. %r* U'' ) '■ n J'i.*’ i\' ! <''■!'. •■'.» t \ ;:^,5b;T:iii'!it; ft-'-ti!.. '|i^;pgilT!4:ig4^^ Sllpii’iliiii iiiiliiiil liliifliiliil lililflilfil iiiii Iliiiiiill ;■■!! ^\ ii.f, , j. i *;» -, Li I ; ,V ♦ .1 1 ; i 1 ^ rt. g'l ri^^'V PEOCEEDINGS OF THE ROYAL SOCIETY EDINBURGH. VOL. XII. NOVEMBER 1882 to JULY 1884. EDINBURGH PRINTED BY NEILL AND COMPANY. MDCCOLXXXIV. CONTENTS. PAGE Election of Office-Bearers, . . . . . .1 President’s Address, . . . . . . .2 Dr Guebhard’s Electro-Chemical Method of Figuring Equipotential Lines. By Kev. Dr W. R. Smith, . . . . .7 Message from the Nautical Almanac Office, in reference to the Transit of Venus, December 6, 1882, Communicated by the Astronomer- Royal, . . . ... . . .7 On the Laws of Motion. Part I. By Professor Tait, . . 8 On Illegitimacy in Scotland. By George Seton, M.A., Oxon, . 18 On the Absorption of Low Radiant Heat by Gaseous Bodies. By Professor MacGregor, . . . . . .24 Note on the Compressibility of Water. By Professor Tait, . . 45 Note on an Application of Mendeleieff’s Law to the Heats of Combin- ation of the Elements with the Halogens. By Mr A. P. Laurie. Communicated by Professor Crum Brown, . . .46 The Diurnal Variation of the Force of the Wind in the Open Sea and near Land. By Alexander Buchan, M.A., . . .47 On the Semitic and Greek Article. By the Rev. Dr Teape, . 47 On the Nature of Solution. By W. W. Nicol, M.A., B.Sc., . ' .47 On the Relative Electro-Chemical Positions of Wrought Iron, Steels, Cast Metal, &c., in Sea Water and other Solutions. By Thomas Andrews, Assoc. M. Inst. C.E., F.C.S. Communicated by Prof. Crum Brown, . . . . . . ,47 Observations of the Rainband from June 1882 to January 1883. By Hugh Robert Mill, B.Sc., F.C.S. Communicated by Professor Tait. (Plate I.), . . . . . . .47 The Theory of Monopressures applied to Rhythm, Accent, and Quantity. By the Rev. J. L. Blake. Communicated by Prof. Crum Brown, . . . . . . .56 On the Effect of Oil on a Stormy Sea. By Mr John Aitken, . 56 Communication from the Astronomer-Royal for Scotland. Read by Professor Tait, . . . . . . .75 Diagnoses plantarum novarum Phanerogamarum Socotrensium, etc. ; quas elaboravit Bayley Balfour, Scientiae Doctor et in Universitate Glascuensi rerum botanicarum regius professor. Pars Tertia, . 76 On Scientific Method in the Study of Language. By Emeritus Prof. Blackie, . . . . . . . .98 Further Remarks on the Mirage Problem. By Professor Tait, , 98 IV Contents. PAGE On Ancient Tenure of Land in Scotland. By Mr G. Anldjo Jamieson, . . . . . . * . .99 On the Microscopical ApjDearances of Striped Muscular Fibre during Eelaxation and Contraction. By Professor Eutherford, . .126 Election of Honorary Fellows, . . . . .126 On the so-called Bicipital Kibs. By Professor William Turner, . 127 Oscillations and Waves in an Adynamic Gyrostatic System. By Sir William Thomson, . . . . . . .128 On Gyrostatics. By the Same, ..... 128 On the Dynamical Theory of Dispersion. By the Same, . .128 On the Impossibility of Inverted Images in the Air. By Edward Sang,. ........ 129 On the Thermo-electric Positions of pure Ehodium and Iridium. By Professor Tait, . . . . , . .136 Observations on the Growth of Wood in Deciduous and Evergreen Trees. By the late Sir E. Christison, Bart, and Dr Christison, . 136 The Variation of Temperature, with Sun-Spots. By Mr A. Buchan, 136 On some Laboratory Arrangements. By Dr John Gibson, . .137 On the Thermo-electric Position of pure Cobalt. By Professor Tait, 141 Transmission of Power by Alternate Currents. By Professor George Forbes, ........ 141 On the Homology of the Neural Gland in the Tunicata with the Hypophysis Cerebri. By W. A. Herdman, D.Sc., F.L.S., Pro- fessor of Natural History in University College, Liverpool, . 145 On the Quaternion Expression of Finite Displacements of a System of Points of which the Mutual Distances remain Invariable. By Gustave Plarr, Docteur ^s Sciences. Communicated by Prof. Tait, 151 On some Properties of the Line of Simple Flexure. By Edward Sang, C.E. (Plates I.*-IIL), ..... 172 On the Measurement of Eesistance in Electrolytes, By Cargill G. Knott, D.Sc., F.E.S.E., 178 The Electrical Eesistance of Hydrogenised Palladium. By Cargill G. Knott, D.Sc., F.E.S.E., 181 Note on Plane Algebra. By A. Macfarlane, M.A., D.Sc., . . 184 On Heat-Conduction in Heterogeneous Bodies, as modified by the Peltier and Thomson effects. By Professor Tait, . . .186 Note on the Thermo-electric Position of j)ure Euthenium. By Prof. Tait, ........ 186 At the request of the Council Professor Geikie delivered an Address on Eecent Advances in European Pleistocene Geology, . .186 On the Moon and the Weather. By John Aitken, . . . 187 The Acids of Opium. By D. B. Dott, . . . .189 Direct Observations of the Effect of Pressure on the Maximum Density-Point of Water. By Professor Tait, . . . 192 The Diurnal Oscillations of the Barometer. Part II. By Mr A. Buchan, ........ 3«93 Ninth Eeport of the Boulder Committee. Communicated by Mr Milne Home, . . . . . . .193 Contents. y PAGE On a new Entozoon (Pentastomum protelis) from the Mesentery of Proteles cristatus, Sparrmann. By W. E. Hoyle, M.A. (Oxon.), F.R.S.E., Naturalist to the “ Challenger” Expedition Commission, 219 Bright Clouds on a Dark Night Sky. By the Astronomer-Boyal for Scotland, ........ 223 Mathematical Note. By Mr A. H. Anglin, .... 223 Note on the Compressibility of Water, Sea- Water, and Alcohol, at High Pressures. By Professor Tait, .... 223 Note on the little b group of lines in the Solar Spectrum and the new College Spectroscope. By the A.stronomer-Koyal for Scotland, . 225 On Superposed Magnetisms in Iron and Nickel. By Prof. C. G. Knott, D.Sc., . . . . V . . 225 Further Note on the Maximum Density-Point of Water. By Prof. Tait, 226 On Surface Emissivity. By Professor Tait, . . . . 230 On a proposed Edinburgh Marine Station for Biological Research at Granton Quarry. By Mr J ohn Murray, . . . .231 On Work done on board H.M.S. ‘‘Triton” in the Faroe Channel during the Summer of 1882. By Mr John ]\[urray, . . 231 On the Pennatulida dredged in the Faroe Channel during the Cruise of H.M.S. “ Triton” in August 1882. By Prof. A. M. Marshall. Communicated by Mr John Murray, . . . .231 On the Asteroidea dredged in the Faroe Channel during the Cruise of H.M.S. “ Triton” in August 1882. By Mr W. Percy Sladen, F.L.S., F.G.S. Communicated by Mr John Murray, . . 231 On the Pycnogonida dredged in the Faroe Channel during the Cruise of H.M.S. “ Triton” in August 1882. By Dr P. P. C. Hoek. Communicated by Mr John Murray, .... 231 On the Crustacea dredged in the Faroe Channel during the Cruise of H.M.S. “ Triton” in 1882. By Rev. A. M. Norman, D.C.L. Communicated by Mr John Murray, . . . .231 On the Tunica ta dredged in the Faroe Channel during the Cruise of H.M.S. “ Triton” in August 1882. By Professor W. A. Herdman, 231 On the Proofs of Proportionality of Emissive and Absorptive Power. By Professor Tait, . . . . . . .231 A Contribution to the Chemistry of Nitroglycerine. By Matthew Hay, M.D., Assistant to the Professor of Materia Medica in the University of Edinburgh. Communicated by Prof. Crum Brown, 234 The Elementary Composition of Nitroglycerine. By Matthew Hay, M.D., and Orme Mason, M.A., B.Sc. Communicated by Prof, Crum Brown, ....... 234 President’s Closing Remarks, ...... 235 Mathematical Note. By Mr R. H. Hallam Anglin, M.A., LL.B., M.R.I.A., . . . . . . . .236 Election of Office-Bearers, ...... 245 An Essay upon the Limitations in Time of Conscious Sensations. By John B. Hay craft, M.B. Edin., F.R.S.E., &c. ; Professor of Physiology in the Mason Science College, and Lecturer on Physi- ology at Queen’s College, Birmingham, . . . . 246 VI Contents. PAGE The Old Englisli Mile. By Wm. Flinders Petrie. Communicated by Professor Robertson Smith, . . . . . 254 A Re-Statement of the Cell Theory, with Applications to the Mor- phology, Classification, and Physiology of Protists, Plants, and Animals. Together with an Hypothesis of Cell-Structure, and an Hypothesis of Contractility. By Patrick Geddes. (Plate IV.), . 266 On the Change in the Peltier Effect due to Variation of Temperature. By Albert Campbell. Communicated by Professor Tait, . 293 On the Problem of the Lathe-Band, and on Problems therewith con- nected. By Edward Sang, . . . . . 294 Notes on the Madi or Moru Tribe of Central Africa. By Robert W. Felkin, F.R.S.E., F.R.G.S., Fellow of the Anthropological Societies of London and Berlin, &c. (Plate V.), . . . . 303 On the Crinoidea of the North Atlantic between Gibraltar and the Faroe Islands. By P. Herbert Carpenter, D.Sc. (Camb.), Assist- ant Master at Eton College. With some Notes on the Myzostomida, by Prof. L. von Graff, Ph.D. Communicated by Mr John Murray, 353 On the Structure of the Pitcher in the Seedling of Nepenthes, as compared with that in the Adult Plant. By Prof. Alexander Dickson, M.D., ....... 381 Approximation to the Roots of Cubic Equations by help of Recurring Chain Fractions. By Edward Sang, LL.D., . . . 387 The Researches of M. E. de Jonquieres on Periodic Continued Frac- tions. By Thomas Muir, M.A., . . . . . 389 Additional Note. By the Same, ..... 398 New Forms of Nerve Terminations in the Skin of Mammals. By George Hoggan, M.B. (Edin.). Communicated by Prof. Turner, 400 Diagnoses Plantarum novarum Phanerogamarum Socotrensium, etc. ; quas elaboravit Bayley Balfour, Scientise Doctor et in Universi- tate Glascuensi rerum botanicarum regius Professor. Pars quarta (Supplementum), ....... 402 Abstract Report on the “ Porcupine” Tunicata. By Professor W. A. Herdman, ........ 412 Arrangement of the Metals in an Electro-Frictional Scale. By A. Macfarlane, D.Sc., . . . . . . .412 On Distant Vision. By E. E. Maddox Esq. Communicated by Professor Crum Brown, . ... . . . 433 On the Formation of Small Clear Spaces in Dusty Air. By Mr John Aitken, . . . . . . . 440 The Remarkable Sunsets. By Mr John Aitken, . . . 448 President’s Address, giving a Review of the Hundred Years’ History of the Society, . . . . . . .451 On the Microscopic Characters of Volcanic Ashes and Cosmic Dust, and their Distribution in the Deep-Sea Deposits. By Mr John Murray and M. I’Abbe Renard. Communicated by Mr John Murray, ........ 474 On the Nomenclature, Origin, and Distribution of Deep-Sea De- posits. By J ohn Murray and M. I’Abbe Renard. Communicated by John Murray, ....... 495 Contents. vii PAGE iSTote on a large Crystal of Calc-spar found in Lough Corrib by Pro- fessor Tait. By M. I’Abhe Ecnard, .... 530 On Kadiation. By Professor Tait, . . . . .531 On the Need for Decimal Subdivisions in Astronomy and Naviga- tion, and on Tables requisite therefor. By Edward Sang, LL.D., 533 An Electro-Magnetic Declinometer. By A. Tanakadate, Assistant to the Professor of Physics in the University of Tokio, Japan. Coni- 'municated by Prof. J. A. Ewing, University College, Dundee, . 544 On an Equation in Quaternion Differences. By Professor Tait, . 561 On Vortex Motion. By Professor Tait, .... 562 Award of the Keith, Makdougall-Brisbane, and Neill Prizes, . 562 On Efficiency of Clothing for maintaining Temperature. By Sir W. Thomson, 568 On the Law of Inertia ; the Principle of Chronometry ; and the Principle of Absolute Clinural Rest, and of Absolute Rotation. By Professor James Thomson, LL.D., D.Sc., C.E., . . 568 On a Modification of Gauss’s Method for determining the Hori- zontal Component of Terrestrial Magnetic Force, and the Magnetic Moments of Bar Magnets, in Absolute Measure. By Sir William Thomson, ........ 578 On the Phenomenon of “ Greatest Middle” in the Cycle of a Class of Periodic Continued Fractions. By Thomas Muir, M.A., F.R.S.E., 578 The Old Red Sandstone Volcanic Rocks of Shetland. By Messrs B. N. Peach and John Horne, of the Geological Survey of Scotland, 593 On the Principles of Economics. Part I., Mathematical. Part II., Physical. By Mr P. Geddes, ..... 593 An Integrating Hygrometer. By Professor C. Michie Smith, . 593 On the Philosophy of Language. By Emeritus Professor Blackie, . 594 On the Principles of Economics. Part III., Biological and Psycho- logical. By Mr P. Geddes, ..... 594 Note on a New Form of Galvanometer. By Prof. James Blyth, . 594 On Galvanic Currents passing through a very Thin Stratum of an Electrolyte. By Professor H. von Helmholtz, . . . 596 On Cosmic Dust. By M. I’Abb^ Renard, .... 599 Esempio del metodo di dedurre una superficie da una figura piana, dal Professore Luigi Cremona, . . . . .599 On the Construction of the Canon of Logarithmic Sines. By Edward Sang, LL.D., . ...... 601 On Stichocotyle nephropis, a new Trematode. By Mr J. T. Cunning- ham, B.A. Communicated by Mr John Murray, . . .619 Scottish Vital Statistics. By Mr George Seton, Advocate, M.A. Oxon., ........ 619 Experiments on the Chief Disinfectants of Commerce, with a view of ascertaining their Power of Destroying the Spores of the Anthrax bacillus. By A. Winter Blyth, Medical Officer of Health and Public Analyist. Communicated by Professor Turner, . . 633 Sur la Reduction des Integrates Hyperelliptiques, extrait d’une lettre adressee a M. le Professeur Chrystal, par M. Hermite, . 642 Vlll Contents. PAGE At the request of the Council, Professor Schuster give an Address on the Discharge of Electricity through Gases, with Experimental Illustrations, ....... 646 The Enumeration, Description, and Construction of Knots with fewer than Ten Crossings. By the Rev. T. P. Kirkman, F.R.S. Communicated by Professor Tait, ..... 646 On Knots. Part II. By Professor Tait, .... 647 Second Note on the Remarkable Sunsets. By Mr John Aitken, . 647 Thermometer Screens. By Mr John Aitken. (Plate VI.), . . 661 Abstract of Paper on Micrometrical Measures of Gaseous Spectra. By Professor C. Piazzi Smyth, ..... 696 On the Computation of Recurring Functions by the aid of Chain- Fractions. By Edward Sang, LL.D., .... 703 On Extensions of Euclid I. 47. By Mr A. H. Anglin, . . 703 Report on the Ophiuroidea of the Faroe Channel, mainly collected by H.M.S. “ Triton” in August 1882, with some Remarks on the Distribution of the Order. By Mr W. E. Hoyle, M.A. (Oxon.), M.R.C.S., Naturalist to the “Challenger” Commission. (Plate VII. ), 707 On the Principles of Economics. By Mr P. Geddes. Part V., Psychological, . . . . . . .730 A Problem on Point-Motions for which a Reference-Frame can so exist as to have the Motions of the Points relative to it. Rectilinear and Mutually Proportional. By Professor James Thomson, . 730 Note on Reference Frames. By Professor Tait, . . . 743 Note on the Occurrence of Drifted Trees in Beds of Sand and Gravel at Musselburgh. By Professor James Geikie, LL.D., F.R.S., . 745 On a Special Class of Partitions. By Professor Tait, . .755 Observations on a Green Sun, and Associated Phenomena. By Prof. C. Michie Smith, . . . . . . .755 Analysis of the Principles of Economics. Part V., Psychological. By Mr P. Geddes, . . . . . , . . 755 On a Singular Electrical Result. By Mr Harry Rainy. Communi- cated by Professor Tait, . . . . . . .756 Observations on Coral Reefs and Calcareous Formations of some of the Islands in the Solomon Group. By H. B. Guppey, M.D., H.M.S. “ Lark,” with Notes by Mr John Murray. Communicated by Mr John Murray, . . . . . .757 Further Note on the Compressibility of Water. By Professor Tait, 757 Critical Note on the latest Theory in Vertebrate Morphology. By Mr J. T. Cunningham, B.A., ..... 759 Tenth and Final Report of the Boulder Committee ; with Appendix, containing an Abstract of the Information in the Nine Annual Reports of the Committee ; and a Summary of the Principal Points apparently established by the information so received. (Plates VIII. to X.), 765 Remarks by Mr Milne Home on presenting the Tenth Report of Boulder Committee, ...... 907 Contents. ix PAGE Notice of Two Localities for Remarkable Gravel Banks or Kaimes, and Boulders, in the West of Scotland, in Supplement of the Boulder Committee’s Tenth Report. By David Milne Home, LL.D. (Plates XL to XIIL), 913 On the Periodic Variation of Temperature in Tidal Basins. By Hugh Robert Mill, B.Sc.. F.C.S. Communicated by Professor Crum Brown. (Plate XIV.), ..... 927 On the Isothermals and Adiabatics of Water near the Maximum Point. By Mr W. Peddie. Communicated by Professor Crum Brown, ........ 933 Review of the Session, by the President, .... 937 Address from the Society to the University on the occasion of the Tercentenary, ....... 940 An Analysis of the Principles of Economics. By Patrick Geddes, 943 Donations to the Library, . . . . . .981 Index, ........ 1000 PROCEEDINGS OF THE EOYAL SOCIETY OF EDINBUEGH. VOL. XII. 1882-83. No. 113. The Hundredth Session. GENERAL STATUTORY MEETING. Monday^ November 1882. Professor M ACL AG AN, Vice-President, in the Chair. The following Council were elected : — President. The Right Hon. LORD MONCREIFF. Vice-Presidents. Prof. Douglas Maclagan, M.D. Prof. H. C. Fleeming Jenkin, F.R.S, Rev. W. Lindsay Alexander, D, D. J. H. Balfour, M.D., F.R.S. Thomas Stevenson, M.In.C.E. Robert Gray, Esq. General Secretary — Professor Tait. Secretaries to Ordinary Meetings. Professor Turner, F.R.S. Professor Crum Brown, F.R.S. Treasurer. — Adam Gillies Smith, Esq., C.A. Curator of Library and Museum — Alexander Buchan, Esq. , M. A. Councillors. Professor Chrystal. Sheriff Forbes Irvine. Professor A. Dickson. The Right Rev. Bishop Cotterill. Rev. Professor Duns. Dr Ramsay Traquair. John Murray, Esq. William Ferguson, Esq. Professor Cossar Ewart. Professor James Geikie. Rev. Dr W. Robertson Smith. Stair Agnew, Esq. By a Resolution of ther Society (19th January 1880) the following Hon. Vice-Presidents, having filled the office of President, are also Members of the Council : — His Grace the DUKE of ARGYLL, K.T., D.C.L. Sir WM. THOMSON, LL.D., D.C.L., F.R.S., Foreign Associate of Insti- tute of France. VOL. XII. A 2 Proceedings of the Royal Society Monday, 4dh December 1882. The Eight Hon. LOED MONCEEIFF^ President, in the Chair. The President gave a short historical sketch of the Society on the occasion of the commencement of its Hundredth Session. He said that, before the business commenced, he ought to call attention to a peculiarity of the present meeting, and to make one or two observa- tions upon it. This was the hundredth session of the Eoyal Society. Most cordially did he congratulate the Society and its members on having arrived at that interesting period of its history. But it was right he should say that it would he a mistake to suppose that, although this was the hundredth session, they were absolutely centenarian. This was not the anniversary of the birth of the Eoyal Society. For some reason or other — he did not know how — the hundredth session began before the Society was absolutely a hundred years old. How it exactly came about he was not quite sure. The Eoyal Society’s charter bore date March 1783; and he supposed, like other great institutions, they had a previous autumn session — and in that way, possibly, the difference was to be accounted for. But, in any view, it is a great occasion for meditation and observation, and there may come a time for such a word, but on the present occasion he had not the material sufficient to do anything like justice to a theme so large. Only in a few sentences would he go back to March 1783, and glance upon the long career which the Society had run. A long and distinguished course, he thought they might say, seeing it w^as to their distinguished predecessors they owed its glory and its present flourishing existence. There had been many speculations as to where the Eoyal Society came from, and its feeders had been examined and searched for with great assiduity. There was a Eankinian Club in Edinburgh towards the beginning of last century, and it was claimed as the foundation of the Eoyal Society. Then there was a Select Society, a debating club — somewhere about 1750 — where Dr Eobertson and the great men of those days practised the oratory which they afterwards used with such effect ; and they had been told that that to a large of Edinlurgli, Session 1882-83. 3 extent was the origin of the Royal Society. He had looked into the Appendix to Diigald Stewart’s Life of Robertson, and there he found a list of members of the Select Society — and it contained many, if not all, of the names of the great men who were in 1783 among its members. One distinctive thing he could gather from the notice was, that Adam Smith and David Hume were both members of it, and that neither one nor the other ever opened their lips in the Society during the time they were members of it. But he rather thought a third institution had more claim, and that was the Philosophical Society, founded by Colin Maclaurin, the great mathematician. Undoubtedly it did survive till the period when the Royal Society was formed. Colin Maclaurin, unfortunately for himself, was the engineer employed to defend Edinburgh at the time of the advance of the Pretender in 1745, and he had to leave Edinburgh. Observations had sometimes been made as if Mac- laurin had made a somewhat precipitate retreat on that occasion, but the real fact was, he was the last man who left, for he found, after all the fortifications were complete, that there was nobody to man them, and no army to help in the defence. He was not the only man who had to retreat, for he rather thought the Court of Session also took that course, and before the Pretender arrived the Judges had departed to their country seats. Such was the parentage of the Royal Society. In 1783 these streams all seemed to meet, and this institution was the result. They had originally a literary side and a physical or mathematical side. At the first start they had 104 on the physical side and 114 members on the literary side. He was looking back to an address by his much valued and lamented friend Professor Eorbes, which was delivered in 1862, and he would go over a few names given there as belong- ing to the physical side and to the literary side, and they would probably agree with him (there were many more who might go alongside of them) that it would be difficult to find in any part of Britain, or in any country out of Britain, an assemblage of persons more distinguished in their respective spheres. The physical side embraced Joseph Black, Clerk of Eldin, Lord Hailes, James Gregory, James Hutton, John Playfair, Dugald Stewart, Lord Bute, Lord Dundonald, Sir James Hall, James Watt, Dr Small (Dundee), and Patrick Wilson. And on the literary side there were 4 Proceedings of the Royal Society the Lord President, Chief Baron, the Lord Advocate, John Home, David Hume, Henry Mackenzie, Alexander Tytler, the Duke of Buccleuch, Archibald Alison, Dr Beattie, Edmund Burke, Lord Morton, Lord Hopetoun, John Hunter, Thomas Beid, Young of Glasgow, and Mr Liston. That was a nucleus for a great Society ; and certainly from that time forward it grew and prospered until the position of a Eellow of the Eoyal Society of Edinburgh became one of the highest distinction. How, it appeared, they had lasted for one hundred years. Whether they all of them could come up to the mark of the great men whose names he had read he did not know. Eor one thing, we knew many things they did not know, although they possibly knew a great many that we did not know ; hut, looking hack from 1783 till now, it was a wonderful retro- spect in point of knowledge and invention and progress — owing, to a large extent, to the labours of the men whose names he had just mentioned. The literary side was presided over hy Sir Thomas Miller of Barskimming, who held the office of Lord Justice-Clerk, the office the speaker had the honour to hold. He was a man of very great powers — a great lawyer, and a man of very strong lite- rary tastes. But he did not know that the. literary side had quite made the progress they might have looked for during that time. It did last for about twenty years in great vigour. He had the curiosity to see what the subjects were that were treated of. There w^ere some very vigorous papers; and among them he found a dissertation by John Maclaurin, the son of the mathematician, the object of which was to prove that Troy was not taken by the Greeks after all, which he tried to prove with a wonderful amount of learning. Perhaps he might be excused if he suggested that possibly it would be an improvement if in this respect also they followed more closely in the footsteps of their predecessors. These observations he concluded by wishing the Eoyal Society all pro- sperity in the next hundred years. of Edinhurgh, Session 1882-83. 5 The President read the following statement in regard to the number of the Pellows of the Society : — I. Honorary Fellows — Royal Personage — His Royal Highness the Prince of Wales, . 1 British Subjects at November 1881. John Couch Adams, LL.D., Cambridge ; Sir George Biddell Airy, K.C.B., Greenwich ; Thos. Andrews, M.D., Belfast ; Arthur Cay- ley, LL.D., Cambridge; Chas. Darwin, M.A., F.R.S., Kent ; J ohn Anthony Fronde, LL.D., London ; Sir William Robert Grove, London ; Thomas Henry Huxley, LL.D., D.C.L., London; James Prescott Joule, LL.D., D.C.L., Manchester ; Richard Owen, C.B., M.D., London ; Thomas Romney Robinson, D.D., D.C.L., LL.D., Armagh ; General Sir Edward Sabine, K.C.B., London ; Rev. George Salmon, D.D., LL.D., D.C.L., Dublin ; Henry John Stephen Smith, LL.D., Oxford ; Balfour Stewart, LL.D., Manchester; George Gabriel Stokes, LL.D., D.C.L., Cambridge ; James Joseph Sylvester, LL.D., Baltimore; Alfred Tennyson, D.C.L., Isle of Wight. Total, Of these Charles Darwin and Dr T. Romney Robinson died during the Session, Deduct, Total Number of British Honorary Fellows at November 1882, Foreign Honorary Fellows at November 1881. Robert Wilhelm Bunsen, Heidelberg ; Michel Eugene Chevreul, Paris ; James D. Dana, Newhaven, U.S. ; Alphonse De Candolle, Geneva ; Franz Cornelius Donders, Utrecht ; J ean Baptiste Dumas, Paris ; Carl Gegenbaur, Heidelberg ; Asa Gray, Harvard, U.S. ; Hermann Ludwig Ferdinand Helmholtz, Berlin ; Jules Janssen, Paris. ; August Kekule, Bonn ; Gustav Robert Kirchhuff, Berlin ; Hermann Kolbe, Leipzig ; Albert 18 2 16 Carry forward. 17 6 Proceedings of the Royal Society Brought forward, 17 Kolliker, Wurzburg ; Ernst Eduard Kum- mer, Berlin ; Eichard Lepsius, Berlin ; Ferdinand de Lesseps, Paris ; Eudolph Leuckart, Leipzig ; J ohann Benedict Listing, Gottingen ; Joseph Liouville, Paris ; Sven Loven, Stockholm ; Carl Ludwig, Leipzig ; J. N. Madvig, Copenhagen ; Henry Milne- Edwards, Paris ; Theodore Mommsen, Berlin; Simon Newcomb, Washington; Louis Pasteur, Paris ; Emile Plantamour, Geneva ; Carl Theodor von Siebold, Munich ; Johannes Japetus Smith SteenstrUp, Copen- hagen; Otto Wilhelm Struve, Pulkowa; Bernard Studer, Bern; Otto Torell, Lund; Rudolph Virchow, Berlin ; Wilhelm Edu- ard Weber, Gottingen; Friedrich Wohler, Gottingen. Total number at November 1881, 36 Of these three died during the course of last Session, — Joseph Liouville, Emile Plantamour, and Friedrich Wohler. Deduct . . 3 Total Number at November 1882, . 33 Total Number of British and Foreign Honorary Fellows at November 1882, . 50 IL Ordinary Fellows — The Ordinary Fellows of the Society at November 1881 were .408 Fellows since elected — Sir Peter Coats; Andrew Young, Esq. ; D. B. Dott, Esq.; Dr James Clerk Rattray ; Alexander Leslie, Esq. ; John Sturgeon Mackay, Esq. ; Dr Henry Barnes ; James Sorley, Esq. ; William Thomson, Esq. ; Thomas Graham Young, Esq. ; W. Dyce Cay, Esq. ; J. A. Dixon, Esq.; Professor C. 'Michie Smith; D. H. Marshall, Esq. ; Josiah Livingston, Esq. ; Dr David Pryde ; J. W. Inglis, Esq. ; Frank W. Young, Esq. ; T. R. Buchanan, Esq., M.P. ; Dr George Wilson ; Frank E. Beddard, Esq. ; Andrew Jamieson, Esq. ; J. A. Wenley, Esq. 23 Carry forward. 431 of Edinburgh, Session 1882-83. 7 Brought forward, 431 Deceased during Session 1881-82 — David Anderson, Esq. of Moredun ; Charles D. Bell, Esq. ; Dr John Brown ; Sir Robert Christi- son, Bart. ; Sir John Bose Cormack ; J. Anthony Dixon, Esq. ; Sheriff Frederick Hallard ; James Hay, Esq. ; William King, Esq. ; John McCulloch, Esq. ; Sir Daniel Macnee ; Dr Charles Morehead ; Dr John Muir; Richard Parnell, Esq. ; Samuel Raleigh, Esq. ; Dr William Robertson ; John Scott Russell, Esq. ; Professor Spence ; SirWyville Thomson ; James Walker, Esq. ; Robert Wilson, Esq. Deduct .21 Total Number of Ordinary Fellows at November 1882, . 410 Total Number of Honorary Fellows at November 1882, . 50 Total Number of Fellows of the Society at November 1882, 460 Obituary Notices were read of Charles Darwin, l^mile Plantamour, Charles Davidson Bell, Dr William Robertson, Sir Daniel Macnee, David Anderson, John McCulloch, Samuel Raleigh, and Professor James Spence, deceased Fellows of the Society. The following Communications were read:— 1. Dr Guebhard’s Electro-Chemical Method of Figuring Equi- potential Lines. By Rev. Dr W. R. Smith. 2. Message from the Nautical Almanac Office, in reference to the Transit of Venus, Dec. 6, 1882. Communicated by the Astronomer-Royal. Royal Observatory, Edinburgh, Uh December 1882. The following despatch has just been received from Mr J. R. Hind, Superintendent of the Nautical Almanac, London : — “First external contact at 1 h. 48 m. 24 sec., mean time at Edinburgh ; the place of it being at 147° N. to E. for direct image. “First internal contact will be 21 minutes later.” The above notification indicates that the phenomena will occur 5 minutes and a few seconds later than the times printed four years ago, under difficulties, in the Nautical Almanac. 8 . Froceedings of the Royal Society Observers should therefore be warned and prepared accordingly : viz., for 2 b. 1 m. 7 sec. in place of 1 b. 55 m. 57 sec. p.m. of Greenwich mean time as per Time-Ball and Time-Gun here in Edinburgh. The place of first external contact will also be 2 degrees on the sun’s limb nearer to its south pole, but on the east side, as before. C. PiAzzi Smyth, Adronomer-Royal for Scotland. To General Secretary, Royal Society, Edinburgh. BUSINESS. The following Candidates were balloted for and declared duly elected Fellows of the Society : — Dr E. H. Gunning ; Alexander Bruce, M.A., M.B. ; Dr Charles D. E. Phillips. Monday, IWi Decemher 1882. EOBEET GRAY, Esq., Vice-President, in the Chair. The following Communications were read : — 1. On the Laws of Motion. Part I. By Professor Tait. {Abstract.) The substance of part at least of this paper was given in 1876 as an evening lecture to the British Association at its Glasgow meeting. While engaged in writing the article “ Mechanics ” for the Ency. Brit., I had to consider carefully what basis to adopt, and decided that the time had not yet come in which (at least in a semi-popular article) Newton’s laws of motion could be modified. The article was therefore based entirely on these laws, with a mere hint towards the end that in all probability they would soon require essential modification. It is well, however, that the question of modification should now be considered ; and this should be done, not in a popular essay but, before a scientific society. The one objection to which, in modern times, that wonderfully complete and compact system is liable, is that it is expressly founded on the conception of what is now called “ force ” as an agent which “ compels” a change of the state of rest or motion of of Edinburgh, Session 1882-83. 9 a body. This is part of the first law, and the second law is merely a definite statement of the amount of change produced by a given force. (Next comes a digression as to what was Newton's expression for what we now mean by the word force, when it is used in the correct signification above.) There can be no doubt that the proper use of the term force in modern science is that which is implied in the statement — Force is whatever changes a body’s state of rest or motion. This is part of the first law of motion. Thus we see that force is the English equivalent of Newton’s term vis impressa. But it is also manifest that, on many occasions, hut only where Ms meaning admitted of no doubt j Newton omitted the word impressa and used vis alone, in the proper sense of force. In other cases he omitted the word impressa, as being implied in some other adjective such as centri- peta, gravitans, &c., which he employed to qualify the word vis. Thus (Lemma X.) he says i—Spatia, quoe corpus urgente qudcunque vi finitd describit, &c. It is needless to multiply examples. But that this is the true state of the case is made absolutely certain by the following: — Definitio IV. Vis impressa est actio in corpus exercita., ad mu- tandum ejus statum vel quiescendi vel movendi uniformiter in directum. Contrast this with the various senses in which the word vis is used in the comment which immediately follows, viz, : — Constitit haec vis in actione sola, neque post actionem permanet in corpore. Perseverat enim corpus in statu onini novo per solam vim inertise. Est autem vis impressa diversarum originum, ut ex ictu, ex pressione, ex vi centripeta. These passages are translated by Motte as below : — “ Definition IV. An impressed force is an action exerted upon a body, in order to change its state, either of rest, or of moving uni- formly forward in a right linef^ “ This force consists in the action only, and remains no longer in the body when the action is over. For a body maintains every new state it acquires, by its vis inertioe only. Impressed forces are of different origins ; as from percussion, from pressure, from centripetal force. ” 10 Proceedings of the Royal Society The difficulty which Motte here makes for himself, and which he escapes from only by leaving part of the passage in the original Latin, is introduced solely by his use of the word force as the equi- valent of the Latin vis. If we paraphrase the passage as follows, with attention to Newton’s obvious meaning, this difficulty disappears, or rather does not occur : — “This kind of vis consists in,” &c. Lor the “body continues .... by the vis of inertia,” &c. However, we may quote two other passages of Newton bearing definitely on this point. Definitio III. Materim vis insita est potentia resistendi, qua corpus unumquodque^ quantum in se est, perseverat in statu suo vel qidescendi vel movendi uniformiter in directum. It is perfectly clear that, in this passage, the phrase vis indta is one idea, not two, and that vis cannot here be translated by force. Yet Motte has “ The vis insita, or innate force of matter, is,” &c. Definitio V. Vis centripeta est, qua corpora versus punctum cdiquod, tanquam ad centrum, undique trahuntur, impelluntur, vel utcumque tendunt. It is obvious that the qualifying term centripeta here includes the idea suggested by impressa, defining in fact the direction of the vis, and therefore implying that its origin is outside the body. After what has just been said, no farther comment need be added to show the absurdity of the terms accelerating force, innate force, impressed force, &c. All of these have arisen simply from mis- translation. Yis, by itself, is often used for force ; but vis accelera- trix, vis impressa, vis insita, and other phrases of the kind, must be taken as wholes ; and, in them, vis does not mean force. The absurdity of translating the word vis by force comes out still more clearly when we think of the term vis viva, or living force as it is sometimes called; a name for kinetic energy, which depends on the unit of length in a different way from force. It must be looked upon as one of the most extraordinary instances of Newton’s clear- ness of insight that, at a time when the very terminology of science was only as it were shaping itself, he laid down with such wonderful precision a system absolutely self-consistent. From the passages just quoted, taken in conjunction with the of Edinburgh, Session 1882-83. 11 second law of motion, we see that (as above stated) in Newton’s view — Force is whatever causes (but not, or tends to cause) a change in a body's state of rest or motion. Newton gives no sanction to the so-called statical ideas of force. Every force, in his view, produces its effect. The effects may be such as to balance or compensate one another ; but there is no balancing of forces. (Next comes a discussion as to the objectivity or subjectivity of force. . An abstract of this is given in §§ 288-296 of the article above referred to, and therefore need not be reproduced here.) But, just as there can be no doubt that force has no objective existence, so there can be no doubt that the introduction of this conception enabled Newton to put his Axiomata in their exceed- ingly simple form. And there would be, even now, no really valid objection to Newton’s system (with all its exquisite simplicity and convenience) could we only substitute for the words “ force ” and “ action,” &c., in the statement of his laws, words which (like rate or gradient, &c.) do not imply objectivity or causation in the idea expressed. It is not easy to see how such words could be intro- duced ; but assuredly they will be required if Newton’s system is to be maintained. The word stress might, even yet, be introduced for this purpose ; though, like force, it has come to be regarded as something objective. Were this possible, we might avoid the necessity for any very serious change in the form of Newton’s system. I intend, on another occasion, to consider this question. How complete Newton’s statement is, is most easily seen by con- sidering the so-called “ additions ” which have been made to it. The second and third laws, together with the scholium to the latter, expressly include the whole system of “ effective forces,” &c. for which D’Alembert even now receives in many quarters' such extraordinarily exaggerated credit. The “ reversed effective force ” on a particle revolving uniformly in a circle is nothing but an old friend — “ centrifugal force.” And even this phantom is still of use, in skilled hands, in forming the equations for certain cases of motion. The chief arguments for and against a modern modification of the laws of motion are therefore as follows — where we must remember that they refer exclusively to the elementary teaching of the subject, 12 Proceedings of Hie Royal Society and have no application to the case of those who have sufficient knowledge to enable them to avoid the possible dangers of l^ewton’s method : — I. For. Is it wise to teach a student by means of the conception of force, and then as it were to kick down the scaffolding by telling him there is no such thing ? II. Against. Is it wise to give up the use of a system, due to such an altogether exceptional genius as that of Newton, and which amply suffices for all practical purposes, merely because it owes part of its simplicity and compactness to the introduction of a concep- tion which, though strongly impressed on us by our muscular sense, corresponds to nothing objective! Everyone must answer these questions for himself, and his answer will probably be determined quite as much by his notions of the usefulness of the study of natural philosophy as by his own idio- syncrasies of thought. To some men physics is an abomination, to others it is something too trivial for the human intellect to waste its energies on. With these we do not reason. To others again all its principles are subjects of intuitive perception. They could have foreseen the nature of the physical world, and they know that it could not have been otherwise than they suppose it to be. Many minds find delight in the contemplation of the three kinds of lever ; others in the ingeniously disguised assumptions in Duchayla’s “ proof” of the parallelogram of forces ; some, perhaps, even in the wonderful pages of Vis Riertice Vida! _ The case of these men is only not more hopeless than that of the former classes because it is impossible that it could be so. But those who desire that their scientific code should be, as far as possible, representative of our real knowledge of objective things, would undoubtedly prefer to that of Newton a system in which there is ' not an attempt, however successful, to gain simplicity by the introduction of subjective impressions and the corresponding conceptions. In the present paper simplicity of principle, only, is nought for ; and the mathematical methods employed are those which appeared (independent altogether of the question of their fitness for a beginner) the shortest and most direct. A second part will be devoted to simplicity of method for elementary teaching. 13 of Ediiiburgh, Session 1882-83. (1) So far as our modern knowledge goes there are but two objective things in the physical world — matter and energy. Energy cannot exist except as associated with matter, and it can be per- ceived and measured by us only when it is being transferred, by a “ dynamical transaction,” from one portion of matter to another. In such transferences it is often transformed ” ; but no process has ever been devised or observed by which the quantity, either of matter or energy, has been altered. (2) Hence the true bases of our subject, so far as we yet know, are — 1. Conservation of matter. 2. Conservation of energy. 3. That property (those properties of matter, in virtue of which it is the necessary vehicle, or as the case may be, the store- house, of energy. (3) The third of these alone presents any difficulty. So long as energy is obviously kinetic, this property is merely our old friend inertia. But the mutual potential energy of two gravitating masses, two electrified bodies, two currents, or two magnets, is certainly associated (at least in part, and in some as yet unknown way) with matter, of a kind not yet subjected to chemical scrutiny, which occupies the region in which these masses, &c., are situated. And, even when the potential energy obviously depends on the strain of a portion of ordinary matter, as in compressed air, a bent spring, a deformed elastic solid, &c., we can, even now, only describe it as due to “ molecular action,” depending on mechanism of a kind as yet unknown to us, though, in some cases, at least partially guessed at. (4) The necessity for the explicit assumption of the third principle, and a hint at least of the limits within which it must be extended, appear when we consider the very simplest case of motion, viz., that of a lon,e particle moving in a region in which its potential energy is the same at every point. For the conservation of energy tells us merely that its speed is unaltered. We know, however, that this is only part of the truth : the velocity is constant. It will be seen later that this has most important dynamical consequences in various directions. (The remarkable discussion of this point by Clerk-Maxwell is then referred to, in which it is virtually shown that, were things other- 14 Proceedings of the Boy al Society wise, it would be possible for a human mind to have knowledge of absolute position and of absolute velocity.) (5) But Maxwell’s reasoning is easily seen to apply equally to any component of the velocity. Hence, when we come to the case in which the potential energy depends on the position, the only change in the particle’s motion at any instant is a change of the speed in the normal to the equipotential surface on which the particle is at that instant situated. The conservation of energy assigns the amount of this change, and thus the motion is com- pletely determined. In fact, if a? be perpendicular to the equi- potential surface, the equation -f 2/^ + — const, gives mx= - dY dx ’ Generally, in the more expressive for y and z are independent of x. language of quaternions, mp— - vy. In fact, this problem is precisely the same as was that of the motion of a luminous corpuscle in a non-homogeneous medium, the speed of passing through any point of the medium being assigned. (6) It is next shown that the above inertia-condition (that the velocity parallel to the equipotential surface is the same for two successive elements of the path) at once leads to a stationary ” value of the sum of the quantities vds for each two successive elements, and therefore for any finite arc, of the path. This is, for a single particle, the Principle of Least Action, which is thus seen to be a direct consequence of inertia. (It is then shown that the results above can be easily extended to a particle which has two degrees of freedom only.) But it is necessary to remember that, in these cases, we take a partial view of the circumstances ; for a lone particle cannot strictly be said to have potential energy, nor can we conceive of a constraint which does not depend upon matter other than that which is con- strained. Hence the true statement of such cases requires further investigation. (7) To pass to the case of a system of free particles we require 15 of Edinburgh, Session 1882-83. some quasi-kinematical preliminaries. These are summed up in the following self-evident proposition : — If with each particle of a system we asssciate two vectors, e.g., ©j, with the mass &c., we have ^m©$ = %{m) . where ® = ©o + ^, d> = d>o + <^, and . ©0 ^m = ^{m) . Q, so that ©0 and are the values of © and $ for the whole mass collected at its centre of inertia ; and 0, those of the separate particles relative to that centre. (8) Thus, if © = P = Pq -P p he the vector of d> = © = P = P^ -I- p, its velocity, we have ^mVV = S(m) . PqPq '%mpp the scalar of which is, in a differentiated form, a well-known pro- perty of the centre of inertia. The vector part shows that the sum of the moments of momentum about any axis is equal to that of the whole mass collected at its centre of inertia, together with those of the several particles about a parallel axis through the centre of inertia. If ©-$=P, we have SmP2 = :S(m).P2 + Smp2, ^.e., the kinetic energy, referred to any point, is equal to that of the mass collected at its centre of inertia, together with that of the separate particles relative to the centre of inertia. If we integrate this expression, multiplied by dt, between any limits, we obtain a similar theorem with regard to the action of the system. Such theorems may be multiplied indefinitely. (9) From those just given, however, if w^e take them along with 3 above, we see at once that, provided the particles of the system be all free, while the energy of each is purely kinetic and inde- pendent alike of the configuration of the system and of its position in space. IG Proceedings of the Royal Society 1. The centre of inertia has constant velocity. 2. The vector moment of momentum about it is constant. 3. So is that of the system relative to any uniformly moving point. 4. '%fmvds is obviously a minimum. (10) The result of (7) points to an independence between two parts of the motion of a system, z.e., that relative to the centre of inertia, and that of the whole mass supposed concentrated at the centre of inertia. Maxwell’s reasoning is applicable directly to the latter, if the system be self-contained, ^.e., if it do not receive energy from, or part with it to, external bodies. Hence we may extend the axiom 3 to the centre of inertia of any such self- contained system, and, as will presently be shown, also to the motion of the system relative to its centre of inertia. This, though not formally identical with Hewton’s Lex III., leads, as we shall see, to exactly the same consequences. (11) If, for a moment, we confine our attention to a free system consisting of two particles only, we have ^iPi + ^^2^2 = (% + ^2K or + = 0 (1) This must be consistent with the conservation of energy, which gives + m2P|)=/(T(/)i-p2)) ...... (2) since the potential energy must depend (so far as position goes) on the distance between the particles only. Comparing (l) and (2) we see that we may treat (2) by partial differentiation, so far as the coordinates of and are separately concerned. For we thus obtain m^pi = Vpi “ P2) ^2/^2 ~ Vp2 • f~ ~f •^(Pi ~ ^2)* Each of these, again, is separately consistent with the equation in § (5) for a lone particle. Hence, again, the integral f{m^fis^ + m^v^dsc^ has a stationary value. Hence also, whatever be the origin, provided its velocity be constant, 'XmY pp = 0. of Edinburgh, Session 1882-83. 17 Thus, even when there is a transformation of the energy of the system, the results of § 9 still hold good. And it is to be observed that if one of the masses, sa}'' m.j,, is enormously greater than the other, the equation '^\9\ + '^2/^2 ^ shows that is excessively small, and the visible change of motion is confined to the smaller mass. Carrying this to the limit, we have the case of motion about a (so-called) “ fixed centre.” In such a case it is clear that though the momenta of the two masses relative to their centre of inertia are equal and opposite, the kinetic energy of the greater mass vanishes in comparison with that of the smaller. These results are then extended to any self-contained system of free particles, and the principle of Varying Action follows at once. It is thus seen to be a general expression of the three propositions of § 2 above. (12) So far as we have yet gone, nothing has been said as to how the mutual potential energy of two particles depends on their distance apart. If we suppose it to be enormously increased by a very small increase of distance, w^-. have; practically the case of two particles connected by an inextensible string — as a chain-shot. But from this point of view such cases, like those of connection by an extensible string, fall under the previous categories. The case of impact of two particles falls under the same rules, so far as motion of the centre of inertia, and moment of momentum about that centre, are concerned. The conservation of energy, in such cases, requires the consideration of the energy spent in perma- nently disfiguring the impinging bodies, setting them into internal vibration, or heating them. But the first and third of these, at least, are beyond the scope of abstract dynamics. (13) The same may be said of constraint by a curve or surface, and of loss of energy by friction or resistance of a medium. Thus a constraining curve or surface must be looked upon (like all physical bodies) as deformable, but, if necessary, such that a very small deformation corresponds to a very great expenditure of energy. (14) To deal with communications of energy from bodies outside the system, ah we need do is to include them in the system. Treat as before the whole system thus increased, and then consider only VOL. XIL B 18 Proceedings of the Royal Society' the motion of the original parts of the system. This method applies with perfect generality whether the external masses he themselves free, constrained, or resisted. (15) Another method of applying the same principles is then given. Starting from the definition dA = '^mSpdp, the kinematical properties of A are developed. Then, by the help of § 2, these are exhibited in their physical translations. (16) The. paper concludes with a brief comparison of the funda- mental principles of the science as they have been introduced by hfewton, Lagrange, Hamilton, Peirce, Kirchhoff, and Clerk-Maxwell, respectively ; and also as they appear in the unique Vortex-system of Thomson. 2. On Illegitimacy in Scotland. By Mr Geo. Seton, M.A. Oxon. In the year 1860, at the meeting of the Social Science Association in Glasgow, I read a paper on “The Causes of Illegitimacy in Scot- land,’’ which was published shortly afterwards; and eleven years later (1871), at the meeting of the British Association in Edinburgh, I read another paper on “ The Illegitimacy of Banffshire,” which was privately printed. On the present occasion I intend to confine my ob- servations to the facts exhibited by the Eegistrar-General’s returns. Eor a good many years a perceptible improvement has been going on in England in the matter of illegitimacy ; and I am glad to be able to add that in Scotland also we have evidence of a gradual, and nearly as satisfactory, diminution in the number of illegitimate births. During the two decades, ending 1870 and 1880 respectively, the decrease in England was rather more, and in Scotland rather less, than 1 per cent. Percentage of Illegitimacy. 1861-70. 1871-80. Decrease. England 6-1 5-0 11 Scotland, .... 9-7 8-8 0-9 From the Forty-second Annual Report of the English Registrar- 19 of Edi7ibu7''gli, Session 1882-83. General it appears that, during the thirty -four years ending 1 87 9, the proportion of illegitimate children to every 100 births gradually fell from 6 '7 to 4*7 per cent., or exactly 2 per cent., as shown in the* following table : — ENGLAND. Children Born, ori’ of Wedrock to 100 Births. 1846-50, . ., , . . . . . 6-7 1851-55, . . 6-6 1856-60, 6*5 1861-65, ..... , . . 6-4 1866-70, > 5-8 1871-75, ........ 5-2 1876-^79, ........ 4-7 As in Scotland, the rates have always greatly varied in different counties. While the average for the whole of England during the ten years ending 1879 was 5*1 per cent., that for Cumberland was as high as 8*9 — little more, however, than half the percentage for Banff- shire, and only a fraction above the average for Scotland, In the extra-metropolitan portion of Middlesex the percentage was as low as 3 ’6. With regard to illegitimacy, England may be roughly divided into three zones. : — (1) a southern zone witli the rate below the average;, (2) a midland zone with the rate somewhat above the average ; and (3) a northern zone with an excessively high rate. Perhaps, therefore, our English neighbours will feel disposed to suggest that the proximity of the northern counties to Scotland may have something to do with their high rate of illegitimacy.* Both the English and Scottish returns show that in the great centres of population the percentage of illegitimacy is much smaller than in the rural districts. It must, however, be constantly borne in mind that a comparison of the numbers of illegitimate births in town and * It has been frequently alleged that under thq Scottish system of registra- tion the illegitimate births are more accurately recorded than in England ; and that if the respective returns were equally trustworthy, the difference in the ratio of illegitimacy on the two sides of the Tweed would not be so great as it has hitherto appeared. I am disposed to think that there is some truth in the. assertion. Roughly speaking, the percentage of illegitimacy in England and Scotland, as indicated by the returns, is at present about 5 and 9 respec- tively. Probably 7 and 9 per cent, is nearer the actual fact. The object of this paper, however, is not to compare the two countries, but to show the vast differences in the percentage of illegitimacy which present themselves in the various counties of Scotland. 20 Proceedings of the Royal Society country districts respectively is not in itself sufficient to afford any indication of the true state of morality. Every statist is aware that the unrestrained passions which in rural districts result in illegitimate births are in large towns diverted into the channel of barren prosti- tution. The English Eegistrar-General remarks that, “ it is probable that a considerable portion of illegitimate children are the offspring of country girls who have gone into domestic service in towns, and have there been seduced ; and such girls will often return to the country for their confinement, and thus increase the country rate of illegitimacy by the addition of births which from their origin should duly be reckoned as belonging to the towns.” On the other hand, however, it is quite as likely that a good many mothers of illegitimate children conceived in rural districts resort to private lodgings or maternity hospitals in large towns for the purpose of being confined. In Scotland, during the two decades ending 1870 and 1880 respectively, there had been a diminution in the rate of illegitimacy to the extent of nearly 1 per cent., viz., 8 ‘8 instead of 9 *7. If a wavy line be drawn from Portskerry, about twelve miles west of Thurso, to ForhGeorge, and thencOj l)y the eastern boundaries of Inverness, Argyll, Stirling, Lanark, and Ayr, to the mouth of Loch Ryan, it will be found that all the counties to the west of the line present a percentage of illegitimacy below the ratio for the whole of Scotland while two-thirds of the counties to the east of the line present a per- centage above that ratio — the majority of the others yielding a percentage closely bordering on the national rate. There were thus ten counties on the west of the line in question below the national ratio ; while of the twenty-one counties on the east of the line, fourteen ranged from 9*0 (hTairn) to 16’6 (Banff), and the remain- ing seven from 7 ’3 (Fife) to 8*7 (Selkirk). One of these seven (Edinburgh) contains a large city, while three others (Fife, Clack- mannan, and Selkirk) embrace towns of considerable size, thereby probably accounting, by the barren prostitution of large centres, for the comparatively siuall number of illegitimate births. The insular counties (Orkney and Shetland) were . considerably below the national average — having respectively 6’0 and 4*8 per cent. In 1881 the population of the Western area amounted to 1,859,000, and of the Eastern area to 1,814,000 — a difference of 21 of Edinburgh, Session 1882-83. only 45,000. By far the larger portion of the Western area is oc- cupied by an almost purely Celtic population ; while the inhabitants of the Eastern area, with the exception of the county of Perth, are chiefly Scandinavian or Teutonic. In three of the eleven counties constituting the northern division of Scotland, — viz., Nairn, Aberdeen, and Kincardine, — and in all the counties south of Banffshire, with the exception of four, — amounting in all to twenty, — the decrease in the rate of illegitimacy ranged from 0’5 per cent, in the case of Roxburgh, to 1*9 per cent, in the case of Clackmannan. On the other hand, in eight of the eleven northern counties, and also in Argyll, Linlithgow, Dumfries, and Kirkcudbright — in all twelve counties — there had been an increase in the rate, ranging from OT per cent, in Ross and Cromarty, and Dumfries, to no less than 2 '2 per cent, in Caithness. In both decades Banffshire retained the discreditable distinction of being at the top of the list, showing the slight increase of 0*4 per cent. (16*6 instead of 16 ’2) — in other words, one illegitimate child in every six births, or nearly double the percentage for the whole of Scotland. One county (Wigtown) was stationary at 16T per cent. The two blackest spots have always been three adjoining counties in the north (Elgin, Banff, and Aberdeen), and three adjoining southern counties (Wigtown, Kirkcudbright, and Dumfries), the collective per- centage of the two groups being almost identical. In the case of rather more than one-fourth of the whole illegiti- mate births the paternity was acknowledged at registration ; in a good many instances the paternity was subsequently found by decree of court and recorded in terms of the statute ; while about 3 per cent, of the children were legitimated by the subsequent marriage of their parents.* * During the four years ending 1861, of the 7517 births registered in Banff- shire, 1189 were illegitimate. In the case of 389 of these children— or nearly a third of the whole — the paternity was acknowledged at registration • in 64 instances the paternity was subsequently found by decree of court and recorded in terms of the statute ; and in 28 cases the children were legitimated per subsequens matrijnoriium, such alteration of statu being also duly registered. In a few instances the judicial findings relate to children whose paternity was acknowledged at registration, from which it would appear that, notwithstanding the reputed father’s adhibition of his signature to the register, the mother is occasionally induced to raise an action against him. Of course the paternity of some more of the “fatherless” 22 Proceedings of the Boyal Society ^PERCENTAGE OF ILLEGITIMACY IN SCOTLAND AND ITS COUNTIES. 1861-70. 1871-80. Increase or Decrease. SCOTLAND, . . . 0 9-7 8*8 -0*9 COUNTIES. Northern, Sh!etlan(J, .... 4-2 4-8 + 0*6 Orkney, .... . 5-b 6*0 + 1*0 Caithness^ 8-7 10-9 + 2*2 Sutherland, 6 '8 6*9 + 1*1 North-Western. Ross and Cromarty, . 4'5 4^6 +0*1 Inverness, . , • ' ^ 8-0 8-3 + 0-3 North-Eastern. Nairn, .... 10-7 9-0 -1*7 Elgin, .... 14-0 15U + 1*7 Banff, ..... 16*2 16-6 + 0-4 Aberdeen, . 15-2 14-3 -0*9 Kincardine, • 14*4 13-3 -1*1 East Midland.. Forfar, 11-9 10*5 -1*4 Perth, . . . 11-0 9*8 -1-2 Fife, .... 8-1 7-3 -0*8 Kinross, . . . , 11 -.2 10-3 , -0*9 Clackmannan, . , * 9-9 8-0 -1*9 West Midland. Stirling, . ‘ . 8-4 7*0 -1*4 Dumbairton, 7-4 5*8 -1-6 Argyll, .... 7-3 7*8 + 0-5 Bute, . . ... - • 8-0 7*4 -0*6 South-Western. Renfrew, . ■7 -4 6-2 -1*2 Ayr, .... 9-1 8-0 -1*1 Lanark, .... 8-4 7*3 -1*1 South-Eastern. Linlithgow, 7*9 8*3 + 0*4 . Edinburgh, 9-1 7-8 --1*3 Haddington, 9-5 8*2 -1*3 Bermck, .... 10-9 10*3 -0-6 Peebles, .... 9*9 8*5 -1*4 Selkirlc, .... 9-3 87- -0-6 Southern. Roxburgh, 11-5 ll'O -0*5 Dumfries, 14-9 15-0 + 0*1 Kirkcudbright, 15-0 15*2 + 0-2 Wigtov/n, • 16-1 16-1 0-0 of Edinbiirgh, Session 1882-83. 23 In Ms report relative to the year 1880, Mr Daniel Stewart, the intelligent examiner of registers in the southern district of Scotland, gives some very startling information regarding the illegitimacy of the counties of Eoxhurgh, Dumfries, Kirkcudbright, and Wig- town. In no fewer than 33 parishes in these four counties, the ille- gitimate births amounted to 20 per cent, and upwards — a certain small parish in Eoxburghshire exhibiting the enormous ratio of 36 ’3 per cent. ! He refers to the large number of cases in which sisters give birth to illegitimate children, and to the numerous instances of the same woman being the mother of several children. Thus, in each of twelve specified parishes, two sisters registered illegitimate births during 1880. These 24 women had given birth to 41 chil- dren. In the case of twelve of them it was the first child, while the remaining twelve had collectively produced 29 children. In each of three parishes in three of the counties in question, three sisters have had nine children among them, while a trio in a certain Berwickshire parish have had at least ten. In nine parishes, mothers recorded their fifth, and in five parishes, their sixth child ; most of them being either domestic servants or engaged in some kind of agricultural labour. In two cases, in the counties of Kirkcudbright and Selkirk respectively, a charwoman and a dressmaker each recorded their seventh child. To only a small extent is the illegitimacy of the counties in question to be accounted for by the prevalence of concubinage. The result of Mr Stewart’s inquiries seems to point irresistibly to a wide-spread low moral tone among domestic and farm servants in rural parishes,” and mainty to that cause he is disposed to attribute the large proportion of illegitimate births constantly occurring in the southern counties. Many registrars have told him that “ language of the most immoral kind is quite common among out-workers and other women engaged in farm work; and when they have once fallen they appear to lose all sense of shame and self-respect,” Note. — Mr Stewart’s report for 1881 (which has been received since this paper was written) furnishes further evidence of the pre- majority may yet be judicially established, and other cases of legitimation by the subsequent marriage of the parents may also take place ; but no very material addition is likely to he made to the figures specified. 24 Proceedings of the Royal Soeiety valence of illegitimacy, especially in the four counties already referred to. The following table exhibits some very startling facts : — S0UTHEE,N DiSTRICT — 1881. Number of Per- centag^eof Ulegiti- mutes. Number of Child of Mother. Total Number Total Number County. lilegiti- mate Births, ; 2Eid. SiU. •Mu 5th. iSth. 7th. StK. 9th, 10th. of Women Confined before. of Children among them. Eoxburgh, 170 10*4 11 9 4 1 1 ... ... ... ... 25 71 Dumfries, 349 14*8 28 11 1 ‘ 5 I ... 1 ... 47 132 Kirk cud- ) bright, I 157 12;-4 9 6 2 ' ... 1 2 ... ... ... 20 64 WigtoAvn, 18^ 15*3 9 10 2 2 1 ... 1 1 26 90 858 ... 57 36 9 7 4 2 2 ... 1 118 357 In a small Dumfriesshire palish a domestic servant, who recorded her third (or fourth) illegitimate child, has three sisters, each of whom has given birth to tliree bastard children — “ who make a trade of the offence ” (ia the Vv^ords of the local registrar), as they after- wards go out as nurses.” In another parish in the same county, the percentage of ill^itimacy had i^ached the alarming ratio of 40 ‘7 per cent! In the county of Wigtown there was not a single parish without illegitiniate births, and only in two parishes was the rate below the national average. In the other 15 parishes, the per- centage ranges from 9*6 to 244. Numerous instances of hereditary illegitimacy occur in the southern counties — many women (them- selves iilt^itimate) and their daughters recording bastards in the same register. 3. Oa the Absorption of Low Rudiant Heat by Graseous Bodies. By Professor MacGiegor. The following pages contain an account of experiments made by myself and Mr T. Lind^y, at the request of Piofessor Tait, to determine the absorption of damp air containing a known quantity of water vapour, by findkig in what proportions dry air and olefiant gas must be mixed in order that the absorption of the mixture may be the .same as that of the damp air. The experiments were made of Edinhurgh, Session 1882-83. 25 according to the method described by Professor Tait in a letter read by Sir William Thomson at the Southampton meeting of the British Association (see Nature, vol. xxvi. p. 639, 1882). They consist of two series — the first, a series of rough experiments made, first, to determine whether or not the method would work, and, secondly, to find the dimensions of the apparatus which would give the best result ; the second, a series of more careful experiments made when the method was found to give satisfactory results. 26 Proceedings of the Royal Society The apparatus which we used for the preliminary experiments is shown in diagrammatic section in the figure. It consisted of a cylin- drical gas reservoir (A, A) of tinned iron, about 4 feet in length and 4 '5 inches in diameter. This reservoir may be • called the absorber. It was placed with its axis vertical. It had three openings B, C, D, of which the two (B and C) were fitted with metal tubes and stopcocks, and were used for filling the reservoir with the gas under investigation, and the third (D) was fitted with a metal tube holding the manometer E. The curved surface and the bottom of the absorber were surrounded by another cylindrical vessel F, F, also of tinned iron, whose sides were everywhere about 0-5 inch from the sides of the absorber. This outer casing had two openings (G, H) fitted With tubes and stopcocks, the one at the bottom, the other at the top. By their means the space between A and F could be kept full of running water. On the upper end of the absorber was a flat cylindrical box (K) about 1 inch in depth. The upper end of the cylinder formed the bottom of the box. This box, which may be called the radiator, was also provided with two stopcocks and tubes L, M, placed as in the diagram, by means of which it could be filled with either water or steam. For this purpose an india-rubber tube from M dipped under water in a sink, while B could be put in communication by means of a three-way tube with either a boiler or the water supply. The absorber was thus completely surrounded by a jacket divided into two compartments, one of which was the radiator. The manometer E consisted of a bent tube of about 1“”" bore. It was provided with a stopcock N, was fitted in the tube D by means of an india- rubber stopper, and contained dilute sulphuric acid of known density. The levels of the liquid were read off by the aid of a card, with a divided scale, which was attached to the tube. The following is a description of 'our mode of observation. The absorber was first filled with the gas under investigation. Thus, to fill with dry air, B was attached to a series of drying tubes (sulphuric acid and chloride of calcium) and C to the suction pump, and a current was kept up until the dry air had displaced the damp air which at first filled A. To fill with moist air, the drying tubes were replaced by wetting tubes. To fill with olefiant gas, C was left open, and the gas driven in from the generator at B until the of Ediiiburgh, Session 1882-83. 27 air initially filling A had been displaced. Meantime water had been kept running through both compartments of the jacket. The water from the laboratory reservoir was found to be practically invariable in temperature during the course of any one experiment. When the absorber had been filled, and the water had been running through the jacket for some time, the stopcocks B and C were closed and D opened. The water was then kept running through the jacket until the gas in the absorber had attained a practically constant temperature, until the liquid in the manometer therefore indicated a practically constant pressure, The barometer and manometer were then read, and the temperature of the water jacket noted. Then L was put in communication with the boiler, and the water in the radiator was displaced by steam, after which the variation of the manometer with time was noted until it had again reached a constant state, when the barometer was again read. If the readings of the barometer before and after any set of observa- tions were not the same, it was supposed to have varied uniformly with time in calculating pressures. In all cases the difference was very slight, the sets of observations lasting only from 20 to 30 minutes. From the readings of the barometer and manometer the j^ressures were easily calculated. No precautions were taken specially to exclude dust, so that, when water was present in the gas operated on, it was not necessarily all in the state of vapour. The following are details of some of the experiments made. The unit employed in the measurement of pressure is that due to a millimetre of the dilute acid solution used in the manometer. Its density was 1T038. Zero of time is the moment at which com- munication was broken between the radiator K and the water supply, and established between the radiator and the boiler. Shortly after that the upper end of the absorber begins to rise in temperature, and the pressure of the gas contained in it to increase. When the steam issues freely from the radiator, it may be supposed to have very nearly reached a constant temperature. I. Dry Air. — Air had been drawn from the drying tubes through the absorber for 2 hours. The following table shows the pressures after given intervals of time : — 28 Proceedings of the Boyal Society Time. Pressure. Time. Pressure. m. s. m. s. 0 0 9316-9 4 15 9344-7 0 20 9319-7 5 30 9346-7 0 30 9325-7 6 20 9347-7 0 37 9335-7 7 30 9348-7 0 j Steam issuing 9 33 9350-7 \J freely. 10 52 9351-7 0 56 9337-7 12 32 9352-7 1 17 9339-7 13 47 9353-9 1 43 9340-7 15 17 9354-7 2 15 9341-7 18 17 9356-7 3 0 9342-7 20 52 9357-7 3 45 9343-7 II. Damp Air.- —Air had been drawn through the absorber for 15 minutes, after having passed through a Woulfe’s bottle of water. Time. Pressure. Time. Pressure. m. s. m. s. 0 0 9311-2 1 8 9331-7 0 15 9311-7 1 55 9332-2 0 20 9319-7 - 3 6 9332-7 0 26 9325-7 5 10 9334-7 0 31 9330-7 6 0 9335-7 0 37 J Steam issuing 9 15 9337-7 ( freely. 10 30 9338-7 0 54 9331-2 14 5 9340-7 III. Damp Air.—T\iQ air had for 2 hours been drawn through the absorber, after passing through a Woulfe’s bottle containing water. Time. Pressure. Time. Pressure. m. s. m. s. 0 0 9314-6 0 45 9336-6 0 15 9316-6 1 15 9336-6 0 22 9328-6 2 25 9336-6 0 27 9333-6 3 55 9337-1 0 35 9335-6 4 25 9337-6 0 36 ( Steam issuing 5 25 9338-1 ( freely. 12 0 9338-1 29 of EdinhurgTiy Session 1882-83. IV. Damp Air. — The same air as in No. III. Time. Pressure. Time. Pressure. m. S; m. s. 0 0 9314-1 2 30 9333-6 0 2T 9323-6 3 45 9334-1 0 32 93,28-6 4 20 9334-6 0 40 93,3.2-6 5 30 9335-6 0 41 ( Steam issuing 7 45 9337-1 \ freely* 8 45 9337-6 1 6 9333-1 13 45 9338-1 1 35 9333-5 15 0 9338-1 V. Dry Air. — The a,ir had he^n drawn through the absorber and drying tubes for hours. Time. Pressure. Time. Pressure. m. s. m. s. 0 0 9334-9 2 0 9356-4 0 24 9336-4 2 15 9357-4 0 32 9338-4 2 35 9358-4 0 40 9341-4 3 25 9359-4 0 45 9343-4 4 45 9362-4 0 50 9346-4 5 15 9363-4 0 57 9348-4 6 20 9364-4 1 5 9351^4 7 45 9368-4 1 6 i ' Steam issuing 9 35 9370-4 1 freely. h 12 9372-4 1 20 9354-4 12 54 9373-4 1 30 9355-4 16 0 9375-4 VI. Dry Air. — The same ait as in No.' V. Time. Pressure. Time. Pressure. m. s. m. s. 0 0 9326-4 2 30 9350-4 0 20 9336-4 3 0 9351-4 0 25 9342-4 3 25 9352-4 0 30 9346-4 3 45 9353-4 0 36 9348-4 ; 5 0 9356-4 0 36 * f Steam issuing 5 ’25 9357-4 1 freely. 6 20 9358-4 0 46 9349-4 8 40 9362-4 1 5 29349-6 12 15 9364-4 30 Proceedings of the Royal Society VII. Dry Air. — Air was again drawn througb. the drying tubes and absorber for one hour. Time. Pressure. Time. Pressure. m. s. m. s. 0 0 9334-9 1 4 9358-9 0 18 9343-4 1 46 9359-4 0 23 9348-4 2 20 9361-4 0 28 9353-4 3 25 9363-4 0 34 9356-4 4 45 9367-4 0 34 1 Steam issuing 6 30 9372-4 i freely. ■ 8 20 9375-4 0 43 9358T YIIL Damp Air. — The air was drawn through the wetting tubes and the absorber for 2*75 hours. Time. Pressure. Time. Pressure. m. s. ni). s. ■ 0 0 9333-8 3 •0 9354-8 0 20 9343-8 4 15 9356-8 0 29 9350-8 5 10 9357-8 0 34 9351-8 ■ 5 55 9358-8 0 34 ^ C Steam issuing 7 55 9361-3 [ freely. 8 35 9361-8 0 45 9352-6 11 0 9362-8 1 28 9353-3 13 25 9363-8 2 25 9353-8 19 0 9364-8 IX. Damp Air. — The same airi as in No. VIII. Time. Pressure. Time. Pressure. m. s. m. s. 0 0 9323-4 2 5 9342-7 0 9 9323-9 2 50 9342-9 0 18 9325-9 3 35 9343-9 0 23 9329-9 4 25 9345-9 0 2‘9 93.35-9 6 40 9349-9 0 35 9339-9 7 13 9350-9 0 40 9341-9 9 20 9351-9 0 40 j f Steam issuing 10 40 9351-9 freely. 13 0 9351-9 0 56 9342-7 of Edinburgh, Session ' 31 X. Olefiant Gas. — The absorber was now carefully dried, dry air being drawn through it, while steam was driven through both com- partments of the jackets. Then the jacket was filled with water, and the air in the reservoir displaced by dry olefiant gas, made according to the method recommended by Eoscoe and Schorlemmer in their Treatise on Chemistry. The ofefiant gas was driven through drying apparatus into the absorber, the tube C being open to the atmosphere, until the gas issuing from C burned with a white flame. Time. Pressure. Time'. Pressure. m. s. m. s. 0 0 9232-3 1 30 9255-3 0 18 9233-3 1 45, 9256-3 0 24 9236-3, 2 4 9257-3 0 28 9241-3 2 22 9258-3 0 33 9245-3 2 50 9259-3 0 38 9248-3 a 50 9261-3 0 44 9250-3 4 45 9264-3 A A A J Steam issuing 45 9266-3 u 4:4: < freely. 8 0 9271-3 0 50 9251-3 10 0 9274-3 1 0 9252-3 13 7 9277-3 1 10 9253-3 17 0 9277-3 . 1 18 9254-3 XI. Dry Air. — The olefiant gas was next displaced by dry air. Time. Pressure. Time. Pressure. m. s. m. s. 0 0 9087-9 3 3S 9120-3 0 10 9088-8 4 56 9124-6 0 15 9093-8 6: 45 9130-4 0 20-5 909:9-0 8 23 9139-0 0 27 9105/0 10 Q, 9143-6 0 36 9107-2 11 54 9150-6 0 48-5 9108-3 14 41 9158-4 0 49 Steam issuing 16 34 9165-4 freely. 20 10 9,174-a 1 0 9110-1 23 0 9181-7 1 11 9110-8 26 15 9190-0 1 25 . 91120 29 53 9197-6 1 57 '9114.-0 . 3,4 53 9202 •6_ 2 40 9117-3 35 40 9209-2^ 32 Proceedings of the Royal Society XII. Dry Air^ containing a small quantity of Olefiant Gas. — A very small quantity of dry olefiant gas was driven into the absorber which contained the dry air already used for Experiment XI. Time. Pressure. Time. Pressure. m. s. m. s. 0 0 9256*6 0 53 9274*1 0 8 9257*6 1 5 9274*6 0 15 9258*6 1 51 9275*6 0 20 9259-6 3 44 9276*6 0 24 9261*6 5 45 9278*6 0 29 9266*6 6 32 9279-6 0 34 9268*6 7 54 9281-8 0 40 9272*6 8 51 9282-6 0 41 ( Steam issuing 10 37 9284*6 i freely. 17 46 9286*6 0 44 9273*6 23 18 9288*6 If the above experiments be represented by curves, with intervals of time as abscissae and increments of pressure as ordinates, it will be seen (1) that the curves have all, except in the case of Experi- ment XL, the same general form ; (2) that the curves for dry air tend, after different intervals of time, to the same value of ordinate, except in the curiously anomalous case of Experiment XI. ; (3) that the curves for air containing different quantities of water vapour occupy in all cases a lower position on the diagram than those for dry air ; (4) that the curve for olefiant gas is above that for dry air ; and (5) that the curve for dry air, containing a small quantity of olefiant gas, is in the same region of the diagram as those for moist air. We thought it worth while, therefore, to try to find how much olefiant gas must be added to dry air to give a curve coinciding with that of air containing a known quantity of vapour. It seemed advisable, however, to increase the radiating surface relatively to the surface of the absorber. The apparatus which we used for subsequent experiments therefore differed from that already described in two respects. The diameter of the cylindrical absorber was 18 inches, and the plate separating the radiator K from the absorber A was of copper, and in. thick. It was made thick to prevent, as much as possible, its giving way under the pressure to which it was subjected, when the radiator was in com- of Edinhurgli, Session 1882-83. 