, Surrey 205 Gemmell, John Edward, M.B., C.M., Hon. Surgeon Hospital for Women and Maternity Hospital ; Hon. Gyneecologist, Victoria Central Hospital, Discard, 28 Rodney Street, Liverpool. * Gentle, William, B.Sc., 12 Mayheld Road, Edinburgh * Gibb, Alexander, A.M. Inst. C. E. , St Martin’s Abbey, by Perth * Gibb, David, M.A., B.Sc., Lecturer in Mathematics, Edinburgh University, 15 South Lauder Road, Edinburgh * Gibson, Arnold Hartley, D.Sc., Professor of Engineering, University College, Dundee 210 * Gibson, Charles Robert, Lynton, Mansewood, by Pollokshaws Gibson, George A., M.A., LL.D., Professor of Mathematics in the University of / GlasgoAV, 10 The University, Glasgow \ Gidney, Henry A. J. , L.M. and S. Socts. Ap. (Lond.), F.R.C.S. (Edin.), D.P.H. (Camb.), D.O. (Oxford), Army Specialist Public Health, c/o Thomas Cook & Sons, Ludgate Circus, London Gilchrist, Douglas A., B.Sc., Professor of Agriculture and Rural Economy, Armstrong College, Newcastle-upon-Tyne Gilruth, George Ritchie, Surgeon, 53 Northumberland Street, Edinburgh 215 Gilruth, John Anderson, M.R.C.V.S., D.V.Sc. (Melb. ), Administrator, Govern- ment House, Darwin Northern Territory, Australia * Gladstone, Hugh Steuart, M.A., M.B.O.U., F.Z.S., 40 Lennox Gardens, London, S. W. Gladstone, Reginald John, M.D., F.R.C.S. (Eng.), Lecturer on Embryology and Senior Demonstrator of Anatomy, Middlesex Hospital, London, 22 Pegent’s Park Terrace, London, N.W^. * Glaister, John, M.D., F.R.F. P.S. Glasgow, D.P.H. Camb. , Professor of Forensic Medicine in the University of Glasgow, 3 Newton Place, Glasgow Goodall, Joseph Strickland, M. B. (Loud.), M.S.A. (Eng.), Lecturer on Physiology, Middlesex Hospital, London, Annandale Lodge, Vanbrugh Park, Blackheath, London, S.E. . 220 Goodwillie, James, M.A., B.Sc., Liberton, Edinburgh * Gordon, VVilliam Thomas, M.A., D.Sc. (Edin.), B.A. (Cantab.), Lecturer in Geology, University of London, King’s College, Strand, W.C. Gordon-Munn, John Gordon, M.D., Heigham Hall, Norwicli Graham, Richard D. , 11 Strathearn Road, Edinburgh "Giay, Albert A., M.D., 4 Clairmont Gardens, Glasgow 225 Gray, Andrew, M.A., LL.D., F.R.S., Professor of Natural Philosophy in the) University of Glasgow | Gray, Bruce M‘Gregor, C.E., A.M. Inst. C. E. , AVestbourne Grove, Selby, York- shire * Gray, James Gordon, D.Sc., Lecturer in Physics in the University of Glasgow, 11 The University, Glasgow Green, Charles Edward, Publisher, Gracemount House, Libertoir Greenfield, W. S. , M.D., F.R.C. P.E. , LL.D., Emeritus Professor of General Pathology in the University of Edinburgh, Kirkbrae, Elie, Fife 230 Greenlees, Thomas Duncan, M.D. Edin., Rostrevor, Kirtleton Avenue, Weymouth, Dorset * Gregory, John Walter, D.Sc., F. R. S., Professor of Geology in the University of Glasgow, 4 Park Quadrant, Glasgow Greig, Edward David Wilson, C.I.E., M.D., D.Sc., Major, H.M. Indian Medical Service, United Service Club, Calcutta, India Greig, Robert Blyth, LL.D., F.Z.S., Board of Agriculture for Scotland, 29 St Andrew Square, Edinburgh * Grimshaw, Percy Hall, Assistant Keeper, Natural History Department, The Royal Scottish Museum, 49 Comiston Drive, Edinburgh 235 * Guest, Edward Graham, M.A., B.Sc., 5 Newbattle Terrace, Edinburgh * Gulliver, Gilbert Henry, D.Sc., A.M.I.Mech.E., 99 Southwark Street, London, S.E. * Gunn, James Andrew, M.A., M.D., D.Sc., Department of Pharmacology, University Museum, Oxford 355 Service on Council, etc. 1869-72, 1874-76, 1879-82. 1905-08, 1912-13, 1903-06. V-P 1906-09. 1913-15. 1908-11. 356 Date of Electioi 1888 1911 1911 1905 1899 1896 1914 1888 1914 1881 1880 1892 1893 1890 1900 1908 1890 1881 1894 1902 1904 1885 1911 1881 1896 1904 1897 1912 1893 1899 1883 1910 C. B. C. C. c. c. c. c. c. c. C. N. C. N. C. C. C. Proceedings of the Poyal Society of Edinburgh. Guppy. Hemy Brougham, M.B., Rosario, Salcombe, Devon * Guy, William, F.R.C.S., L.R.C.P., L.D.S. Ed., Consulting Dental Surgeon, Edin- burgh Royal Infirmary ; Dean, Edinburgh Dental Hospital and School ; Lecturer on Human and Comparative Dental Anatomy and Physiology, 11 Wemyss Place, Edinburgh 240 Hall-Edwards, John Francis, L.R.C. P. (Edin.), Hon. F.R.P.S., Senior Medical Officer in charge of X-ray Department, General Hospital, Birmingham, 141a and 141b Great Charles Street (Newhall Street), Birmingham * Halm, Jacob E., Ph.D. , Chief Assistant Astronomer, Royal Observatory, Cape Town, Cape of Good Ho]>e Hamilton, Allan M‘Lane, M.D., LL.D., Great Barrington, Mass., IJ.S.A. * Harris, David Fraser, B.Sc. (Bond.), D.Sc. (Birm.), M.D., F.S.A. Scot., Professor of Physiology in the Dalhousie University, Halifax, Nova Scotia Harrison, Edward Philip, Ph.D., Professor of Physics, Presidency College, Uni- versity of Calcutta, The Observatory, Alipore, Calcutta 245 Hart, D. Berry, M.D., F.R. C.P.E. , 13 Northumberland Street, Edinburgh Harvey-Gibson, Robert John, M.A., F. L.S., D.L. for the County Palatine of Lancaster, M. R.S.G. S. , Professor of Botany, University of Liverpool, 18 Gambin Terrace, Liverpool Harvie-BroAvn, J. A., of Quarter, LL.D., F.Z.S., Dunipace House, Larbert, Stirlingshire Haycraft, J. Berry, M.D., D.Sc., Professor of Physiology in the University College of South Wales and Monmouthshire, Cardiff * Heath, Thomas, B.A., formerly Assistant Astronomer, Royal Observatoiy, Edin- burgh, 11 Cluny Drive, Edinburgh 250 Hehir, Patrick, M. D. , F.R.C.S.E. , M.R.C.S., L.R.C. P.E., Surgeon -Captain, Indian Medical Service, Piincipal Medical Officer, H.H. the Nizam’s Army, Hyderabad, Deccan, India Helme, T. Arthur, M.D., M.R.C.P., M.R.C.S., 3 St Peter’s Square, Manchester Henderson, John, D.Sc., A.Inst.E.E., Kinnoul, Warwick’s Bench Road, Guild- ford, Surrey * Henderson, William Dawson, M.A. , B.Sc., Ph.D., Lecturer, Zoological Laboratories, University, Bristol Hepburn, David, M.D., Professor of Anatomy in the University College of South Wales and Monmouthshire, Cardiff 255 Herdman, W. A., D.Sc., F.R.S., Past Pres. L.S., Professor of Natural History in the University of Liver})Ool, Croxteth Lodge, Ullet Road, Liverpool Hill, Alfred, M.D., M.R.C.^, F.I.C., Valentine Mount, Freshwater Bay, Isle of Wight * Hinxman, Lionel W., B.A., Geological Survey Office, 33 George Sq., Edinburgh Hobday, Frederick T. G. , F.R.C.V.S., 6 Berkely Gardens, Kensington, London, W. Hodgkinson, W. R. , Ph. D. , F. I. C. , F. C. S. , Professor of Chemistry and Physics at the Ordnance College, Woolwich, 89 Shooter’s Hill Road, Blackheath, Kent 260 Holland, AVilliam Jacob, LL.D. St Andrews, etc., Director Carnegie Institute, Pittsburg, Pa., 5545 Forbes Street, Pittsburg, Pa., U.S.A. ^ Horne, John, LL.D., F.R.S., F.G.S., formerly Director of the Geological Survey _ of Scotland (Pbesident), 12 Keith Crescent, Blackball, Midlothian Horne, J. Fletcher, M.D., F.R.C.S.E., The Poplars, Barnsley ^ *Horsburgh, Ellice Martin, M.A. , B.Sc., Lecturer in Technical Mathematics, University of Edinburgh, 11 Granville Terrace, Edinburgh Houston, Alex. Cruikshanks, M.B., C.M., D.Sc., 19 Fairhazel Gardens, South Hampstead, London, N.AV. 265 * Houstoun, Robert Alexander, M.A. , Ph.D., D.Sc., Lecturer in Physical Optics, University, Glasgow, 11 Cambridge Drive, Glasgow Howden, Robert, M.A., M.B. , C.M., D.Sc., Professor of Anatomy in the University of Durham, 14 Burdon Terrace, Newcastle-on-Tyne Howie, W. Lamond, F.C.S., 26 Neville Court, Abbey Road, Regent’s Park, London, N.AV. Hoyle, AVilliam Evans, M.A., D.Sc., M.R.C.S., Director of the Welsh National Museum ; Crowland, Llandaff, AVales Hume, W^illiam Fraser, D.Sc. (Lond.), Director, Geological Survey of Egypt, Helwan, Egypt 270 Service on Council, etc. 1902-05, 1906- 07, 1914- 15. V-P 1907- 1913. P 1915- Date of Election. 1886 1911 1887 1887 1908 1912 1904 1904 1914 1875 1894 1889 1901 1912 1906 1900 1895 1903 1874 1905 1888 1915 1907 1912 1909 1908 1903 1891 1913 1908 1886 1907 1880 1883 1878 1901 1907 Alphabetical List of the Ordinary Fellows of the Society. Hunt, Rev. H. G. Bona via, Mus.D. Dub,, Mus.B, Oxon., The Vicarage, Burgess Hill, Sussex Hunter, Gilbert MacIntyre, M.Inst.C.E., M.Inst.E.S. , M.Inst.M.E,, Resident Engineer Nitrate Railways, Iquique. Chile, and Maybole, Ayrshire Hunter, James, F.R.C.S. E., F. R. A.S., Rosetta, Liberton, Midlothian Hunter, William, M.D., M.R.C.P.L. and E. , M.R.C.S., 54 Harley Street, London Hyslop, Theophilus Bulkeley, M.D,, M.R.C.P.E., 5 Portland Place, London, W. 275 * Inglis, Robert John Mathieson, A. M.Inst.C.E., Engineer, Northern Division, North British Railway, Tantah, Peebles Innes, R. T. A., Director, Government Observatory, Johannesburg, Transvaal * Ireland, Alexander Scott, S. S.C. , 2 Buckingham Terrace, Edinburgh Jack, John Noble, Professor of Agriculture to the County Council of Sussex, Elsenburg. The Avenue, Lewes, Sussex Jack, William, M.A., LL.D. , Emeritus Professor of Mathematics in the University of Glasgow 280 Jackson, Sir John, C.Y.O., LL.D., 48 Belgrave Square, London James, Alexander, M.D., F.R.C. P.E., 14 Randolph Crescent, Edinburgh *Jardine, Robert, M.D., M.R.C.S. F.R.F.P.S. Glas., 20 Royal Crescent, Glasgow * Jeffrey, George Rutherford, M.D. (Glasg.), F.R.C.P. (Edin.), etc., Bootham Park Private Mental Hospital, York » * Jehu, Thomas James, M.A., M. D. , F.G.S., Professor of Geology in the University of Edinburgh 285 * Jordan, David Smiles, M. A., D. Sc. , Ph.D. , Temora, Colinton, Midlothian Johnston, Col. Henry Halcro, C.B., Late A.M.S., D.Sc., M.D., F.L.S., Orphir House, Kirlnvall, Orkney * Johnston, Thomas Nicol, M.B., G.M., Pogbie, Hiimbie. East Lothian Jones, Francis, M. Sc. , Lecturer on Chemistry, 17 AVhalley Road, Whalley Range, Manchester Jones, George AVilliam, M.A., B.Sc. , LL. B., Scottish Tutorial Institute, Edinburgh and Glasgow, 25 North Bridge: Coraldene, Kirk Brae, Liberton, Edinburgh 290 Jones, John Alfred, M.Inst.C.E., Fellow of the University of Madras, Sanitary Engineer to the Government of Madras, c/o Alessrs Parry & Co., 70 Grace- church Street, London Kemnal, James Hermann Rosenthal, IMauaging Director and Engineer-in-Chief of Babcock & Wilcox, Ltd., Kemnal Manor, Chislehurst, Kent * Kemp, John, M.A. . Sea Bank School, North Berwick Kennedy, Robert Foster, M.D. (Queen’s Univ., Belfast), M.B., B.Ch. (R.U.I.), Assistant Professor of Neurology, Cornell University, New York, 20 West 50th Street, New York, U.S.A. Kenwood, Henry Richard, M.B., Chadwick Professor of Hygiene in the University of London, 126 Queen’s Road, Finsbury Park, London, N. 295 * Kerr, Andrew William, F.S.A. Scot., Royal Bank House, St Andrew Square, Edinburgh , * Kerr, John Graham, M.A., F.R.S., Professor of Zoology in the University f of Glasgow \ I Kerr, Joshua Law, M.D., The Chequers, Mittagong, Sydney, Australia i * Kerr, Walter Hume, M.A., B.Sc., Lecturer on Engineering Drawing and Structural i Design in the University of Edinburgh Kidd, AVal ter Aubrey, Al.D., Heatherdowu, Alum Bay, Freshwater, I. of AY. 300 | Kidston, Robert, LL.D., F.R.S. , F. Stirling * King, Archibald, M.A., B.Sc., formerly Rector of the Academy, Castle Douglas ; Junior Inspector of Schools, La Maisonnette, Clarkston, Glasgow King, W. F., Lonend, Russell Place, Trinity, Leith Kinnear, the Right Hon. Lord, P. 0., one of the Senators of the College of Justice, 2 Moray Place, Edinburgh Kintore, the Right Hon. the Earl of, P.C. , G. C. AI.G., M.A. Cantab., LL.D. Cambridge, Aberdeen and Adelaide, Keith Hall, Inverurie, Aberdeen- shire 305 * Knight, Rev. G. A. Frank, M.A., 52 Sardinia Terrace, Hillhead, Glasgow * Knight, James, M.A., D.Sc,, F.C.S., F.G.S., Head Master, St James’ School, Glasgow, The Shieling, Uddingston, by Glasgow G.S. (Seceetaky), 12 Clarendon Place J 357 Service on Council, etc. 1888-91. 1904-07, 1913- 1891-94, 1903-06. Sec. 1909- 358 Date of Election. 1880 1886 1878 1910 1885 1894 1910 1905 1910 1903 1874 1910 1914 1905 1889 1912 1912 1903 1903 1898 1884 1888 1900 1894 1887 1907 1883 1903 1905 1897 1904 1886 1904 Proceedings of the Eoyal Society of Edinburgh. r Knott, C. G., D.Sc. , Lecturer on Applied Mathematics in the University of Edinburgh (formerly Professor of Physics, Imperial University, Japan)< (Gen. Secretary), 42 Upper Graj?^ Street, Edinburgh c Laing, Rev. George P. , 1 7 Buckingham Terrace, Edinburgh Lang, P.R.Scott, M.A., B.Sc., Professorof Mathematics, University of St Andrews 310 * Lauder, Alexander, D.Sc., F. I.C., liccturer in Agricultural Chemistry, Edinburgh and East of Scotland College of Agriculture, 13 George Square, Edinburgh Laurie, A. P., M.A., D.Sc., Principal of the Heriot-Watt College, Edinburgh | * Laurie, Malcolm, B.A., D.Sc., F.L.S., 19 Merchiston Park, Edinburgh * Lawson, A. Anstruther, B.Sc., Ph.D., D.Sc., F.L.S., Professor of Botany, Univer- sity of Sydney, New South Wales, Australia Lawson, David, M.A., iM.D., L.R.C.P. and S.E., Druimdarroch, Banchory, Kincardineshire 315 * Lee, Gabriel W., D.Sc., Pal?eontologist, Geological Survey of Scotland, 33 George Square, Edinburgh * Leighton, Gerald Rowley, iM.D., Local Government Board, 125 George Street, Edinburgh Letts, E. A., Ph.D., F.I.C., F.C.S. , Professor of Chemistry, Queen’s College, Belfast Levie, Alexander, F.R. C.V.S., D.V.S.M., Yeterinary Surgeon, Lecturer on Veterinary Science, Veterinary Infirmary, 12 Derwent Street, Derby Lewis, Francis John, D.Sc., F.L.S., Professor of Biology, University of Alberta, Edmonton South, Alberta, Canada 320 Lightbocly, I'orrest Hay, 56 Queen Street, Edinburgh Lindsay, Rev. James, M.A., D.D., B.Sc., F.R.S.L., F.G.S., M.R.A.S., Corre- sponding Member of the Royal Academy of Sciences, Letters and Arts, of Padua, Associate of the Philosophical Society of Louvain, Annick Lodge, Irvine * Lindsay, John George, M.A., B.Sc. (Edin.), Science Master, Royal High School, 33 Lauriston Gardens, Edinburgh * Linlithgow, The Most Honourable the Marquis of, Hopetoun House, South Queen sfeny Liston, William Glen, M. D., Captain, Indian Medical Service, c/o Grindlay, Groom <& Co., Bombay India 325 * Littlejohn, Henry Harvey, M.A., M. B., B.Sc., F.R.C.S.E., Professor of Forensic Medicine, Dean of the Faculty of Medicine in the University of Edinburgh, 11 Rutland Street, Edinburgh * Lothian, Alexander Yeitch, M.A., B.Sc., Training College, Cowcaddens, Glasgow Low, George M., Actuary, 11 Moray Place, Edinburgh Lowe, D. F. , M.A., LL.D. , formerly Head Master of Heriot’s Hospital School, Lauriston, 19 George Square, Edinburgh Lusk, Graham, Ph.D., M.A., Professor of Physiology, Cornell University Medical College, New York, N.Y., U.S.A. 330 * Mabbott, Walter John, M.A., Rector of County Pligh School, Duns, Berwickshire M‘Aldowie, Alexander M., M.D., Glengarritf, Leckhampton, Cheltenham MacAlister, Donald Alexander, A.R.S.M., F.G. S., 26 Thurloe Square, South Kensington, London, S.W. M‘Bride, P., IM.D., F.R.C.P.E., 10 Park Avenue, Harrogate, and Hill House, Withypool, Dunster, Somerset *M‘Cormick, Sir W. S., M.A., LL.D., Secretary to the Carnegie Trust for the Universities of Scotland, 13 Douglas Crescent, Edinburgh 335 * Macdonald, Hector Munro, M. A., F.R.S., Professor of Mathematics, University of Aberdeen, 52 College Bounds, Aberdeen * Macdonald, James A., M.A., B.Sc., H.M. Inspector of Schools, SteAvarton, Kilmacolm * Macdonald, John A., M.A., B.Sc., King Edward YII. School, Johannesburg, Transvaal Macdonald, the Right Hon. Sir J. H. A. (Lord Kingsburgh) P.C. , K.C. , K.C.B., J LL.D., F.R.S., M.Inst.E.E., 15 Abercromby Eace, Edinburgh Macdonald, William, B.Sc., M.Sc. , Agriculturist, Editor Transvaal Agricultural Journal, Department of Agriculture, Pretoria Club, Pretoria, Transvaal 340 Service on Council, etc. 1894-97, 1898-01, 1902-05. Sec. 1905-1912. Gen. Sec. 1912- I 1908-11, 1913- 1910-13. 1908-11. 1889-92. Y-P 1914- Alphabetical List of the Ordinary Fellows of the Society. 359 Date of Election. 