33 mimication with the boiler or the water supply. It was made of copper, that its conductivity might be as great as possible. The curved sides and bottom of the absorber were made as before of the stoutest commercial tinned iron. We thought it unnecessary to have it made more rigid, as the pressure of the water in the jacket was constant during each experiment. The copper plate bent under the pressure of the water and the steam, however, more than we anti- cipated, and the differences in the amount of the bending caused perceptible changes of form in the sides. The pressures given below are subject therefore to sudden slight variations, which depend upon sudden changes of volume of the absorber, not upon absorption. Hence the numbers given below cannot be taken as exact results. It will be noticed in the experiments made with this apparatus, that after the steam is turned on in the radiator, previously filled with running water, the pressure at first diminishes, and only after a certain time increases. This is not due to absorption, but to the fact that the water pressure in the laboratory was slightly greater than the boiler pressure which we used. When, therefore, the water pressure was taken off the sides of the radiator K, and the steam pressure was put on, the copper plate became less bent, and the reservoir therefore became suddenly larger, the pressure conse- quently falling. As might be expected, in the case of an apparatus not sufficiently rigid, the first experiments made with it were much more unsatisfactory than the last. The apparatus took gradually the set determined by the pressures employed. If the measurements, given in the tables below are plotted, the resulting curves will be found far smoother in the case of the later than in that of the earlier experiments. Tor more exact experiments a more rigid apparatus should be employed. Tor the following experiments a new manometer was used. It was made from a carefully selected tube of practically uniform bore. The mode of procedure in the experiments with the new reservoir was practically the same as that described above. Tests were applied more frequently to find if the reservoir was air-tight, and to find if the' drying tubes were efficient. Their efficiency was tested by weighing at intervals the last of the series. XIII. Air saturated with Water Vapour at 13° ‘2 C. — The absorber being full of air, a small quantity of water was introduced VOL. XII. c 34 Proceedings of the Royal Society by the opening D, and poured over the bottom. then left standing for an hour, the jackets was 13°*2 C. Time. Pressure. m. s. 0 0 9023-8 0 27 9019-8 0 45 9018-8 1 13 9018-8 1 20 9019-8 1 36 9020-3 1 45 9020-8 2 4 9021-8 2 26 9022-8 2 46 9023-8 3 0 9024-8 3 15 9025-8 3 35 9027-8 3 37 9028-8 3 51 9029-8 4 7 9031-8 4 25 9033-8 4 36 9034-8 4 55 9036-8 5 5 9038-8 5 15 9039-8 5 53 9044-8 6 40 9049-8 6 55 9051-8 the water jacket was 13° C. Time. Pressure. m. s. 0 0 9017-8 0 12 9016-8 0 20 9014-8 1 25 9015-8 The absorber was The temperature of the water in Time. Pressure. m. 7 s. 24 9054-8 7.. 42 9056-8 8 30 9059-8 9 5 9062-8 9 40 9064-8 10 35 9067-9 11 5 9074-9 11 40 .9076-9 12 23 9080-9 13 2 9089-9 14 20 9094-9 15 20 9099-9 16 ^ ( Steam issuii 1 freely. 17 20 9109-9 18 18 9111-9 19 10 9112-9 19 30 9113-9 20 36 9114-2 21 6 9124-0 21 38 9125-0 22 30 9125-0 23 50 9125-0 25 25 9126-0 at 13° C. — The water Temperature of Time. Pressure. m. 1 s. 37 9017-8 2 0 9018-8 2 17 9019-8 2 35 9020-8 XIV. Air saturated with Water .Vapour and air in the absorber as in Experiment XIII. of Edinburgh, Session 1882-83. 35 Time. Pressure. Time. Pressure. m. s. . m. s. 3 .2 ■ 9022-8 10 0 9067-8 3 20 9024-8 11 1 . 9072-8 3 41 9027-8 11 42 ■ *■ 9077-8 4 8 9030-8 12 15 9082-8 4 24 9032-8 13 0 9097*8 4 40 • 9034-8 13 35 9100-8 5 16 9038-8 14 10 9102-8' 6 . 6 9044-8 14 50 ■ r Steam issuing 6 27 9047-8 1 freely. 6 50 9050-8 15 20 9107-8 7 5 9052-8 16 10 9109-8 7 28 9055-8 16 55 9112-8 7 55 9057*8 19 40 9122,-8 8 50 9062-8 21 16 9123-8 9 15 9064-8 22 50 9124*8 XY. Di-y Air. — The absorber was dried by keeping both compart- ments of tbe jacket full of steam, and drawing dry air tbrougb tbe absorber until a U-tube of carefully dried calcium chloride placed between C and the suction-pump showed no change of weight in the course of an hour. Both compartments of the jacket were then kept full of running water, of temperature 12° *2 C., until the pressure of the air in the absorber had become constant, when as usual the radiator was put in communication with the boiler. Time. Pressure. Time. Pressure. m. s. m. s. 0 0 9088-3 7 0 9117*3 0 19 9087-3 7 50 9122*3 0 28 9086-3 8 7 9127*3 0 45 9085-3 8 50 . 9133*2 1 10 9086*3 9 15 ( Steam issuing 1 22 9087*3 ( freely. 1 47 9088-3 9 25 9137-3 2 25 9090-3 10 0 9142-3 2 53 9092-3 11 5 9147-3 3 40 9095-3 16 . 0 9148-3 4 0 9097*3 18 15 9151*3 5 0 9102*3 23 0 9152*3 5 45 9107-3 24 5'5 9154*3 6 30 9112-3 28 0 9154*3 7 0 9115-3 36 Proceedings of the Royal Society XYI. Dry Air. — The same air as in the last experiment, both compartments of the jacket having been again filled with water until the pressure had become constant. Time. Pressure. Time. Pressure. m. s. m. s. 0 0 . 9085-3 5 30 9107-3 0 14 9084-3 . 6 20 9113-3 0 20 9083-3 6 47 9117-3 0 26 9082-3 ' 7 25 9122-3 0 36 9081-3 8 0 9127-3 0 53 9080-3 8 0 r Steam issuing 1 5 9081-3 i freely. 1 14 9082-3 8 31 9132-3 1 40 9084-3 9 ■ 16 9137-3 1 55 9085-3 11 10 9140-3 2 9 9087-3 13 2 9141-3 2 50 9092-3 15 50 9142-3 3 37 9097-3 21 35 9142-5 4 35 9102-3 • 24 0 9142-5 XYIL Mixture of Air and Olefiant Gas, containing 1*1 yer cent, hy volume of Olefiant (ras.— The absorber being full of the dry air of last experiment, both compartments of the jacket were filled with running water of temperature 12° G. When the pressure had be- come constant, and had the value 9154T, dry olefiant gas was driven into the absorber at B (C being kept closed) until the pressure had risen to 9256 ’S. Of the gas which the absorber contained, therefore 1 T per cent, by volume was olefiant gas. The olefiant gas was prepared in the same manner as before, from rectified spirit and pure sulphuric acid. Time. Pressure. Time. Pressure, m. s. 0 0 9173-8 m. s. 1 25 9174-3 0 11 9173-2 1 38 9176-3 0 24 9172-2 1 47 9178-3 0 30 9171-2 2 4 9181-3 0 45 9170-2 2 21 9184-3 0 55 9171-2 2 30 9186-3 1 7 9172-2 2 38 9189-4 of Edinburgh, Session 1882-83. 37 Time. Pressure. Time. Pressure. m. s. ni. s. •2 47 9191-4 6 30 9251-8 3 2 9194-4 6 50 9256-8 3 10 9196-4 7 0 ( Steam issuing 3 19 9198-4 1 ( freely. 2 35 9201-4 7 20 9266-9 4 10 9206-4 7 33 9271-9 4 30 9211-5 7 45 9276-9 4 53 9216-5 8 10 9282-0 5 0 9221-6 8 23 9287-0 5 13 9226-6 9 5 9292-0 5 29 9231-6 10 12 9297-1 5 45 9236-6 11 40 9298-1 6 5 9241-7 13 12 9299-1 6 17 9246-7 XVIII. Mixture of Air and Olefiant Gas, containing 1 *1 per cent, by volume of Olefiant Gas. — The absorber contained the same gas as before. Both compartments of the jacket had again been kept filled with running water at 12° C. until the pressure had become con- stant. Time. Pressure. Time. Pressure. m. s. m. s. 0 0 9102-8 6 18 9181-3 0 45 9104-8 . 6 31 9186-3 1 15 9105-8 6 50 9191-4 1 27 9107-8 7 7 9196-4 1 45 9110-8 7 33 9201-4 2 12 9115-9 8 0 1 Steam issuin 2 35 9120-9 ( freely. 3 0 9125-9 8 12 9211-5 3 18 9131-0 8 24 9216-5 3 40 9136-0 8 51 9221-6 3 57 9141-0 9 25 9226-6 4 17 9146-1 9 50 9231-6 4 40 9151-1 11 35 9233-6 4 55 9156-1 14 10 9235-7 5 15 9161-1' 16 20 9236-7 5 32 9166-2 17 17 9239-7 5 48 9171-2 21 5 9240-7 6 4 9176-2 24 0 9241-7 38 Proceedings of the Boyal Society XIX. Mixture of Air and Olefiant Gas, containing *06 per cent, hy volume of Olefiant Gas. — The mixture of dry air and olefiant gas used in Experiment XVIII. was driven out of the absorber by a current of dry air, which was drawn through the absorber for about twenty hours. When both compartments of the jacket had been filled with cold water, and B and C closed, the pressure took the constant value 9289*2. Dry olefiant gas was then driven into the absorber until the pressure took the constant value 9295*4. The gas which filled the absorber contained therefore *05996 or about *06 per cent, by volume of olefiant gas. The temperature of the gas at starting was 12°*9 C. Time. Pressure. Time. Pressure. m. s. m. s. 0 0 9299*6 5 40 9349*1 0 22 9298*7 5 55 9354*2 0 48 • 9298*7 a j Steam issuing 1 10 9298*5 D D 1 freely. 1 30 9299*9 6 20 9359*4 1 43 9301*0 6 37 9364*5 2 0 9303*1 7 0 9369*6 2 16 9306*1 7 32 9371*6 2 28 9308*2 7 47 9375*8 2 55 9313*3 8 27 9377*1 3 20 9318*4 10 35 9378*3 3 45 9323*5 12 32 9379*8 4 13 9328*7 14 10 9381*2 4 35 9333*8 18 10 9383*0 4 57 9338*8 20 54 9383*4- 5 15 . 9344*0 XX. Mixture of Air and Olefiant Gas, containing *06 per cent, hy volume of Olefiant Gas. — The absorber contained the gas used in Experiment XIX. Both compartments of the jacket having been filled with water at 12°*8 C., and the pressure having taken a constant value, the steam was turned on in the radiator. Time. m. 0 0 16 Pressure. Time. Pressure. m. s. 9296*1 0 24 9294*3 9295*3 0 30 9293*3 of Edinburgh, Session 1882-83. 39 Time. Pressure. Time. Pressure. m. S. ' m. s. * 0 54 9292-3 5 15 9341-6 1 15 9293-3 5 35 9346-6 1 30 9295-3 • 5 55 9351-7 1 40 9296-3 6 15 9356-7 2 14 9301-4 6 35 9361-7 2 37 9306-4 A 50 ( Steam issuing 3 8 9311-4 0 I freely. 3 32 9316-4 7 4 9367-8 4 0 9321-4 7 23 9371-8 4 9326-5 7 48 9376-8 4 36 9331-5 8 27 .9381-9 4 55 9336-6 9 13 9383-9 The bursting of the steam tube brought this experiment to an end. XXL Mixture of Air and Olefiant Gas, containing per cent, by volume of Olefiant Gas. — The same gas as that used in Experi- ment XIX. and XX. The absorber had a^ain been completely surrounded by water at 12° -85 C., and the pressure had become constant. Time. Pressure. Time. Pressure. m. s. m. s. 0 0 9303-9 5 52 9353-2 0 ■5 9302-9 6 13 9358-3 0 23 9301-9 6 33 9363-3 0 30 9299-9 6 55 9368-3 0 47 9298-9 n 0 1 Steam issuinj 1 7 9299-9 1 1 freely. 1 30 9302-9 7 15 9373-4 2 10 9308-0 7 35 9378-4 2 42 9313-0 8 0 9383-4 3 12 9318-0 8 30 9388-5 3 45 9323-0 9 50 9391-5 4 7 9328-1 11 3 9392-5 4 30 9333-1 12 32 9393-5 4 55 9338-1 i5 33 9394-5 5 13 9343-2 19 30 9395-5 5 32 9348-2 22 25 9396-0 40 Proceedings of the Eoyal Society XXII. Mixture of Air and Olefiant Gas^ containing per cent, hy volume of Olefiant Gas. — The absorber, containing the same gas as in the Experiments XIX,, XX., and XXL, was surrounded by- water at 12° *8 C., and the pressure when constant was found to be 9305-6. Dry olefiant gas was then driven in until the pressure had taken the constant value 9318*3. The mixture therefore contained *19969 or about *2 per cent by volume of olefiant gas. Time. Pressure. Time. Pressure. m. s m. s. 0 0 9318*3 6 12 9375*1 0 19 9317*7 6 30 ■ 9380*2 0 29 9315*7 6 52' 9385*2 0 41 9314*7 7 10 9390*2 0 57 9315*7 7 30 9395*3 1 7 9316*7 7 50 9400*3 1 31 9319*8 8 0 r Steam issuing 2 14 9324*8 1 freely. 2 45 9329*8 8 16 9405*3 3 12 9334*9 8 45 9410*4 3 36 9339*9 9 15 9412*4 4 1 9344*9 10 2 9415*4 4 28 9350*0 10 45 9416*4 4 50 9355*0 14 51 9418*4 5 12 9360*0 17 0 9419*4 5 34 9365*1 21 15 9419*4 5 55 9370*1 XXIII. . Mixture of Air and Olefiant Gas, containing per cent. hy volume of Olefiant Gas. — The absorber, containing the same mixture as in Experiment XXII., was surrounded by water at 12° *8 C., till the pressure had assumed a constant value. Then as usual the water was turned off from K, and the steam turned on. Time. Pressure. Time. Pressure. m. s. m. s. 0 0 9323*1 0 58 9320*1 0 13 9322*1 1 5 9321*2 0 27 9321*1 1 23 9323*2 0 33 9320*0 1 44 9326*2 0 46 9319*0 2 15 9331*3 of Edinhurgh, Session ^‘6, 41 Time. Pressure. . Time. Pressure. m. s. m. s. 2 41 9336-3 6 47 9397-0 3 10 9341-4 7 8 9402-1 3 35 9346-4 7 15 f Steam issuing 3 55 9351-5 1 freely. 4 16 9356-5 7 25 9407-1 4 37 9361-6 7 48 9412-2 4 57 9366-7 8 33 9417-3 5 16 9371-8 10 20 9419-4 5 45 9376-8 12 45 9420-6 6 0 9381-9 18 0 9421-6 6 13 9386-9 20 0 9421-8 6 30 9391-9 XXIV. Dry Air. — The mixture of air and olefiant gas contained in the absorber in Experiment XXIII. was displaced by a current of dry air of about 47 c.c. per second (as determined by experiment), which was drawn through the apparatus for seven hours. At the end of that time (as determined by calculation) only about *2 X *0005 or *0001 per cent, of the gas contained in the absorber would he olefiant gas.^ A set of observations was made with this practically pure air, the temperature of the water jacket being 12°*9C. Time. Pressure. Time. Pressure. m. s. m. s. 0 0 9375-2 5 45 9417-5 0 51 9374-2 6 20 9422-6 1 18 9377-3 7 0 ( Steam issuing 1 46 9380-3 \ freely. 2 0 9382-3 7 3 9427-6 2 30 9387-3 .7 47 9432-6 3 13 9392-4 9 15 9435-6 3 43 9397-4 10 15 9436-6 4 13 9402-4 14 0 9437-7 4 40 9407-5 22 0 9438-2 5 15 9312-5 1 If v is the volume of air entering in unit time, w the percentage of olefiant gas present after t units of time, Wq the percentage present at beginning, and V the volume of the reservpir, V V' = Wffi 42 Proceedings of the Royal Society XXV. Mixture of Air and Olefiant Gas, containing *032 yer cent. Jyy volume of Olefiant Gas. — The absorber, filled with the dry air of Experiment XXIV., was surrounded by water at 12°‘6 C. When a constant pressure of 9338*5 had been attained, dry olefiant gas was driven into the vessel, raising the pressure to 9341*5. Hence the mixture contained *032 per cent, by volume of olefiant gas. Time. Pressure. Time. Pressure. m. s. m. s. 0 0 9340*9 5 30 9374*0 0 17 9339*9 6 13 9379*1 0 26 9338*9 6 52 9384*1 0 54 9336*9 7 15 / Steam issuing 1 14 9338*9 1 freely. 2 0 9343*9 7 50 9394*1 2 38 9349*0 8 24 9399*1 3 10 9354*0 10 15 9404*1 3 41 9359*0 12 20 9405*0 4 13 9364*0 13 50 9406*0 4 53 9369*0 19 10 9406*4 XXVI. — Damp Air, containing per cent, hy volume of. Water Vapour. — A current of the damp air of the laboratory was drawn through the absorber, which contained initially the gas in Experi- ment XXV., until, as determined by calculation, it contained a quantity of olefiant gas so small as to be negligible. The quantity of water vapour present in the damp air, with which the reservoir was then filled, was found by determining the dew-point. The room in which the experiments were carried out was large, and there was a slow passage of air through it. The dew-point was determined by observation of wet and dry bulb thermometers. The temperatures they indicated were respectively 15° and 12° *8 C. The barometric pressure (reduced to 0° C.) was 759*83 mm. The pressure of the water vapour was therefore 9*71 mm., and the damp air contained consequently 1*278 (or about 1*3) per cent, by volume of water vapour. Time. Pressure. Time. Pressure. . m. s. m. s. 0 0 9331*6 0 55 9329*1 0 25 9330*1 1 17 ‘9330*0 43 of Edinhurgli, Session 1882-83. Time. Pressure. Time. Pressure. m. s. 1 35 9333*0 m. 7 s. • 0 ■ ( Steam issuir 2 8 9338*0 1 1 freely. 2 35 9343*0 7 9 9400*1 3 0 9348*0 7 24 9405*1 3 27 9354*1 7 42 9408*1 3 48 9358*1 8 8 9413*1 4 8 9363*0 8 30 9418*2 4 25 9368*0 9 42 9423*1 4 47 9373*1 11 42 9425*0 5 30 9378*1 13 45 9425*9 5 58 9383*1 14 35 9426*8 6 25 9390*1 21 0 9427*1 6 42 9392*1 ’ XXVIL Air saturated with Water Vapour at IT AC, — Water had been put inside the absorber twelve hours before the experiment, and some of it was still lying unevaporated in the vessel. The air therefore was saturated. The temperature of the water jacket when the reservoir was completely surrounded by water, and the pressure was constant, was 12° ’4 C. Hence the pressure of water vapour was about 10 ‘68 mm. The barometric pressure (reduced to 0° C.) was 757*65 mm. Time. Pressure. Time. Pressure. m. s. m. s. 0 0 9306*4 6 14 9353*0 0 33 9304*4 6 56 9358*1 1 8 9304*4 ■ • 7 27 9363*2 1 30 9307*4 8 2 9368*3 2 8 9312*5 8 25 9373*3 2 43 9317*5 8 30 f Steam issuing 3 14 9322*6 ( freely. 3 42 9327*6 8 51 9378*4 4 10 9332*8 10 0 9383*5 4 35 9337*8 12 45 9387*6 4 59 9342*9 16 30 9388*9 5 20 9348*0 19 30 9390*1 If these experiments be represented by curves after the same 44 Proceedings of the Euycd Society manner as the. former ones, the following results become apparent : — (1) The manometric effect is very much greater with, the new than with the old apparatus. (2) The curves for any one gas, or mixture of gases, do not coincide with one another. Thus corresponding ordinates of the two curves for air containing IT per cent, of olefiant gas differ by about 4 or 5 per cent., or, as it may be put, one curve is 4 or 5 per cent, lower than the other. Of the two curves for air with 0*2 per cent, of olefiant gas, one is. 2 to 4 per cent, lower than the other. Of the two for air with 0*06 per cent, of the same gas, one is from 6 to 10 per cent, lower than the other. Hence the apparatus used was incapable of giving perfectly accurate results. As we have pointed out above, the reservoir was not sufficiently rigid. With a rigid reservoir the curves for any one gas, or gaseous mixture, would coincide at any rate in those portions corresponding to considerable intervals of time ; but the inevitable difference in the initial conditions of the experiments must in general prevent entire coincidence in portions corresponding to short intervals of time. (3) The dry air curves are with this apparatus the lowest on the diagram. To us this result was unexpected ; but Professor Tait had foreseen it as a consequence of the change of dimensions of the apparatus. (4) As in the preliminary experiments, the curves for air containing olefiant gas and for air containing water vapour occupy the same region of the diagram. The relative positions of the curves may be used to determine the relative absorptive powers of the gaseous mixtures. (5) The curves for air containing dif- ferent quantities of olefiant gas occupy positions extending over a considerable area of the diagram, and they are higher the greater the percentage of olefiant gas (from *032 up to IT). By deter- mining a sufficient number of such curves a scale of absorptive power may be formed, to which the absorption of air containing known quantities of vapour may be referred. With our apparatus it was impossible to form such a scale accurately for the reasons given above. But an approximate result is given by our experi- ments. The curve for air with 1 *3 per cent, of water vapour (not saturated) has above it the two curves for air with 0’2 per cent, of olefiant gas, and below it the two curves for air with 0*06 per cent, of olefiant gas. Hence we may conclude that the absorption of air containing 1 -3 per cent, of water vapour is between that of air con^ of Edinhurgh, Session 1882-83. 45 taining 0*06 per cent, and that of air containing 0'2 per cent, of olefiant gas. With a rigid reservoir it would he possible to deter- mine exactly the constitution of mixtures of air and olefiant gas, and of air and water vapour having equal absorptive powers. The above experiments were made in Professor Tail’s laboratory during the summer vacation of 1882. By the time they had advanced thus far my vacation was at an end, and I could not wait to get a new reservoir constructed and to complete them. I hope Professor Tait may be able to complete them at an early date. I must mention with gratitude the enthusiastic assistance ren- dered me by Mr Lindsay. His cheerful contempt of failure and his ready resource in difficulty contributed largely to whatever of success we attained. We are deeply indebted to Professor Crum Brown for the use of apparatus necessary for the making of olefiant gas. Of course Professor Tait took a most lively interest in our results, and we had at all times the benefit of his advice. 4. Hote on the Compressibility of Water. By Professor Tait To test by an independent process the accuracy of the unit of my pressure gauge, on which the estimated corrections for the “Challenger” deep-sea thermometers depend, it was arranged that H.M.S. “Triton” should visit during the autumn a region in which soundings of at least a mile and a half could be had. A set of manometers, filled with pure water, and recording by the washing away of part of a very thin film of silver, were employed. They were all previously tested, up to about 2-|- tons weight per square inch, in my large apparatus. As I was otherwise engaged. Professor Chrystal and Mr Murray kindly undertook the deep-sea observa- tions ; and I have recently begun the work of reducing them. The first rough reductions seemed to show that my pressure unit’ must be somewhere about 20 per cent, too small. As this was the all but unanimous verdict of fifteen separate instruments, the sur- vivors of two dozen sent out, I immediately repeated the test of my unit by means of Amagat’s observed values of the volume of air at very high pressures. The result was to confirm, within 1 per cent., the accuracy of the former estimate of the unit of my gauge. I then had the manometers resilvered, and again tested in the compression 46 Proceedings of the Boyal Society apparatus. The results were now only about 5 per cent, different from those obtained in the Triton.” There could he no essential difference between the two sets of home experiments, except that the first set was made in July, the second in Kovemher, — while the temperatures at which the greatest compressions were reached in the “ Triton ” were at least 3° C. lower than those in the latter set. Hence it seems absolutely certain that water becomes considerably more compressible as its temperature is lowered, at least as far as 3° C. (the “ Triton ” temperature). This seems to be connected with the lowering by pressure of the maximum density point of water, and I intend to work it out. It is clear that in future trials of such manometers some liquid less anomalous than water must he employed. Another preliminary result, by no means so marked as the above, and possibly to be explained away, is that by doubling (at any one temperature) a high pressure we obtain somewhat less than double the compression. This, however, may be due to the special con- struction of the manometer, which renders the exact determination of the fiducial point almost impossible. 5. Hote on an Application of Mendeleieff’s Law to the Heats of Combination of the Elements with the Halogens. By Mr A. P. Laurie. Communicated by Professor Crum Brown. Monday, Ibth January 1883. Peofessor MACLAGAH, Vice-President, in the Chair. The Chairman, in accordance with the Laws, announced to the meeting the names of proposed new Foreign and British Honorary Fellows, to be submitted for Ballot at the Second Meeting in February, viz. — As British Honorary Felloius : — Sir Joseph Dalton Hooker, Dr William Spottiswoode, Professor Alexander William Williamson, Colonel H. Yule. As Foreign Honorary Fellows : — Professor Luigi Cremona, Dr Julius Hann, Professor Charles Adolphe Wurtz. of Edinburgh, Session 1^‘^'2-^Z. 47 The following Communications were read : — 1- The Diurnal Variation of the Force of the Wind on the Open Sea and near Land. By Alexander Buchan, M.A. 2. On the Semitic and Greek Article. By the Eev. Dr Teape. 0. On the Nature of Solution. By W. W. Nicol, M.A., B.Sc. 4. On the Kelative Electro-Chemical Positions of Wrought Iron, Steels, Cast Metal, &c., in Sea W^ater and other Solutions. By Thomas Andrews, Assoc. M. Inst. C.E., E.C.S. Communicated by Professor Crum Brown. BUSINESS. The following candidate was balloted for, and declared duly elected a Fellow of the Society : — Dr E. Peel Eitchie. Monday, 2^th January 1883. THOMAS STEVENSON, Esq., M. Inst. C.E., Vice- President, in the Chair. 1. Observations of the Eainband from June 1882 to January 1883. By Hugh Eobert Mill, B.Sc., F.C.S. Communicated by Professor Tait. (Plate I.). The series of observations to be described was undertaken in order to ascertain how far a small pocket spectroscope could be relied upon for the prediction of rain, with a view to its popular use for that purpose. The instrument employed was Hilger’s smallest sized direct- vision spectroscope, its length being one inch and a half, and its diameter half an inch. It was furnished with the ordinary adjustable slit, and had no special provision for the exclusion of dust. It is desirable, however, to use an instrument which has the eyehole protected by a plate of thin glass, and the slit covered with a thicker plate. In this case care must be taken to keep the glass free from scratches, which greatly obscure the spectrum. When the spectroscope is to be used the slit is made as narrow as 48 Proceedings of the Royal Society possible, and the focus adjusted until the spectrum appears bright and clear, with the black solar absorption lines crossing it vertically. If there is dust on the slit each grain appears drawn out into a thick black line running through the spectrum horizontally. When these horizontal lines are seen the slit should be cleaned by gentle brush- ing with a camel-hair pencil. The spectrum of clear sky or a bright cloud, in the instrument used, is a coloured strip apparently about an inch long and half an inch wide. On one side a band of red, apparently f^ths of an inch wide, emerges from blackness and shades into a strip of yellow, which merges into a quarter inch space of green, passing into an equal area of blue which dies away in hardly visible violet. Two or, in favourable circumstances, three black lines (a, B, C) are seen in the red, one (D) appears to separate the red from the yellow, a wide nebulous line divides the yellow from the green, several very thin lines appear in the green together with two thicker ones (E and &), and in the beginning of the blue there is a still darker line (F); besides which a glimpse may sometimes be had of other lines in the darker part of the spectrum beyond F. On looking directly at the sun many of the lines are split up into a number of very fine components, and the whole spectrum seems ruled with lines intensely black and geometrically narrow, most of which are invisible in diffused light. The nebulous line between the yellow and .green is usually mistaken for the rainband at first, for it varies in intensity from time to time. A more particular observation shows that its intensity at any time is proportional to the sun’s nearness to the horizon, but it appears to be sometimes affected by other causes. Professor Piazzi Smyth has shown that this is a dry air absorption band, and he defines it as “a function of dry air and low sun.” The real rainband cannot be seen by itself in the little spectroscope, but an acquaintance with the spectrum soon show-s that the width of the D-line is not constant, and that when widest it seems to shade off gradually towards the red, resembling a line ruled by a fine pen with a very small hair in its point. It can easily be shown that this widening is not due to a widening of the solar sodium absorption line, by looking at the sky spectrum througlj the flame of a Bunsen lamp faintly tinged yellow with a sodium salt. The D-line proper is thus replaced by a brilliant yellow streak, and the rainband is seen 49 of JEdinhurgh, Session 1882-83. as a blatjk line clinging to its red side. This narrow blurred line represents the hundreds of thin lines produced by the absorptive power of the water-vapour in the atmosphere, which can be seen by using an instrument of sufficient • power ; and although it is never seen alone or measured by itself, it can be employed as a valuable weather indicator. The rainband was always observed by looking as near the horizon as possible, so as to take advantage of the greater depth of air seen through; the focus was carefully adjusted to give the sharpest possible definition of the solar lines, and then the intensity of the band together with the D-line was noted. The rainband has been represented by the letter tt, and the compound line, which was always measured, may be written shortly as D tt. The great difficulty in recording observations is to obtain a constant scale of intensities. It has usually been the practice to judge of the intensity of the band by the eye, and to record it on a scale of 1 to 5 or 1 -to 10, or else to measure it in terms of the low-sunband. The former plan possesses the disadvantage common to all purely mental scales, that there is no guarantee of the intensity which is represented by a certain figure one day being recognised as corresponding to that figure on another occasion. Changes in the illumination of the spectrum or in the condition of the observer can hardly fail to make some difference. The second plan is free from this defect to a great extent, but it is inconvenient, for beginners 'at least, because of the diurnal variations. of the low- sunband. Various mechanical arrangements were tried in order to furnish a scale which would remain constant and could be readily reproduced, but the results of the experiments were hot very satisfactory, and it therefore seemed advisable to employ a relative scale supplied by the spectroscope itself. The spectrum observed was so small that the principal Fraunhofer lines were brought near enough to be used as standards of comparison, and as the moisture in the air does not affect their relative intensities, the three most prominent (E, h, and F) were fixed upon as the units of the scale. The three increase in darkness in the order E, h, F, and they are,, ronghly speaking, darker in proportion to their distance from D. The method of measuring by this scale does not altogether get over the objection attached to the use of a mental scale, although that VOL. XII. D 50 Proceedings of the Royal Society objection is reduced to a minimum ; and the method at best is only- applicable to small instruments. A spectroscope of sufficient disper- sion to split D,- or even h, in diffused light would entirely alter the appearance of the lines, and the rainband would appear as a hand incapable of comparison with them. With the small spectroscope used on a clear sky the D-line appears about equal to E in intensity when the rainband is at a minimum. As the band increases the D-line appears -wider, becoming in turn equal to &, equal to E, and greater than E. . In this way six shades of intensity may be easily distinguished, and these may be represented shortly as — D -1- 7T = E. „ >E<&. . .■ „ „ >J, =r. ” The words, luide, dark, hlach, and intense, when applied to the rainband and the larger spectral lines, mean the same thing, for it is difficult to say whether a large rainband makes the D-line apparently blacker, or wider, or both, when viewed by the small spectroscope. Another point of some importance in the prediction of rain is, as has been pointed out by Mr Kand Capron, the visibility of the thin, lines in the green. These vary greatly in distinctness, being sometimes invisible and at other times very apparent, but it is difficult to avoid changing the value of the words used to express the different degrees of visibility. A long and intimate acquaiutance with the spectrum in its different appearances is necessary in order to overcome this difficulty. A regular record of the intensity of the rainband has been kept since June 1882, and the weather which followed within twelve hours of each daily observation at 9 a.m. has also been noted. Other meteorological observations were subsequently introduced to supplement those of the rainband, but during the first seven months the latter alone were considered, and a prediction founded- thereon was written down each morning. The degree of intensity warranting a prediction of rain was, of course, entirely a matter of experience, each success or failure modifying to a. certain extent the of Edinhurgli, Session 1882-83. 51 basis of the next prediction. At first it was only necessary to use the lines h and F for comparison, since D + tt was very rarely < h dur- ing the months of June, July, August, and September. It was soon observed that rain seldom fell within twelve hours when the D-line at 9 A.M. appeared less than or equal to &, and that rain almost always followed when it appeared equal to or greater than F. . Intermediate* intensities were much more common, and in order to make predictions in these cases the degree of visibility of the thin lines in the green was taken into account. From the daily observa- tions in the month of June the following table for predicting was drawn up : — D + TT = or<5 >6F I Thin lines | No rain | Eain . I Ti. Distinct Indistinct I I Probably Probably No rain Eain This table held closely during July. In that month the intensity was =or>F on fourteen occasions, and rain followed on thir- teen of these. The intensity was > 6 < F with thin lines indistinct seven times, and rain followed six times ; on six days the intensity was the same, but the thin lines were distinct, and rain (in each case only a slight shower) followed on three. Once the intensity was = 5, and it was followed by a slight shower. The table was also applicable, though less accurately, to August, September, and Oc- tober, but in November its predictive power completely broke down. The intensity was — or<& twenty-four times in that month, and rain followed on fourteen of these days. The probable reason of this is the low temperature which prevailed, in consequence of which a small quantity of water-vapour produced saturation, which was thus indicated by a fainter rainband than in previous months. A new table of predictions required to be framed for the winter months, in which the intensities D -f tt > E < 5, and = E were con- sidered. The following table (Table I) shows the number of times which 52. Proceedings of the Royal Soeiety the rainband attained each intensity in each of the seven months, and how often it was followed (within twelve hours) by rain in each case : — Table I. • 1882. Month. D-t-7T>F. Rain fol- lowed. D-t-7T = F. Rain fol- lowed. D-f 7t>6 6 ,, 9 » 3 „ ■5 1 n 4 „ 9 „ October, . . 7 „ fi „ 4 ,, 4 „ 9 „ 6 „ 2 „ 0 V 8 „ 3 „ November, . 0 „ 0 n 3 „ 3 „ 1 » 1 „ 2 „ 2 „ 24 „ 14 „ December, . 4 „ 4 „ 2 „ 2 „ 7 „ 5 „ 1 „ 1 n 12 „ 5t „ Total, . . 37 „ 34 ,, 35 „ 26 „ 43 „ 27 „ 32 „ 12 „ 28 „ *Very slight showers. t Observations this month were made at Callander. tRain or much snow. The following summary (Table II) shows that the probability of rain falling increases with the increase of intensity of the rain- band in a very regular manner. When D -F tt was = or< 5 rain fol- lowed more frequently than might be expected, but fourteen of these occasions were in the cold month of November and five in December, and on many occasions there were only slight showers. Table II. D -f 7T Number Rain followed. of times. No. of times. or per cent. = or< h 58 28 48 > 5 < F Thin lines distinct 32 12 37 j t 1 ^ 50 > & < F Thin lines indistinct 43 27 63 ] 1 = F 35 26 74 >F 37 34 .92 The dependence of the rainband on the probability of rain is 53 of Edinhurgh, Session 1882-83, perhaps more clearly seen when one or two very slight showers on an otherwise fine day are classed as “no rain,” and this is evidently a fairer way of estimating the predictive power than by considering a day on which “ no rain ” was predicted and a trifling shower occurred as a failure. A better plan would be to omit all days on which there were only slight showers, and simply take account of those on which there was no rain at all or else heavy rain, suffi- ciently heavy, for example, to interfere with outdoor work. In Table III. it is seen that the increase in intensity of the rainband is not followed by a perfectly regular increase in the percentage of rainy days, which is probably due to the scale not being perfectly uniform, and that a dark rainband is a much surer prognostic of a wet day than a faint one is of dry weather. Table III. Intensity D + tt Percentage of rain following. Percentage of “no rain” following. = or< 5 27 73 >^F 92 8 This table represents the results for seven months, classing one, or at most two, slight showers as “no rain.” Since the extreme values of the intensity of the rainband illustrate its predictive power most strikingly, it may help to show the importance of such observations, if a short account is given of the various cases in which D -H tt was registered as >F and as <5 during the seven months under con- sideration. During these months there were thirty-seven cases of D-f-7T>F, and on three of these no rain followed vdthin twelve hours. Two of these mornings of failure were very misty, but the third was bright and clear. On ten occasions heavy showers came on in the afternoon. On one of these occasions (July 1st) there was a thunderstorm, on another (September 1st) the rainband, according to Professor Piazzi Smyth, was the darkest for the whole year. There were heavy showers in the forenoon on three days and showers at irregular intervals on -ten, two of which (July 6th 54 Proceedings of the Boy at Society ftnd August IStli) were accompanied by thunderstorms. On nine days rain fell continuously, and on two there was continual snow. There were thus 8 per cent, of unsuccessful, and 92 per cent, of successful, predictions when the rainband was at its maximum. It was found that on twenty-eight- occasions D tt was < h. On eighteen of these no rain whatever followed for twelve hours, on four one, or at most two, slight showers followed. On four con- siderable rain, and on two a considerable amount of snow fell. There were thus 21 per cent, of erroneous, and 79 per cent, of success- ful, predictions when the rainband was its minimum of intensity. Table IV. gives a summary of all the predictions made from June to December 1882, with the fulfilments. These predictions were Table IY. June. July. Aug. Sept. Oct. Nov. Dec. Total. Rain predicted, 17 22 20 21 20 12 13 125 , , followed, Per cent, fnl- ) filled pred, , ^ 15 20 12 12 16 li 11 97 88 91 60 57 80 92 85 78 “No rain” pred.. 13 7 10 9 10 18 13 80 ,, followed. 7 3 9 8 7 9 8 - 51 Per cent, fulfilled. 54 43 90 89 70 50 62 64 Total predictions, ,, fulfilments. 30 29 30 30 30 30 26 205 22 23 21 20 23 20 19 148 ,, percentage. 74 79 70 67 77 67 73 72 made from spectroscopic evidence alone, the barometer and ther- mometer were not consulted. In the ’ table “ no rain ” means that no rain whatever fell during' the twelve hours following the pre- diction. This, as explained when describing Table II., accounts for the apparently greater accuracy of “ rain ” than no rain ” pre- dictions. The success of a prediction has been judged of uniformly from the frequency, duration, and intensity of the showers which followed, and not. by the rainfall in inches. This was done because the situa- tion of 'the observing station (in the south side of Edinburgh) was unfavourable for the use of a rain-gauge; and as each prediction was made for a period of twelve- hours, the published rainfall for the of Edinhurgh, Session 1882-83. 55 vicinity for periods of twenty-four hours did not form a trustworthy index of the success of a prediction. If observations could be made twice' or three times a day, so that each prediction would cover a shorter time, and if the intensities of the rainband in different directions were compared each time, much more decided proofs of the utility of the spectroscope as a short-period predictor might reasonably be expected. Situation and circumstances rendered it possible only to make an observation on the north-west sky each morning at 9 a.m., hence all the results described in this paper are deduced from observations in that direction at that hour. If possible the observation should be made on a piece of clear sky, but the spectrum of the light from clouds is not necessarily untrust- worthy. Out of 120 consecutive predictions 75 percent, of those made on a clear, and 73 per cent, of those on a cloudy, sky were verified. The spectroscope cannot be used in a thick mist or a snow- storm, and its indications in frosty weather are usually too faint to be of much value, although it may almost always be relied upon to predict a thaw at least one day beforehand. Remarks on the Chart for January 1883. During the .month of January 1883 the barometer and thermo- meter were observed as well as the spectroscope, and the accompany- ing chart embodies the results obtained. The shading in the upper half of the column allotted to each day represents the prediction, that in the lower half shows the degree of fulfilment. When the upper half is blank {e.g., the 2nd) no rain ” was predicted, and a blank lower half {e.g., the 4th) shows that no rain fell. A very light shading in the upper half {e.g., the 3rd) denotes a prediction of “probably a little rain,” slightly darker {e.g., the 5th) means “some rain,” while the very dark (as on the 1st) stands for “rain.” The lower half shows the rain which followed up to 9 p.m., the length, position, and darkness of the parts shaded representing approximately the duration, time, and heaviness of the showers. Snow is shown by peculiar shading, as on the 27th. The first and second curves join the points at which the barometer and thermometer stood each morning at 9 o’clock, and the third exhibits the intensity of the rainband in a similar manner. A rise in this curve corresponds to an increase in the 56 Proceedings of the Royal Soeiety intensity of tlie band. The fourth line, which could scarcely he represented by an ordinary curve, illustrates the visibility of the thin lines in the green on the scale — Invisible, Indistinct, Pretty distinct. Distinct, but for reasons already stated this curve is less reliable than the others. Summing up the results, it is seen that on sixteen days the predic- tion was that more or less rain would fall, and that this was verified on fourteen, or 87 per. cent. “ JSTo rain ” was anticipated on the remain- ing fifteen days, and on twelve of them, or 80 per cent., there was no rain. The mean percentage of successful forecasts (83*5) is not altered by omitting those days on which only slight showers occurred. The 11th and 19th are the most marked instances of erroneous pre- diction shown on the chart. It is interesting to notice the general closeness with which the rainband curve follows that of temperature. This is strikingly shown for maxima on the 1st, 17th, and 24th, and for minima on the 4th, 8th, 26th, and 31st When the divergence of the curves is considerable the nature of the weather to follow is always decided. Thus, when the thermometer is low and the rain- band strong, rain is certain to follow, as it did on the 3rd and 21st for example, and when there is a high thermometer and a faint band there will be no rain, for instance, the 7fch, 15th, and 20th. One great secret of successful rainband predicting seems to lie in making proper allowance for the temperature, and the direction and force of the wind have also a share in modifying the data. 2. The Theory of Monopressures applied to Ehythm, Accent, and Quantity, By the Eev. J. L. Blake. Communicated by Professor Crum Brown. 3. On the Effect of Oil on a Stormy Sea. By Mr John Aitken. The calming effect of oil on troubled wafers is so well known and so often referred to, that we might have expected there would, by this time, have been a considerable amount of written informa- tion on the subject. This calming effect of oil is not only well 57 of Edinburgh, Session 1882-83. known, but it has also become so stereotyped by constant repetition, that it seems to have acquired the stamp of classical antiquity upon it, yet one is surprised to find ‘that reference to it in early writers is strangely conspicuous by its absence. Our knowledge of the sub- ject seems to have lived almost entirely in tradition. It is only within the last year that anything like definite attempts have been made to test practically and on a large scale the effect of oil on the waves of the sea. The first of these experiments were made in March last at Peterhead by Mr Shields of Perth, who has taken great interest in the matter. Later on in December last he made other experiments at the entrance to the Aberdeen harbour. The place selected by Mr Shields for the latter experiments was within the entrance channel, at a point about 270 yards inside the furthest point of the north pier, and at rather more than 700 yards outside the entrance to the tidal harbour. The channel is at this point somewhat contracted, and has a breadth of about 240 yards. To distribute the oil over the water, Mr Shields erected a. hand pump on the north pier, and connected it with a pipe 1 inch in diameter, which was laid on the bottom of the channel and carried out more than half way across it. The oil was pumped through this pipe, and escaped near the middle of the channel by three valves and roses placed across it 50 feet apart, so as to distribute the oil over some breadth. The oil pumped through the pipe rose to the surface in small globules and spread itself over the water. The effect was very marked and decided. The oil smoothed over the waves and prevented the formation of dangerous crests ; the entrance to the harbour was thus made much safer for vessels. Mr Shields .deserves great credit for these experiments made on so large a scale, and it is much to be regretted that this method of calming the waves is not less expensive. Each of the experiments' at Aberdeen lasted for one hour j the value of the oil used in each was about £20, and though the effect remained for an hour after the pump was stopped, yet the expense does seem great. I am not aware if any experiments were tried to use less oil, but it is evident that it is possible to use too much. There is just one quantity which will give the maximum effect ; more or less will not do so well. Since the experiments at Peterhead and Aberdeen called attention anew to the subject, a number of explanations of this peculiar action 58 Proceedings of the Eoyal Society of oil have been given j none of these, however, appear to me to account for the facts. I have therefore ventured to place the fol- lowing experiments and a theory built upon them before this Society ; and though this theory may not appear to some to explain all the phenomena, yet, as it calls attention to certain effects of an oily film, the importance of which has not previously been taken notice of, I trust the subject may not be uninteresting, and may at least be of some little aid in helping forward a proper understanding of this most interesting and difficult subject. The wonderful effect of oil on water has suggested to many observers the idea that the effect was due to the oily film offering less resistance to the wind than the clean water surface ; that the oil so to speak greased the wind. The first thing therefore which seemed necessary to be done was to test whether there was any truth in this supposition ; to arrange some experiment to ascertain whether there was less friction between air and an. ‘oily film than between air and a clean film. The method adopted was to place some water in a circular vessel, and arrange a jet of air so that it should blow over the surface of the water, and cause it to take up a motion of rotation. Under these conditions the rate of rotation of the water would — if the pressure of the air jet was kept constant — depend on the amount of friction between the air and the water surface. If .the oil decreased the friction the water would be driven less quickly under an oily than under a clean film. In order to measure the amount of motion communicated by the air to the water, a horizontal paddle, completely submerged, was hung in- the middle of the vessel by means of a fine platinum wire, the upper end of the wire being attached to a torsion- head. A needle, rigidly attached to the paddle, indicated oh a circular scale the amount of torsion produced by the moving water, that is, showed the amount of energy communicated by the air jet to the water. The air jet was supplied from a gasometer, which could be loaded to different pressures. The following is the method adopted in working this instrument. The circular glass vessel was carefully washed, and filled with water up to a certain height, which was accurately adjusted for each experiment, so that the water was always exactly the same distance below the jet. Air at a low pressure was then blown over the water. 59 ■ of Edinburgh, Session 1882-83. and the angle of torsion noted. The pressure in the gasometer was then raised, a stronger current was blown over the water, and the reading again taken. In this way a number of readings were taken at different pressures, the angle of course increasing with the pressure. After taking two or three series of such readings to get an average for the clean water surface, a little oil was put on the water, and another series of readings taken. The result of these experiments was that there was no decrease in the amount of deflection after the oil was added to the- water ; which shows that as the air communicated the same amount of motion to the oily 'surfaced water as it did to the clean surface, therefore oil does not reduce the bite, grip, or friction of the air on the water. In working with this apparatus it was found very difficult to get constant readings. On making a new experiment, after washing the glass vessel, some change seemed to take place, and the read- ings for the corresponding pressures were. not always the same as the previous ones. The general result, however, was that the oil in a few cases slightly decreased the readings, but in most cases it increased them a little. The difference in the readings in the experiments with clean water, seems in some way to be connected with the resistance offered by the film where it is attached to the sides of the vessel, and the slight increase given in most cases by the oily film may possibly be due to the weakening of this film by the oil. In the experiments described, the surfa’ce film simply circulated in the vessel and but little free surface was developed ; if, however, a division plate was put across the vessel just deep enough to stop the easy circulation of the film, an interesting and curious result was ob- tained. When the pressure of the air jet was low, so that it did not greatly agitate the surface, and the surface film could circulate quickly enough, there was then scarcely any difference between the readings given by the clean and by the oily surface. But when the pressure rose and the agitation of the water became great, a sudden increase in the amount of deflection took place; but this increase always occurred at a lower pressure with the oily than with the clean film, the explanation of which would seem to be, that when greatly agitated by the air new surface film requires to be rapidly developed, and, as it gets no aid from the contracting film 60 Proceedings of the Boyal Society in front, tliis new surface film can be developed by a lower air pressure in the weak oily film than it can in the stronger clean film. This extreme condition of matters, however, seems never to present itself in nature. Experiments such as these made in the laboratory on water films are in the highest degree unsatisfactory. Since I have begun them I have found this surface film of water to be far more delicate and variable than I had previously any idea of, and find it almost im- possible to get it in a uniform condition. If the experimenting vessels are not cleansed with something to destroy the last trace of soap used in washing off the oil, if the vessel or the water is touched with the fingers or exposed for any length of time to the air of the laboratory, changes take place in the surface tension. It therefore seems that more satisfactory experiments might be made on large sheets of water. As yet I have been unable to do anything in this direction except one experiment, which, on account of the smallness of the sheet of water, may not be of much value. The object of the experiment was to see if the wind communicated less horizontal motion to the surface water under an oily than under a clean film, which would be the case if the wind has a less grip or bite of oily than of clean filmed water. It will be observed here that I leave out of consideration any question as to a possible slipping of the oily film over the water, without dragging the water film underneath along with it. If there is any depth of oil, its upper surface cannot slip over the lower more easily than the same depth of water could, as oil is more viscous than water, though we might imagine the bounding surface might prevent the formation of eddies and the deepening of the motion; but we have seen from the experiment with the jet of air on water in a circular vessel, that there is no evidence of any slipping forward, as the body of water underneath takes up the same amount of motion whether the surface is oily or not. In the experiments made on the small sheet of water, the rate of motion communicated by the wind to the surface water was tested by means of small circular floats 9 cm. diameter and 4 cm. deep. The floats were submerged 2 or 3 m. and only a thin stem projected above the water. Two of these floats were dropped into the pond near that end from which the wind was blowing, and at some distance 61 of Ediiiburgli, Session 1882-83. apart, at right angles to the direction of the wind. These floats were allowed to drift to the opposite end of the pond to see that the rate of motion was the same at both sides. Some oil was now poured over the water at one side, and other two floats started over the same routes as the first two. It was found that the two floats still travelled at the same rate, that oiling had not perceptibly altered the rate of motion. We might almost have expected a different result, on account of the waves on the clean water affording a better catch to the wind, but possibly this advantage might be lost by the eddies and irregular motions resulting from the waves. I do not place any great reliance on the accuracy of these experi- ments, and the last one is evidently on too small a scale j yet I think if the effect of oil on troubled waters is due to its reducing the grip of the wind, the reduction would require to be very great, so great that there would have been, some evidence of it even in these imperfect experiments. There is, however, another consideration which indicates that the oil does not produce its effects by reducing the friction between the air and the surface of the water. Oil itself when exposed to wind is driven into waves very much as water is. It may be that the waves are not so marked in oil as in water, but this is chiefly due to the greater viscosity of the oil. This -was seen in some experi- ments made on a small scale for the purpose of observing the effect of wind on a body of oil. For this purpose two shallow vessels about half a metre square were placed in an exposed part of a field, where the wind could blow freely over them. One vessel was filled with oil, and the other with water as a standard with which to compare the movements of the oil. It was observed that if the oil was thick and viscous there was but little effect, and scarcely any surface circulation produced ; and it required a strong breeze to drive the oil into waves. But with paraffin oil, which is thin and mobile, the result was very different ; it seemed more easily driven into waves than even water. This was probably due to the oil having a less specific gravity than the water, but I think the com- paratively greater agitation observed in the oil was partly owing to the water surface not being quite clean, on account of the paraffin vapour which could not easily be prevented from condensing upon it, so that the water was not so easily driven into waves as it ought 62. Proceedings of the Royal Soeiety to have been. When a little of the paraffin oil was put on the surface of the water it made it much quieter than the body of oil. When we pour a little oil on a wind-driven surface of water, the effect is so marvellous, the smoothing of the waves is so instan- taneous, that the imagination is carried away, and we at once attribute to the oil some wonderful property, though^we may not understand what that property is. When, however, * we examine its action and consider what is taking place, we see that it is not doing, it is preventing something which previously took place, and we are driven to consider what it has prevented. In fact, we are driven to examine how the wind gives rise to waves. It will therefore be necessary for us, before saying anything about the effect of oil, to examine how wind acts on the surface of water, and gives rise to waves; we shall afterwards better understand the effect of oil. The upper surface of water, where it is in contact with the air, is covered with a film having a well-known and definite tension. The tension of this film is always in a state of equilibrium, and the slightest stress acting on a part of it causes the surface to move in the direction of the strain. When a part of the film moves, new film or free surface is formed in the rear of the moving area, and covers the water which was previously covered by the displaced film, while the film in front of the moving film is diminished in area, part of it being absorbed by the water. No work is required to develop this new filing as the work done hy the contracting part of the film in front is equal to the tuorh spent in developing the new film in rear of the moving area. The result of this is, that the slightest stress acting on the surface of the water determines a move- ment of that surface, its motion being in no way checked by the surface tension. Suppose, now, the wind to blow over the surface of a sheet of water, which, for the present, we will suppose to be quite motionless, and for clearness let us suppose further that the wind strikes the water at only one place. The result is that the surface film where the air strikes is blown forwards, and .in sliding over the water it produces waves, one set of waves being produced in front of the moving film, and another set produced by the moving film being raised in the act of being driven over the water underneath. Now if, of Edinhurgli, Session 1882-83. 63 instead of supposing the wind to act at only one place, we consider what actually takes place in nature, namely that the wind strikes the surface of the water at all points, hut more strongly at some points than at others, on account of the eddies produced in the air in its passage over the resisting water, it is evident under these conditions that certain parts of the surface film are more powerfully urged for- wards than others, and the water yielding to this unequal action is driven into a series of waves, having a gradually accumulating effect. This effect is intensified by one side of the wave being thrown up into such a position that the wind acts more powerfully on it than on the other side, or than on a horizontal surface. Let us now look at the action of the same water surface, hut over which there has been thrown a film of oil. The surface has entirely changed its character. New free surface or film cannot now he developed without the expenditure of energy. If we try to move forwards one part of the surface, we find its motion is resisted by the tension of the surface behind it increasing on account of the removal of the oil, and the tension in front of the moving area does not increase hut diminishes. The forward move- ment of the film is therefore checked. Suppose now the wind to ' blow over such a surface, the parts where the wind strikes strongest will tend to move forwards, hut will he unahle to do so on account of the increasing tension behind and reduced tension in front. Further, the parts upon which the wind strikes least are drawn for- wards by the greater tension in front of them and behind the parts tending to move most quickly, and where the wind has developed an increased surface tension. The result of this is, that the wind cannot drive forwards isolated patches of film or surface so as to cause waves, but the whole of the surface is caused to advance at nearly a uniform rate, and the formation of waves is thereby pre- vented. In illustration ' of these points the following experiments were shown * — Two large shallow rectangular vessels with parallel sides were prepared. Both vessels were filled with water, and over the surface of one was put a little oil, the other being kej3t clean. Narrow strips of paper, about 2 or 3 cm. broad, were cut to such a length that they would when expanded by the water be slightly shorter than the breadth of the vessels. One of these strips of 64 Proceedings of the Royal Society paper was put across tlie middle of each vessel. For the purpose of moving these papers over the surface of the water two threads were previously attached to each of them near their ends. Taking first the vessel with the clean surfaced water, the paper strip was by means of the threads moved into its position right across the middle of the vessel. It was shown that the paper strip could he moved backwards and forwards over the surface of the water, with the very slightest expenditure of energy, the film not in the slightest degree resisting the movement, the free siirface or film in front contracting quickly and pulling as strongly as the new film which was developed in the rear. It was further shown that after the paper strip had been moved backwards or forwards into any position, it remained where it was put.* Turning to the oily surfaced water, it was shown that the move- ment of the paper strip on its surface was resisted, the threads by which it was moved becoming tightened when it was dragged from its original position ; and further, that when the tension was dis- continued the paper returned to. the place from which it had been moved. It did not matter whether it was moved backwards or forwards, it always returned to its original position, so long as no surface film was allowed to pass round the ends and get to the other side of the paper. The tension on the threads in these ex- periments represents the resistance which an oily film offers to the forward movement by the wind of isolated areas of surface film. This resistance is not, however, the most important effect of the oil. It is, so to speak, the secondary effects that are most powerful in checking the formation of waves. On oily surfaced water the forward moving area reduces the tension in front, and causes the film there to advance on account of the greater tension in front ; it also increases the tension behind, and so causes the film in the rear to be drawn forwards, and the irregular film advance which takes place in clean water is converted into a uniform and regular advance by the oil. This was illustrated by the arrangements used in the previous experiments. A small piece of paper to act as a float to ^ This was found to be an excellent test of the cleanness of a surface film. If there is the slightest impurity on the surface it gets collected in front of the strip, and the paper cannot he moved quite to the end of the vessel without meeting with resistance. of Edinhiirgli, Session 1882-83. 65 sliow tlie movements of the surface film, was dropped on the clean water and near the long narrow strip of paper. The long strip was now moved away from the float, when it was seen that its move- ment had no influence on the float, as it remained in its original position, and furthm, the float did not move when the strip was moved towards it. The long strip might he moved in any direc- tion, hut the small piece of paper had no tendency to move till it was almost touched hy it. The reason for this want of sympathy, so to speak, between the two pieces of paper is due to the surface tension heing everywhere alike, and free surface appears and dis- appears without any disturbance of the surface tension. When the same experiment was repeated on the oily water the result was very differenti There was now a bond of union between the two pieces.- If the long piece was drawn away the small piece followed it, if moved up to it the small piece receded from it These movements of the float were pointed out to be the result of the disturbance produced in the surface tension by the movement of the strip. The forward movement of the strip causes the oily film in front to become thicker, its tension therefore becomes less, and it tends to expand forwards, or rather is , drawn forwards, by the thinner film in front, and the free surface which is developed in the rear of the strip is rapidly covered by the advance of the oily film which brings with it the paper float. It was shown from this that the forward movement by the wind of isolated areas of oily film was not only resisted, but that their forward movement gave rise to forward movements of the film, both in front and in rear of them. Trom these experiments it will be seen that a clean water surface acts towards the horizontal force of the wind as if it had no surface tension whatever, whereas an oily film acts very much as if the water was covered with a thin skin of india-rubber. Or the stability of a clean water surface might be compared to that of a perfect sphere on a perfectly horizontal plane, and the stability of an oily surface to that of an egg on its side. The effect of this regulating influence of the oil on the surface tension uiay be illustrated in another way, which shows that the uniform rate of advance of the surface film produced by the oil prevents the formation of waves or ripples. If the long narrow strips of paper in the previous experiments are moved quickly over VOL. XII. E 66 Proceedings of the Royal Society the surface of the water, the following effects are seen. On the clean water, the advance of the strip gives rise to a series of very- evident and well-marked waves or ripples in front of it, whereas on the oily surface no waves are formed. The film is seen simply to contract in front of the moving paper. In order to regulate the motion of the strips in the different experiments, a convenient arrangement is to attach to a pendulum the threads which are fixed to the paper strips, and, by drawing the pendulum and strip aside to the same amount in each experiment, we can regulate its drag on the strip with considerable precision. If we wish to compare the effects of equal amounts of energy spent in each case, so as to get results corresponding to equal blasts of wind, then the pendulum should be light ; and if we wish to see the effects of equal rates of motion the pendulum ought to be heavy. When we examine the surface of a sheet of water under the action of the wind, we observe that the floating bodies on its sur- face are all moving forwards— all are carried forwards by a surface current, but a closer examination of the smaller bodies lying close to the surface shows that the advance of the surface film is a jerky one ; one part of the surface advances quickly, then stops, then another part gets into rapid movement, and the general appearance is that of a patchy and irregular advance of the surface film. With oil on the surface all this is changed ; the floating bodies are all now seen to be hurrying forward at a nearly uniform rate, the oil having entirely checked the patchy and irregular advance which gave rise to waves. Paradoxical as it may at first sight appear, it is nevertheless true that the weakening of the surface film by the oil is a source of strength to the surface of the water, and enables it to resist the action of the wind. The oil, in fact, makes the surface film inex- tensible to small strains, and so regulates the action of the wind that waves are prevented, and no effect produced save a nearly uniform sliding forward of the surface. Supposing the explanation here given to be true as regards the formation of small waves or ripples, yet a cause so small seems at first sight quite inadequate to explain so wonderful an effect as that of oil on a stormy sea, and I can easily imagine the question being asked, What effect can this very weak resistance of the surface film of Edinburgh, Session 1882-83. 67 have on the mighty energy of an all hut irresistible ocean wave ? They indeed seem to have hut little relation to each other. Before coming to any conclusion on this point it will he necessary for us narrowly to examine what really is the effect of oil on already formed waves. Let us therefore examine any small sheet of water over which there is passing a series of well-formed waves, and see if the explana- tion we have given of the formation of small waves or ripples applies here to the effect of oil. As we look upon the waves as they pass us, we observe that their surface is very far from being smooth ; on the contrary, a regular series of waves are being formed by the wind on the surface of the large ones. These waves are small at the bottom of the large waves, and grow in size as they approach the top. In fact, the wind is repeating on the waves very much the same process as when it first begins to blow on calm water. This action on the large waves is, however, infinitely more rapid than on the calm water, as the wind is blowing with far greater violence than ever it does on calm waters ; and further, the slope of the surface of the water on large waves being towards the wind, causes its action to be much more powerful than on a horizontal surface. Now, the breaking of large waves is very evidently connected with the formation of these smaller ones which form on them, and grow in strength towards their tops, where they form crests and break, thereby adding dangerous qualities to the wave. We have already seen that oil prevents the formation of small waves on calm water ; it will therefore prevent the formation of small waves on the surface of large ones, and will thereby prevent the formation and breaking of their crests. In order to test whether this conclusion is correct or not, let us again examine the surface of the small sheet of wind-driven water, and, while watching the waves as they glide past, let us pour over them a little oil. At once a change takes place j small waves no longer form on the already made waves, the latter simply continue on their course smoothed and rounded on their surface. We see that the oil by precluding the formation of small waves, has prevented the roughness and the pointed crests which previously formed on the waves and which break when the wind is sufficiently violent. Further, it seems probable that the smoothness of the large waves, produced by the 68 Proceedings of the Royal Society oil preventing the formation of small waves on their surface, must not he neglected, as it will reduce the bite or grip of the wind, and thereby reduce its action on the already fornied waves. Carrying out this process of reasoning, we see how the great waves of the ocean are increased and made dangerous by exactly the same process which we have seen in operation in smaller ones, only intensified and made more dangerous by the greater surface of the large waves, while the oil, by preventing the formation on their surface of smaller waves, hinders the development of dangerous crests. That oil has no other effect on the great waves of the sea is confirmed by the experiments made at Aberdeen. I am informed by Mr Smith, the harbour engineer, that there was no perceptible lowering of the waves after the water was covered with oil. Its action was simply to smooth over the waves and prevent them from cresting or breaking, an effect of great importance and value in making the entrance to the harbour safer during stormy weather. It will be observed, according to the explanation here offered, that oil has no power to calm waves ; it simply acts by preventing their formation and growth in certain ways. The resistance to ex- tension offered by an oily film will also have, no doubt, a slight effect in checking the up and down motion of the water, but the practical effect of this resistance must be very small and quite un- appreciable. It may be as well for us to note that the general question of the growth of waves has not been under consideration here, our atten- tion having been entirely confined to the effects of surface tension on their birth and development. Properly to understand the vast importance of so small a cause as the slight difference of tension produced by the oily film, we have only to remember that large waves have their genesis in tiny ripples, which by the cumulative action of the wind grow into large waves, and the oil, by preventing the formation of the ripple, strangles the wave in its birth. On the other hand, the perfectly balanced tension of the surface of clean water is as the “ letting out of waters,” as the thin edge of the wedge,” as the stone detached from the top of the mountain which brings along with it the irresistible avalanche. Prevent the beginning and the disastrous results are obviated. It might be thought that the difference between the surface ten- of Edinhurgh, Session 1882-83. 69 sion of clean water and oily water is too small to give rise to surface currents or film movements of sufficient velocity to produce these effects, and that the film would break, that is, that all the oil would he blown away before the film behind could be dragged for- wards. The ease with which the film glides over the water, and the velocity with which one part of the film can drag another is, however, much greater than might at first be imagined. Take the following examples : — Drop some oil on the surface of water ; note the extremely rapid spread of the oil. Now, the rapidity of that surface movement is the measure of the power which that particular oil confers on the water of dragging forwards surface film. In fact, the rapidity of that advance is the same as that with which the film can rush forwards in rear of a wind-driven area. That sur- prisingly rapid movement seems sufficient to perform the duty the theory here propounded lays, upon it. Another experimental illustration, better suited to the lecture- room, is made by taking a small piece of paper, say 10 cm. long by 2 cm. broad, and attaching to the opposite sides of the ends of it two small pieces of camphor. This is easily done with a little bees-wax. If this piece of paper with the attached camphor be placed on the surface of clean water, it at once starts into a rapid motion of rotation, which will be kept up for hours, till all the’ camphor is dissolved if the vessel of water is large enough. The rapid movement is here due to the tension of the pure water surface on one side of the strip being greater than the tension of the weak solution of camphor on the other.. The paper is thus dragged round by the unbalanced tension of the clean surface. Or we may vary the experiment by placing a number of pieces of camphor on one side of the paper. If this paper is placed on the surface of a pond, it will be rapidly drawn over the water. Take another example of the wonderful effect of this difference of surface tension. Till two vessels full of water; put a little oil on one of them, then dust some fine powder over the surface of the water in both vessels. The powder must be free from greasy matter — well-burned ashes sifted through fine wire gauze does well. Now direct a jet of air vertically downwards on the surface of the water. When this is done on the clean water, it will be observed that the very slightest possible current of air causes the surface film 70 Proceedings of the Royal Society and the dust floating on it to move away from the place where the air strikes, leaving a perfectly dustless surface. Repeat the experi- ment with the oily surface. It will now he found that however hard you blow you cannot drive back the oily surface, and that when the jet of air is sufficiently strong to cause a deep depression in the surface of the water, the dust particles are seen rushing at certain places into the depression and running out at others with a velocity perfectly surprising. This easy slipping of the surface film may also he seen when the water is in motion and the film at rest. Recently I observed a small stream flowing quickly enough to give rise to slight disturbance of the surface flatness, and yet the surface film was quite motionless. While the stream was flowing underneath, the advance of the surface film was checked by some weeds and grasses forming a floating bridge ' across the stream. If the surface had been quite clean this would not have taken place, but a film of weak tension had collected in front of the grasses, caused by impurities derived probably from the bed of the stream, and not from the air, as the stream was in the country, and far from towns and factories. The tension of the surface in front being less than that behind, the strain put on it by the under current was not great enough to cause it to be absorbed in front of the floating obstruction. A somewhat similar effect may be noticed when we stir up — not round — a cup of tea and then drop in a little cream. The surface film movements of the oily tea are seen to stop while the tea mixing with the cream can still be seen in active movement. The drag of the tea on the surface film is not sufficient to develop new free surface against the resistance of the increasing surface tension of the cleaner film, and all surface movements are stopped, save circular ones, which do not re- quire the development and absorption of free surface. These surface movements are sometimes stopped by a rigid pellicle forming on the surface, but they are also stopped when no such covering is present. It is generally recognised that rain and small floating bodies have an influence on the water somewhat similar to that of oil, and tend to calm its surface. In the case of the rain it seems possible that the great amount of free surface added by the drops causes the surface film to expand and act somewhat in the same manner as •oil, as we know that water dropped on the surface of water causes of Edinhurgli, Session 1882-83. 