1886 1901 C. 1910 1888 C. 1885 C. 1897 1878 1903 1911 I 1869 C. N. 1895 1914 C. 1873 C. B. 1912 C, 1900 c. 1910 c. 1911 1894 1904 1910 1904 1869 1899 1888 ! c. c, 1913 1 1907 1898 c. 1913 1908 1912 1913 1880 i c. 1909 : c. B. i 1882 1 i C. Macdonald, William J., M.A., LL.D., 15 Comiston Drive, Edinburgh * MacDougall, R. Stewart, JM.A., D.Sc., Professor of Biology, Royal Veterinary College, Edinburgh, 9 Dryden Place, Edinburgh Macewen, Hugh Allan, M.B., Ch.B., D.P. H. (Bond, and Camb.), Local Government Board, Whitehall, London, S.W. M‘Fadyean, Sir John, M.B., B.Sc., LL.D., Principal, and Professor of Comparative Pathology in the Royal Veterinary College, Camden Town, London Macfarlane, L M,, D.Sc., Professor of Botany and Director of the Botanic Garden, University of Pennsylvania, Philadelphia, Pennsylvania, U.S.A. 345 * MacGillivray, Angus, C.M., M.D., D.Sc., 23 South Tay Street, Dundee M'Gowan, George, F. I.C., Ph. D., 21 Montpelier Road, Ealing, Middlesex * j\lTntosh, Donald C., M.A., D.Sc., 3 Glenisla Gardens, Edinburgh MTntosh, John William, A.R.C.V.S., 14 Templar Street, Myatts Park, London, S.E. MTntosh, William Carmichael, M.D., LL.D., F.R.S., F.L.S., Professor of Natural History in the University of St Andrews, Pres. Ray. Society, 2 Abbotsford Crescent, St Andrews 350 * Macintyre, John, M.D., 179 Bath Street, Glasgow *M‘Kenhick, Archibald, F.R.C.S.E., D. P.H., L.D.S., 2 Coates Place, Edinburgh M'Kendrick, John G. , M. D., F.R.C.P.E., LL.D., F.R.S., Emeritus Professor of Physiology in the University of Glasgow, Maxieburn, Stonehaven M'Kendrick, Anderson Gray, jM.B. , Major, Indian Medical Service, Officiating Statistical Officer to the Government of India, The Pasteur Institute, Kasauli, India *M‘Kendrick, John Souttar, M.D., F.R.F.P.S.G., 2 Buckingham Terrace, Hill- head, Glasgow 355 * Mackenzie, Alister, M.A., M.D., D.P.H., Principal, College of Hygiene and Physical Training, Dunfermline * MTvenzie, Kenneth John, M. A., Master of Method to Leith School Board, 24 Dudley Gardens, Leith * Mackenzie, Robert, M.D., Napier, Nairn * Mackenzie, W. Leslie, M.A., M.D., D.P.H., LL.D., Medical Member of the Local Government Board for Scotland, 4 Clarendon Crescent, Edinburgh '*■ MacKinnon, James, M.A., Ph.D., Professor of Ecclesiastical History, Edinburgh University, 12 Lygon Road, Edinburgh 360 * Mackintosh, Donald James, M.V.O., M.B. , C.M. , LL.D., Supt. Western Infirmary, Glasgow Maclagan, R. C., M.D., F.R.C.P.E., 5 Coates Crescent, Edinburgh Maclean, Ewan John, M.D., M.R.C.P. Lond., 12 Park Place, Cardiff Maclean, Magnus, M.A., D.Sc., M.Inst.E.E., Professor of Electrical Engineering in the Royal Technical College, 51 Kerrsland Terrace, Hillhead, Glasgow *M‘Lellan, Dugald, M. Inst.C. E., District Engineer, Caledonian Railway, 20 Kingsburgh Road, Murrayfield, Edinburgh 365 "" Macnair, Peter, Curator of the Natural History Collections in the Glasgow Museums, Kelvingrove Museum, Glasgow Mahalanobis, S. C., B.Sc., Professor of Physiology, Presidency College, Calcutta, India Majumdar, Tarak Nath, D.P.H. (Cal.), L.M.S., F. C S. , Health Officer, Calcutta, IV., 37 Lower Chitpore Road, Calcutta, India Mallik, Devendranath, Sc. D. , B.A., Professor of Mathematics, Astronomical Observatory, Presidential College, Calcutta, India Maloney, William Joseph, M.D.(Edin.), Professor of Neurology at Fordham University, New York City, N.Y., U.S.A. 370 Marchant, Rev. James, F.R A.S., Director, National Council for Promotion of Race- Regeneration ; Literary Adviser to House of Cassell ; 42 Great Russell Street, London, W.C. Marsden, R. Sydney, M.D., C.M., D.Sc., D.P.H., Hon. L.A.H. Dub., M.R.I.A., F.I. C., M.O.H., Rowallan House. Cearns Road, and Town Hall, Birkenhead ^Marshall, C. R., 1\1.D., M.A., Professor of Materia Medica and Therapeutics, IMedical School, Dundee, Arnsheen, Westfield Terrace, West Newport, Fife Marshall, D. H., M.A., Professor, Union and Alwington Avenue, Kingston, Ontario, Canada Service on Council, etc. 1914- 1885-88. 1875-78, 1885-88, 1893- 94, 1900-02. V-P 1894- 1900. 1915- 360 Date of Election. 1901 1903 1912 1913 1885 1898 1911 1906 1902 1901 1888 1902 1885 1908 1910 1909 1905 1905 1904 1886 1899 1889 1897 1900 1899 1911 1906 1890 1887 1896 1892 1914 1901 1892 1874 1888 Proceedings of the Royal Society of Edinburgh. * Marshall, F. H. A,, Sc. D., Lecturer on Agricultural Physiology in the Uni- versity of Cambridge, Christ’s College, Cambridge 375 Martin, Nicholas Henry, F.L.S., F.C.S., Ravenswood, Low Fell, Gateshead. * Martin, Sir Thomas Carlaw, LL.D., J.P. , Director, Royal Scottish Museum, 18 Blackford Road, Edinburgh Masson, George Henry, M.D., U.Sc., M.R.C.P.E., Port of Spain, Trinidad, British W est Indies Masson, Orme, D.Sc, , F. R.S., Professor of Chemistry in the University of Melbourne * Masterman, Arthur Thomas, M.A., D.Sc,, Inspector of Fisheries, Board of Agriculture, Whitehall, London 380 Mathews, Gregory Macalister, F.L.S., F.Z.S., Foulis Court, Fair Oaks, Hants * Mathieson, Robert, F. C.S. , Rillbank, Innerleithen j Matthews, Ernest Romney, A. M.Inst C.E., F.G.S., Chadwick Professor of Municipal Engineering in the University of London, University College, Gower Street, London, W.C. Menzies, Alan W. C,, M. A., B.Sc., Ph.D,, F.C.S., Professor of Chemistry, Princeton University, Princeton, New Jersey, U.S.A. Methven, Cathcart W., M.Inst.C.E., F.R.I.B.A., Durban, Natal, S. Africa 385 Metzler, William H., A. B. , Ph.D., Corresponding Fellow of the Royal Societx of Canada, Professor of Mathematics, Svracuse University, Svracuse, N.Y., U.S.A. Mill, Hugh Robert, D.Sc., LL.D., 62 Camden Square, London * Miller, Alexander Cameron, M.D., F.S.A. Scot., Craig Linnhe, Fort-William, Inverness-shire * Miller, John, M.A., D.Sc., Professor of Mathematics, Royal Technical College, 2 Northbank Terrace, North Kelvinside, Glasgow Mills, Bernard Langley, M.D., F.R.C.S.E., M.R.C.S., D.P.H., Lt.-Col. R.A.M. C. , formerly Army Specialist in Hygiene, c/o National Provincial Bank, Fargate, Sheffield 390 * Milne, Archibald, M.A., B.Sc., Lecturer on Mathematics and Science, Edinburgh Provincial Training College, 108 Comiston Drive, Edinburgh * Milne, C. H., M.A., Head Master, Daniel Stewart’s College, 4 Campbell Road, INlurray field, Edinburgh * Milne, James Robert, D.Sc., Lecturer on Natural Philosophy, 5 North Charlotte Street, Edinburgh Milne, William, M.A., B.Sc., 70 Beechgrove Terrace, Aberdeen * Milroy, T. H., M. 1)., B.Sc., Professor of Physiology in Queen’s College, Belfast, Meloyne, Malone Park, Belfast 395 Mitchell, A. Crichton, D.Sc., Hon. Doc. Sc. (Geneve), formerly Director of Public Instruction in Travaiicore, India, 103 Trinity Road, Edinburgh Mitchell, Geoi'ge Arthur, M.A. , 9 Lowther Terrace, Kelvinside, Glasgow * Mitchell, James, M.A., B.Sc., Cruach, Lochgilphead * Mitchell-Thomson, Sir JMitchell, Bart., 6 Charlotte Square, Edinburgh Modi, Edalji Manekji, D.Sc., LL.D., Litt.D., F.C.S., etc.. Proprietor and Director of Arthur Road Chemical AYorks, Meher Buildings, Tardeo, Bombay, India 400 Moffat, Rev. Alexander, ]\LA., B.Sc., Professor of Physical Science, Christian College, Madras, India Mond, R. L., M.A. Cantab., F.C.S., Combe Bank, near Sevenoaks, Kent Moos, N. A. F. , L.C.E., B.Sc., Professor of Physics, Elphinstone College, and Director of the Government Observatory, Colaba, Bombay, India * Morgan, Alexander, M.A., D.Sc., Principal, Edinburgh Provincial Training College, 1 Midmar Gardens, Edinburgh Morrison, J. T. , M.A., B.Sc., Professor of Physics and Chemistry, Victoria College, Stellenbosch, Cape Colony 405 Mort, Spencer, M.D., Ch.B., F.R.C.S.E., Lieut.-Col. R.A.M.C., Medical Officer in Chai'ge, Edmonton Military Hospital, Silver Street, Upper Edmonton, London, N. Moses, 0. St John, I.M.S., M.D., D.Sc., F.R.C.S., Captain, Professor of Medical Jurisprudence, 26 Park Street, AVellesley, Calcutta, India Mossman, Robert C. , 15 The Mamsions, Hillfield Road, AVTst Hampstead, London, N.W. Muir, Sir Thomas, C.M.G., M.A., LL.D., F.R.S., Superintendent-General of Education for Cape Colony, Education Office, Cape Town, and Mowbray Hall, Rosebank, Cape Colony ! Muirhead, George, Commissioner to His Grace the Duke of Richmond and Gordon, . K.G., Spey bank, Fochabers 410 ' Service on Coimcil, etc,. 1902-04. 1915- 1885-88. y-p 1888-91. Date of Election. 1907 1887 1891 1896 1907 1902 1888 1897 1906 1898 1884 1880 1878 1888 1888 1886 1895 1915 1914 1908 1905 1914 1901 1886 1892 1881 1907 1914 1904 1889 1887 1893 1913 Alphabetical List of the Ordinary Fellows of the Society. 361 Muirhead, James M. P. , J.P., F.R.S.L., F.S.S., c/o Dunlop Rubber Co,, Ltd., 3 Wallace Street, Fort, Bombay Mukhopadhyay, Asutosli, M.A., LL.D., F.R.A.S., M.R.LA., Professor of Mathe- matics at the Indian Association for the Cultivation of Science, 77 Russa Road North, Bhowanipore, Calcutta, India ^ Munro, Robert, M.A., M. D., LL.D., Hon. Memb, R. I.A., Hon. Memb.J Royal Society of Antiquaries of Ireland, Elmbank, Largs, Ayrshire | * Murray, Alfred A., M.A., LL, B., 20 Warriston Crescent, Edinburgh Musgrove, James, M.D., F.R.C.S. Edin. and Eng., Emeritus-Professor of Anatomy, University of St Andrews, The Swallowgate, St Andrews 415 Mylne, Rev. R. S. , M.A., B.C. L. Oxford, F.S. A. Lond. , Great Amwell, Herts Napier, A. D, Leith, M.D., C.M., M.RC.P., 28 Angas Street, Adelaide, S. Australia Nash, Alfred George, B.Sc. , F.R.G.S., C. E., Belretiro, Mandeville, Jamaica, AV.I. * Newington, Frank A., M.Inst.C.E., M.Inst.E.E., 7 Wester Coates Road, Edin- burgh Newman, Sir George, j\I.D., D. P.H. Cambridge, Lecturer on Preventive Medicine, St Bartholomew’s Hospital, University of London : Grim’s AVood, Harrow AV'eald, Middlesex 420 Nicholson, J. Shield, M.A., D.Sc., Professor of Political Economy in thej University of Edinburgh, 3 Belford Park, Edinburgh j Nicol, W. W. J., M.A. , D.Sc., 15 Blacket Place, Edinburgh Norris, Richard, M.D., M.R.C.S. Eng., 3 Walsall Road, Birchfield, Birming- ham Ogilvie, F. Grant, C.B., M.A. , B.Sc., LL.D., Secretary of the Board of Education for the Science Museum and the Geological Survey, and Director of the Science Museum, 15 Evelyn Gardens, London, S.W. Oliphant, James, M.A., 11 Heathfield Park, Willesden Green, London 425 Oliver, James, M.D., F.L.S., Physician to the London Hospital for AA^omen, 123 Harley Street, London, AAL Oliver, Sir Thomas, M.D. , LL.D.. F. R.C.P., Professor of Physiology in the University of Durham, 7 Ellison Place, Newcastle-upon-Tyne * Orr, Lewis P. , F.F.A. . Secretary of Scottish Life Assurance Co. , 14 Learmonth Gardens, Edinburgh * Oswald, Alfred, Lecturer in German, Glasgow Provincial Training College, Nordheim, Bearsden, Glasgow Page, William Davidge, F.C.S., F.G.S., M.Inst.M.E.. 10 Clifton Dale, York 430 Pallin, William Alfred, F.R.C.V.S., Veterinary-Major, Royal Horse Guards, London Pare, John AVilliam, M.B., C.M., M.D. , L.D.S., Lecturer in Dental Anatomy, National Dental Hospital, 64 Brook Street, Grosvenor Square, London, AV. * Paterson, David, F.C.S., Lea Bank, Rosslyn, Midlothian Baton, D. Noel, M.D., B.Sc., F.R.C.P.E., F.R.S., Professor of Physiology in ( the University of Glasgow, University, Glasgow 1 * Paulin, Sir David, Actuary, 6 Forres Street, Edinburgh 435 Peach, Benjamin N., IjL.D., F.R.S., F.G.S. (Vice-President), formerly District ( Superintendent and Acting lAlaeontologist of the Geological Survey of-! Scotland, 72 Grange Loan, Edinburgh * Pearce, John Thomson, B.A., B.Sc., School House, Tranent Pearson, Joseph, D.Sc., F.L.S., Director of the Colombo Museum, and Marine Biologist to the Ceylon Government, Colombo Museum, Ceylon * Peck, James Wallace, M.A., Chief Inspector, National Health Insurance, Scotland, 83 Princes Street, Edinburgh Peck, AAUlliam, F.R.A.S., Town’s Astronomer, City Observatory, Calton Hill, Edinburgh 440 Peddie, AVm., D.Sc., Professor of Natural Philosophy in University College, Dundee, Rosemount, Forthill Road, Broughty Ferry Perkin, Arthur George, F.R.S., 8 Montpellier Terrace, Hyde Park, Leeds * Philip, Alexander, M.A., LL.B. , AA^riter, The Mary Acre, Brechin Service on Council, etc. 1894-97, 1900-03. V-P 1903-08. 1885-87, 1892-95, 1897-1900. 1901-03. 1894-97, 1904- 06, 1909-12. 1905- 08, 1911- 1912. V-P 1912- 1904-07, 1908-11. 362 Date of Election. 1889 1907 1914 1905 1908 1911 1906 1886 1888 1902 1892 1875 1915 1908 1903 1911 1898 1897 1899 1884 1914 1911 1891 1904 1900 1883 1889 1902 1902 1913 1908 1914 1913 1908 1875 1914 1906 Proceedings of the Royal Society of Edinburgh. Philip, Sir R. W. , M.A. , M. D., F.R.C.P.E., 45 Charlotte Square, Edinburgh Phillips, Charles E. S., Castle House, Shooter’s Hill, Kent 445 * Pilkington, Basil Alexander, 20 Queen’s Avenue, Blackhall, Midlothian * Pinkerton, Peter, M.A., D.Sc., Rector, High School, Glasgow, 44 Hamilton Park Terrace, Hillhead, Glasgow * Pirie, James Hunter Harvey, B.Sc. , M.D., F. R.C.P.E., Bacteriological Laboratory, ISTairobi, British East Africa Pirie, James Simpson, Civil Engineer, 28 Scotland Street, Edinburgh Pitchford, Herbert Watkins, F.R, C.V.S., Bacteriologist and Analyst, Natal Government, The Laboratory, Pietermaritzburg, Natal 450 Pollock, Charles Frederick, M.D., F.R.C.S.E., 1 Buckingham Terrace, Hillhead, Glasgow Prain, Sir David, Lt.-Coh, Indian Medical Service (Retired), C. M.G., C.I.E., M.A., M.B., LL.D., F. L.S., F.R.S., For. Menib. K. Svensk. Vetensk. Akad. ; Hon. Memb. Soc. Lett, ed Arti d. Zelanti, Acireale ; Pharm. Soc. Gt, Britain ; Corr. Memb. K. Bayer Akad. AViss, , etc. ; Director, Royal Botanic Gardens, Kew, Surrey Preller, Charles Du Riche, M.A. , Ph.D., A.M. Inst.C.E., 61 Melville Street, Edinburgh * Pressland, Arthur J., M.A. Camb. , Edinburgh Academy Pre^mst, E. AV. , Ph.D., AVeston, Ross, Herefordshire 455 Price, Frederick AVilliam, M.D., M.R. C.P. Edin., Physician to the Great Northern Hos])ital, London, 133 Harley Street, London, AV. * Pringle, George Cossar, ]\1.A., Rector of Peebles Burgh and County High School, Bloomfield, Peebles * Pullar, Laurence, Dunbarney, Bridge of Earn, Perthshire Purdy, John Smith, M.D., C.M. (Abeid.), D.P. H. (Camb.), F.R.G.S., Chief Health Officer for Tasmania, Islington, Hobart, Tasmania * Purves, John Archibald, D.Sc., 52 Queen Street, Exeter 460 * Rainy, Harry, M.A., M.B., C.M., F.R.C.P. Ed. , 16 Great Stuart Street, Edin- burgh * Ramage, Alexander G., 8 AA^estern Terrace, Alurrayfield, Edinburgh Ramsay, E. Peirson, M.R. I. A., F.L.S., C.AI.Z.S., F.R.G.S., K.G.S., Fellow of the Imperial and Royal Zoological and Botanical Society of Vienna, Curator of Australian Museum, Sydnejg N.S. AA'. * Ramsay, Peter, M.A., B.Sc., Head Mathematical Master, George AA^atson’s College, 63 Comiston Drive, Edinburgh * Rankin, Adam A., A^ice-President, British Astronomical Association, AVest of Scotland Branch, 324 Crow Road, Broomhill, Glasgow, AV. 465 Ranking, John, K.C., M.A., LL.D., Professor of the Law of Scotland in the University of Edinburgh, 23 Ainslie Place, Edinburgh Ratcliffe, Joseph Riley, M.B., C.M., c/o The Librarian, The University, Birmingham Raw, Nathan, M.D., M.R. C.P. (London), B.S., F. R.C.S., D.P.H., 66 Rodney Street, Liverpool Readman, J. B., D.Sc., F.C.S., Belmont, Hereford Redwood, Sir Boverton, Bt., D.Sc. (Hon.), F. I.C., F.C.S., A. Inst.C.E., The Cloisters, 18 Avenue Road, Regent’s Park, London, N.AV. 470 Rees-Roberts, John Vernon, M.D. , D.Sc., D.P.H , Barrister-at-Law, National Liberal Club, AVhitehall Place, London Reid, George Archdall O’Brien, M.B., C. M., 9 Victoria Road South, Southsea, Hants Reid, Harry Avery, F.R.C.A^.S., D.V.H., Bacteriologist and Pathologist, Depart- ment of Agriculture, Wellington, New Zealand * Rennie, John, D.Sc., Lecturer on Parasitology, and Assistant to the Professor of Natural History, University of Aberdeen, 60 Desswood Place, Aberdeen Renshaw, Graham, M.B., M.R.C.S,, L.R.C.P., L.S.A., Surgeon, Bridge House, Sale, Manchester 475 * Richardson, Harry, M. Inst.E.E., M. Inst. ALE., General Alanager and Chief Engineer, Electricity Supply, Dundee and District, The Cottage, Craigie, Brough ty Ferry Richardson, Linsdall, F.L.S., F.G.S., Organising Inspector of Technical Educa- tion for the Gloucestershire Education Committee, 33 Cecily Hill, Cirencester, Glos. Richardson, Ralph, AV.S., 10 Alagdala Place, Edinburgh * Ritchie, James Bonnyman, B.Sc., Science Alaster, Kelvinside Academy, Glasgow * Ritchie, AVilliam Thomas, AI.D., F.R. C.P. E., 9 Atholl Place, Edinburgh 480 Service on Council, etc. Alphabetical List of the Ordinary Fellows of the Society. 363 Date of Election. 1898 1880 1900 1890 1902 C. c. 1896 C. 1910 I I 1881 I 1909 ! C. j 1906 I 1902 C. K. 1880 ! 1904 1906 1914 j 1912 i 1903 1903 1891 1900 C. 1885 1880 1889 1902 1871 1908 1900 1911 C. C. c. c. 1900 1903 1901 1891 1882 1915 1911 C. K. C. Roberts, Alexander William, D.Sc., F.R.A.S., Lovedale, South Africa Roberts, D. Lloyd, M.D., F.R.C.P.L., 23 St John Street, Manchester * Robertson, Joseph M'Gregor, M.B., C.M,, 26 Buckingham Terrace, Glasgow * Robertson, Robert, M.A., 25 Mansionhouse Road, Edinburgh * Robertson, Robert A,, M.A. B.Sc. , Lecturer on Botany in the University of St Andrews 485 * Robertson, W. G. Aitchison, D.Sc., M. D., F. R. C.P.E., 2 Mayfield Gardens, Edin- burgh * Robinson, Arthur. M.D., M.R.O.S., Professor of Anatomy, University of Edin-J burgh, 35 Coates Gardens, Edinburgh (Secretauy) 1 Rosebery, the Right Hon. the Earl of, K.G., K.T., LL.D., D.C.L., F.R.S., Dalmeny Park, Edinburgh * Ross, Alex'. David, M.A. , D.Sc., F.R.A.S., Professor of Mathematics and Physics, University of Western Australia, Perth, Western Australia * Russell, Alexander Durie, B.Sc., Mathematical Master, Falkirk High School, Dunaura, Heugh Street, Falkirk 490 * Russell, James, 22 Glenorchy Terrace, Edinburgh Russell, Sir Janies A., M.A., B.Sc.,M.B., F.R.C.P.E., LL.D., Woodville, Canaan Lane, Edinburgh Sachs, Edwin 0., Architect, Chairman of the British Fire Prevention Committee, Vice-President of the International Fire Service Council, 8 Waterloo Place, Pall Mall, London, S.W. Saleeby, Caleb William, M.D., 13 Greville Place, London * Salvesen, Theodore Emile, 37 Inverleith Place, Edinburgh 495 * Sampson, Ralph Allen, M.A., D.Sc., F.R.S., Astronomer Royal for Scotland, Professor of Astronomy, University, Edinburgh, Royal Observatory, Edin- burgh * Samuel, John S. , 8 Park Avenue, Glasgow ^ Sarolea, Charles, Ph.D., D.Litt., Lecturer on French Language, Literature, and Romance Philology, University of Edinbnrgh, 21 Royal Terrace, Edinburgh Sawyer, Sir James, Kt. , M.D., F. R.C.P., F.S.A., J.P. , Consulting Physician to the Queen’s Hospital, 31 Temple Row, Birmingham * Schafer, Sir Edward Albert, M.R.C.S., LL.D., F.R.S. (Vice-Puesident), I Professor of Physiology in the University of Edinburgh 50C j Scott, Alexander, M.A. , D.Sc., F.R.S., 34 Upper Hamilton Terrace, London, N.W. Scott, J. H., M.B., C.M., M.R.C.S. , Professor of Anatomy in the University of Otago, New Zealand Scougal, A. E., M.A., LL.D., formerly H.M. Senior Chief Inspector of Schools and Inspector of Training Colleges, 1 AVester Coates Avenue, Edinburgh Senn, Nicholas, M.D., LL.D., Professor of Surgery, Rush Medical College, Chicago, U. S. A. Simpson, Sir A. R., M.D., Emeritus Professor of Midwifery in the University of Edinburgh, 52 Queen Street, Edinburgh 505 * Simpson, George Freeland Barbour, M.D., F.R.C.P.E., F.R.C.S.E., 43 Manor Place, Edinburgh * Simpson, James Young, M.A., D.Sc., Professor of Natural Science in the New College, Edinburgh, 25 Chester Street, Edinburgh Simpson, Sutherland, M.D., D.Sc. (Edin.), Professor of Physiology, Medical College, Cornell University, Ithaca, N.Y., U.S.A., 118 Eddy Street, Ithaca, N.Y., U.S.A. Sinhjee, Sir Bhagvat, G.C.I.E., M.D., LL.D. Edin., H. H. the Thakur Sahib of Gondal, Gondal, Kathiawar, Bombay, India ^Skinner, Robert Taylor, M.A., Governor and Head Master, Donaldson’s Hospital, Edinburgh 510 * Smart, Edward, B.A., B.Sc., Tillyloss, Tullylumb Terrace, Perth * Smith, Alexander, B.Sc., Ph.D., Department of Chemistry, Columbia University, New York, N.Y., U.S.A. Smith, C. Michie, C. I.E., B.Sc., F.R.A.S. , formerly Director of the Kodaikanal and Madras Observatories, Winsford, Kodaikanal, South India * Smith, Janies Lorrain, Professor of Pathology, University of Edinburgh, 11 Bruntsfield Crescent, Edinburgh * Smith, Stephen, B.Sc., Goldsmith, 31 Grange Loan, Edinburgh 515 Service on Council, etc. 1910-1912. Sec. 1912- 1912-1915. V-P 1915- 1900-03, 1906-09. Y.P. 1913- 364 Date of Election. 1907 1880 1899 1880 1910 1889 1911 1882 1896 1874 1906 1891 1914 1912 1910 1886 1884 1888 1902 1889 1906 1907 1903 1905 1912 1885 1904 1898 1895 1890 1870 1899 1892 1885 1907 1905 1887 Proceedings of the Poyal Society of Edinburgh. Smith, Vyhlliam Ramsay, D.Sc., M.D., C.M., Permanent Head of the Health iJepartment, South Australia, Belair, South Australia Smith, William Robert, j\LD., D.Sc., LL. D., Professor of Forensic ]\ledicine and 'I'oxicology in King’s College, University of London, and Principal of the Royal Institute of Public Health, 36 Russell Square, London, W.C. Snell, Ernest Hugh, M.D., B.Sc., D.P.H. Canib., Medical Otlicer of Health, Coventry Sollas, W. J., M. A., D.Sc., LL.D., F. R.S., Fellow of University College, Oxford, and Professor of Geology and Palteontology in the University of Oxford * Somerville, Robert, B.Sc., Science Master, High School, Dunfermline. 31 Cameron Street, Dunfermline 520 Somerville, Wm., M.A., D.Sc., D.Oec., Sibthorpian Professor of Rural Economy and Fellow of St John’s College in the University of Oxford, 121. Banbury Road, Oxford * Sommerville, Duncan McLaren Young, M.A., D.Sc., Professor of Pure and Applied Mathematics, Victoria College, W’’ellington, New Zealand Sorley, James, 82 Onslow Gardens, London * Spence, Frank, M.A., B.Sc., 25 Craiglea Drive, Edinburgh Sprague, T. B., M.A., LL.D., Actuary, 29 Buckingham Terrace, Edinburgh 525 Squance, Thomas Coke, M.D., F.R.M.S., F.S.A.Scot., Physician and Pathologist in the Sunderland Infirmary, President Sunderland Antiquarian Society, Sunderland Naturalists’ Association, 15 Grange Crescent, Sunderland Stanfield, Richard, Professor of Mechanics and Engineering in the HeriotAVatt College, Edinburgh *Steggall, John Edward Aloysius, IM.A. , Professor of Mathematics at University College, Dundee, in St Andrews University, Woodend, Perth Road, Dundee Stephenson, John, IM.B., D.Sc. (Loud.), Indian IMedical Service, Professor of Biology, Government College, Lahore, India. * Stephenson, Thomas, F.C.S., Editor of the Prescriber, Examiner to the Pharma- ceutical Society, 9 W’'oodburn Terrace, Edinburgh 530 Stevenson, Charles A., B.Sc., M.Inst. C.E., 28 Douglas Crescent, Edinburgh Stevenson, David Alan, B.Sc., M.Inst.C. E., 84 George Street, Edinburgh Stewart, Charles Hunter, D.Sc., M.B., C.M., Professor of Public Health in the University of Edinburgh, Usher Institute of Public Health, ’Warrender Park Road, Edinburgh * Stockdale, Herbert Fitton, Director of the Royal Technical College, Glasgow, Clairinch, Upper Helensburgh, Dumbartonshire Stockman, Ralph, M.D., F.R. C.RE., Professor of Materia Medica and Therapeutics in the University of Glasgow 535 Story, Fraser, Professor of Forestry, University College, Bangor, North AVales * Strong, John, M.A., Rector, Royal High School, Edinburgh, 27 Grange Road, Edinburgh Sutherland, David AA^., M.D., AI. R. C. P. , Captain, Indian Aledical Service, Professor of Pathology and Alateria Aledica, Aledical College, Lahore, India Swithinbank, Harold AVilliam, Denham Court, Denham, Bucks * Syme, AVilliam Smith, AI.D. (Edin. ), 10 India Street, Glasgow 540 Symington, Johnson, M.D., F.R.C.S.E. , F.R.S. , Professor of Anatomy in Queen’s College, Belfast * Tait, John W., B.Sc., Rector of Leith Academy, 18 Netherby Road, Leith Tait, William Archer, D.Sc., Al.Inst. C. E., 38 George Square, Edinburgh Talmage, James Edward, D.Sc., Ph.D., F.R.AI.S. , F.G.S., Professor of Geology, University of Utah, Salt Lake City, Utah, U.S.A. Tanakadate, Aikitu, Professor of Natural Philosophy in the Imperial University of Japan, Tokyo, Japan 545 Tatlock, Robert R., F.C.S. , City Analyst’s Office, 156 Bath Street, Glasgow * Taylor, James, M.A., Alathematical Alaster in the Edinburgh Academy Thackwell, J. B. , AI.B., C.AI. , 423a Battersea Park Road, London, S. W. ! Thompson, D’Arcy AV. , C.B., B.A. , F. L.S., Professor of Natural History in | University College, Dundee \ * Thompson, John Hannay, AI.Sc. (Durh.), AI.Inst.C.E., AI. Inst. Alech.E., Engineer to the Dundee Harbour Trust, Sorbie, 10 Balgillo Terrace, Broughty Ferry 550 * Thoms, Alexander, 7 Playfair Terrace, St Andrews Thomson, Andrew, ALA., D.Sc., F. I.C., Rector, Perth Academy, Ardenlea, Pitcullen, Perth Service on Council, etc- 1885-87- 1903-05- 1892-93- 1914- 1892-95, 1896-99, 1907-10, 1912-15. Alphabetical List of the Ordinary Fellows of the Society. 365 Date of Election. 1911 1896 1903 1906 1887 C. 1906 C. 1880 1899 1912 0. 1870 1882 1876 1911 C. 1914 1915 1888 1905 1906 C. * Thomson, Frank Wyville, SI. A., Si.B., C.M., D.P.H., D.T.SI., Lt.-CoL I.M.S. (Retired), Bonsyde, Linlithgow ■^Thomson, George Ritchie, Sl.B., C.SI., General Hospital, Johannesburg, Trans- vaal Thomson, George S., F.C.S., Ferma Albion, Slarculesci, Roumania 555 * Thomson, Gilbert, SI. Inst.C.E., 164 Bath Street, Glasgow Thomson, J. Arthur, SI. A., LL. D. , Regius Professor of Natural History in the University of Aberdeen Thomson, James Stuart, T.L.S., Zoological Department, University, Slanchester Thomson, John Millar, LL. D., F. R.S., Professor of Chemistry in King’s College, London, 18 Lansdowne Road, London, SV. * Thomson, R. Tatlock, F.C.S., 156 Bath Street, GlasgoAv 560 Thomson, Robert Black, SI.B., Edin., Professor of Anatomy, South African College, Cape Toavii Thomson, Spencer C., Actuary, 10 Eglinton Crescent, Edinburgh Thomson, SVin. , SI. A., B.Sc. , LL.D., Registrar, University of the Cape of Good Hope. University Buildings, Cape Town Thomson, AVilliam, Royal Institution, Slanchester * Tosh, James Ramsay, SLA., D.Sc. (St Ands.), Thursday, Island, Queensland, Australia 565 Tredgold, Alfred Frank, L.R.C.P., SI.R.C.S., Hon. Consulting Physician to National Association for the Feeble-minded, 6 Dapdune Crescent, Guildford, Surrey * Trotter, George Clark, Sl.D., Ch. B. Edin., D.P.H. (Aberdeen), Sledical Officer of Health, Paisley, Remuera, Paisley Turnbull, Andrew H., Actuary, The Elms, SS^hitehouse Loan, Edinburgh * Turner, Arthur Logan, Sl.D., F.R.C.S. E., 27 AValker Street, Edinburgh * Turner, Dawson F. D., B.A., Sl.D., F.K.C.P.E., SI.R.C.P., Lecturer on Sledical Physics, Surgeons’ Hall, Physician in charge of Radium Treatment, Royal Infirmary, Edinburgh, 37 George Square, Edinburgh 570 ^ 1861 K. N. C. Turner, Sir William, K.C.B., SI.B., F.R.C.S. L. and E., LL.D., D.C.L., D.Sc., F.R.S., Late Pres. R.S.E., Knight of the Royal Prussian Order Pour le^ Mey'itc, Principal and ATce-Chancellor of the University of Edinburgh, 6 Eton Terrace, Edinburgh 1895 1898 C. 1889 1910 1911 C. 1891 C. B. 1873 1902 1886 C. c. 1898 1891 1907 1901 c. 1911 1900 1907 1911 1911 Turton, Albert H., SI. LSI. SI. , 171 George Road, Erdington, Birmingham * Tweedie, Charles, SI. A., B.Sc., Lecturer on Slathematics in the University of Edinburgh, Chirnside, Berwickshire Underhill, T. Edgar, Sl.D., F.R.C.S. E., Dunedin, Barnt Green, AA^orcestershire Vincent, Swale, Sl.D. Lond., D.Sc. Edin., etc.. Professor of Physiology, University of Slanitoba, AVinni})eg, Canada 575 * AValker, Henry, SLA., D.Sc., Head Physics Slaster, Kilmarnock Academy and Technical School, 30 SI‘Lelland Drive, Kilmarnock Walker, James, D.Sc., Ph.D., LL.D., F.R.S., Professor of Chemistry in the University of Edinburgh, 5 AVester Coates Road, Edinburgh AAMlker, Robert, SLA., LL.D., University, Aberdeen * Wallace, Alexander G., SLA., 56 Fonthill Road, Aberdeen Wallace, R. , F.L.S. , Professor of Agriculture and Rural Economy in the University of Edinburgh 580 AVallace, AAMi., SLA., Belvedere, Alberta, Canada AAMlmsley, R. Mullineux, D.Sc., Principal of the Northampton Institute, Clerken- well, London AVaters, E. Wynston, Sledical Officer, H.B.SI. Administration, E. Africa, Slalindi, British East Africa Protectorate, via Slombasa * AVaterston, David, SLA., Sl.D., F.R.C.S.E. , Professor of Anatomy, University, St Andrews * AA^atson, James A. S., B.Sc., etc.. Assistant in Agriculture, University of Edin- burgh, 15 Dick Place, Edinburgh ' 585 * AA^atson, Thomas P., SI. A., B.Sc., Principal, Keighley Institute, Keighley * AA^att, Andrew, SI. A., Secretary to the Scottish Sleteorological Society, 6 AA^oodburn Terrace, Edinburgh AVatt, James, AV.S., F.F.A., 24 Rothesay Terrace, Edinburgh * Watt, Rev. Lauchlan Maclean, B.D., Minister of St Stephen’s Parish, 7 Royal Circus, Edinburgh Service on Council, etc. 1906-08. 1866-68, 1895-97, 1913- Sec. 1869-91. V-P 1891-95, 1897-1903. P. 1908-1913. 1907-10. 1903-05, 1910-13. 1912-14. 366 Proceedings of the Royal Society of Edinburgh. Date of Election. 1896 1907 1903 1904 1896 1909 1896 1911 1912 1879 1908 1910 1900 1911 1902 1895 1882 1891 1902 1908 1886 1884 1911 1890 1896 1882 1892 1896 1904 B. C. C. C. c. c. c. c. c. Webster, John Clarence, B.A., M.D., F.R.C.P.E., Professor of Obstetrics and Gynae- cology, Rush Medical College, 1748 Harrison Street, Chicago, 111., U.S.A. 590 * Wedderburii, Ernest Maclagan, M.A., LL. B., W.S. , D.Sc. , 7 Dean Park Crescent, Edinburgh * AVedderburn, J. H. Maclagan, M. A., D.Sc., 95Mercer Street, Princeton, H.J., U.S.A. Wedderspoon, William Gibson, M.A., LL.D., Indian Educational Service, Senior Inspector of Schools, Burma, The Education Office, Pangoon, Burma , Wenley, Robert Mark, M.A., D.Sc,, D.Phih, Litt.D., LL.D., D.C.L., Professor of Philosophy in the University of Michigan, Ann Arbor, U.S.A. | * AVestergaard, Reginald Ludovic Andreas Emil, Ph.D. , Professor of Technical j Mycology, Heriot-AVatt College, Hafnia, Liberton, Edinburgh 595 j White, Philip J., M.B., Professor of Zoology in University College, Bangor, North Wales * Whittaker, Charles Richard, F. R.C.S. (Edin.), F.S. A. (Scot, ), Lynwood, Hatton Place, Edinburgh * Whittaker, Edmund Taylor, Sc. D., F.R.S., Professor of Mathematics in the University of Edinburgh, 35 George Square, Edinburgh AA^ill, John Charles Ogilvie, of Newton of Pitfodels, Al.D., 17 Bon-Accord Square, Aberdeen * AVilliamson, Henry Charles, M.A., D.Sc., Naturalist to the Fishery Board for Scotland, Marine Laboratory, Aberdeen 600 * Williamson, William, 79 Alorningside Drive, Edinburgh AVilson, Alfred C. , If.C.S., V'oewood Croft, Stockton-on-Tees ■^AVilson, Andrew, M.Inst. C.E., 51 Queen Street, Edinburgh * AVilson, Charles T. R., ALA., F.R.S., 14 Cranmer Road, Cambridge, Sidney Sussex College, Cambridge AA^ilson- Barker, David, R.N.R, , F. R.G.S., Captain-Superintendent Thames Nautical Training College, H.AI.S. “ AVorcester,” off Greenhithe, Kent 605 AVilson, George, AI. A. , AI.D., LL.D. AVilson, John Hardie, D.Sc., University of St Andrews, 39 South Street, St Andrews AVilson, AVilliam AVright, F.R.C.S.E., A'l.R.C.S., Cottesbrook House, Acock’s Green, Birmingham * Wood, Thomas, AI.D., Eastwood, 182 Ferry Road, Bonnington, Leith AVoodhead, German Sims, AI.D., F.R.C.P.E., Professor of Pathology in the University of Cambridge 610 AVoods, G. A., ALR.C.S., 1 Hammelton Road, Bromley, Kent * AVrigley, Ruric AA^hitehead, B.A. (Cantab.), Assistant Astronomer, Royal Observa- tory, Edinburgh AVright, Johnstone Christie, Conservative Club, Edinburgh * Wright, Sir Robert Patrick, Chairman of the Board of Agriculture for Scotland, Kingarth, Colinton, Alidlothian Young, Frank W., F.C.S. , H.AI. Inspector of Science and Art Schools, 32 Buckingham Terrace, Botanic Gardens, Glasgow 615 Young, George, Ph.D., “Bradda,” Church Crescent, Church End, Finchley, London, N. * Young, James Buchanan, M. B. , D.Sc., Dalveen, Braeside, Liberton Young, R. B., AI.A., D.Sc., F.G.S., Professor of Geology and Alineralogy in the South African School of Alines and Technology, Johannesburg, Transvaal 618 Service on Council, etc. 1913- 1912-15. 1887-90. LIST OF HONORARY FELLOWS OF THE SOCIETY At January 1, 1916. HIS AlOST GRACIOUS AIAJESTY THE KING. Foreigneks (limited to thirty-six by Laav XII). Elected 1900 Adolf Ritter von Baeyer, Universitiit, Miinchen, Germany. 1905 Waldemar Christofer Brogger, K. Frederiks Universitet, Christiania, Norway. 1905 Moritz Cantor, Gaisbergstrasse 15, Heidelberg, Germany. 1902 Jean Gaston Darboux, Secretariat de ITnstitut, Paris, France. 1910 Hugo de Vries, Universiteit, Amsterdam, Holland. List of Honorary Fellows, etc. 3G7 Elected 1908 Emil Fischer, Universitiit, Berlin, Germany. 1910 Karl F. von Goebel, Universitat, Miinchen, Germany. 1905 Paul Heinrich von Groth, Universitat, Miinchen, Germany. 