71 an expansion of the film where the drop enters. There is, however, another way in which these rain drops act. In falling on the sur- face, the drops mix up the shallow film current — which makes the ripple — with the water underneath, and thus destroy it. Much of the calming effect of rain is, however, no doubt due to the falling of the wind, which generally accompanies rain. Small floating bodies act on the surface of water in different ways. Professor James Thomson, in a paper containing his own and Sir William Thomson’s observations on Calm Lines on a Eippled Sea,” shows that these calm lines are associated with long sinuous lines of floating bodies, such as leaves, weeds, &c., and they attribute the calmness in part to the damping action of these bodies acting like floating breakwaters, and destroying small ripple undulations. The author of the paper referred to also points out that part of the calmness is due to oily scum or film ; he also shows how these floating bodies and scum may be collected in long sinuous lines by the surface currents produced by descending currents due to difference of temperature. These surface currents, coming from opposite directions, bring with them floating bodies and scum, which collect over descending areas or lines. That part of the calmness of these lines is due to the film at the place having a low surface tension pro- duced by some impurity is confirmed by my own observations made under somewhat different conditions. If we examine the surface of a canal when the wind is blowing very nearly straight along it, we see that on the side of the canal towards which the wind inclines to blow, there is a strip of smooth glassy water extending for about a meter from the bank. This smoothness is evidently not caused by the protection of the bank, but is due to impurities on the surface collected there by the wind, as the calm area has a well- marked line of demarcation, and is present when the wind is almost directly along the canal, the other side of the canal having no corresponding calm area.t The calm areas in the canal in the cases * “ Calm Lines on a Rippled Sea,” Philosophical Magazine, Sept. 1862 (Fonrtli Series), vol. xxiv p, 247, Proceedings of Philosophical Society of Glasgow, l5tli Feb. 1882. t I have also observed that rapidly flowing streams when they enter still water often have calm areas in front of them. This calmess seems to be due to the rapid absorption of the surface film of the stream which here takes place, and any surface impurities brought by the stream get concentrated and become sufficiently great to reduce the surface tension. 72 Proceedings of the Royal Soeiety observed were not due to floating bodies, as scarcely any were present. Further, an examination of water where a number of small floating bodies were present, showed theic action to be quite distinct from that of oily scum. Small floating bodies destroy the waves, but wind can ripple or roughen the surface of the water amongst them, whereas oily scum does not destroy waves, but pre- vents ripples or darkening of its surface. My observations on the appearance of the canal suggest another way, in addition to the one given by Professor Thomson, in which oily scum and small floating bodies collect near other floating bodies. One evident effect of floating bodies is to check the forward advance by the wind of the surface film of water, and the shallow surface current is thus converted by floating bodies into a deeper but slower current. The result of this is that more surface film with its impurities comes to the floating bodies than goes away. Surface impurities therefore tend to collect in the neighbourhood of these floating breakwaters. In addition to this action of small floating bodies in destroying waves there is another way in which small bodies, such as ice- spicules, &c., act, and smooth the water by preventing the formation of ripples. Small floating bodies prevent the formation of ripples or waves by deepening the current, and so, offering a resistance to the rapid advance of any part of the upper film of water. Weeds and grasses lying on the surface of the water prevent the irregular advance of the surface film, by the resistance they offer to the irre- gular advance of any part of it, and by the drag or pull they exert on the water behind the parts tending to move quickly. Weeds and grasses thus tend to promote uniform rate of advance at all parts of the surface, and thereby prevent the formation of ripples or waves. It is obvious that all oils will not have the same power to pre- vent the formation of waves. It is therefore desirable that we should have some information as to the value of. different oils or other substances for this purpose. The value of an oil will depend on a number of things, the most important of which are (1) the rate at which the particular oil will distribute itself over the sur- face of the water. This will depend greatly on the difference of tension between the surface of clean water and the surface of the water covered with the oil. The greater this difference the more 73 of Edinburgh, Session 1882-83. powerful will that particular oil he. The rate of movement will also probably depend on the viscosity of the oil. The value of the oil will depend (2) on the amount of it required to cover unit area. With these two properties will require to be taken into con- sideration a third point, namely, the market price of the oil. Besides these points, attention will require to be given to the specific gravity of the oil, its solubility in water, and the rate of its evaporation into air. I have been able as yet to give attention to only one of these points. A few oils have been tested to find the amount to which their presence reduced the surface tension of water. Most of the methods for ascertaining the surface tension of a liquid are not suitable for testing that of an oily film. In the oily surfaced water we have not only to measure the, tension of the oil, but also the tensions of the bounding surfaces of the oil and the water. As these combined tensions vary with the amount of oil on the sur- face, the ordinary methods of testing are not suitable, as they do not admit of uniform conditions. It may be as well to remark here, that there is not, as many people suppose, a distinct line of demarcation between the surface covered with clean film and that covered with oily film. That is, the oil wherever present does not always reduce the surface tension to the same amount. On the contrary, there is no line of demarca- tion between the clean and the oily film; the one shades imper- ceptibly into the other, and the amount to which the oil reduces the surface tension depends on the quantity of oil present. Very little oil gives a very slight reduction of tension, and as more is added the tension becomes less till a minimum is reached, after which no reduction takes place. This condition is indicated by the oil ceasing to spread rapidly. Its movements after this stage is reached depend upon whether the oil is lighter or heavier than water. If lighter, it very slowly spreads itself over the water, its movements being now due to gravity. If the oil is heavier than the water, it collects and forms on the surface depressions, which deepen, and ultimately a large drop of oil breaks away and slowly sinks in the water. The breaking away of these droj3S forms a very beautiful experiment, and the slowness of the process gives an oppor- tunity of studying some interesting phenomena. 74 Proceedings of the Royal Soeiety Tor testing the surface tensions an indirect way of measuring the tension of the surface of water in a vessel was adopted. This was done by finding the amount of pull necessary to raise a flat disc off the surface of the water. The disc in rising brings with it a certain quantity of water, and the amount of water lifted depends on the height to which the disc can he lifted above the surface before the film yields, and, as this depends on the strength of the film, the weight of water lifted forms an indirect way of measuring the strength of the film. The apparatus used consisted of a cir- cular disc 4-5 cm. diameter. In order that this disc might hang horizontally as nearly as possible, it was accurately turned on the end of a metal rod. The upper end of this rod was hung to one end of the beam of a balance. To the other end of the beam was hung a glass tube, inside which was placed a scale with the zero point near the top of the tube. A tall narrow vessel full of water was placed underneath, and so that the tube hung in the water. The tube was loaded with mercury till it just balanced the metal disc with the beam of the balance horizontal, and the tube im- mersed in the water up to the zero point. In order to get good contact between the water and the metal disc, a coating of plain Collodion was put on the disc. After all the collodion solvents had escaped, the apparatus was ready for a test. The vessel with water to be tested was placed under the disc and at the correct height, the beam, when the disc touched the water, being slightly inclined downwards at the disc end. The tall vessel of water was now slowly lowered. As the level of the water gradually went down, the weight of the graduated tube increased. While the level of the water descended, a careful watch was kept to observe at what number on the scale the disc broke away from the water. The object of using the submerged tube was that it allows of an increase of weight being put on very gradually and without shock. With this instrument the different readings for the same sample of water always agreed easily to 1 per cent., though they varied 3 or 4 per cent, for different samples if the vessel which held the water was not carefully cleaned. Owing to the principle of the construction of this instrument, it does not give absolute readings, nor do the readings of the scale repre- sent numerically the relative strengths of the different films, so that of Edinburgh, Session 1882-83. 75 readings got from the different oily surfaces do not correctly represent their relative values. The readings, however, enable us to arrange the different oils in the relative order of their strengths. A few of the more easily obtained oils were tested with this instrument. In the following table these are arranged in the order of their tensions on the surface of water, beginning with the weakest tensions, or those which would he most powerful in checking the formation of waves : — Sperm oil. Linseed oil. Eape seed oil. Cloves, Oil of. Cod-liver oil. Olive oil. Anise seed oil. Almond oil. Paraffin oil. Lubricating oil (mineral). Mineral oil. The first few oils in this list are the best, and do not differ much from each other. Cod-liver oil is not quite so good, olive is decidedly less powerful, while the three mineral oils are by far the worst of all, as they reduce the surface tension very much less than the others. The same result was, T believe, got in the experiments at Aberdeen. Mineral oil was there found to he less effectual in calming the waves of the sea than seal or cod oil. 4. The following communication from the Astronomer-Eoyal for Scotland was read by Professor Tait : — In case you should not have any better account of it from those who keep hourly, or perhaps continuous, observations, you may like to mention to the Society this evening, on no more than my twelve-hour testimony, — the occurrence of a decided meteor, of meteorology, last night. The maximum outside temperature yesterday about 2 p.m. was 40° -5, and the minimum temperature, self-registered, for the night was 37°‘0 ; while at 10 a.m. this morning the then temperature was 41"-0, or nothing very different from the day before. And yet for all that, and some time during the darkness of the night, there had been an influx of warm wind, with a temperature of 51°’0 ! It lasted, too, sufficiently long to impress an inside maximum self- registering thermometer’ as well; for while this should not have 76 Proceedings of the Royal Soeiety read through the night higher than 52°‘0, it was found this morning to have marked 61° -5. One consequence of this has been, that while the snow of last Saturday held its own very tenaciously all yesterday on the top of the Calton Hill, there is not the smallest particle of it visible this morning on any side, or in any nook and corner ; while the grass of the hill looks fresher, greener, healthier than it has done through several years past, at the same date. The present winter began indeed in a very threatening manner with its great snow-storm early in December. But, as I had the. opportunity of mentioning in the Eegistrar-General’s return for that month, the appearance would probably be found to be exceptional, rather than characteristic of the whole season : for we were too far advanced at the present time into the middle of a sun-spot cycle, to fear any of those thoroughly and throughout severe winters which, according to the Edinburgh Koyal Observatory observations, have never occurred but at, or near, the heginning of such a cycle. 5. Diagnoses plantariim novarum Phanerogamarum Socotren- sium, ete. ; quas elaboravit Bayley Balfour, Scientise Doctor et in Universitate Glascuensi rermn botanicarum regius Professor. Pars Tertia. PLDMBAGINEH^. 87. VoGELiA PENDULA, Balf. fit. \ fruticosa ramis pendulis; foliis plus minusve spathulatis; infiorescentia diffusa paniculata; sepal- orum marginibus membranaceis vix • bullatis intus glandulis instructis ; corollse lobis sinu non-mucronulato. Socotra, in montibus Haghier. B.C.S. No. 411. Schweinf. No. 586. SAPOTACEiE. 88. SiDEROXYLON FiMBRiATUM, Balf. fit. \ arboreum glabrescens ramis rugosis ; foliis petiolatis. exstipulatis ellipticis v. oblongo- ellipticis v. obovatis obtusis, basi subcuneatis, subtus pallidis ; fasci- culis sessilibus; pedicellis brevibus validisj calycis lobis suborbicul- aribus ; corolla calyce longiore ; staminum filamentis glabris ; staminodeis petaloideis obovatis fimbriatis ; fructu rostrato. Socotra, in convallibus prope Kadhab. B.C.S. No. 339. of Edinburgh, Session 1882-83. 77 OLEACEiE. 89. Jasminum rotundifolium, Balf. fit. ; fruticosum scandens velutino-puberulum ; folds trifoliolatis, foliolis petiolulatis siibee- qualibus V. terminali majore rotundatis v. ellipticis obtusis ; cymis paniculatis terminalibus j floribus majoribus pedicellatis ; calyce truncato ; corollse tubo elongato, lobis 5-6 obloiigis ; baccis saepe 2 globosis. Socotra, in montibiis non infrequens. B.C.S. I^7o. 173, Scliweinf. No. 649. APOCYNE.dE. SOCQTORA, Bcdf. fil. Calyx brevis 5-partitns basi intus glandiiloslis segnientis aciitis. Corolla late campanulata, ttibo brevissimo, fauce squamis 2-seriatis connatis gnstructa, exterioribus 5 flagelliformibus sinnbus oppositis, interioribus 10 rotundatis obliquis per pares lobis oppositis; lobi 5, oblongo-ovati, obtusi, emarginati, ecaudati, antice rubro glandulo pannosi, contorti, dextrorsum obtegentes. Stamina 5 tubo affixa, filamentis validis, decurrentibus, basi dilatatis et inter se squamis connatis; autberae exsertae subovatae, acutae, circum stigma con- niventes non adhaerentes, connectivo lato dorso villoso, loculis basi cassis in appendiculas breves rotundatas productis. Pollen granulosum in quoque loculo in massas 2 cohaerens. Discus 0. Ovarii carpella 2 coujuncta; stylus validus brevis; stigma dilatatum, vertice depresso- conicum, lateraliter 5-gonum, galeis 5 cinctum et appendicula stig- matica ab quoque angulo pendula instructum ; ovula in quoque loculo numerosa. Eolliculi lineares divaricatim adscendentes et basi connati. Semina lanceolata trigoiio-compressa apice comosa ; albumen copiosum firmum; cotyledones lineari-oblongae, rectae, planae, crassiusculae, radicula supera longiores. — Erutex scandens, glaber, crassiusculus, apbyllus. Folia catapbyllaria opposita. Elores solitarii axillares. Genus monotypicum bene distinctum in tribu Echitidearum . inclusum. 90. S. APHYLLA, Balf. jil. : species unica in montium clivis prope Galonsir crescens. B.C.S- No. 327. 78 Proceedings of the Eoyal Society ASCLEPIADACE.^. 91. Ectadiopsis brevifolia, . fruticosa rigida erecta foliis sparsis brevibus sessilibus saepe fasciculatis oblongis v. obovatis obtusis emarginatis mucronatis v. apicalatisj cyinis sessilibus; floribus brevissime pedicellatis. Socotra, in campis calcareis. B.C.S. l!^os. 583, 615. 92. Ectadiopsis volubilis, Balf fit. : fruticosa yolubilis ; foliis diversis ab forma lineari ad obovatam variantibus subsessilibus saepe fasciculatis ; cymis pedunculatis ; floribus breviter pedicellatis. Socotra, frequens. B.C.S. Nos. 259, 696. Scliweinf. Nos. 472 667. Mitolepis, Bdlf. fit. Calyx 5-partitus, glandulosus, segmentis oblongis obtusis. Corolla campanulata, tubo brevi. lobis angustis linearibus obtusis contortis dextrorsum obtegentibus. Coronae squamae 5, basi fusiformes, apice filiformes, medio tubo corollas afflxae qua paullo breviores. Stamina prope basin tubi afiixa, filamentis liberis ; antherae erectae, basi stigmati adhaerentes, apice conniventes, acutae, liberae, dorso glabrae. Pollen granulosum appendicibus oblongo-ellipticis corpusculorum applicitum. Stigma depresso-conicum medio 2-lobatum. Eolliculi divaricati teretes striati subtiliter puberuli. Semina comosa. — Erutex erectus multo-ramosus. Folia opposita fasciculata linearia. Flores solitarii breviter pedicellati. Genus monotypicum Periplocearum Bctadis et generibus vicinis verisimiliter afflne. 93. M. INTRICATA, Bcdf. fit. : species unica in montibus Hagbier crescens. B.C.S. No. 508. Scbweinf. No. 651. CoCHLANTHUS, Bolf. fit. Calyx urceolatus, alte 5-fidus lobis longe acutis recurvis, intus basi 5-squamatis, squamis dentatis. Corolla campanulata alte 5-partitus, tubo brevi, segmentis angustis obtusis valide sinistrorsum contortis dextrorsum obtegentibus. Coronae squamae 5, tubo corollas affixae, breves, validae, crassae, apice 2-lobatae, basi leviter latiores, subcom- planatae tubo corollas aequilongae et supra gynostegium conniventes. Stamina intracoronam afiixa, filamentis brevissimis distinctis; antherae of Edinhurgh, Session 1882 -83. 79 deltoidesB, stigmati adhaerentes, conniventes, apice in appendices breves subiilatos abrupte refiexos productae, imberbes. Pollen granul- osum, corpusculornm appendicibus linearibus paullo concavis. Stigma late conicum vertice bilobatum; ovula numerosa. Polliculi crassi breves oblongo-ovoidei leves divaricati. Semina comosa. — Frntex alte scandens. Folia opposita glabra. Cymae in paniculos corymbosos pedunculatos terniinales dispositae. Flores pedicellati. Genus monotypicum Periploceamm, corolla, coronae squamis et antlieris ab aliis bene notatum. 94. C. socoTRANUs, Ealf. fil. : species imica in montibus Hagbier crescens. B.C.S. JSTo. 525. 95. Secamone socoteana, Bcdf. fil. : volubilis ramis ferrugineo- tomentosis ; foliis obovatis ; cymis subsessilibus ; corollae tubo intus lineari-villoso j stigmate capitato spongioso ; folliculis breviter pube- scentibus. Socotra, in montibus et campis. B.C.S. No. 179. Scliweinf. No. 739. 96. ViNCETOXiouM LiNiPOLiUM, : volubile glaucum ramis flagelliformibus • foliis filiformibus; cymis extra-axillaribus lateralibus longe pendunculatis ; corona 5-fida lobis carnosulis obtusis. Socotra, in campis frequens. B.C.S. No. 208. 97. Maesdenia eobusta, Balf fil. : fruticosa robusta erecta ramulis petiolisque pubescenti-tomentosis ; foliis cordatis v. ovatis obtusis ; inflorescentiis petiolis brevioribus ; corollae laciniis oblongis obtusis, tubo intus dense villosoj stigmate rostrato obscure lobato j folliculis pubescentibus. Socotra, prope Galonsir et Kadbab. B.C.S. No. 522. Sebweinf, No. 741. 98. Boucerosia socoteana, Balf. fil. : ramis tetraquetris mar- ginibus angulato-sinuatis, lobis in spinas productisj corolla atro- sanguinea ; corona alte 5-fida ; segmentis apice trifidis, lobo medio minimo incurvo, lobis lateralibus erectis subulatis. Socotra, in campis abundans. B.C.S. No. 524. Sebweinf. No. 740. 80 Proceedings of the Royal Society GENTIANEiE. 99. Exacum ciERULEUM, Balf. fit. : suffmticosum humile glabrum; foliis sessilibus v. subsessilibus ovatis trinerviis ; floribus pentameris magnis terminalibus solitariis v. in dicbasia paucifiora dispositis ; calycis lobis alatis ; corollse segmentis cseruleis ellipticis ; antheris lateraliter ad medium debiscentibus. Socotra, in montibus Hagbier crescens ad altitudinem supra 3000 ped. B.C.S. No. 403. Scbweinf. No. 672. 100. Exacum affine, Balf fit. ; annuum Orectum ramOsum; foliis ellipticis v. ovatis acutis longe petiolatis 5-nerviis; floribus pedicellatis cernuis 5-meris ; calycis lobis late alatis j corollge lobis obovatis violaceis ; antberis ad apicem debiscentibus. Socotra^ in ripis viridibus fluviorum abundans, B.C.S. No. 82. Scbweinf. No. 466. 101. Exacum gracilipes, Balf fil. ; annuum erectum ramosis- simum : foliis lanceolatis acutis petiolatis 3-nerviis ; floribus graciliter pedicellatis cernuis 5-meris; calycis lobis anguste alatis; corollse lobis obovatis cseruleis ; antberis ad medium lateraliter debiscenti- bus. Socotra, in locis aridis frequens. B.C.S. No. 84. BOEACINE^. 102. CoRDiA OBOVATA, Balf. fil. : arborea; foliis petiolatis obovatis v. oblongo-obovatis apice obtusis et dentato-crenatis, basi cuneatis, subtus subscabridulis, supra tuberculatis ; cymis pauci- floris terminalibus ; pedicellis validis brevissimis ; floribus mediocri- bus 4-fidis ; calyce enervio extus dense pubescente, subfructu cupulse- formi glabro ; corolla omnino glabra ; fructu aurantiaco ovoideo 1-3- loculari. Nom. Yern. Abeteb. Socotra, per totam insulam abundans. B.C.S. Nos. 277, 427. Scbweinf. No. 379. 103. CoRDiA OBTUSA, Balf. fil. ; arborea; foliis petiolatis ellipti- cis V. elliptico-obovatis obtusis v. late acutis integris glabris siccitate nigricantibus; cymis pseudo -axillaribus paucifloris ; pedicellis validis of Edmhurgli, Session 1882-83, 81 brevilbns ; floribns ignotis ; calyce sub fructu ciipulasformi glabro ; dmpa ovoidea aurantiaca 1-loculari. Socotra, in montibus prope Galonsir. B.C.S, No. 325, 104. Heliotropium (Monimantha) dbntatum, Balf. fil. : annuum ramulis a coUo patentibus; folds linearibus v. lineari-lanceolatis dentatis hispidis ; inflorescentiis laxe ramosis paucifloris ; corollso tubo calyce longiore j styli lobis non exsertis ; nucibus glabris. Socotra, in campis prope Galonsir et Tamarida, B.C.S. No. 40, Scliweinf. Nos. 781, 789, 105. Heliotropium (Heliophytum), odorum, Balf. fil. : suffruti- cosum plus minusve scabrido-puberulum ; folds alternis petiolatis oblongis V, oblongo-ovatis basi subcuneatis j spicis conjugatis ebracteatis ; fructu bifido, pyrenis bilocularibus bispermis, Socotra, in montibus Hagdier, B.C.S. No, 181, Scdweinf. No, 461, 106. Heliotropium (Orthostachys) nigricans, Balf. fil. : suf- fruticosum intricato-ramosum decorticans ramulis strigosis angulosis ; folds subopposifcis breviter petiolatis parvis, ab forma eldptica ad formam obovatam variantibus, nigricantibus strigosis ; inflorescentiis paucifloris bracteatis ; corollse tubo calyci sequilongo, limbo magno ; stigmate truncato vix bilobato ; nucibus seabridis. Socotra, prope Gdarriah. B.C.S. No. 581, 107. Trichodesma Sootti, Balf fil. \ fruticosum; folds magnis eUipticis acutis basi angustatis sparsim setosis ; floribus magnis in corymbos magnos terminales dispositis; nucuds magnis poll, longis anguste marginatis, Socotra, in montibus altissimis, B.C.S. No, 438. Scdweinf, No. 623, 108. Trichodesma microcalyx, Balf fil. : annuum liispido- asperum ; fodis eldpticis v. ovatis, inferioribus petiolatis ^ floribus mediocribus; calycis segmentis lanceolatis subfructu non auctis ; nuculis deltoideis dorsadter vadde muricatis non marginatis. Socotra, in regionibus altioribus Hagdier montium. B.C.S. No, 538. Scdweinf. No. 632. 109. Trichodesma laxiflorum, Balf fil. : annuum sparsim VOL. XU. F 82 Proceedings of the Royal Society setulosum; foliis ovatis v. oblongo-ovatis, inferioribus petiolatis ; inflorescentiis laxe ramosis ; floribus parvis ; calycis segmentis lanceolatis subfructu non auctis ; nuculis obovatis dorsaliter minute tuberculatis margine alatis. Socotra, frequens. B.C.S. bTo. 532. Schweinf. ISTo. 788. Cystostemon, Balf fit. Calyx 5-partitus, segmentis linearibus, fmctifer auctus nuculas includens. Corolla campanulata, supra staminum insertionem dilatata, fauce nuda ampliata ; lobi 5, ovati, acuminati, imbricati, per antbesin patentes revoluti. Stamina 5, medium tubum versus affixa, exserta, filamentis obcordatis expansis inflatis basi annulo villoso cinctis ; antherse oblongo-lineares, longe acuminatse, erectae, conniventes, cobaerentes. Ovarii lobi 4, distincti, gynobasi parvae planae impositi; stylus filiformis erectus, stigmate subintegro ; ovula erecta. Nuculae 4, erectae, acutae, angulatae, verrucosae, areola basalari. Semina recta ; embryo rectus, cotyledonibus ovatis crassis planoconvexis, radicula supera. — Herba canescens, setoso-bispida pilis simplicibus. Folia alterna. Cymae scorpioideae terminales, bracteis parvis inferioribus foliaceis. Flores azurei, pedicellati. Genus monotypicum Boragini forsan maxime affine. 110. C. socoTRANUM, Balf. fit. : species unica montes altos calcareos Socotrae incolans. B.C.S. bTo. 309. Scbweinf. JNTo. 593. CONYOLYULACE^. 111. Ipomcra (Quamoclit) laciniata, Balf fil. : annua depressa radiatim ramosa ramis prostratis; foliis laciniatis pinnatisectis longe petiolatis sparsim pilosis ; floribus subsessilibus in axillis solitariis; sepalis exterioribus subtrifidis ; corolla angusta ; ovario rostrato ; seminibus maculosis pubescentibus. Socotra, in campis arenosis circa Galonsir. B.C.S. No. 100. 112. Convolvulus filipes, Balf fil. : suffruticosus inermis ramosissimus ramis scopariis filiformibus strigosis v. subsericeis; foliis linearibus strigosis ; floribus longe pedicellatis laxos racemes terminales formantibus ; calycis lobis corolla multo-brevioribus ; ovario glabro; seminibus pubescentibus. Socotra, per insulam totam abundanter crescens. B.C.S. No. 116. Scbweinf. No. 238. of Edinburgh, Session 1882-83. 83 113. Convolvulus sarmentosus, Balf.fil.: subpulvinatus in- ermis lignosus pereniiis argenteo-sericeus ramis brevibus basi congestis cum ramiilis panels virgatis sarmentosis ; foliis basalibus rosulatis oblanceolatis, superioribus ovato-acutis v. lanceolatis ; floribus pedicellatis breves racemes simplices formautibus; ovario glabro ; seminibns piiberirlis. Socotra, in montibus ealcareis ad alt. 1500 ped. B.C.S. No. 302. 114. PoRANA OBTUSA, Balf. fil. \ frutlcosa scandens; foliis oblongo-obtusis ; sepalis subfructu paullo auctis ; corollse lobis induplicato-valvatis ; stylis duobus. Socotra, inter scopnlos apud extremitatem occidentalem campi Kadbab scandens, B.C.S. No. 355, 115. Brewbria pedunculata, Balf. fil.i suffruticosa virgata incana pnbescente-tomentosa ; foliis oblongis subsessilibns ; floribus valide pedunculatis in axillis solitariis; calyce corolla breviore; ovario birto ; stylis 2. Socotra, in campis ealcareis, B.C.S. No. 158, 116. Breweria glomerata, : suffruticosa nana prostrata lignosa albido-tomentosa ramis congestis; foliis ovatis v, ellipticis subsessilibns ; floribus in capitula hirta terminalia confertis ; calyce corolla longiore ; ovario birto ; stylis 2. Socotra, in campis prope Galonsir. B.C.S, No. 114. Sebweinf. No. 258. 117. Breweria PASTiGiATA, : suffruticosa argenteo-sericea fastigiatim denseque ramosa ramis strictis ; foliis approximatis subimbricatis lanceolatis sessilibus ; floribus sparsis in axillis sub- sessilibus ; sepalis apice conniventibus corolla brevioribus ; ovario glabro ; stylo breviter bilobato, Socotra, in campis ealcareis abundans, B.C.S. Nos, 73, 273. Sebweinf. No. 349. SOLANACE^. 118. WithaniaEiebeceii, Schweinf. : frutexbabitn foliisque W. somniferoe sed ab ea differens calyce profunde diviso et fructifero non vesicoso oreque subaperto, Nom. Vern. Abab, 84 Proceedings of the Boycd Society Socotra, freqiiens in palmetis ad Taniarida et Galonsir. B.C.S. No. 32. Schweinf. Nos. 326, 794. SCROPHULARINEiE. 119. Camptoloma viLLOSA, Balf. fit. \ lierba perennis villosa ; foliis rotundato-cordatis crenulato-dentatis ; floribus panels in racemos terminales breves dispositis \ capsula calycem excedente. Socotra, in locis scopulosis ad 3000 ped. alt. B.C.S. No. 237. 120. Campylanthus spinosus, RaZ/. : suffruticosus intricato- ramosissimus incanus spinosus j foliis minntis crassiuscnlis lineari- bns obtusis; floribus solitariis subsessilibns axillaribus; corollae tiibo calyce duplolongiore ; capsula oblonga glabra. Socotra, in canipis prope mare abundans. B.C.S. No. 101. Sebweinf. No. 261. 121. Graderia FEUTicosA, Ra//. : fructicosa; foliis oblongo- ellipticis v. ellipticis minute aculeolatis ; floribus breviter pedicellatis racemos formantibus ; corolla sesquipollicari ; filamentis et antberis staminiim glabris. Socotra, in montibus Haghier ad alt. 3000 ped. crescens. B.C.S. No. 398. Sebweinf. No. 634, Xylocalyx, Balf. fit. Calyx campanulatus, ad medium v. alfcius 5-fidus, fructifer accrescens lignascens, laciniis angustis. Corollse tubus vix exsertus, superne ampliatus, paullo incurvus ; limbus patens, lobis 5 latis integris subsequalibus 2 posticis interioribus. Stamina 4, didy- nama, exserta j antberse liberae, glabrae, per paria approximatae, loculis distinctis parallelis rectis, altero cujusque antberae tenuiore. Stylus filiformis, apice stigmatoso leviter incrassato obtuso ; ovula in loculis numerosa. Capsula basi globosa, apice compressa, in calyce aucto inclusa, loculicide debiscens, valvis integris medio septiferis. Semina numerosa, obcuneata, testa foveolata. — Sufirutex rigidus, lignosus, nanus, minute aculeolatus, siccitate nigricans. Folia opposita, interdum plura alterna, oblonga v. elliptica, Integra. Flores in axillis superioribus subsessiles v; breviter pedicellati, 2 bracteolati. Bracteoli calyci adbaerentes, proventu lignascentes. 85 of Edinburgh, Session 1882-83. Genus monotypicum tribui Gerardiese referendum atque Micrar- gerice et Gmderi(^ valde affine. 122. X. ASPER, Balf. fil. : species unica in locis aridis camporum Socotrensium crescens. B.C.S. Xo. 111. ACAXTHACE^. 123. Ruellia insignis, Balf. fil. : fructicosa; foliis petiolatis ellipticis v. subrbomboideis obtusis, lamina glabra supra papulosa cystolitbifera ; lloribus axillaribus solitariis ; bracteolis calyce viscido brevioribus viscid is ; corolla magna ; capsula 4-sperma. Xom. Yern. Ojebit. Socotra, in montibus Hagbier frequens. B.C.S. Xo. 376. Scbweinf. Xo. 440. 124. Ruellia carnea, Balf. fil. : fruticosa dense stellatim tomen- tosa et viscida ; foliis cordatis ; floribus solitariis axillaribus ^ bracteolis calyce brevioribus ; corolla magna ; capsula pubescente. Socotra, in campis prope Galonsir. B.C.S. Xo. 510. Scbweinf. Xo. 714. 125. Blepharis spiculifolia, Balf. fil. : fruticosa nana ramulis lateralibus contractis ; folia rigida oblanceolata v. sublinearia rarius subbastata spinosa ; floribus solitariis terminalibus ; bracteolis calyce brevioribus ; calycis lobis integris. Socotra, in campis. B.C.S. Xo. 183. Scbweinf. Xo. 442. 126. Barleria ACULEATA, Balf. fil.'. fruticosa non-spinosa fere- glabra j foliis petiolatis obovatis v. subellipticis coriaceis aculeatis ; floribus axillaribus solitariis ; bracteolis calyce brevioribus ; stami- nibus 2 j staminodiis 3 ; capsula obovoidea basi vix contracta 4- sperma. Socotra, in montibus Hagbier. B.C.S. Xos. 399, 408. Scbweinf. Xo. 553. 127. Barleria tetracantha, Balf fil. : fruticosa nana glabra ramis lateralibus axillaribus verticellatim tetracantbis ; foliis crassis lanceolatis oblanceolatis v. obovatis apice aculeatis ; floribus axillari- bus ; bracteolis pungente-subulatis calyci sequilongis ; staminibus 4, 2 brevioribus ; ovarii loculis 1-ovulatis. Socotra, in campis frequens. B.C.S. Xo. 605. Scbweinf, Xo. 374. 86 Proceedings of the Boyal Society • 128« Barleria argentea, Balf. fit. : fruticosa inermis argeiitea caneseens ; foliis ianceolatis v. oblanceolatis strigulosis aciitie v. sub mucronulatis ; floribus in cymas bifloras axillares pedunculatas dispositis ; bracteolis lineari-subulatis calyce brevioribus y stamina 2 ; staminodiis 2j ovarii loeulis 1-ovulatisj capsula rostrata pubescente 2-sperma. Noiii, Yern. Sbiramban. Socotra, in clivis montium„ B.C.S. No. 544. 129. Neuracanthus aculeatus, Balf fit. i suffmticosus incaniis 1-pedaiis ramulis brevibiis ; foliis linearibus sinuato-undulatis ; spicis axillaribus bxevibus ; bracteis apice lignosis subulato- pungentibus. Socotra, in campis. B.C.S. No. 502, 130. Neuraoanthus capitatus, Balf . fit. ; suffruticosiis incanns nanus ramis elongatis decumbentibus ; foliis ellipticis v. obovatis sinuato-undulatis ; spicis congestis in inflorescentias capitatas aggregatis j bracteis angustis apice siibulato-pungentibus. Socotra, in campo Kadhab solum repertus. B.C.S. No. 360. Ballochia, Balf. fit. Calyx 5-partitus, segmentis angustis acutis subaequalibus. Coroilse tubus longiusculus recurvatus oxtus pubescens intus glanduloso- puberulus, fauce ampla; limbus 2-labiatus, labio postico exteriore oblongo erecto concaviusculo breviter 2-lobato, antico 3-partito segmentis planis inter se subaequalibus lateralibus erectis inter- medio intimo patente. Stamina 2 antica perfecta, fauci affixa, labio postico paullo breviora v. sublongiora, filamentis decurrentibus validis complanatis postice cum staminodiis parvis sublinearibus uncinatis subconnatis; antberge 1-loculares, oblongs, medio dorso affixse, muticse, apertge late membranacese. Discus pulvinatus. Stylus filiformis apice integer obtusus v. brevissime bifidus ; ovula in quoque loculo 3. Capsula oblonga, basi in stipitem solidum longe- contracta. Semina 4 v, abortu pauciora, compressa, suborbiculata, rugosa, scrobiculata, retinaculis tenuibus fulta ; embryo normalis. — Frutices elati v. bumiles, lignosi, rigidi, infiorescentia glanduloso- puberula excepta glabri. Folia parva, integerrima, crassa. Flores flammeo-flavi v. flavidi, pedicellati, in axillis solitarii v. diebasia axillaria simplicia formantes. Bractese minimae, angustce. of Edinbm'‘gli, Session 1882-83. 87 Genus species ties includens Oreacantlio valde • affine sed liabitu, inflorescentia, corolla et staminodiis recognoscendum. 131. B. AM (ENA, Balf. Jil. : virgata ramulis albis ssepe subspine- scentibus ; foliis parvis siibsessilibus oppositis v. fasciculatis oblongis obtusis margine revolutis ; doribus solitariis axillaribus pedicellatis pedicellis foliis longioribus glandulosis ; stylo apicJe bifido. ^lom. Yern. Misah. Socotra, in campis Kadhab et Tamarida. B.C.S. ISTos. 364, 430. Scbweinf. Nos. 648, 700. 132. B. ROTUNDiFOLiA, : subarborea nonnunquam nana ramulis obscure alatis ; foliis brevissime petiolatis late ovatis v. sub- rotundatis acutis v. obtusis margine ravolutis subtus albido- lepidotis; floribus in dicbasia axillaria dispositis rarius solitariis, pedicellis longis glanduloso-puberulis ; stylo apice obtuso integro. Socotra, in montibus frequens. B.C.S. No. 300. Scbweinf. No. 605. 133. B. ATRO-viRGATA, Bolf. fit. \ orecta ramulis strictis nigris ; foliis brevissime petiolatis elongato-oblongis v. oblanceolatis obtusis margine undulatis subtus glaucis \ floribus solitariis axillaribus, pedicellis foliis multo brevioribus glabris j stylo apice breviter bifido. • Socotra, in montibus. B.C.S. No. 578. ' 134. JusTiciA (Gbndarussa) rigida, Balf. jil. \ fruticosa rigida lignosa cano-velutina ; foliis minutis obovatis v. oblanceolatis ; floribus spicatis axillaribus j bracteolis minutis >calyce brevioribus j capsula cana strigulosa. Socotra, in campis. B.C.S. No. 358. Trichocalyx, Balf. jil. Calyx alte 5-partitus, segmentis angustis linearibus acutis apice subu- latis sequalibus. CoroUae tubus extus pubescens, intus glaber, limbo aequilongus paullo incurvus sursum ampliatus; limbus 2-labiatus, labio postico interiors erecto concaviusculo brevissime 2dobato, antico oblongo patents breviter 3-lobato lobo medio extimo, palato nullo. Stamina 2, fauci affixa, labio postico aequilonga, filamentis leviter arcuatis decurrentibus ; antberse 2-loculares, loculis discretis, altero altius affixo mucronato v. submutico, altero inferiors basi calcarebrevi parvo albo appendiculato; staminodiaO. Discus cupu- 88 Proceedings of the Royal Society laris V. pulvinatus dentatus v. integer. Stylus filiformis apice obtusiis minute 2-lobatusj ovula in quoque loculo 2. Capsula oblonga, basi in stipitem solidum contracta. Semina 4 v. abortu pauciora, compressa, suborbiculata reniformia, papilloso-tuberculata, retinaculis obtusis complanatis fulta. — Frutices parvi. Folia integra crassiuscula. Flores sordide purpurei ad extremitates ramorum in cymas densas congesti. Bracteolae calycis segmentis similes iisque parum breviores. Gibbi 2 pilosi ab extero basi corollse tubum intrusi. Genus species duas includens in sectione Justiciearum locatum, Justiciece affine etiamque Isoglossoe et Anisotidi sed ab omnibus calyce, corolla antherisque bene separatum. 135. T. ORBicuLATUs, ramulis tomentoso-pubescentibus ; foliis orbiculatis. Socotra, in montibus prope Galonsir. B.C.S. 175. 136. T. OBOVATUS, Balf. fit. : ramulis glaucis lepidotis pilisque- brevibus puberulis ; foliis anguste obovatis v. oblongo obovatis. JSTom. Yern. Elba!. Socotra, in montibus Hagbier prope Tamarida. B.C.S. FTos. 428, 541, 597. Scbweinf. No. 371. 137. Anisotes diversifolius, Balf. fit: fruticosus; foliis plus minusve obovatis; cymis axillaribus v. terminabbus. Nom. Yern. Elban. Socotra, in montibus Hagbier. B.C.S. Nos. 506, 576. Scbweinf. • No. 477. 138. Ehinacanthus scoparius, Balf. fil.\ berba subglabra scoparia ramulis striatis; foliis longis linearibus. Socotra, prope Tamarida, B.C.S. No. 687. Scbweinf. Nos. 448, 783. Angkalanthus, Bat. ft. Calyx alte 5-partitus, segmentis lanceolatis acutis 3-5-nerviis sub- sequalibus. Corolla extus pubescens; tubus limbo brevior, incurvus, superne ampliatus, intus basi dense villosus; limbus longe 2-labiatus, labio postico exteriore ligulato truncate eroso recurvo apice spiraliter revoluto, antico subsequilongo recurvo patente lato elliptico-oblongo trifido lobis linearibus obtusis spiraliter revolutis intermedio latiore 89 . of Edinhiirgli, Session 1882-83. intimo. Stamina 2 , fauci affixa, labio postico vix sequilonga, filamentis complanatis breviter decurrentibus ■ antherse oblongsQ 2-loculares sagittatse, loculis parallelis sequalibus muticis ; stamin- odia 0. Discus inconspicuus. Ovarium glabrum; stylus filiformis exsertus apice breviter bilobatus; ovula in quoque loculo 2. Capsula ignota — Frutex. Folia subintegra. Flores flammeo-flavi in spicas longissimas terminales v. axillares dispositi. Bractese bracteolseque minutse ovatse. Alabastri falciformes. Genus monotypicum EujusticiearUm ad Africanum Himantichilmn et Brasiliensem Schaueriam relatum sed bene distinctum. 139. A. OLiGOPHYLLA, Bcilf.fil.’. species unica in campo FTogad Socotrae crescens. B.C.S. No. 610. 1 40. Ecbolium striatum, Balf. fil. ; fruticosum ramis striatis ; folds longe petiolatis plus minusve ovatis; bracteis integris pilosis viscidis; bracteolis calyce longioribus; corollse limbo tubo subaequi- longo calyceque duplolongiore. .Socotra, in montibus Haghier. B.C.S. No. 504. Scbweinf. No. 652. Var. MINOR, Balf.fll. : omnino minor; spicis longioribus; bracteolis calyce brevioribus. Socotra, abundans. B.C.S. Nos. 433, 462. 141. Dicliptera effusa, fil.’. annua diffusa ramosissima subglabra nitida; folds ovatis longe petiolatis pungente-cuspidatis ; dicbasds longe pedunculatis solitariis axillaribus ; bracteolis viscidis lanceolatis v. oblanceolatis pungentibus ; corolla bracteolis breviter longiore; capsula viscida. Socotra, frequens. B.C.S. Nos. 117, 566. Scbweinf. No. 463. 142. Dicliptera ovata, Balf. fil. : annua parva pubescens prostrata ; folds ovatis breviter petiolatis ; dicbasiis breviter pedicellatis solitariis axillaribus; bracteolis sparsim viscidis; corolla bracteas longe excedente. Socotra, prope Tamarida. B.C.S. No. 577. 143. Hypoestes pubescens, Balf. fil. : annua parva pubescens; folds petiolatis ovatis ; cymis paucifloris terminalibus v. axillaribus ; bracteolis involucri 4 inaequalibus calyce longioribus, exterioribus 90 Proceedings of the Pi,oyal Society niajoribus; corolla resupinata, labio postico loiige mucronato; capsula pnbescente. Socotra, apud Kiseben. B.C.S. No. 509. Sebweinf. No. 612. SELAGINE^. CoCKBUENIA, Balf. fit. Calyx 5-fidus, tubulosus, lobis angustis acutis aeqiialibus. Corollse tubus brevis superne ampliatus; limbus 2-labiatus, patens, labio postico 2-lobato, antico parum longiore 3-lobato lobis sub- sequalibus. Stamina 4, didynama, supra medium tubum affixa, exserta; antberse versatiles, confliientia — loculares, medio vix con- strictse. Ovarium 1-loculare, 1-ovulatum ; stylus apice minute bilobatus. Eruct. ignot. — Erutex incanus ramis diffusis virgatus. Eolia alterna, obovata, integerrima. Elores csesii, parvuli, in spicas breves terminates ssepe compositas dense conferti, singuli in axillam bractese sessiles ebracteolati. BracteBe non involucratse, anguste lanceolatse, calyce parum breviores, cum calyce birtse. Genus montoypicum Glohularice valde affine sed ab ea ob inflores- centiam spicatam sine bracteis involucratis et corollse differentias prsecipue separatur. 144. C. socoTRANA, Balf. fil.\ species unica monies Socotrm incolans. B.C.S. Nos. 262, 317, 558. Sebweinf. Nos. 568, 610. VEKBENACE^. CcELOCARPUM, Balf fil. Calyx tubuloso-campanulatus, membranaceus, 5-costatus costis in mucrones productis, fructifer patens cupularis drupaque bre- vier. Corollse tubus cylindraceus, sequalisj limbus patens, 5-fidus, lobis oblongis obovatis obtusis parum iuBequalibus, 2 posticis min- oribus. Stamina 4, didynama, supra medium tubum affixa, inclusa, filamentis brevibusj antberse cordiformes, inappendiculatse, loculis divergentibus. Ovarium integrum, 4-loculare, loculis 1-ovulatisj stylus inclusus apice brevissimebifidus,lobo antico majore stigmatoso, postico erecto levi. Drupa succosa calyci patenti imposita, endo- carpio osseo, pyrenis 2 2-locularibus lacuna intermedia separatis. of Eclinhurgh, Session 1882-83. 91 Semina exalbuminosa. — Friitex piibescens, inermis. Folia opposita, elliptica, crenata, venulis subtus prominentibus. Eacemi terminales breves. Flores parvuli in axilla bractese minutse breviter pedicellati, ebracteolati, secus rbacbin alterni v. suboppositi, approximati. Genus monotypicum Citherexylo Americano generi arete affine. 145. C. socoTRANUM, Bctlf. fit. \ species unica per monies Socotrse crescens. B.C.S. Nos. 299, 520. 146. Clerodendron (Cyclonema) galeatum, Balf. fil.\ fruti- cosum fusco-tomentosum; foliis petiolatis ellipticis v. subobovatis; cymis strictis terminalibus ; bracteis magnis foliaceis; corollse lobo postico cucullato. Nom. Vern. Dunha. Socotra, in montibus Haghier prope Tamarida. B.C.S. No. 441. 147. Clerodendron leucophceum, Balf. fit. \ arboreum cortice albo-tomentosum ; foliis parvis oblongo-ellipticis; fioribiis solitariis axillaribiis racemos longe pedunculatos formantibus ; calyce subfructu patente; fructu cernuo. Socotra, abundans. B.C.S. Nos. 182, 385. LABIATE. 148. Orthosiphon perrugineus, Balf. fil.\ suffruticosus tomen- toso-pubescens demum glaber j foliis longe petiolatis late ovatis v. subcordiformibus rarius obovatis obtusis crenatis utrinque pubemlis ferrugineis; racemis 6-8-floris glandulosis; corollse tubo calyce triplo- longiore, fauce nuda; staminibus corolla brevioribus. Socotra, in montibus abundans. B.C.S. No. 420. Sebweinf. No. 518. 149. Leucas (Ortholeucas) virgata, Balf. fil.: suffruticosa virgata ramis fulvisj foliis petiolatis plus minusve obovatis v. spatbulatis v. subellipticis integris v. superne trilobatis crassiusculis velutino-pubescentibus ; verticellastris 3-floris ; bracteis calyce multo- brevioribus; calycis dentibus brevissimis. Socotra, frequens. B.C.S. Nos. 141, 274, 543, 548. Sebweinf. No. 343. 92 Proceedings of the Royal Society 150. Lasiocarys spiculifolia, Balf. fil.\ suffruticosa nana; foliis spiculiformibus v. triaculeatisj floribns solitariis axillaribus. Socotra, in campis non freqnens. B.C.S. ]^o. 261. 151. Lasiocarys flagellipera, Balf. fit.: flagellifera; foliis spatbulatis v. cocbleariformibiis cum dentibus 5-7 pungentibus ; floribns solitariis axillaribus. Socotra, inter rupes calcareas prope Galonsir crescens. B.C.S. No. 233. 152. Teucrium (Folium) prostratum, Balf fit. : prostratum ramis incanis ; foliis petiolatis oblongis apice truncatis dentatis, basi abrupte contractis, revolutis; floribns in capitula pauciflora dispositis; corolla calyce pubescente duplolongiore. Socotra, ad basim montium calcareorum prope Galonsir et Tamarida. B.C.S. Nos. 342, 547. 153. Teucrium (Folium) petiolare, Balf. fil. : perenne a collo ramosum ramis adscendentibus plus minusve incanis ; foliis longe- petiolatis ellipticis, superne serrato-crenatis, inf erne integris obtusis, parum revolutis, supra viridibus, subtus incanis; calycis dentibus deltoideis ; corolla calycem pubescentem excedente. Socotra, in montibus prope Galonsir. B.C.S. No. 431. Schweinf. No. 566, 578. AMARANTACE^. 154. A^rua revoluta, Balf. fil. : suffruticosa incana parva ramis erectis complanatis ; foliis obovatis obtusis alternis revolutis subtus incanis supra demum glabrescentibus ; spicis oblongis brevibus ad extremitates raiiiorum spicatim dispositis ; floribns baud nitidis ; periantbii segmentis uninerviis bracteolis multo longioribus ; staminodiis brevissimis deltoideis. Nom. Vern. Teb. Socotra, in montibus Hagbier. B.C.S. No. 478. Schweinf. No. 558. THYMELiEACEA^. 155. Lasiosiphon socotranus, Balf. fil.\ fruticosus glaber; foliis obovatis v. oblanceolatis glaucis ; bracteis involucri coriaceis glabris latis ; calycis fauce esquamato. of Edinhurgh, Session 1882-83. 93 Nom. Vein. Legief. Socotra, frequens. B.C.S. IN’o. 518. Scliweinf. No. 567. SANTALACEiE. 156. OsYRis PENDULA, Bolf. fil. I arbotca glabra ramis pendulisj foliis breviter petiolatis alternis lanceolatis v. suboblanceolatis acutis glaucis ; floribus dioicis ; J dimorphicis in cymas 3-4-floras longe pediinculatas dispositis, plurimis minutis perianthio rotato 3-4-lobato discoque carnoso, paucis majoribuspyriformibus lobis conniventibus; $ ign. Socotra, in montibus Hagbier. B.C.S. No. 630. EUPHOEBIACE.E. 157. Euphorbia (Eremophyton) socotrana, Balffil.'. arborea glabra ; foliis magnis breviter petiolatis late obovatis apiculatis ; capitulis magnis solitariis terminalibus j involucre glabro, bracteis fimbriatis ; glandulis 6 ; staminibus paucis ; capsulis seminibusque pulverulentibus. Socotra, in montibus convallibusque. B.C.S. No. 464. Scliweinf. No. 531. 158. Euphorbia (Tirucalli) obcoedata, Bolf. fih : fruticosa ramis juvenilibus puberulis j foliis breviter petiolatis late obovatis V. obcordatis crassiusculis ; cymis solitariis terminalibus 3-cepbalis ; involucre extus pubescente, bracteis fimbriatis, glandulis rubrisj staminibus paucis. Socotra, in montibus. B.C.S. No. 268. 159. Euphorbia (Tirucalli) oblanceolata, Balf fil. suffrutb cosa ramis glabris j foliis subsessilibus oblanceolatis mucronulatis ; umbellis cymosis terminalibus ramulis brevibus, bracteis magnis rotundatis ; involucre extus glabro intus villoso, bracteis fimbriatis, glandulis flavis ; capsulis glabris ; seminibus tuberculatis. Socotra, in montibus Hagbier. B.C.S. No, 639. 160. Euphorbia (Tirucalli) arbuscula, Balf. fil. : arborea 94 Proceedings of the Boyal Soeiety carnosa aphylla ; cymis terminalibus sessilibus ; involucri glandulis 5 concavis substipitatis j capsulis tomentosis ; seminibus levibus cariinculatis. Socotra, abundans. B.C.S. l^o. 207. Scbweinf. I7os. 241, 525./ 161. Phillanthus (Euphyllanthus) filipes, Balf. fil. : suffrati- cosus ramis disticbopbyllis florigeris angulatis apicalibus ; folds oblongis, stipulis scariosfs basi nonproductis ; floribns monoids paucis fasciculatis ; staminibus 5, filamentis ad medium connatis, autberarum loculis contiguis ; stylis G j capsulis glabris trisulcatis longe filiformiter pedicejlatis ; seminibus scrobieulatis. Socotra, in campis rarus. B.C.S. I7o. 332. Scbweinf! !Mo. 615 B. 162. , Jatropha (Adbnoeopium) unicostata, Balf. fil. : arbuscula resinifera ; folds lanceolatis v. oblanceolatis glands unicostatis ; stipulis minutis glandulosis ; floribus majusculis ; staminibus 8 ; capsulis magnis glabris. ISTom. Vern. Sibrba. Socotra, frequens. B.C.S. l!7os. 13, 89, 137. Scbweinf. l!7os. 256, 378. Perry. 163. Croton (Eluteria) sarooarpus, Balf. fil.: arbor; folds ovatis penniveniis longe petiolatis lamina basi patellari-glandulosa subtus argenteo-lepidota ; stipulis subulatis ; inflorescentiis pseudo-ter- minalibus ; floribus dioicis ; J racemis multifloris, alabastris globosis, staminibus ultra 20; ? umbellis paucifloris, stylo bis bifid 0, capsula dense setigera, seminibus levibus. Socotra, in montibus. B.C.S. ISTos. 298, 318, 640. Scbweinf. Nos. 517, 666. 164. Croton (Eluteria) sulcipructus, Balf. fil.: fruticosus ; folds ovatis penniveniis petiolatis lamina basi patellari-glandulosa subtus argenteo-lepidota ; stipulis subulatis ; glomeruli florium in spicas dispositi ; fl. 5 supremi subsessiles, staminibus sub 20 ; fl. $ pauciores basales pedicellati, stylo bis bifido, capsula 6-sulcata lepidota lepidibus planis, seminibus levibus. Socotra, in montibus Hagbier ad alt. supra 2500 ped. B.C.S. Nos. 484, 496. Scbweinf. No. 621. 95 of Edinburgh, Session 1882-88. 165. Croton (Eluteria) elcbagnoides, Balf. fil. : arboreus ; foliis auguste ovatis penniveniis long© petiolatis lamina basi patellari- glandulosa subtus metallico - lepidota j stipulis inconspicuis : fl. ^ ignotis ; fi. $ in nmbellas dispositi, stylo bifido, capsula lepidib’us umbonatis dense vestita. Socotra, in montibus Haghier infrequens. B.C.S. ISTo. 492. 166. Croton (Eluteria) socoTRANUs, ^a^/. : frnticosus; foliis penniveniis petiolatis bidentibns ab parvis ellipticis v. obovatis ad formas oblongas ovatas variantibus Ijamina basi patellari-glandulosa, pagina iitraqne pilis stellatis sparsim vestita ; stipulis obsoletis; llori- bus pedicellatis in nmbellas unisexnales terminales dispositis; stami- nibus ultra 20 ; foeminei floris petalis,. linearibus ; stylo bis bifido ; capsula dense pilis setosis penicillatis vestitas ; seminibus levibns. Socotra, freqnens. B.C.S. Nos. 1, 278, 494. Scbweinf. Nos. 449, 798. 167. Cephalocroton sogotranus, Balf. fil. : fructicosus : foliis ad extremitates ramnlornm lateralinm contractorum ssepe fasciculatis rotundatis v. obovatis subintegris penniveniis ; fl. $ sepalis integris. Nom. Vern. Than v. Tebn. Socotra, in montibus altissimis et in campis inaritimis. B.C.S. Nos. 391, 633. Scbweinf. Nos. 430, 544, 797. 168. Tragia (Tagira) dioica, Balf fil. : volubilis lignosa urens ; foliis oblongo cordatis grosse dentatis pilosis et bispidis : floribus dioicis j J 3-meris j $ calyce 5-lobato, lobis palmatimb-fidis subfructu ampliatis et induratis, laciniis linearibus bispidis j ovario bispido ; stylo fere ad basin trifido, segmentis revolutis. Socotra, per montes abundans. B.C.S.^Nos. 366, 626. Scbweinf Nos. 360, 479. . UETICACE^. 169. Dorstenia GiGAS, Schweinf. : caulescens caudice crassissimo carnoso ramoso ; foliis oblanceolatis bullatis; receptaculo orbicular! margine 6-8-radiato, 96 Proceedings of the Boijal Society Socotra, inter rapes ad montes. B.C.S. N'o. 638. Scliweinf, 737. 170. Ficus (Urostigma) socotrana, Balf. fit. : arborea raniulis pubescentibus j foliis rotundato-cordatis molliter pubescen- tibus 5-nerviis utrinque alterne 5-8-costatis; stipulisvillosis; bypanth- odiis obovatis pubescentibus j acbseniis ovoideis levibus peri- anthio membranaceo inclnsis, Nom. Yern. Tuk. Socotra, abundans. B.C.S. bTo. 283i Scbweinf. No. 414. ORCHIDE^. 171. Habenaria socotrana, Balf. fil.: glabra caule gracili; foliis meinbranaceis oblanceolatis v. oblongis ; racemis elongatis floribus distantibus ; bracteis ovario brevioribus attenuato-acuminatis ; sepalis petalisque obtusis j labello 3-partito lobis linearibus calcare gracillimo ovario longiore. Socotra, in montibus prope Galonsir. B.C.S. No. 315. DTOSCOEEACE^. 172. Dioscorea lanata, Balf. fl: volnbilis caule tereti piloso ; foliis cordatis v. rotundatis v. reniformibus apice spinoso-mucronatis 7-9-nerviis subtus lanatis ; spicis solitariis axillaribus ; fl. J glomeratis, staniinibus 6, ovarii rudimento depresso triquetro ; fl. $ solitariis, capsulis pubescentibus. Socotra, in montibus Hagliier. B.C.S. No. 482. Nimmo. AMAEYLLIDE^. 173. Hjimanthus GRANDiFOLius, Balf. fil. : glaber et immaculatus; foliis magnis ssepe IJ ped. longis f ped. latis ovatis v. elliptico- ovatis acutis basi parum attenuatis v. plerumque rotundatis v. rotundato-cordatis margine vix uiidulatis tenuibus delicate veuul- osis, petiolo 1-1 J poll, lougo non vaginante. Socotra, in montibus Hagliier prope ^Tamarida. B.C.S. No. 194. f' 7 ! P of Edinhurgli, Session 1882-83. 97 LILIACE^. 174. Aloe (Eualoe) squarrosa, Baker : caulescens caudice sim- plex ; foliis parvis laxe dispositis lanceolatis patiilis maci'latis apice recur vatis aculeis marginalibus magnis crebris deltoideis ; scapo brevi simplici ancipiti ; racemo simplici cernuo ; pedicellis brevibus ascendentibus bracteis lanceolatis j peiiantliii cylindrici tubo brevi ; staminibus incliisis ; stylo exserto ; capsula parva. Socotra, in niontibus calcareis prope Galonsir infreqiiens. B.C.S JHo. 282. GEAMINE^. 175. Eriochloa vestita, Balf. fil. : oninino niolliter pubescens rigide ramosa; foliis crassiusculis rigidis brevibus; racemis paniculi 6-8, spiculis.compressis ovoideis; gluniis vacuis villosis pungentibus, glumis fertilibus muticis. Socotra, in cam pis calcareis prope Galonsir. B.C.S. N. 574. 176. Panicum rigidum, Balf. fil. : csespitosum ramis decumben- tibus radicantibus ad nodos villosis ; foliis brevibus rigidis ad apiceni vaginae villosis; paniculis laxis ramis ramosis plerumque glabris, spiculis omnibus pedicellatis ; gluma extima brevissima, glumis interioribus 2 subaequalibus 5-nerviis glabris obtusis, gluma florali levi obtusa. Socotra, prope Galonsir et Tamarida. B.C.S. ETos. 130, 56 L Scbweinf. E’o. 346. 177. Ehynchelytrum microstachyum, Balf. fil. : vix pedale plus minusve puberulum tenue; paniculi parvi spiculis 4 poll, longis; glumis secundis et florentibus tertiis apice bifidis lobis rotundatis, aristis glumis vix excedentibus. Socotra, apud Galonsir et Tamarida. B.C.S. i^os. 124, 254. Scbweinf. jNo. 467. 178i Eepturus tenuis, Balf. fil. : caespitosus breviter repens tenuis ; foliis angustis linearibus glaucis longis piloso^-puberulis ; spiels compressis ; gluma vacua solitaria plurinervia florenti gluma et palea dtiplolongiore ; stipite glumam minutam hyalinam gerente. Socotra, in campis orientalibus insulae. B.C.S. I^o. 572. VOL. XII. G 98 Proceedings of the Royal Society ISCHNURUS, Balf. fit. Spiculee l-florte in spica simplici ad excavationes rhaclieos com- pressse solitarisB, alternse, sessiles, rliacliilla brevissima supra glnmam inferiorem articulata ultra florem in stipitem brevem plerumque lloreni imperfectum gerentem producta, flore hermapbrodito. Gluma infinia vacua, rliaclii opposita, brevis, rigida, oblonga, truncata v. obtusa,basi incrassata tumida, 8-nervia,margine menibranacea; Horens tequilonga, membranacea, trinervia, apice obscure trifida ciliata; palea sequilonga, membranacea, 2-neryia. Stamina 3. Styli breves, dis- tinct!, stigmatibus pluiuosis. Caryopsis late ellipsoidea, compressa, glabra, gluma paleaque inclusa, libera. — Gramen perenne, nanum V. elatum, csespitosum, multicaule, foliis glaucis pilosis. Spica terminalis, rigida, tenuis, recta, spiculis parvis dissitis in rhacbi alte excavata quasi inclusis, gluma infima vacua semper adpressa. Genus nionotypicum novum Hordeearum bene distinctum sed Oropetio et forsan Lepturo affine. 179. I. PULCHELLUS, Balf. fit. : species unica in locis arenosis apud Galonsir crescens. B.C.S. Nos. 109, 301. Monday, Wi Febrnary 1883. Professor JENKIN, E.RS,, Vice-President, in the Chair. The following Communications were read 1. On Scientific Method in the Study of Language. By Emeritus Professor Blackie. 2. Further Bemarks on the Mirage Problem. By Professor Tait. BUSINESS. The following candidates were balloted for, and declared duly elected Fellows of the Society: — The Hon. Lord Kinnear j Mr W. Bowman ; and Mr K. H. B. Wickham. of Edhiburgli, Session 1882-83. 99 Monday, IWi February 1883. Shekiff FOEBES IEVINE in tlie Chair. The following Communications were read : — 1, On Ancient Tenure of Land in Scotland. By Mr Auldjo Jamieson. I deem no apology due for introducing to the notice of the Eoyal Society the subject of the present paper. The close and accurate 'criticism which distinguishes modern scholarship has allied all branches of knowledge in a common scientific system ; and the laws which regulate the development of human society are now recognised as being not less inexorable than those of which the operation on material objects is the more frequent theme in this room. To exhume the forms and types of ancient society, to subject them to close analysis, to identify their prototypes and trace their evolution in our modern life is not less a scientific study than to dig out the nodules of remote ages from those ancient records the rocks, and to subject them to that analysis which detects their identity with forms of life still extant. But with this difference in our present inquiry : the forms of existence of which the nodule is the repre- sentative have transmitted their characteristics through so great a succession and variety of forms as to make their identity with, or even relation to, any modern type distinguishable in most cases only by subtle processes of analysis ; they are themselves callous and dead, and have no direct contact with the life of the present day ; but the systems of ancient society have not undergone that process of extinction and disintegration in transmitting their characteristics ; it is less in the alembic that decomposes than by the scalpel that exposes, that their characteristics are discoverable; they do touch, and that often closely, the living present, and there is danger therefore that in the search for ancient truth a nerve may be sometimes touched that may send a thrill into living organisms in our modern society, aflame as some of these are at present with fevered sensa- tion and debate. I must disclaim at the outset all pretence to originality in either my investigations or their results ; my object and purpose will be to present in a brief and conventional form some of the more salient 100 Proceedings of the Boycd Society results wliicli recent scientific investigation lias reached as to the relations in which men have stood with reference to the soil of this land in the earliest days of which we have a record, and to trace hack to these pristine forms such of the main characteristics of our modern land system as derive their origin therefrom. The study of such subjects has of late progressed so rapidly, and the light thrown on the dark records of the distant past by the patient labours and skilful investigation of such scholars as Dr Skene, Sir H. Maine, and others, has been so clear and so searching that the time seems to have come at which it may be fitting for a mere- disciple to enter on the task — not perhaps altogether inappropriate to one brought often into practical contact with existing phenomena of the nature we are to consider — of identifying those characteristics of human experience in this relation of life which in the long evolution of society have stood the test of survival as the fittest for the later development of human life. • The task I thus undertake would necessitate at its outset an ethnological sketch of our Scottish land as we now know it ; but I will leap over many perplexing difficulties by assuming a general assent to the view that when the curtain rises on its modern history Scotland was thus peopled, — the Lothians, Fife, Forfar, and Aber-. deen, with a population almost wholly Saxon j Sutherland and Caith- ness with a race also Saxon, but largely Danish andl^orwegian; and all the rest of Scotland Gaelic, saturated in Galloway with Saxon or Frisian influences, and characterised in the same district by traces of a more ancient race; with fringes of Irish Gaels on the coasts of Argyll and of Danes and Norwegians in the Isles. I suppose the rough view which most men who thought on the subject at all had, until a comparatively recent period, formed of the growth of society, was its development from a family into the patriarchal form, and then a number of patriarchs combining with their respective families to form a community, a country, or a state* But nothing in this inquiry is now more clearly determined than that the unit of primitive society, and the centre of all archaic land systems was not the family, but the tribe. The family as we know it was a comparatively late creation, and I think we may doubt whether it had any definite place among our own forbears until Christianity lent its sanction to the domestic relations. Commu- of Edinburgh, Session 1882-83. 101 nity of wives unquestionably characterised that system out of which the Gaelic and the Saxon alike proceeded, and contemporaneous therewith was the community of land which was unquestionably the first form of tenure, if that can be called tenure which nobody held. The earliest traces that exist of social life in the past, and all the analogies that scientific investigation has discovered in the more modern types of archaic society which survive, point irresistibly to the conclusion that while individual rights existed and were recognised in personal property, the soil was regarded and treated as the common property of the tribe ; and naturally so, while as yet man sought his scanty subsistence in the 'chase and in the waters, and the untamed earth yielded to him in common with the beasts he hunted only the spontaneous tribute of its wild berries and roots. While it would be affectation to assert anything definite of a state of society which has left behind it so few traces, and these necessarily so indefinite, still one can discern the first germ of right and title in land in the right which the tribe itself naturally came to assert as against other tribes in the region within which it first began to settle ; the choice corries of the deer, the favourite pools of the salmon, above all, the dwellings of their dead, would begin to possess an individual value to that tribe which first began to haunt these localities, and other tribes would be taught to reverence what the one tribe had begun to value; and this was probably the dawn of land right and land tenure. The tribe first emerges with us from the darkness of barbarism at that epoch of its existence when restrained and coerced by the growth of population the nomadic habits of the race began to give place to pastoral life, and man began to assert his supremacy over the brute creation otherwise than by hunting them. When first the tribe or its individual components began to feed cattle the necessity of feeding ground made itself felt, and it is just at that point that economic history really begins; there is no trace of which I am aware of a common estate in cattle. On the contrary everything tends to the conclusion that among the early inhabitants of this land cattle was the form of property over which the individual rights of man was first asserted, and cattle became the measure in and by which other rights and property were appreciated. Cattle was the money ■ of the ancient people with whom we are now dealing, and 102 Proceedings of the Royal Society was at the same time the measure and token as well as the substance of their wealth. It is in Ireland that we must seek both the origin of our Gaelic tenure and the only reliable records of its early growth, while the original features of our Saxon system must be sought in the records that survive of the systems of our German ancestry. One important element in differentiating the Gaelic and the Saxon systems was the earlier Christianity of the Irish and Scottish Gaels, an element— that early Gaelic Christianity of ours — so thoroughly distinctive and so full of special influence, which has left deeper and more frequent traces on our national character and habits than those who distinguish only the catastrophes that signalise abrupt revolution can recognise or are likely to acknowledge. Giving therefore its due precedence to the more ancient system, the land which the Gaelic tribe held when first we can throw any real light upon it had ceased to be the mere grazing ground of the cattle : agriculture of a rude type had begun to be practised, and the land over which the tribe asserted its sway was of four classes — the land appropriated to the dwelling and its immediate surroundings, the land appropriated to cultivation, the land appropriated to pasture, and the land left free for the chase or otherwise unappropriated. This is the pristine and rudimentary form of land tenure and of society based thereon, which must be accepted as the uniform and invariable type which has prevailed over every part of the world in which man has risen above the level of the savage. ISTot only in Aryan communities of every variety and of all circumstances, but- in communities of Mongolian, African, and Polynesian descent. Modified it was of course by climate, and by soil, and by the innate habits of the people j but wherever men have begun to assert their supremacy over the earth and its products we find these four distinct stages of tenure : — first, the homestead with its yard, the only private or separate property of the tribesman j second, the cultivated zone round the aggregated homesteads, the ‘‘ field ” of the robust inhabit- ant of temperate climes, or the garden of those more bounteous climates where vegetables more than grains are the food of the people ; third, in races of a pastoral type the common pasture land ; and lastly, in all, the waste or unappropriated — the hunting grounds of Edinhurgh, Session 1882-83. 103 perhaps— but always the magazine from which, as it grew, the tribe drew its supply of fresh land for its increasing numbers. A very pleasing and simple picture of pristine society is thus presented, and one to which it would rather seem that there is an anxiety in some quarters to revert; it is well therefore to dispel delusions and to point out that this typical condition of ancient life existed with us only as an imaginary point from which to measure the advance to more developed systems. The influences which sway mankind now, swayed them in these olden times : the inexorable laws which operate now among the myriad incidents of our modern life ojDerated then with the same force; and it is interesting to distinguish their operation where we can discern the immediate succession of cause and effect so clearly as we can in those simple communities, just as we can best discern the growth of the organs of riper life in the rudimentary forms they present in the lower types of creation. ' What then are the influences to which the historian and the social economist attribute the growth and development of our race 1 Laying aside the influences of religion as operating in a different plane from that in which we are now moving in this inquiry, I apprehend physical energy and money, the active potentiality of brute strength, and the passive and accumulative force of labour and self-denial, of which wealth or money is the result and embodi- ment— are those forces which have operated and do operate most strongly on human action; the strong man and the rich man, the strong nation and the rich nation are those which dominate, and in our primitive society no sooner has the curtain risen on the simple pastoral scene I have briefly sketched, than the action of the drama begins by the strong man rushing in on the stage — the Saul of the tribe, lofty in stature and bold of heart, to claim the share of the common property due to his superior prowess — and we find the social equilibrium at once disturbed in order to find for this Kingly man his fitting tribute. Therefore in the Celtic tenure the mensal lands of the king and the lands devoted to his special maintenance were the first to be cut out of the common property ; the king had his own share of the lands as a member of 'the tribe, and he had the mensal lands besides to support his royal state. These mensal lands remained no doubt 104 Proceedings of the Boyal Society still vested in the tribe, and the king had hut a user of them for his life or office. Then came the church, and another part of the tribal lands — the ternal — was set aside for it. But an influence more powerful, perhaps because more subtle than even the regal and the religious, operated to disturb the equilibrium — money began to exercise its sway : dealing with the Irish as the oldest type of the Gaelic tenure, we find the share of the annual allotment of land was regulated by the extent of the herd of each member of the tribe perfect equality even in these early days was a matter of theory, and was maintained not because men ivere equal, but only until the supremacy of the fittest had asserted itself according to the inviolable law of progress; and as personal property was undoubtedly separate and individual, the thrifty, the skilful, the industrious, would soon become the rich in cattle, and would soon come to have an increas- ing share , of the common arable land, while the pasture was still common to all equally. Thence arose a very peculiar form of tenure; when one of the tribe became so rich as to have more cattle than he could find pasture for on his own allotment, he lent his surplus stock to less careful or less fortunate members of the tribe, who thus became his tenants'^ It is very notable that in this, which we must accept as the most pristine form of the relation between landlord and tenant, the landlord was required to contribute the stock as the essential element in the transaction, and the rent was paid not for the land but for the stock ; it is evident that the idea of a separate personal possession of the land was very imperfectly developed at that stage in the history of the tribe at which the power of money first began to effect a differentiation between the members of the tribe, and we have the germ presented to us of the relation now so familiar of landlord and tenant. But this rudimentary differentiation which we recognise in the Irish tribe rapidly grew, and it developed into one of the worst and most fatal, but still essential, characteristics of all early tenures and of all early society ; if it contained within it the germ of the land- lord and tenant of later days, it contained a germ of more dangerous import tO; and more immediate influence on, infant communities. * Skene’s Celtic Scotland, vol. iii. p. 142. t Idem, p. 147. of Eclinhutgli, Session 1882-83. 105 When the richer man contributed only a portion of the stock to a freeman of the tribe who already possessed some of his own, that poorer freeman had to return a third of the value of the stock annually for a specific period ; but when the freeman had no stock of his own, he had to give security for the return of the stock lent, and to pay a food tribute, the type and evidence of vassalage, twice a year. The former, the “ Saer Ceile,” were the antetypes and pro- genitors of the vassals of later times ; and the latter, the ‘‘ Daer Ceile ” or bond tenants, were the antetypes and ancestors of the serfs and servile races, from whom the charity of the church and the chivalry it begot in long years after, and with many a painful effort, struck the shackles of slavery. Dr Skene says : — With the Saer Ceile the basis was a mutual contract for a fixed period, usually of seven years, by which the chief gave a portion of stock proportionate to the food- rent he was to receive in return, and was entitled along with this to the homage of the tenant during the subsistence of the contract, and to a certain amount of service in the erection of a dun or fort, the reaping of his harvest, and the sluaged or hosting ; but the contract would be terminated and the parties to it return to their original relation to each other, either by the tenant returning the stock he had received or the chief reclaiming it. A more permanent connection was formed between him and the daor ceile or bond tenant. Here the ceile placed himself formally under the protection of the chief as his permanent follower by receiving a certain number of seds or cows, by way of subsidy or gift from the superior, and paying him a Certain tribute as the price of his protection. As soon as this relation was constituted he received an additional amount of stock in proportion to the food-rent he had to return, in the same manner as in the case of the free ceile. The real distinction probably was, that in the one case the ceile was in a more independent position, and possessed stock of his own as well as a share of the tribe land, besides what he received from the chief. In the other he was dependent upon what he received from the chief for the whole of his stock. When the chief reclaimed his stock from the free ceile, the latter had the option of becoming a bond ceile if he preferred doing so to returning his stock, and the chief was then bound to add the returnable seds to the stock he had originally given, which constituted the relation between him and the ceile as 106 Proceedings of the Boyal Society a permanent dependant. This process, therefore, not only led to the freemen of the tribe being gradually absorbed into the .class of the dependants or following of the chief, but placed a powerful weapon in the hands of the latter, by which he could transform his temporary free ceile into permanent and more servile dependants.” * The separate ownership of land by inheritance seems to have resulted in the Celtic tribes at first from a tacit prescription, the precise origin and foundation of which it would be very difficult to determine. The firm hold which from the first each member of the tribe evidently had on his homestead gave to the skilful breeder or the careful tender of his herd a fulcrum no doubt on which he could work the lever of his wealth; and when for three generations a family retained possession of land, that possession became the basis of title and of a right transmissible by the holder to the succeeding members of his family;! originated, it would seem almost by accident or intuitively the right of separate perpetual tenure, on which was raised the superior class of territorial magnates — ^the original chieftains of the septs and clans into which in its later development in Scotland, preparatory to its final extinction, the tribe broke up. And when that time for its extinction came, when Alexander III. died in 1286, and the fresher, freer, nobler influences of Saxon and Norman life stirred the stagnant system of Celtic society and gave life and vigour to our Scottish institutions, the form which the tribe had assumed in Scotland was this ; there was the central figure, the thane, possessing a large part of the lands as his demesne, represent- ing the mensal lands of earlier days, and very large rights of superiority and service from the inferior members of the tribe ; over these thanes there held rule more or less defined, and originating in circumstances exterior to the tribal organisation, the earls of the seven provinces, but that rule was less, I apprehend, a matter of land tenure than of personal rule; below the thanes came a class which can best be described as freeholders holding their lands in absolute fee, but bound as the condition of their tenure to give personal service and to pay certain definite and elaborately regulated duties; below them again came a class of free or kindly tenants, * Skene’s Celtic Scotland, vol. iii. pp. 172, 173. t Idem,^, 144, 107 of Edinhirgh, Session 1882-83. ‘‘liberi et generosi,” wbo held portions of land for ten or twenty years, or for life, with remainder to one or two heirs; these were the representatives of the Ceile of the Irish system, for in many cases the landlord provided the stock and implements, and the rent paid was higher in proportion to the value of these steelhow goods, the rent of the land itself being probably a fixed quantity. With these ended the grades of free tenure, but below these came two grades very important- to us as interesting historical types the agri- colse or rustici, who held land from year to year on payment -of a fixed rent, but were from their tenure of those servile lands them- selves serfs; and second, another class of serfs by whose forced labour the chief or thane cultivated his demesne, and who were in the strictest sense slaves. All ancient systems of society and of tenure are tainted by this bane of slavery, but the Celtic system seems to have been saturated with it, and it is a lurid light which these two classes of serfdom throw on the expiring system of our Celtic land tenure, a light which, before I conclude, I will seek to throw into some regions where I humbly think its illumination may be salutary. The whole framework of this Celtic tenure, with all its intricate arrangements of the clans and septs presenting an elaborate system of order and gradation, conforms but little with our notions of the freedom and breadth of the childhood of our race. The Eastern influence in the Celtic church is unquestionable, and the church exercised a paramount influence in forming the infant society of the Celtic race ; the same hard and inexorable rule, the same elaborate gradation, the same spirit of exclusiveness, and the same family pride which characterised the Celtic church as it expired before the more vigorous system of the Eoman obedience charac- terised the Celtic tribal development as it too passed from the stage of history. Was it from the unchanging East, that weird museum in which even now the worn out theories of human society seem preserved for our modern study, that the seeds of the disintegration as well as the germs of the development of Celtic society came ? The records of Saxon tenure, if in some respects less interesting than those of Celtic holding, are at least less obscure and indistinct ; and the labours of Freeman, Maine, and German inquirers, whose 108 Pfoceedings of the Boyal Society researches have been summarised with shill in an admirable paper by Mr Morier,* have thrown a vast deal of light on this subject. It is, however, at a comparatively late period of its development that the Saxon tenure can have had much influence on our Scotch land, at a period too when the orderly influences of the Western church had modified considerably its original character, and had prepared it to receive with ready plasticity the more sharply defined features of the Norman mould. The unit of the Saxon system was the mark,” which in analogy with Celtic and other Archaic systems may be described as the heritage of the tribe. Just as in the Celtic tenure part of this mark was held jointly by the whole com- munity as common pasturage or woodland j another section was divided into lots tilled by separate members of the community, but strictly according to fixed rule, and thrown ‘Open to common use so soon as the crop was removed; a third section was divided into small paddocks or holdings immediately adjoining the township. There seems to have been from very early times separate ownership in these last enclosures, and a separate ownership also in the tillage lands qualified by the common use of them for pasture after harvest. This system has often been referred to as containing the germ of that co-operative system of cultivation that commends itself to many in the present day as the most advantageous. It is perhaps somewhat fortunate that tliere have remained until a comparatively recent period traces of this system in both England and Scotland, which enable us to appreciate its real effects, and to discern its appropriateness or the reverse to our modern life. One of the most graphic instances of that survival we have thus recorded : — The two large pieces of common land called Dolemoors, which lie in the parishes of Congresbury, Week, St Lawrence, and Puxton in Wiltshire, were allotted in the following manner. On the Saturday preceding Midsummer day, o.s., the several proprietors (of the estates having any right in these moors) or their tenants were summoned at a certain hour in the morning, by the ringing of one of the bells at Puxton, to repair to the church in order to see the chain (kept for the purpose of laying out Dolemoors) measured. The proper length of such chain was ascertained by placing one end thereof at the foot of the arch, dividing the chancel from the body of the * Systems of Land Tenure, Cassell, 1870, p. 297. of Edinhiirghy Session • 109 church, and extending it through the middle aisle, to the foot of the arch of the west door under the tower, at each of which places marks were cut in the stones for that purpose. The chain used for this purpose was only eighteen yards in length, consequently four yards shorter than the regular land-measuring chain. After the chain had been properly measured, the parties repaired to the commons. Twenty-four apples were previously prepared, bearing the following marks, viz., five marks called ‘Pole-axes,’ four ditto ‘Crosses,’ two ditto ‘Dung-forks, or Dung-pikes,’ one mark called ‘Pour Oxen and a Mare,’ one ditto ‘Two Pits,’ one ditto ‘Three Pits,’ one ditto ‘Pour Pits,’ one ditto ‘Pive Pits,’ one ditto ‘ Seven Pits,’ one ‘ Horn,’ one ‘ Hare’s-tail,’ one ‘ Duck’s-nest,’ one ‘ Oven,’ one ‘ Shell,’ one ‘ Evil^ and one ‘ Hand-reel.’ It is necessary to observe that each of these moors was divided into several portions called furlongs, which were marked out by strong oak posts placed at regular distances from each other, which posts were constantly kept up. After the apples were properly prepared they were put into a hat or bag, and certain persons fixed on for the purpose began to measure with the chain before-mentioned, and proceeded till they had measured off one acre of ground j at the end of which the boy who carried the hat or bag containing the marks took out one of the apples, and the mark which such apple bore was immediately cut in the turf with a large knife kept for that purpose; this knife was somewhat in the shape of a scimitar with its edge reversed. In this manner they proceeded till the whole of the commons were laid out, and each proprietor knowing the mark and furlong which belonged to his estate, he took possession of his allotment or allotments accordingly, for the ensuing year. An adjournment then took place to the house of one of the overseers, where a certain number of acres reserved for the purpose of paying expenses, and called the ‘ out-let ’ or ‘ out- drift ’ were let by inch of candle. “ During the time of letting, the whole party were to keep silence (except the person who bid) under the penalty of one shilling. When any one wished to bid he named the price he would give and immediately deposited a shilling on the table where the candle stood, the next who bid Mso named his price and deposited his shilling in like manner, and the person who first bid was then to llO • Proceedings of the Boyal Society take up his shilling. The business of letting thus proceeded till the candle was burnt out, and the last bidder, prior to that event, was declared the tenant of the outlet, or outdrift for the ensuing year. “ Two overseers were annually elected from the proprietors or their tenants. A quantity of strong ale or brown-stout was allowed for the feast, or ‘ revel,’ as it was called ; also bread, butter, and cheese, together with pipes and tobacco, of which any reputable person, whose curiosity or casual business led him to Puxton on that day, was at liberty to partake, but he was expected to deposit at his departure one shilling with the overseer by way of forfeit for his intrusion. The day was generally spent in sociality and mirth, frequently of a boisterous nature, from the exhilarating effects of the brown-stout before alluded to.”* But we have, as is well known, in our immediate vicinity in the burgh of Lauder and at Newton of Ayr equally interesting survivals; —that of Lauder especially, where 105 burgess lots are held under a charter of 1502 renewing more ancient charters which had perished, and conferring power on the burgesses and community to break up and plough their common lands. The possession of one of these burgess acres or lots is essential to being a burgess, and only burgesses are members of the Town Council. The burgess acres consist of lots of from one and a half to three and a half acres, but the burgh holds besides a common of 1700 acres, which is thus dealt with. Once in every five or seven years about 130 acres of the common is set off to be ploughed up and culti- vated ; the part thus broken up is divided into 105 lots, and each owner of a burgess acre is entitled to a lot which is determined by lot. On the rest of the moor such of the 105 burgesses as are residents pasture each fifteen sheep and two cows, and the widow of a burgess pastures twelve sheep and one cow. Here then we have the Lauder burgess with his homestead” in Lauder, his share of the “ arable mark” in his acres, and his share of the “pasture” and “ waste” in the moor; and we have the Council of Lauder prescrib- ing to each burgess the kind of cultivation he is to pursue on the lot of the common land assigned to him. Somewhat similar tenures pre- vailed in Newton of Ayr,f in Crawford in Dumfriesshire,^ where * Holie’s Booh of Lays, vol. ii. p. 918. t Statistical Account of Scotland, vol. ii. p. 263. X Idem, vol. iv. p. 512. of Edinhwrgli, Session Ill even more primitive rules prevail, and Whitsome in Berwickshire and the system of cultivation which this tenure prescribed — by which the holder of each lot had to conform to the general directions of the community — prevailed widely in the run rig system which was so largely the rule a hundred years ago. The parish of Smailholni was all cultivated in that manner, and at Lihberton in Lanarkshire, and many other places, this system of agriculture, testifying mani- festly to the prior existence of some quasi-communal cultivation, may he distinctly identified, f And there are some other traces of a regulation which reflects much light on the real nature of this tenure. At hTewton of Ayr there were very special provisions as to the succession to a burgess ; and it not unfrequently happened that as females were excluded, a lot lapsed by the failure of an heir qualified to take it up ; it then reverted to the Community^ which disposed of it to the most industrious and fit inhabitant of the place. This, if it could he traced in other cases, would be most interesting, for it would con- nect this old Saxon tenure of ours very closely with its pristine origin in the distant past in the very cradle of mankind — showing as it does that the tribe or commune was still the radical owner of the soil, and the tenure of individuals only accidental^and con- necting this tenure of the Lowland village with those tenures of Eastern and some German types where the right of pre-emption is re- served to the community or its members, and with that provision we are all familiar with, whereby at stated periods of jubilee the tribe re- claimed its lost inheritance from private ownership, and the members of the tribe started afresh on a fresh lease from their mother tribe. J In the rapid and necessarily very incomplete sketch which I have thus given of the early tenures in this country there are some notable features which challenge observation in these days. The first of course is the trite but by no means unchallenged observation that the very origin and germ of progress and civilisation is the recognition of individual right. Mankind in the mass remained inert and indolent in the dim twilight of the earliest days : it was man that rose to vigour and action and progress when he asserted his * New Statistical Account, vol, ii., suh voce. t Statistical Account, vol. iii. p. 217, vol. ii. pp. 98 and 242. t New Statistical Account, sub voce. See also Fenton’s Early Hebrew Life, pt>. Vl-73. 112 Proceedings of the Eoyal Soeiety individualism, and when the leaders of men, spurning the dead level of uniform stolidity, became the pioneers for their fellow-men. No progress — no attempt at progress— is discernible during the dim, ages when the land owned no separate title ; it was only when what for lack of a better word I must call selfishness contributed its ferment to the inert mass of humanity that the individual sporades developed that activity which we call progress, and of which the product is civilisation. The second observation flows out of the first : the cultivation of the soil, though the oldest of the arts, is still an art itself of which the basis is experience and the spirit is experiment. Even with our- selves those who are the most proficient in the art desire to free our agriculture from the trammels which seem to them to repress and restrain its still nascent capacity ; the freedom of culture desired by many is justified on the ground that successful experiment may reveal fresh methods and more adequate modes of culture. But under any conceivable modification of the Saxon tenure progress was impossible, because experiment was impossible and change impracticable. The same uniform rule of culture had to he followed in even the separate tillage lots because all were interested in the con|- mon cultivation ; every one had to sow the same crop and to cultivate it in the same way, and the fields had to be cleared for the common pasture on the same day; much of the sluggishness of English agricul- ture may be distinctly traced to the surviving influences of that Saxon tenure which imposed those fetters of iron custom on the cultivation of the soil from which hardly yet have English agriculturalists emancipated themselves. In Scotland the Board of Agriculture in 1798 say: — “In former times there were several commons in which the cattle belonging to different proprietors went promiscuously under one herd or keeper. The arable land also was possessed in alternate ridges, separated by broad balks, on which the large stones were when the indolent husbandman could take that trouble, and was pastured by the cattle after being freed from the crops. Lands thus awkwardly possessed and wretchedly managed, might not im- properly be called wastes ; and though Acts of Parliament passed as early as 1695, for dividing at the instance of any proprietor having interest, yet no advantage was taken of such beneficial laws till the 1738 or 1739, when the lands were parcelled out among the several proprietors in proportion to the valuation or rate by which they 113 of Edinburgh, Session 1882-83. paid the land tax.”* ISTor where Celtic customs prevailed can we discern any greater evidence of progress : we have few traces of how the Highlands were cultivated in very ancient times, hut when we first begin to acquire definite knowledge there is much to show that the effect of the ancient tenures had been to arrest rather than pro- mote active and beneficial cultivation of the soiLf Time will not permit of my adducing detailed evidence of this — let me call one witness, no unfriendly one, to the past he reverenced or to the Highlands he loved. Cosmo Innes says, speaking of the rental in 1600 of the Gordon estates, which extended from Banff through the heart of the country to the western sea : — “ In all that vast estate reaching from sea to sea, and across ranges of mountains now every- where pastured by sheep and cattle, there is no payment of wool or woollen cloth, nor of hides or skins, nor any amount of sheep and cattle beyond the occasional mart or wedder for the lord’s table. In fact there were at that time no cattle or sheep reared in large flocks and herds in our Highlands. The space and pasture were the same as we know them now, but the thousands and millions of sheep which graze them now had not yet taken possession. The first introduction of large flocks of sheep into the Highlands was in the last quarter of last century. Gough the antiquary, writing in 1780, says that Mr Loch’s plans for introducing sheep had been ‘ attended with some success,’ and that the sheep promised to thrive very well in the Highlands. But at this time (1600) there were nothing but the petty flock of sheep or herd of a few milk cows grazed close round the farmhouse, and folded nightly for fear of the wolf or more cunning depredators.” J The third observation I would make is this, that the admiration and affection for these ancient tenures professed of late appears to be based on the idea that they were of a highly dem^ocratic and Universalist type ; there can be no greater mistake ; whether we take the Celtic sept and clan or tribe, or look at the Saxon community \vith its mark and its gemote, we find a system of rigid exclusiveness, an aristocracy in tenure, an oligarchy in government. There was * See Antiquary, vol. iv. p. 101. t See Letters, vol. ii. p. 34 et seq., for condition of agiiciilture even in the last century. + Cosmo Innes, Scot. Legal Antiquities, p. 263, VOL. XII. H 114 Proceedings of the Poyal Society originally no doubt a certain rude equality, but it was only “ pares cum paribus,” and tlie “ peers ” were few, tlie commons were tlie many. Tlie Celtic tribe was an exclusive corporation to which birth within its own purple was as essential as it was at the Court of the Empire : the Saxon freeholder was an aristocrat of the bluest blood — no base intruder was permitted to share the privileges or the powers to which the freeholder alone was born — ■ it was oligarchy saturated with caste. The essay in which Mr. Freeman identifies the wittengemote, which has been to many the type of popular self-government by landowners of a common estate with the House of Lords, not the House of Commons, forcibly illustrates what I say ; but the case of Lauder illustrates it in a startling though a more homely fashion. There there are 105 free- men, and they have successfully resisted the claims of the profane vulgar of that august city to participate in their privileges : one would regret that anything should happen to shatter so interesting a petrefaction and crystallisation of ancient tenure, but a tenure which maintains an exclusive right of 105 persons to appropriate the ancient common property of the “ gemote ” is not what I should designate as a peculiarly popular system ; it is most interesting that these village aristocrats should share the arable mark and feed their fifteen sheep apiece on the common waste of Saxon tenure, as their fathers did in the , time of the Maid of Norway ; but though history would have lost a graphic illustration it would not seem to me that humanity would have suffered an irremediable loss had the common estate of Lauder assimilated itself to modern tenure and been devoted to the homely function of bringing in water and clearing out the sewage of that ancient, not to say archaic burgh, even if in the process individual had taken the place of communal right. It is seven centuries since these ancient systems we have been considering have exercised any direct or practical control over the tenure of the land in which we live, seven centuries full of change and of incident, powerful enough even if compressed into a briefer period to have severed any connection which the active life of the present day could have had with the defunct systems of an almost prehistoric age. But while no doubt much pedantry and affecta- tion have been of late exhibited in the attempt to ascribe to these archaic systems an influence on our modern institutions which it of Edinburgh, Session 1882-83. 115 is ini2:)ossible for the real student to recognise or admit, still we must bear in mind that those feelings and sentiments which affect the relation of man to his mother earth are deep enough to permit the roots of society to sink into them far below the stage on which the prominent drama of history is enacted ; that relation underlies the very framework of society itself, and systems which have regulated the relation of man to the earth which bears him and feeds him continue to exercise a powerful influence over his imagina- tion and feelings long after they have ceased to operate on the actual circumstances of his outward life. Nor from the analogy of other sciences need we be surprised if this recent stirring of these substrata of our early society gives birth to strange efforts to revert to ancient types; these efforts are no doubt due rather to individual eccen- tricity than to general conviction, just as in nature we find occasional specimens of highly developed species which exhibit a sportive in- clination to revert to primeval types from which lengthened cultiva- tion has really far removed the whole class to which they belong. There are, however, not a few side lights which the fitful gleams we get in studying these ancient types of society may throw into the origin and pristine circumstances of those relations which subsist in our own day. For instance, the theory of rent most acceptable to modern economy and most consonant with modern circumstances is that which represents the rent as the share falling to the land- owner of the profits of a quasi-partnership, to the capital of which the owner contributes his land and the tenant his stock, his labour, and his skill. Very ancient types of society justify this theory, and in many parts of Europe more subject to Latin influ- ences than we have been it survives in the metayer systems which prevail ; but it is on the whole a modern development, and bears abundant evidence of its origin in a state of society much more cultivated than any of those we have been considering. The rent of our ancient tenures was originally in the main personal service, and even when it began to assume the form of money payment it was a pecuniary substitution for such services or for that direct mainten- ance in bed and board which the king or the chief exacted ; and it was always fixed and definite, bearing no necessary relation to the value of the land. The foundation of our ancient relation between landlord and tenant was not, I apprehend, partnership but sale ; a tenant did not share the produce with his landlord, he bought the 116 Proceedings of the Royal Society temporary use of his farm for a certain price payable by instalments during the lease ; he was more a temporary feuar, or a copy holder, than a tenant in our sense of the term. And herein lies a very important and curious distinction between ancient and modern economy, which is the key to many difficulties ; with us, the price of an article and its value are almost convertible terms, but it was not so of old, it was not so not very long ago. Price was fixed in the ancient times I speak of by custom, and when we read with wonder of statesmen in even modern times seeking to fix the price of viands by enactment they were only struggling with the idea which in pristine societies fixed price by inveterate custom. Even now in India there are districts where the price of shoes for instance is fixed by inviolate custom, and the shoemakers adapt themselves to circumstances not by altering the price but by modifying the quality of their goods ; and not very long ago in some European countries the price of the loaf was fixed and its dimensions fluctuated. How in England we know that the rent of the land has not even yet borne the same intimate relation to its value it has done in Scotland ; the rent which a man’s father and grandfather paid before him has lingered there as an almost customary rent different in degree rather than in principle from the really customary rent of the copyhold tenure ; and the commercial principle which our modern practice especially in Scotland has introduced of close identity between value and price has in England penetrated with the slow- ness proverbial to agriculture into the relations bearing on land. I think there may be some of the unsolved problems of this relation upon which the consideration of what I have thus referred to may throw a little light. Another ancient fact bearing on the landlord and tenant of our modern experience seems worthy of some note j the pristine form of that relation was, as I have already shown, of an alternative character. The tenancy might be one practically of steelbow, in which the land- lord supplied stock, implements, and the scanty housing if any ; or it might be that by which the landlord sold temporarily the use of his land only, leaving the tenant to supply himself with all that he required for its cultivation. It was this latter form mainly that survived into later times. "We have of course no written leases re- maining to us of the very early times to which I have been specially referring; but those early leases which do remain entered into at a of Edinburgh, Session 1882-83. 117 (late when owing to the inveterate habits of a rural people, the main features of the early contract must have survived, the stipulation that the tenant should supply the houses, (fee., required for the proper cultivation of the farm is to be found. In a lease, for instance, so early as 1312* it was stipulated that the tenant should supply suit- able buildings for himself and his husbandmen, which were to be left at the end of the lease ; after an interval of two centuries, under the next earliest lease of which I have seen any note, in 151 1 the tenant is taken bound to build three onsteads to be inhabited by himself and his dependants under pain of forfeiture j a crofter is taken bound to build a rood of enclosure for every, cow he has on the lands of the principal tenant j and in two cases tenants were taken bound to build houses on their farms, but were allowed to retain a part of their rents to assist them in doing so. These were church lands, and we may be sure these stipulations represent nothing more severe than the usual tenure, but probably the reverse. Now such a system was quite consistent with the idea of a partial or temporary sale of the subject, which was the bare land, not as in steelbow the land equipped with stock and appliances of which the wattled houses of these early days formed probably no very important part ; but it was quite inconsistent with the more developed ideas of modern economy basing the lease on quasi-partnership, and was not suited for our modern use with the more important outlays now required for modern agriculture. It is well, however, to discern from these examples that the principle now universally recognised as the best, which imposes on the modern landlord the necessity of supplying all that is required for the full equipment and beneficial cultivation of the farm, or of recouping to the tenant what he may dispense for such purposes, is ho exhumation, as has been often represented, of ancient custom or tenure ■ — no reverting to a more generous system long forgotten. Antiquity knew nothing of the kind, or if the steelbow form of lease is to be taken as the archaic type of what is advocated, then the experience of seven centuries and the advance in independence of the agricul- tural class have demonstrated that that system is unsuitable, for it has failed to survive. It may be less interesting but it is certainly safer, instead of searching for principles and precedents for our present guidance among the archaic systems of the past, to recognise that even the highest forms of these were datum lines from which to * Innes, Legal Antiquities, pp. 263, 264, 118 Proceedings of the Fi,oyal Society measure our own advance. The history of land tenure is the history of progressive emancipation ; to represent the changes neces- sary to adapt it to our advance in economic science and social de- velopment as a process of reverting to the spirit of ancient practice is to subvert the teaching of history; it is to the progress, not the retrogression of ideas on this as on other topics that we have to ascribe the advance we have made and are making ; it is what is most fit for our modern life that survives, not what may he most interest- ing or picturesque. hTo section of the inquiry into the relation of man to the soil is so difficult of solution as that which relates to the poor, and none to us of the present day is more interesting. If, as seems to he thought hy many, there were days in this land in which the poor were not always with us, no wonder longing glances are thrown backward to catch even amidst the darkness of barbarism glimpses of so happy a condition. But a closer study of the facts dispels the illusion ; besides the abnormal growth of population to which the Duke of Argyll referred in a recent essay (which is, in my humble opinion, the ablest contribution yet made to the economical treatment of this subject)* there are other elements — two especially — which do not appear to me to have received adequate consideration ; if the days to which we have been referring were ignorant of poverty, it was greatly due to these facts, that slavery held its place in their economy, and that the habits of all classes of the people rendered them to a large extent independent of external supply — they were largely self- sufficing. The nature of the slavery of these remote times it is very difficult accurately to distinguish ; it was certainly of at least two distinct forms. There were the serfs, the nedivi, probably the descendants of an ancient race, often the members of tribes which had been subjugated by stronger neighbours, always attached to the land, and not apparently removable from it even with their assent, and almost certainly not without it. These serfs were slaves in this respect that they had neither in the Celtic nor in the Saxon economy any rights; but if the land held so tight a grip on them, they in turn held a tight grip on the land, and had certainly claims on their lord or owner, though whether these claims were those of an * See Contemporary Review, January 1883. of Edinhurgh, Session 1882-83. 119 inherent right to support or proceeded merely from the self interest of the lord himself in the preservation of his property, it is very difficult to say. But below these there was a class of slaves who were mere personal property ; probably orignally captives of war, but latterly in many instances freemen who had been reduced to want, and who sold themselves as a condition of receiving maintenance and pro- section from the powerful and rich ; and this sale affected their posterity. While there seems very little doubt that the position of the pre- dial serfs even if originally equivalent to that of slavery became latterly a mere form of tenure of service, and that they had probably to endure none of the degradation of positive slavery, there can be no doubt that it was not so with the other class. Theirs was a slavery from which men fled in horror, and to which they were dragged back in terror and in chains. The early Acts of Parliament abound with evidence of this and with directions for the recovery of fugi- tives, and even in the 14th century slaves were recaptured, and handed back to their owners under sanction of the law. These were the poor of the ancient tenures, and we can readily discern why they were so largely dependent on the lords of the soil for maintenance and defence ; their gradual emancipation from actual serfdom or slavery followed insensibly on the development of the church and the progress of society, but their dependence on the chief or lord continued, and while they swelled the train of his followers they looked to him for support. This was a burden which speedily began to press on the chiefs in the Highlands, and although plague, pestilence, and famine came largdiy to their relief, the growth of the population impelled them insensibly into that turbulence and rest- lessness which distinguish the annals of our Highland life ; it is not perhaps so picturesque as one would wish to ascribe the frequency and the fierceness of Celtic feuds to the mean necessities of the larder, but these economic forces were too powerful to be ignored in any veritable history of the clans. It is very interesting to those who study these ancient forms of life to find extant, or only recently extinct, forms of society possess- ing all the main features which we have reason to believe character- ised these early days in our own country. The practical experience 120 Proceedings of the Boyal Society of men like Sir H. Maine and Sir George Campbell and other scholars who have applied their knowledge of the Aryan races in India to the elucidation of our Scotch archaic history has thrown much light on the subject; but I think a speech made a few weeks ago by Dr Hunter in the council of the viceroy on the treatment of the people of the Deccan is singularly illustrative of the subject I am now treating. “The peasantry of the Deccan,” he said, “have been suffering from economic causes sufficient to break the spirits and to ruin the fortunes of any race. Seventy-four years ago, when the Mahrattas and the peasantry of the Deccan passed under our Government, they had five great sources of liveli- hood. The economic and political changes brought about by British rule have deprived them of four of these sources and left them only one. In the first place, the Mahratta race had, during nearly two centuries, derived a large, although a fluctuating, income from war. Its pillaging invasions of wealthier provinces were reduced to a system of strictly mercantile adventure, which enriched alike the fort of the chief and the cottage of the peasant. For the Deccan hordes were not the accidental product of any single leader, but the natural result of an overflowing peasant population under the guidance of a hereditary administrative caste.” I thought I had read this before, and turning to Cosmo Innes’s charming essays on our early Scotch life, I found this : — “ The power of the chief or laird was measured by the number of men he could turn out under arms, and he had every inducement to maintain the full number of dwellings and inhabitants. In summer the people of the glen might exist upon the produce of their pasture lands, and there was a little corn for the beginning of winter, but for the rest of the year they must necessarily have sought sustenance elsewhere. They could not dig, to beg they were ashamed. There was a third alternative, they left their glens and lifted'' Dr Hunter goes on to show how the advance of civilisation has dried up the sources of the former wealth and even subsistence of the Deccan peasantry, and we could tell the same story of our own land ; the looms of Galashiels and Hawick have silenced those in the Highland glens, and all the manifold changes that railways and steamers have introduced into the habits of a people formerly so self-contained and self-suflicing have conduced to the reduction of * Innes, Scottish Legal Antiquities, p. 269, of Eclinhurgh, Session 1882-83. 121 the value of such labour as the Highlands supplied. Lassalle and Karl Marx in their crusade against modern plutocracy have depicted with great force and skill the vast difference which there is between a system of society which is content to supply only its own necessities from day to day and that high pressure of modern life, which, stimulated by capital ever eager and hungry for gain, manu- factures on speculation, and anticipates demand by an ever-ready and often over-abundant supply. Lassalle, speaking of the feudal lord of Germany, says : — “ Look upon the landed proprietor during the middle ages, the noble lord surrounded by his castles, his manors, his vassals, serfs, and dependants, his allodial villages and tributary towns. Was this man a capitalist*? Let no one suppose that people lived on the produce of the land only, which is the crude notion of some people. Production was sufficiently developed, luxury considerable, and the articles of consumption manifold and refined.” He then proceeds to give from mediseval writings a description of prevailing fashions in wearing apparel, furniture, and the like, showing the advanced state of fashionable society then and its varied requirements. He shows how all these are provided by the combined contribution of vassalage, by what he calls a “ mosaic work of services.” Under this system man is no longer a slave, but his will is the private property of another. There is an exchange of services and natural products without the intervention of money as a general measure of value. “ The acres of the feudal lord” he points out “are cultivated not only by serfs but with the help of man and beast, by means of villenage more or less reasonable in extent, varying from three days in the week to five or six weeks in the year, according to the position of the feudal dependant.” Then again, he says, “ put your- self in imagination back to one of the days for collecting the yearly revenue, when the -feudal lord receives his dues. Then you will see heaps of corn and barley, chicken and bacon, oxen and swine, eggs and butter, oil, fruits, wax, candles, honey, yea even cakes, bouquets, and cliajpeaux de rose^ all contributed by his faithful lieges. The tailors and shoemakers of the small town under his protectorate, re- membering the principle nuUe terre sans seigneur ^ bring their clothes and shoes which have been made during the week’s service they owe him.” Similarly he enumerates the various tradesmen and artisans 122 Proceedings of the Eoyal Boeiety who are bound to contribute their respective portion of the lord’s requirements in natural or manufactured goods ; and a long invem tory of services rendered to his household by their wives and others belonging to them follows, all to show “ that scarcely a want can be conceived which is not provided for by some special obligation in this system of natural services. Even professional men like advocates must give their advice as a duty, free of charge, to the lord of the manor. His amusements even are provided for him by his own dependants free of charge. He is a wealthy man, without the possession of money ; for he cannot turn these services or com- modities into capital. He avails himself with a vengeance of all these means of enjoyment which are thrown with such profusion around him, and he does it cheerfully without care or worry, and thus is more happy than the rich speculator of modern days whose tranquil enjoyment may be disturbed by a passing thought about the money market as he listens to the music of Beethoven or Mozart. But beyond consuming with enjoyment the feudal lord has nothing. He has no means to multiply his wealth by itself ; not money but service was the common bond uniting all the mem^ bers of the empire among themselves and under a common head, “ By this system of fixed services and mutual obligations no room is left for capitalistic enterprise or industrial progress, the whole pro- cess of production receives a stereotyped form, agriculture and the trades run on without change in the same groove.” * The Highland chief of old lived very much as, Lassalle so pictur- esquely points out, the old feudal lords lived, if upon their people, yet with them and among them ; they supplied all his wants, and these supplies and their personal services fulfilled all their obliga- tions. The people had no money, and they needed none ; they paid their rent in kind or by service, their necessities were few, and their commerce had not risen above the rudimentary Stage of exchange ; the chief had no money wherewith to import foreign commodities, and he lived in the rude plenty which his people supplied ; when his supplies failed we know how they were replenished. All these influences have told on the poorer class in the Highlands especially, and it is interesting and may be useful to inquire how modern economy has coped with the difficulties presented to it by the extinction of ancient habits and resources. * Socialism. Henry S. King & Co., 1874, p. 73. of Eclinlurgh, Session 1882-83. 123 To translate the serf and the slave of ancient life into modern language, I would use the word dependant ” ; that I think con- veys more of the spirit of the ancient relation with its mutual ser- vice and protection than the terms of slave and serf, which convey a harsher meaning than probably describes the true nature of the tie which bound the earliest predecessors of the chiefs to those below them. ^^"ow, in our modern life, how has this relation adapted itself to modern systems? The chief, though deprived of the ser- vices of his dependants, has been forced to maintain and protect them; not in the grand patriarchal manner of ancient times, and with none of their pomp and panoply of war, and with none of their keen zest for raids and marauds ; he has to pay poor rates. Eut translated into the vernacular of our modern life he has no light burden thus to defray. I have taken ten parishes in Inverness, and eight in Ross, of which the gross rental in the one case is £58,000, in the other £64,000; of the £58,000 in Inverness, £15,800 is paid by tenants under £10 ; of the £64,000 in Ross, £17,500 is paid by tenants of the same class. The poor rates paid in the ten Inverness parishes amount to £6200, in the eight Ross parishes to £8300. I cannot state accurately the school rate, but one of the inspectors in his last report says it varies in one of these districts from 2s. to 6s. 8d. per £. I have taken it at the lowest amount, and we have thus in the Inverness group an assessment of £12,000, and a rental under £10 of £15,800 ; in the Ross-shire group an asse.ssment of £14,700 a rental under £10 of £17,500. Now I cannot here attempt to determine what precise proportion of that assessment is due to the special necessities of the small tenants under £10, but everyone will admit it must be very large. For the maintenance and education of the poor in these districts the land has to pay annually about 90 per cent, of the nominal rental under £10, and a proportion of course very much greater of the real rental actually drawn. It is safe to say that more than the whole rental under £10 is required to defray the expense of maintaining and educating the poor. It can hardly therefore be said that the survival of the relation between the land and the poor from ancient times, if it has been in many respects painful to those who were the dependants of the old chiefs, has been favourable to the successors of the chiefs themselves — the fathers no doubt ate sour 124 Proceedings of the Eoyal Society grapes in tlxe olden time, and the teeth of the children have been set very much on edge by the operation. But the landlords are not the only survivals of those on whom the poor of the ancient times were dependent; as stated by Mr Innes, and as illustrated by many a stirring tale of old, others besides the landlords were made to contribute to the necessities of the noble peasantry of the glens. When in 1856 and in other years, as now, the successors of the douce provosts of olden times invite us to contribute to relieve the urgent necessities of the suffering Highland poor, they are only putting into modern language the levy their predecessors would have made upon us to pay the black mail the clans would have exacted when their domestic means of subsistence failed, as they have done. At no time within modern history, since population began to grow beyond very narrow limits, have several of the poorer districts of the Highlands been able to supply their own needs ; there has never been a time when the plenty of one period has there sufficed to meet the scarcity of another ; whether the levy has been by war, or by tax, or by charity, extraneous aid has always had to contribute its quota. As the Duke of Argyll has recently reminded us, nature in old times, when population outgrew its bounds, asserted her inexorable laws by sending plague, pestilence, and famine to clear off the surplus ; our modern civilisation has curbed these powers, as well as repressed the social characteristics which accompanied and assisted them, and thus is presented to us the same problem, though within far narrower limits, which is pressing on the Government of India — the growth of a population at a rate far in excess of that in ancient times, bringing on our modern economy and social science burdens due to their own beneficence. The suggestion so frequently made of late that the poorer cottars and crofters of the Highlands are the inheritors of ancient tribal rights in the land is, as I have already shown, quite fallacious ; the relation of dependence in which that class unquestionably stood not only in feudal times to the later lords and chiefs, but in still earlier days to the original freeholders of the tribal organisation, did not permit of their having any rights ; the exclusive system of the tribe, the restriction of all rights to the freemen, forbid the possibility of any rights in the land having been held by those who were below that rank ; and there can be no doubt that the freemen of the tribe of Edinh'imjh, Session 1882-83. 125 grew into the chiefs and the lairds, the feuars and kindly tenants of later days, of whom the- cottars and crofters are in no sense repre- sentatives. Here, again, I would point out how dangerous it is to refer to analogies in those early days without due care in establish- ing their identity with the modern circumstances they are intended to illustrate. It is a safer course to let these dead systems bury their dead — and to apply ourselves to the careful study of our own social problems by the brighter light of our own social progress. In that light it humbly appears to me that the frequent recurrence of Highland distress is a reproach on our modern economy from which ancient systems were free, however that freedom was obtained. It is foreign to the subject of which I treat to pursue this subject, but this I may say, that dealing with people who have been for ages habituated to be led, to be dependent for guidance on others, to be protected by others, who are only emancipated but not yet free, if our modern system is to fulfil the duties it has inherited from the past, it must supply that initiation and guidance and motive power and influence which of old, under very different circumstances and in very different directions, the chiefs of these people supplied : to parody a well-known aphorism, relief is no cure : it is the proper task of modern economy to show these people the method, to induce them to adopt the measures, and even to supply them with the means to win that independence which is a nobler, and will be a more useful inheritance than any that they claim from the distant past. I had intended to say something as to the taxation on the land of these ancient days and its relation to our modern imposts, but I have already far exceeded the limits of my paper and must conclude. I have fulfilled my purpose if I have directed attention to, and created any interest in, the salient features of those ancient tenures which are in any way reflected in our present social system ; and if I have succeeded in demonstrating that after all it is more as studies and as cabinet specimens than as models that we must regard them j that they were only the nurseries of society, not even its schools ; interesting and picturesque no doubt, attractive but deceptivej festooned with the mosses and encrusted with the lichens that adorn the decay while they conceal the defects of hoar antiquity^ 126 Proceedings of the Boyal Society. Table showing Rental, Poor Rates, and School Rates of certain Highland Parishes, 1881-82. Gross Rental. Rents under £25. Poor and School Rates on Gross Rental. PARISH. £25-10. £10-4. £4-0. Total. Over £25. Poor Rates assessed. School Rates assumed at 2s. To- gether. 1. Portree, . . £ 2. Kilmuir, . . 3. Snizort, . . 4. Diurinish, 5. Strath, . . 6. Sleat, . . . 7. Barra, . . . 8. S. Uist, . . 9. N. Uist, . . 10. Harris, . . 1 8,314 6,119 5,802 7,702 5,308 4,440 2,217 6,680 5,443 6,141 2 1,697 1,071 674 531 366 233 167 609 458 370 3 1,454 1,195 1,162 1,697 739 440 186 1,874 1,281 1,014 4 467 48 202 678 492 542 483 1,084 381 359 5 3,618 2,314 2,038 2,906 1,597 1,212 836 3,567 2,120 1,743 6 4,593 3,736 3,715 4.646 3;587 3,099 1,345 3,018 3,152 4,278 7 1,039 484 628 481 552 481 369 807 681 665 8 831 611 580 770 530 440 221 668 544 614 9 1,870 1,095 1,208 1,251 1,082 921 590 1,475 1„225 1,279 £ 58,166 6,176 11,042 4,736 21,954 35,169 6,187 5,809 11,996 1. Barvas, . . £ 2. Lochs, . . 3. Stornoway, . 4. Uig, . . . 5. Lochbroom, . 6. Gairloch, . . 7. Lochcarron, . 8. Applecross, . 3,212 4,671 14,139 5,229 15,089 11,588 5,758 4,401 203 69 3,106 92 498 493 833 299 678 420 2,542 706 1,465 930 574 619 1,581 1,686 2,475 732 1,007 1,096 278 698 2,462 2,175 8,123 1,530 2,970 2,519 1,685 1,616 668 2,423 4,556 3,656 12,085 9,005 4,052 2,732 535 855 2,002 620 2,011 1-,158 359 751 821 467 1,413 522 1,508 1,158 575 440 855 1,322 3,415 1,142 3,519 2,316 934 1,191 £ 64,087 5,593 7,934 9,553 23,080 39,177 8,291 . 6,404 14,695 The sum under column 1 includes in addition to Nos. 5 and 6, the rental of land held by school boards, &c. 2. On the Microscopical Appearances of Striped Muscular Fibre during Eelaxation and Contraction. By Pro- fessor Eutherford. BUSINESS. In terms of the Laws, a ballot took place for the following pro- posed Honorary Fellows : — As Foreign Honorary Fellows — Luigi Cremona, Eome; Julius Hann, Vienna; Charles Adolphe Wurtz, Paris. As British Honorary Fellows— Joseph Dalton Hooker^ Kew; Dr Spottiswoode, London; Professor Williamson^ London; Col. Henry Yule — who were all declared duly elected as Honorary Fellows. PROCEEDINGS OF THE EOYAL SOCIETY OF EDINBURGH. VOL. XII. 1882-83. No. 114. Monday, March 1883. The Eight Hon. LOED MONCEEIFF, President, in the Chair. The President read a communication from the Science and Art Department, South Kensington, London, in reference to the Inter- national Electrical Exhibition to he held in Vienna. The following Communications were read : — 1. On the so-called Bicipital Eibs. By Professor William Turner. In this paper an anatomical peculiarity was described which is occasionally found both in Man and the Cetacea. It is not due to a bifurcation of the shaft of a single rib at its vertebral end into two heads, but to the fusion of what ought to have been the shafts of two distinct ribs into a common body, and it invariably occurs at the apex of the thorax. Although the author had long been familiar with dried specimens from the human body in the Anatomical Museum of the University of Edinburgh, two cases which he now describes were the first that he had seen in the subject itself in the course of nearly thirty years’ experience as a teacher of anatomy, and it is remarkable that they should both have occurred within a few months of each other. A third specimen occurred in a skeleton in the possession of one of his pupils, Mr Minas S. P. Aganoor. A specimen from a large Cetacean was also shown and described. It formed a part of the skeleton of a Balcenopfera, some of the bones of which were found in 1859, others in 1863, embedded in clay in VOL. XII. I 128 Proceedings of the Royal Society Christie’s brickfield, in the carse land near the town of Stirling, and about 100 yards from the bed of the Eiver Forth. They were lying in the “blue slink,” from 13 to 14 feet below the present surface, and from 3 to 4 feet above the present high-water mark. The following conclusions were stated : — 1. In both Man and the Cetacea cervical ribs are occasionally developed in connection with the 7th vertebra. 2. In both the cervical ribs may remain free or be fused with the 1st thoracic rib, so as to make it bicipital. 3. In Man a similar bicipital form may be due to fusion of the shafts of the 1st and 2nd thoracic ribs with each other at their verte- bral ends, and it is probable that this may also occur in the Cetacea. 4. In either of the forms of fusion specified in 2 and 3, the two limbs, into which the vertebral end is divided, lie in different trans- verse planes, and the bifurcation is due to the partial fusion of two morphologically distinct rib-elements. 5. The presence of a cervical rib, or the bicipital form of the 1st rib, is only an individual peculiarity, and is not to be regarded as affording any evidence of either specific or generic difference. The paper will appear in extenso in the Journal of Anatomy and Physiology, April, 1883. 2. Oscillations and Waves in an Adynamic Gyrostatic System. By Sir William Thomson. 3. On GyrostaticSo By the Same. 4. On the Dynamical Theory of Dispersion. By the Same. Professor Tait laid upon the table a series of Photographs of Astronomical Instruments made at the new works of the Geneva Society for the Manufacture of Scientific Instruments. These photo- graphs were sent by the Astronomer-Eoyal for Scotland. BUSINESS. The following candidates were balloted for, and declared duly elected Fellows of the Society: — Mr WiUiam Evans Hoyle, M.A., M.R.C.S. ; Mr James Duncan Matthews; Mr Janies Greig Smith, M.A., M.B. ; Mr John Archibald, M.B., C.M. ; Mr Robert Rowand Anderson ; Mr Andrew Gray. of Ediiibiirgh, Session 1882-83. 129 Monday, 19^^ March 1883. Professor DOUGLAS MACLAGAN, M.D., Vice-President, in the Chair. The following Communications were read : — • 1. On the Impossibility of Inverted Images in the Air. By Edward Sang. It is narrated that a physician, having given cogent reasons to show that there could be no recovery, and somewhat disconcerted by the return of sound health, yet maintained the cogency of his pathological arguments. The present may be a new edition of the same story ; however, we shall advance the arguments, and leave it to futurity to tell whether there be any patient at all. In order that an inverted image of any object be seen in the air, it is, in the first place, requisite that the light from that object, proceeding obliquely upwards, be bent again down to reach the eye of the observer; and, in the second place, that this retrofleetion occur in a determinate manner, so that the lights proceeding from different parts of the object may arrive in contiguous directions. These effects must be produced by the action of the air. The law according to which transparent media change the direction of light has been well known from direct experiment, and the index of re- fraction of air has been carefully measured. In proceeding upwards, the light reaches air of gradually decreas- ing refractive power, so that the path is curved, the form of the curve depending on the law of diminution of the air’s density, and also on the earth’s roundness. The manner of the diminution of density is imperfectly known, and hence astronomers encounter great difficulty in investigating the amount of refraction for the stars ; that amount, in fact, being computed from empirical formulm. Yet there are relations among the heights, refractive powers and directions, very easily investigated ; and, because of its great sim- plicity as well as for the sake of those who may not previously have looked at the matter or who may have been frightened by the dis- play of algebraic symbols, I shall here give the analysis. If the air were composed of concentric layers, each, within itself, 130 Proceedings of the Royal Society of uniform density, tlie path of the light would be a series of straight lines, AB, BC . . . GS ; refraction taking place at each junction. If 0 be the earth’s centre, and AB the path of the light in the first layer, the angle O AB, called by astronomers the nadir-distance. is the incidence of the light upon the surface at A, while OBA measures the incidence of the same light upon the surface at B ; and according to the most elementary laws of geometry, we have the proportion sin OAB : sin OBA : : OB : OA . If now be the indices of refraction for the first and second layers, the refraction at B must, according to the well-known law, be such that- sin OBA : sin OBC : : : /Xq , so that, on combining the two ratios, we have sin OAB : sin OBC : : OB . : OA . , which proportion may also be represented by the equality sin OAB . OA . sin OBC . OB . /Xj . The analogous equality holds for the path BC, and so along the whole course of the light, wherefore the continued product of the sine of the incidence, the radius vector and the index of refraction, is constant all along ; that is to say, the equality sin OAB . OA . /x^ ^ sin OGS . OG . of Edinburgh, Session 1882-83. 131 holds good independently of the variations between the points A and G, and of the thickness or thinness of the supposed layers. Hence if these three factors be known for any one point in the path, and if two of them be given for another point, the third factor corresponding to that point may be at once computed. In this part of the theory of atmospheric refraction there is no difficulty ; the astronomer’s trouble is in discovering the geocentric angle AOG. If the earth had been flat, the computations would have been still simpler ; the product of the sine of the zenith distance by the index of refraction would have been constant, independently of the height, and the astronomer would have deduced the true from the apparent place of a star by a simple proportion. M. Biot has given the index of refraction for air at 1.000 294. It varies with the pressure and temperature, and the formula h ''"^■‘‘100 000 in which h stands for the height of the barometer in English inches, is sufficiently near for our purpose, is, perhaps, within the limits of error of the observations. A ray of light rising obliquely from a point on the surface of a flat earth until it arrived at the upper limits of the air would have had the sine of its zenith distance augmented in the ratio of 1.000 000 to 1.000 294 ; and if the apparent zenith distance at the outset had been 88° 38', that is, if its angle of elevation had been 1° 22', whose secant is 1.000 294, the zenith distance at the upper surface of the air would have been 90°, Ho sun, moon, or star could have been seen at a lower altitude than V 22', Ail light reaching the eye from a lower elevation must have come from some terrestrial object after having culminated as at B. The images of terrestrial objects would have been seen constantly in the air, but distorted by the retroflection, — the amount and charactei: of the 132 Proceedings of the Royal Society distortion depending on the manner of diminution of the air’s density. In the actual case of the round earth, the phenomenon of a reflected image must necessarily lie between the above limit and horizontality. If a ray of light leave the point C, culminate at B, and reach the eye at A with a zenith distance, which we shall denote by A, the incidence at B must be 90°, and therefore we must have the equality OA.sin A. 1.000 294 = OB. or counting in English miles, and taking the earth’s radius at 3960, / sin Ax 3961.167 = OB now the smallest possible value of the index of refraction /x^ is unit, hence the maximum value of OB is sin Ax 3961.167 = OB; wherefore, since the greatest possible value of sin A is also unit, it follows that the utmost limit of OB, under any circumstances whatever, is 3961.167 miles; that is to say, no culmination of light in the atmosphere can take place at a height of more than 1’167 miles, or 6200 feet. But this light must reach the eye horizontally. If the angle A be less than 90°, the radius vector OB must be lessened in proportion to the sine; so that for A = 88° 38', OB becomes 3960, — that is to say, no inverted image can be seen at an elevation of 1° 22', unless the atmosphere have only an infinitely small thickness. We are thus brought quite to home. Our researches do not extend into the regions of the aurora and magnetic arc ; they are within the range to which our ordinary barometric measurements are known to apply with very considerable precision. This result comes from the known index of refraction of air, and from the earth’s dimensions, irrespective of all usual or unusual conditions of the air below the limit of culmination ; but it requires that at that limit the air should altogether cease. of Edinburgh y Session 1882-83. 133 Let us examine the conditions needed in order that the light become horizontal at a lower level — say at the height of half a mile. In this case the index of refraction at B is obtained from the equality sin A x 3961.167 = 3960,5 x or sin A X 1.000 168 = , which has possible solutions within two limits — one when = 1.000 000, in which case A would be 88° 57', that is, the elevation would be 1°”03'; the other when A is 90°, giving = 1.000 168, which index of refraction would be due to a pressure of 17 inches of mercury. We have no idea of how such a rarefac- tion of the air at the height of only 2600 feet could be brought about. To come still nearer home, let us propose an altitude of only one- tenth part of a mile, or 528 feet. We then find that with A = 90°, the index of refraction at the culminating point must be 1.000 269, which belongs to air under a pressure of 27 inches of mercury. This diminution of density cannot be due to the lessened pressure of the air, which, instead of 2*5 inches, would only give *6, or about the quarter of the required reduction. In lowering the culminating point, we come nearer to the conditions of a flat earth, and there- fore to the possibility or probability of a reflected image. Let us then inquire into the conditions when the light is close to the earth along its whole path, and tangent to the surface at C and at A, If we put h for the height in miles, and A = 90°, the index of refraction is 3960 or developing the fraction into series — 7^0 I 5960“ 39602 i Even at the absolute limit 7i = lT67, the second and following terms of the series are too small to be of any account in our present inquiry, and thus we may hold that the diminution of the index would need to be at the rate of = *000 2526 for each mile of 5260 altitude. The diminution of the barometric pressure corresponding to this would be 25*26 inches of mercury for each mile, or *00478 134 Proceedings of the Royal Society for each foot of rise. But that caused by the lessening of the at- nnospheric pressure is only *00114, or less than the fourth part of what is needed; and therefore we conclude that no light can ho retroflected in the usual condition of the atmosphere. Inverted images, then, can only be seen when the air is in an un- usual condition ; there must he unusually light air above. Now, in these, as in all investigations on the subject, the air is assumed to be disposed in horizontal layers, each of uniform density ; without such an arrangement no definite refraction can take place, no dis- tinct image, whether distorted or not, can be formed. The absolute need for smoothness of arrangement may easily be illustrated : — The sun’s light is certainly reflected from the surface of the sea ; yet we do not see an image of the sun in the water : we see only a confused brightness. When the air is quite still, the sea becomes smooth enough to give an image, which, however, the slightest breath of wind destroys. We cannot use a dish of water as an artificial horizon, we must cover even our trough of mercury with a glass screen to prevent the ripple caused by the wind. Here gravitation tends to produce and to preserve the evenness of the surface. Water is some seven hundred, mercury is ten thou- sand times heavier than air, and yet the friction of the air produces such disturbance. Suppose then that we had a liquid as light as, or only a little heavier than air, and that we had poured this liquid into a flat dish. Paying no attention to the density of the wind which may blow upon it, let us think how calm the air would need to be that there may be no ripple on the surface. But let us add to this the con- sideration of the fact that the almost equality of the two densities deprives gravitation of its power to stratify, and we must admit that the slightest horizontal motion would be destructive of all smoothness. Imagine a stratum of air of the requisite depth and in its usual state quite level on its upper surface, and let us place upon that a layer of light air of the requisite refractive power, we shall then have inverted images. But our strata are not liquids ; they must be pressed upon to keep them from expanding, there must be air above them. If the superior air have its density conformable to the lower stratum so as to be in equilibrium with the general atmo- sphere beyond, it must be denser than the inserted layer, and the of Edinhurgh, Session 1882-83. 135 two would inevitably mix. If, on the other hand, the superior air be conformable to the upper layer its altitude must be greater than that of the general atmosphere which would press in to displace it. In neither case could there be repose. But the question arises, “how is this layer of lighter air pro- duced!” It cannot be from the sun’s warmth in still weather, because then the heating is at the surface of the earth or of the water. The warmed air mixes with the cold above, ascending while the other descends, and giving rise to the too-well-to-the- astronomer-known boiling of the sun’s edge. The only other source of such warm air is in the south, whence the south-west wind brings it to us in gusts and squalls. At the oncoming of the breeze we may see changes in the appearance of distant objects on the horizon ; they are displaced, distorted, hori- zontally, vertically, obliquely, according to the passing whims of Eolus. Seldom more than telescopic, they are as changeable as the squall itself. We can scarcely imagine that the wind should gently lay a warm coverlet over the quiet cold air of the north and leave it there in repose. But, I shall be told, these images have been seen, your patient is alive and well. Professor Vince saw him from Eamsgate. I have already shown that Vince’s narrative is inconsistent with ordinarily known appearances, and I have pointed out that the same observer, after eight years’ further experience as Professor of Astronomy and of Experimental Philosophy at Cambridge, was able to see through a telescope magnifying thirty times, a building four- teen miles away in all the beautiful proportions of near perspective. This feat could only have been performed by one totally ignorant of, or utterly careless of, the simplest laws of geometry and of optics. Yet I needed not to have gone so far. When a picture is pre- sented to us, we, without requiring an explanation, form an idea of what it means. It may be the picture of a horse, badly drawn, yet still we recognise the limner’s meaning, he meant to have drawn a horse. So when I look at Vince’s figure, I perceive that he meant to have drawn a sloop ; he has succeeded in drawing a sloop such as neither I, nor you, nor any other person ever saw. But I see a great deal more, I recognise in the picture the unmistakable well- known features of an old acquaintance. 136 Proceedmgs of the, Royal Society The picture is that of a sloop floating on a calm sea with its shadow in the water ; the sharpness of the image is considerably overdone, very few, persons have seen it so sharp. But the charac- teristic feature is there ; the image and the ship are united at the water-line it is a well known and understood appearance. Oh ! but Vince saw it up in the air ! When the sea is smooth, the reflection of the sky from the water and the light of the sky itself are so nearly balanced as to be undistinguished, hence the difficulty (sometimes amounting to im- possibility) which the seaman has in bringing down the sun to the water-edge. He is unable to tell where the sea ends or the sky begins. When the breath of a zephyr touches such a sea, it causes a dark space which is foreshortened into a narrow streak. Such streaks are apt to be mistaken for the true horizon, and the sailor-appren- tice may find himself wrong in his latitude ; but the mate or the captain has been on his guard. Here, then, is the whole diagnosis of Vince’s drawing:' — He had seen a sloop floating on a very calm sea, the captain had taken the opportunity to air his canvas, some stray spars or some sea- weed had been on the edge of a ripple in-shore, and the Pro- fessor’s powerful imagination had manufactured wonders out of the vision. 2. On the Thermo-electric Positions of pure Ehodium and Iridium. By Professor Tait. 3. Observations on the Growth of Wood in Deciduous and Evergreen Trees. By the late Sir K. Christison, Bart., and Dr Christison. 4. The Variation of Temperature, with Sun-Spots. By Mr A. Buchan. of Edinburgh, Session 1882-83. 137 Monday, 2nd April 1883. Mr JOHN MUEEAY in the Chair. The following Communications were read : — 1. On some Laboratory Arrangements. By Dr John Gibson. Improved Method of Filtration by Diminished Pressure. This apparatus will be best understood by a reference to the figures. The bell-jar A (fig. 1) rests, during filtration, on a square block of hard wood c, 25 cm. square by 25 mm. thick, over which is laid a sheet of vulcanised rubber d of good quality, and not less than 3 mm. thick. In the centre is a circular disk e also of hard w^ood, 13 cm. in diameter and about 20 mm. thick, which is held in position by four strong brass screws which pass down through the rubber into the square block below. In order to prevent air 138 Proceedings of the Royal Society leaking througli the holes thus made, they are rendered quite air-tight by embedding the screw heads, which are sunk slightly below the surface of e, in red lead, and by laying, previous to screwing down, layers of red lead on both sides of the rubber sheet. The red lead should not, however, spread beyond the disk e on either side of the rubber sheet, so that the latter lies quite free except where it is held down by the disk. In h is fitted a single-bore rubber cork holding the brass tap /. This tap is simply an ordinary brass tap converted into a three-way tap by boring a hole g through one outer wall and through one wall of the plug, which enables the operator to establish communication between (1) The bell-jar and pump. (2) The outer air and both bell-jar and puuip. (3) The outer air and pump, the bell-jar being shut off. (4) The outer air and bell-jar, the pump being shut off. After fitting in the cork and tap, the knee-piece h (fig. 2) is screwed on. The object of this knee-piece will be explained later ou. If the mouth a be closed by a rubber stopper, and the tap / connected by a rubber tube with a water-pump or other exhausting apparatus as the pressure inside diminishes, the rubber sheet bulges up inside the bell-jar, and pressing against the lower edge closes up any interstices due to irregularity of its own surface, or to imper- fect grinding of the glass. A well-made water-pump will give within half an hour a high degree of exhaustion, and this without the use of any lubricant whatever. Where a very high degree of exhaustion is required, the application of a little grease outside round the lower edge of the bell-jar is advisable. The apparatus in this form can therefore be used for drying substances in vacuo, &c. Tor the purpose of rapid filtration such complete exhaustion is not, as a rule, required, and indeed is often positively detrimental, and defeats the object in view. All the essential parts of the apparatus have been now described, everything else which is required for filtration being either in ordinary laboratory use, or else can be made with but little time and trouble, and at almost no cost. When it is desired to collect the filtrate in a beaker or flask, the simplest arrangement is that represented in fig. 1. Fixed in a by means of a rubber stopper is an ordinary correct-angled funnel. of Edinhurghy Session 1882-83. 139 fitted with platinum cone and filter in the ordinary way. To the stem of the funnel the glass tube bent as shown in the figure, and having the lower end ground obliquely, is attached by a short piece of black rubber tubing, the upper end of the tube being pushed up so as to be in actual contact with the stem of the funnel. The bend makes it easy to cause the end of the tube to touch the side of the beaker, which prevents spirting. It will be found convenient to keep several such tubes of different lengths ready made to suit larger and smaller vessels. Before commencing oj)era- tions it is as well to slightly moisten the rubber sheet d with water. This is not by any means absolutely necessary, but causes a quicker gripping of bell-jar and rubber. The tap being in position No. 2, and connected with a water-pump in full action, filtering is commenced by first filling up the filter nearly full with the liquid to be filtered, and then establishing communication between the pump and the bell-jar by turning the tap to position No. 1. During the operation of transferring the precipitate to the filter, it is often necessary to lessen the rate of filtration by diminishing or destroying the difference of pressure outside and inside of the bell-jar. Instead of slipping off the rubber tubing connecting with the pump, this can be far more quickly and easily done by giving the tap a half- turn back to position No. 2, and thus allowing air to rush in both to the pump and to the bell-jar. The use of the knee-piece h will be now apparent, for by it the inrush of air is diverted away from the vessel inside, which might otherwise be blown against the side of the bell-jar, and upset or broken. As it is, however, the vessel inside is not at all affected by the inrush of air, however suddenly the tap be opened. In this connection another use of the knee- piece may be pointed out. Several of the otherwise very convenient and inexpensive high pressure water-pumps, now so much used, have a tendency to allow the water to run back under certain con- ditions, especially when a high degree of exhaustion is attained. Filtering directly into an exhausted flask, such an accident would cause the loss of an analysis, and a valve is therefore usually placed between the pump and the flask. Such a valve is quite unnecessary while using the above apparatus. The running back of the water can be at once stopped without diminishing the pressure inside the bell-jar by giving the tap a quarter turn, so as to admit air to the pump only. Even if water does run back into the bell-jar no harm 140 Proceedings of the Royal Society is done, and by turning the knee-piece downwards the pump will suck back the water again almost to the last drop. It is sometimes necessary in quantitative analysis to filter a small quantity of liquid directly into a small weighed platinum basin or crucible. For instance, in filtering the alkaline chlorides from the last traces of magnesia in a silicate analysis, or, to take another example, in the purification of minute quantities of alkaloids. This may be readily done by the arrangement shown in fig. 3. The small funnel I, instead of fitting into the large stopper at a, fig. 1, is fixed by means of a small cork into the wide end of the stout glass tube m (fig. 3). In order to avoid loss by spirting, the tube does not dip directly into the basin, but into the glass tube n. This tube may be made out of a broken pipette, and is supported by a loosely-fitting cork in the small bell-jar o, which may be most conveniently made by cutting olf the lower half of an ordinary wide-mouthed bottle. When the filtration is over the small funnel I and cork should be removed, and the wide part of the tube m washed with a very little water, which serves at the same time to wash down the inside of the tube n. By this means the amount of wash water is reduced to a minimum. In the estimation of alkaloids the solvent is often chloroform or ether, which dissolve india-rubber, so that in such cases a small ordinary cork should be substituted for the rubber cork in m. It may be further pointed out that with this apparatus it is an easy matter to filter liquids containing hydrofluoric acid, which attack glass, by using a platinum funnel and filtering directly into a platinum basin or other platinum vessel. A Convenient Method for Preserving Sidphuretted Hydrogen Water. A large bottle A (fig. 4) is fitted with a double-bored cork. In the one hole is the syphon tube a leading from the bottom of the bottle to any convenient point lower than the other end of the tube, and closed at this lower end by a short piece of rubber tubing and an ordinary nipper tap. Through the other hole passes the shore glass tube &, bent at right angles, and attached by means of rubber tubing to a piece of lead piping c fitted with a tap, below which tap c is soldered on to a pipe connected with the ordinary coal-gas supply. 