1888 Ernst Haeckel, Universitat, Jena, Germany. 1913 George Ellery Hale, Mount Wilson Solar Observatory (Carnegie Institution of Washington), Pasadena, California, U. S.A. 1883 Jytlius Hann, Universitat, Wien, Austria. 1913 Emil Clement Jungfleisch, College de France, Paris, France. 1910 Jacobus Cornelius Kapteyn, Universiteit, Groningen, Holland. 1897 Gabriel Lippmann, Universite, Paris, France. 1895 Carl Mengei-, Wien ix., Fuchstallerg, 2, Austria. 1910 Elie Metchnikotf, Institut Pasteur, Paris, France. 1910 Albert Abraham Michelson, University, Chicago, U.S.A. 1897 Fridtjof Nansen, K. Frederiks Universitet, Christiania, Norway. 1908 Henry Fairfield Osborn, Columbia University and American Museum of Natural History, New York, N.Y., U.S.A. 1910 Wilhelm Ostwald, Gross-Bothen, bei Leipzig, Germany. 1908 Ivan Petrovitch Pawlov, Wedenskaja Strasse 4, St Petersburg, Russia. 1889 Georg Hermann Quincke, Bergstrasse 41, Heidelberg, Germany. 1913 Santiago Ramon y Cajal, Universidad, Madrid, Spain. 1908 Magnus Gustaf Retzius, Hbgskolan, Stockholm, Sweden. 1908 Augusto Righi, Regia Universita, Bologna, Italy. 1913 Yito Volterra, Regia Universita, Rome, Italy. 1905 Wilhelm Waldeyer, Universitat, Berlin, Germany. 1905 Wilhelm AVundt, Universitat, Leipzig, Germany. Total, 28. Bkitish Subjects (limited to twenty by Law XII). 1900 Sir David Ferrier, Kt. , M.A. , M.D., LL.D., F.R.S., Emer. -Professor of Neuro-Pathology, King’s College, London, 34 Cavendish Square, London, W. 1900 Andrew Russell Forsyth, M.A. , Sc.D., LL.D., Math.D. , F.R.S., Chief Professor of Mathematics in the Imperial College of Science and Technology, London, formerly Sadlerian Professor of Pure Mathematics in the University of Cambridge, Imperial College of Science, London, S.AV. 1910 Sir James George Frazer, D.C.L. , LL.D., Litt.D., F.B.A., Fellow of Trinity College, Cam- bridge, Professor of Social Anthropology in the University of Liverpool, Trinity College, Cambridge. 1908 Sir Alexander B. AY. Kennedy, Kt., LL.D., F.R.S., Past Pres. Inst. C.E., A7, Albany, Piccadilly, London, W. 1913 Horace Lamb, M.A., Sc.D., D.Sc., LL.D., F.R.S. , Professor of Mathematics in the University of Manchester. 1908 Sir Edwin Ray Lankester, K.C.B., LL.D., F.R.S. , 29 Thurloe Place, S. Kensington, London, S.W. 1910 Sir Joseph Larmor, Kt., M.A., D.Sc., LL.D., D.C.L., F.R.S., M. P. University of Cambridge since 1911, Lucasian Professor of Mathematics in the University of Cambridge, St John’s College, Cambridge. 1900 Archibald Liversidge, M.A., LL.D., F.R.S., Em. -Professor of Chemistry in the University of Sydney, Fieldhead, Combe AYarren, Kingston, Surrey. 1905 Sir AVilliam Ramsay, K.C. B., LL.D., F.R.S., formerly Professor of Chemistry in the University College, London, 19 Chester Terrace, Regent’s Park, London, N.W. 1886 The Rt. Hon. Lord Rayleigh, O.M., P.C., J.P., D.C.L., LL.D., D.Sc. Dub., F.R.S. , Corresp. Mem, Inst, of France, Terling Place, Witliam, Essex. 1908 Charles Scott Sherrington, M.A,, M.D., LL.D,, F.R.S., Waynflete Professor of Physiology in the University of Oxford, Physiological Laboratory, Oxford. 1913 Sir William Turner Tbiselton-Dyer, K.C.M.G., C.I.E., M.A., LL.D., F.R.S., formerly Director of the Royal Botanic Gardens, Kew ; The Ferns, Witcombe, Gloucester. 1905 Sir Joseph John Thomson, D.Sc., LL.D., F.R.S., Cavendish Professor of Experimental Physics, University of Cambridge, Trinity College, Cambridge, 1900 Sir Thomas Edward Thorpe, Kt. , C.B., D.Sc., LL.D., F.R.S,, formerly Principal of the Government Laboratories, Imperial College of Science and Technology, South Kensington, London, S.AV., AYhinfield Salcombe, South Devon. Total, 14. 368 Proceedings of the Royal Society of Edinburgh. [Sess. ORDINARY FELLOWS OF THE SOCIETY ELECTED Durmg Session 1914-15. (Arranged according to tlieir date of election.) Wi December 1914. John Edward Aloysius Steggall, M.A. 18^/^ January 1915. Charles Anthony, M.Inst.C.E., M.I.Mecli.E., F.R.A.S. Alfred Archibald Boon, D.Sc. Lewis P. Orr, F.F.A. Is^ February 1915. Raymond Keiller Butchart, B.Sc. Robert Campbell, D.Sc. 1st 31arch 1915. Walter Leonard Bell, M.D. (Edin.), F.S.A. (Scot.). * 3?rZ May 1915. Joseph Robert Fraser, Clergyman. George Clark Trotter, M.D., Ch.B. (Edin.), D.P.H. (Aberdeen). 21s;; June 1915. James Hermann Rosenthal Kemnal, Engineer. James Lorrain Smith, M.A., M.D., F.R.S. July 1915. Frederick William Price, M.D., M.R.C.P. (Edin.). ORDINARY FELLOWS DECEASED During Session 1914-15. William Anderson, F.G.S. J. Macvicar Anderson, Architect. J. B. Buist, M.D., F.R.C.P.E. SirT. S. Clouston, LL.D., F.R.C.P.E. Archibald Constable, LL.D. Principal Sir James Donaldson, M.A., LL.D. FOREIGN honorary Emile Hilaire Amagat. Georg F. J. A. Auwers. Paul Ehrlich. Professor A. Campbell Fraser. Professor James Geikie, LL.D., D.C.L., F.R.S. , F.G.S. Professor D. T. Gwynne-Yaughan, F.L.S. Sir Charles Hartley, K.C.M.G. Archibald Hewat, F. F.A., F.I.A. FELLOVsTS DECEASED. Frederick Ward Putnam. August F. L. Weismann. BRITISH HONORARY FELLOW DECEASED. Sir James A. H, Murray. 1914-15.] List of Library Exchanges, Presentations, etc. 369 List of Library Exchanges, Presentations, etc. 1. 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 Loyal Society of Edinburgh. {For convenience certain Presentations are included in this List.) 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 Degoartmeut. Meteorological Observations, Fol. (Presented by H.M. Acting Commissioner and Consul-General .) AMERICA (NORTH). (See CANADA, UNITED STATES, and MEXICO.) AMERICA (SOUTH). T.P. 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Australasian Association for the Advancement of Science. — Reports. (Pre- sented.) VOL. XXXV. 24 370 p. T.P. P. T.P. P. P. P. P. P. T.P. T.P. P. P. T.P. T.P. T.P. T.P. T.P. T.P. T.P. P. P. Proceedings of the Royal Society of Edinburgh. [Sess. Adelaide — University Library. Royal Society of South Australia. Transactions and Proceedings. — Memoirs. Royal Geographical Society of Australasia {South Australian Branch), Proceedings. Observatory. Meteorological Observations. 4 to, {Presented.) Brisbane — University of Queensland. Royal Society of Queensland. Transactions. Royal Geographical Society {Queensland Branch). Queensland Geographical Journal. Government Meteorological Office. Water Supply Department. Geelong (Yictoria). — Gordon Technical College. Hobart. — Royal Society of Tasmania. Proceedings. Melbourne — Commonwealth Bureau of Census and Statistics. Official Year Book. By G. H. Knibbs. {Presented.) National Museum. Memoirs. {Presented.) University Library. Royal Society of Victoria. Proceedings. — Transactions. Perth, W.A. — Geological Survey. Annual Progress Reports. — Bulletins. Government Statistician's Office. Monthly Statistical Abstract. {Presented.) Sydney — University Library. Calendar. — Reprints of Papers from Science Laboratories. Department of Mines and Agriculture {Geological Surve^j), N.S. W. Records. — Annual Reports. — Palaeontology. Mineral Resources. Linnean Society of Neio South Wales. Proceedings. Royal Society of Neiv South Wales. Journal and Proceedings. Australian Museum. Records. — Reports. — Memoirs. — Catalogues. TP. Government. Fisheries Report. {Presented.) AUSTRIA. Cracow — Academie des Sciences. Rozprawy Wydzialu matematyczno-przyrodniezego (Proceedings, Math, and Nat. Sciences CL). — Rozprawy Wydzialu filologicznego (Proc., Philological Section). — Rozprawy Wydzialu his- toryczno-filozoficznego (Proc., Hist.-Phil. Section). — Sprawozdanie Komisyi do badania historyi sztuki w Polsce (Proc., Commission on History of Art in Poland). — Sprawozdanie Komisyi fizyjograficznej (Proc., Commission on Physiography). — Geological Atlas of Galicia; Text, Maps. — Bulletin International, etc. Gratz — N aturwissenschaftlicher Verein filr Steiermarh. Mittheilungen. Chemisches Institut der K. K. Universitdt. Lemberg. — Societe Scientifigue de Chevtchenko. 1914-15.] List of Library Exchanges, Presentations, etc. 371 Prague — p. Deutscher Nat. -Med. Vereinfur Bdhmen Lotos T — “Lotos.” T.p. K. K. Stermuarte. Magnetische und Meteorologische Beobachtnngen. Astronomische Beobachtungen. T.p. K. Bohmische Gesellschaft. Sitzungsbericlite : Math.-Natiirw. Classe ; Phil.- Hist.-Philol. Classe. — Jabresbericht, — and other publications. T,p. Geskd Akademie Gisare Frantiska Josef a yro Vedy Slovesnost a Umeni. Almanach. — Vestnik (Proceedings). — Eozpravy (Transactions): Phil.- Hist. Class ; Math.-Phys. Cl. ; Philol. Cl. — Historicky Arcliiv. — Bulletin International, Resume des Travaux presentes, — and other publications of the Academy. p. Sarajevo (Bosnia). — The Governor-General of Bosnia-Herzegovina. Ergebnisse der Meteorologischen Beobachtungen. Trieste — p. Societd Adriatica di Scienze Naturali. p. Museo Givico di Storia Naturale. p. Osservatorio Marittimo. Rapporto Annuale. Vienna — T.p. Kais. Akademie der Wissenschaften. Denkschriften : Math.-lSTaturwissen- schaftliche Classe ; Philosophisch-Historische Classe — Sitzungsbericlite der Math.-jSTaturwissenschaftlichen Classe; Abtheil. I., II.a, II.b, III.; Philosoph.-Historische Classe.— Almanach. — Mittheilungen der Erdbeben Commission. T.p. K. K. Geologisehe Reichsanstalt. Abhandlungen. — Jalirbiicher. — Verhand- lungen. T.p. Oesterreichische Gesellschaft f Hr Meteorologie. Meteorologische Zeitschrift. T.p. K. K. Zoologisch - Botanische Gesellschaft. Yerhandlungen. — Abhand- lungen. p. K. K. N aturliistorisches Hofmuseum. Annalen. K. K. Gentral-Anstalt fiXr Meteorologie und Erdmagnetismus. Jalirbiicher. 4to. — Allgemeiner Bericht und Chronik. 8vo. {Presented.) K. K. Militar Geographisches Institut. Astrononiisch-Geodatischen Arbeiten. — Astronomische Arbeiten. 4to. — Langenbestimniungen. 4to. — Die Ergebnisse der Triangulierungen. 4to. {Presented.) Zoologisches Institut der Universitdt und der Zoologischen Station in Triest. Arbeiten. {Purchased.) BELGIUM. Brussels — T.p. Academie Roy ale des Sciences, des Lettres et des Beaux Arts de Belgique. Memoires. — Bulletins. — Annuaire. — Biographic Rationale. T.p. Musee Royal d’Histoire Naturelle. Memoires. T.p. Musee du Gongo. Annales. — Botanique. Zoologie. Ethnograqdiie et Anthropologic. Linguistique, etc. T.p. V Ohservatoire Royal de Belgique, Uccle. Annuaire. — Annales Astronomiques — Annales Meteorologiques. — Annales. — Physique du Globe. — Bulletin Climatologique. — Observations Meteorologiques. 372 T.P. P. T.P. T.P. P. P. T.P. P. P. T.P, T.P. P. T.P. T.P. T.P. F. T.P. Proceedings of the Royal Society of Edinburgh. [Sess. Bkussbls — continued — Societe Scientifique. Annales. Societe Beige Astronomie. Ciel et Terre. {Purchased.) Ghent. — University Library. Louvain. — University Library. BOSNIA-HERZEGOVINA. AUSTRIA,) BULGARIA. Sofia. — Station Centrale Meteorologique de Bulgarie. Bulletin Mensuel. — Bulletins Annuaires. CANADA. Edmonton (Alberta). — Department of Agriculture. Annual Report. — {Presented.) Halifax (Nova Scotia). — Nova Scotian Institute of Science. Proceedings and Transactions. Kingston. — Queen^s University. Montreal — Natural History Society. Proceedings. Canadian Society of Civil Engineers. Transactions. — Annual Reports. Ottawa — Royal Society of Canada. Proceedings and Transactions. Geological Survey of Canada. Annual Reports.— rPalseozoic Fossils. — Maps, Memoirs, and other Publications. Literary and Scientific Society. Transactions. Quebec. — Literary and Philosophical Society. Transactions. Toronto — University. University Studies. (History. Psychological Series. Geological Series. Economic Series. Physiological Series. Biological Series. Physical Science Series. Papers from the Chemical Laboratory.) etc. Canadian Institute. Transactions. Royal Astronomical Society of Canada. Journal. — Astronomical Handbook. CAPE COLONY. {See UNION OF SOUTH AFRICA.) CEYLON. Colombo — Museum. Spolia Zeylanica. Annual Report. CHINA. Hong Kong — Royal Observatory. Monthly Meteorological Bulletin. — Report. 1914-15.] List of Library Exchanges, Presentations, etc. 373 DENMARK. Copenhagen — T.p. Academie Royale de Gopenhague. Memoires : Classe des Sciences, — Oversigt. p. Naturhistorisk Forening. Videnskabelige Meddelelser. p. Danish Biological Station. Report. Conseil Permanent International pour V ExgAoration de la Mer. Publications de circonstance. — Rapports et Proces-Verbaux de Reunions. — Bulletin des Resultats acquis pendant les croisieres periodiques. — Bulletin Statistique. [Presented.) Kommissionen for Havundersogelser. Meddelelser : SAde Fiskeri, Serie Plankton. Serie Hydrografi. — Skrifter. [Presented.) University (Zoological Museum). Reports of the Danish Ingolf-Expedition. (Presented.) EGYPT. T.p. Cairo. — School of Medicine. Records. Ministry of Finance (Survey Dept. : Archaeological Survey of Nubia). Bulletin, Reports, Papers. (Presented.) ENGLAND AND WALES. T.p. Aberystwyth. — National Library of Wales. Birmingham — p. Philoso2:)hical Society. Proceedings, University. Calendar. (Presented f) Cambridge — t.p. Philosophiccd Society. Transactions and Proceedings. T.p. Uriiversity Lihranny. — Observatory . Report. — Observations. T.p. Cardiff. — University College of South Wales. Coventry. — Annual Report of the Health of the City. (Presented by Dr Snell.) p. Essex. — Essex Field Club. The Essex Naturalist. T.p. Greenwich. — Royal Observatory. Astronomical, Magnetical, and Meteorological Observations. — Photo-heliographic Results and other Publications. T.p. Harpenden (Herts.). — Rothamstead Exp. Station. (Lawes Agricidtural Trust.) Leeds — T.p. Philosophical and Literary Society. Reports, p. Yorkshire Geological and Polytechnic Society. Proceedings. Liverpool — T.p. University College Library. p. Biological Society. Proceedings and Transactions, p. Geological Society. Proceedings. London— p. Admiralty . Nautical Almanac and Astronomical Ephemeris. — Health of the Navy (Annual Report). p. Aeronautical Society of Great Britam. Aeronautical Journal. Aeronautical Classics. Reports of the Bird Construction Committee. T.p. Anthropological Institute. Journal. 374 Proceedings of the Royal Society of Edinburgh. [Sess. London— continued — T.P. Athenaeum Club. British Antarctic Expeditions 1907-09. Reports on Scientific Investigations. ( Presented. ) T.P. British Association for the Advancement of Science. Reports. T.P. British Museum {Gopijrujht Office). Reproductions from Illuminated Manuscripts. T.P. British Museum. Natural History Department. Catalogues, Monographs, Lists, etc. National Antarctic Expedition, 190 1-0 Jf. Publications. T.P. Chemical Society. Journal. Abstract of Proceedings, p. Faraday Society. Transactions. T.P. Geological Society. Quarterly Journal. — Geological Literature. — Abstract of Proceedings. T.P. Geological Survey of the United Kingdom. Summary of Progress. Memoirs, p. Geologists’ Association. Proceedings. T.P. Hydrographic Office. T.P. Imperial Institute. T.P. Institution of Civil Engineers. Minutes of Proceedings, etc. T.P. Institution of Electrical Engineers. Journal, p. Institution of Alechanical Engineers. Proceedings. T.P. International Catalogue of Scientific Literature. {Purchased.) T.P. Linnean Society. Journal: Zoology; Botany. — Transactions: Zoology; Botany. — Proceedings, p. Mathematical Society. Proceedings. T.P. Meteorological Office. Report of the Meteorological Committee to the Lords Commissioners of H.M. Treasury. — Reports of the International Meteoro- logical Committee. — Hourly Readings. — Weekly Weather Reports. — Monthly and Quarterly Summaries. — Meteorological Observations at Stations of First and Second Order, and other Publications. Geophysical Journal. — Geophysical Memoirs. Mineralogical Society of Great Britain and Ireland. Mineralogical Magazine and Journal. {Presented.) National Antarctic Expedition, 1901-0 Jf.. {Presented.) Optical Society. Transactions. {Purchased.) p. Pha.rmaceutical Society. Journal. — Calendar, p. Physical Society. Proceedings. T.P. Royal Astronomical Society. Monthly Notices. — Memoirs. T.P. Royal College of Surgeons. T.P. Roycd Geographical Society. Geographical Journal. T.P. Royal Horticultural Society. Journal. T.P. Royal Institution. Proceedings. p. Royal Meteorological Society. Quarterly Journal. T.P. Royal Microscopical Society. Journal, p. Royal Photographic Society. Photographic Journal. T.P. Royal Society. Philosophical Transactions. — Proceedings. — Year-Book. — National Antarctic Expedition, 1901-0 If, Publications; and other Publications. T P. Royal Society of Arts. Journal. 