141 of EdinhurgJi, Session 1882-83. By this arrangement the sulphuretted hydrogen is preserved from oxidation, and can always he run off perfectly clear. The gas tap should as a rule be kept closed, and need only be opened for an instant when the sul- phuretted hydrogen water ceases to flow. It should be well oiled but not greased. The only objection, if any, that I have been able to discover to this method is that after a time the smell of the sulphuretted hydrogen water becomes somewhat altered in char- acter, apparently owing to the formation of traces of some organic sulphur com- pound, the nature of which I have not yet been able to examine. 2. On the Thermo-electric Position of pure Cobalt. By Professor Tait. 3. Transmission of Power by Alternate Currents. By Prof. George Forbes. When a current of electricity is sent through a dynamo machine in the same direction as the current flows when the dynamo is being used as a generator, then the field magnets are polarised in their normal manner, and the magnetism of the armature is such as to cause it to rotate in the opposite direction to that in which it turns when generating a current. The dynamo now acts as a motor. If now the current be sent through the dynamo in the opposite direction, the field magnets are polarised in the opposite manner, ^.e., a north pole is found where a south pole was before. The same is true of the magnetism of the armature. Hence, in this case the 142 Proceedings of the Royal Society poles, both of the field magnets and of the armature, are simply interchanged, and the rotation is again in the direction opposite to that in which it runs as a generator.* It thus appears that when a current of electricity is passed through an ordinary dynamo machine, the armature always rotates in one direction, whatever be the direction of the current. If, however, the field magnets or the armature be furnished with a current fixed in direction, the rotation of the armature may be reversed by reversing the direction of the current in the other part of the machine. Such being the case, it would seem likely that if currents of varying direction be passed through a dynamo they would cause continuous rotation in one direction. I sent the current from a Siemens alternate-current machine through a small Griscom motor, which has a Siemens armature with only two reversals of the commutator in each revolution. Under these conditions the motor did not move at all, in whatever position of the armature it was tried. The reason of this is that the reversals of direction of the current are too rapid to allow of the complete reversal of the mag- netism, both in the field magnets and the armature. This has been noticed before, and consequently it has been supposed that motive power cannot be transmitted by an alternate-current machine. When the apparatus was in the same condition as described above, I gave a rapid rotation to the motor by hand, and a,fter it had reached a certain speed the alternate-current maintained the rotation at a steady and uniform speed. I put some pressure on the spindle of the motor. It rotated at the same speed. I increased this pressure. The speed did not vary. But on continuing this action I arrived at a point where suddenly the driving action ceased, and if the motor continued to turn it was almost entirely owing to its own momentum ; but not entirely so, for on removing the pressure entirely, while the motor was still running slowly, the speed rapidly increased until it reached the previous uniform rate. The sudden diminution of driving power, when a certain amount of friction was applied, was very remarkable. What is the explanation of this action ? The fact that a uniform speed of rotation is maintained, and never exceeded, points to a synchronism between the revolutions of the armature and the * I only speak of the magnetic actions for simplicity of expression. The electric actions are in the same direction as the magnetic. 143 of Eclinhurgh, Session 1882-83. reversals of the alternate-current as being the true cause. In the Griscom motor the current comes from the source of electricity to one arm of the commutator attached to the Siemens armature, whence it is carried by the coil of wire surrounding the armature to the other arm of the commutator. The current leaving this arm of the commutator goes round the arms of the field magnets and magnetises the poles. Suppose now that by the rotation of the armature the reversal of the commutator takes place at the same time as the reversal, of the current, then the two simultaneous reversals will cause the current always to circulate in the same direction through the coils, and one part of the armature will always be north and the other always south. But the current exciting the held magnets is constantly being reversed, although so rapidly as to allow of only a very slight magnetisation. Thus suppose that when the left side of the armature is north, the upper held magnet is north, it follows that when this one is south the other is south also, so that there is always repulsion and consequent rotation in a direction opposite to the hands of a watch. It will be seen now that when we tried to start the motor with alternate currents, we had only the feeble interaction of the two pieces of iron extremely feebly magnetised; but when we have synchronous rotation, we have the more powerful interaction of a continuously excited and strong magnet (the armature), and the still feeble action of reversed magnetism of the field magnets. It is easy to see that if the armature tends to go too quickly or too slowly, the attractions between the movable and fixed parts will tend to check this irregularity. This accounts for the maintenance of the syn- chronism. It is also clear that if the speed be too much diminished VOL. XIL K 144 Proceedings of the Royal Society by causing the armature to do work, the magnetic attraction will not act, and this amount of work will speedily stop the rotation of the armature. It is also clear that if the armature be not revolving in synchronism, and be doing no appreciable work, the magnetic attrac- tions will always be tending to bring it more nearly to synchronism. These conclusions are all in accordance with what I observed. This is all that I have done as yet in an experimental way on the transmission of power by alternate currents. It is easy to follow out the results which must follow when a machine with a Pacinotti collector (or commutator) is used, or when a magneto-electric motor is employed. But I will not enter on this subject until I have experimental data to support these conclusions. I have considered these results, small as they may appear, to be worthy of the attention of this Society, because of the great value which I attach to the transmission of perfect synchronism. It is well known that in the construction of motors a great deal of ingenuity? has been expended in endeavouring to obtain a stead}^ speed, while the motor is doing a variable quantity of work. This difficulty is completely overcome by the use of alternate currents. It is true that the efficiency of my motor was small, owing to the feeble magnetism of the field magnets ; but perhaps this can be overcome. I have said that the motor I used was one of the well- known Griscom motors, and the current I used was IJ ampm’es, measured by a Siemens dynamometer. From an exceedingly rough estimate of the pressure on the pulley which was required to stop the motor, and the surface velocity of the pulley, I believe that I obtained about 200 ft. lbs. per minute. But it is not the regularity of speed of motors which strikes me as important so much as the power to transmit absolute synchronism to a distance. It is, of course, well known that the main feature of many telegraph systems is “ synclironous action.” This is the case with the Hughes printing telegraph, so unfortunately neglected in this alone of all-important European countries. So it is with the Baudot and other modifications of the Hughes, and still more so is it the case with the autograph systems of Caselli, D’Arlingcourt, and others. of Edinhtrgli, Session 1882-83. 145 4. On the Homology of the Neural Gland in the Tunicata with the Hypophysis Cerebri. By W. A. Herdman, D.Sc., F.L.S.^ Professor of Natural History in University College, Liverpool. {Ahstract.) In an ordinary simple Ascidian, where both the branchial and atrial apertures are at or near the anterior extremity of the body, the region lying between them — the interoscular area of Lacaze- Diithiers —is small in extent, and contains three important structures, the nerve ganglion, the neural gland, and the dorsal tubercle, lying close together. The ganglion in such a case is elongated dorso- ventrally, and gives off nerves at its two extremities, one set ventrally and anteriorly towards the branchial aperture, and the other set dorsally and posteriorly towards the atrial. In those species, however, in which the atrial aperture is near or at the posterior end of the body, the interoscular area is large, and forms the dorsal edge of the body. The nerve ganglion may remain ante- lior in position, or it may be placed far back so as to be nearer to the atrial. In this case, the nerves given off from the extremities of 'he ganglion run, the one set anteriorly and the 'other posteriorly. Wherever the ganglion may be, the neural gland is always found in close relation to it, either upon its posterior or ventral surface, according to the direction in which the long axis of the ganglion is placed. This neural gland consists of a mass of more or less ramified csecal tubules imbedded in connective tissue, and all springing from a central space or wider tube which underlies the ganglion. The presence of tliis organ was first distinctly pointed out by Albany Hancock in 1868,* but this able investigator does not seem to have assigned any function to it. The mysterious dorsal or “ olfactory’’ tubercle was first described by Savigny in 1816, under the name of “ tubercule anterieur.” Since then it has been discussed by almost all who have worked at the Tunicata ; it has received many names, but has usually been regarded as some sort of olfactory organ. It is invariably placed at the anterior end of the branchial sac, posterior to the circle of tentacles, and usually in a * “On the Anatomy and Physiology of the Tunicata,” Jour. Linn. Soc. Zool., vol. ix. p. 335. 146 Proceedings of the Royal Soeiety distinct, more or less triangular peritubercular area, whicli is a diver- ticulum of the prebran chial zone, and is formed by the dorsal ends of the peripharyngeal band bending posteriorly to meet the anterior extremity of the dorsal lamina. The dorsal tubercle is, in the simplest form known, a funnel- shaped de]3ression having its wider, circular, anterior end opening freely into the branchial siphon (the tube leading from the branchial aperture to the branchial sac), and separated off from the prebranchial zone by a raised edge or lip. The opposite narrower end is con- tinued into a fine canal running dorsally or posteriorly in the direction of the nerve ganglion. This simple condition is found in Molgula pedunculata, ; in Fjugyra kerguelenensis, the aperture is still wide, although its edge is square in place of being circular. In other simple and compound Ascidians, the anterior half of the edge has been apparently pushed backwards so as to become invaginated and closely applied to the posterior half, thus reducing the circular aperture to a crescentic or semicircular slit. This condition is found in Corella parallelogramma. In most other forms, more or less complication is produced by the ends of the slit, or “ horns ” as they may be called, being prolonged often to a very great extent, and coiled in various directions, sometimes producing beautifully regular and closely placed spirals, as in Molgula gigantea. The patterns produced by this curving of the horns are very numerous, and often complicated ; but their value in classifica- tion is slight, since they differ sometimes to a considerable extent in different individuals of the same species, and on the other hand, are sometimes very similar in members of different genera or even families. Some few forms are known in which, in place of being a single curved or spiral organ, it is formed of several distinct irregularly- shaped apertures, as in Cynthia irregularis ; this has evidently been formed by the lips of the primitive simple dorsal tubercle having become so folded as to divide the single aperture into several. Lastly, there are cases in which the organ is even more complicated, as in Boltenia ’pachydermatina, so that it becomes very difficult to trace its derivation from a simple circular opening. This variously shaped organ is histologically merely a depression in the connective tissue of the mantle, lined by epithelium con- tinuous with the squamous epithelium covering the prebranchial zone. These cells are modified upon the edges of the slit into first of Eclinhurgh, Session 1882-83. 147 cubical, and then columnar ciliated cells. The cilia project into the cavity of the organ. Since the time of Savigny, the dorsal tubercle has been almost universally regarded as a sense organ of some kind — probably olfactory or gustatory, or in some way capable, as Hancock * suggested, of “ testing the quality of the inhaled water.” The reasons for this view have been — 1. The position of the organ at the entrance of the branchial sac, where a sense organ would be of great apparent value. 2. Its structure — a ciliated depression covered in part by columnar cells, some of which closely resemble sense cells. 3. Its intimate relation with the ganglion, and the presence of a nerve arising from the anterior end of the ganglion, running towards the branchial aperture, close past the dorsal side of the tubercle, and presumably supplying it with nerves. In 1876, Ussow f showed that the neural gland lying below the ganglion was continued into a delicate duct, lined by cubical epithelium, which ran forwards and opened into the tubular posterior end of the funnel-like depression forming the dorsal tubercle, so that the variously-shaped slit of the tubercle was thus shown to be merely the aperture of the duct from the neural gland. Long previous to this, in 1861, Keferstein and Ehlers | had shown that the funnel-shaped cavity forming the dorsal tubercle in Doliolum derdiculatitm was continued backwards as a delicate duct to the base of the ganglion, but they regarded this duct and its anterior expansion as a prolongation from the ganglion itself. In 1881, Ch. Julin§ conhrmed Ussow’s discovery, and described minutely the condition of the gland, the duct, and the tubercle in several species of simple Ascidians. He also declared that tiiere was no connection between the nerve running from the ganglion to the branchial aperture and the tubercle, and that consequently the latter could not be a sense organ, and was nothing more than the opening of the duct. In a second pa]rer published shortly after- wards, Julin|l described the condition of these organs in two * Loc. cit. p. 335. t Froc. Imp. Soc. Nat. Hist., ~\ (17) < P'-P2=P(P-P2)1^~^’ ^P - Pi- P{p-Pi)p~\ and by these relations the distances of p from the summits p\, p^, p\ of the displaced triangle are equal to the corresponding distances of p from the summits p^, p^, Pg before the displacement of the system. If we take the scalar of the product member to member, we get, owing to : (18) S(p - p\){p - p^{p - p'g) - + S(p - pi)(p - p^)(p - Pg). We shall refer again to this result when we have the correspond- ing result calculated by the second solution. By the second solution, we must satisfy the condition TV(cZp2 - dp^){dp -dp^) = 0, and as p represents any point of the system, it follows that all the relative displacements dp - dp^ must be parallel to one another. Let us designate by g the unit-vector in the direction of these displacements. We shall then have, when = o - p^, dP=-W = P + li'^ = /3^ + 2gS7j(3-g\ Applying (1), namely T/3' = T^, we get 0 = ff{2Sr,IS-g}. Omitting g = 0, which corresponds to no displacement at all, we get dp==2g^gP, and (19) 13' = (3 + 2gSrjp ; or with the signification of f3 : P -Pi = p-Pi + ^^v(p - Pi) . From this, making successively p = P2, p = P3, and proceeding as in the case of the first solution, we establish, first the invariability of the triangle of which the summits are in p-^, p^, pg, before the displace- ment, and in p\, p^, p^ after the displacement. Secondly, we establish the three relations following: O 158 Proceedings of the Boyal Society (p-p'i = P~Pi + ^V^v(p-Pi), (20) Ip'-P2 = P~P2 + ^V^v(p - P2) » * -P3 = P- Ps + ^^v(p - P3) ? by wbicli the distances of p from p\, p'g, p'3 are respectively the same as those of p from p^, pg, pg. We now take the scalar of the product member to member. This gives for the second member, ^•{p-Pi){p-P2){p-P3) + 2S.7]'^Y(p-p^){p-p^) Sy{p-p^), where represents the summing of the three terms obtained by the circular permutation of the indices. But this sum represents the vector 7^S.(p-pi)(p-p2)(p-p3), and, treated by 2S77, we get a term which reduces itself so as to give : (21) S. (p - p\){p - p'2)(p - p's) = - S. (p - pi)(p - p2)(p - P3) . If Ave compare the sign in the second member of this result (21) with the sign in the corresponding result (18), we see at a glance that the displacements of the second solution produce a state of things which is incompatible with the conditions which constitute a physically rigid system, and that therefore the relation (18) alone characterises the systems which possess the complete rigidity from a geometrical point of view. As we have at our disposition two different expressions of the displacements according to the second solution, namely, the expres- sions (3) (with the values (11) of p and q) and the general expression (19), we will investigate into the properties of the second solution in using both expressions. But we will discuss first the properties of the first solution, and then, taking up the second, we will at the same time be able to show the correspondence (from a formal point of view) of the properties of both solutions. §3. By the first solution we have the expression (17), of AA^hich we Avuite again the first (22) p' - p'l =P{P - Pi)P ■ \ of Edinhurgh, Session 1882-83. 159 and which applies the same operator p ( ) ^ to any point of the system. Let us look upon ^9 as a datum. Moreover as Pi = Pi + ^Pi > p =p + dp , we assume also that the displacement dp-^ of the extremity of p-^ he given, so that the expression (22) will serve to the determination of the displacement dp of the extremity of p, which may be any point of the system, or also, in this case any point invariably connected with the points of the system of given points. Let us determine the point, or locus of points, of which the dis- placement is parallel to the axis ^ of p. If p^ designates such a point we define it by putting (23) = or (23 bis) dp^ = lt, where Hs a scalar to be determined. Applying the first of (17) we get for p = PqI (24) Po + &~ (pi + dp^) =p(pq - p^)p-^ . Transforming this by (5) and multiplying by p~^, we get By this equation S^(po - pf) remains indeterminate. We repre- sent this scalar by - s and add member to member -2=Sf(po-pi). Multiplying the sum by - ^ we get Taking first the scalar of both members gives (25) t + Btdp^ = 0, so that t is determined by this relation, and there remains (26) p„ = f. + [p,+ By this expression we see that p^ represents the vector of any point of a straight parallel to I (z being an indeterminate scalar), and passing through a definite point, of which the vector depends on p and on p^ and dp-^, all the elements of which are given, or supposed to be given. VOL. XII. L 160 Proceedings of the Poyal Society Subtracting (24) member to member from (22) in which we re- place p p + dp, and p\ by p-^ dp-^, we get (27) dp = lt + dcr, where we put (28) «?o- = b(p-Po)y'‘-(p-po)]- The displacement dp is therefore represented by two components. The first, which is parallel to ^ is the same for all the points, because (27) gives, by S^c7o- = 0, - t, and, by (25), the value of t depends on the data alone, and is there- fore a constant. In fact, by this last relation we have the series of equations (29) -t = BCdp^ = ^^dp.^ = = &c., which show that the displacements of all the points of the system, when projected on the direction ^ give one and the same projection, so that we may continue to designate by dp^ as by (23 bis). The component da- is perpendicular to because, owing to ^ we have SCp(p - Po)p-' = ^p~n(p - Po) = SC(p - Po)- Hence, S.^f?o- = 0. This relation assigns to do- a plane perpendicular to As to the direction of da- within that plane, we must deduce it from (28). By its definition, da- represents the displacement of p — pQ after a conical rotation round the axis parallel to I, which passes through the point p^, and which therefore is the straight line (26) repre- senting the locus of pQ ; the angle of rotation being 2u, namely, twice the angle of p, when p = cos u i- 1 sin u . We may transform da- in many ways. As, for example, putting P-Po^^y we have (30) do- = pa-p~'^ - a- . Applying (5), we get (31) do ^2 sin u . pY^o . of Edinburgh, Session 1882-83. 161 If CM represents the projection of o- on a plane perpendicular to ^ (and we assume ^ to be perpendicular to the paper and the posi- tive’part of ^ above it), then CMi perpendicular to CM, Mj being n on the circumference of the circle of radius CM, and to the left of CM, will represent V. tfr. Taking MlC?^l ~u, being on the cir- cumference, we get C??! =^Y.^o- . This gives the direction of do-. We then draw the chord MM' parallel to and CN perpendicular to the chord, so that the angles MCN = MiC7^i = w, and therefore the length M.N = Cn^ x sin u. Hence we have do==2MN = WW. This construction is more laborious than the one which represents do when expressed by (32) rf'qp + C) . If BM be the projection of p - ?;C on a plane passing through O and containing the direction rj, and if represents in the plane of projection the intersection with the plane (38), then MN == rj^r]{p - rjC) and dr = 2MN = MM'. The points M and M' at both extremities of dr are therefore sym- 164 Proceedings of the Royal Soeiety metrical in respect to the plane (38), and we vdll call therefore that plane i\\Q plane of symmetry. The component dr having displaced the point p into its position of symmetry p + dr, the component dp^ parallel to that plane (because perpendicular to rj), and being applied to every point, will shift the system of points p + dr out of their position of symmetry in causing them to move by a translation parallel to that plane, definite in direction and distance. We may designate the result of both the displacements dr and dp^ by the name of perversion. For the second solution we have also the expressions (3) which we may write now for^ and co-axial (by 11) and apply to a =Pi“Pc, ^ =p -Pc, a =Pi-p'c, = p -pe. We will now determine the angles u and v of respectively^ and g. Having ]■ a'=^ap-‘, we get, by (5) and (20), (40) ( c?a = 2 sin M . pY^a = 27jS7}a , t = 2 sin t? . qYl/3 = . Treating these relations by S . ^ we get, as the second members vanish, J S^tZa = 0 , t B^d/3=:0, (41) and consequently also Thus ^ must be in a plane perpendicular to We call ^ the unit-rector perpendicular to ^ and to 77, so that and the system t], ^ will be trirectaiigular, ^ being also in the same plane with and to the left of it when seen from a point of the positive direction of rf. Let us take the origin of that system at the extremity of p^ in the plane of symmetry (38). In treating (40) by V.^, and remarking that Ip—p^, and that Y^pY^a—pYCY. we get (by a change of sign, in replacing V.Ca by V. aC) 2 sin u . pY{CYal) = 2^S?^a , 2Binv. qYaYpQ^2$Sy^p. q/ Edinhurgh, Session 1882 -83. 165 We put remarking that d and /? represent the projections of a and /3 respect- ively on a plane perpendicular to namely, on the plans ^77, we get, by comparison 2 sin u _ sin v 5 This gives separately (42) And we must attribute to the second members the signs respectively of Srja and of S77/5, to be determined in each particular case. In all cases we have [sinM = T. &7ja (sin v = TSrj^ . So that the signs of Srja and of S77/3 give the signs of the second members of (42). The number of arbitrary elements, by which the displacement dp of any point p may depend, will also be six in the most general solution. Having, namely, (43) dp - dp^ + 2rjSrj{p - Pc) , and (44) dp = dp, + 2&inu.~PY^{p- p^) , we may consider p^ as given by 77C which contains three elements, two included in and one in C. Then rj being given we have ^ by one more arbitary element, because ^ already has to satisfy two scalar equations, 877^ = 0, and C“=-l. When 77 and ^ are determined, then ^ will be known by Finally, the value of dp^ is of the form dp^ = , 166 Proceedings of the Royal Society where a and c constitute two more arbitrary elements : in all, six arbitraries, all of them entering in both the expressions (43) and (44). It is true that in the case of one perversion one might define ^ so as to render dp^ parallel to it, and so we would have a = 0, and there would be only five arbitraries ; hut if we want to combine two given perversions, we are not free to dispose of the direction of I arbitrarily. §5. The results of the two preceding paragraphs will now he applied to the demonstration of the proposition according to which two per- versions applied in succession to a given system of points produce a displacement represented by a screw-rotation. This proposition may he looked upon as known already, hut its demonstration in its greatest generality by the quaternion method has perhaps not yet been given. W e assume that the planes of symmetry corresponding to the two perversions have been determined and brought under the form S^T + C = 0, SVr +C' = 0. We assume also that pc? p ’c taken so as to assign to p\ a position on the line of intersection of the two planes. Let more- over pi, p, represent the vectors of two points given arbitrarily before the displacement, and let p\ p^ be the vectors of these points after the first perversion and p\, p" the vectors of the same points after the second perversion. Then putting a = Pi - Pc , a = p'l - p'o, a' = p'\ - p\ , /^ = P-Pc5 /5'=P -p'e, -Pfy we may represent the perversions by a =pap~^ , a ' ^pdp "^ , P' = ql3q~\ = • Hence if we put P'P = Piy = a" =l)ia^r' , r=si/3?r’- we have 167 of Ediiiburgh, Session 1882-83. Looking upon a" - a = d-^a, p" - p = d^j3 as representing any dis- placements, we apply the conditions I. and II. of § 1 in order to determine the nature of these displacements. Generally then they must satisfy the equation (46) T(Yq^-p^)TY(d^ad^(3) = 0 . Let us examine the second factor. We have as to a, d^a = a" — a = (a” — d) + (d - a) = dd + da . Thus . Y{d^ad^(S) = Y{da + dd)(dj3 -f- d^') . But separately da with dj3 on the one hand, and dd with d(B' on the other, give perversions by hypothesis. We have therefore T.Ydad/3 = 0, T.Yddd/3' = 0. Thus we get Y(d^a. d^/3) = V. dd. d/3 + V. dad^'. How let us consider the displacements da, d/3, &o., under their other form (19), da = 2rjSr]a , dd = 2r]'Sr]'d , d/3 = 2rjSrj(3, d/3' = 2fSf/3'. These give Yddd(3 — dYr]'y]^r] d^r]^ , Y dad/3' — — 4Y 7]' rjBf /3'Srja . Taking the sum, and remarking that d = a + da, /3' = /3 + d^, we get for the factor of dYr/yj, ST7'[(a + 2ri^r]a)Sr]l3 — {(3 + 2r]Sr]/3)S'qai] , = S . r]'aSr]/3 - Brj'ftSrja , = S.Yr]yj'Ya^. So that Yd^ad^/3 = iYrj'7)S.Y7irj'Ya/3 . Generally this result cannot vanish, because /3 which is p-~ pc can be any vector. As this factor of (46) cannot vanish, we must have (47) TV(j,-j,,) = 0, a solution which gives a screw-rotation, the operators (48) ),5,-i and q^{ )2f ‘ . 168 Proceedings of the Royal Society becoming identical, because the ambiguity disappears in the expression of the operator. Having arrived at the condition (47), by way of exclusion we will now prove by a direct method the identity of the two operators (48). In the preceding deductions we have admitted that p and q have the same axis, situated in a plane perpendicular to t;, this plane having the definite position of the plane of symmetry. Likewise, we have also admitted that the axis of p' and f be situated in the plane of symmetry corresponding to the second perversion. As these two planes generally intersect each other, we take the direction of the line of intersection for the axis ^ of the four versors y>, p, q. We have then sc>? = o, s^v = o, and in putting (49) 7/77' =- cos ?<; + ^sinw, we assume that the positive half of ^ will be directed so as to have 77' on the left of 77, when the angle w be positive and not outpassing two right angles. Having a =pap'^^ a'p=pay whence we deduce S^a = S^a, and putting a = V(^VaO, cT=V(CVa'0, where d and a represent the projections of a and a on a plane perpendicular to we get This gives Ta = Td. Hence by (42) we have a!p = ^ ^rjoYa sill u Likewise we get, applying (42), p a — 877'^ Ta' Sin u of Edinhurgli, Session 1882-83. 169 Multiplying member to member and observing (a')^ = - (Ta')^, we get , ,,, S'wVSm 'pp= . sin sin But the same calcul, proceeding from — will establish , 8f/3'Sr]l3 qq = — — — — • ^ ^ Sln^; sinu Both results give the same operator ■ m w, whatever the signs of the scalar factors may be in the particular expressions of pp and q'q . Having ^ = rj^=z - , and ^ , we get = fr] . We have already defined rjf by (49). From that definition we deduce (50) 7;'77‘■^ = cos^^; + ^sin^^7 = r, so that the operator will have the canonical form. We have thus : (51) p"-p"o = >-(p-p>-i for all possible values of p. The angle lo is evidently by (50) the angle comprised by the two planes of symmetry, the angle of rotation being = 2w. Let us determine the position of the axis of rotation. By the expression (26), in which we change p^ into Pc , dp^ into p'\ - Pc = = (^a + ^c) + (^a' + ^c') ,, and u into w, p into r = 7} , we get : ^.-1 Now we have Hence po-pc^C^ + lV ^-^{rja + fE) + {ia + f a')~| . Lsin(^? J 170 Proceedings of the Royal Society If we represent by AA', ^'a' by A' A", then also rja + 7) a' = ^AA" = A"A^ , namely at right angles to AA", and of equal length. To construct COS W A"Ai we describe the circle passing through the three points sin?f? ^ A, A', and A", and the point D where A"A^ meets the circumfer- ence will give nrf\ co^io -ttta A D = — A A, . sin V) This is because the angle ADA" is supplementary to the angle AA'A", which itself is supplementary to w; and as the triangle AA"D is rectangular in A" by construction, we have, for the length AAj = AA", A D = cot AA, = — (-na + r? a ) , ^ sin w^' ' ’ of Edinhurgli, Session 1882-83. 171 therefore = ^2 + iAD = ^2 + AC, C being the centre of the circle, because AD is a diameter. In fact the construction reduces itself practically to the determination of the centre C of the circumference passing through A, A'A" ; the axis of rotation being then a line passing through C and being perpendicular to the plane which is parallel to rj and f the normals of the planes of symmetry. 172 Proceedings of the Eoycd Society BUSINESS. The following Candidates were balloted for and declared duly elected Fellows of the Society: — Dr P. M‘Bryde, P.R.C.P. Ed.; Mr G. W. W. Barclay; and Mr Thomas Andrews, E.C.S. Monday, lUh April 18 S3. Mr JOHN MUERAY in the Chair. The following Communications were read: — 1. On some Properties of the Line of Simple Flexure. By Edward Sang, C.E. (Plates The unrestricted problem, “ To find the form assumed by an elastic system when subjected to known strains,” is one of those mechanical problems which haffie the powers even of the modern calculus. It is only when the change of form is exceedingly small that we can obtain approximate results. In the simplest case — that of a straight uniform elastic body — there is, so far as I know, no complete solution ; and thus I venture to suppose that the following remarks may not be devoid of interest : — If a thin flat rectangular plate — a physical line, as it were — be bent by means of a string attached to its two ends, it takes a parti- cular form, to which the name “ curve of simple flexure ” may be given. From the nature of the case, it is clear that if ABC represent the bent plate and AC the string, the curve must be symmetric from the two ends ; so that if B be the middle of the bow and BO the ordi- nate therefrom, the two parts AOB, COB must be alike. Farther, if a second spring of the sam(3 dimensions, and bent by a string of the same length, were placed endways to this one, as at CDE, the strings AC, CE being in one straight line, but the bend being on the other side thereof, the ends may be conceived as united at C, so as to form a continuous elastic plate, while the cord may be supposed attached to the two ende A and E. The same kind of extension may be continued indefinitely both ways ; and thus it follows that the curve of simple flexure is com- 173 of EdMurgh, Session 1882-83. posed of an endless succession of equal waves, disposed alternately on either side of a straight line. It belongs, then, to the class of transcendental curves typified by the curve of sines. Instead of the string we may put two obstacles, one at each end, against which the spring may press. It is obvious that the arrange- ment ABODE would be one of unstable equilibrium, so that some slight guide would need to be placed at C, in order to prevent the spring from flying to the one or to the other side. When the bending is slight, as shown in the first figure (Plate I.'^), the form bears a considerable resemblance to that of the curve of sines when flattened to the same degree ; but when the flexure is con- siderable, as in the second figure, the deviation from that form becomes marked ; the angle of crossing at the points A, C, E, necessarily is increased. The third figure shows the form of the spring, with its continuation, when the ends are so drawn together, as that the curve crosses the axis squarely. In the fourth figure the spring is shown as so much bent that the angle of crossing is obtuse ; the distance between the ends is less than the breadth of the loop at its widest part. In the actual figure this distance is less than half of the breadth, and hence the continuations of the loops intersect each other. When the ends are brought still nearer the loops come to cross each other more frequently. The fifth figure shows the form of the spring when the two ends are brought together. In this case the continuations of the form are all included in its counterpart on the other side and in itself. When the ends of the spring are crossed over each other, it takes the form of what is technically called a Mnk, as shown in the sixth figure. There the distance of the ends is less than half the width of the loop, and the continuations intersect each other. If that distance were augmented the loops would stand detached. In these changes we have a noteworthy instance of the danger of abstract reasoning as to limits. While the point C is being brought nearer to A, the number of undulations of the curve within the limits of the sheet increases, so much so, that if C were very close to A, the paper would be covered by a multitude of lines, which, however fine they may be, would tend to produce blackness. If, after the spring has been crossed, we allow C to come back to 174 Proceedings of the Boyal Soeiety A, we sliall have a corresponding increase in the number of undula- tions comprised within the limits of the sheet ; the tendency again being toward blackness. On making the approach from either side, that is, on taking the functions of a -f 8a and of a - Sa, and attri- buting to the variations 8a an infinitesimally small value, we find, on both sides, the functions to be black ; yet, on making 8a abso- lutely zero, we find whiteness instead of blackness. Such being the general features of the curve, we may obtain its details by an examination of one of the half-waves, such as AOB. Eor this analysis it will be most convenient to place the origin of co-ordinates at the point O. We shall therefore write — 2/ = 0H x = BP I — arc BP r = radius of curvature at P a = inclination of curve at P s = surface BOHP . We shall also write — Y = OA X = OB L = length of BA B = radius of curvature at B A = inclination at A S = area BAO , for the limits of these quantities. Since, in such an arrangement, the angular tension at the point P is proportional to the ordinate HP, the radius of curvature there must be inversely proportional to the same ordinate ; and therefore we must have rx-c^ . . . . ( 1 ) where c is a constant determined by the dimensions of the spring. This equation contains the analytical definition of the curve. Since, from the nature of curvature, dl = r . da the generic equation (1) may be written X . dl — r^. da , (2) of Edinburgh, Session 1882-83. 175 but wherefore dy = cos a . dl X. dy = c^.coB a. da', but the product x . dy represents the increment of the area BOHP, wherefore we have S = c^.sina . . . (3) whence also S = . sin A . When the angle A is acute, as in fig. 7, there is no difficulty in interpreting this equation j but when that angle is obtuse, as in fig. 8, we have to observe that, in supposing the point P to move along the curve from B, carrying with it the ordinate PH, the area OBPH increases until P arrive at D, where the curve becomes per- pendicular to the axis. Beyond that limit the motion is towards BO, the differential of the area becomes subtractive, and thus, for the point p in the figure, s would represent the surface BPD^HO, while S would stand for the area BPD^^AO. And when the spring is crossed so as to take A to the other side of 0, as in fig. 9, the surface AFO must be regarded as subtractive, so that the symbol S then stands for the excess of BDF above FOA. On inserting the value of dl, viz.. - dl = dx. sin a~^ into the equation (2), we obtain - xdx — d^. sin a. da which, when integrated, becomes — -}- c^. cos a -f constant . How, when a? = 0, m) = -I- Vpd'" + Pga;’’"'® 4- . . . -f P,,^ , where P r Pr • hfi _ "k Pr -j- i • h,^^ Pm ‘ h^ _ + r > being the sum oj the homogeneous products of the roots of {A) of n dimensions. of Edinburgh, Session 1882-83. 237 1. In order to establish this proposition it will he necessary to premise the following lemma : — If ttp a^, ttg, . . o be roots of the equation +pxf~‘^ . . .+p^, then K{n>m) +p^ . +^3 . /i^_3 + . . . +p^ . , where is the sum of the homogeneous products of a^, a^, ag, . . . of n dimensions. The proof of this may be briefly indicated thus : — We have x”^-ppe^-'^ -ppe^-^ -ppT-^ - . . . -jv = {X - aj) {x - ttg) {x-a^) ... {x- af) . Writing ^ for x and multiplying off by x"^ we get 1 1 - ppe - ppS‘ -ppx? - ... - p^p!^ 1 _J \_ 1 Oi-j^X 1 (Xpe I “ CLpC 1 (xpXj Thus (1 + . . . + h^_y^. + . . . + h^_2, . x^~^ + . xS^'“ + 1 . x^~^ + . 02" + . . .) (1 -ppx -ppe^ - ppS> - . . . -p^ . 02"*) = 1 ; hence, since this is an identical equation, equating to zero the coeffi- cient of 02" in the first member, we get K -Pl-iu.^-p^. h„ 2 - • ^«-3 - • • • -Pm 0 , or, hn=Pi-K-l+P2’ + ^^n-3 + . • • +Pm>h^_„^. 2. We can now establish our proposition — to express x'^(n>m) in the manner indicated above. For greater clearness we shall first consider a particular case — 02^ =^px^ -I- qx^ -f ro2 + s . 238 Proceedings of the Royal Society Multiplying both sides of this equation by writing for its equivalent value, and arranging, we get =■ ijf + (f)x^ + {yyq + r)P + {jgv + s)x ; but by the lemma and in particular = h^—phj^-q, = ^9/^2 + + r, &c., where /q is the sum of the homogeneous products of the roots of =px^ + qx^^ + TX + S oi n dimensions. Thus = 11^^ x^ + (5/q + r)x‘^ + {rh-^ + s)x + . Kepeating the above process on this equation we shall find, on again applying the lemma, that x^ = /q . x^ + (g/q + rl\ + s)x^ f (r/q + slif)x + sh^ . ITow assume = hn-Z ‘ P" + • P + (^^q-4 + s^q-5)^ + ; operating on this equation in like manner we shall get, since by the lemma + qh^_^ + rhy,. ^ + = /q_2 , + {qhn-z + + {P^n-Z + sK.^X + s/?^_3 , which proves the preposition in a particular case. The general case is established in a similar way, x^ ==ppy"^~^ -{-pp(g^~^ + . . .+p^. Multiplying both sides of this equation by x^ writing for x'^ its equivalent value, and arranging the terms, we shall get, since by the lemma pf-^ +P2 ~ ? + ' = /q . 4- {pf ^ + p^)x^~^ + OVb -\-p^)x^-^ + • . • + (Pm-l . +Pm) • « +ib. . /q • Applying the same process to this equation, it may be shown, since iV'2+i’2?il + P3 = ^'3> »'"+® = 7*3 .x^-' + {pjl^ +X^3\ +Pi)x^~^ + (pJh +Pjh + ■ ■ ■+(Pm-l- ^h+Pr.- h^^+P„- 7*2. of Edinburgh, Session 1882-83. 239 Now assume ^.m-1 '(■n-m + 1 • hfi - w - 2 IPm • b ,1 - 2m+2) • ^ + ilh • bn-m + i^4 • ^^n-m-1 +2^5 • + • • • + Pm • -^M-aiH+s) • + ijK • hn-m-^2^r\+\' ^^n-m-1 +2^r + 2 • ^^n-m-2+ • • • +i^»f ^^^-2^« + r) + (2^m-l • K-m-^V^n • ^ ”1“ P»t • j operating on this equation in like manner it may be finally shown, since by the lemma Pi • hfi _ 4- 1 ”b 2^2 ’ b}i - »w “h Ps ' bfi - m - 1 ”h . t . ”t" pm • b 2^ -fa — br,i _ ^ 2 that ^n+l _ 7; /^m-1 it/ — ' ' « - jn-f 2 “ + (P2 • -^^n-m,-fl+2^3* + + - * • +P^ • ^^n-em-fs) • + (P3- ^^«-m + l + P4- ^bi-m+2^5* 1 + * * • ^ Pm • ^?«-2m-f 4) • + iVx-' ^^«-w-fl +2^r-fl • bn-m-^Pr-^^' + • *' + Pm ' ^^n-2m + r -f l) ' + (Pm-l- ^br-m-fl+P^* ^ + Pm • • Thus the proposition is completely established. 3. The following extensions of the foicgoing lemma, particularly ill the case of a quadratic, may be worthy ci notice. If a, j8 be roots of = px-^q^, then bn = V . . . (1), where is the sum of tlie homogeneous products of a, S dimensions. Kepeating the principle contained in (1) we find =2)2 ^ + 22)2 • bn_^ + (f . ^(P + 1?) . symbolically . . (2). VOL. XII. Q 240 Proceedings of the Royal Society Applying tlie same principle to (2), we shall also get hr, . h„_^ + Zp\ . . hr,.^ + f/ . = (p+?)^[c:; and in like manner while generally K -=p, . K.r + + . . . + - 2r = (p + <2)’’ . [7^]'*]^’^ symbolically . . . (3). Again, hr, may he expressed under another form — in terms of the. coefficients of the equation (p and q) only. Here it will be; necessary to distinguish the cases n even and odd. We have lh^plh + q=p^ + q, • \ =p!h + • By repeated applications of formula (1) we may deduce Ag = + 7 p^q +15 phf + 10 p^^q^ + , /ig + ^P^q + 21p'^2^ + 20p^2^ + bpq^ , and generally K, =F’' + (‘in-\).tr’'-\q + (2» ~ 2) (2w - 3) (2«-3)(2«- 4)(2». l)n ^ 1,2 . 3 . p ?+...+ ^ 2 ' ■ V 9. + q’‘ . . . 0), and + 1 1)(2m - 2) 1.2 . . q^ {2n - 2) (-2« - 3) (‘hi ~ 4) 2m-5 ^3 I (n + '2)(n + l)n "V 1.2.3 • t' ' '1 • • • < 1.2.3 p q + (n + \)pcf . . (5), each of which series consists of ?^ + 1 terms. 241 of Edinhurgh, Session 1882-83. Conversely, the snms of the series (4) and (5) are known ; for they are respectively that is and 4. To obtain results corresponding to (3) in the case of a cubic and of equations of a higher degree, we observe that in the case of a quadratic the number of terms in {p + qY is the same as the number of different li's represented by • Taking the equation = px^ + + r we have K = P ’K-i-^qK-2-^r . . (6), where hn denotes the sum of the homogeneous products of roots of the cubic. By the repeated application of (6) we deduce K . K-i + 2i?2' . K-% + . . . + . 7?,,_s ~{p + q-\-rf . symbolically, where we observe that occurs twice. Again, it will follow that '»»=(?+«+»•)'• the number of terms in {p-\-q-\- r)^ being ten, while there are only seven different /i’s, /i„_5, hn-a, /^«_7 each occurring twice. So it will follow that [h]zi = (i, + 2 + r)‘.[/7]::'. and generally ha = {p-\-q + rj . [/?,] n - > the number of different /i’s being 2r + 1 , and so disposed that in the first pair each h occurs once, in the second pair each Ji occurs ,242 Proceedings of the Boycd Society twice, in tlie third three times, and so on up to the ^th pair, while T the middle /?, i.e., hn-^r^ occurs n + 1 times. The same law holding when we reckon from the end, the total number of terms will be 4^1 4-2 + 3 + . .. + 2^ + 2 + 1, that is, ^ 1) 2), which is the number of terms in {p + q-^ ry. Again, if we consider the equation ■x^ =px^ + qx^ + rx + , we have hn=P • K-l + 2' • ^ • ^^n-3 + 5 . ^n-4 ) from which it may be deduced in the same manner as beforh that + ^q . /?n- s + • • • + = (p + g + r + s/ . [hjfl symbolically, in which , /r„_5, /i„_ occur twice. So it will follow that hn = {p-\-q + r^sf . {p + q-\- r + sf . [h]l and generally ^n = (p + q + r + sY .[h]f I, the number of different 7z’s being 3r + 1 , which are repeated by the same law in going from the beginning and the end, and such that the sum of the number of all their coefficients is equal to the sum of the series, l+3 + G + 10 + ... + ^(r+l)(r + 2) that is (r+l)rr + 2) (r + 3) 1.2.3 which is the number of terms in (jj + ^ + r + sy . of Edinburgh, Session 1882-83. 243 Finally, in the case of the equation + . . . +p>m ) since K==Pl-K_^+P^. A^_2+i93. /i„-3 + . • it will follow in like manner that A» = {Pl +1>2 +P3 + --- +P«f ■ 2 =( =( and generally = (Pi +P2 +Ps+'--+pT- will > the number of different h’s being (m--l)r+l, which are repeated by the same law in going from the beginning and the end, and such that the sum of the number of all their coefficients is equal to the sum of the series, m-\ (m-l)m (m-l)m{in + l) 1:2 + 47273 (r + 1) (r + 2) (?• + 3) . . . {r + m - 2) 1.2.3... (792-2) ’ that is (r + 1 ) (?* + 2) (r + 3) . . . (r 4- m - 1 ) 172.3... (m-1) ’ which is the number of terms in (pi+p2+^^3+* • • Chart for Uanuarv 1885 Proa Roy Soc. Edirf Vol XE Plate 1 Hobe-rt SiiiU, Delf Proc.Tioy:3ocIiitn^ VolMI FlateS* 5 4 Proc. Roy SocRdm 5 VolXII Rlate.U. B Proc, Roy. Soc. Edit TAYNISH LOCH IfILLESPORT Diag.5. SMOOTHED ROCK COVERED BY BOULDERS ROCK FACE SLOPES DOWN WESTWARD C LOCH SWEYN Fig.7. ROCK SURFACE SMOOTHED AND STRIATED WITH HOLES ON SURFACE Length about 25 Ft Breadth 8 F! tig. a SPECIMEN OF CUP MARKS ON GLACIATED ROCKS LOCH GILP HEAD I FT WIDE LOCH SWEYN Diag.8. BOULDERS ON H ILL S I DE, HEAPED ON ONE ANOTHER Diag. I. TOP OF HILL ON LOCH KILLESPORT COVERED WITH BOULDERS Diag. 2. INDIVIDUAL BOULDERS FROM HILL SHOWN IN FIG. I LOCH KILLESPORT West East ' &A-K.Jolm.stoiL Ediiibwr^li- OF THE KOYAL SOCIETY OF EDINBUKGR VOL. xiL 1883-84 No. 115. GENERAL STATUTORY MEETING. Monday, 2^th November 1883. THOMAS STEVENSON, Esq., Vice-President, in the Chair. The following Council were elected : — President. The Right Hon, LORD MONCREIFF. Vice-Presidents. Prof, H. C. Fleeming Jenkin, F.R.S, Rev. W, Lindsay Alexander, D.D. Thomas Stevenson, M.Inst.C.E. Robert Gray, Esq. A. Forbes Irvine, Esq. of Drum. Edward Sang, LL.D. General Secretary — Professor Tait. Secretaries to Ordinary 3Ieetings. Professor Turner, F.R.S, Professor Crum Brown, F.R.S. Treasurer. — Adam Gillies Smith, Esq., C.A, Curator of Library and Museum — Alexander Buchan, Esq., M.i\, . Councillors. Rev. Professor Duns. Dr Ramsay Traquair. John Murray, Esq. Wm. Ferguson, Esq. of Kinmundy. Professor Cossar Ewart. Professor James Geikie, F.R.S. Rev. Dr W. Robertson Smith. Stair Agnew, Esq., Registrar-Gen, Prof, Douglas Maclagan, M.D, The Hon. Lord MacLaren. Rev. Professor Flint, D.D. Professor T. R, Fraser, M.D, By a Resolution of the Society (19th January 1880) the following Hon. Vice-Presidents, having filled the office of President, are also Members of the Council : — His Grace the DUKE of ARGYLL, K.T., D.C.L. Sir WILLIAM THOMSON, LL.D., D.C.L., F.R.S., Institute of France. Foreign Associate of / VOL. XIL 24G Proceedings of the Royal Society Monday, Zrd Becemher 1883. The Eight Hon. LOED MONCEEIFF, President, in the Chair. The following Communications were read 1, An Essay upon the Limitations in Time of Conscious Sen- sations. By John B. Haycraft, M.B. Edin., F.E.S.E., &c. ; Professor of Physiology in the Mason Science CoEege, and Lecturer on Physiology at Queen’s College, Birming- ham. I propose to describe in this essay some experiments which I have conducted upon the limits in time of separate tactile and thermal sensibilities. I shall endeavour to account for the variations seen in the limitations in conscious sensation of the different senses; and also to formulate a general proposition as to the effect on con- sciousness of stimuli increasing gradually in rapidity of application. If the finger he touched with a pin, one is both conscious of the point in time at which the contact is made, and also when it is broken ; this is likewise true of the other sensations. In the case of hearing, for example, a note struck upon the pianoforte is localised in time as of a certain duration. In moving an object through the field of vision, it is seen definitely to pass into, and also out of that field. There is, however, a limit to this which can he determined, for if the image just alluded to be brought — by means of a revolving wheel — fifteen or twenty times a second in front of the same point of the visual field, it will now he seen as a stationary object, and the separate stimuli will produce a continuous sensation. In the case of hearing, Helmholtz has shown {The Sensation of Tone as a Physiological Basis for the Theory of Music, p. 262) that the limits in time are sharper and more exact. The ear can, according to this observer, distinguish 132 heats (produced hy high notes) in a second ; even this being probably not the extreme limit. It is also !;,nown that over 1400 impacts from a revolving toothed wheel must of Edinhurgh, Session 1883-84. 247 affect the finger ti|) in a second, before the sensations are com- pletely fused in consciousness ; and before it becomes indistinguish- able from a revolving smooth metal disc. It is, then, to be noted that stimuli, separate in themselves, are, when sufficiently rapid, formulated in consciousness as continuous and uninterrupted ; and that this fusion occurs sooner in the consciousness of some sensations than in others. Some experiments which I have lately performed shed, I think, some light on these facts, and enable us to state them in greater amplitude ; above all indicating where the fusion occurs. I n)ay anticipate by stating that this is during the transformation of the stimuli into nerve energy. My experiments have been chiefly concerned with the investiga- tion of the results in consciousness of repeated stimulation of the nerves of tactile and thermal sensibilities, the apparatus being usually of the simplest possible kind. The skin was stimulated interruptedly in many ways, either Ijy tuning forks of various degrees of pitch, or by a revolving toothed wheel. The most satisfactory results, however, were obtained by a vibrating steel rod fixed in an iron vice. By altering its fixed point, and therefore the length of the vibrating portion, the period of its vibrations, and the impacts made upon the finger tip held near its free end, could be altered at will. Its exact pitch was easily obtained by attaching to it a light writing style which recorded its vibrations on a revolving smoked cylinder. If the finger be pressed lightly upon a revolving toothed wheel, whose motion is made to increase slowly in rapidity, the following sensations may be noted. When no more than forty or fifty taps are made upon the finger in a second, there is produced a conscious- ness of distinct stimuli, separated one from another by periods of rest. Each stimulus produces a distinct sensation, limited in time from the one that follows. Stimulate more rapidly, and it becomes no longer possible to distinguish in consciousness one stimulus from another. They give rise, however, to a sensation which we term “ roughness,” which becomes less marked — less rough — as we increase the rapidity of the revolving wheel. If, at this point, the fingers be very gently pressed against the wheel, there is a sensation of tickling — such as tliat produced by drawing a feather over the 248 Proceedings of the Royal Society face. If, as a final step in tlie experiment, we cause the wheel to revolve very rapidly, the sensation becomes less rough, and, at last, when as many as 1400 impacts are made upon the finger tip, the sensation cannot be distinguished from that of a revolving toothless metal disc. There is, in fact, a sensation of ‘‘smoothness,” which, but for the shearing produced upon the skin, could not be distinguished from the “ touch ” of a stationary smooth metal surface. We see then that three distinguishable conditions are produced by stimu- lating the skin more and more rapidly. At first, each stimulation is formulated separately in consciousness, then we have a sensation of roughness, and finally one of smoothness. Before proceeding further it will be well to insist upon the fact, that when we consider the subject more generally, we can find analogous conditions in the other sensations. There is certainly in hearing and sight, for instance, a period of “ roughness,” which is irritating in its nature, and is a distinct sensation preceding the com- plete fusion of the stimuli in consciousness. Moreover, the nature of its cause is known only by experience gained from other sensa- tions ; it not being evident in the consciousness of the special sensations above mentioned. The tick of a watch is not irritating — on the contrary, it may produce hypnotism. An alarum with more rapidly repeated sounds has a well known effect, upon which it will be needless to insist. My colleague, Professor Poynting, suggests that the very low notes of a large organ are, in like manner, irritating from their rapid intermittence. In the numbers quoted from Helmholtz, pro- bably the “ beats ” are no longer separately heard, but produce the harsh dissonance which characterises them ; a much lower number would indicate the number of stimuli which can be heard separately. This number I am unable to state, as a double syren is not in my possession. Pew things are more annoying than the flickering of a gas jet, or the slow vibration of a body which gives a blurred unsteady image. The tickling of a vibrating tuning fork held to the lips, or still more the tickling that results from stimulating in rapid succession adjacent points of the skin, is calculated in extreme cases to give excruciating agony. A few minutes’ consideration will also show that this condition of of Edinhurgli, Session 1883-84. 249 roughness ” is not a sensation of intermittent stimulation. That this is its cause is hut a matter of experience aided hy the use of the other senses. A child blowing the sharp edge of a piece of tissue paper stretched between its lips, remarks that “ it tickles,” but is quite unaware of the cause of the sensation. Again, on touching the rapidly revolving wheel, it is conscious only of a con- tinuous sensation \ but turn it more slowly, and it feels each separate tap. We have then in tactile sensibility a condition analogous to the cause of dissonance in music, and to the annoying flickering of recur- rent visual stimuli. Moreover, we can recognise degrees or qualities of this “roughness,” a most important factor in adding to our know- ledge of the external universe. On drawing a file, or the edge of a fine saw across the finger, the sensation is quite difierent from that produced by the back of a knife. Moreover, within limits, we can distinguish a coarse from a fine file. The sensation in each case is different, and experience especially gained by the use of the eye, tells us of the nature of the substance which has produced the feeling. It is a well known fact that all parts of the skin are not equally sensitive. The skin of the finger-tips and the front of the hand can be stimulated by the impact of a lighter body than will affect the skin of the back of the hand. Again, the skin of the front of the arm is more sensitive than that of the dorsal surface, and still more so than the skin covering the back of the shoulders. Together with this difference in actual sensitiveness, the brain is unable to localise impacts which affect the less sensitive parts, so exactly as those which affect the more sensitive. As a result of this, tvro impacts made on points of the skin near enough may be fused into one in consciousness. If the points of a pair of compasses less than one millimetre apart touch the finger-tip they ma.y be dis- tinguished as two, the localisation of each point in consciousness being very exact. Over the back, however, the points must be removed for more than an inch before they can be distinguished. This difference, not to be discussed here, is probably due to the anatomical distribution of the peripheral nerves. It becomes an interesting question whether the limits in time of conscious tactile sensations vary in like manner over different sur- faces of the body. 250 Proceedings of the Royal Society As a result of my experiments I am led to believe that, whereas the limitations in space are widely different, this does not hold with the limitations in time. If a rod vibrating about forty times in a second be held to the finger tips or lips, sensations of distinct impacts may be felt. Allow the rod to vibrate upon a surface less sensitive, and with niiicli wider limitations in space, say the skin over the sternum, and the impacts are still felt as such. I should mention that, inasmuch as the skin is less sensitive, the amplitude of the vibra- tions, and therefore the force of the impacts, should be increased. So far we have considered the limitation in time of tactile sensi- bility ; but there remains another very important function of the skin, which we have to discuss. I refer to thermal sensibility. On touching a good conductor, such as an iron ball, any difference of temperature will not at once be noted, the cold will not be felt instantly. On withdrawing the ball, the sensation of cold remains for a short time. The limits in time are very wide, for the applica- tion of the cold body on several successive occasions — even with intervals of a second — producing, of course, successive sensations of impact, gives rise to a continuous and uniform sensation of cold. If the good conductor be applied every second to the skin of the hack or arm, distinct sensations of cold will be produced each time. This is not due to these parts being covered and sensitive to cold, for the same obtains with the thin skin between the fingers, and the hack of the hand, although in a less degree. The difference must alone be due to the variations in thickness of the epidermis — a bad conductor — which separates the body touclied from the nerve end-organs in the lower layers of the skin. In studying these phenomena, I have used a very simple piece of apparatus. A long and slowly vibrating rod is fixed in an iron vice, and to its free end a small glass bottle is attached. This is fitted with a cork, through which passes an iron rod about half an inch wide. The bottle is filled with a mixture of ice and salt, which cools the rod in its whole length. The portion outside the bottle is caused to impinge upon the finger-tip periodically. In order that the action of external stimuli may affect our con- sciousness, a certain period of time is necessary. This period varies with many factors which we propose to discuss. A correct estirna- of Eclinburgli, Session 1883-84. 251 tion of the value of these factors is all the more necessary, as they are hopelessly confounded in most works on mental science. We have, first, the irritation of the peripheral sensitive nerve; secondly, the transmission of some change thus produced in the nerve ; and thirdly, that effect produced upon centrally placed nerve-cells associated with the production of feeling, and a con- sciousness of that feeling. The time elapsing between the impact of a body on the hand and the consciousness of that impact is much less than between the application of a drop of sugar solution to the tongue and the resulting sensation of sweetness. This period is different in the case of each sensation. On what does this depend ? I shall endeavour to show that the dependence is not mainly on differences of time taken by the impression to pass along different nerves, nor need we look to differences affecting central cells ; but we have, in the nature of the stimulus applied and in that of the stimulated end-organ, a cause which will account for everything. Herbert Spencer, in his Principles of Psychology (vol. i. p. 169, third edition), would actually distinguish between peripherally initiated feelings caused by internal disturbances — some of which, he says, are extremely indefinite, and few or none definite in a high degree — and feelings caused by external disturbances which are mostly related quite closely, alike by coexistence and sequence, among the highest of them the mutual limitations in time and space or both being extremely sharp. He illustrates this by the fact that our states of consciousness in connection with vision and hearing are more sharply limited in time and space than those in connection with smell and taste, and, still more, hunger. How, discarding the fact that when considered developmentally the retina at any rate is far more interjial than the mouth and nose, the former being really a portion of the brain, the latter puckerings-in of the surface, I would suggest, that the all-import- ant factor producing this difference, is not the brain, or the pro- duced feelings, as Herbert Spencer seems to me to indicate, but the nature of the peripheral end-organ stimulated. If the point of a pin impinges upon the fingertip, the epithelium is depressed, and at the same time the nerves of tactile sensibility are stimulated ; and on withdrawing the pin, they are at that moment unstimulated, and in a condition of rest. Also in the ear, the sound vibrations 252 Froceedings of the Royal Society travelling rapidly into tlie internal ear cause the structures there (the basilar membrane and rods of Corti) to vibrate,, and- — as we are aware from our knowledge of the action of one vibrating body upon another — they do this very rapidly. Tar otherwise with the senses of smell and taste. When odorous particles pass into the olfactory or upper part of the nasal cavity — in which the nerves of smell are placed — it is by diffusion from the lower or respiratory part of the nose. If the breath be held, and a piece of incense paper be burnt in front of the face, some time may elapse before the scent is perceived, because the odorous particles have ill fact to diffuse into a closed sac. If, on the other hand, the experimenter “ sniffs ” the air, the stimulus will be more rapidly perceived, because the odorous particles are carried rapidly through the lower chamber of the nose, inducing out-currents from the upper chamber, which consequently becomes immediately filled by odorous particles. In like manner, the closed sac has to get rid of odorous particles from within it by this same slow process of diffusion, before the odour ceases to be felt. From the nature of the stimulation and position of the end-organ, the limitations in time of the sensations are not well marked. In the case of the sense of taste, the same holds true. Substances held in solution are alone tasted; the tongue is covered with a layer of mucin derived from mucous and salivary glands, and the nerves are not superficial but embedded in the epithelial covering. It will be easily understood, that in this case also, the accession of a sensation must, from the nature of the stimulus, and the position of the end-organ, be gradual in its production and slow in passing off, and therefore not strictly limited in time. The watery solution has to mix in the first place with the mucin covering the tongue before it can reach the end-organs situated in the epithelium. In the case of hunger again, the limitations in time are due entirely to a condition of things other than mental. The fulness of the alimentary canal is associated with a feeling of comfort, and when no food is present therewith a feeling of hunger ; and as there is every conceivable transition between a condition of full stomach and an empty one, so the passage of the one sensation into the other must pass through innumerable transition states. If it be needed, another example may be mentioned in the case 253 of Edinhurgli, Session 1883-84. of the cold body applied to the horny tip of the finger, and to the thin skin covering the sides. The nerve-endings are stimulated by the addition or ^vithdrawal of heat from the nerves of the skin. This is gradual, and does not correspond to the application of the cold body to the surface because of the horny epithelial covering. Where this covering is thin, the limitation in time of the sensa- tion is more definite than where it is thick ; and could we apply the cold body directly to the nerve end-organ, the limits would then be very sharply defined. Cover the hand with a glove, and the limits would be very ill-defined indeed. Sufficient evidence has, I think, been adduced to show, that where the limits of a sensation are not well defined in time, we may conclude that this is not due to anything in the nature of the sensorium, but depends upon the way the external energy is changed into nerve energy in the terminal end-organ. Let me define a sensation as the result of a transformation of the energy travelling along a nerve of sensation from without, into the energy manifested by the nerve cell to which it passes. We have, I insist, no reason to doubt that if that nerve energy travelled twenty times a second along a nerve of smell, of taste, hearing, or of sight, we should be conscious of twenty separate sensations in each case. That such a transmission is impossible in every case we know, but it is due to the fact that in these cases the nerve cannot be stimulated from without so frequently. In the case of the ear, the limits in time of high notes are sharper than those of the low notes, and probably this is due to a better damping apparatus in the ear. Could we increase the perfection of this damping, the limits of the consciousness in hearing would probably be sharpened almost indefinitely, for we must remember that the cause of the different sensations of sound is a difference of pitch, or periods of stimulation recurrent in time to which the sen- sorium is extremely sensitive. If this be true, the period of time taken by a stimulus to produce a sensation depending upon the time taken by its energy to be transformed into nerve energy in the peripheral end-organ, will be some indication of the manner of this transformation. For instance, there is a very marked interval between the moment at which the 254 Proceedings of the Boyal Society rays of light strike the retina, and the production of the sensation ; and further, the sensation remains for some time after withdrawal of the stimulus. It is unlikely, therefore, that the energy of light is directly transformed into nerve energy. In shortly summing up the chief points alluded to in this paper, it may he stated — (1) That stimuli applied to sensitive peripheral end-organs with increasing frequency, produce at first consciousness of the separate stimuli ; then, their individual characters are lost, and a disagreeable sensation — “ roughness” in the case of tactile feeling — is produced; and lastly, we feel a sensation indistinguishable from a constantly applied stimulus. (2) For the development of nerve energy from external stimuli in a sensory nerve a latent period is necessary, and it elapses be- tween the application of the stimulus and the resultant effect on the nerve. On withdrawing the stimulus, the nerve is still in a condition of activity, and remains so for a certain period (after- period). When this nervous energy is transformed into nerve-cell energy in the sensory centres, there is probably neither a well- marked latent nor an after-period. (3) When, as in the sense of touch, the consciousness of the stimulus corresponds more exactly in time with the application of the stimulus than in the sense of sight, we are to look not to any differences in the limitation of consciousness itself, but to the time elapsing in each case before the nerve is excited by the stimulus and the length of the corresponding after-period. 2. The Old English Mile. By Wm. Flinders Petrie. Communicated by Professor Eobertson Smith. The length of the old English mile has been hitherto so uncertain, that any fresh light upon it is well worthy of study ; and an im- portant source of information — the map in the Bodleian Library — has not yet been brought to bear upon the question. The present inquiry was suggested by the sight of this map, which seems to add so much to our knowledge that a review of the whole subject has become desirable. It is proposed, therefore, in this paper to bring together all the data worth consideration, beginning with the most 255 of Edinburgh, Session 1883-84. recent ; and by deducing what the mean conclusion is from each source, to be thus able to compare together the various results, and so arrive at some definite statements within known limits of uncertainty. The only discussion of the subject that has yet been made is that by Professor de Morgan * in the article Mile,’’ in the Penmj C ijdopoedia ; in other encyclopaedias no notice is taken of the history of the English mile, and D’Anville makes only a rough deduction as to the old mile being longer than the statute mile ; he uses but few data, complicates these with unproved theories, and is somewhat vague in his statements, f It will be necessary first to briefly mention some of the conclu- sions in De Morgan’s most valuable article in order to point out their bearing on the inquiry. In beginning the article he seems strongly inclined to disbelieve in the existence of any old mile longer than the statute mile, mainly relying on the fact of Bernard (1688) and Greaves (1647) not describing any longer mile. He says, on the authority of the silence of Bernard and Greaves above referred to, we must remain of a contrary opinion (I'.e., to D’Anville), and must suppose that the computed miles preserved by Ogilby (1675) had been intended to represent the number of statute miles, but erroneously given. What then may these computed miles mean which had served the common purpose in the estimation of distances? The word computed never meant reputed, but was always applied to a result of reckoning of some kind or other.” How it so happens that, in the Travelled s Guide (1699) | (a typo- graphical edition of Ogilby ’s Atlas), these miles are variously described as “computed,” “vulgar computation,” and “reputed;” so that the objection raised by De Morgan to their being those in common repute and use is not borne out by the name employed. He notices Ogilby’s guess that the computed distances read a less number by omitting the lengths of the towns ; and, rejecting that idea as an insufficient explanation (as it certainly is), he concludes * Notes and Queries, i. xii. 195. + As when he describes 15 '2 miles as being “ quelque chose de plus que 14,” in Mesurcs Itineraires, chap. x. X De Morgan does not seem to have seen this book at all, as he refers to The Complete Tradesman, by H. H. (1684), as giving the lists of computed and measured miles, which this edition of Ogilby gives far more completely. 256 Proceedings of the Royal Society that the ‘‘computed” distances were derived from the straightdine measurements of statute miles from a map, thus omitting the length of windings of the roads. But this explanation also is quite in- sufficient, as, in the first place, the windings will not account for even as much as half of the difference of numbers of computed or reputed and statute miles ; secondly, the difference between com- puted and statute miles exists just as plainly on the straight Roman roads, where no windings exist, as on the winding roads ; and finally, as we shall see, these computed miles are the same as those in use in the thirteenth century, when maps were very scarce, and it is quite unlikely that the populace should have adopted their current reckoning of every-day journeys from the measurements of a few distorted monastic manuscripts. Hence, De Morgan’s explanation is certainly insufficient; and in the latter part of his article he argues for an old mile equal to 1 J statute miles, concluding thus : “We think it by no means improbable that 100 ancient miles are as much as 150 statute miles, and tolerably certain that they exceeded 145 such miles.” Thus he agrees with Sir Henry Ellis, who writes, “ the ordinary mile of England was nearly a mile and a half of the present standard.”'^ A point on which De Morgan lays much stress is the shortening of the roads in modern times, and the much greater length he supposes them to have formerly been. The only evidence adduced is a com- parison of four of the distances by Ogilby (1675) in statute miles with modern statements of the same, which may not have followed exactly the same route. But on measuring the modern distances f of about ninety of Ogilby’s statements, there does not appear to be any constant difference between his reckoning and the present roads; and in single lengths Ogilby was certainly in error occasionally, since he sometimes gives a less distance than the shortest practicable line. | Eroni a general consideration of the history of roads, and the * Introduction to Domesday Book (1833), i. 145 et seq. 4 Tlie actual distances in statute miles are here ascertained from the county maps of The National Gazeteer (1865 ?); these are very clear, and appear to be accurate on comparison with the Ordnance Survey. The windings of the roads are in all cases carefully attended to in the measurement. %E.g., High Wycombe to Tetsworth, 12’0 Ogilby, =:13'6 miles really; Frestein to lihyadergowy, 127 Ogilby, =14 ‘4, or more, really; Eoyston to Huntingdon, 19 '2 Ogilby, =21 ’4, or more, really. 257 of Edinburgh, Session 1883-84. manifestly ancient course of most of them, it seems very unlikely that any notable alteration has taken place in their length since they were the first tracks through waste lands. After what has been remarked above, there does not seem any reason for not taking the statements of distances in various books and maps to be what they profess to be, that is, the ‘‘reputed” or “vulgar” long miles between the places in question, reckoned exactly like the statements of the same distances in statute miles. It may seem rather astonishing to see in all maps, until within recent years, such a careful definition of miles as “ statute miles, 69 J to 1°”; but the need for this explicitness arose from the great confusion which existed between different miles. In Gibson’s edition of Camden (1695) there are no less than three mile scales on nearly all the maps ; these scales vary a good deal, but by measuring each of them, and a distance between two places on each map to give the true scale, the values of the three miles, “ great,” “middle,” and “small,” may be deduced.'^ On thus obtaining a value from each of the forty or more maps, and taking the mean result for each sort of mile, we find the miles to be respectively 1290 ±16, 1167 ±14, and 1037 ±11 thousandths of the statute mile, t How these values are very exactly in the proportion of 10, 9, and 8 ;l and since we cannot doubt but that 1037 was intended for the statute mile of 8 furlongs, it seems that these three miles were of 10, 9, and 8 furlongs respectively. Hext before this there is the great authority of Ogilby, the surveyor of England, to whom the first accurate road maps and measurements are due. He published his atlas, Itinerariimt Angliee, in 1675, stating the miles of “ horizontal distance ” {i.e., as the crow flies), of “vulgar computation” {i.e., the old long miles), and of “ dimensuration ” {i.e., the statute miles measured by his perambula- * The degrees on the borders of the maps cannot be trusted, as they bear no fixed relation to the miles, and the longitudes of the western counties are very erroneous. t Throughout this paper all miles will be thus stated in thousandths of the statute mile. 7 Thus, 1290^10 = 129-0±l-6. 