1914-15.] List of Library Exchanges, Presentations, etc. 375 London — continued — T. p. Royal Society of Literature. Transactions. — Reports. T.p. Royal Society of Medicine. Proceedings. T.p. Royal Statistical Society. Journal. T.p. Society of Antiquaries. Proceedings. — Arcliseologia ; or Miscellaneous Tracts relating to Antiquity. Society of Chemical Industry. Journal. {Presented.) Society for Psychical Research. Journal. — Proceedings. {Presented hy W. C. Graioford, Esq.) Solar Physics Committee. Annual Report, and other Publications. {Presented.) T.p. United Service Institution. T.p. University College. Calendar. T.i’. University. T.p. Zoological Society. Transactions. — Proceedings. T p. The Editor of Nature. — Nature. T.p. The Editor of The Electrician. — Electrician. T.p. The Editor of Science Abstracts. — Science Abstracts. Manchester — T.p. Literary and Philosophical Society. Memoirs and Proceedings. T.p. University. — Publications — Medical Series. Public Health Series. Anatomical Series. Physical Series. Biological Series. Lectures. Manchester Museum {University of Manchester). Annual Reports — Notes from the Museum, p. Microscopical Society. Transactions and Annual Report. Newcastle-on-Tyne — p. Natural History Society of Northumberland.^ Durham, etc. Transactions. T.p. North of England Institute of Mining and Mechanical Engineers. Transac- tions.— Annual Reports. Cullercoats Dove Marine Lahorator y . Annual Report. {Presented.) p. Literary and. Philosophical Society. University of Durham Philosophical Society. Proceedings. {Presented.) p. Norwich. — Norfolk and Norivich Naturalists Society. Transactions. Oxford — T.p. Bodleian Library. p. Ashmolean Society. Proceedings and Report. p. Radcliffe Observatory. Results of Astronomical and Meteorological Obser- vations. University Observatory. Astrographic Catalogue. {Presented.) p. Penzance. — Royal Geological Society of Cormvall. Transactions. T.p. Plymouth. — Marine Biological Association. Journal. Richmond (Surrey) — T.p. Kew Observatory. p. Scarborough. — Philosophical Society. T.p. Sheffield. — University College. Southport. — Meteorological Observatory. Results of Observations. Joseph Baxendell, Meteorologist. {Presented.) T.p. Teddington (Middlesex). — National Physical Laboratory. Collected Researches. — Annual Reports. 376 p. T.P. T.P. T.P. P. T.P. P, P. P. P. T.P. T.P. P. T.P. T.P. T.P. P. P. TP. P. T.P. Proceedings of the Poyal Society of Edinburgh. [Sess. Trueo. — Royal Institution of Cornwall. Journal. York — Yorkshire Philosophical Society. Reports. FINLAND. Helsingfors — Academice Scientiarum Fennicoe. Annales. Sitzungsberichte. — Documenta Historica. {Presented.) Hydrographisch Biologisch Untersuchungen. {Presented.) Societas Scientiarum Fennica {SociHe des Sciences de Finlande). Acta Societatis Scientiarum Fennicae. — Ofversigt. — Meteorologisches Jahrbuch. — Bidrag till Kannedoni om Finlands Natur ocli Folk. Societas pro Fauna et Flora Fennica. Acta. — Meddelanden. Societe de Geographie de Finlande. Fennia. — Meddelanden. FRANCE. Besancon. — Universite Ohservcdoire National. Bulletin Chronometrique et Bulletin Mdteorologique. {Presented.) Bordeaux — Societe des Sciences Physiques et Natur elles. Memoires. — Observations Pluviometriques et Tberinometriques.— Proces-Verbaux des Seances. Societe de Geographie Commerciale. Bulletin. n Observatoire. Catalogue Photograpliique du Ciel. Cherbourg. — Societe Nationale des Sciences Naturelles et Mathematiques. Memoires. Concarneau. — College de France {Lahoratoire de Zoologie et de Physiologie Maritime). Travaux Scientifiques. Dijon. — Academie des Sciences. Mmnoires. Lille — Societe des Sciences. Societe Geologicque du Nord. Annales.— Memoires. Universite de France. Travaux et Memoires. Lyons — Academie des Sciences, Belles Lettres et Arts. Memoires. Societe d' Agriculture, Histoire Nat. et Arts. Annales. Universite. Annales, Nouv. Serie : — I. Sciences, Medecine. II. Droit, Lettres. Societe Botanicque. Annales. — Nouveaux Bulletins. Societe Linneenne. Annales. Marseilles — Faculte des Sciences. Annales. Societe Scientifique Industrielle. Bulletin. Montpellier. — Acadhnie des Sciences et Lettres. Memoires : Section des Sciences ; Section des Lettres ; Section de Medecine. Bulletin Mensuel. 1914-15.] List of Library Exchanges, Presentations, etc. 377 T.p. Xantes. — Societe Scientijique des Sciences Natiirelles de V Quest de la France. Bulletin. T.p. Nice. — VOhsermtoire. Annales. Paris— T.p. Acad.emie des Sciences. Comptes Rendiis. — Ohservatoire d’AbhacUa : Observations, 4to, and other Publications. T.p. Acadhnie des InscriiMons et Belles-Lettres. Comptes Piendus. T.p. Association Francaise jgour V Avancement des Sciences. Comptes Rendus, T.p. Bureau International des Poids et Mesures. — Proces-Verliaux des Seances, — Travaux et Mmnoires. T.p. Bureau des Longitudes. Annuaire. p. UEcole des Fonts et Chaussees. T.p. Alinistere de la Alarine. {Service Hydrograg)liique.) Annales Hydro- graphiques. Expedition de Charcot, 1903-05. {See Presentation List.) T.p. Ecole des Mines. Annales des Mines. T.p Ecole Normale Superieure. Annales. T.p. Pcole Pohjtechnique. Journal, p. i^cole Libre des Sciences Politiques. T.p. Institut Oceanographique. Annales. T.p. Ministere de V l7Lstruction Publiqu^. Expedition de Charcot, 1908-10. {See Presentation List.) T.p. Mnsee Guimet. Revue de FHistoire des Religions. — Annales. — Bibliotheque d’Etudes. T.p. Aluseum dMistoire Naturelle. Nouvelles Archives. — Bulletin. T.p. V Observatoire. Rapport Annuel sur I’Etat de I’Observatoire.- — Annales — Memoires. — Carte Photographique du Ciel. Eol. — Catalogue Photo- graph ique du Ciel. 4to. E Observatoire E Astronomic Physique de Aleudon. Annales. {P resented.) T.p. Societe Nationale di Agricidture. Bulletins. — Memoires. p. Societe di Antlir op ologie. Bulletin et Memoires. T.p. Societe Nationale des Antiquaires. Memoires. — Bulletin. T.p. Societe de Biologic. Comptes Rendus. T.p. Societe E Encouragement pour V Industrie Nationale. Bulletin. T.p. Societe Frangaise de Physique. Journal de Physique. — Annuaire. — Proces- Yerbaux. T.p. Societe de Geographic. La Geographie. T.p. Societe Geologique de France. Bulletins. — Memoires (Paleontologie). p. Societes des Jeunes Naturalistes et E Etudes SciBntijiques. Feuilles des Jeunes Naturalistes. T.p. Societe Mathematique. Bulletin. P. Societe Pliilomathique. Bulletin. T.p. Societe Zoologique. Hulletin. — Memoires. p. Revue Generate des Sciences Pures et Appliquees. T.p. Rennes. — Societe Scientifique et Medicate de VOuest. Bulletin. Toulouse — T.p. Universite. — Faculte des Sciences. — U Observatoire. Annales. p. Academic des Sciences. Memoires. 378 Proceedings of the Royal Society of Edinburgh. [Sess. GERMANY. Berlin — Carte Geologique inteniationale de V Europe. Livres I. -VI II. (complete). {Presented.) T.p. K. Akademie der Wissenscliaften. Abhandlungen. — Sitzimgsberichte. T.p. Physikalische Gesellschaft. Fortschritte der Physik : P® Abtheil : Physik der Materie. 2*® Abtheil ; Physik des Aethers. 3® Abtheil ; Kosmische Physik. — ■Verhandlungen. T.p. Deutsche Geologische Gesellschaft. Zeitschrift. — Monatsberichte. p. Deutsche Meteorologische Gesellschaft. Zeitschrift. p. Konigl. Preussisches Meteorologisches Pistitut. p. Gesellschaft Naturforschender Freunde. Sitzimgsberichte. — Archiv fiir Biontologie. p. Kgl. Technische Hochschule. Prograinm. T.p. Zoologisches Museum. Mitteilungen. Bonn — p. Naturhistorischer Verein der Preussischen Rhemlande und Westfalens. Ver- handlungen. Nied.errheinische Gesellschaft fur Natur- und Heilkunde. Sitzimgsberichte {Presented.) T.p. Bremen. — N aturwissejischaftlicher Verein. Abhandlungen. p. Brunswick. — Verein f ur Naturioissenschaft. Jahresberichte. p. Carlsruhe. — Technische Hochschule. Dissertations, p. Cassbl. — Verein fur Naturkunde. Berichte. T.p. Charlottenburg. — Physikalisch-Technische Reich sanst alt. Abhandlungen. p. Chemnitz. — Naturivissenschaftliche Gesellschaft. Berichte. T.p. Dantzic. — Naturforschende Gesellschaft. Schriften. W estpreussischer Botanisch-Zoologischer Verein. Bericht. {Presented.) Erlangen — T.p. University. Inaugural Dissertations, p. Physikalisch-Medicinische Societdt. Sitzimgsberichte. T.p. F RANKFURT - AM - Main. — Senckenhergisclie Naturforsch ende Gesellschaft. Ab- handlungen.— Berichte. p Frankfurt-am-Oder. — Natur wissenschaftlicher Verein. Helios, p. Freiburg- i Br. — Naturforschende Gesellschaft. Berichte. Giessen — T.p. University. Inaugural Dissertations. p. Oherhessische Gesellschaft fur Natur- und Heilkunde. Berichte. T.p. Gottingen. — K. Gesellschaft der Wissenschaften. Abhandlungen, Neue Folge ; Math.-Phys. Classe ; Phil. -Hist. Classe. — Nachrichten : Math.-Phys. Cl. ; Phil. -Hist. Cl.; Geschaftliche Mittheilungen. — (Gelehrte Anzeigen. Purchased.) Halle — T.p K. Leopold- Gar olinisch- Deutsche Akademie der Naturf or seller. Nova Acta (Verhandlungen). — Leopoldina. T.p. Naturforschende Gesellschaft. Abhandlungen. p. Verein fiir Erdkunde. Mittheilungen. 1914-15.] List of Library Exchanges, Presentations, etc. 379 Halle — continued — p. Naturwissenscliaftlichei' Vereinf ilr Sdchse?i und Tlmringeii. p. Deutsche MathemaMker Vereinigung. Jahresbericht. Hamburg — T.p. Kaiserliclie Marine Deutsche Seewarte. Annaleii der Hydrographie, etc. — Jahresbericht. T.p. Naturioissenscliaftliclier Vereia. Abhandlungen aiis deni Gebiete der Natur- ivissenschaften. — Verhandlungen. T.p. Naturhistorisches Museum. Jahrbiich. — -Beihefte. — Mitteilungen. p. Verein fiir NaturiuissenschaftHche Unterhaltung. Yerhandlungen. T.p. Hannover. — Naturhistorische Gesellschaft. Jahresbericht. T.p. Helgoland. — K. Biologisches Anstalt. Wissenschaftliche Meeresunter- suchiingen (Abtheilimg Helgoland). T.p. Jena. — Medicinisch-Natur wissenschaftliche Gesellschaft. Jenaische Zeitschrift fiir Naturwissenschaft. — Denkschriften. Kiel — T.p. Universltdt. Dissertations. T.p. Kommission zur Wisseuschaftlichen Untersnchung der Deutschen Meere. Wissenschaftliche Meeresuntersuchnngen (Abtheilung Kiel), p. N aturwissenschaftlicher Verein fiir Schlestoig-Holstein. Schriften. T.p. Konigsberg. — University. Leipzig — Filrstlich J ablonowskische Gesellschaft. Preisschriften. {Presented.) T.p. Konigl. Sdchsische Gesellschaft der Wissenschaften. Berichte : Math.-Phys. Classe ; Philologisch-Historische Classe. — Abhandlungen der Math.-Phys. Classe ; Phil. -Hist. Classe. T.p. Editor of Annalen der Physik. Annaleii der Physik. p. Naturforschende Gesellschaft. Sitzungsberichte. Deutsche Mathematiker Vereinigung. {See Halle.) p. Lubeck. — Geographische Gesellschaft und Naturhistorisches Aluseum. Mitteil- ungen. p. Magdeburg. — N aturwissenschaftlicher Verein. Abhandlungen u. Berichte. T.p. Munich. — K. Bayerische Akadernie der Wissenschaften. Abhandlungen: Matheinatisch-Physikalische Classe ; Philosophisch-Philologische Classe ; Historische Classe. — Sitzungsberichte: Matheinatisch-Physikalische Classe; Philosophisch-Philol. und Historische Classe. — Jahrbuch. K. Sternwarte. Keue Annalen. {Presented.) p. Offenbach. — Vereinfilr Naturkunde. Berichte. p. OsNABRiiCK. — N aturwissenschaftlicher Verein. Jahresbericht. T.p. Potsdam. — Astrophysikalisches Observatorium. Publikationen. p. LIegensburg. — Historischer Verein von Oberpfalz und Regensburg. Verhand- luiigen. p. Rostock-i-M. — Naturforschende Gesellschaft. Sitzungsberichte und Abhand- lungen. p. University. T.p. Strassburg. — University. Inaugural Dissertations. Bureau Central de V Association International de Sismologie. Publications. {Presented. ) 380 Proceedings of tlie Royal Society of Edinburgh. [Sess. T.p. Stuttgaet. — Verein filr vaterldndisclie Naturhunde in Wiirttemherg. Jaliresliefte. T.p. Tubingen. — ■University. Inaugural Dissertations. GREECE. Athens — T.p. University Library. T.p. Qhservatoire National. Annales. HAWAIIAN ISLANDS. p. Honolulu. — Beniice Pauahi Bishop Museum of Polynesian Ethnology. Occasional Papers. — Fauna Hawaiiensis. — Memoirs. HOLLAND. Amsterdam — T.p. Kon. Akademie van Wetenschap])en. Verbandelingen : Afd. Natuurkunde. Sectie. 2^® Sectie ; Afd. Letterkiinde. — Verslagen en Mededeelingen Letterkunde. — Verslagen der Zittingen van de Wis- en Naturkundige Afdeeling. — Jaarboek.— Proceedings of the Section of Sciences. — Poemata Latina. T.p. Konmldijk Zoolog Isch Genootschap Natura Artis Magistral Bijdragen tot de Dierkunde. p. Wiskundig Genootschap. Nieuw Archief voor Wisknnde. — Wiskundige Opgaven. — Revue Seniestrielle des Publications Matliematiques. p. Delft. — Ecole Poly technique. Dissertations. T.p. Groningen.— NmremYy. Jaarboek. T.p. Haarlem. — Pdollandsche Alaatschappij dxr Wetenschappen. Naturkundige Verbandelingen. — Archives Neerlandaises des Sciences Exactes et Naturelles. T.p. Musee 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. — Recueil des Travaux Botaniques Neerlandaises. T.P. Rotterdam. — Bataafsch Genootschap der Proefondervindelijke Wijsbegeerte. Nieuwe Verbandelingen. p. Utrecht. — Provinciaal Utrechtsch Genootschap van Kunsten en Weten- schappen. Verslag van de Algemeene Vergaderingen. Aanteekeningen van de Sectie Vergaderingen. 8vo. Koninklijk Nederlandsch Meteorologisch Institut. Observations Oceano- graphiqiies et Meteorologiques — Oeuvres Oceanographiques. (Presented.) U Qhservatoire. — Recherches Astronomiques. ( Presented.) 1914-15.] List of Library Exchanges, Presentations, etc. 381 HUNGARY. ]^uda-Pbsth— T.p Magyar Tudomdnyos Akademia {Hungarian Academy). Mathemat. es termeszettud. kozlemenyek (Coniiminications Math, and Nat. Sciences). — Nyelvtiid. kozlemenyek (Philology).— Mathemat. es termeszettud. Ertesito (Bulletin, Math, and Nat. Sciences). — Nyelvtudom. Ertekezesek (Philol. Memoirs). — Tortenettud. Ertekezesek (Historical Memoirs). — TMsadalmi Ertekezesek (Memoirs, Political Sciences). — Archseologiai Ertesito. — Rap- ports.— Almanack. — Mathematische und Naturwissenschaftliclie Berichte aus Ungarn. — And other publications of the Hungarian Academy, or works published under its auspices. T.p. Kir-Alagy. TermesrMtudomanyi. Tarsulat {Royal Hungarian Society of Nat. Sciences). p. Magyar Kirdlyi Ornitliologicii Kozpont {Royal Hungarian Central-Bureau for Ornithology). Aquila. ICELAND. p. Reikjavik. — Islenzka Fornleifafelag. INDIA. Bangalore. — Meteorological Results of Observations taken at Bangalore, Mysore, Hassan, and Chitaldroog Observatories ; Report of Rainfall Regis- tration in Mysore. {Presented hy the Alysore Government.) Bombay — T.p. Royal Asiatic Society {Bombay Branch). Journal. T.p. Elphinstone College. Archaeological Survey of Western India. Progress Reports. {Presented.) Government Observatory. Magnetic and Meteorological Observations. {Presented.) Burma. — Reports on Archseological Work in Burma. {Presented by the Government.) Calcutta — T.p. Asiatic Society of Bengal. Journal and Proceedings. — Memoirs. Board of Scientific Advice for India. Annual Report. {Presented.) Ethnographical Survey {Central Indian Agency). Monographs. {Presented.) T.p. Geological Survey of India. Records.— Memoirs. — Palieontoiogia Indica. T.p. Meteorological Office, Government of India. Indian Meteorological Memoirs. — Reports. — Monthly Weather Review. Archaeological Survey of India. Epigraphia Indica. — Annual Reports. {Pre- sented by the Indian Government.) Botanical Survey of India. Records. 8vo. {Presented by the Indian Government.) Imp)erial Library. Catalogue. {Presented.) Linguistic Survey of India. Publications. {Presented by the Indian Government.) 382 Proceedings of the Royal Society of Edinburgh. [Sess. Calcutta — continued — Royal Botanic Garden. Annals, (^Presented.) T.p. Indian Museum. Annual Reports. — ^Records. — Memoirs. — Catalogues, etc. Great Trigonometrical Survey. Account of Operations.— Records. — Professional Papers. 4to. [Presented.) Fauna of British India, including Ceylon and Burma. 8vo. [Presented hy the Indian Government.) Indian Research Fund Association. Indian Journal of Medical Research. [Presented.) ,Scientific Memoirs, by Medical Officers of the Army of India. 4to. [Presented.) p. ^Coimbatore. — Agricultural College and Research Institute. Madras — T.p. Literary Society. Observatory. Report on the Kodaikanal and Madras Observatories. 8vo. — Bulletins, — Memoirs. [Presented.) 4to. Government Central Museum. Report. [Presented.) A Descriptive Catalogue of the Sanskrit MSS. in the Government Oriental Manuscripts Library, Madras. By M. Seshagiri Sastri. 8vo. [Presented by the Government of Madras.) Rangoon. [See Burma.) Simla. Committee for the Study of AIala,ria. Transactions (Paludism). [Presented by the Sanitary Commissioner.) 8vo. IRELAND. Belfast — p. Natural History and Philosophical Society. Proceedings. T.p. Queen's University . Calendar. Dublin — T.p. Royal Irish Academy. Proceedings. — Transactions. — Abstract of Minutes. T.p. Royal Dublin Society. Scientitic Proceedings. — Economic Proceedings. — Scientific Transactions. T.p. Library of Trinity College. T.p. National Library of Ireland. p. Dunsink Observatory. Department of Agriculture and Technical Instruction for Ireland — Fisheries Branch. Reports on the Sea and Inland Fisheries of Ireland (Scientific Investigations). 8vo. — Geological Survey Memoirs. [Presented by the Department.) 8vo. ITALY. Bologna — T.p. Accademia di Scienze delV Istituto di Bologna. Memorie. — Rend icon ti. University Observatory. Osservazioni Meteorologiche. [Presented.) T.p. Catania. — Accademia Gioenia di Scienze Naturali. Atti. — Bolletino Mensile. T.p. Societd degli Spettroscopisti Italia7ii. Memorie. T.p. Genoa. — Museo Civico di Storia Naturale. Annali. p. Messina. — Reale Accademia Peloi'itana. Atti. 383 1914-15.] List of Library Exchanges, Presentations, etc. Milan — R. Osservatorio di Brera. Piiblicazioni. {Presented .) T.p. Reale Istituto Lombardo di Scienze, Lettere, ed Arti. Memorie : Classe di Scienze Mat. et Nat.; Classe di Lettere Scienze Storiche e Morali. — Rendiconti. Modena — T.p. Regia Accademia di Scienze, Lettere, ed Arti. Memorie. p. Societd dei Naturalisti. Atti. T.p. Naples. — Societd Reale di Napoli. Accademia di Scienze Fisiche e Matema- tiche. Alemorie. — Rendiconti. Accademia di Scienze Morali e Politiclie. Atti. — Rendiconti. Accademia di Archeologia, Lettere e Belle Arti. Atti. — Rendiconti. — Memorie. t.p. Stazione Zoologica. Mittheilungen. T.p. R. Istituto dNncoraggiamento. Atti. p. Museo Zoologico della R. Universita. Annuario. T.p. Padua. — R. Accademia di Scienze, Lettere, ed Arti. Atti e Memorie. T.p. Palermo. — Societd di Scienze Naturali ed Economiclie. Giornale di Scienze Natiirali ed Economiclie. p. Pisa. — Societd Italiana di Fisica. “II Nuovo Cimento.” Rome — T.p. R. Accademia dei Lincei. Classe di Scieiize Fisiche, Math, e Nat. Memorie. — Rendiconti. Classe di Scienze Morali, Storiche e Filol. — Notizie degli Scavi di Antichita. — Rendiconti.— Memorie. — Annali delt Islam. T.p. Accademia Ponteficia dei Nuovi Lincei. Atti. — Memorie. T.p. Int. Institute of Agriculture. Monthly Bulletins. T.p. R. Comitato Geologico. Memorie descrittive della Carta Geologica. — ■ Bollettino. T.p. Societd Italiana di Scienza {detta dei XL.). Memorie. p. Sassari. — Istituto Fisiologico della R. Universita di Sassari. Studi Sassaresi. Turin — T.p. Reale Accademia delle Scienze. Memorie. — Atti. Osservatorio della R. Universita. Osservazioni Aleteorologiche. 8vo„ {Presented.) T.p. Venice. — R. Istitido Veneto di Scienze, Lettere, ed Arti. Atti. — Osservazioni Meteorologiclie. JAMAICA. p. Kingston. — Institute of Jamaica. JAPAN. p. Formosa. — Bureau of Productive Industry. leones Plantai um Formosanarum. p. Sendai. — Tohoku Imperial University. Science Reports. — Tolioku Mathe- matical Journal. Tokio — T.p. Imperial University of Tokio {Teikoku-Daigaku). Calendar. — College of Science. Journal. — Medicinische Facultdt der Kaiserlicli-Japanischen U niversitdt. Mittheilungen . 384 Proceedings of the Royal Society of Edinburgh. [Sess- Tokio — continued — p. Zoological Society. Annotationes Zoologicae Japonenses. p. Asiatic Society. Transactions. p. Deutsche Gesellschaft fiir Natur- und Volkerkunde Ostasiens. Mittheilungen. p. Imperial Museum. Earthquake Investigation Committee. Bulletin. {Prese7ited.) T.p. Kyoto. — Imperial University {College of Science and E7igineering). Memoirs. JAVA. Batavia — T.p. Bataviaascli Genootschap van Kunsten en W etenschappen. Verliandelingen. — Tijdschrift voor Indisclie Taal-, Land- en Yolkenkunde. — Notulen. T.p. Magnetical and Meteorological Ohservatoi'y . Observations. — Begenwaar- neiningen in Nederlandscli-Indie. — Verliandelingen. p. Kon. N atuurkundige Vereeniging. Katuurkundig Tijdschrift voor Neder- landscli-Indie. LUXEMBOURG. p. Luxembourg. — Ulnstitut Royal Grand-Ducal. Archives trimestrielles. MAURITIUS. T.p. Roycd Alfred Ohse^'vatory . Annual Beports. — Magnetical and Meteorological Observations. MEXICO. Mexico — T.p. Miisee National d’Histoire Naturelle. La Xaturaleza, etc. T.p. Sociedad Cientifica ^'‘Antonio Alzatef'^ Memorias. T.p. Ohservatorio Aleteorologico-Magnetico Central. Boletin Mensual. p. Istituto Geologico. Boletin. Parergones. p. Academia Mexicana de Ciencias Exactas^ Fisicas y Naturales. p. Tacubay^a. — Ohsemjatorio Astronomico. Annuario. — ^Boletin. MONACO. T.p. Monaco. — Musee Oceanographique. Bulletins. — Besultats des Campagnes Scientifiques. NATAL. (See UNION OF S. AFRICA.) NEW SOUTH WALES. (See AUSTRALIA.) NEW ZEALAND. Wellington — T.p. Neiv Zealand Institute. Transactions and Proceedings. New Zealand Government. Statistics of New Zealand. — The New Zealand Official Handbook. (Presented by the Government.) Colonial Museum and Geological Survey. Publications. (Presented.) 1914-15.] List of Library Exchanges, Presentations, etc. 385 NORWAY. T.p. Bergen. — Museum. Aarsberetning. — Aarbog. — An Account of the Crustacea of Norway. By G. 0. Sars. Christiania — T.p. K. Norsks Frederiks Universitet. Nyt Magazin for Naturvidenskaberne. — Archiv for Mathematik og Natuiwidenskab. T.p. Meteorological Institute. Jahrbuch. Videnskahs-Selskah. Forhandlinger. — Skrifter (Math. Nat. Kh). {Presented.) p. Stavanger. — Museum. Aarshefte. T.p. Throndhjem. — Kgl. Norsks Videnskahers Selskab. Skrifter. p. Tromso. — Museum. Aarshefter. — Aarsberetning. PHILIPPINE ISLANDS. p. Manila. — Bureau of Science. Ethnological Survey Publications. Bureau of Forestry. Annual Report. PORTUGAL. T.p. Coimbra. — University. Annuario. Archivo Bibliographico. — Revista. Lisbon — T.p. Academia das Sciencias de Lisboa. Boletim. — Actas. T.p. Sociedade de Geograpliia. Observatorio do Infante D. Luiz. Annaes. {Presented.) Porto. Academia Polyteclinica. Annaes Scieutificos. QUEENSLAND. {See AUSTRALIA.) ROUMANIA. Bucharest — T.p. Academia Romana. Analele. Bulletin de la Section Scientifique. — Also Publications relating to the History, etc., of Roumania. Bibliografia Romanesca. — Catalogues, etc. p. Institid Meteorologique. Analele. RUSSIA. T.p. Dorpat (Jurjew). — University. Inaugural Dissertations. — Acta — Sitzungs- berichte der Naturforscher Gesellschaft bei der Universitat. — Schriften. T.p. Ekatherinebourg. — Societe Ouralienne d’ Amateurs des Sciences Naturelles. Bulletin, Kazan — T.p. Imperial University. Uchenuiya Zapiski. p. Societe Physico-Mathematique de Kazan. Bulletin. T.p. Kiev. — University. Universitetskiya Isvyaistiya. VOL. XXXV. 25 386 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. T.P. P. P. P. P. P. T.P. P. T.P. T.P. P. P. P. Proceedings of the Poyal Society of Edinburgh. [Sess. Moscow — Societe Im^eriale des Naturalistes. Bulletin. — Nouveaux Memoires. L’Observatoire Imperial. Annales. Societe [mperiale des Amis d^Histoire Naturelle, d^ Anthropologie et c?’ Etlinograpliie. Imperial University. Musee Poly technique. Ohservatoire Magnetique et Meteorologique de VUniversite Imperiale. Odessa. — Societe des Naturalistes de la Nouvelle Russie. Zapiski. PouLKOVA. — Nicolai Hauptsternioarte. Publications. — Annales. St Petersburg — Academic Imphdale des Sciences. Memoires: Classe Phys.-Math. ; Classe Hist.-Pliil. — Bulletins. Commission Sismique Permanente. Comptes Eendus. — Bulletin. Comite Geologique. Memoires. — Bulletins. — Carte Geologique : Begion AurifMe d’lenissei : de I’Amour ; de Lena. Commission Roy ale Russe pour la Mesure d'un Arc de Meridien au Spitzherg. Missions Scientifiques pour la Mesure d’un Arc de Meridien au Spitzberg enterprises en 1899-1902, sous les auspices des Governements Suedois et Russe. Mission Russe. 4to. {Presented .) Imperial University. Scripta Botanica. Institut Imphial de Medecine Experiment ale. Archives des Sciences Biologiques. Physihalisclie Central-Observatorium. Annalen. Physico-Chemical Society of the University of St Petersburg. Journal. Russian Ministry of Marine. Imperial Russian Geographical Society. K. Alineralogische Gesellschaft. Yerhandlungen (Zapiski). — Materialien zur Geologie Russlands. Societe des Naturalistes {Section de Geologie et de Miner alogie). Travaux et Supplements. Societe Astronomique Russe. Tiflis. — Physikalisches Observatorium. Beobachtungen. SCOTLAND. Aberdeen. — University Library. Calendar. — University Studies. — Library Bulletin. Berwickshire. — Naturalists Club. Proceedings. Dundee. — University College Library. Edinburgh — Advocates Library. Botanical Society. Transactions and Proceedings. Carnegie Trust for the Universities of Scotland. Report. {Presented.) Faculty of Actuaries in Scotland. Transactions. Fishery Board for Scotland. Annual Reports. Scientific Investigations. — Salmon Fisheries. Fifth Report of the Fishery and Hydrographical Investi- gations in the N. Sea and Adjacent Waters (I908-I91I). Fol. Lond. 1913. 387 1914-15.] List of Library Exchanges, Presentations, etc. Edinburgh — continued — p. Geological Society. Transactions. Geological Survey of Scotland. jMemoirs, Maps, etc. {Presented by H.M. Government.) T.p. Highland and Agricultural Society of Scotland. Transactions, p. Mathematical Society. Proceedings. — Mathematical Notes, p. Pharmaceutical Society. {Noidh British Branch). Registrar-GeneraV s Returns of Births, Deaths, and Marriages. {Presented.) T.p. Royal Botanic Garden. Notes. T.p. Royal College of Physicians. p. Royal College of Physicians^ Laboratory. Laboratory Reports. T.p. Royal Medical Society. T.p. Royal Observatory. Annals. — Annual Report. T.p. Royal Physical Society. Proceedings. Royal Scottish Academy. Annual Reports. {Presented.) p. Royal Scottish Geographical Society. Scottish Geographical Magazine, T.p. Roycd Scottish Society of Arts. Transactions, p. Scottish Aleteorological Society. Journal. Scottish National Antarctic Expedition. Publications. {Presented.) T.p. University Library. Calendar. Glasgow — p. Geological Society. Transactions. Royal Technical College. Calendar. {Presented.) T.p. Inst, of Engineers and Shipbuilders in Scotland. Transactions, p. Marine Biological Association of the West of Scotland. Annual Report. See Millport. p. Natural History Society. — Glasgow Naturalist. T.p. Royal PhilosoiDhical Society. Proceedings. T.p. University. Calendar, p. University Observatory. p. Millport. — Alarine Biological Association of the West of Scotland. Annual Report. T.p. Perth. — Perthshire Society of Natural Science. Proceedings. T.p. St Andrews. — University Library. Calendar. SPAIN. Madrid — T.p. Real Academia de Ciencias Exactas, Fisicas y Naturales. Memorias. — Revista. — Annuario. T.p. Instituto Geologlco de Espaha. Boletin. — Memorias. p. Yilafranca del Panades (Cataluna). — Observatorio Meteorologico. SWEDEN. p. Gothenburg. — Kongl. Vetenskaps och Vitterhets Samhdlle. Handlingar. T.p. Lund. — University. Acta Universitatis Lundensis (Fysiografiska Sallskapets Handlingar. — Theologi. — Medicina). 388 Proceedings of the Royal Society of Edinburgh. [Sess. T.p. Stockholm. — Kong. Svenska Vetenskaps-Akademie. Handlingar. — Arkiv for Zoologi. — Arkiv for Matematik, Astronomi ocli Fysik. — Arkiv for Botanik. — Arkiv for Kemi, Mineralogi och Geologi. — Meteorologiska lakttagelser i Sverige. — Astronomiska lakttagelser. — Lefnadsteckniiigar. — Arsbok. — Accessionskatalog. — Meddelanden Mii K.Vetenskaps Akademiens Nobelinstitiit. — Les Prix Nobel. p. Svenska Sdllskapet for Antropologi och Geograji. Ymer. Commission Roy ale Suedoise pour la Mesure d\in Arc de Aleridien au Spitzherg. Missions Scientifiques pour la Mesure d’un Arc de Meridien au Spitzberg entreprises en 1899-1902, sous les auspices des Gouverne- ments Suedois et Busse. Mission Suedoise. 4to. {Presented.) Ups ALA — T.p. Kongliga Vetenskaps Societeten {Regia Societas Scientiaruin). Nova Acta. T.p. University. Arsskrift. — Inaugural Dissertations (Medical and Scientific). — Bulletin of the Geological Institution. Ohservatoire de V Universite. Bulletin Meteorologique Mensuel. SWITZERLAND. T.p. Basle. — Naturforscliende Gesellschaft. Verhandlungen. Bern — Commission Geodesique Suisse. Arbeiten. {Presented.) T.p. Societe Helvetique des Sciences Naturelles. {Allgemeine Schweizerische Gesellschaft fiir die gesammten Naturwissenschaften.) Comptes Eendus. — Actes (Verhandlungen). — Nouveaux Memoires. p. Naturforschende Gesellschaft. Mittheilungen. T.p. Geneva. — Societe de Physique et d’Histoire Naturelle. Memoires. — Comptes Eendus. p. Lausanne. — Societe Vaudoise des Sciences Naturelles. Bulletin. — Observations Meteorologiques. Neuchatel — T.p. Societe des Sciences Naturelles. Bulletin, p. Societe Neuchdteloise de Geographie. Bulletin. Zurich — T.p. University. T.p. Commission Geologique Suisse. Beitrage zur geologischen Karte der Schweiz. T.p. Naturforschende Gesellschaft. Yierteljahrsschrift. p. Schweizerische Botanische Gesellschaft. Berichte (Bulletin). Schiveizerische Aleteorologische Central- Anstalt. Annalen. 4to. {Presented.) TASMANIA. {See AUSTRALIA.) TRANSVAAL. {See UNION OF S. AFRICA.) 1914-1 5. J List of Library Exchanges, Presentations, etc. 389 TURKEY. p. Constantinople. — SocAMe ImphAale de Medecine. Gazette Medicate d’Orient. UNION OF SOUTH AFRICA. Cape Town — p. Royal Society of South A frica. Transactions. T.p. Royal Astronomical Observatory. Reports. — Annals. — Meridian Observations. — Independent Day Numbers. p. Geological Commission (now Survey). Annual Reports. T.p. South African Museum. x\nnals. p. South African Association for the Advancement of Science. Journal. J OHANNESBURG 'I’.p. Geological Society of South Af rica. Transactions and Proceedings. T.p. Union Observatory. Circulars. Pietermaritzburg — p. Geological Survey of Natal. Annual Reports. — Reports on the Mining Industry of Natal. 'I'.p. Government Museum. Annals. — Catalogues. Pretoria — Dept, of Mines — Geological Survey. Reports. — Memoirs. — Maps. {Presented.) T.p. Transvaal Museum. Annals. UNITED STATES OF AMERICA. Albany — T.p. Neiv York State Library. Annual Reports. — Bulletins. State Museum. Annual Reports. — Bulletin. Netv York State Education Department. Annual Reports, p. Allegheny. — Observatory. Publications, etc. p. Ann Arbor. — Michigan Academy of Sciences. Reports. {University.) 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. Bulletins. — Reports. {Presented.) T.p. Maryland Geological Survey. Publications. Maryland Weather Service. Reports. {Presented.) Peabody Institute. Annual Reports. (Presented.) Berkeley (California) — T.p. University of California. — University Chronicle. — Reports of Agricultural College. — Publications (Zoology, Botany, Geology, Physiology, Pathology, and American Archaeology and Ethnology). — Memoirs. Academy of Pacific Coast History. Publications. 