1167-^ 9 = 129-7±r5 1037± 8 = 129-6±l-4. 258 Proceedings of the Boyal Society tor) ; but as lie only gives tbe totals in this way, the details must be sought in the typographical edition of his work called The Travellers Guide For comparing the “computation,” “vulgar com- putation,” or “reputed” miles, with the real distances, Ogilby’s statute miles have been here adopted, as he has no constant error in one direction, and his fluctuating errors are much less than those of the reputed miles, so that no further inaccuracy will be caused by taking his statement. In this investigation the roads were broken up into lengths of about forty miles each for purposes of com- parison of the mile lengths ; and besides this, there are shorter lengths of cross roads. The lengths compared together are in all 154 in number, of which 134 belong to the old mile, eight to the N.W. mile, and twelve to the Welsh mile. From the mean of these 134 lengths, the old mile appears as 1307 ± 5. The local miles we pass over for the present ; but the posting miles which are given, though agreeing in general with the old miles, yet in nine cases are shorter, and in two cases a little longer ; the shortest form is equal to the statute mile. From Ogilby’s work lists of miles were reprinted more or less abbreviated, as in the The Complete Tradesman, by IST. H. (1684), which gives both “computed” and “measured” miles. In The Exact Dealer, by J. H. [John Hill] (1688), the miles are generally the reputed or long miles of Ogilby, but sometimes the post miles, or others. In The Description and Use of two Arithmetic^ Instruments, by Sir Samuel Morland (1673), just before Ogilby’s publication, the miles are the same as the post miles in Ogilby, where they differ occasionally from Ogilby’s reputed miles. The next earlier information is in the maps of Eugland com- monly known as “The Quartermaster’s Map” (1644). This gives a scale on each of the six sheets ; and on measuring two distances on each sheet to obtain the absolute value, it appears that these maps are far more accurate than any others of that period, the average error being but a third of that of Saxton, Speed, or Gibson. The mile value from this source averages 1255 ±10. In the year before this A Direction for the English Traveller * This is catalogued under Ogilby in Brit, Mus. ; but he died in 1676. There is no editor’s name to it. 259 of Eciinlurgli, Session 1883-84. (1643)* first appeared; tliis consists of a series of small copper- plate maps of each county with a cross-line table of the distances between places in the county, besides a similar plate of all England. The same plates were printed from again by the same publisher in A Book of the Names of all Parishes, &c, (1662 and 1668). Taking from each plate two of the distances stated between places in miles, and comparing the 73 distances thus extracted with the true road distances, the mean mile is 1375 ±12. But this is so decidedly longer than the mean mile of any other authority, that it seems as if these distances had been compiled and tabulated by measurement from the plates, or from some older maps, in straight lines. If this were the case we should subtract about 7 per cent., f and the true mile will then be 1280 ± 20, and thus in accordance with other authorities. Speed’s maps of counties preceded this by some time (1610); and on measuring the mile scale, and a distance between towns, on each plate, and then taking the mean of the 43 results, the mile comes out 1300 ±12, omitting the Welsh counties. Saxton’s county maps (1575) also have scales, and were examined like Speed’s for extracting the mile. Erom thirty plates the mean result is 1310 ± 16, omitting the Welsh as before. William of Worcester (1473) gives measurements and distances continually, throughout his rambling note-book ; and by extracting all the distances, his mean mile may be obtained. But it is not desirable to include any of less than 5 miles, as such are necessarily much less accurate, being only stated to single miles ; and all sea distances, and rough statements of the dimensions of districts or countries, should be omitted. There then remain 92 distances, and on measuring all these on modern maps, it appears that his mile was 1310 ± 20. Sir Gilbert de Lannoy’s distances in Palestine (1422), quoted by De Morgan (article “ Mile ”), give by five examples a mean mile of 1180 ± 20, about 8 per cent, for winding of roads, and therefore probably about 1280 ± 20. * Published by Thos. Jenner, under whose name it is catalogued in the Brit. Mus. t By careful map-measurement of six long distances in England of 50 to 200 miles each, the excess due to windings is 127 on the 1000; and on short distances, of 12 to 25 miles, the windings make an increase of 66 on the 1000, beyond the direct distances in straight lines. 260 Proceeamgs of the Poyal Society Eoger Bacon’s distances in Palestine (1253), also quoted by De Morgan, give by fifteen examples, a leuca equal to 2 miles of 1230 ± ^0,'^ plus about 7 per cent, for windings, = 1320 ± 60. Neither this nor the previous statement are worth much, as they depend on the estimates of a few foreigners in a strange country, and not on the well-known reckoning of places where the writers and all their acquaintance had always lived, as in England. We now come to what is the oldest authority, and also one of the most complete. This is the vellum map of England, Wales, and Scotland, in the Bodleian Library, which has the roads and distances marked on it throughout England and Wales. This map is attributed to the thirteenth century, and is by far the finest map known for such an early period. It is written in red with brown lines, and with the sea coloured green ; and it is in very fair con- dition. It w^as published in copper-plate facsimile by Basine, with a partial description by Gough (to whom it belonged) in British Topography^ i. 76 f (1780). It has also been published in coloured facsimile, with a key-plate of the names printed, in National Monu- ments of Scotland, part iii., edited by C. Innes. Basine omitted things altogether wLen he could not easily read them, and his renderings often differ from Gough’s aceount. Generally his map has a better reading than Gough’s text ; but they both have many errors. I Gough continually omitted the numerals, even when Basine read them rightly; and he made curious mistakes in the places. § Of course, no attempt was made to utilise the distance in such a manner of treatment. The facsimile by C. Innes is a fine piece of work, and apparently very correct ; but the names are often omitted from the key-plate if hard to read ; no attempt is made to supply lost names, by considering the positions of places ; and the words have been merely read, as well as might be, without a reference to a modern map to check the reading. || The main * There is a manifest mistake in the place names ; they should read Joppa to Caesarea, Caesarea to Aco, &c. t The map in the Brit. Mus. copy is wrongly bound in at vol. ii. p. 76. t For errors in common, see Colebrook to Maidenhead, x. in Gough and Basine, but vii. in Innes, which is the true reading by the distance ; Whitby to Guisborough, xii. Basine, xiii. Gough, but xvii. Innes, the true reading. § T.g., applying ‘‘ Burgh ” to Carlisle, while it belongs to a separate town on the map. 11 Thus there is the curious transcription of Coxton for Tuxford, of Lenning 261 of Edinhurgli, Session 1883-81. attention of the editor was given (very properly in such a work) to the Scotch topography, and the far more valuable part of the map — as a map — was treated as an annex of little importance to the subject in hand, attempt to transcribe or examine the mile distances was made either by Innes or by Gough. When I saw this map at Oxford, and transcribed as well as I could in an hour or two the lists of distances, it seemed very evi- dent that all the distances in the south and east of England had been rewritten by some hand well accustomed to mediaeval script ; and this accounts for the ends of many words going off into a mere series of strokes, since the re writer was not certain of part of the name, and just inked over what he could see. This rewriting deserves careful study in considering the map ; and as it was ap- parently done before the sixteenth century, and the old writing must have been fading then, and yet is not illegible in parts even now, it is some evidence as to the great age of the map. What is now much needed is a critical examination of this map, identifying all the places by comparison with modern maps, and recovering any traces of the first writing of names and distances where it has become all but illegible. This work needs a good palaeographer ; but for the question of the miles, which is what we have at present to consider, such care is not required ; for, if a few doubtful dis- tances are omitted, it will not perceptibly affect our results. From a comparison of the readings of Basine, Gough, Innes, and my own notes, the distances may be pretty safely settled in all legible cases ; and after omitting those in Wales and Cheshire, which show a different mile, there are 130 distances available for examination. The mean value of the old mile from these is 1265 ± 9. Having now described the various data available for fixing the old mile, we will place the results all together and compare them, in terms of thousandths of the statute mile ; stating the mean result from each source, the probable error ( ± , i.e., what amount of varia- tion the truth is as likely to exceed as to lie Vv^ithin), and the average error of a single length, which shows the relative accuracy of the different sources. for Leeming, and the placing of Abergavenny on the west coast of AVales for a town which must be Aberdovy. * The map is framed and glazed, and screwed high up against a pillar in a poor light ; hence it is not easy to study. VOL. XII. s 2G2 Proceedings of the Boycd Society A.D. Mean mile. Mean error. 1695 Gibson’s maps,. . 40 maps. 1290±16 no 1675 Ogilby’s numbers,. 134 distances. 1307 ± 5 65 1644 Quartermaster’s map, 11 distances. 1255±10 35 1643 Tenner’s numbers, . 73 distances, (1375±12) no or allowing for windings, probably 1280 ± 20 1610 Speed’s maps, . 43 maps. 1300±12 90 1575 Saxton’s maps, . . 30 maps. 1310±16 100 1473 Wm. Worcester’s notes, 92 distances. 1310±20 200 1422 Lannoy’s account, 5 distances. 1280±20 60 1253 Eoger Bacon’s account, 15 distances. 1320±60 480 1250? Bodleian map. 130 distances. 1265± 9 120 The question now before us is, what probability is there of any change in the popular mile during the four centuries in which we have traced it ? The possibility of change certainly lies within narrow limits, since (looking to the accurate authorities) the later examples cannot be taken to exceed 1307, nor the earlier to fall short of 1265.* Xow, it is very unlikely that the Bodleian mile was as long as 1300, in fact it is more than 100 to 1 against its being so ; therefore, the oldest form cannot be taken as a mere careless variant of Ogilby’s value of 1307. Bacon, Lannoy, and William of Worcester are all too uncertain to decide on the difference in ques- tion. Coming down to the seventeenth century, the Quartermaster’s maps, which agree very well among themselves, corroborate the earlier value, but we can hardly set them up against the large mass of information in Ogilby’s tables. On the whole, I should incline to fix the value of the old English mile at 1300 ± 10 during the end of the fifteenth and on to the seven- teenth centuries, and to suppose that during the fourteenth century and the beginning of the fifteenth, it was lengthening from a value of 1265=1= 10, which it had in the thirteenth century. As it had lengthened thus, it is not improbable that the original value of it was still shorter, perhaps not exceeding 1250, or \\ statute miles. In any case the range of uncertainty is now reduced to very narrow limits, * The mile in Italy having lengthened 1 per cent., though many of the old Roman milestones remained standing in the country, shows in which direction itinerary measures are likely to change. of Edinhurgli, Session 1883-84. 263 compared with the vague conclusions that have been hitherto adopted. We will now briefly notice the miles of the IST.W. counties and of Wales. That a longer mile was in use in Lancashire, Cheshire, and Shropshire is certain both from the various authorities that we have just discussed agreeing in it, and also from the fact of a longer perch surviving in those parts.* On taking out the distances in Cheshire and Shropshire, they yield the following mile : — Bodleian. 1540±100 Speed. 1340±50 Wm. Worcester. 1570±70 Ogilby. 1400±15 Saxton. 1420±10 Gibson. 1385 ±60 Lancashire is 1400 in Saxton, but comes down to the usual old mile in Speed and Ogilby. Thus it seems that the old iST.W. mile was about 1560 ±80, and was somewhat assimilated, as time went on, to the usual old mile of England, 1300 ±10. There are not suf- ficient accurate data to allow of a complete disentanglement of local miles ; but the Bodleian map distances in the eastern counties are not over the average, while later on they are higher. The southern and S.W. counties generally have a lower mile than the northern. But there is nothing necessarily to show more than accidental varia- tion in the unit, except in the IST.W. counties, considered above, and in Wales, which we will now notice. The Welsh distances give mile values of — Bodleian. Saxton. Speed. Ogilby. Gibson. 1465 ±45 1410 ±20 1360 ± 20 1383 ±20 ]N^o great mile. Here there appears to have been an old mile of about 1460 i 50, probably identical with the Cheshire mile ; and, like that, gradually approximating to the usual old English standard. The origin of the old English mile, which we have seen to be L265 statute miles, now remains to be considered. * Lancashire perch 7| yards, therefore mile=l‘360 statute miles. Cheshire ,, 8 ,, ,, ,, — Notes and Queries, vi. i. 264. Herefordshire perch 7 yards, therefore mile = 1 "270 statute miles. Staffordshire ,, 8 ,, ,, =i"460 ,, — Ency. Brit, 3d edit, art ‘‘ Perch.” 264 Proceedings of the Royal Society First we must note that the statute mile and furlong were prob- ably independent of each other originally. The earliest mile near the statute mile was one of 5000 feet, defined as 7^ furlongs 3 perches and 2 palms,* about 1350 ad. Then about 1470 a.d. a mile appears of 8 furlongs,* which first received legal recognition in 1593 A.D.t Now, if the mile of 8 furlongs had always existed, it is very unlikely that one containing a fractional number of fur- longs would have arisen, so that it is probable that the furlong is the older measure, and that the mile was adapted to fit it. And this is also indicated by the register of Battle Abbey mentioning furlongs but not miles ; so that the furlong appears a long time before the mile of 8 furlongs. The furlong, though now defined by the yard standard, was ori- ginally independent of the present foot and yard; for it is im- possible to suppose a length of 5J yards being selected without any reason. This is manifestly the nearest translation into the lesser standards of a measure which was originally incommensurable with them. Thus it seems most likely (as De Morgan supposes) that the statute mile was originally 5000 feet of 12 inches, and that it was modified to 5280 feet in order to agree with the furlong, with which — as being the nearest measure in size, and the basis of land measurement — it was most required to accord. And the furlong was an independent unit, not having any exact relation to the foot of 12 inches, or the mile of 5000 feet. Now we have seen by Gibson’s maps that the long mile was evidently reckoned as 10 furlongs, being exactly of the statute mile there ; and we have seen that the old mile was originally 1'265 A 10 statute miles, or even slightly less. The furlong, then, would be T265 statute mile, —8015 ±64 inches, or rather less. The chain, or of the furlong, would be 801 ‘5 ± 6 inches. Below J of a chain, or a perch, we lose sight of the original subdivisions, as the link is a modern invention of land surveyors, and the 5|^ yards is merely an approximate adaptation of a different standard. Turning now to other countries, we meet at once with a mile * Canterbury registers, fourteenth century, quoted by De Morgan, art. “ League,” Penny Cydopsedia. t De Morgan, in art. “ Mile.” 265 of Edinburgh, Session 1883-84. closely similar to the old English mile ; this is the old Erench mile, which is equal to 1'21 statute miles, or within 3 per cent, of what we have seen to he probably the earliest English mile. And this resemblance is not only in length, but also in subdivision, as the Erench mile is 1000 toises, and this is decimally divided like the 10 furlongs in the mile, and the 10 chains in the furlong. Also, the English league consisted of two old English miles,* like the French league. This continued decimal division of the Erench mile suggests that perhaps the old English mile may have had lesser subdivisions than the chain ; of the chain would be SOT 5 ± ’6 inches ; and if this fathom was subdivided into 6 feet, like the Erench toise, we should have a foot of 13*36 ±T inches, or rather less perhaps by the original mile. Now, on referring to Inductive Metrology, p. 107, it will be seen that the commonest foot known in the medimval remains in Eng- land is 13*22 ±“01 inches in length; this being more commonly found even than our modern foot of 12*0 inches. Here then we have found the basis of the old mile appearing quite independently as the most frequent measure in mediaeval England. This foot ap- pears to be the same as the classical “Drusian foot,” which may have been introduced by the Komans into both France and England. The series of measures thus connected with the old English mile run thus : — Inches (by the mile). Inches (by the foot). Foot . . . 13*36+ ‘1 or 13-22+ -01 6 feet =1 fathom . 80-15+ -6 79-32± +6 10 fathoms =1 chain . 801*5 + 6- statute miles. 793-2 + -6 statute miles. 10 chains ^1 furlong 8015- + 60-= -1265+-001 7932- ± 6-= -1252±-0001. 10 furlongs = 1 mile 80150“ + 600- = 1-265 ±-01 79320- ± 60-=l-252 ±-001. The second determination, working from the foot, which is far more accurately known than the mile, is probably the most trustworthy ; and as we have observed that the original form of the mile was probably rather shorter than 1*265, therefore this restoration of the old mile from the foot, shown by various buildings, represents the data that we have as well as anything can, and is far more accurate than anything that we can hope to recover from itinerary measures. See Eoger Bacon’s distances, before quoted. 266 Proceedings of the Eoyal Society We see, tlieii, that by the exclusive survival of the 12-inch foot, we have lost the basis of a decimal system of measures, and thus, complicated our land measure in a most troublesome manner. In this examination, then, we have traced the old English mile back through four centuries, and seen that it varied but little in different times, and as used by different persons. And, following the analogy of the old French mile (with which it seems to have been identical), we see that it was part of the decimal system of the fathom, chain, furlong, and mile, based upon the most usual mediseval foot of England. Whether this mile was introduced by the hlormans, or whether its basis had remained in England (like other measures) from Roman times, is still unsettled ; and this question, as well as the local variations of the mile, and the origin of the miles of Wales and Cheshire, must remain for future discus- sion, when other and more complete materials may be discovered. 3. A Re-Statement of the Cell Theory, with Applications to the Morphology, Classification, and Physiology of Protists, Plants, and Animals. Together with an Hypothesis of Cell-Structure, and an Hypothesis of Contractility.* By Patrick Geddes. Plate IV. Position and Im,portance of the Cell Theory in Morphology. — Vast though is the literature of vegetable and animal morphology, it becomes more readily grasped than that perhaps of any other science, when we classify it in relation to the few great works which initiated and for ever mark the successive waves of advance. Thus o-f the early pre-niorphological or encyclopaedic stage, when materials were being little more than heaped together, the works of Pliny or Gesner may be taken as types, to which the other encyclopaedias of Natural History by Jonston, &c., furnish at first mere supplements. The Sy sterna Natures of Linnaeus closes the old and marks a new era, and initiates that systematic enumeration of the flora and fauna of the globe which has since made such vast progress. All subse- quent systematic literature, no matter how important, no matter how much exceeding in quantity of new forms, involves no essential, no qualitative advance : thus the greater part of the proceedings of such * Prelim. Rote in Zool. Anzeiger, No. 146, 1883. Proc.Tloj Soc.EdnP, VolEII, Plate PP Ml of Edinhurgh, Session 1883-84. 267 Societies as the Zoological or the Linnean, such new and important faunistic literature as that contained in the magnificent volumes of the “ Challenger ” Expedition, or even the greatest systematic works, find their highest place not as superseding, hut as supplementing the fundamental classic of Linnaeus. Similarly all works of detailed anatomical research united with exact comparison and clear gene- ralisation, are in botany simply to be regarded as supplementary to the little work in which Antoine de Jussieu founded the dvatural System, or in zoology to the Regne Animal of Cuvier, himself also an intellectual heir of Yesalius; Embry ological literature in like manner finds its place in the appendix and commentary to the works of Eobert Brown or Von Baer respectively; at the head of all investigations of serial homologies stands Goethe’s memorable essay On the Metamorgihoses of Plants; while all evolutionary literature may be arranged round the works of Lamarck and Darwin. The morphological investigator, unless claiming to initiate some new line of thought, has thus to take his place simply as an assistant to one or more of a few immortal masters. But the cell theory? This is apt to be excluded from general morphology altogether, and to have a separate subordinate province — of histology — erected for it, a vicious tendency, which although by no means fully adopted, still somewhat injures the continuity of treatment in the writer’s recent essay on Morphology.* To ascer- tain its position, we must first briefly glance at its history. Here the fundamental classic is undoubtedly the Anatomie GhiP rale of Bichat, though in this the name of cell does not even occur, the “ tissue ” being assumed as fundamental. The analysis of the organism into definite structural components is, however, the main idea ; after this the history of histology is little more than of accumu- lating observations with improving optical and technical appliances, until we come to Schleiden, who boldly referred all vegetable tissues to the cellular type, and the plant embryo to a single nucleated cell; while Schwann, by immediately extending the generalisation to the animal world, fully constituted the ceil theory. This idea then is fundamental in morphology; for the innumerable species and genera of plants and animals made known under the leadership * Ency. Brit., xvi. p. 837 ; amended in German translation, JenuiscM Zeitschr., 1884. 268 Proceedings of the Royal Society of Linnseus, and the numberless anatomical resemblances and differ- ences investigated by Cuvier and his disciples, become reduced to resemblances and differences in the details of structure and position of fundamentally similar unit masses ; while the resemblances of development made known by embryologists become the connecting link between the cell theory and these generalisations of adult structure. It is not necessary to do more than merely allude to such applications of the cell theory, or to that of the study of patho- logical structure initiated by Goodsir and Virchow, or to that brilliant confirmation of the unity of the animal and vegetable cell which has lately been afforded by the detailed study of the processes of cell multiplication. Agassiz* was fully justified in the opinion that the most brilliant result of modern science was the ovum-theory, and thus it is beyond dispute that “ in our own day, as in those of Bichat and Schwann, the labours of the histologist, when inspired by higher aims than that of the mere multiplication of descriptive detail, are of supreme morphological importance, and result in the demonstration of a unity of organic structure deeper even than any which we owe to Linnseus or Cuvier, Goethe or Geoffroy.” f Cell — The position and importance of the cell theory being thus defined, the fundamental necessity for a precise conception of the cell itself will be sufficiently obvious. The early progress of this is well known ; at first the vegetable cell-wall gave the type, while Schwann’s cells were essentially nucleated vesicles with fluid con- tents. Dujardin described the sarcode ” of Foraminifera ; Von Mohl discovered the “ protoplasm ” of the vegetable cell ; while Max Schultze identified both as the same substance; showed it, and not the membrane to be essential ; and gave an amended definition of the cell as a unit mass of nucleated protoplasm. For working purposes it is this conception which is generally accepted, and almost every dissertation or treatise upon the general questions of botany or zoology, histology or physiology, commences by postulat- ing it, the amoeba being most frequently taken as the standard type. J Unsolved Problems. — Such a conception of the fundamental * Essay on Classification. t “Morphology,” Ency. Brit., xvi. sec. 3, p. 840. % Of this no better instance can be afforded than the introduction to the admirable Manual of Physiology of Dr Michael Foster. of Edinhurgli, Session 1883-84. 269 cellular unit, however valuable, yet throws no light upon a large number of problems at present under dispute ; and it is the aim of the present paper to draw attention to some of these, and by the aid of a re-statement of the cell theory (a new appendix as it were to the Anatomie Ghi'erale, or to the work of Schwann), to propose a solution of them. The problems then which it is proposed to discuss may he briefly enumerated for convenience under separate heads, as follows : — (1) The classification and affinities of the Protozoa. (2) The classification and affinities of the Protophytes. (3) The systematic position of the Myxomycetes and other peculiar forms. (4) The acceptance or rejection of Haeckel’s third intermediate sub-kingdom Protista. (5) The phytogeny of the low^er plants and animals, and their origin from one or several stocks. (6) The relation of the Protophytes to the higher plants. (7) The relation of the Protozoa to the higher animals. (8) The morphological relations of plants to animals and their origin from a common stock, or from separate ones. (9) The classification of animal tissues. (10) The physiological rationale of changes of cell-form. (11) A theory of the origin of sexual reproduction, and its relation to conjugation and other cases of cell union. (12) The relation between normal and pathological tissues. (13) The influence of the environment on the origin of organic forms. (14) A theory of cellular variation (since the theory of descent involves a theory of variation, and all variations, normal and patho- logical alike) must ultimately be expressible in terms of cellular ones. 1. Classification and Ajfinities of the Protozoa. — The Protozoa have long been thrown into a few main groups, of which the Rhizo- poda, embracing all essentially amoeboid forms like the Protoplasta, Foraminifera, Heliozoa, and Eadiolaria, and the Infusoria, including all those of permanent and usually ciliated type, are the oldest and most important. The position of the Gregarinida, of the Monads, and still more of forms like Chlamydomyxa and the Labyrinthulida, 270 Proceedings of the Royal Society or Haeckel’s Protomyxa, is still disputed, nor is that of Ehizopods to Infusors, despite their more or less intermediate forms, as yet settled. But our current conceptions of the groups of Protista are based upon their more prominent and permanent characters only. An infusorian is constantly thought of as a permanently ciliated or flagellate organism ; a radiolarian is constantly described as a highly differentiated rhizopod, with two layers of protoplasm, a gelatinous envelope, yellow cells, and siliceous skeleton ; or again its simpler ally the heliozoon is seldom or never thought of without its radiat- ing pseudopodia with their peculiar axial filaments. Yet such conceptions involve a morphological fallacy of the most serious kind. These are indeed the most highly differentiated, the most frequent, the most permanent, and therefore the most striking forms in which these organisms are known to us, but of late years it has been becoming more and more obvious that each of these well- known forms is at best but the most important stage of a life-history, during which the organism passes through one or more other phases of form, which may indeed be transitory, but thereby lose no whit of their morphological distinctness or importance. Thus, thanks to the researches of Dallinger and Drysdale, Butschli, Savile Kent, and others,* we know that a monad is not a permanently flagellate form, but appears at one time encysted, at another becomes amoeboid ; the ciliated embryos of the Acinetse have long been known, f while more recent investigations have estab- lished the multiplication of radiolarians by zoopores, | or the frequent union of several individuals of various species of Heliozoa§ or of Gregarines|| into a single mass. In short, the progress of recent research among these forms has largely lain in revealing the exist- ence in even the most highly differentiated forms of a life-cycle of several distinct phases. In lower forms more attention is paid to the whole life-cycle, yet not sufficiently so. The Amoeba is still constantly spoken of as if its encysted stage were of no morphological interest, whereas no permanently amoeboid form has ever been proved by continuous * Savile Kent, Manual of the Infusoria. + Ihid. J Brandt, Monatsh. d. Berlin Akad., 1881. § Gruber, Zool. Anzeiger, No. 118, 1882. II Gabriel, “ Z. Classif. d. Gregarinen,” Anzeiger, 1880. 271 of Edinburgh, Session 1883-84. observation to exist; in the Gregarine, on the other hand, the amoeboid state is often practically ignored by. classifiers. In the remarkable Protomyxa of Hseckel, however, we have an organism in which several phases of form are almost equally pro- minent, so that its description as an amoeboid, or a ciliated or as an encysted organism, has been alike impossible. For here is no per- manent highly differentiated form ; but an eventful life-history in which one protean mass of protoplasm passes through a cycle of several distinct phases. Let us careftdly examine then these phases, since light may thus be thrown upon the life-histories of the higher Protozoa already referred to. Starting then from the encysted stage, in which a mass of proto- plasm is surrounded by a dense envelope, we find that from this after a time (in which division of the protoplasm has in this case occurred), there issues a swarm of somewhat pear-shaped, naked, motile, flagellate organisms. After a brief period of active locomo- tion, these lose their flagellum and their permanent form alike, extrude pseudopodia, in short, melt down into amoebae. After some period of amoeboid life they flow together into a single proto- plasmic mass — unite into a plasmodium, as it is termed, and this after another brief but remarkable period of locomotion and pseudo- podial activity, settles down into a spheroidal mass ; this re-encysts itself, and the whole cycle commences anew (Plate IV. fig. 1). If now we make a diagrammatic representation of this life-history (or rather form-history, as it should more accurately be termed), of Protomyxa, exhibiting (1) the encysted, (2) the ciliated, (3) the amoeboid, and (4) the plasmodial stages, we shall find that all those temporary phases of form observed among the higher Protozoa may at once be referred to one or other of these (figs, 3, 8). If tljis be so, those curious phenomena of the exhibition of ciliated forms by organisms usually of amoeboid type like the Radiolarians, or of amoe- boid forms by organisms almost permanently encysted or motile, like Gregarines or Monads respectively, lose their anomaly, and come under a generalisation at once simple and comprehensive, viz,, that a form-history essentially similar to that of Protomyxa (with blanks it is true, but blanks which the progress of discovery is constantly filling up, and may not unlikely almost wholly fill), may be sketched out for all the higher Protozoa. The same idea 272 Proceedings of the Royal Society may be better expressed in the statement that tbe higher Protozoa may be regarded as organisms of fundamentally Protomyxoid form- history, in which, however, some one phase has attained compara- tively high specialisation and differentiation, together with relatively greater permanence. Or the same idea may be stated in the exactly converse way, that the Protozoa may be viewed as organisms of fundamentally Protomyxoid form-history, in which, however, one, two, or three of the phases become abbreviated into merely em- bryonic ones, or may even (by that shortening of development with which embryologists are so familiar in the higher organism) become completely suppressed. Thus then, if illustration be needed, a Heliozoon differs from Protomyxa merely * in tbe higher differentiation and relative per- manence of the amoeboid phase of its life-cycle, since more or less brief encysted, ciliated, and plasmodial phases have all been observed. The more specialised but kindred Eadiolarian seems to have lost its plasmodial phase ; so too, perhaps, has the monad, while in the Gregarine only the ciliated state is wanting. 2. Affinities of the Protophyta. — Passing now to the second problem proposed at the outset, that of the affinities of the Proto- phytes, the same conception may be at once applied. Too much importance is here attached to the encysted phase, for the life-cycle is clearly apparent in many forms. Treviranus, in 1811, made the notable discovery that the spores of Confervse move like Infusoria, f Many years later Unger described the same phenomena in Vaucheria clavata, as “the plant in the moment of transition to the animal,” J while Von Siebold and others argued against this essentially just view, with more ingenuity than soundness. The wide prevalence of this change is constantly being confirmed. Uot only have we a thoroughly well-defined and constant cycle between the resting and the ciliated sbate, but we may fairly reckon the brief phase of inactivity, which so often is observable between the loss of cilia and the return to the encysted state (when the organism closely resembles * The possession or non-possession of a nucleus is of course immaterial, so far as the form-history is concerned. t Treviranus, Beitr. z. Pfl. Physiol., Gott. 1811, p. 78. J Unger, Die Pflmize in Momente d. Thierwendung , Wien, 1843. Siebold, Dissert, de ffnibus int. reg. an. et reg. constit, Erlangen, 1844. 273 of Eclmhurgh, Session 1883-84. a contracted amoeba), as representing tlie amoeboid form. A distinct assumption of the amoeboid state at the close of the ciliated one, is sometimes to be observed, — as lately by Reinke* in Bangia. And thus the cycle is complete, save only for the plasmodial phase. The importance of this view for the Protophytes then, is scarcely less than for the Protozoa. With a tendency of the encysted state to predominance, more marked even than in the Gregarines, the other phases are by no means obliterated, and we thus — and only thus — obtain an intelligible explanation of that alternation between the resting and the motile phase which is so frequent and so charac- teristic. The inevitable applicability of this to classification, and the light it yields, will be sufficient!}^ obvious. "Without prematurely proposing a detailed classification, it will be obvious that we must regard those forms, which like Torula, exhibit only the resting state, not as primitive, but as exceedingly specialised, and those which exhibit more and more of the cycle as less so. 3. Affinities of the Myxomijcetes. — Passing to the Myxomycetes, it will at once be evident, that unless the present theory can, be entirely overturned, they have no place among the fungi proper — where it is the encysted phase that predominates, the others being greatly reduced or suppressed; but are in fact morphologically as remote from these as are the monads. The Myxomycetes must be placed next Protomyxa ; in fact, Frotomyxa is simply the least differentiated known Myxomycete. Their higher forms are interest- ing— first, in very frequently showing less of the ciliated stage, and secondly (a more important character, since here they are unique among living beings), in affording an enormous differentiation of their plasmodial stage ; the complicated forms which many of them exhibit being simply those of their plasmodial froth, to which per- manent shape is then given by the formation of a cellulose envelope. The resemblance to fungi is thus as purely superficial and adaptive as that, for instance, of Hy droids to Polyzoa, and, like it, is of physio- logical interest alone. 4. The Protista S — The general non-adoption of Hseckel’s pro- posal of a third intermediate Regnum Protisticum, has been due to three main reasons, — of which the first is that the proposal seems only to double the difficulty, since it does not enable us to distinguish * Mitthcil. d. Zool. Stat. in Neajjel., 1883. 274 Proceedings of the Royal Society Protista from animals on the one hand, or plants on the other ; the second, closely related to the first, that Protista are too heterogeneous, and do not admit of exact definition ; hut the third and most potent reason has, however, simply heen that excessive specialisation which allows most otherwise competent students of the Protozoa to remain in entire indifference to the Protophytes, and the even more general and deplorable ignorance of the Protozoa which prevails among microscopic botanists. The present theory, however, does away with the apparent heterogeneity of the Protista. On the view that Protozoa and Protophytes alike exhibit more or less specialised and abbreviated forms of a common life-cycle, the thirteen groups of Haeckel* are seen to he hut forms of one, and there remains absolutely no morphological reason for their continued separation (nor for that matter, any physiological reason either, were such considerations, irrelevant as they are to morphological taxonomy, any longer admissible). Hor is the objection of Huxley really valid. The limit between Protista and Animalia remains simply that between Protozoa and Metazoa ; and that between Protozoa and Protophytes being given up, there remains no more difficulty of separating the higher plants than ' there was before — a difficulty which, however undoubted, is not increased by unitiug the lower forms. The thorough unity and naturalness of the Protista being thus obvious, they naturally fall into a series corresponding to the stages of the life-cycle. In the Schizomycetes and the Palmellaceas the resting and motile stages are almost equally prominent, while in Gregarines, and still more in Desmids and Diatoms, and especially Saccharomycetes, the encysted stage predominates. The Protoplasta, Foraminifera, Heliozoa, and Kadiolaria represent of course the predominatingly rhizopod or amoeboid stage, while the Infusoria represent the ciliated, and the Myxomycetes, as has heen said, the plasmodial. It may at first sight seem as if the old grouping of Protophytes and Protozoa were not seriously modified, since the Protophyta always essentially corresponded to the series of generally encysted forms. And so far true ; the encysted series may still he termed Protophytes without any serious harm. But it must he clearly * Die Protisten. of Edinburgh y Session 1883-84. 275 observed that there remains not one morphological type merely, to be discriminated as Protozoa, but three — the ciliated, amoeboid, and plasmodial, — all, indeed, physiologically analogous in exhibiting movements (a phenomenon of which pure morphology takes abso- lutely no cognizance), but as distinct in form from each other as from the encysted form. The utter confusion which has too long main- tained as to the distinction of plant and animal life is thus seen to be due to the want of that discrimination of morphological from physiological considerations, which is now happily nearly complete in the study of higher organisms. In short, though the encysted and usually non-motile cells or cell-aggregates may be conveniently termed plants by the physiologist, and though usually non-encysted and motile cells or cell- aggregates may similarly be grouped as animals, — yet the morphologist, distinguishing form-history from life-history, must recognise among the Protista four main lines of differentiation, or four series, which may perhaps conveniently be termed Protojphijta, Rhizopoda, Ciliales, and Plasmodlales. (See Plate IV. figs. 1-13 in first series.) 5. Phytogeny of Protista, — On this view also there is no necessity for the assumption lately coming into view of the origin of the Protista from several distinct stocks, or for accepting, with Bergh,* so specialised a form as Peridinium as a type of the primeval Protozoon, for all are naturally derivable from a simple Myxomycete or Protomyxoid ancestor. Of course, this view by no means excludes the possibility of the remoter and simpler Protamoeboid progenitor assumed by Haeckel. 6. Relation of the Protoghytes to the Higher Plants, — Transverse division may of course occur in the encysted, amoeboid, or ciliated stage of the life-cycle of a cell. When this takes place chiefly in the encysted state the tough and coherent wall holds the resultant cell-aggregate together ; this cell-aggregate soon becomes moulded by the force of the environment into some definite form ; and what we term a vegetable organism (a Metaphyte corresponding to a Meta- zoon) is the result. But the cells of our multicellular plant do not lose their tendency to cycle. Alike in linear, superficial, or solid aggregates, the cycle is * Bergh, ‘‘D. Org. d. Cilio-flagellata,” Morph. Jahrh.. vii. 2; Abstract by T. J. Parker, N, Z. Jour, of Sci., October 1882. 276 Proceedings of the Royal Society plainly seen : and it is scarcely necessary to remind the reader of the zoospores of a confervoid Alga, or of the similar mode of reproduc- tion of an Ulva. It may he objected that here only two stages of the cycle are present ; hut a third, the amoeboid, not uncommonly occurs, for that the brief quiescent state of the zoospore before re-encystment may fairly he considered amoeboid, is demonstrated by such observations as those of Keinke,* who has lately figured a true amoeboid stage in the settling zoospore of Bangia. In Fucus, again, the ovum- cell has rejuvenesced, in other words has gone through an amoeboid stage, while other cells rejuvenesce as antherozoids into the ciliated phase. In the terrestrial Arche- goniata, too, we have the same phenomena; even in the Phanerogams, condemned as all their cells seem to perpetual incarceration, there remains one fleeting and imperfect recapitulation of the cellular life- cycle in the embryonic rejuvenescence of the pollen grain and ovum cell (see fig. 15). 7. Relation of Protozoa to Higher Animals. — If transverse division occur in the ciliated state, the new cells must necessarily almost invariably separate, must row apart, and thus it is natural that only comparatively few and transitory cases of ciliated aggre- gates are known. In the amoeboid state, however, the aggregate produced by division remains much more readily in continuity, and it would thus seem much more probable that the Metazoa should originate from Protista in which the amoeboid stage was somewhat more permanent and more subject to division, than from the ciliated forms, as has sometimes been suggested, particularly for the sponges. 8. Common or separate Descent and Affinities of Animalia and Vegetahilia. — If the preceding facts and deductions he accepted, it need only he briefly pointed out, that the affinities of plants and animals are far closer than botanists and zoologists are generally accustomed to assume, since both are descended from a Protomyxoid ancestor, and may, in fact, from our present point of view, be described not merely, as the common phrase goes, as amoeboid or encysted cell-aggregates, but as aggregates of Protomyxomycetes, variously grouped and arranged indeed, hut never so highly spe- cialised as to lose all traces of their individual ancestral life-cycle. The notion of three kingdoms of nature — animal, vegetable, and * Op. cit. of Edinburgh, Session 1883-84. 277 mineral — that disastrous philosophic and scientific aberration ” bequeathed by the alchemists to the last encyclopaedist of Gesner’s school, and unfortunately adopted and sanctioned by Linnaeus, has not of course been seriously adopted by any philosophical biologist of the century ; hardly the narrowest specialist among zoologists or botanists any longer seriously doubts the validity of the classifica- tion of natural objects into two groups only — inorganic and organic — yet, at the same time, the vicious results of the earlier dogma still everywhere survive, and indeed necessarily so. For the unity of plant and animal life requires morphological demonstration, and that more precise than has hitherto been afforded by merely separating off the lowest plants and animals into a third still heterogeneous group of Protista. This deficiency is supplied by the present argu- ment, for if the Protista, the Yegetabilia and the Animalia have indeed been correctly interpreted, as somewhat variously specialised cell-alggregates derived from an ancestral Protomyxomycete, their con- solidation into a single kingdom is a matter of course. In one edition of the Systemd Naturce, Linnaeus clearly recognised the fundamental unity of plants and animals, by uniting them in opposition to the non-living wmrld {Conserta) as Organisata, and this term it is accord- ingly not only convenient, but necessary forthwith to revive. 9. Morphologicat Classification of Animal Tissues. — Histologists are accustomed to recognise three main groups of animal tissues. Thus Cornil and Panvier"^ distinguish (1) connective tissues, in which the cells are united and separated by a substance of charac- teristic form and properties; (2) muscular and nervous tissue, in which the cells have undergone extraordinary modifications, both structural and functional; (3) epithelial tissue, in which the cells possess a regular and constant evolution. In this classification, however, as in so many others, morphological and physiological characters are not kept distinct. In briefly glancing at morphological characters only, it is evident we may best approach the problem by first noticing some of those cellular trans- formations made known by the recent students of embryology. Histogenesis must underlie histology. An ovum is at first a naked amoeboid cell, then assumes tho encysted state, then segments into an aggregate of amoeboid cells ; this * Manuel cC Histologic Tatliologigue, i. p. 11, Paris, 1881. VOL. XII. T 278 Proceedings of the Royal Society becomes perhaps a ciliated morula, this again a gastrula, with ciliated ectoderm and amoeboid endoderm ; this may settle down as in sponges, its cells re-cycling anew, the ectodermic layer becoming amoeboid, the endodermic ciliated (fig. 18). The endodermic cells remain per- manently more or less amoeboid, as the recently much investigated phenomena of intercellular digestion have so clearly established. The amoeboid ectodermic cells, on the other hand, may give rise to muscle — and a muscle is but an amoeba elongated so as permanently to contract along one line ; on the other hand, they may pass into a quiescent state, or throw out encysting material, which may either enclose them individually, as in Ascidians, or form a collective external envelope, as in Arthropods. The niesodermic cells may either remain unspecialised as amoeboid corpuscles, may specialise as muscular tissue, or cycle into the resting state, z’.e., develop into connective tissue (see fig. 19). And if the cell cycle persist thus long in the life-history of the organisms, why should it' disappear? In reality, it does not disa]3pear completely. The amoeboid corpuscles of the perivisceral fluid of an invertebrate — say an Echinus — develop, largely at least, from the ciliated epithelium lining of the coelome — permanently exhibit, that is to say, one of the most characteristic phenomena of the cycle. And when under proper precautions we examine a fresh drop of the fluid, we observe the corpuscles as they die running together into a plasmodium,* so perfectly similar to that of a Myxomycete as actually to have been described by a recent observer as a new genus and species, f And this phase of the cycle takes place, in the so-called coagulation of corpusculate fluids of inver- tebrates generally. Numerous other instances of the occurrence of some phase of the cell-cycle have been recorded, and have already been collected by the writer in a series of papers which have led to the present one ; it is unnecessary to call attention to others, save perhaps the especially interesting announcement by Professor Had- don,§ of the occurrence of a plasmodial union of cells during the normal histolysis of Polyzoa. * Geddes, “Observations s. 1. fiuide perivisceral des Oursins,” Arch. Zool. Exp. VIII. t OompUs Rendus, t. Ixxxii. ISTo. 21, J Geddes, “ On the Coag. of Amoeb. Cells into Plasmodia,” kc,., Proc. Roy. Soc. Loud., No. 202, 1880, and Trans. Roy. Rhys. Soc. Edin., 1882. § Haddon, “ On Budding in Polyzoa,” Quart. Jour. Micros. ScL, 1883. of Edinhurgli, Session 1883-84. 279' Thus then it will be sufficiently evident that the morphological classification of tissues must be based upon the cell-cycle, the various permanent tissues being viewed as specialisations of one or other of its fundamental forms, or perhaps sometimes as synthetic types between them. And, finally, compressing the gist of several possible papers into as many passing allusions, it is evident that the theory affords us a basis for the criticism and compression of the recent literature — (1) of intercellular digestion (natural to the amoeboid phase); (2) of that long dispute respecting the origin of the sexual elements of Hydrozoa, from ectoderm to endoderm (the cells of both of which show the cycle, and either layer thus develop ova or sper- matozoa); (3) of the coelome theory. 10. Physiological Rationale of the Cell-Cycle. — It is now time to demand some physiological rationale for this cycle, which has been hitherto regarded as of morphological interest alone. A mass of protoplasm anywhere is under constantly varying conditions — at one time receiving abundant energy 'from the environment, at another little or none. These variations are at least of three main kinds — (1) temperature, (2) light, (3) food. Thus, then a rhythm of more or less vital activity in definite relation to these conditions of the environment is inevitable. It is unnecessary to remind the histological reader how often and how easily the existence of this rhythm is verified by actual obser- vation. Every student is shown the intensification of amoeboid or ciliary movement by heat, and its depression by cold or electric shock, and knows too the influences of various reagents or gases (he., of modification oifood in the general sense) in stimulating or retarding activity. The dependence on climate of the cell-cycle of the lower organisms, e.y.. Protococcus or Amoeba, is familiar to every microscopist. The amoeboid state varies widely with food and temperature ; while the actual transition from the ciliated stage to the amoeboid, and conversely, have been repeatedly observed ; witness the papers of Haeckel, Lankester, and others including the writer.* They can only be viewed in fact as distinct from the morphological point of view ; physiologically, they show but the extremes of one motile state. * “On the Morphology and Physiol, of the Cell,” Trans. Roy. Rhys. Soc. Edin., 1882. 280 Proceedings of the Royal Society Vast importance lias been attached to the cellulose wall, as an assumed characteristic of plants, yet not only the cyst of a Myxo- mycete, but that of an Amoeba, is now known to consist of cellulose. How is this cellulose wall to be accounted fori Why should the resting phase possess a cyst 1 What is the physiological rationale of this morphological characteristic of the resting phase 1 Contracting muscle evolves carbonic acid and water, with evolu- tion of heat j the quantity of heat and water products evolved diminishes as contractile activity diminishes ; and this physiological common-place must hold true of every contracting cell, ciliated or amoeboid. But contractility implies waste of formed materials, diminution of contractility therefore implies diminution of this dis- integration of matter and dissipation of energy, of this combustion which we term waste. Cessation of contractility, therefore, involves cessation of the combustion of some product — of some fuel which was formerly required to maintain the process. The cellulose wall ivhich appcai^s on the assumption of the quiescent state is thus the equivalent of the carbonic acid and water which were being formed and excreted during the sioie of contraction. Being no longer required as fuel, it becomes itself thrown out as a waste pro- duct— which simply by reason of its chemical and physical proper- ties— its insolubility and coherence — acquires at once its morpho- logical permanence and its protective use.* The applicability of this physiological conception to a new series of problems can here only be briefly hinted at. Without more than mentioning the discovery of Durin as to the formation of cellulose from cane sugar, f it may be briefly pointed out (1) that the occurrence of cellulose in Ascidians, or in pathological cases in the human brain, &c., is by no means unintelligible — the difflculty is rather the reverse — to explain why it is not invariably present in resting cells. These are never destitute of external intercellular substance, and the A vivid confirmation of the preceding theory of the origin of the cellulose wall has been suggested to me since the reading of this paper by my friend Dr Milne Murray, who reminds me that a quiescent muscle, instead of evolving carbonic acid and water, produces an enormous store of muscle-sugar or inosite, and that this is an isomer of cellulose, CgHioO^. The same conception may throw light upon the physiological chemistry of other carbohydrates, such as glycogen, starch, &c. t Ann. Sci. Nat. BoL, 1877. of Edinburgh, Session 1883-84. 281 hypothesis thrown out many years ago by M. Frdmy, our leading authority upon the chemistry of cellulose — that chitin and other analogous bodies really consist of cellulose linked with a proteid, seems well worth reviving. On this point the researches of Kruken- berg,* especially are promising light, f 1 1 . Origin of the process of Sexual Reproduction. — The plasmodial stage which terminates the cycle, seems in the first place little more than a mere mechanical union of cells exhausted by prolonged activity ; in all normal cases it is soon followed by prolonged repose in the encysted state, and in the experiment upon invertebrate cor- puscles, by quiescence and death. In the plasmodia of Protomyxa, Myxomycetes, and of invertebrate corpuscles alike, notably Echinus, the union is followed by a brief but extraordinary intensification of amoeboid activity J — the cause of which, as passing from cellular to protoplasmic physiology, must be discussed in a subsequent paper. Some years ago considerable weight was attached by Sachs § to the hypothesis that the plasmodium formation of Myxomycetes might be regarded as a process of multiple conjugation. This view he now, however, withdraws, |j mainly on the ground that the nuclei have been shown not to coalesce as in true conjugation. It appears to me, however, that on the present theory the revival of that hypo- thesis, though in a somewhat different form, is inevitable. hfo one doubts that the sexual elements of plants and animals are represented by the very slightly differentiated conjugating cells of Spirogyra, or the almost undifferentiated cells of Mesocarpus. With these the conjugation of two Amoebse, two Actinosphseria or two Gregarines, are classified as a matter of course. But the recent observations of Gabriel upon the multiple conjugation of Actino- sphseria, or of Gruber upon that of Gregarines, leave no doubt that in these cases at least conjugation may be multiple. The only difficulty is that offered by the non-coalescence of the nuclei. But even if there were any certain grounds for supposing that the essence of the process lies in the union of the nuclei, rather than in * Krukenberg, Vergleich. Physiol. Studien, Bd. ii. t Ann. Sci. Nat. Bot., 1877. X See figure of plasmodium of Echinus in author’s papers in Arch. Zool Exp. VIII.; Proc. Roy. Soc. Bond., 1880, or Trans. Roy. Phys. Roc. Edin., 1SS2. § Manual of Botany, 1st Eng. ed. 11 lUd., 2nd ed., Appendix. 282 Proceedings of the Royal Society the union of the protoplasm, we must expect on the' evolution theory an incipient stage in which only the latter phenomenon should occur. That the nucleus is not invariable, much less indispensable, is of course evidenced by the existence of the Monera, or if their dis- tinctness he questioned, we may appeal to the recent demonstration, apparently by the most refined histological appliances, that in young Actinophrys a nucleus is really absent,"^ and develops independently in adult life. Moreover, on the present view of the almost primordial nature of the Myxomycetes, their plasmodium is the only phenomenon which at all resembles conjugation, and since we have already viewed amoeboid, ciliated, and resting forms as specialisations of the cor- responding phases, it is no great extension of the theory to view conjugation as specialised from the plasmodial phase. This view will he strengthened when in the, next paper we leave the cell-cycle to consider the physiological processes in the protoplasm itself. 12. Relation between Normal and Pathological Tissues. — Unless the step taken by Goodsir and Virchow — of regarding all patho- logical variations as ultimately expressible in terms of cellular structure and function, ^.e., of the cell theory, be deliberately re- traced, we cannot avoid the application of the present re-statement of the cell theory to pathology. To do this in detail would, of course, require far more than the writer’s knowledge, but a few brief and tentative suggestions may be put forward. Pathologists are reducing tumours to a common type — which seems essentially that of cell multiplication in the resting or encysted stage. It is certainly more easy to suppose, on the present view, that the appearance of a con- nective tissue tumour has been due to the placing of ordinary cells in new conditions favourable to the assumption of that phase of the ancestral cycle ; or from a slightly different point of view, to say that that inhibition of the cycle essential to the permanence of the whole organism has been locally removed, than, for instance, to suppose, with Cohnheim, the existence of a long dormant mass of embryonic tissue. Again, we can easily modify the environment of living cells under the microscope^ — we can accelerate or diminish the activities of ciliated epithelium, by heat and cold, oxygen and carbonic acid, by alkali and chloroform. I have elsewhere f pointed out that the * Gruber, Zool. Anzeiger, No. 118, 1882. t Op. cit., Proc. Roy. Soc. Loud., 1879. of Edinburgh, Session 1883-84. 283 solution of the old dispute, as to whether the integument of certain planarians was amoeboid or ciliated, was afforded by specimens of Convoluta which had been kept for many days in a shallow aquarium, scantily protected at nights from the cold of a severe winter. The normally ciliated cells of the ectoderm could be watched in actual progress of collapse into the amoeboid state, and their cilia figured during their passage into pseudopodia (fig. 24), Here was a definite pathological change, in approximately known conditions, and distinctly in terms of the cell-cycle. Why should not a dis- order of the ciliated epithelium of the bronchial passages be at least partly susceptible of essentially the same explanation 1 (fig. 25). May not the formation of pus be partly interpreted in terms of degeneration to the amoeboid stage, and may not inflammatory changes be regarded as temporary and excessive intensifications of cellular activity, indicating a tendency to reversion to the amoeboid state ? Whether these particular instances be acceptable to professed pathologists or not is after all a minor consideration, their aim has been merely to suggest that the phenomena of the cell-cycle — and particularly of those changes occurring under definite experi- mental conditions — may be applicable in their hands to fruitful research, not only in pathological histology, but in cellular physi- ology and therapeutics.'^ Its adaptability to the treatment of physiological speculations is also obvious. Since the activities of the body are the aggregate activities of its component cells, not merely such phenomena as those of varying ciliary activity, but those of fatigue and sleep, of muscular and nervous tonus, and in fact every rhythm of increas- ing and decreasing cellular activity, become intelligible when viewed from this most highly generalised standpoint of physiology, as specialisations of that primeval cellular rhythm Which lies before us in this life-history of the Protomyxomycete. 13. Influence of the Emironment upon the origin of Plants and Animals. — One further physiological consideration may be briefly indicated, from its bearing on general morphology. The cell-cycle in its entirety is only possible in a fluid medium. Without water cilia cannot play, without fluid the amoeba and the plasmodium must * This conception is somewhat developed in the subsequent paper. 284 Proceedings of the Royal Society alike become stationary, and either dry up or encyst themselves. The cell-cycle in plants therefore is only found in its entirety in algae. Archegoniates are indeed terrestrial, hut their brief cell-cycle during fertilisation is absolutely dependent upon the abundant moisture, without access to which neither moss, liverwort, nor pro- thallium ever occurs. Thus it is that the higher terrestrial plants have become restricted to the encysted phase. Only to escape death, has the dryad become thus shut up within the tree ; but once so protected the extensive replacement of the cryptogams by the phanerogams, in all the less humid climates of the world, is readily accounted for. Passing to animal life, the vast preponderance of aquatic forms over terrestrial, is very similarly to be accounted for by the aid of the present theory. Only the higher members of a few groups have successfully emerged from their native element, and their existence depends upon their differentiation of an internal fluid medium, of that “ milieu int6rieur” upon which Claude Bernard was wont to lay such stress,* this in turn depending upon the early differentiation of in- ternal cavities. The interdependence of morphological and physio- logical theory will be sufflciently obvious from such considerations, f 14. Theory of Variation. — The more completely one accepts and reflects upon the theory of natural selection, the more one feels the necessity for some view more satisfactory than heretofore of the causes of variation. J The present conception of the cell-cycle seems to go far towards supplying this. On the ordinary conception of the cell theory, that of the plant as an aggregate of encysted cells, and of the animal as an aggregate of essentially amoeboid ones, the organism cannot be credited with any innate variability — its ob- served variations are merely those which it receives, so to speak, between hammer and anvil — from the forces of the environment. The present conception, however, of all cells, however varied and specialised, being essentially differentiations from an encysted, an amoeboid or a ciliated form, and of these forms as phases of a single form-history, enables us to credit the cells and the resultant organism with an innate tendency to variation, and this along * Phenomenes de la vie communs aux an. et auxveg., Paris, 1879. t “Morphology,” Ency. Brit, ‘Eel. of Morphol. to Physiol.’ X Of. Origin of Species. 285 of Edinhurgli, Session 1883-84. certain definite and investigable lines. These modifications would still of course be largely determined by modification in the environ- ment, yet the change of view is considerable. On the former view the organism is a plastic but essentially inert mass, yielding pas- sively to the forces of the environment ; on the latter, it is an active community, of which some or many members, under the influence of any favourable change of conditions, or the removal of any restraints, external or internal, immediately press into other positions and functions, which however apparently new, are either specialisa- tions of the existing, or reversions to an earlier type. Variation and disease are thus most closely akin ; for since all variations are ultimately cellular, pathological changes are simply definable as those variations which happen not to be conducive to success in the struggle for existence. And thus we might proceed further and further with the discussion of aetiology. The preceding theory then, although its range of application, un- limited in the scale of organic nature, may at first sight alarm the specialist, is actually founded on a simple but solid basis of observed facts ; it has been seen fairly to meet and co-ordinate the very numerous and hitherto, for the most part quite unrelated problems which were enumerated at the outset, and even to be applicable to numerous minor and unexpected problems which these suggested. And thus, were it even viewed from the standpoint of mathematical probability alone, it has received the most overwhelming verification. {Explanation of the Plate at page 292. ) II. An Hypothesis of Cell Structure. 1. Statement of the Prohlem. — Great attention has, especially of recent years, been paid to the problem of cell structure, and a vast body of observations have been accumulated. Of these many are generalised; many, however, still remain unco-ordinated, and an hypothesis which attempts at once to unify these, to throw light upon the structural and functional aspects of contractile protoplasm, and to unite all these with that theory of the cell-cycle above pro- pounded, is therefore not untimely, and may, even if not completely exhaustive or satisfactory, be at least suggestive of a better explana- tion. Let us survey a few of the main peculiarities of protoplasmic structure which any such hypothesis must aim at unifying. 286 Pr.ocmlings of the Royal Society The lowest amceboid organisms are simply granular masses of protoplasm, but higher forms exhibit a differentiation of a hyaline zone of “ ectoplasm ” around a more fluid and granular “ endoplasm/’ The immense variability of form, size, and general appearance pre- sent among the rhizopods has never been sufficiently allowed for ; so that there is ample reason for doubting whether great numbers of described species have any real distinctness. Yet the elongated and reticulated, granular and circulating pseudopodia of the Fora- minifera, and the radiating, clear, and far less contractile pseudo- podia of the Heliozoa and Eadiolaria present a most vivid contrast, which we have as yet no means of explaining. The remarkable changes presented by ova both before and during fertilisation,* and the doubtless fundamentally similar phenomena exhibited during cell division, require to be accounted for; while the long dispute as to whether the “ granules ” of protoplasm are really granules at all, or are the optical expression of the intersections of a stroma or network of denser protoplasm, cannot be omitted. Such a hypothesis must also aim at throwing light upon the mystery of muscular structure, and must also deal even with such apparently peculiar and exceptional phenomena as that “aggregation of the proto- plasm,” first described by Mr Darwin as occurring in certain cells of insectivorous plants f (which, when in active digestion, or when subjected to chemical, electrical, or even mechanical stimuli, exhibit an aggregation, or rather segregation of the protoplasm into two portions — the outer more or less hyaline, but containing irregular and constantly-changing streaks and granules of a more refracting and fluid substance, in which the colouring matter, when present, became accumulated). 2. Statement of the Hypothesis. — Darwin soon extended these observations to the protoplasm of root hairs, and went on to indicate its wide prevalence throughout the vegetable kingdom. His re- searches were verified and extended by Francis Darwin, J who showed that these granules did not consist of sap, as some vegetable histologists had suggested, but were essentially protoplasmic in their nature. It is the object of the present paper to apply these facts to * Balfour, Embryology, vol. i. f Darwin, InsectivoroiLS Plants, London, 1875. X Quart. Jour. Micros. Science, xvi. oj Edinburgh, Session 1883-84. 287 the explanation of such problems of cell structure and contractility as those briefly enumerated above. On this view, the granules of such a low vegetable organism as Torula (disregarding, of course, sap vacuoles and fat globules) are aggregation products, an assumption by no means excessive, espe- cially when we bear in mind the activity of the chemical changes which are going on during its life and growth. But if this step be taken, we cannot resist regarding the Amoeba in the same way ; its granules too are aggregation products, and the clear ectoplasm, when present, may be viewed as protoplasm in which aggregation is not occurring. The variations of amoeboid organisms in more or less granular character (a fact familiar to every observer) is thus brought into ob vious relation with the state of nutrition, or with the quality and quantity of external stimuli ; and its observed increase when stimulated, and its diminution during the resting state, are thus naturally accounted for. In the same way, in the granular pseudopodia of the Foraminifera, aggregation is in progress, in the hyaline processes of the Heliozoon not so. The granules of cells in higher animals m^ay be, at least to a very large extent, similarly explained ; while the disputes as to the presence or absence of a stroma become clearer when we bear in mind the fact that Darwin’s aggregation-masses are at least as often greatly elongated or spherical, and that they may run in any direction, and unite or separate to any extent. The remarkable differentiations of protoplasm visible during cell-division, as exhibited by ova (of course excluding yolk granules, &c.), may not improbably admit of the same explanation. 3. Contractile Structures — Muscle. — The excessively difficult problem of muscular structure has not as yet received any widely- accepted solution, and even respecting matters of observation the widest discrepancies exist. In many invertebrates we cannot even be certain whether the muscles are striped or non-striped, so contra- dictory are the observations, while in a recent important paper by Professor Haycraf t,* the homogeneity even of striated muscle is main- tained. Brilliant light has, however, been lately thrown upon the arena of controversy by Professor Eutherford’s recent elaborate demonstration f that the discrepancies in observation are largely * Proc. Roy. Soc. Lond., 1881. t Proc. Roy. Soc. Edin., 1883. 288 Proceedings of the Royal Society if not indeed altogether, to be explained by the fact that the different observers have studied their specimens in different stages of contraction. When fully extended, and then alone, the full com- plexity of the structure of striped muscle can be realised; with slight contraction Flogehs granules disappear, then Dobie’s globules ; finally, in completed contraction, the heads of adjacent sarcous elements come together, and the fibril is momentarily homogeneous, the former complexity reappearing on extension. So far Professor Eutherford’s explanation — how does this come into relation with the present hypothesis? The doubly refracting portions of the mu'^cle-fibrils may, on this view, be regarded as aggregation granules ; for these must inevitably exhibit considerable regularity of form and arrangement, Avhen we bear in mind that, if we admit the exist- ence of muscle-fibrils at all, we imply that these possess a limiting surface, — of course tubular in form and ultra-capillary in fineness, — and still more so, if we assume with many histologists the existence of fixed points afforded by Krause’s membrane.* In short, it is attempted to compare the aggregation-granules of a sundew, not only with those of an amoeba, but even with those most complex and most peculiar differentiations of protoplasm observable in muscular tissue. 4. Confirmatory Evidence. — The present hypothesis is thoroughly in accordance with recent researches as to the nature and composi- tion of protoplasm. Thus Brass f distinguishes cells into two layers, — the outer sensory, the inner nutritive, and describes phenomena which seem at least closely akin to aggregation. Our knowledge of the development of muscle also supports the hypothesis. Thus, for instance, W agener j: shows that muscular fibres at first differentiate from the protoplasm of multinucleate cells, as j^erfectly smooth fibrils (“vollig glatte Faden”), with interfibrillar substance. Later there arises, as a secondary differentiation, the refracting and non-refracting elements (“ Isotropen and Anisotro- pen”), which can extend and diminish, also fuse together and again separate. In young heart-muscles these come and go under the observer’s eye. * Cf. Author’s Prel. Note in Zool. Anzeiger, No. 146, 1883. t Brass, Zool. Anzeiger, 120, 1882. 4 G. Wagener, “Ueb. d. Entstehuiig. d. Qiierstreifen auf d. Muskeln,” Arcliiv f. Anal. u. Physiol., Anat. Ahtheil, p. 543. of ^^dinhurgli, Session 1883-84. 289 5. Further Study of Aggregation — Cellular Therapeutics. — High, as is the importance of observations upon preserved tissues, the present hypothesis clearly points towards the importance of con- tinuous observation of living cells when treated with various re- agents— aline of research which Professor Prommann* is at present almost alone developing, and with such remarkable results. We must observe the effects, not of ammonic carbonate only, but of the whole pharmacopoeia, and not upon the tentacles of Drosera merely, but upon vegetable and animal cells and tissues from the lowest to the highest ; noting the changes which take place in all the structures and functions of the cell, and this, under all variations of temperature, light, electric state, and for various periods of time. Of the practicability and interest of such an investigation only a single instance need be taken. When one treats an Actinosplimrium with dilute ammonic carbonate, the most striking change results; its pseudopodia disappear, its complex protoplasmic structure vanishes; it loses its regular spherical shape, and collapses into an irregu- gular granular amoeboid mass with blunt pseudopodia — (the very likeness of the ancestral amoeba), — and then soon breaks up. And similarly there is little doubt thkt such a reagent would pro- duce marked effect upon the epidermic cells of growing tadpoles, — a convenient means of research. Thus we set out from these re- searches of Mr Darwin upon a general investigation into what changes chemical substances produce upon cells,- — an investigation which touches the general question of pharmacy and therapeutics in the most direct way, and which we may in fact speak of as Cellular therapeutics. The interest of the admission of a drug does not end when it has been conteyed into the stomach, but really begins there. We must know what happens to the component cells of the organism, — we must, in short, observe the therapeutic effects of reagents upon the cells of vertebrates, — an investigation which points far. Such observations would not require constant but only frequent attention for long periods, and are thus perhaps especially suitable for the skilled pharmacist, f * Frommann, “tJntersuch. ueb. Struktiir, Lebenserscheiniingen n. React- tionen thier, u. pflanz. Zelleu,” Jena Zeitsclir., xvii. and sep. pub., Jena, 1884. t Cf. Author’s paper in /oitr. Pharmaceutical Soc. Loud., No. 714, 1884, 290 Proceedings of the Eoycd Soeiety 6. Further Chemical Considerations. — It is an observed fact tbat when amoeboid cells unite into a plasmodium, there takes place the most remarkable intensification of the activities of the mass. The compound amoeba seem possessed of all and more than all the activities of its component amoeba — pseudopodia of the most extra- ordinary length and size are thrown out, and motion is far more rapid ; in short, it would seem that not only are the activities of the component amoeba summed but multiplied. The coalescing amoebae may be regarded as serving as food to one another — their waste pro- ducts and their surplus water are squeezed out and got rid of, and thus we can readily understand the summation of their activities. But how is this apparent multiplication of activity to be explained ? We have seen how carbonate of ammonia, an oxidised body isomeric with urea, is exceedingly stimulating to protoplasm; and Mr Darwin’s researches have also shown that other alkaloids and waste products are excessively stimulating, and set up the most extraordinary aggregation ; and that a poison, for instance, may act by excessively exaggerating this normal process. Here then is a use, not merely for the protoplasm, but actually for the waste pro- ducts— the waste product of one cell acting as a stimulant w^hen it meets the protoplasm of another. And from this consideration again new series of speculative applications radiate off in all direc- tions. One may suggest that the use of the alkaloids in the coffee or strychnine or Calabar bean is not merely to protect the young embryo from being eaten by animals, but as a stimulant to germina tion. Or we may introduce the same conception into our specula- tions as to the uses of manures, in which the most valued consti- tuents are precisely those salts which, like carbonate of ammonia, produce great aggregation. Again, passing from the plasmodial union of cells to the probably derived union of ovum and spermatozoon, we cannot avoid imagining the latter bringing not merely a trifling contribution of additional protoplasm, but a store of substances especially stimulating to the vast mass of the ovum. And the identification above suggested of aggregation with the protoplasmic changes visible in the ovum after fertilisation, is thus seen to be by no means so improbable as might at first appear. 7. Need of an Explanation of the Phenomena of Aggregation. — of Edinhurgli, Session 1883-84. 291 How is it that if we treat living protoplasm with certain reagents it breaks up into two substances? How are we to explain this observed fact ? Is there any case known to chemists or physicists where a chemical reagent separates a substance, at first apparently homogeneous, into two distinct substances which afterwards reunite ; or where an electrical or mechanical stimulus temporarily separates a complex mixture into its components ? I am not aware of any parallel case ; hut the absence of an explanation underlying the phenomenon of aggregation itself is after all entirely outside, and subsequent to both the main thesis and the speculative corollaries of the present paper. III. An Hypothesis of Contractility. If we imagine a single drop of more or less fluid substance sus- pended in a surrounding medium with which it does not mix, its surf ace- tensions tend to keep it in a spherical form. This can of course he observed in a drop of oil or water, most conveniently in the well-known experiment in which oil is suspended in a mixture of alcohol and water of the same specific gravity. If now we interfere and elongate this drop, its surface tensions at once enable it to resume the spherical form, even against the resistance of the surrounding medium. It is inevitable to transfer this simple physical conception to explain the function of muscle. If the elongated components of the muscular fibre he more or less fluid (as we almost certainly know them to be, whether aggregation granules or not), they must needs also possess surface tensions; they must, therefore, also tend to shorten and broaden, and draw themselves into a sphere. And if all these multitudinous elements of the muscle are shortening ^and broadening, we have of course an explanation of that general shortening and broadening which we term the contraction of a muscle. Moreover, just as the ^‘contracting” drop of oil overcomes a resistance, so the “contracting” muscle overcomes a resistance equal to the sum of the minute resistances which the millions or thou- sands of millions of simultaneously contracting elements can over- come. Finally, an expenditure of energy must needs take place, and of this the “negative variation” of contracting muscle (perhaps of the contracting oil-drop also ?) may afford the indication. 292 Proceedings of the Royal Society Be the latter suggestion valid or not, it is important to observe (1) that we have here (and for the first time so far as the writer is aware) an hypothesis which explains {a) the shortening and broad- ening of a contracting muscle, (h) its overcoming a mass resistance, in other words, that we have an explanation of the mode in which almost molecular movements are converted into movements of masses, a solution long sought by physiologists ; and (2), that this hypothesis depends simply upon the more or less fluid nature of the essential muscular components, and is entirely independent of the acceptance or rejection of the hypothesis of the preceding paper, which suggests the identification of these muscular components with aggregation granules. Explanation op Plate IV. In columns allotted to the four stages of the cell-cycle (encysted, cili- ated, amoeboid, and plasmodial) are arranged the corresponding phases of the form-history of a few typical Protozoa and Protophytes, as also a series of diagrams illustrating the normal and pathological form-history of the cells of higher plants and animals. All are thus seen to be refer- able to the Protomyxan or Myxomycete type. Among the Protozoa proper (figs. 3-8) the cell-cycle is almost com- plete ; the encysted and amcehoid stages are invari&ihly represented. The plasmodial phase is of frequent occurrence : in Infusorians, Gregarines, and Heliozoa that of multiple conjugation representing it, and demon- strating its essential continuity with conjugation, e.g.^ diatoms and algse (figs. 10-13), aiid even with fertilisation in plants and animals (figs. 14 and 16). Fig. 18 shows the cell-cycle in a developing gastrula, e.g., sponge. In fig. 19 the various tissues are classified in relation to the cell-cycle ; the connective tissues to the encysted, the muscular to the amoeboid type, &c., even the plasmodial phase being represented during the histolysis of Polyzoa. Fig. 19 represents the development of an invertebrate amoeboid corpuscle, and fig. 20 its formation of a plasmodium when drawn, while figs. 20-25 continue the application of the same theory to the explanation of pathological change. of Edinburgh, Session 1883-84. 293 Monday, Vlth December 1883. EGBERT GRAY, Esq., Vice-President, in the Chair. The^following Communications were read : — 1. On the Change in the Peltier Effect due to Variation of Temperature. By Albert Campbell. Communicated by Professor Tait. The object of this short paper is to give the results of some further experiments made with a view to determine the variation in the Peltier Effect due to change of temperature. These experi- ments are the continuation of a set of similar experiments described in a paper read to the Society in summer 1882. The arrangement used was almost exactly the same as that employed in the former experiments — the measurements being made by means of an iron-German-silver thermopile bent into the shape of an arch, with the ends about \ inch apart, and placed so as to almost touch the junctions of the metals whose Peltier Effect was to be measured. The neutral-points of the various pairs of metals were also measured in the usual way by heating up a junction in oil, plotting the temperature-deflection curve, and from it deducing the neutral- point. According to theory, the ratio of the Peltier Effect at temperature to that at ifg, is determined solely by the values of q, and the neutral-point of the metals used; therefore it was not necessary to draw the thermo-electric lines of the metals. As I have no satisfactory measurement of the neutral-point of Pb-Arg, in this case the calculated ratio in column V. is from Professor Tait’s diagram. In the subjoined table, column I. gives the name of the pair of metals ; II. and III. the lower and upper temperatures at which the Peltier Effect was observed ; IV. the ratio of the Peltier Effects at these two temperatures from the direct measurement ; V. the ratio calculated from the observed neutral-point given in VI. VOL. XII. u 294 Proceedings of the Royal Society I. II. III. IV. V. VI. Ee-Zn . . 23°*8 C. 99° C. 1-43 1-404 198° C. Pe-Zn . . 28°-25 94° 1-373 1-3397 198° Fe-Zn . . 24°*5 94° 1-429 1-353 198° Pb-Zn . . 17° 96°-8 -416 •4275 - 79° Pb-Zn . . o 00 r— 1 96°-5 -488 •434 - 79° Zn-Arg . . 18° 98°-5 -730 -638 -330° Zn-Arg . . 18°-5 86°-5 -718 • -678 - 330° Pb-Arg . 18°*6 95° -5 -682 r(-636) \_Note, — Mr Camplbell sent me portions of his iron and German- silver wires to test. The electromotive force of a circuit of these wires was found to he almost exactly proportional to the difference of temperatures of the junctions between 10° C. and 100° C. — P.G.T.] 2. On the Problem of the Lathe-Band, and on Problems therewith connected. By Edward Sang. That of the lathe-band is one of those simple-looking problems in elementary mechanics- which present serious difficulties to the investigator. The problem is this — “ So to arrange the several diameters on the fly-wheel and pulley-cone of the turning-lathe, as that the Same band may suit for all.” The solution consists of two steps converse to each other, the one being “ to compute the length of the band from given diameters,” the other “ to compute new diameters which may suit the length so found.” If A represent the lathe centre, B the centre of the fly-wheel, and if a circle be described round B, having its diameter KBH equal to the difference between the diameters of the wheel and pulley, the two tangents GA, Ag, together with the arc gHG, give the excess of the length of the band over the circumference of the pulley, while the same two tangents exceed the arc GKg by as much as the band of Edinhurgli, Session 1883-84. 295 is longer than the circumference of the wheel. Now, if we write i for the angle GAB, and regard AB as the unit of linear measure, we easily find AG + G H = cos ^ + ( Jtt + i) sin i = l^ AG - GK = cos i - (Jtt - i) sin i = V. Since ^ can be found from the difference of diameters, or that difference from i, the two branches of our problem come eventually to be “ to find I and V from if and “ to find i when I or V is given.” The first question is solved by help of the canon of sines; the second presents greater difficulty, we can get the value of i from that of I only by a series of trials. Yet, in truth, there is no essential difference between the two processes, both consist of trials ; but the existence of the canon of sines, renders the trials in the former case so easy, that we come to regard the operation as direct. If we had a table of the values of I corresponding to all values of i from zero to the right angle, we would be able to resolve both problems with like facility. 296 Proceedings of the Royal Soeiety In applying such, a table to the business in hand, we should have to compute the circumference from the diameter, and afterwards the diameter from the circumference. This double arithmetical operation may be avoided by the simple contrivance of counting all in diameters ; for the length of the hand, we substitute the diameter of the circle which it would gird. Writing them W = diameter of wheel, P = diameter of pulley, B = diameter for band, we have W - P = 2 sin ^ , B _W=^-('l-~')sin^. hir \ Itt/ Prom a table constructed according to these formulge, the dimen- sions of the lathe may be got by little more than inspection. The actual table and the mode of using it, exhaust the mechani- cian’s interest in the subject, but, to the speculative mathematician, some connected points may appear to be deserving of notice. Our ordinary tables, arranged according to the ancient graduation, are exceedingly inconvenient, because the ratio— expressed in ¥ degrees and minutes would involve, in each case, a troublesome division. The decimal subdivision of the gradient was therefore preferred, and the computations made for each thousandth part, that is for intervals of 10' centesimal. A manuscript canon of sines to 15 places (using however only 10 of these) rendered easy the computation of the terms 1 + r~ ) ^ f 1 - ^ sin i . \ The canon of “ sines measured in degrees ” had been prepared, in order to compile the table of circular segments, used for the compu- tation of the anomalies of the planets ; the term was thus ready to hand. In this way the construction of the table for lathe-bands was greatly facilitated. Ill all such calculations, the residual last-place errors may happen of Edinhurgli, Session 1883-84. 297 to balance each other, or may happen to concur in one direction, hence there is a possibility of error in the last place, proportional to the complexity of the work. This error may, in the present instance, amount to 2 or even 3 units in the last place. Hence it follows that, in shortening from ten places to the six places in the final table, an uncertainty in the sixth place must occur when the rejected figures are within the limits 4997 and 5003, as happens thrice in the course of the work. Hence the necessity for founding our working tables on more extensive ones. All possible cases of the mechanical problem are comprised between the limits i = 0 and ^ = Jtt ; while i passes from the one to the other of these limits, the line AG makes the quarter of a turn, and we naturally inquire. What happens when the motion is farther continued ? or how was it on the other side of the zero ? On changing the sign of ^, the expressions for B - P and B - W change places ; the wheel takes the place of the pulley. This is clearly seen in the second figure ; the change from DC with its inclination inwards, to D'C' inclined outwards, is accom- panied by a reversion in the sizes of the circles. Hence it will suffice for us to examine the phases for values of i be- yond the right angle. In order to this, let the circle described with the radius AE, fig. 3, represent the pulley, which we shall suppose to re- main unchanged while the inclination of the band varies. When that inclination is zero, as in the' position D^Cq, the wheel is of the same size as the pulley; but when the band is Fig. 2. inclined, as in the position DC, the radius of the wheel has grown to be BD or BM, and the half length of the band is made up of the three parts ED, DC, CE. When i becomes a right angle, the points 298 Proceedings of the Royal Society I) and C have come np E, and the hand encompasses the whole circle whose radius is BE. Imagine now that the point of contact C has passed beyond E into the position c ; the tangent takes the position dc^ so that the course of the hand is from F along the arc FDMc? and hack along s cfcE to E ; the halfdength being still made up of the three parts Ftf, dc, cE j hut in counting the length dc and cE must he regarded as subtractive. In this way the imaginary hand is shorter than the circumference of the wheel, by as much as, in the symmetric position, the actual hand had been longer. Beyond the limits f = ± Jtt, the mechanical arrangement fails to illustrate the properties of the above expressions, and therefore, regarding them as purely analytical formulae, we may proceed to examine their characters. Placing the arc f, representative of the inclination, along the line of abscissae, and setting up the values of I and V as ordinates, we of Edinburgh, Session 1883-84. 299 obtain the curves shown in fig. 4 ; symmetrically placed in regard to the origin 0 ; the one curve being converse to the other. We may put these formulae in a more convenient form by trans- posing the origin of abscissae in the one case to - Jtt, in the other to + Jtt ; for this purpose we write x — ^ir + i ov —x = ^7r-i, and in this way confine our attention to one of the curves, whose equa- tion now becomes l = xcosx- sina;. In order to determine the singular points in the curve, we must take the first and second derivatives (differential coefficients) of this expression; these are SI or iJ = x.sina;, Sx ’ sn ^ or = -\-x.ao?ix + sin x ; and continuing the derivation, or 3^Z= -fl?.sinar-f 2cosa* hx^ or J = - xaoBx - 3sina; , etc. etc. The remarkable simplicity of this progression suggests the con- tinuation in the opposite direction ; taking the successive primitives (integrals), we get fSx. I on = - a^.sina? — 2cosaj, ffSx^.l or +x.Q,OBx- 3sina?, fffSx^Aov -f- a?, since -1- 4cosiu , and so on ; and it is obvious that, in this endless progression of derived functions, the appropriate middle term is ce. since, which also has its conjugate a?.cosce. Denoting the one of these functions by the other by we have the conjugate progressions : — 300 Proceedings of the Pioyal Society -4- .^x= + iij.cosic - 3sinx _d^x— — - 2cos^i7 - £C.C0S£I7 + silliC ^x= +i^.sinii? iFx= +x.cosfl? + sinic 2Fx= — iij.sina: + 2cosa? 3^^= - ^(7. coscc - 3sinx r^= +^.siiiii? - 4cosd7 etc. f'x= + sinii? + 4cosic etc. etc. _4^(j>x= +ic.cosiu- 4sini:i7 _^x= + a?, sins? - 3cosi^J 4<^x= + it;, cos a: + 4 sin ^ etc. eacli term being the derivative of that above it. On equating any one of these functions to zero, we get (1st) the intersection of its curve with the line of abscissae, (2nd) the cul- minations of the curve belonging to the function immediately above, and (3rd) the points of reflexure of the curve of two steps up ; hence we are mostly concerned with the solution of the general equation The equation Fx = a;.sinii? = 0 is satisfied in two ways, by making x = 0 or by making since = 0. Now since becomes zero for every value of x = mr, n being any integer positive or negative number, and hence the curve, shown in fig. 5, crosses the line of abscissae at equal intervals of tt, counting from the zero point ; and since ce = 0 coincides with one of the values since = 0, the curve touches the axis at the origin. The conjugate equation ^cc = ce.cosce, is also satisfied by putting = 0 or by cosce = 0, the latter condition giving for x any value of the form (?^ + 2)7t ; hence, besides the crossing at the origin, this curve crosses the axis of abscissae at points distant by the interval 7T, reckoned, from on either side of the zero. The solution of the adfected equations is somewhat more complex. Beginning -with the case _ifx= -cccoscc-fsincr, which is that of the actual lathe-band, we observe that the function becomes zero when the condition n- Px or „(px = 0 . x~ tanx of Edinburgh, Session 1883-84. 301 is satisfied. We have thus the problem “ to find an arc equal to its own tangent.” Having applied, at the end of the radius OA, a tangent to the circle, let us suppose two points thence to set out with equal velocities, the one q to travel along the tangent, the others to move along the circumference of the circle, carrying with it an indefinitely extended radius Op. At first this secant will precede the point q, and by the time q has reached the distance Ah, equal to the quad- rant AB, the intersection has moved off to an infinite distance along to tangent. After this the point of intersection reappears on the other side and comes up to A just when q reaches the distance Ac equal to the half -circumference ABC. The intersection now chases the travelling point q and comes up to it at Q, somewhat before p has reached the third quadrant. The first root of our equation, that is AQ or ABCP, is below the value x = In the same way we readily perceive that the next root is when p> has made more than an entire revolution by nearly a quadrant, that is when it has come to P' a little before B ; the root, then, is rather less than §77. The numerical values may be found by a very rapid approxima- tion. Assuming x = \tt = An, we compute the arc of which this is the tangent ; we regard the length of this arc as a new tangent, compute the length of the arc thereto belonging, and so continue until there be no change within the limits of the precision at which we aim. Three or four operations exhaust the precision of seven- place tables. The successive approximations are thus represented by the symbols tan"^(|7r), tan-2(|7r), and so on, so that we have ic = tan~®(§7r) ; where 00 stands for an indefinitely large integer number. 302 Proceedings of the Royal Soeiety The roots of this equation are actually c r 257-27 = 286-06= 4-4934 442-37 = 491-80= 7-7252 624-46 = 694-17 = 10-9041 805-56 = 895-48 = 14-0662 For the crossings of the curve belonging to the function jFa;, we get the condition x= -timx, and, in this case, the points p and q must move away from A in opposite directions, and the first coincidence will take place when 70 is somewhat beyond the extremity of the quadrant AB ; the phases are so closely analogous to those of the preceding case that it is unnecessary to detail them. The functions jf>x and give the conditions x = cotx and x = - toix . In these cases, when q begins its motion from A along the tangent, the travelling point p must leave B, in the one case travel- Fig. 7. ling backwards towards A, in the other case forwards towards C. Thus the same artifice serves for the detection of the roots in all the four equations. As an example of the other cases, we may take the function _3Fa? = ircosit;“ 3sina?; this, when equated to zero, becomes X — 3tan^i?. Vol. XII., Platr, V. Froc. Roy. Roc. Edin., A MAD I OR /AORN BOY, AGE ABOUT 17. ^4 i -i i ''j of Edinburgh, Session 1883-84. 303 We shall therefore suppose that the travelling points p and q leave A simultaneously in the same direction^ but that p moves thrice as fast as q ; here we see that the radius Op must make more than half a turn before its intersection with the tangent can over- take q. Proceeding by the same method of approximation, wo readily find the arc AP to be 233° 40', its tangent AQ being 1.359f in terms of the radius. Each succeeding coincidence must occur after an interval of rather more than half a turn, so that the approximations are rapid. The second coincidence is when = AP'PAP' reaches 428° 07', the tangent AQ' being 2.4907. The same method is applicable to the other cases of the general problem. Thus the consideration of this elementary problem in mechanical construction leads us to examine the properties of a whole class of functions, which, again, may serve to suggest further extensions and inquiries. 3. Notes on the Madi or Mom Tribe of Central Africa. By Eobert WT Eelkin, E.E.S.E., E.E.G-.S., Bellow of the Anthropological Societies of London and Berlin, &c. (Plate V.) The following notes have been compiled from my own observa- tion, when in Central Africa in 1880, from inquiries I made on the spot, and from the information I have obtained from a native who has been my faithful servant during the past few years. They treat of a people inhabiting a large tract of country situated 5° N. lat., 30° 20' E. long, of Greenwich, of which the chief town is said to be Bengu6. The Arab customs, which are being introduced among the races in Central Africa, are rapidly breaking down the boundaries which exist between the tribes, and superseding their primitive habits and customs, which in a few years will be things of the past. For this reason I have been induced to bring together all the information it has been my good fortune to collect, and whilst regretting that the record is not so complete as one could have wished, I yet hope that it may prove of some value, or at all events of interest, to those engaged in the study of anthropology. 304 Proceedings of the Royal Society The tribe called Madi by the Arabs give themselves the name of Morn, and must not be confounded with the Madis on the east of the Nile, or with another so-called Madi tribe on the west. I am not able to give the exact population of the district, but I have ascertained that it has diminished considerably during the last ten years, owing to the fact that many of the people have been taken away as slaves, while numbers of the young men have been drafted into the Egyptian army, where they have obtained a reputa- tion for courage, fidelity, and veracity. I will commence by giving a description of the way in which the Madi builds his hut, so that you may first see him in his home, and then follow him as he goes to his daily work, or enters into the various pursuits of a far from monotonous life. Habitations. — The process of constructing a hut is as follows ; — A circle is marked on the ground by means of a string attached to a stick in the centre, and in this circle poles are fixed into the earth. These poles are made from thick straight peeled branches of a tree called “pi,” and they are encircled by rows of supple saplings, which are tied to them at intervals of about IJ feet. Grass is then taken, cut the same length as the poles, about 6 feet, and placed upright in bundles round the framework, after which saplings are again tied round to keep the grass in position. The roof is made on the same plan, a strong circular foundation of wood being first put together, into which wooden rafters are fixed, and being brought together in the centre, are secured at their upper ends. Circles of saplings are fixed on to the rafters, and then grass is laid on, and fastened as in the case of the wall. The top of the roof is formed of a large bundle of grass cut even and bound firmly together at the lower end. A stake about 4 feet high is thrust through it, and then fastened on to the top of the roof. The loose ends of grass are then bent downwards, and secured to the roof, and the free end of the stake is ornamented by an ostrich egg and feather. There are no windows in these huts, and only one entrance, about 3 1 feet high and 2|- feet wide; a door of wicker work is made to slide backwards and forwards inside across this entrance, and is kept in place by two poles fixed firmly in the ground, and tied at the top to the roof. 305 of Edinlurgli, Session 1883-84. Trenches are dug round the huts before the rains set in at a sufficient distance for the water dripping off the roof to fall into them. A small channel from the trench carries off this water to a convenient distance. Furniture. — These dwellings do not contain many articles of furniture. The principal one is the bed, which is made from the stem of a plant called yougo, resembling the sugar cane. Narrow pieces of the stem are cut about 6 feet long, laid side by side, fastened together by strips of cow hide, and then fixed on to three wooden cross bars. This is raised from the ground about 3 feet upon six thick round wooden legs, to which the cross bars are tied, the whole is then covered with a cow hide. A large earthenware jar is an indispensable piece of furniture. It is about 4 feet deep and 5 feet wide, with a narrow neck, and is placed on a wooden stand, generally formed of the forked branch of a tree. It contains a good supply of semsem seed (Egnoir), which is used for making porridge, and from which oil is obtained. Another jar of the same shape, but smaller, contains water, and is placed near the entrance. The bare ground, which is well trodden and beaten to make it firm, forms the floor, and a wood fire is generally burning in the centre of it. Jars of varying shapes and sizes are placed round the hut on the floor, or hnng from the walls in string nets. They contain different kinds of dhurra, also honey, butter, dried sugar cane, salt, &c. Baskets made of dhurra stalks are also hung round the hut, more for ornament than use it would seem. Bundles of arrows, spears, bows, and knives serve the same purpose when not in use. Besides the principal hut, each family usually has a hut for strangers ; and as soon as children arrive at the age of four or five years, the father builds a separate hut for the girls and one for the boys, or several neighbours club together in these huts. These additional buildings contain only beds, a water jar, and a few basket work ornaments. Granaries. — Another erection is constructed as a storehouse for dhurra. The circular wall is made like that of the other huts, of poles and grass, but it has a flat wooden roof upon which is fixed an upper chamber of basket work (literally a huge basket), in which the dhurra is kept. Over it is placed a roof similar to the one de- 306 Proceedings of the Royal Society scribed above. This roof is kept in place by three poles which pass through its outer rim, and are fixed into the ground below, apart from the walls. The lower part of this building is used as a kitchen, and contains a number of large stones for crushing corn, and jars for holding it. Meat is also hung from the ceiling. The dhurra can only be taken out of the granary from above. The roof is pushed up with a long pole, which when rested on the ground keeps it raised ; a woman then ascends from outside by means of one of the three supporting poles, which is a kind of ladder, for it is made of a tree stem, the broken stumps of branches forming the steps. Gardens. — Flowers are cultivated close round the dwelling huts, but the garden, which seems to be an indispensable belonging, lies behind the hut, covers generally a large extent of ground, and is devoted to the cultivation of fruits and vegetables. The beds are circular and raised about 3 feet, falling abruptly to the ground all round. Melons, gourds, and vegetable marrows are grown on them, and creep gracefully down the sides and along the unoccupied ground beneath. Some beds are 3 feet wide, and of great length, and are planted with sogo (yams'?), which twine up a double row of sticks about 12 feet in height. A poisonous bulb, in appearance like our onion, is planted round the dwelling, and its leaves are put about the huts to keep away serpents and mosquitoes. Arrows are also poisoned with it. Cattle. — Cattle forms the chief wealth of the tribe. A rich man may have as many as 200 head, a very poor one only three or four. The average number possessed by one man is from thirty to forty. A large enclosure (or kraal) is erected for them at a short distance from the village, and cows belonging to different families herd together in one kraal. This is circular, with strong wooden walls and no roof. Inside there are two smaller enclosures — one for the calves, and one for the man in charge, the latter having a roof of wood and grass. A fire is made between these two divisions. Should the rains be very heavy, a temporary roof is constructed for the calves ; sometimes even, the people take them into their own huts. The care of the cattle is not the work of one man in par- ticular, but the owners take it in turns to sleep with them at night, and take them to grass by day. Cattle are never let out to graze of Edinburgh, Session 1883-84. 307 till the dew is off the grass ; eating wet grass is said to cause a plague. They are milked by men, and women make butter from the milk in gourds. The cows are called by names, either accord- ing to their marking, or, if favourite ones, after some near relation of the owner. They are not branded or marked in any way, hut identified without. If a cow is troublesome, a bell is put round its neck. In the holiday season the cows are taken by young men and boys to a distance, for change of air and food, and brought back after a few weeks. The people in whose district the cattle feed are per- mitted to use the milk, and in r6turn provide the keepers with food and shelter. There is a special kind of black cow (sometimes red), whose milk is kept solely for its master’s use, or for its calf. A man usually possesses at least one such animal. It is usual to kill cattle at the beginning of the rains, when they are needed for food by the people eaiployed in sowing the crops. Cows suffer from sore legs and serpent bites. In the first case, they are killed and eaten, but the flesh of those bitten by snakes is considered to be injurious. Food. — The Madis consume a large amount of animal food, of which there is a great variety, especially in the hunting season. The buffalo, tetel, wild boar, gazelle, and hippopotamus are all commonly eaten ; while the elephant, rhinoceros, crocodile, eland, and fox are partaken of occasionally. Among domestic animals consumed are the cow, sheep, and goat, though cows are only eaten at harvest time and at funeral ceremonies. Wild ducks, pigeons, fowls, and guineafowls may be added to the list, and sometimes ostriches ; but fowls are only eaten by young children and old people. Several varieties of fish are found in the rivers, and eaten. Of the vegetables cultivated, marrows, cucumbers, sweet potatoes, yams, peas, beans, and greens are the principal; and the most common fruits are figs, nuts, melons, and the fruit of the date palm. Several varieties of dhurra are made into bread, as also occasionally a root called morako, but the bread is usually of the consistency of our porridge. A substitute for our butter is found in the semsem seed, which is roasted, ground, and eaten with 308 Proceedings of the Royal Society bread. When peoj^le cannot afford this, they have recourse to “ bottled white ants.” Eutter is made, however, and when used, is melted and poured over the porridge. Eoth cows’ and goats’ milk is largely used. Marrow, which is extracted from bones with a stick, is much relished. There do not appear to be any articles of food forbidden, but some people do not think it well to eat liver, fish, sheep’s head, or goats. The earth thrown up by ants is sometimes eaten, but those who do it aie considered mad. Oil is made from semsem seed. The seed is ground, boiling water poured over it, and the oil squeezed out with the hand on a grinding stone, caught in a gourd, and poured into jars. No spices are used, but redeb, a stone fruit, is made into a pulp, and mixed with porridge, when the latter is boiled. Salt is used, and is kept by some people for sale. Honey and deli stem are added to sweeten food. The most expensive articles of food appear to be semsem, milk, cows, sheep, and goats. Cooh’ng. — The cooking is either done in the room under the granary, or outside the entrance to the dwelling hut, where three stones are always placed. Between these a fire is made, and the cooking vessels are placed upon the stones. The women are the sole cooks. They have a superstitious practice of putting white ashes on the pots before placing anything inside ; some words are muttered at the same time, and this is supposed to make the food more satisfying when cooked. Small cooking operations are at times done in the hut. Eefuse is deposited in heaps about 100 yards from the hut, and cleared away periodically. Meat will keep two days, but is considered at its best on the first day after killing. It is boiled and also roasted over the fire. Meat and fish are dried in the sun for keeping. Fresh fish is boiled ; dried fish boiled or broiled. Fowls and all kinds of birds are boiled. No spit is used to roast meat ; it is laid across two pieces of wood arranged over the fire. Meat is not fried. The use of hot stones in boiling is unknown. Porridge and bread are mixed in a pot over the fire, and bread is really only a very stiff porridge. Porridge mixed with redeb and semsem is made with water ; that made of of Edinhurgli, Session 1883-84. 309 dokn flour, witli a little butter added, is boiled with milk. Vege- tables are eaten alone, bread being used with meat. The cooking vessels are earthenware jars. Mixing sticks are the only cooking utensils used besides knives. They are cleaned after use. No vegetable broths or stews are made. Farinaceous puddings are unknown. Meat very well cooked is preferred. Preserving of fruit with sugar and pickling of vegetables are unknown. The only beverages are water, milk, and dhurra beer. This beer is made by the women in large quantities, and kept in jars in a hut set apart for the purpose. To this hut the people go to drink. It is common property, and not paid for. They do not take the beer home, or drink it at meals. There are three meals in the day — before sunrise, at midday, and at sunset. No ceremonies are observed at the commencement of meals, nor are there any religious rites connected with them. When fine, meals are taken outside the entrance to the hut near the cooking place. It is customary for members of different house- holds to meet together for dinner, each family providing a bowl of food, round which they sit, and eat from one bowl after another, using their fingers as spoons and forks. They always wash their hands before and after meals, a jar of water being provided for the purpose, but the water is not poured over the hands. The men and boys sit in one group, the women and girls in another. The women do not wait on their husbands, the food when ready being fetched by the children. Any stranger who may chance to pass by is invited to share the meal. Water is always kept at the door of the hut to give to passers by. Wooden stools are used outside the dwelling, but it is not considered proper to use them at meals. The gathering does not disperse directly the meal is over, but digestion is aided by telling and hearing tales^ No cannibalism exists in the country, and the people express great abhorrence of the custom as practised by their neighbours the Nyam-Nyams. Fire. — Wood is used for fire, and lighted with dried grass. The fire is produced by friction of wood, one piece of wood about the size and shape of a large pencil being rapidly rotated in a hole in a flat piece of hard wood. One man holds the hard wood steady, whilst two others take it in turn to rotate the stick VOL. XII X 310 Proceedings of the Royal Society Smoking. — Tobacco is used to a great extent for smoking, but it is not chewed, nor used as snuff. The native name is tabba, which is, however, commonly used in other tribes also. I believe the tobacco smoked to be indigenous, for none is imported. It is very good, but exceedingly strong. It is cultivated, and the leaves, being sun-dried and broken up in small pieces, are then mixed with a small proportion of dried cows’ dung and urine, and moulded into conical cakes, weighing about J lb. to 1 lb. each. These cakes are dried in the sun, and stored away in baskets hung up in the huts. Two kinds of pipes are used, both made of clay. One measures about six inches long, with a very thick stem and oval bowl ; the stem is not put into the mouth, but the lips are pressed round the hole in it. The other pipe is itself small, but has a wooden stem about three feet long ; this pipe is rarely carried about, but smoked in or near the huts. The pipe is ignited by burning charcoal being placed on the top of the tobacco; a flaming stick is never used. Two small sticks serve as tongs to take the bit of charcoal from the fire. Water pipes are unknown, and I have not heard of any substitute for tobacco ; as that plant grows in great profusion, I should not imagine that one would be required. The people smoke a great deal, but do not carry the practice to any injurious degree. Other nar- cotics are to the best of my belief unknown. A root, however, is sometimes chewed, which has the repute of exciting sexual passion. Agricidture. — A large area of land is cultivated. After the forest has been cleared away by felling and burning, the ground is hoed. Hoeing and weeding are the only processes which it undergoes. There is no irrigation, but the soil is prepared for the seed as soon as the first rain falls, after which there is plenty of water. The land is usually marked out in long narrow strips by large stones placed at equal distances. Each man cultivates his own land ; and if it is of considerable extent, and requires more hands than his family can give, he calls in the aid of his friends and neighbours. On such occasions no pay is given or expected, but all are ready to give and receive help in this way. The hoeing is done by men, and the hoes used are made of iron with wooden handles. The process of weeding is delegated to the women, and there are three kinds of hoes used for the purpose. Sometimes they kneel down between the rows of corn, and use a of Edinburgh, Session 1883-84. 311 short one; or if standing, there are two other shapes employed. The two first kinds of hoe are made of wood and iron, the last solely of wood. The married women always carry a knife in their girdles, which they use amongst other things for cutting corn. Its wooden handle is either carved or ornamented with iron. These implements are all of home manufacture, there being a good supply of iron in the country. The wooden handles are often ornamented, and differ much in shape. One very common shape I noticed was much that of a tortoise, but apparently there was no design in it ; and no attempt seems made by these people to represent anything by carving, as obtains in other tribes. Hammers and anvils are often made of iron, but stone ones are also used; there are no other stone implements. The weeds are gathered together into little heaps, and left on the ground until it is prepared for seed again, when they are hoed in with the soil. Underwood is burnt on the field. Digging and mowing are dispensed with. Ho animals are used in the cultivation of the soil. Six months of the year are dry, and six months more or less rainy. At times the rains are very heavy. The corn is sown at the com- mencement of the rains, and some early kinds are reaped in fine periods between the rains. Most of the crops ripen and are reaped when the dry weather sets in. The soil is so fertile that two and three crops may be sown in one year. There are four varieties of dhurra, besides dokn and telaboon, which are species of dhurra having very small grain. The seed of some of these kinds is mixed and sown together. An early and a late kind are sown in different rows in the same field. After the early sort (Dli) has ripened and has been reaped, semsem is sown in its place, or sometimes the ground is planted with a kind of cucumber. A cereal called deli is sown in the gardens ; its grain, however, is not eaten, but only kept for seed. The stems, which grow as high as 20 feet and about 2 inches in diameter, are sweet, and resemble sugar-cane. They are dried, peeled, and eaten un- cooked ; sometimes they are cut in small pieces, dried over the fire, ground, and mixed with semsem. Dokn stalks are dried in the huts, tied into bundles, and used as torches. The dhurra stalks are 312 Froceedings of the Royal Society used as food for tlie cattle, or made into baskets. Salt is also ob- tained from them. The women burn them to ashes, which are mixed with water and well boiled, the water is then skimmed, stirred, and boiled down, and the salt dried. Salt is also made from the root of a tree, from the stalk of a cereal (yobung) grown for the purpose, and some is also obtained from salt springs. When the corn is ripe, the women cut it, and tie it into sheaves, laying the stalks in opposite directions. The men collect these bundles, and carry them on their heads to the “langas.” These “ langas ” are frames constructed for the purpose of drying the corn. They consist of wooden poles placed at equal distances apart, and supporting cross beams of wood, which are again crossed by others. On this frame the sheaves are placed; they remain for about a month, and then the ears are removed to the granaries. When required for use, the corn is thrashed by women, who beat it with sticks over a basket. It is then winnowed. Dokn is thrashed in a different way ; the ears are placed in a tall wooden tub, and beaten with a pole, much like our dollying. The corn is ground between two stones, like the Egyptian mohakka. One very large heavy stone is placed on the ground and chipped with a small one till it is flattened, then it is rubbed smooth with another stone, the process occupying two or three days. A small oval-shaped stone is used for grinding the corn upon the large one. Land. — The acquisition of land appears to be an easy matter. It may be obtained from a neighbour by mutual arrangement, or by reclaiming it from forest or jungle. A piece of land once appropriated descends from father to son, and the chief of the tribe has no right to any but his own landed property, hlo definite boundaries exist to mark the limits of villages or districts; but a sort of indefinable understanding appears to obtain. Landmarks may be seen dividing strips of land owned by different people in one village ; they consist of large stones placed at intervals of about 100 yards. Hedges are unknown, and no corresponding protection is found necessary to ward off wind. Plots of land are protected from depredation by watchmen. Pits and traps are also made to catch elephants, buffaloes, and gazelles. These larger animals are, however, not so troublesome as ants and mice, which often eat the corn. It is also frequently injured by the intense heat of the sun, which shrivels it up before it is ripe. of Edinburgh, Session 1883-84. 313 Crops are grown on the same plot of land for several years running, and often twice in a year. When at last the produce yielded begins to degenerate, the ground is left fallow for a year or two. Migrations are frequent, as the result of a discovery of good soil ; sometimes a whole village will migrate to a new place. On such occasions the people may be seen flitting by small companies at a time, about ten men leaving at once, making a sufficient number to carry the wooden framework of the roof of a hut, which they take with them. The only exportation consists in corn being sold or given to neighbouring tribes when they are suffering from bad crops. Measurements of an Average Man. No. 1. Height from ground to vertex, 161 ’5 2. Greatest breadth from glabella backwards, . . . 19-0 3. Greatest breadth above ears, 14*7 4. Length of face from root of nose to lower border of chin, 1 1 *5 5. Breadth of face from one foremost under edge of cheek- bone to other, 11 -3 6. Breadth of face from one angle of lower jaw to the other, 11*4 7. Greatest breadth of zygomata, . . . . . 12* 8. Length of nose from root to junction of nose and upper lip, 4*7 9. Height of head from chin to vertex, . . . . 21*2 10. Length of neck from Adam’s apple to sternal notch, . 6*7 11. Length of body from sternal notch to pubes (upper edge), 50*0 12. Length of navel from ground, 99*5 13. Length of upper edge of pubes from ground, . . 84*2 14. Height of head from meatus auditorius to vertex, . . 11*8 15. Distance between two ears at top of opening of meatus auditorius, 13*5 16. Upper breadth of nose from one can thus to the other, . 2*9 17. Lower breadth of nose on cheeks, 4*3 18. Length of nose from root to lip, 4*4 19. Breadth of mouth, 5*2 20. Distance from meatus auditorius to junction of nose and upper lip, middle line, 12*3 21. Distance from meatus auditorius to root of nose, . . 13*7 22. Distance from meatus auditorius to middle of upper lip, 14*8 23. Distance from meatus auditorius to chin, lower edge, middle line, ........ 14*5 314 Proceedings of the Royal Society Ko. 24. Greatest circumference of head at glabella, 25. Arc from tragus to tragus over top of head, 26. Circumference of chest just above mammae, 27. Distance between nipples, 28. Breadth of shoulders across back, ..... 29. Circumference of waist at navel, ..... 30. Breadth of haunches, 31. Length of arm from shoulder to tip of middle finger, 32. Length of arm from shoulder to condylus external osis humeri, ........ 33. Length of arm from olicranon to end of ulna, 34. Length of hand, wrist-joint to tip of middle finger, 35. Length of leg from trochanter major to ground, 36. Length of thigh from trochanter major to condylus ex- ternal osis femoris, 37. Length of leg from condylus external osis femoris to ex- ternal edge of external malleolus, .... 38. Length of foot from os calcis to tip of great toe, 39. Arc from root of nose to union over head, 40. Circumference of neck, maximum, 41. Circumference of thigh, „ .... 42. Circumference of calf, „ 43. Circumference of arm, „ .... 44. Circumference of forearm, „ .... 45. Circumference of haunches, „ .... 46. Circumference of trochanter, „ .... 47. Span of outstretched arms, „ .... 48. Span of thumb and mid finger, 49. Length of thumb from second joint to tip, 50. Greatest breadth of head from chin upwards and back- wards, ......... Pulse, 68. Respirations, 20. Temperature, 97°‘5. F. 54-5 34-0 84-6 20-1 34-7 66-1 27-9 74-2 30- 5 28-0 19-4 87-0 41-2 41 -2 24- 6 31- 9 33-8 49 '8 35-3 27-9 25- 9 80-2 155-7 17-3 3-5 24-0 TaMe of Principal Indices. Cephalic Index. Measure No. 3 x 100 No. 2 Nasal Index. Measure No. 17 x 100 = 77‘91 . No. 8 Facial Index A. Measure No. 4 x 100 = 91-48. = 101-7. No. 5 315 of Edinburgh, Session 1883-84. Facial Index B. Measure No. 4 x 100 No. 6 = 100-8 Facial Index C. Measure No. 4 x 100 No. 7 = 92-0. Skin dark brown. Iris brown. Conjunctivse dirty orange-yellow. Palms and soles lighter shade of brown. Teeth good ; none re- moved. Well nourished; not tattooed. Hair short, crisp, curly black. Slight down on upper lip, none on other parts of body. Not circumcised. Eyes between I and 2 Broca’s Table, only deeper. Darker when out of health. Skin between 27 and 42, colour varies ; but is lighter in shade than the hair, and has a more reddy hue. Hair (41 Broca’s Table). — The hair is extremely frizzly, fine in texture, and abundant, and grows in spiral tufts, the roots being equally distributed over the head, but thickest at the top. It appears to be capable of growing to a considerable length, its growth being favoured by a very free use of grease (without which it dries and comes out). The men allow their hair to grow about 6 inches, i.e., when untwisted and measured. The women wear their hair rather longer, and with them the hair is trained to hang down ; the men’s, on the other hand, is more upright. When it has grown to these lengths they shave it entirely off. In shaving, some people leave a narrow ring of hair all round their heads like a crown ; others leave three or four tufts, according to the tribal number ; others again leave a great many small tufts growing. This is a fanciful arrangement, and has no particular signification. Dyeing the hair is not practised. Baldness before old age is very uncommon. The hair is rather darker in colour than the skin ; it turns grey about middle life. Oniy women practise the art of shaving ; they make it a profession, and unite with it the extraction of teeth ; the four upper and lower incisors being extracted from both sexes alike at puberty. A curved knife is used for shaving, the outer edge being sharp. Having placed the man’s head in her lap, the barber proceeds to cub off the tufts of hair, she then squirts 316 Proceedings of the Royal Society milk from her own breast on to the scalp, rubs it well in, and applies the razor. Scissors are unknown. The eyebrows are also removed, as is all other hair found on the body. The hair from the upp lip and chin is often pulled out by the roots. Sometimes very old men will permit a few white hairs to grow on the chin. The women are paid for their services with an arrow. Odour, — Notwithstanding their frequent ablutions, the Madis have an odour peculiarly their own. It cannot be said to be produced by dirty habits. It is always present, is varied by the oil and fat with which they anoint themselves, and is much intensified by muscular exertion, e.p., running, carrying loads, &c. Clothing. — The Madis do not wear any clothes, unless the word can be applied to a string which the women put round their waists, and from which hang a few leaves before and behind. Physical Poivers. — With regard to the physical powers of the Madis I can only give some very general notes, as I was not able to put their strength to the test with any amount of accuracy. The following remarks will give some idea of their strength : — They make admirable porters, being very careful of the loads entrusted to them, and display no little forethought and ingenuity in preserving them from injury. The rule is that no load should exceed 50 lb. in weight, and that it should be either square or oblong, the latter being preferred. They always carry the load on the head, on a pad made of grass, very rarely steadying it with the hand unless going over very rough ground. They strongly object to carry loads over 50 lbs.; but if pressed will take them up to 70 lbs., if the distance to be marched is not more than three days, and extra food is given them. Loads of 100 or 120 lbs. are carried by two men, hung on a pole, which they balance on their heads ; but they do not like the work. If a very heavy load has to be carried, e.g., a man, they place him on a native bed and carry him, two at a time, changing relays of men at about each mile. This they prefer to carrying by four men at once. I can testify from personal experience that it is far better to be carried by two men than four, for they go much more easily, and do not run against so many trees or overhanging branches. The relief men march before those who are bearers, and cry out when obstacles occur. of Edinburgh, Session 1883-84. 317 As regards distance, they carry loads of 50 lbs. 20 miles a day, for eight or ten consecutive days without showing signs of distress ; hut on the march they appear to require a great deal of water, and will sooner burden themselves with a gourd full than go without it for more than two hours at a time. If they go by a road where water is scarce, they generally take a few women or children with them to carry it. When they arrive at a stream, all loads are put down, and they bathe if the water is deep, or sit down and wash themselves if it he shallow, and then take a long drink. Europeans would probably prefer to drink first I The Madis can scarcely ever he prevailed upon to march at night, even in bright moonlight, on account of had roads, which is strange, as their eyesight is remarkably good. JSTeither will they start until the dew has disappeared from off the grass, or if made to do so by promises of reward they tie hunches of grass or skins before them, to avoid as much as possible being wet by the dew. In crossing a river of four or five feet deep, they stand in the water in a double row, and hand the loads from one to the other. Should the stream be very strong, they break down branches which have broad forks, and placing one end firmly in the bed of the stream, lean against the fork, and so get the needed support. They march at a quick pace, but generally halt for 10 or 20 minutes after each three or four miles. Should heavy rain come on they like to stop and shelter themselves and their loads under quickly improvised shelters. In carrying the Egyptian post these men make long and quick marches, 60 or 70 miles often being accomplished in twenty-four hours. Pathology. — The Madis are a healthy race, and do not suffer very much sickness. Coughs occur during and after the rains, but very few people die of pulmonary complaints. There are male and female doctors, but the males confine their practice to wounds, accidents, and snake bites, and do not receive payment, but have their food given to them when they are attending a case. Wounds of the extremities heal very quickly. They are washed and covered up with a paste made from the roots of shrubs, ground and mixed with a little cold water. Scalp wounds give more trouble, 318 Froceedinys of the Roycd Society often suppurating, and at times causing death. Wounds of the chest are not much feared, hut when they occur in the abdomen they are almost always fatal. The people suffer from abscesses, which are opened, well washed with water, and then dressed with the above-mentioned paste. Hydrocele is not as common as among neighbouring tribes. They try to cure it by long-continued pressure of the hands, but without much success. The treatment of a broken arm or leg is noteworthy. When it is a simple fracture, the limb is pulled as straight as possible, and then sticks are placed as splints to keep it in position, and are tied with cords. When the bone is broken in pieces and the limb swells, so that they cannot properly straighten it, a number of small cuts are made, and cupping horns applied. These horns are made of cows’ horns. If when the swelling has been reduced they still cannot straighten the limb, they cut the broken bones out, and fix on splints, applying a powdered root to the wound. Haemorrhage is stopped by actual cautery. This operation is rarely successful, as most people who undergo it die in a few days. The doctors impart their knowledge to young men, but their own sons do not follow their profession. If a man is bitten by a snake, the wound is well sucked or the parts scarified, and cupping horns applied if handy, and then a powdered root is freely applied. This root is very expensive, a cow being often given in exchange for a small quantity of it. Women doctors treat all cases besides those mentioned above, and receive one cow, two sheep, or a bundle of arrows for their services. They have but few medicines, and seem to make frequent use of magic. When a women doctor is called to visit a patient she brings with her a basket containing what I may call her magic wand. It is a kind of double tube about a foot long, each tube being about 4 inches in diameter. The one tube is partly filled with smal stones, the other is empty, to allow of the doctor performing her manipulations in it. This instrument is painted red, and oiled all over. The doctor shakes the wand, and mutters to herself for some little time, then feels the patient all over and draws her wand over him. When pain is complained of in the abdomen or chest, she first rubs the part with oil, and then places her wand over the of Edinburgh, Session 1883-84. 319 painful spot, introducing her hand into the empty tube. After working about for some time she at last draws out a substance which she calls the disease, taking care that the people shall not have any opportunity of seeing it closely. If pain is felt in the head, she cups the patient on the temples or nape of the neck by making small cuts with a sharp stone ; an iron knife is not used. Cupping is also employed for very severe pain in other parts of the body. These women doctors appear to he generally right in their prog- nosis. When their work is over they are always accompanied home by the head of the house (see Odi for the treatment of children). Medicine is given internally for fevers, which are generally caught through bathing or getting wet after sunset. An infusion is made from a root after it has been dried and scraped, and this is drunk by the patient at frequent intervals. Profuse perspiration results after a few doses. Toothache occurs in old people, but only rarely are caries seen. They do not extract the tooth at once, but loosen it gradually by working it about a little each day until it comes out. Epileptic fits would seem to be of rare occurrence, as I could not hear anything of them. Small-pox occurs in epidemics ; great numbers of the people die from it ; and it is rare to see a person pitted, as only very strong constitutions recover. When a man is attacked by it, he is placed in a hut which has a sand floor, and a large fire is made in it to keep the patient very warm. Meat is never given him, and only a small quantity of food, such as thin porridge. When the pustules are well formed they are all opened with a thorn, and then an infusion of roots and leaves is given to the patient to drink twice a day. The people are very particular to rub their bodies all over frequently with oil, for if this be neglected a scaly eruption results, which is, however, soon cured by an extra amount of oil. As yet there is very little syphilis in the country, but it is gradually making its way from the north and east. There are very few dwarfs ; they are considered to be great curiosities, but are not ill-treated. Hunchbacks are more common, and occur in about equal proportions among men and women, so far as I could discover. 320 Proceedings of the Boycd Soeiety Marriage Customs. — The Madis are not allowed to marry amongst their own friends, but generally obtain wives from neighbouring villages. Just about the time when a young man arrives at puberty his father makes a tour of the surrounding villages in search of a suitable bride for his son. Having found one to his mind, he ties a twig of a certain tree round her wrist, usually the left one, and then seeks her father’s permission for her to marry the youth. If the price to be paid in cows and sheep can be amicably settled, there is seldom any further difficulty in obtaining his consent. If a young man meets a girl during his travels and she takes his fancy, he is at liberty to ask her to marry him, and if she is willing he ties a twig round her wrist. She then goes home and tells her mother what has taken place, and the mother informs the father, who sends for the young man, and if he approves of him, gives his consent to the union, at the same time stating the price he wants for his daughter. The young man has then to obtain his own father’s permission. He tells him of his choice, and the price to be paid for her, and as a rule the father does not withhold his consent. The news is then published abroad that So-and-so’s son is to marry So-and-so’s daughter, and so much is to be the marriage portion. Should the parents not come to terms, the marriage does not take place, for the young people must always obey their parents in this matter, and runaway matches do not occur. Both young men and maidens appear to be faithful to their choice, and I have not been able to hear of a case of jilting. Before the marriage takes place, the young man may go and see his lianc6e whenever he likes. Meanwhile he works hard to get together as many cattle and as much grain as possible, to enable him to begin housekeeping. When he has passed the age of puberty by a year or so, the girl being also of a marriageable age, their friends are informed that the wedding will soon be celebrated. The girl’s father builds her a new hut, into which she goes a few days before the marriage ceremony takes place. The dancing ground is also swept and made ready. The young man, on his part, collects together the cattle to be given for his bride. His friends all make him presents, the most substantial help coming from his father, mother, and father’s brothers. The payment must be made in cows of one year old, or 321 of Edinhurgli, Session 1883-84. bulls of two or three years, also one one-year-old fat cow as an extra gift for the feast to take place at the bride’s village. On the morning of the day on which the ceremonies are to begin, a band of youths proceed from the bride’s village to the bridegroom, who hands over to them the stipulated number of cattle. Each youth leads one cow by a rope tied to its leg, its neck being orna- mented by a garland of leaves. Thus they are taken to the bride’s father. A group of unmarried girls, from the bridegroom’s village, accompany the youths, and the bridegroom’s brothers and sisters make up the party. Should he be an only child, two of his best friends or unmarried relations join the band. He himself remains behind. On their arrival the cattle are counted before the bride’s hut, and if found correct as to number and quality, as is usually the case, they are sent to the cattle pen, but are not mixed with cattle belonging to the bride’s father, which are previously removed to a distance. Should the tale not be correct, a messenger is sent to the bridegroom’s village, if it be near, to fetch the remainder ; but if at a distance, the ceremonies are delayed a day, or may be more. This mishap, however, rarely happens, as care is taken by the bride’s father that the right number of youths are sent, and the bridegroom is particular to provide the corresponding number of cows, so that mistakes are usually avoided. The fatted cow is killed by the bridegroom’s brothers in front of the bride’s hut, and their cooking operations commence and a great feast is held, after which dancing takes place. Very often nothing but water is drunk at the feast and if beer is provided it very rarely, if ever, leads to drunkenness. During the feast and subsequent dancing, which lasts two days, the bride is not allowed to leave her hut; but she is not left quite alone, as her future brothers and sisters-in-law keep her company, and expatiate meanwhile on the virtues of her future husband, and the delights of married life. They also fetch her food, but retire while she eats, as it is not proper for them to see her at her meals. On the third day there is another feast, on which occasion the bride’s father provides the cow, and dancing follows as before. Then the bride, for the first time, leaves her hut, and goes to the dancing ground, accompanied by her brothers-in-law, who walk one before and one behind her. They proceed to the centre of the dancing 322 Proceedings of the Royal Society ground, round which an assembly of spectators sit or stand under the shade of the trees. The brothers-in-law then retire to a short distance from the bride ; she is welcomed by a loud shout, and then begins to dance the particular marriage step, which lasts a long time, and is accompanied by special music and clapping of hands. The longer she keeps on dancing the more creditable it is to her. It is a proud time to the lady, and she takes great pains to show off well, and to please the spectators. Afterwards she retires to her hut, and word is sent to her bridegroom that she has acquitted herself well. The next day she rests after her tiring exertions, and the day following the bridegroom arrives, attended by his unmarried friends of both sexes, relieves his brothers of their charge, enters the hut, and claims his bride. The happy pair remain eight or ten days together in that village, being supplied with food by friends, who also fetch them water and firewood, in order to save them trouble. During this time the father of the bridegroom is engaged in constructing for his son a new hut, and on the eighth or tenth day the newly-married couple come and pay a visit to it. A sheep is killed at the door, after which they enter over the body and blood of the animal. The bride is then only presented to her father and mother-in-law, and remains there two days, but never eats in the presence of her husband’s parents. The young couple return to the lady’s village, re-occupy her hut, and remain there a variable time — until, in fact, the lady is in an interesting condition. As soon as this occurs, they return to the husband’s hut, and settle down to their usual pursuits. Divorce is not common, and if a woman is barren it rarely occurs. It may, however, take place if a wife makes herself disagreeable to her husband, friends, and relations, and also if she should prove unfaithful; but this is a rare occurrence. Should divorce take place for any just cause, the wife is sent back to her father, and he refunds the greater part of the cattle, the number varying according to cir- cumstances. If a wife wishes to visit her friends or relations at a distance, her husband accompanies her, and fetches her back at the end of the visit. Polygamy is permitted, but is not very common, and seems to be regulated more by a man’s wealth than anything else. The greatest number of wives allowed appears to be four, and a long of Edinhurgh, Session 1883 -84 323 period (two years?) elapses between each new marriage. Each wife has a separate hut, and the husband passes a definite number of days with each in rotation. This is regulated as circumstances may re- quire, but each wife expects her full allowance. When this is granted, as it usually is, the wives live on good terms with one another. Should a woman who has a child be divorced, if the divorce has been for her adultery, after the child is weaned it belongs to the husband ; but if she should be divorced from, any other cause, she keeps the child. In either case, the father and mother can visit the child, or it may go on a visit for a few weeks to either parent. Women who have been divorced may, but seldom do, marry again; should they do so, they are to be had cheap, and the children, if there be any, from the previous marriage remain with the grandfather. The Madi women generally make very good wives, and married life is apparently a smooth one. Prostitution in a general sense is unknown. Before marriage the girls are very carefully looked after, but as marriage usually takes place very early, there is not mucli cause for them to go wrong. This also applies to the men. Reproduction and Birth, ^c. — Early marriages appear to be the rule, and, as before mentioned, polygamy obtains only to a limited extent. It is very difficult to give facts as regards the number of children born, &c., but a few notes may be of interest. Four children would seem to be a fair average family. Few die directly after birth. Twins occur at times, and are considered very lucky both to the parents and to the village at which they are born. Many congratulations are offered, but no special ceremonies take place at their birth. I could not hear of a single case of triplets, but one woman was said to have had four children at a birth. Girls and boys are equally valued, but a boy is generally preferred as the first child. As a rule, labours are very easy. As soon as a woman thinks that she is near her time of delivery, she abstains from meat, but eats a good deal of vegetable food. She gets a neighbour to help to clear out her hut, sends her children, should she have any, to friends, and when labour commences, she walks round her hut, while her friends place a deep layer of dry sand at a short distance from the door. Sometimes two good-sized stakes are driven into the ground, about 324 Proceedings of the Royal Society 2|- feet apart ; and the sand is banked up near them. The woman then sits down on a skin placed on the sand, puts her feet up against the stakes, and clasps her ankles with her hands, her arms being inside the knees. Her friends take it in turn to support her back, and at times aid her by pressing or rubbing the abdomen. Another friend squats down before her to receive the child as soon as born. The sand, of course, moulds itself to the woman’s body, and being pushed down in front, might almost be said to support the perinseum. A lire is kept burning in the hut, and a very thin porridge is given the woman at short intervals. She keeps remarkably quiet, and often never moves from her first position until after the child is born, her friends keeping up all the time a low kind of chant, and doing all they can to encourage her. When the child is born, the cord is cut by a stone knife as a rule, but sometimes it is bitten. Should the cord bleed, the woman who has received the child takes the cord in her mouth and squeezes it with her teeth, so stopping all haemorrhage. They never tie the cord. The placenta is buried in a hole dug outside the hut — that of the boys on one side, that of girls on the other. Still births are very rare. When all is over, the mother is gently moved to the side of the lire, where she lies down on a bed made of dried grass covered with a skin. As soon as the child is born, it is cleaned by gentle rubbing, and then smeared with oil and wrapped up in a soft skin, after which it is shown to its father, grandfather, and other friends. In about an hour after birth it is put to the breast. The mother gets about again in three or four days. She then sits with her child in the 'door of her hut, and receives the congratulations of her friends. The woman is not allowed to eat meat for about a week after her confinement. On the occasion of a child’s name being given it, a fowl is killed by the father and grandfather before assembled friends. They cut off the animal’s head, apply some of the blood to the child, and pronounce the name. It is not at all Uncommon for children to be named according to the season in which they are born — e.y., Kran- obu = famine ; Kradaru = hunting seasom At other times they are called after their deceased relations, rarely after living ones. Family names do not obtain, but a son bears his father’s name in addition to his own; more frequently, however, pet names are used. of Edinburgh, Session 1883-84. 