390 Proceedings of the Eoyal Society of Edinburgh. [Sess. Boston — T.p. Bowditch Library. T.p. Boston Society of Natural History. Memoirs. — Proceedings. — Occasional Papers. T.p. American Academy of Arts and Sciences. Memoirs. — Proceedings, p. Brooklyn. — Institute of Arts and Sciences. Museum Reports. — llulletins. p. Buffalo. — Society of Natural Sciences. Bulletin. California. {See San Francisco, Sacramento, Berkeley, Mount Hamilton, Mount Wilson and Stanford.) Cambridge — t.p. Harvard University. — Museum of Comparative Zoology. Memoirs. — Bulletins — Annual Reports. T.p. Astronomical Observatory^ Harvard College. Annals. — Annual Reports. — Observatory Circulars. p. Chapel Hill (I^orth Carolina). — E. Mitchell Scientific Society. Journal, p. Charlottesville. Philosophical Society, University of Virginia. Bulletin ; Scientific Series and Humanistic Series. — Proceedings. Chicago — T.p. Field Museum of Natural History. Publications : Geological Series ; Botanical Series ; Zoological Series ; Ornithological Series ; Anthropo- logical Series. — Annual Reports, p. University of Chicago. T.p. Yerkes Observatory {University of Chicago). Publications, p. Academy of Sciences. Bulletins. — Special Publications. — Bulletins of the Natural History Survey. Cincinnati — p. Observatory (University). Publications. — University Record, p. Society of Natural History. Journal. T.p. Cleveland (Ohio). — Geological Society of America. Bulletins. T.p. Clinton (Iowa). — Litchfield Observatory, Hamilton College. Colorado Springs, — Colorado College. Colorado College Studies. (Pre- sented.) p. Connecticut. — Connecticut Academy of Arts and Sciences. Transactions. — Memoirs. p. Davenport. — Academy of Natural Sciences. Proceedings, p. Denver (Colorado). — Scientific Society of Colorado. Proceedings. T.p. Des Moines (Iowa). — loioa Academy of Sciences. Proceedings, p. Garrison, N.Y. — Editor, American Naturalist. T.p. Granville (Ohio). — Denison University and Scientifc Association. Bulletin of the Scientific Laboratories. p. Indianopolis. — Indiana Academy of Sciences. Proceedings. Iowa City — p. Geological Survey. Annual Reports. T.p. State University. Laboratories of Natural History. Bulletins. — Contribu- tions from the Physical Laboratories. Iowa. {See Des Moines.) Ithaca (N.Y.)— p. The Editor, Physical Review. (Cornell University.) 1914-15.] List of Library Exchanges, Presentations, etc. 391 Ithaca (N.Y.) — continued — p. The Editors, Journal of Physical Chemistry . (Cornell University.) T.p. Lawrence (Kansas). — University of Kansas. Science Bulletin (University Quarterly). p. Lincoln (Kebraska). — University of Nebraska. Agricultural Experiment Station. Bulletins. Madison — T.p. Wisconsin University. Washburn Observatory. Observations, p. Wisconsin Academy of Sciences, Arts, and Letters. Transactions, p. Geological and Natural History Survey. Bulletins, p. Massachusetts.— College Library. Tufts College Studies, p. Meriden (Conn.). — Aleriden Scientific Association. Michigan. {See Ann Arbor.) Minneapolis (Minn.) — ^ p I University of Minnesota. Studies. — Bulletin of the School of Mines. ( Geological and Natural History Survey of Minnesota. Eeports. p. Botanical Survey. Missouri. {See St. Louis and Kolla.) p. Mount Hamilton (California). — Lick Observatory. Bulletins. — Piddica- tions. T.p. Mount Wilson (California).— Observatory. Contributions. — Reports. T.p. Kewhaven (Conn.) — Yale College. Astronomical Observatory of Yale University. Transactions. — Reports, p. Kew Orleans. — Academy of Sciences. Kew York — T.p. American Mcdhematical Society. Bulletins. — Transactions. T.p. American Museum of Natural History. Bulletins. — Memoirs. — American Museum Journal. — Annual Reports. — Anthropological Papers. — Guide Leaflets. — Handbook Series.— Monograph Series, p. American Geographical Society. Bulletin, p. American Institute of Electrical Engineers. Proceedings. Yew 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, Literature, and Archseology, Mathematics, etc. Contributions from the Zoological and Botanical Laboratories. University Bulletins. — Theses. — Calendar. T.p. Geological Survey of Pennsylvania. p. Wagner Free Institute of Science. Transactions, p. Geographical Society. Bulletin, p. Commercial Museum. p. Portland (Maine). — Society of Natural History. Proceedings, p. Princeton, N.J. — University. Annals of Mathematics. — University Obser- vatory. Contributions. p. Rochester. — Academy of Science. Proceedings. T.p. Rolla (Miss.). — Bureau of Geology and. Mines. Biennial Reports, etc. 392 Proceedings of the Royal Society of Edinburgh. [Sess. T.p. Salem. — Essex Institute. Saint Louis — T.p. Academy of Sciences. Transactions. p. Missouri Botanical Garden. Annual Reports. p. Washington University. University Studies. T.p. San Francisco (California). — Academy of Sciences. Proceedings. — Memoirs. — Occasional Papers. p. Stanford (California). — University. Publications. {Presented.) p. Topeka. — Kansas Academy of Science. Transactions. T.p. Urbana. — University of Illinois. Bulletins of State Geological Survey^ State Laboratory of Natural History^ and Engineering Experiment Station. Washington — T.p. U.S. National Academy of Sciences. Memoirs. T.p. Bureau of Ethnology. Annual Reports. — Bulletins. T.p. U.S. Coast and Geodetic Survey. Annual Reports, etc. T.p. U.S. Commission of Fish and Fisheries. Reports. — Bulletins. T.p. U.S. Naval Observatory. Reports. — Observations. T.p. U.S. Geological Survey. Bulletins. — Annual Reports. — Monographs. — Geologic Atlas of the United States. — Mineral Resources. — Professional Papers. — Water Supply and Irrigation Papers. Geological Society of America. {See Cleveland.) T.p. Weather Bureau. {Department of Agriculture.) Monthly Weather Review. — Bulletins. — Reports. — Bulletin of the Mount Weather Observa- tory (now embodied in Monthly Weather Review). T.p. Smithsonian Institidion. Miscellaneous Collections. — The same (Quarterly Issue). — Contributions to Knowledge. — Reports. — Annals of the Astro- physical Observatory. — Harriman Alaska Expedition, Yol. XIY. 4to. T.p. Surgeon-GeneraVs Office. Index Catalogue of the Library. 4to. T.p. Carnegie Institution of Washington. Year-Books. — Publications. Classics of International Law. — Carnegie Foundation for the Advancement of Teaching. Annual Report. — Bulletin. T.p. American Association for the Advancement of Science. Proceedings. p. U.S. National Museum. Bulletins. — Reports. — Proceedings. — Contributions from the U.S. National Herbarium. p. Department of Agriculture. {Division of Economic Ornithology and Mammalogy. ) Bulletin . p. U.S. Patent Office. Washington Academy of Sciences, Journal of the. {Purchase.) Bureau of Standards. Department of Commerce and Labour. Bulletins. {Presented. ) — Technologic Papers. Wisconsin. {See Madison.) VICTORIA. {See AUSTRALIA.) 1914-15.] Purchases, etc., for the Library. 393 List of Periodicals and Annual Publications added to the Library by Purchase, etc. Periodicals not found in this List icill he found in Exchange List. Annuals [Works of Reference)^ see end of List. Acta Mathematica. American Journal of Science and Arts. * — Naturalist. * Journal of Mathematics. Chemical Journal. * Journal of Philology. Anatomischer Anzeiger. — Erganzungshefte. Annalen der Chemie (Liebig’s). * der Physik. * der Pliysik. (Beiblatter.) Annales de Chimie. d’Hygiene Publique et de Medecine Legale. de Physique. des Sciences Naturelles. Zoologie et Paleontologie. des Sciences Naturelles. Botanique. Annali dell’ Islam. (Presented.) Annals and Magazine of Natural History (Zoology, Botany, and Geology). of Botany. * of Mathematics. (Princeton, N.J.) Anthropologie (L’). Arbeiten-Zoologisches Institut der Universitat und der Zoologischen Station in Triest. * Archiv for Mathematik og Naturvidenskab. * Archiv fiir Biontologie. Archives de Biologie. de Zoologie Experimentale et Generate. * des Sciences Biologiques. des Sciences Physiques et Naturelles. Italiennes de Biologie. * Arkiv for Matematik, Astronomi och Fysik. (Stockholm.) * for Kemi, Mineralogi och Geologi. ,, * for Botanik. ,, * for Zoologi. ,, Astronomic (L’). Astronomische Nachrichten. Astrophysical Journal. Athenaeum. Bericht liber die Wissenschaftlichen Leistungen in der Naturgeschichte der niederen Thiere Begriindet von R. Leuckart. Bibliotheca Mathematica. Bibliotheque Universelle et Pevue Suisse. See Archives des Sciences Physiques et Naturelles. * Received by exchange. 394 Proceedings of the Royal Society of Edinburgh. [Sess. Biologisehes Centralblatt. Blackwood’s Magazine. Bollettino delle PuLblicazioni Italiaue. {Presented.) Bookman. Botanische Zeitiing. Botanisclies Centralblatt. Beilieft. British Rainfall. Bulletin Astronomique. des Sciences Matlieniatiques. Mensuel de la Societe Astronomique de Paris. See L’Astronomie. Cambridge British Flora. By C. E. Moss. Catalogue of Scientific Papers, 1800-1900. Subject Index. Centralblatt fiir Bakteriologie und Parasitenkunde. fiir Mineralogie, Geologie und Palaeontologie . Ciel et Terre. Contemporary Review. Crelle’s Journal. See Journal fiir Reine und Angewandte Mathematik. Dictionary, Rew English. Ed. by Sir J. A. H. Murray. Dingler’s Polytechnisches Journal. Edinburgh Medical Journal. Review. Egypt Exploration Fund. Publications. * Electrician. Encyklopadie der Mathematischen MGssenschaften. Engineering. English jMechanic and World of Science. * Essex Naturalist. Fauna und Flora des Golfes von Neapel. Flora. Fortnightly Review. * Gazette Medicate d’Orient. * Geographical Journal. * Geographical Magazine (Scottish). Geographic (La). Geological Magazine. Gbttingische Gelehrte Anzeigen. Indian Antiquary. Engineering. {Presented. ) Indian Journal of Medical Research. {Preseiited.) Intermediaire (L’) des Mathematiciens. International Catalogue of Scientific Literature. Internationale Revue der Gesamten Hydrobiologie und Hydrographic. Jahrbiicher fiir Wissenschaftliche Botanik (Pringsheim). Jahresbericht liber die Fortschritte der Chemie und verwandter Theile anderer Wissenschaft. Journal de Conchyliologie. * Received by exchange. Purchases, etc.-, for the Library. 395 1914-15.] Journal des Debats. de Matliematiques Pures et Appliquees. de Pharmacie et de Chimie. * de Physique. des Savants. — — — fiir die Peine iind Angewandte Mathematik (Crelle). fiir Praktische Chemie. of Anatomy and Physiology. of Botany. of Pathology and Bacteriology. * of Physical Chemistry. ^ — of the Royal Society of Arts. of the Society of Chemical Industry. {Presented.) — of the Washington Academy of Sciences. Knowledge. Manual of Conchology. Mathematische imd Katurwissenschaftliche Berichte aus Ungarn. Mind. Mineralogical Magazine. {Presented.) Mineralogische und Petrographische Mittlieilungeii (Tschermak’s). Monist. ■* Kature. (La). Keiies Jahrbuch fiir Mineralogie, Geologie, und Palaeontologie. * Beilage. Nineteenth Century. Notes and Queries. Nuova Notarisia (De Toni).' * Nuovo Cimento ; Giornale di Fisica, Chimica e Storia Natiirale. * Nyt Magazin for Naturvidenskaberne. Nyt Tidsskrift for Mathematik. Observatory. 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Who’s Who in Science (International). Willing’s Press Guide. Year-Book of Scientific and Learned Societies of Great Britain and Ireland. Zoological Record. * Received by exchange. 1914-15.] Additions to Library by Gift or Purchase. 397 Additions to Library by Gift or Purchase. (The nine books and manuscripts marked * belonged to the late Dr Gustav Plarr, and have been presented by his son, Mr Victor G. Plarr, Librarian, Royal College of Surgeons of England.) * Allegret (M.). Essai sur le Calcul des Quaterniones de M. W. Hamilton. 4to. Paris, 1862. Annals of the Andersonian Naturalists’ Society. Yols. I-II. 8vo. Glasgow, 1893- 1900. {Presented by Dr Kidston.) * Balbin (Yalentin). Elenientos de Calculo de los Quaterniones y sus Aplicaciones principales a la Geometria, al Analisis y a la Mecanica. 8vo. Buenos Ayres, 1887. Bensaude (Joaquim). Eegimento do Estrolabio e do Quadrante. Tractado da Spera do Mundo. 8vo. Munich, 1914. {Presented by the Author.) Collection de documents publics par ordre du Ministk’e de I’lnstruction publique de la Eepublique Portugaise. Yol. I. Regimento do Estrolabio — Tratado da Spera. 8vo. Munich, 1913. Yol. III. Almanach perpetuum. Par Abraham Zacuto. 1496, Leiria. 8vo. Munich, 1915. Yol. lY. Tratado del Esphera y del arte del marear. 8vo. Munich, 1915. Yol. Y. Tratado da Esphera. Par Pedro Nunes. 1537, Lisboa, Crown fol. Munich, 1915. L’ Astronomic Nautique au Portugal a Pepoque des grandes decouvertes. 8vo. Bern, 1912. {Presented by the Author.) Bolton (Herbert). The Fauna and Stratigraphy of the Kent Coalfield. 8vo. London, 1915. {Presented by the Author.) British Antarctic Expedition, 1907-1909. Reports on the Scientific Investigations. Geology. Yol. I. 4to. London, 1914. {Presented by Mr Wm. Heinemann.) Census of the Commonwealth of Australia taken for the Night between 2nd and 3rd April 1911. Yols. II. and III. 4to. Melbourne, 1914. {Presented}) Elliot (G. F. Scott). Prehistoric Man and His Story. A Sketch of the History of Man- kind from the Earliest Times. 8vo. London, 1915. {Presented by the Author.) * Graefe (Dr Friedrich). Yorlesungen fiber die Theorie der Quaternionen mit Anwendung auf die Allgemeine Theorie der Flachen und der Linien Doppelter Krfimmung. 8vo. Leipzig, 1883. Green (C. E.). The Local Incidence of Cancer in France in Relation to Fuel. 8vo. Edinburgh, 1915. {Presented by the Author.) Grove (W, B.). The Families of British Flowering Plants. 8vo. Manchester, 1915. {Presented by the Author.) Hoare (Alfred). An Italian Dictionary. 4to. Cambridge, 1915. {Purchased.) Liston (Major W. Glen). Report of the Bombay Bacteriological Laboratory for the year 1913. Fol. Bombay, 1914. {Presented by the Author.) Mayer (Alfred Goldsborough). Medusae of the Philippines and of Torres Straits. Being a report upon the Scyphomedusae collected by the United States Fisheries Bureau Steamer Albatross in the Philippine Islands and Malay Archipelago, 1907-1910, and upon the Medusae collected by the Expedition of the Carnegie Institution of Washington to Torres Straits, Australia, in 1913. 8vo. Washington, 1915. {Presented.) 398 Proceedings of the Koyal Society of Edinburgh. Morison (Captain J.), M.B., etc. The Causes of Monsoon Diarrhoea and Dysentery in Poona. (From the Indian Journal of Medical Research, voh xi, No. 4, April 1915.) 8 VO. Calcutta, 1915. {Presented, hy the Author.) Murray (Sir John), and Dr Johan Hjort. The Depths of the Ocean. 8vo. London, 1912. {Purchased.) ■ Report on the Scientific Results of the “Michael Sars ” North Atlantic Deep Sea Expedition, 1910. Vol. Ill, Part I, Zoology. 4to. Bergen, 1913. {Purchased.) * Odstrcil (Dr J.). Kurze Anleitung zuni Rechnen mit den (Hainilton’schen) Qiiaternionen. 8vo. Halle a/S, 1879. Papers from the Geological Department, Glasgow LTniversity. 8vo. Glasgow, 1915. {Presented hy Professor Gregory.) Philip (Alex.). The Dynamic Foundation of Knowledge. 8vo. London, 1913. Essays towards a Theory of Knowledge. 8vo. London, 1915. {Both presented hy the Author.) Records of the Geological Survey of New South Wales. Yols. 1-V. La. 8vo. Sydney, 1890-1898. {Presented hy Dr Kidston.) Ross (Dr E. Denison). Three Turki Manuscripts from Kashgar. (Archaeological Survey of India.) 4 to. Lahore, 1915. {Presented.) * Salmon (G.). Lecons d’Algebre Superieure. Traduit de I’Anglais j3ar M. Bazin. Augmente de Notes par M. Hermite. 8vo. Paris, 1868. * Sarrus (M.). Recherches sur le Calcul des Variations, piece pour le Concours sur la question relative aux Alaxima et Minima des Integrates Multiples. 4to. Paris, 1846. * Alethode d’Eliniination par le plus grand comniun diviseur. 8vo. Paris, 1834. * Schlomilch (Dr 0.), and Witzschel (Dr B.). Zeitschrift fiir Mathematik und Physik. Jahrgang 1-3. 8vo. Leipzig, 1856-1858. Scottish National Antarctic Expedition. Report on the Scientific Results of the S.Y. Scotia during the Years 1902, 1903, and 1904. Yol. lY. Zoology. 4to. Edinburgh, 1915. {Presented hy Dr W. S. Bruce.) Serkowski (Dr Stanislaw). Epidemiologia i ProfilakWka Cholery. 8vo. YMrsaw, 1915. {Presented hy the Author.) Sinioes (Jose Maria de Oliveira). Curso Elementar sobre Substancias explosivas. Yol. 1. Materias primas e polvoras. 8vo. Lisboa, 1904. {Presented.) Stieltjes (Thomas Jan). CEuvres Completes de, publiees par les soins de la Societe Mathematique d’ Amsterdam. Tome I. 4to. Groningen, 1914. {Presented hy La Societe Mathematique cV Amsterdam.’’^) Suter (Henry). Alphabetical Hand-List of New Zealand Tertiary Mollusca. Srn. 4to. Wellington, N.Z., 1915. {Presented .) Tables Annuelles de Constantes et Donnes Numeriques de Chimie, de Physique et de Technologie. Yols. I-III. Annees 1910, 1911, 1912. 4to. Paris, 1912, 1913, 1914. {Purchased.) *Tait(P. G.). Elementares Handbuch der Quaternionen. (Autorisierte Ueberset- zung, von Dr G. v, Scherff.) 8vo. Leipzig, 1880. Urquhart (James). The Life and Teaching of William Honyman Gillespie. 8vo. Edinburgh, 1915. {Presented hy the Author.) * Various AISS. on Quaternions, in particular the wmrked-out Answers to the Exercises set in Tail’s Treatise on Quaternions. Zeiller (R.). Travaux de Biologie Yegetale. Sur Quelques Plantes Wealdiennes recueillies au Perou par M. le Capitaine Berthon. 8vo. Nemours, 1914. {Presented hy the Author.) INDEX. Ammonium Halides, The Densities and Degrees of Dissociation of the Saturated Vapours of the, by Alexander Smith and Robert H. Lombard, 162-167. Antarctic Meteorology, Notes on, by R. C. Mossman, 203-216. Arabinose, Optical Rotation of, by J. E. Mac- kenzie and S. Ghosh, 22-45. Autotomy, A Comparative Study of, by J. H. Paul, 232-262. Baleen Whales of the South Atlantic, by Sir i William Turner, 11-21. Bauschinger (J.). Formulse and Scheme of Calculation for the Development of a Func- tion of Two Variables in terms of Spherical Harmonics, 63-69. Calcium Phosphate : Increase of the Amount in the Ration as alfecting the Composition of Cow’s Milk, by A. Lauder and T. W. Fagan, 195-202. Chalk Boulders from Aberdeen and Fragments of Chalk from the Sea Floor off the Scottish Coast, by the late William Hill, 263-296. Chalk : the Structure of the Chalk on the West of Scotland, by the late William Hill, 297- 304. Climatic Features of M‘Murdo Sound, the South Orkneys, and the West Coast of Graham’s Land, by'R. C. Mossman, 203-216. Climatology of Victoria Land during 1911, by R. C. Mossman, 203-216. Cochrane (Charles). The Reflective Power of Pigments in the Ultraviolet, 146-152. Cretaceous Rocks, Micro-organisms from, by David Ellis, 110-133. Crosse (R. ). Studies on Periodicity in Plant Growth. Part II — Correlation in Root and Shoot Growth, 46-53. Crustacea, Autotomy in Decapod, by J. H. Paul, 232-262. Decapoda, Regeneration from the Breaking- plane of the Limb in, by J. H. Paul, 78-94. Densities and Degrees of Dissociation of the Saturated Vapours of the Ammonium Halides, by Alexander Smith and Robert H. Lombard, 162-167. Differential Equation, Lame’s, and Integral- Equations, by E. T. Whittaker, 70-77. Electrical Conductivity of Aqueous Hydro- chloric Acid, saturated with Sodium Chloride ; and on a new form of Conductivity Cell, by F. D. Miles, 138-145. Ellis (David). Fossil Micro-organisms from the Jurassic and Cretaceous Rocks of Great Britain, 110-133. Equation, Integral, whose Solutions are Lame’s Functions, by E. T. Whittaker, 70-77. Expansion in Series of Polynomials, in connec- tion with the Interpolation-Theory, by E. T. Whittaker, 181-194, Fagan (T. AV, ). See Lauder, A. Fluid, Resistance of, to a Body moving through it, by H. Levy^ 95-109. Formamide, Optical Rotation of Sugars dissolved in, by J. E. Mackenzie and S. Ghosh, 22-45. Formuhie and Scheme of Calculation for the Development of a Function of Two Variables in terms of Spherical Harmonics, by J. Bauschinger, 63-69. Fossil Micro-organisms from the Jurassic and- Cretaceous Rocks of Great Britain, by David Ellis, 110-133. Fructose, Optical Rotation of, by J. E. Mac- kenzie and S. Ghosh, 22-45. Function, Cardinal, in connection with the Interpolation-Theory, by E. T. Whittaker, 181-194. Galactose, Optical Rotation of, by J. E. Mac- kenzie and S, Ghosh, 22-45. Ghosh (S. ). See Mackenzie, J. E. Gilchrist (Elizabeth), See Marshall, C. R. Glucose, Optical Rotation of, by J. E. Mackenzie andS. Ghosh, 22-45. Growth, Correlation in Root and Shoot, by R. Crosse, 46-53. Gyroscope, Theory of, by Horace Lamb, 153-161. Harmonics, Spherical, Scheme of Calculation, by J, Bauschinger, 63-69, Hill (the late William). Chalk Boulders from Aberdeen and Fragments of Chalk from the Sea Floor off the Scottish Coast, 263-296, Notes on the Structure of the Chalk occurring on the West of Scotland, 297-304, Hitchcock (F. L. ). Quaternion Investigation of the Commutative Law for Homogeneous Strains, 170-180. Homogeneous Strains, Commutative Law for, i by F. L. Hitchcock, 170-180. Hydrochloric Acid (Aqueous) saturated with I Sodium Chloride, On the Electrical Con- i ductivity of, by F. D. Miles, 138-145. Hydrogen and Sodamide, Reaction between, by F. D. Miles, 134-137. 400 Proceedings of the Eoyal Society of Edinburgh. Integral-Equation whose Solutions are Lame’s Functions, by E. T. Whittaker, 70-77. Interpolation-Theory, Functions which are re- presented by the Expansions of, by E, T. Whittaker, 181-194. Iron and Steel, Magnetic Quality of, as affected by Transverse Pressure, by Wm. J. Walker, 217-226. Jurassic Rocks, Micro-organisms from, by David Ellis, 110-133. Lactose, Optical Rotation of, by J. E. Mackenzie and S. Ghosh, 22-45. Lamb (Horace). The Theory of the Gyroscope, 153-161. Lame’s Functions, an Integral -Equation whose Solutions are, by E. T. Whittaker, 70-77. Lauder (A.) and T. W. Fagan. On the Com- position of Milk as affected by Increase of the Amount of Calcium Phosphate in the Rations of Cows, 195-202. Letts (E. A.) and Florence W. Rea. On a Modification of Pelouze’s Method for deter- mining Nitrates, 168-169. Levy (H.). On the Resistance experienced by a Body moving through a Fluid, 95-109. Linear Vector Functions, Classification and Commutative Properties of, by F. L. Hitch- cock, 170-180. Lombard (Robert H.). See Smith, Alexander. Mackenzie ( J. E. ) and S. Ghosh. The Optical Rotation and Cryoscopic Behaviour of Sugars dissolved in («) Formamide, (6) Water, 22-45. Magnetic Quality of Iron and Steel as affected by Transverse Pressure, by Wm. J. Walker, 217-226. Mannose, Optical Rotation of, by J. E. Mac- kenzie and S. Ghosh, 22-45. Marshall (C. R.) and Elizabeth Gilehrist. The Interaction of Methylene Iodide and Silver Nitrate, 227-231. Methylene Iodide and Silver Nitrate, Inter- action of, by C. R. Marshall and Elizabeth Gilchrist, 227-231. Micro-organisms, Fossil, from Jurassic and Cretaceous Rocks, by David Ellis, 110-133. Miles (F. D.). On the Electrical Conductivity of Aqueous Hydrochloric Acid, saturated with Sodium Chloride ; and on a New Form of Conductivity Cell, 138-145. The Reaction between Sodamide and Hydrogen, 134-137. Milk, Composition of, as affected by Increase of the Amount of Calcium Phosphate in the Rations of Cows, by A. Lauder and T. W. Fagan, 195-202. Mossman (R. C.). On a See-Saw of Barometric Pressure, Temperature, and Wind Velocity between the Weddell Sea and the Ross Sea, 203-216. Muir (Dr Thomas). Properties of the Deter- minant of an Orthogonal Substitution. 54- 62. Mutarotation of Sugars, by J. E. Mackenzie and S. Ghosh, 22-45. Nitrates, On a Modification of Pelouze’s Method for Determining, by E. A. Letts and Florence W. Rea, 168-169. Orthogonal Substitution, the Determinant of, by Dr Thomas Muir, 54-62. Paul (J. H. ). A Comparative Study of the Reflexes of Autotomy in Decapod Crustacea, 232-262. Regeneration of Limbs in Decapod Crustacea, 78-94. Pelouze’s Method for Determining Nitrates, On a Modification of, by E. A. Letts and Florence W. Rea, 168-169. Periodicity in Plant Growth, by R. Ci'osse, 46- 53. Phosphoric Acid in Milk: Effect of increasing the Amount of Calcium Phosphate in the Ration on the Percentage in the Milk, by A. Lauder and T. W. Fagan, 195-202. Pigments, Reflective Power of, in the Ultra- violet, by Charles Cochrane, 146-152. Plant Growth, Periodicity in, by R. Crosse, 46-53. Pressure and Temperature Correlations between M‘Murdo Sound and other Places in the Southern Hemisphere, by R. C. Mossman, 203-216. Quaternions, CommutativeLaw for Homogeneous Strains investigated by, by F. L. Hitchcock, 170-180. Rea (Florence W.). See Letts, E. A. Reaetion between Sodamide and Hydrogen, by F. D. Miles, 134-137. Reflective Power of Pigments in the Ultraviolet, by Charles Cochrane, 146-152. Regeneration. Limb-regeneration from the Pre- formed Breaking-plane in Decapods, bv J. H. Paul, 78-94. Resistance experienced by a Body moving in a Fluid, by H. Levy, 95-109. Saturated Vapours of the Ammonium Halides, Densities and Degrees of Dissociation of the, by Alexander Smith and Robert H. Lombard, 162-167. Silver Nitrate and Methylene Iodide, Inter- action of, by C. R. Marshall and Elizabeth Gilehrist, 227-231. Smith (Alexander) and Pobert H. Lombard. The Densities and Degrees of Dissociation of the Saturated Vapours of the Ammonium Halides, 162-167. Sodamide and Hydrogen, Reaction between, by F. D. Miles, 134-137. Spherical Harmonics, Scheme of Calculation, etc. , by J. Bauschinger, 63-69. Stability of Trails of V ortices in wake of Body moving in a Fluid, by H. Levy, 95-109. Substitution, Orthogonal, the Determinant of, by Dr Thomas Muir, 54-62. Index. 401 Sugars, Cryoscopic Behaviour of, by J. E. Mac- kenzie and S. Ghosh, 22-45. Optical Rotation of, by J. E Mackenzie and S. Ghosh, 22-45. Theory of the Gyroscope, by Horace Lamb, 153-161. Turner (Sir William). The Baleen Whales of the South Atlantic, 11-21. Ultraviolet, Reflective Power of Pigments in the, by Charles Cochrane, 146-152. Vortices, Trails of, generated by Motion in a Fluid, by H. Levy, 95-109. Walker (Win. J.). The Magnetic Quality of Iron and Steel as affected by Transverse Pressure, 217-226. Whales, Baleen, of the South Atlantic, by Sir William Turner, 11-21. Whittaker (E. T. ). On the Functions which are represented by the Expansions of the Interpolation-Theory, 181-194. On an Integral- Equation whose Solu- tions are the Functions of Lame, 70-77. Xylose, Optical Rotation of, by J. E. Mackenzie and S. Ghosh, 22-45. [List of Papers published, etc. 26 VOL. XXXV. 402 Proceedings of the Eoyal Society of Edinburgh. List of Papers published in the “Transactions” during Session 1914-15. (^Arranged under the Auihord Names.) Ashworth (J. H.). On a New Sjjecies of Sclerocheilus, with a Revision of the Genus, vol, 1, 405-422. Benson (Margaret J. ), Sphoerostoma ovale. A Lower Carboniferous Ovule from Pettycur, Fifeshire, Scotland, vol. 1, 1-15. Campbell (Robert). Rocks from Gough Island, South Atlantic (collected by the Scottish National Antarctic Expedition, 1902-1904), vol. 1, 397-404. Carlgren (Oskar). On the Genus Porponia and Related Genera, collected by the Scottish National Antarctic Expedition, vol. 1, 49-71. Davie (R. C.). The Pinna-Trace in the Ferns, vol. 1, 349-378. Dawson (James W. ). The Histology of Dis- seminated Sclerosis, vol. 1, 517-740. Evans (T. J.). The Anatomy of a New Species of Bathycloris, and the Affinities of the Genus: Scottish National Antarctic Expedi- tion, vol. 1, 191-209. Ferguson (D. ). Geological Observations in South Georgia, vol. 1, 797-816. Fraser (Sir Thomas R.). The Poisoned Arrows of the Abors and Mishmis of North-East Africa, and the Composition and Action of their Poisons, vol. 1, 897-930. Fulton (Angus R.). Rupture Stresses in Beams and Crane Hooks, vol. 1, 211-224. Gregory (J. W.). The Geological Relations and some Fossils of South Georgia, vol. 1, 817- 822. Haig(H. A.). A Description of the Systematic Anatomy of a Foetal Sea-Leopard {Stenorhyn- chvs leptonyx), with Remarks upon the Micro- scopical Anatomy of some of the Organs, vol. 1, 225-251. Kidston (R. ). On the Fossil Flora of the Staffordshire Coal Fields Part III. : The Fossil Flora of the Westphalian Series of the South Staffordshire Coal Field, vol. 1, 73-190. On the Fossil Osmundacege, vol. 1, 469- 480. M'Lintock (W. F. P.). On the Zeolites and Associated Minerals from the Tertiary Lavas around Ben More, Mull, vol. li, 1-33. Marshall (C. R.). Studies on the Pharmaco- logical Action of Tetra-alkyl-ammonium Compounds. I. : The Action of Tetra- methyl-ammonium Chloride, vol. 1, 17-40. II. : The Action of Tetra-ethyl-am- monium Chloride, vol. 1, 379-396. III. : The Action of Methyl-ethyl-am- monium Chlorides, vol. 1, 481-516. Ramsay (L. N. G). Polychseta of the Family Nereidee collected by the Scottish National Antarctic Expedition, vol. 1, 41-48. Stebbing (Thomas R. R.). Stalk-eyed Crus- tacea Malacostraca of the Scottish National Antarctic Expedition, vol. 1, 253-307. Stephens (Jane). Atlantic Sponges collected by the Scottish National Antarctic Expedition, vol. 1, 423-467. Stephenson (J. ). On Rcemonais laurentii., n. sp. , a Representative of a little-known Genus of Naididse, vol. 1, 769-781. On a Rule of Proportion observed in the Setae of certain Naididae, vol. 1, 783-788. On the Sexual Phase in certain of the Naididae. I. : The Anatomy of Sexal Indi- viduals of the Genus Dero ; with Remarks on Hcemonais. II. : The Genital Organs in the Genus /S'Zarma, vol. 1, 789-795. Thompson (D’Arcy Wentworth). Morphology and Mathematics, vol. 1, 857-895. Thompson (J. M‘L. ). On the Anatomy and Affinity of Deparia Moorei, Hook, vol. 1, 837-856. Topsent (Emile). Spongiaires Recueillis par la Scotia dans I’Antarctique (1903-1904), Supplement, vol. li, 35-43. Turner (Sir Wm. ). The Aborigines of Tasmania. Part III. : The Hair of the Head compared with that of other Ulotrichi and with Australians and Polynesians, vol. 1, 309- 347. Tyrrell (G. W. ). The Petrology of South Georgia, vol. 1, 823-836. Wedderburn (E. M.), and A. W. Young. Temperature Observations in Loch Earn. Part II., vol. 1, 741-767. Young (A. W.), see Wedderburn (E. M.). PRINTED IN GREAT BRITAIN BY NEILL AND CO., LTD.. EDINBURGH. INSTRUCTIONS TO AUTHORS. The ‘ copy ’ should be written on large sheets of paper, on one side only, and the pages should be clearly numbered. 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Index Slips. — In order to facilitate the compilation of Subject Indices, and to secure that due attention to the important points in a paper shall be given in General Catalogues of Scientific Literature and in Abstracts by Periodicals, every author is requested to return to the Secretary, along with his final proof, a brief index (on the model given below), of the points in it which he considers new or important. These indices will be edited by the Secretary, and incorporated in Separate Index Slips, to be issued with each part of the Proceedings and Transactions. MODEL INDEX. Schafer, E. A. — Ou the Existence within the Liver Cells of Channels which can be directly injected from the Blood-vessels. Proc. Roy. Soc. Edin., vol. . 1902, pp. Cells, Liver, — Intra-cellular Canaliculi in. E. A. Schafer. Proc. Roy. Soc. Edin., vol. Liver, — Injection within Cells of. E. A. Schafer. Proc. Roy. Soc. Edin,, vol. , 1902, pp. , 1902, pp. IV CONTENTS. PAGE Appendix — Laws of the Society, . . . . . .321 The Keith, Makdougall-Brisbane, Neill, and Gunning Victoria Jubilee Prizes, ...... 326 Resolution of Council in regard to the mode of awarding Prizes, ....... 328 Awards of the Keith, Makdougall-Brisbane, Neill, and Gunning Victoria Jubilee Prizes, ..... 329 Proceedings of the Statutory General Meeting, October 1914, . 334 Proceedings of the Ordinary Meetings, Session 1914-1915, . 335 Proceedings of the Statutory General Meeting, October 1915, . 340 Accounts of the Society, Session 1914-1915, . . . 342 The Council of the Society at January 1916, . . . 348 Alphabetical List of the Ordinary Fellows of the Society at January 1916, ...... 349 List of Honorary Fellows of the Society at January 1916, . 366 List of Ordinary Fellows of the Society elected during Session t 1914-1915, . . . . . . . 368 Honorary Fellows and Ordinary Fellows Deceased and Resigned during Session 1914-1915, ..... 368 List of Library Exchanges, . . . . . 369 List of Periodicals Purchased by the Society, . . . 393 Additions to Library during 1915, by Gift or Purchase, . .397 Index, ......... 399 List of Papers -published in the “ Transactions ’’ during Session 1914-15, ....... 402 The Papers published in this Part of the Proceedings may he had separately, on application to the Publishers, at the follow- ing prices : — . Price 6d. ,, Is. 9d. Price 5> 2s. 6d. No. XXII, . No. XXIII, . No. XXIV, . No. XXV, . ' S