325 In this district women do at times bring forth their children on the march, and then continue marching ; hut this is by no means a frequent occurrence, and is guarded against as much as possible. I have known it happen on two or three occasions, but the result in one case was fatal to the mother. When a hard labour occurs, and a woman remains a long time undelivered, so that her strength begins to give way, a man is sent for to deliver the child. He, however, uses no instruments \ and should he fail, which, I am told, hardly ever happens, mother and child as a rule perish, for abdominal section is not practised here. Barren women are uncommon. Very few births occur out of wedlock, but I was not able to obtain much information on that point. The women suckle their children about two years, but the period of their separation from their husband is only six or eight months. If several mothers are suckling at the same time, it is not uncom- mon for them to suckle each other’s children; and I have once or twice seen a small child, who did not find sufficient milk in his own mother’s breasts, toddle off to another sitting by and commence to suck away without rebuff. During lactation the breasts are of an unusually large size. After several children have been born they become very flabby, and hang down like long flaps of skin. A cord is then tied round the chest to prevent them flapping about and causing inconvenience. When born, the babies are of a reddish tinge, and they get dark gradually. The women carry their infants in skins which have been dried in the sun and scraped clean and smooth with stone, and softened with butter. The skins of goats, gazelles, sheep, and calves are used, the legs being tied together and strung over the mother’s shoulders. The baby is placed in the skin under the woman’s arm, with its head behind. Sometimes a gourd is placed over the head to protect it from the sun. When older the child is carried on the arm. Infanticide is unknown. Education of Children, — A good deal of attention is paid to the instruction of children in matters of conduct. They are taught to behave well at meals, not to put their hands into the dish till after their elders have helped themselves, to rise as soon as finished, and having washed their hands, to remove to a little distance. They VOL. XII. Y 326 Proceedings of the Royal Society are also taught to he quiet when older persons are holding a council or chat. They are made to salute people in passing, and to show kindness to the aged and to the sick. The girls are taught to cook, to sweep out the huts (with bundles of fine dried grass), to show hospitality to strangers, to fetch water and firewood, to elude arrows at a fight, to dance, and to perform “ Ionian ” movements. The boys are taught to shoot, to fight (blunt arrows being used), the proper way to treat an enemy, &c. The education of boys and girls is not considered to be com- plete until they have travelled. When about ten years of age they are sent away from home to visit friends and relations at distant villages or among neighbouring tribes. They remain away during the fine months of the year. The girls may return at any time, but the boys are usually anxious to, remain away as long as possible, in order to learn as much as they can from contact with other people. Should the girls wish to come home, the boys will bring them, and as soon as they have seen them safe with their relations, they start off again. The boys must, however, return home when the rains begin, and remain during the wet months, to help their fathers in agricultural work ; whereas the girls, if they choose, may stay away ; if wanted, they are sent for. When out on these visits the young people take part in the hunts, dances, or what- ever else may be going on. Sometimes a father will take his children a round of visits. Both boys and girls are taught to find their way about, so that if the path should be lost they are not long in discovering their whereabouts. Family Gatherings. — There does not appear to be any special occasion for family gatherings, but from time to time all the sons, daughters, and grandchildren meet at the father’s house. The love for children causes great interest to be expressed about the babies. At such family gatherings the father directs the thoughts of all to grandparents and old friends who have passed away, enforcing at the same time the duty of attention and care to relatives and friends when ill, and of mourning for them when dead, as they then are beyond the reach of help. Tribal Signs. — Each division of the tribe has a number, by which those who belong to it are known. Persons are said to carry so of Edinburgh, Session 1883-84 327 many stones, but this is merely a form of speech, as the stones are not literally carried. The lumps of earth thrown into a man’s grave correspond to his number of tribal stones, and in this way also will a man often regulate the number of tufts of hair to be left on his head after shaving. Burial Customs. — Immediately it is known that a man is fatally wounded, the news is sent to his wife, who hastens to him, taking their children with her. A touching scene is witnessed when they reach the dying father. The little children are placed upon his knee, and the others stand round about him, while he gives them his “blessing” by putting his hands on their head and moving his mouth as if spitting. After telling them to be good, and not to grieve too much for him, he solemnly addresses his eldest son, giving into his charge his mother, brothers and sisters ; also the fields and cows. He also is careful to tell him through what tribe he has met with death, in order that his son may some day revenge him by killing one or two men of that tribe. Then follows an affecting farewell to his wife. If he is a well-known man, and not far from his home, a great company of his friends and acquaintances gather round to take leave of him. While the body is being carried to his hut, a drum is sounded as an intimation that he is dead. This is also done at the hut if a man dies at home, and is repeated at the burial. The body is usually buried one day after death, close by the man’s hut, but sometimes by his father’s, A deep round hole is made in the ground, and at the bottom of this a deep recess is scooped out. In this recess the corpse is placed, being laid on the right side with the head leaning on the right hand. Lumps of earth are then thrown into the hole by the children, first with their backs towards it, and then their faces, the number of lumps coinciding with the number by which the deceased’s tribe is known, the girls throwing one less each time than the boys. A pole or tree trunk is then fixed in the ground at the bottom of the hole, which is not filled up, but covered by two large stones placed against the pole. Sometimes there is no pole, if a stone can be found large enough to cover the hole. Over this is erected a conical mound of earth, three or four feet high, which is stabbed by flat stones. If a pole has been placed in the grave it projects above this mound, and is surmounted by the horns of cows killed by the 328 Proceedings of the Royal Soeiety grave. Four cows are killed by the friends out of respect for the departed, and the eldest son often kills his favourite ox. If a great man has died, friends and relations come from a distance to the burial, and stay a few weeks (four?) mourning for the dead. For the first four nights they sleep on skins by the grave, and during the remainder of the time they pay frequent visits to it and make lamentations. The deceased’s widow resigns all household duties to a sister or friend, and gives herself up to weeping during a month. At the end of this time a lamb is killed ; it is subsequently eaten by the friends, as were the cows killed on the day of burial. The son leads the lamb to the grave, but it is killed by a man of a semi-priestly order (whose office it is to perform such like duties on various occasions). This man, after killing the animal, sprinkles its blood on the people and the grave. After speaking at length on the virtues of the deceased, he sprinkles the people with water, exhorts them to put away their sorrow, and to show kindness towards each other. The friends then take their leave, but a year after the man’s death all his relations and friends who live near meet again and celebrate the day by a feast and dance; and on these occasions the dance is never followed by a fight. If a woman die her friends mourn her loss also for a month, but for children the time of mourning is only a few days. If a man should be killed at a fight or hunt, and the place and manner of his death be unknown, his friends go and search for his body, and if they cannot identify it, they bury any bones they may find about the place of supposed death. As soon as the period of mourning for a father is over, the children (if young) are taken to their father’s family, and a consulta- tion is held as to what is the best thing to be done with them. They are usually placed inside the circle of consulting relations, and if old enough are asked whether they will stay and live with their father’s people, or go with their mother. The mother is urged to remain in the village, but she usually prefers to go to her own relations, and as a rule the children go with her. Sometimes the eldest son, if he is old enough, will remain on his late father’s property and look after it, the mother with the rest of the children going, for a time at least, to live with one of her brothers. Later of Edinburgh, Session 1883-84. 329 on she may return to her old home, or more rarely still she never leaves it. Treatment of Superiors. — There appear to he no rules of precedence nor any difference in the treatment of rich and poor. The poor are generally those whose parents have died when they were young, or those whose father’s cows have been stolen by an enemy. In this case the children are adopted by relations, and when they marry, a small number of cows are given to them as presents to start them in life. Each village is quite independent, having a president or sub-chief at its head ; only in time of war must the men from each village assemble, under the head chief, who resides in the largest town. The village head-men and even the chiefs are treated with great familiarity, no spirit of subjection or fear apparently existing. Hospitality. — Hospitality is inculcated and universally practised to kinsfolk, neighbours, strangers and enemies. A passer-by is invariably invited to share any meal which is pro- ceeding, and a refusal to partake of the proffered kindness is con- sidered as an offence. If he is in a hurry, and does not wish to be delayed, politeness requires him to dip his hand in the dish and to eat a mouthful before proceeding on his way. At a meal the guests sit on the ground, and help themselves out of the common dish. Water is brought them to wash their hands, children per- forming this duty. Water is always at hand to offer to passing travellers. Every family has a hut for the special use of visitors, and if guests arrive unexpectedly when the hut is already occupied, the children are turned out to sleep at a neighbour’s, and their hut appropriated to the visitors. Treatment of Women. — Women are treated with respect and politeness by the men, who always show them preference, resigning to their use the best places, and paying them such like courtesies. They eat at the same time, though not out of the same dish as the men; but associate with them on equal terms, being consulted and honoured. Any insult to a woman is revenged, and is frequently the cause of war. Drunkenness is very little known, but in the case of a man becoming intoxicated, and in that condition insulting a woman, he is punished by being tied up until perfectly sober. Treatment of the Aged and Infirm. — In the training of children, obedience and great respect for parents and elders are inculcated. 330 Proceedings of the Royal Society Great care and attention are paid to the aged, and counsel and teaching from them is considered of special value. The sick and infirm are cared for and nursed with much solicitude. Much affec- tionate care is exhibited by husbands to their sick wives. Communications. — The construction of the roads is very simple, a track of some two feet wide being formed by merely cutting down the underwood of the forest. More than this is not attempted; a network of small paths in the forest being made by use. Swamps are usually passed by wading, although occasionally a way across them is made by filling in with stones, sticks, and grass. Kivers are crossed by swimming, an art which is learnt very early, as is also an acquaintance with the haunts of crocodiles and hippopotami and the shallow parts of the rivers, so that should a man be carried down by a swift current he is quite at home, and knows where best to make for land. Boats and even rafts are unknown, but bridges are occasionally constructed over rivers, and are made as follows : — Trunks of trees are firmly fixed in the bed of a river in the dry season, being supported by stones, and having forked tops along which is laid a single row of logs^ — thus forming a simple kind of bridge. Xo accommodation is provided for travellers between villages ; they rest where rivers or wells supply them with water, and then continue their journey till a village is reached. On a journey, if a man cannot find a stream, he digs for water in the ground; and the wells thus formed last for a time, and serve for the use of other travellers. When a village is reached there is no lack of accommodation, hospitality being universally shown alike to friends and enemies. Immediately a stranger is seen, he is asked how many stones he carries (see Tribal Signs). If the man who accosts him is of the same number, they fraternise directly; but in any case, the stranger is escorted round the place to see all there is to be seen, and a hut and food are given him. Ho vehicles of any description are used, the only mode of con- veying persons who are too old or too ill to walk is by means of a kind of litter made of branches laid side by side, and fastened together on to cross pieces of wood. Upon this rude contrivance the individual lies or sits, and is carried by two or four men. of Edinlurgli^ Session 1883-84. 331 Horses are not known, nor are any animals used as beasts of burden; but their need is little felt, as the necessaries of life are very few. Heavy weights, such as animals or fish, are often slung on a pole, and carried between two men ; while trunks of trees are transported by the simultaneous efforts of men, pulling to the sound of their voices. It is customary for meeting travellers to exchange greetings, a phrase answering to our “ How do you do ” beginning the conversa- tion. The young are carefully instructed by their elders to show a friendly spirit even towards an enemy if met on the road, unless he should appear to be bent on insolence, in which case high words are to be returned, and they are frequently followed by violence. It is not necessary to obtain permission before passing through the territory of another tribe; and even if travelling among a hostile tribe, a man is unmolested unless he himself provokes attack. When a man encounters a stranger on the road and is accosted by him, he stands in the usual position of ease (the right foot resting on the left calf), with his bow and arrows in the left hand, and talks to him in a friendly manner, at the same time on the watch for lurking enemies. If the traveller prove to belong to a hostile tribe, and become insolent, the pleasant tone must not be maintained (it would be taken for cowardice or fear), but he must be met with ‘^flashing eyes and angry expostulation;” should he wax more angry, and use insulting language about the man's mother, a fight is unavoidable. In this case it is possible that others (friends of the stranger) will be in ambush near, and at a given signal will surround the man, so that for a long time he must try by great agility to avoid their arrows. There is a leaf which is believed to possess peculiar virtue, and if any of it is at hand the man will endeavour to seize some of the leaves and rub himself with them. He then aims at the stranger who accosted him, and if possible shoots him. If he is successful in killing his assailant, he may escape if he please; but to do this is considered a disgrace unless he has killed his enemy, or at least one of his tribe. Should the man be completely outnumbered, but contrive to escape, he summons assistance by means of his horn, and then, reinforced by others, returns to the scene of conflict, and should the enemy still be there, the fight is renewed. 332 Proceedings of the Royal Society It is usual for young persons to travel over the surrounding country often to considerable distances, and thus they acquire a practical knowledge of the country, and without the help of mile- stones, sign-posts, or other landmarks (all of which are unknown), they become expert in finding the way from place to place. Salutations. — The modes of salutation coincide almost exactly with our own — greeting being expressed by shaking of the hand and kissing. Members of a family kiss, but the boys shake hands with their father and each other. Husbands kiss their wives and female relations, and friends kiss each other. Matutinal greetings are usual. Great joy is manifested at the return of a member of a family from a long absence, the brothers and sisters running out to welcome him ; and frequently a lamb is killed as an expression of joy, and great virtue is believed to be in the blood, some of which is put upon the returned traveller. Swimming. — Swimming is practised by both men and women in the Madi tribe, and the art is acquired very early in life. It is put to practical use by crossing rivers, fishing, &c. They do not take a header into the water, but simply walk or jump in. Diving is not practised. They swim as a rule hand over hand, and splash about and make as much noise as possible to frighten away crocodiles. Sometimes they carry children on their backs when in the water. They have a habit of taking in mouthfuls of water and spitting it out forcibly when in the act of making a stroke. On coming out of the water they rub themselves all over with their hands, to get rid of as much water as possible. If near home they rub themselves with oil after bathing. Bathing and Cleanliness. — The Madis bathe each day in a river or other water near their homes ; small children wash themselves at home in large earthenware jars. Ho soap is used or any substitute for it. They have no sponges. They always rub oil over their bodies after each bath. When they cut their nails, they bury the parings in the ground. Division of Labour. — In the division of labour the woman’s sphere is at home. She may help at times in the lighter field work in the cool of the morning, but must return home before the middle of the day, the men continuing at work. If, however, a woman has a family of young children to look after, she seldom leaves home at of Edinhurgh, Session 1883-84. 333 all. Her duties are domestic j she lights the fire, sweeps out the huts, fetches water twice a day from the river or well, makes butter, stores the food in jars, and cooks, &c. Children are early taught to he useful in helping their mother; and should she he ill, the husband fetches the water, lights the fire, and a neighbour is called in for aid, as the father cannot cook. Ho one is paid for such services any fixed price, hut some present is as a rule given. The women attend sick persons with much solicitude. The man’s work consists in hunting, fishing, agriculture, procuring wood for hows and arrows, and firewood. He partly makes the hows, milks the cows, and sometimes helps in making the butter. The men also build the huts. When removing from one place to another the men carry all the heavy things, as well as the roofs of the huts, and fix them before they fetch the w^omen. In hunting expe- ditions the women carry water in small jars for their husbands. Religion. — With regard to the religious beliefs of the people, I have not been able to ascertain much, their ideas being so vague that a much longer sojourn among them than I made would be necessary to discover what is really or partially believed by them. They appear to have an undefined belief in a great Being who made the world and men. They also believe in “isa” = the soul or thinking part of man, which however perishes with his body. There is no belief in a resurrection or after life for man, though ideas and speculations on the subject are indulged in. The first man is said to have come from the sky, but departed friends are thought of as being under ground, and their bodies are thought to turn into white ants, or to grow up as grass, mushrooms, &c. I have been told that sometimes people imagine they hear their departed friends speaking to them, and that when they look to see the familiar forms nothing is visible but smoke. When this happens there is a general lamentation among the friends of the departed, and a lamb is killed and its blood is sprinkled on them all. One man, tradition says, dreamt that his isa ” (soul) left his body sleeping, and went up to the sky. It is a common thing for lost friends to be seen in dreams, and to seem to turn into lions or some other object of terror. However vague their notions of a Deity or of themselves as spiritual beings may be, they teach and practise very sound principles of good. 334 Proceedings of the Eoyed Society A good man to them is one who is brave and not afraid to fight or die, who seeks the welfare of others, and is always ready to show kindness to them, who respects the aged, helps the sick and infirm, and gives to those who are in need. Superstitions. — Among the superstitious practices in vogue in the Madi tribe, is the detection of guilt by ordeal. Three means of trial by ordeal are used, through which it is believed guilt can be detected. If a man is accused of an offence and denies it, he goes with his accuser to have the matter settled by ordeal. In one mode of trial they both receive a red feather of great value, and have to bite it through. This is considered very dangerous, for after a few weeks the guilty one will fall ill and die. Unless very sure of their own innocency they rarely try this ordeal. At other times seed is given to be eaten, which will be innocuous to the innocent, but fatal to the guilty. Another method is by throwing down small sticks of equal lengths. In the case of an innocent man, the sticks will fall against each other, standing up like the legs of a Gipsy table, whereas a guilty man’s sticks fall flat. Before any of these trials the men look up and solemnly invoke some invisible being to punish him if guilty, or help him if innocent. If a man is seen committing an injury and does not deny it, the injured person challenges him, and they fight until one is killed or badly wounded. Sometimes the men of the village come together and separate them, and then a kind of rough trial takes place, and the defaulter is obliged to make restitution in kind, e.g., a cow and a goat for a cow injured, a hut and a cow for a hut, &c* There are three classes of men who possess authority in villages and districts. Class A. preside over ordeals ; class B. possess the power to try j^ersons accused of murder or any great crime ; and class C., perhaps the most Important of all, consists of the men who kill the lambs on particular occasions, as described elsewhere. Madmen are always hanged. If birds afterwards feed on the body, it is taken as a proof that the person was really mad, their absence showing that he was wrongly put to death. Great faith is placed in the power of a certain plant, a piece of v/hich, after being spit upon, is applied to a man’s shoulders and of Edinhiorgli, Session 1883-84. 335 legs, and is believed to strengthen him, to preserve him from danger, to make his enemy “see crooked,” or to enable him to slip out of his hand, just as the stem of the plant slips like soap when it is grasped. With this idea mothers frequently apply this plant to their sons. Sometimes also they sprinkle the boys with water, with a similar notion. Omens are believed in. One of the most common is sneezing ; it appears to forebode good or evil, according to what is being said at the time, producing a contrary effect to what is expected. Trip- ping one’s foot against any thing is considered ominous. To trip on the same foot twice on the same day is a bad sign, once on each foot is a good one. Some people consider one of their feet lucky, one unlucky. It is thought to be unlucky to return by the same road that a man goes by, both for long journeys and short walks ; a different route is always chosen when possible. Odi. — There appears to be a belief in the existence of elves or spirits, though this would seem to be an invention of the female doctors to gain a hold on the people. “ Odi ” is the name by which these beings are known. They are supposed to live underground, and their help is sought in cases of illness among children. If a child is ill, the lady doctor first examines it, and then retires to a quiet spot at a distance from the hut, where she erects a miniature hut of sticks and grass. She is followed to this place by the mother and one of her little boys, laden with a pot of food and a live fowl. She then proceeds to invoke the Odi to appear, but often gives out that they cannot come till the next day, being busy. At last they make their appearance inside the small hut, but are visible to none but the doctor, others only hearing them speak. Two usually appear, a male and a female, more than that number refusing to come at once. The doctor says they have human faces and serpent’s bodies. She pretends to give them food to eat out of the pot, and asks their aid towards the sick child’s recovery, shaking all this time her magic wand or rattle. When they have had enough food they vanish, and the doctor falls down right over the small hut. She strikes the ground with her hand, and appears to have a fit, unconsciousness lasting a few minutes. Before falling she tells the mother and boy to run home as fast as possible, and shut the door. A strong women is always present at this incanta- 336 Proceedings of the Royal Society tion, who is ready to raise the fallen doctor, and give her water to drink. After she has recovered from her real or supposed exhaus- tion, she is supported to the sick child’s hut to see her patient. Before the door is opened a certain formula is gone through, after which she enters the huts, feels the child all over, and gives her opinion as to whether it will get well or not. She is then escorted home by the father, who takes with him her fee, in the shape of a goat, cow, or arrows. The Custom of Killing u Lamb. — A remarkable custom is observed at stated times — once a year, I am led to believe, I have not been able to ascertain what exact meaning is attached to it. It appears, however, to relieve the people’s minds, for beforehand they evince much sadness, and seem very joyful when the ceremony is duly accomplished. The following is what takes place ; — A large concourse of people of all ages assemble, and sit down round a circle of stones, which is erected by the side of a road (really a narrow path). A very choice lamb is then fetched by a hoy, who leads it four times round the assembled people. As it passes they pluck off little bits of its fleece and place them in their hair, or on to some other part of their body. The lamb is then led up to the stones, and there killed by a man belonging to a kind of priestly order, who takes some of the blood and sprinkles it four times over the people. He then applies it individually. On the children he makes a small ring of blood over the lower end of the breast bone, on women and girls he makes a mark above the breasts, and the men he touches on each shoulder. He then proceeds to explain the ceremony, and to exhort the people to show kindness, for example — If rich, not to deny a cow or sheep to a poor man that asks one. If eating, not to appear unaware of a passer-by, but invite him to share in the meal. If children see a stranger, they should run to their mother for water to offer to him ; or if they see an old woman fall, they should not laugh, but give her assistance. When this discourse, which is at times of great length, is over, the people rise, each places a leaf on or by the circle of stones, and then they depart with signs of great joy. The lamb’s skull is hung on a tree near the stones, and its flesh is eaten by the poor. This cere- mony is observed on a small scale at other times. If a family is in of Edinhurgli, Session 1883-84. 337 any great trouble, through illness or bereavement, their friends and neighbours come together and a lamb is killed ; this is thought to avert further evil. The same custom prevails at the grave of de- parted friends, and also on joyful occasions, such as the return of a son home after a very prolonged absence. Harvest Feasts. — A harvest feast is held as soon as the corn has been reaped and placed on the “ langas ” to dry. It is then too that the general holiday time commences ; there is very little work done from this period until the rains begin, hunting, dancing, and fighting occupying the interval. The harvest feast is held in each village, and is only attended by the inhabitants of the place. It takes place on the open space which is usually found in the centre of the village. At the con- clusion of the feast speeches are made. It appears that one man presides, and after an opening speech by this president, women as well as men address the company. The old people are listened to with great respect, and give advice to the young. The belle of the village is reserved to make the last speech, after which all disperse. The enthusiasm evoked by a favourite orator or palatable senti- ment is expressed by clapping of hands ; but weariness or impatience is merely shown by sullen looks, only those who are rude covering their faces with their hands. Music. — The Madis are very fond of music, and have several kinds of musical instruments — drums, harps, horns, and flutes. There are large and small drums. The small ones are made out of a tree, the trunk of which is more than a foot in diameter, and their length varies from 2 to 3|- feet. The block of wood is either hollowed out by fire, or more rarely by the knife. Pithon or goat skin is usually fixed over one end by means of wooden pegs. Sometimes, however, both ends are covered, and then the skins are caught together by long laces of hide. The larger drums are very different both as regards size and shape. Logs of wood about 12 feet long are hollowed out, and placed on four wooden legs, four handles also being cut out of the wood (see fig. 13). A narrow opening is left along the under surface of the block, and not covered in. The drum is beaten by large sticks, having a somewhat globular end. All drums are well warmed before use, and near the larger one a fire is kept burning during its use. 338 Proceedings of the Royal Society The harps are made as follows : — The half of a large gourd is taken and two round holes made in it, into which are fitted two upright sticks, which diverge a little from each other. They are united above by a cross bar, from which strings made of sinews or fibres are carried down, and passed through small holes made in the gourd, on the inside of which they are fastened to small hits of wood. When in use the gourd is placed against the belly of the player, and so acts as a kind of sounding hoard. The flutes are made out of hollow canes, having eight holes and a mouth hole. They are held as in Europe. They also use rattles made of gourds, partly filled with dried dhurra or small stones. Small hows are used as musical instruments. They are strung with liair from a giraffe’s tail ; one end of the how is placed against the teeth, and then the string is struck with a switch. I fear it is beyond my power to, describe the music produced by these instruments, hut I can testify that on a moonlight night the melodies they give forth are very weird and yet sweet, and at times fantastic. Dances. — The harvest feast is usually followed the next day by a dance — this being the first dance of the season. One of the larger villages is chosen as the scene of the dancing festivities, which are held in a large open space outside the village. Great numbers of people assemble from the surrounding country ; and as most of the inhabitants have to be present on these occasions, often only the old and very young people are left behind in a village. The holiday makers are accompanied by their cows, and these are left to graze outside in the forest, boys remaining in charge of them. This is done as a precaution, for if the cattle were left unprotected, raids might be made on them by enemies. The band consists of a large drum and several small ones sus- pended on a pole ; horns and rattles are also used. The musicians are placed in the centre of the ground, being encircled by the dancers. The old people present stand round the ground, and clap their hands in time to the music. The young men are grouped together and the young women placed opposite them. The married women dance together, and the married men in a group by them- selves. The dancing is chiefly from side to side, not forwards. Some- 339 of Edinhurglb, Session 1883-84. tin. % however, a young woman dances across, and invites a young man to advance into the centre and perform a pas seul; and when he has finished, he in his turn asks a young woman to exhibit her skill, but they do not dance together. The men paint themselves with various colours for these occasions, and the women are adorned with brass necklaces, rings on their waists, arms, and ankles, and flowers round their necks. Fights. — These dances are usually ended with a fight ; in fact, it seems that the dance would not be supposed to have gone off properly without some such finale. The fight is begun in this way : A man shoots an arrow high in the air, so that it falls among the dancers, who immediately cease dancing, and range themselves into different sides, according as is their division of tribe. Then the game begins by a shower of arrows. The women remain with the men, carefully eluding the arrows ; should a man be hit, some of his female relations rush up to him, carry him to a place of safety, and wash his wound. They do not try and stop the bleeding, for fear of causing inflammation. Should inflammation occur, light incisions are made to allow the blood to run freely. A special knife is used for this purpose. Should a woman be killed, there is great excite- ment, and the fighting becomes desperate. War goes on between the tribal divisions, until the offending one is considered to be suffi- ciently punished, and pays a large indemnity in cows. If no fight- ing is desired at the dances, all the bows and arrows are hidden. Boys are early taught by their fathers the art of war, especially how to elude an enemy’s arrow. This requires great dexterity and much practice, and young children are trained from very early days, shooting at their father with blunt arrows. The young men also instruct large classes of boys, and mothers train their daughters in the art of eluding arrows. As in Europe, women at times take a dislike to one another, and very occasionally even come to blows. If they do, a very fierce and bloody encounter takes place, for the women, before fighting, put on iron bracelets with spikes both straight and curved projecting from them ; with these they tear one another very badly. The Arab slave dealers do not appreciate these bracelets, and when in their raids they see a woman with them on, she is generally shot down at once, for at close quarters the Arabs are no match for them. 340 Proceedings of the Royal Society Weapons. — The weapons employed in hunting are bows, arrows, and spears ; arrow heads have various shapes. Arrows. — The heads are made of iron, and are barbed and orna- mented. Sometimes they are poisoned for killing lions, &c. The shafts of the arrows have a hole made at the top by a red- hot iron j into this the head is fitted and kept in place by flat iron wire ; similar wire is also used to ornament the shaft. The arrows are notched, but have no feathers. The arrows used in war are made of the hard wood of the “ pi ” tree. The barb is also made of wood sharpened at both ends and fitted into the shaft. The end of the shaft is bound round with red string to prevent it splitting. In withdrawing the arrow from a wound the head is left behind. Spear Heads. — These do not vary much in shape, but different sizes are made. Very large heads are used for elephants. The women, if on a long journey, carry small spears with ornamented handles. The spear shafts are tipped with an iron spike; both heads and spikes have a hole made in them, through which iron wire is passed to fasten them firmly to the shaft. No blunt-headed arrows are used, save those employed to instruct the children. When hunting or fighting, the left hand is protected by a woven string “gauntlet”; it covers the palm of the hand and fingers, the thumb being left free. Bows are made of several species of wood. The strings are formed of twisted tendons. Sometimes the bows are made quite plain, others are ornamented by rings of crocodile skin, but the middle of the bow is always left plain. One side of the bow is generally flattened, and there is enough difference between them for each man to know his own. Animals speared or caught in pit-falls are as follows : — Ehino- ceroses, hippopotami, giraffes. Animals shot with arrows : lions, gazelles, wild boars, leopards, foxes, elands, tetels, ostriches, buffaloes, baboons. Crocodiles are killed by a barbed spear, the iron head of which has a line attached to it, and is readily detached from the handle as soon as the beast is speared. Baboons are only attacked by a number of men together ; it would be unsafe for a single man to attempt it. No nets, palings, or trenches are used in capturing game. There are no firearms in the country. Clubs are used; a favourite pattern is egg-shaped. of Edinhurgli, Session 1883-84. 341 Animals. — The jungles abound in wild animals, the number and variety of which afford a wide field of sport for the hunter, and a choice abundance of food for the whole tribe. The following animals are hunted, and all except leopards, baboons, and foxes are used as food : — Elephants, buffaloes, gazelles, rhinoceroses, hippopotami, crocodiles, wild boars, leopards, giraffes, elands, baboons, tetels, rabbits, porcupines, ostriches, guineafowls, wild ducks, pigeons, and various other species of beasts and birds which I am unable to identify. The animals in a state of domestication are cattle, sheep, goats, dogs, and fowls. Fowls are fed with semsem and dhurra, A conical stone house is made for them close by the dwelling-hut, but no porches are provided. The people keep bees. The hives are made of basket-work, and fixed on the branches of a tree. The man who takes them up makes at the same time a sort of whistling noise, which seems intended to be a call to the bees. A hole is left at the bottom of the hive to allow of the bees getting in, and of the honey being subsequently taken out. To accomplish this a basket is pulled up, filled, and let down again, the use of a branch as a pulley being evidently unknown. Sheep and goats are kept in large numbers. Their sheds have wooden walls with thorns fixed on them, as a protection from hyenas, and they are roofed in like the dwelling- huts. Gazelles and tetels are tamed when caught young, the former being fed on goats’ milk and the latter on cows’ milk. The tetels are kept for the purpose of milking. Eabbits are tamed, but not very successfully, as when they are full grown they generally manage to escape. Birds are not kept in captivity. The domesti- cated dogs are all smooth, and do not vary much in size, being about as large as our fox terriers. In colour they are either white, black, or brown, or black or white. They are intelligent, and show much affection and fidelity to their own masters. They are liable to hydrophobia, and when seized with it are at once killed. There is also a kind of wild dog, of smooth skin, reddish-brown colour, and a fox-like head and long ears. Dogs are the only animals which are trained. They prove of great use in hunting gazelles, buffaloes, and some small animals. Horses are unknown, and only very recently have a few asses VOL. XII. z 3-12 Proceedings of the Royal Society been introduced by tbe Arabs. There are no mule animals. Cas- tration is not practised. Two kinds of migratory insects visit the country. When the dhurra is ripe, green flies about IJ inches long arrive in swarms; many are caught and eaten, and the remainder take their departure in the opposite direction from which they came. Swarms of locusts follow them. These are also eaten. When they leave, a species of small red bird takes possession of the fields. They build their nests in the trees near the fields of th.e dhurra, and remain until the corn is too dry for them to eat. Once a year the white ants swarm ; when this is expected a fire is lighted near the ant hill, the ants are knocked down, gathered, preserved in jars, and much relished as food. Tleas and mosquitoes are very abundant. There is no worship of animals, and the people do not believe in the interchange of souls between men and animals. There exists, however, some sort of superstition concerning one small bird called dadir.” It is caught when young, and small rings are fastened to its legs, after which it is set free, and no one is permitted to harm it in any way. They think that it is unlucky to hurt it ; and should a man by accident break its leg, they expect one of his cows to get its leg broken. The feathers of another highly-valued red bird are used to try by ordeal persons accused of falsehood. It is considered to be a bad omen if a gazelle crosses a man’s path ; and if it should occur, the man usually turns back and gives up his project, whatever it may be. The lizard is known, and no one is allowed to kill it. Various curious legends prevail with regard to animals. I will mention one as a specimen. ^ A monster lion is said to have shaken the earth by his roars. The shock was so great that all the people fell to the ground, and the lion proceeded to eat them. One man, however, entreated the Being, who had created both man and beast, to make the lion a little smaller, as he was too great and powerful for men ; his request was granted, and the lion forthwith was reduced in size to his pre- sent dimensions. Among numerous fables, the following may be given : — On a certain occasion the animals all meet together to dance and of Edinburgh, Session 1883 -84 0^0 oio enjoy themselves. Soon, however, they found that they M^ere encircled by men, who set fire to the grass on all sides. The rabbit was most officious in proposing plans of escape. One of his sugges- tions was that the weasel (?) should make a hole in the ground, into which they might all flee for refuge. When the danger came quite near, he forgot every one else in his endeavours to save himself, but without avail, for they were all burnt up except the weasel (?), and a small bird who had been on the watch, and who, as soon as he saw the danger, warned his friends, and then flew away. The rabbit came to his end as follows : — The weasel (?) had taken his advice and dug a hole in the ground, into which he entered, but the rabbit bit off his tail and pulled him out, getting into the hole himself. In revenge, the weasel told the men where the rabbit was, and as they looked for him the weasel managed to make good his own escape. Hunting. — The hunting season is a very important time in the Madi country, for it immediately follows a period of agricultural labour, and finds the people ready for the enjoyment of a holiday, and of a sport which they keenly appreciate. When the corn is all dried and stowed away in the granaries, the hunting begins, and continues for several months — that is, until the rain commences again. Very large hunting parties are formed, people from numerous villages assembling together, and being sometimes joined by parties from other friendly tribes. The following is the way in which the notice of a hunt is given : — A man is sent round to all the villages, and as he passes by each hut he strikes with a peculiar stick one of the stones by the door of the hut. This signal is followed by a formal declaration that a hunt is arranged for a given day, and that all who wish to take part are to meet at a given place. When the time has arrived, and the hunters assembled, they divide into companies, and encircle a tract of country often several miles in extent. One company takes up its position on the side from which the wind blows, and sets fire to the long grass; as it is burnt down, the animals rush towards the other companies, who stand in long double rows, shooting their prey as they pass by. If a buffalo happens to be amongst the fugi- tives, he usually proves an awkward customer, as instead of running straight forward he will rush into the ranks of his foes, and cause 344 Proceedings of the Royal Soeiety no little commotion, often killing or wounding several of the hunts- men. When an animal is killed, it is the prize of the man who first shoots it, though its death is probably accomplished by others. The right of possession does not appear to he decided by dis- tinguishing arrow marks, but great care is taken to identify the shooter, and quarrels often arise about it, and are frequently only settled by a fight. It is virtually a case of much ado about nothing, for this right, which is so jealously guarded, concerns only the tail or the horns of the animal, which are kept as a trophy. Any one who has taken part in a hunt has a perfect right to his share in the booty, which is shared alike by all, each man getting an almost equal part of the spoil. Even should one party be more successful than another, the unlucky hunters get the same share as those who have been successful. Should an animal be first shot with a borrowed bow and arrow, the lender gets the trophy ; but such transactions only take place between brothers or very intimate friends. Successful hunters are long kept in remembrance, and their exploits are handed down from father to son. The Madis do not appear to have any special ceremonies or dances connected with their hunting expeditions, but in subsequent dances, those who have been distinguished in hunting, or women who have been very active in giving water to the men and won special renown, are celebrated in song, hlo great feast takes place after a hunt, but friends are sometimes invited in small parties to eat buffalo, &c. Before going to the hunt the men paint their faces in stripes of different colours, and put iron rings on their necks, arms, and (some- times) ankles, and the white tail of some animal round their necks. They carry their arrows in a goat-skin bag, hung over the shoulder or by a string which passes round the neck. In the left hand they hold the bow and two or three arrows; in the right hand they carry the spear. They start very early, so as to reach the hunting ground soon after sunrise, and they hunt all day. The women start later, carrying water on their heads in earthen jars, in the neck of which bunches of leaves are placed to keep the water cool. A small gourd floats on the top of the water to keep it from spilling, and serves as a drinking-horn. These large hunting parties are only undertaken in the hunting of Edinburgh, Session 1883-84. 345 season, but individuals bunt at other times. Young people and children hunt rabbits, gazelles, &c., not far from home. Women catch guineafowl by driving them about, as they soon get tired and cannot fly far. Sometimes large companies of boys undertake a hunt for the old women. On their return they all walk together in regular order to the huts where the old women live, laden with the spoil, and for this good work they are always invited to dinner. Should the old women have too much meat brought to them, they make presents to their friends. All the wild uninhabited land surrounding a tribe belongs to the tribe as a whole, and may be hunted in by anyone. Individuals or parties may also hunt in the country which belongs to a neighbour- ing tribe, if that tribe is friendly. Should a man go alone to hunt in an enemy’s country, he will not be interfered with, if he behaves well ; but if he be insolent, the people will fight with him. The chiefs do not often take part in the hunt; possibly the people do not like them to be needlessly exposed ; and there is a tradition of a great chief having been killed in a hunting fray, and his body having been lost. Gazelles are hunted as follows : — Some of the dogs run in front of the animal to distract its attention, whilst two or three creep quietly up from behind, and seize it. The dogs ^are kept by indi- viduals, and not in large packs. All large animals are cut up when killed, and not carried away whole. There is much waste, as what cannot be easily taken away is left. Small game is carried home on the head^ or slung on a pole and carried by two men. The Madis are very skilful with bow and arrow, and can hit birds on the wing. l!lo tribute is paid in game. Water only is drunk while hunting. The meat is dried over a fire to preserve it. The people are not influenced to migrate by the habits of the animals they hunt ; good land is their great desire. Traps. — The various modes employed for entrapping animals are of interest. Hippopotami and rhinoceros are caught in pits. Deep holes are dug in the ground, into the bottom of which wooden stakes are driven with spikes projecting from the upper end, and then the holes are covered over with sticks and grass, strong enough to bear a man’s 346 Proceedings of the Royal Soeiety weight, but unable to sustain large animals, which, falling in are often killed by the spikes, or at least badly wounded. Buffaloes are caught by means of a skin rope attached to a pole which is stuck into the ground at the end of the rope there is a noose, which is arranged round a small hole dug in the ground ; the rest of the rope is hidden by twigs and leaves. The buffalo puts his foot into the hole, and in getting it out the noose is drawn tight, and the animal has to drag the heavy pole. He is thus easily tracked and speared. To trap guineafowl, a string is made of hair from a cow’s tail, a noose is placed among the small branches of a low plant in their run, into this they run their heads and are held fast. Another trap is made of a long basket with a narrow opening at one end. It is placed on the ground in one of the narrow paths running through the high grass; small animals find their way into it, but cannot get out again, as the twigs of which the basket is made are so arranged inside that they fly back from the sides and prevent the animal retreating. Birds are caught in the following ways : — 1. A noose is attached to a bent bough, and so arranged as to spring back and snare any bird that touches it. 2. One end of a flat stone is placed on the ground, and the other supported by a stick to which is tied a piece of string. The birds being attracted to food placed underneath the stone, pull the string, and the stone falls on them. 3. A number of sticks are driven into the ground, and nooses fastened to them; dhurra is then scattered about, and as the birds scratch the ground they get their legs caught. String traps are arranged at the doors of the fowl huts to catch the wild cats when they try to steal the poultry. At night boys are very fond of catching rats by firelight ; they lie flat on the floor, very still, holding a round pan with dhurra in it, the rats come to eat, and as soon as near enough an inverted jar is quickly put over them. Fishing. — The Madis adopt various methods of fishing. Sometimes they dive into the water and while swimming under- neath stick the fish with an iron hook ; a line is fastened to this, the one end of which is wound round the fisher’s hand, with which of Edinhiirgli, Session 1883-84. 347 lie also holds the wooden handle. The hook looses from the handle and remains in the fish, the man then swims to land and hauls it in. Sometimes they fish at night by firelight, shooting the fish with iron-headed arrows. Nets are also used. They are drawn across a river and held at both ends. Men go up stream, and then swim down with a splashing stroke driving the fish to the net. In this way large numbers are caught, and a general distribution of the spoil takes place. These are the methods employed in catching very large fish. A smaller kind of fish is caught by the women in shallow water. They use a poisonous fruit, about the size of a gooseberry. This fruit they grind into a coarse powder, and carry to the Svater in baskets. They then scatter it oh the surface, and the fish eat it, and soon die. They are afterwards collected in baskets, and as the poison is not injurious to men, they are good for food. Children also fish by shooting with bow and arrow, and swimming after the fish they hit; many lives are lost through boys venturing into rapid rivers. Sometimes in small rivers, instead of a net, a wickerwork barrier is constructed across the stream; another movable one is then introduced up stream, and gradually carried down until a short distance from the first barrier ; the fish thus brought together are then caught by hand, and thrown on to the bank. A fish trap is also made of wooden latticework, several feet across at one end and narrow at the other ; this is placed beneath waterfalls or below rapids. Sometimes nets like our landing nets are held under waterfalls, to catch the fish as they come down. Wooden dams are also erected across rivers. Poles are fixed in the ground and cross beams fastened to them, holes being left of such a size that the fish in trying to get through stick fast and are collected each morning. These dams are left until the river gets swollen by the rains, and washes them away. Pish are cured by being dried by the fire or in the sun, and keep good for considerable time. Manufactures — Woodworh. — Numerous articles are manufac- tured from wood. Ladles, stools, handles for agricultural imple- ments, bows, arrows, and walking-sticks. Nails are not used, bu the articles are either cut out of blocks of wood, or tied together with string, leather thongs, or iron wire. The instruments em- 348 Proceedings of the Pooycd Society ployed are — knife, axe, and a kind of plane. Fire is also used to hollow out wood and to harden it. Smelting. — A hut or shed is set apart for carrying on smelting operations, several men working in the same hut. A number of fires are kept going, and the bellows are used as follows: — A large earthenware howl with a hole at the side near the bottom is placed near the fire, and a clay pipe is constructed from this hole to the fire. The top of the bowl is covered with a soft skin, in the middle of which a hollow stick is fastened. This stick being moved up and down, and the top being closed by a finger when moving down, causes the draught. The anvils and hammers used are of iron, the hammer being flat in shape. They are thus a little in advance of the surrounding tribes, who only use stone. Some few stone anvils and hammers are, however, still in use in the Madi tribe. Very good knives, hoes, and bracelets are constructed, as well as arrow-heads. The smelting furnaces are conical in form, and about 5 feet high, layers of iron ore and charcoal being placed alternately. Six pairs of bellows are often used, each man working two, one with each hand. There is not very much beer drinking during the smelting, but a good deal of singing, the men working in time to the song. Eelays of men work at this tedious operation. Baslcet WorTc. — The manufacture of baskets is carried on largely. Various shapes and sizes are constructed of open wickerwork ; they are made by men much after our own manner. Baskets of dhurra stalks are woven by women in the following way : — The pulp is removed, the stalks opened out flat and cut into the requisite lengths. The bottom of the basket is first made, and the sides worked up from it, being woven very close. Some kinds of baskets are so closely made that they will hold milk, and small ones are made to serve as cups on a journey, as they are lighter than earthenware, and less fragile than gourds. The shapes vary, being round, square, or otherwise, and of different colours, according to the kind of dhurra stalk used. Sometimes the various colours are blended. Women also make baskets of young doleb palm leaves. Pots are covered by a loose wickerwork for carrying. Spring baskets are made by men. They are chiefly used for ornamental purposes, and not of much practical use. 349 of Edinhurghj Session 1883-84. Pottery. — The manufacture of pottery is carried on by the women. A grey clay having been freed from stones is mixed with water to the consistency of dough ; much care is taken that there should be no lumps in it, and that it should not be too wet or too dry. This dough is left in a hut for a day, being placed on and covered by leaves. The women then commence to make the jars, forming the bottom first on a wooden tray, working the sides up wuth their hands and moulding it into shape. No wheel is used. The vessels made vary very much in size and shape. Some are round and open like our basins, some have narrow necks widening out again at the top. When formed they are ornamented by lines made horizontally and at right angles below the top rim, which is often made to curve over. This marking is done with a sharp bit of stone such as is used for cupping, or with a sharp pointed stick. The jars are then painted black, or black with a red neck. They are left in a hut for a day or two to dry, then put in the sun for a day or two more, and lastly they are fired. Quite a trade is carried on by the makers of pottery, who keep a store of their goods for sale. Some very large sized jars are made for holding semsem ; these are made by men, and in forming them a grass mould is used. Painting. — The Madis decorate their bodies with paint for dances, washing it off again when the festivities are over. Red, blue, white, and black paints are used. The red is oxide of iron, the black is made from charcoal. The paint is applied with the finger in stripes about half an inch broad on the face, arms, shoulders, and chest. Women paint their faces, chest, and upper part of their arms, and some confine the paint to one part of the body only. The designs vary with taste. No application is made to the eyes. They do not stain their nails. String. — String is made from the fibrous bark of five or six different trees. This substance is first dried in the sun for a day or two, then wetted, and buried for two or three weeks, at the end of which time it is taken out and heaped up under a tree. Here the men work, beating the fibrous pulp with a piece of wood on the smooth trunk of a tree which lies on the ground. They then work the fibres into string by rubbing them into a twist with their hands on their thighs. To make cord, they fasten two pieces of string to their toes, and 350 Proceedings of the Tfoycd Society twist them together with their hands, repeating the process until the cord is of the required thickness and leugth. In making rope a cord is tied between two trees, and others wound round it in a spiral manner. String is made of various other substances — of the hairs from the cow’s tail, of animal skins cut into stripes and twisted (these are very strong, and are used for trapping buffaloes); also from the tendons of cattle and wild animals ; this kind is made very fine, two men being needed to work it. It is used for how strings. String is also made from doleh palm leaves. Fishing nets are made with fibre strings, which is tied into knots by the hand, forming diamond-shaped meshes like our own netting. No dye is used in making string, hut it is sometimes of a red colour, because made with red fibres. No wax is used in this manufacture, hut the string is sometimes rubbed with grease. A lump of fat is taken in the hand, and the string drawn rapidly through it. This is also done to the how strings and nets, hut not to the large ropes. As a rule, men make the ropes, and nets, and how strings; hut women make fine twine, and small nets for holding gourds, and for forming hags on which to hang up fruit, &c., to dry in the sun, or from the rafters of the huts. Money.' — A regular system of exchange is carried on in arrows, heads, head necklaces, teeth necklaces, brass rings for the neck and arm, and bundles of small pieces of iron in flat, round, or oval discs. All these different articles are given in exchange for cattle, corn, salt, arrows, &c. The nearest approach to money, in one sense, is seen in the flat round pieces of iron, which are of different sizes from J to 2 feet in diameter, and f inch thick. They are much employed in exchange. This is the form in which they are kept and used as money, hut they are intended to he divided into two, heated and made into hoes. They are also fashioned into other implements, such as knives, arrow heads, &c., and into little hells to haug round the waist for ornament, or round wandering cows’ necks. Ready-made hoes are not often used in barter ; iron as above mentioned is preferred, and is taken to a blacksmith to finish according to the owner’s requirements. of Edinburgh, Session 1883-84. 351 Any tools may be obtained ready made from a smith, and may be used in barter when new. Compensation for killing a woman or for any serious crime must be paid in cattle. JSTo cowries are used as coin in this district. No drawing or writing is known, but certain marks are used to distinguish between arrows, pots, and the like. Measures. — A year is made up of twelve months or divisions, but the number of days in each division is said to vary — I could not make out how or why. A day is from sunrise to sunset. The year begins about the first month of harvest, when the grain is quite dry. Distance is reckoned by time. If you ask the distance to a place not very far away, they will often point to the sky and say — “ When the sun is at that spot you may be there.” No measure of weight, quantity, or length is used. The number of cows given to a son, or the number of things lent or borrowed, is remembered by means of small lengths of grass, bundles of which are kept in a basket on the wall of the hut. Dried beans are sometimes used for the purpose. The Madis count by tens ; hundreds are known, but not thousands. Sticks are sometimes notched to remember numbers. Astronomy, — The twilight in this district is very short. The Madis divide the day into three parts — morning from about 5.30 to 10 a.m.; mid-day 10 to 3 p.m.; and afternoon from 3 to 6.30 p.m. So that, roughly speaking, sunrise and sunset begin and end the day. The names for sunrise and sunset are kadro-ersa, kadro-lobo. There are names too for several of the stars (calu). The Pleiades, Minge Minge. The larger star by which they tell the time, Torn. The milky way, Guguree (road). Their study of the stars does not seem to go further than giving names to some of them. The winds are called Bluku. East, Duwerie ; West, Huwerie. Night, Endo ; Morning, Demindo. 352 Proceedings of the Royal Society Shoet Vocabulary of Madi Words. Antelope . . Kula. Arm . . Kallah. Arrow . Etu. Bedstead . . Surah. Beads . Biallah. Bow . . Keiuyah. Boy . . Uiskorah. Brother . . Undii. Brook . Eanga. Buffalo . Kohi. Cat (wild^. . Yow. Child . Wistissi. Chin . Sisi. Cow . . Isah. Chief . Wisyerra. Crocodile . . Tamorah. Dog . . Wihi. Drum (large) . Dattei. „ (small) . Kurai. Ear . . Mhilli. Earth . Kang-u. Elephant . . Kidi. Eye . . Komang. Father . Dada. Face . . Komomah. Fire . . Wado. Fish . . Censa. Fish-hook . Mongo. Finger . Denjerida. Flute . Traiilei. Foot . . Mindima. Forest . Wevu. Fowls . Yaru. Giraffe . Kerri. Girl . . Uiyo. Goat . ^ Wanya. Grass . Lomah. Head . Do. Harp . Taumu. Hair . . lavu. House . Loko. Iron . . Kor-hi. King . Yerra. Knife . Evu. Lake . Ulu. Leg . . Ndi. Lion . . Ubiu. Man . . Kurah. Moon . Niahoa. Mother . Ma. Mouth . Haw. Mouse . Lusie. Mountain . . Doku. Morning . . Deniindo. Night . Endo. Nose . Kano. Ox . . Dangmo. Pipe . . Tuku-taha Rain . . Mire. River . Rodi. Rope . Kordi. Serpent . Wiri. Sister . Emi. Sun . . Kadroa. Star . . Calu. Sleep . Kemelli Tongue . Ndenda Water . Weni. Woman . . Mbara. Bad . . Eineddi. Big . . . Kiedra. Black . Korndu. Blue . . Muri. Good . Eniettakin Green . Yowi. Heavy . E-ebtu. Little . Tissi. No . . Lah. Red . . Ei-hi. White . . Einyi. Yes . . Wah. 1 . Korlo. 2 . Irio. 3 . Utah. 4 . Suwor. 5 . Mwi. 6 . . Dakka. 7 . Demrio. 8 . . Dumtac 9 . . Dumsor. 10 . . Dumte. 11 . . Dumte Korlo. 12 . „ Irio. 13 . „ Utah. 14 . „ Suwar. 15 . . „ Mwi. 16 . „ Dakka. 17 . „ Demrio. 20 . . Bute-Irio. 30 . . Bute-Otah. I consider that these notes would he far from complete were I to omit some mention of the Madi language. I have, therefore, given above an extract from the vocabulary I collected The language is of Edinburgh, Session 1883-84, 353 rich and melodious, and apparently lends itself well to oratory and song. It belongs to the Negro group of languages, for the Madis are pure negroes. Note. — I liad at first intended to illustrate this paper with drawings from objects in my collection, which are interesting as being the only ones that have yet found their way into Europe, Finding, however, that somewhat similar articles may be found depicted in Geschichte der Waffen, Band iii. , Berlin und Leipzig, 1877, and in Schweinfurth’s Aries Afi'icance^ Sampson Low, 1875, this has been deemed unnecessary. 4. On the Crinoidea of the North Atlantic between Gibraltar and the Faeroe Islands. By P. Herbert Carpenter, D.Sc. (Camb.), Assistant Master at Eton College. With some Notes on the Myzostomida, by Prof. L. von Graff, Ph.D. Communicated by Mr John Murray. Introduction. This communication falls conveniently into two sections — I. dealing with the specimens obtained by H.M.SS. “Lightning” and “ Porcupine,” during what may be called the pre-Challenger period of deep-sea exploration ; II. concerning those dredged by the “ Knight Errant ” and “ Triton ” during the surveys of the Wyville Thomson ridge, which were conducted in the years 1880-82. All the species wiU be properly described and illustrated in the “Challenger” Eeports ; but many reasons seem to render it desirable that some of them, and more especially the Comatulce^ should be briefly noticed before the larger report can be published. My friend Professor L. von Graff has kindly sent me a short account of the Myzostomida, from which it will appear that four species of these parasites have been added to the two already known in the British seas. I. The Crinoids obtained by H.M.SS. Lightning and Porcupinef 1868-70. The detailed zoological results of the preliminary dredging expe- ditions of the “Lightning” and the “Porcupine,” in the years 1868-70, have been so completely cast into the shade by the mag- 354 Proceedings of the Royal Sccicty nificent collections of tlie “ Challenger,” that little is known about many of the deep-sea animals obtained by these expeditions beyond the first references to them in the reports of Sir Wyville Thomson, Dr Carpenter, and Dr Gwyn Jeffreys, in the Proceedings of the Royal Society. The Annelids, Corals, Echinids, and Mollusca soon found their way into able hands, and have been fully described in the publica- tions of various learned societies. But as regards most of the other groups no detailed results have ever been published. This want of systematic information about our earlier expeditions is not to be wondered at, when it is remembered that the “ Challenger ” sailed but little more than two years after the return of the ‘‘ Porcupine ” from the Mediterranean, and that Sir Wyville Thomson, in whose hands the collections mostly remained, was in bad health, with his time much occupied by his professional duties and by the prepara- tions for his four years’ absence. When he returned the “ Porcu- pine” collections were entirely dwarfed by those of the “Challenger;” and it is only now that they have been examined by Mr Murray that specimens dredged nearly fifteen years ago are coming into the hands of specialists, who are working them up together with the “ Challenger ” material, and wdth that of the “ Knight Errant ” (1880) and “Triton” (1882). Nearly the same thing has taken place on the other side of the Atlantic, little being yet known about many of the types obtained by the U.S. ships “Corwin,” “Bibb,” and “Hassler” (1868, 1869, 1872); and they are now being described by those specialists, in whose hands have been placed the larger collections of the “ Blake ” (1877-80), second only in importance to those of the “Challenger.” Before sailing in the “ Challenger,” Sir Wyville Thomson read before the Society a paper* entitled “On the Crinoids of the ‘ Porcupine ’ Deep-Sea Dredging Expedition.” It was, however, by no means complete, as regards either the list of species obtained or their geographical distribution ; and in the following pages I propose to partially make good this deficiency. When our knowledge of the Crinoids fifteen years ago is taken into consideration, the material obtained by the “Porcupine” must be regarded as com- * Proc. Roy. Soc. Edin., vol. vii, pp, 764-773. A large portion of tins paper was also printed in The Depths of the Sea, pp. 434-454. of Edmhurgk, Session 1883-84. 355 jDaratively rich. For it includes four stalked Crinoids, three of which were new to European seas and also new to science, while one represents a new generic type altogether ; and among the seven Comatula species were three or possibly four new forms, one repre- senting a genus which, up till very lately, has scarcely been known to occur outside the limits of the tropics. Sir Wyville Thomson’s list embraces only seven species of Crinoids altogether ; whereas eleven different types were really obtained, seven being Comatulcp, and four stalked Crinoids, the latter including three additions to the four species then known. These facts seem to me of sufficient interest to merit being treated separately, so that they may not be lost sight of in the general account of the Crinoids which will appear in the “ Challenger ” Keport. Family Pbntacrinid.Eo Genus PentacriniLS, Miller. Cainocrimis, Forbes. Picteticrmus, de Loriol. 1. Pentacrinus wyville-tliomson% Jeffreys. H.M.S. “Porcupine,” 1870. Station 17. Lat. 39° 42' N,, long. 9° 43' W. 1095 fathoms, Temp. 39°'7 F, Ooze. “About twenty specimens.” Remarks. — This fine species was v/orthily dedicated to Sir Wyville Thomson, in the Report of Drs Carpenter and Gwyn Jeffreys] but no further description of it was published until the appearance in 1872 of The Depths of the Sea. This contains a good figure, with a description by Sir Wyville, which is identical with that given in his paper on the “ Porcupine ” Crinoids. A series of five beautifully executed plates, illustrating the anatomical characters of the skeleton, which were drawn by Mr Hollick for Dr Carpenter, will appear in the “ Challenger ” Report. P. iDyville-thomsoni has a closed ring of basals, and would there- fore belong to Forbes’ genus Gainocrinus, which has recently been revived by de Loriol.* I have elsewhere given my reasons for regarding Gainocrinus as indistinguishable from Pentacrinus. f * Monographic des Crinoidcs fossiles de la Suisse, p. 111. t Journ. Linn. Soc. Zool., vol. xv. p. 210 ; and Bull. Mus. Comp. Zool., vol. X. Fo. 4, p. 168. 356 Proceedings of the Royal Society Family Bourgubticrinid^, de Loriol. Genus Rhizocrinus, M. Sars, 1868. Bourgueticrinus^ Pourt., 1868. Democrinus, Perrier, 1883. 2. Rhizocrinus lofotensis, M. Sars, 1868. Bourgueticriniis hotessier% Pourt. 1868. Rhizocrinus lofotensis, Wyv. Thomson, 1872 (pars). H.M.S. “Lightning,” 1868. Station 12. Lat. 59° 36' N., long. 7° 20' W. 530 fathoms. Temp. 47°’3F. Globigerina ooze. Three small specimens without arms. Station 16. Lat. 61° 2' hi ; long. 12° 4' W. 650 fathoms Globigerina ooze. Two small specimens without arms. “ Once or twice we found a fragment of the stem of Rhizocrinus in the cold area.” * Remarks. — So far as my information goes, this widely distributed species was never dredged by the “ Porcupine,” not even on the the “ LToZi^ewm-ground ” in 1869. But according to Sir Wyville,t “ several occurred attached to the beards of the Holteiiioe off the Butt of the Lews.” This would be at Stations 47 and 90, both of them close to hsTo. xii. of the “Lightning” cruise, which was the original LToZ^e^m-ground, and was described by Sir Wyville as being in the Faeroe channel. There is, however, no mention of Rhizo- crinus in the accounts of the dredgings at these stations, either in The Depths of the Sea, or in the Koyal Society Keport ; and I suspect therefore that Sir WyviUe was speaking from memory only, and confounded the dredgings of the two years. At any rate, if the “ Porcupine ” did obtain specimens on the HoUenia-gco\mdi in 1869, they have since disappeared. Sir Wyville mentioned individuals of considerable size as having been dredged by the “ Porcupine ” in 862 fathoms off Cape Clear. They really belong, however, to the species which three years later was met with off Barbadoes by the “ Hassler,” and was subsequently described by Mr Pourtales under the following name : — The Depths of the Sea, p. 124. t Ibid., p. 450. 357 of Ediiiburgh, Session 1883-84. 3. Rliizocrinus rawsoni, Pourt., 1872. Rhizocrinus lofotensis, Wyv. Thomson, 1872 (pars). Rhizocrinus raivsoni, P. H. Carpenter, 1882. Democrinus Parfaiti, Perrier, 1883. H.M.S. “Porcupine,” 1869. Station 42. Lat. 49° 12' N., long. 12° 52' W. 862 fathoms. Temp. 39°’7 F. Ooze with sand and shells. Two armless specimens. Station 43. Lat. 50° 1' N., long. 12° 26' W. 1207 fathoms. Temp. 37° '7 F. Globigerina ooze. Two young specimens, one without arms. RemarlhS. — These four specimens, as already indicated, were really the first discovered examples of R. rawsoni ; but they differ from R. lofotensis far less than the Caribbean individuals do."" [Those from Station 42 were noticed by Sir Wyville at the time they were obtained, and described as unusually large examples of R. lofotensis. But I am not aware that he ever made a closer examination of tbem. After reading Pourtales’ descrij^tion of the Caribbean R. rawsoni., I came to the conclusion that tlie “ Porcupine ” specimens should really be referred to this type ; and this view was confirmed when the originals of Pourtales’ description were sent to me last year (1882), as I have pointed out in my “ Blake” report. The two young individuals from Station 43 seem to have been altogether overlooked ; for they are not mentioned either in the Eoyal Society’s Beport, The Depths of the Sea, or the paper on “Porcupine” Crinoids. They did not come into my hands until August last, having been discovered by Mr Murray among Sir Wyville’s collections at the University. They are the youngest specimens of this type which I have seen. Each has 28 joints in the stem, from the calyx to the root ; but its length, which is only 20 mm. in the smaller, is 2 4 ‘5 mm. in the larger individual. The majority of the joints are cylindrical and elongated, only a very few at the base of the stem showing the characteristic dice-box shape with expanded ends. The length of the calyx is almost the same in both specimens, 1 *8 mm. ; though its diameter across the * “The Stalked Crinoids of the Caribbean Sea,” Bull. Mus. Comp. Zool., vol. X. No. 4, pp. 174, 175. 2 A VOL. XII. 358 Froceedings of the Royal Society radials is greater in that which has the longer stem. It is mainly composed of the hasals, which are 1-2 mm. in height, and form a nearly cylindrical tube, at the top of which are the short radials, having a more decided upward and outward slope. This causes the calyx to appear slightly constricted at the level of the basiradial suture, a feature which is very marked in some varieties of the adult form. As compared with equal sized specimens of R. lofotensis, these young individuals of R. raivsoni are distinguished by the relatively great height of the calyx in proportion to its width, the length of the basals, and the expansion of the calyx at the basiradial suture. The basals of R. lofotensis (uppermost stem -joint, Sars.) have a smaller share in the formation of the cup, and it expands uniformly upwards from the stem to the upper margin of the radials. It is noteworthy that even these two young individuals from the same locality present differences in the shape of the calyx such as are more distinct in adult sj)ecimens from different localities in the East and West Atlantic. Perrier’s genus Bemocrinus^ is founded upon a variety of unusual size, with a great disproportion in the heights of basals and radials, and a somewhat strongly marked circular furrow at the level of the highest points of the basals, so that it crosses the middle of the radials. Genus Bcdhycrinus, Wy. Th., 1872. IlycrinuSy Danielssen & Koren, 1877. 4. Bail lycr inns gmciUs, Wy. Th., 1872. H.M.S “Porcupine,” 1869. Station 37. Lat. 47° 38' N., long. 12° 8' W. 2435 fathoms. Temp. 36° *5 F. Globigerina ooze. One nearly complete specimen, and one stem with the basal ring attached, but wanting the rest of the calyx. Remarks. — A figure of this species was given by Sir Wyville Thomson on page 453 of The Depths of the Sea, together with the same description which he published in his paper on the * Sur un nouveau Crino'ide fixe, le Democrinus Tarfaiti, provenant des dragages du “ Travailleur, ” Comptes Rendus, Tome xcvi. No. 7, pp. 450, 451. See also “ Note on Democrinus Parfadi," Ann. & Mag. Nat. Hist., May 1883, p. 335. I am indebted to Professor Perrier’s kindness for a drawing of this interesting type. 359 of Edinlurgh, Session 1883-84. “ Porcupine ” Crinoids. This, however, is not quite accurate, for there is no mention of any calyx-plates below the radials, the lower portion of the head being said to consist “ of a gradually expanding funnel-shaped piece, which, seems to be composed of coalesced upper stem-joints.” Subsequently, however. Sir Wyville found that in B. aldricliianus, from the Southern Sea, there is “ a series of basals which are soldered together into a small ring, scarcely to be distin- guished from the upper stem-joint.”* The existence of basals in Ilijcrinus {Bathycrinus) carpenteri was also recognised by Daniels- sen & Keren, f who were fortunately able to see the interbasal sutures in young individuals, though they entirely disappear in the adult j and there is a similar basal ring in B. gracilis, intervening between the radials and the numerous thin joints at the top of the stem. The two outer radials and the two lowest brachials of B. gracilis, and also of B. aldrichianus, were described by Sir Wyville as re- spectively united by syzygy, while Danielssen and Koren made the same statement respecting B. carpenteri. In all these cases, how- ever, the supposed syzygy is really a modification of the ordinary bifascial articulation permitting lateral movement only, which is so common in the Gomahdm, and is also characteristic of four species of Pentacrinus ; for a third and smaller bundle of fibres is inserted into a deep pit at the lower or dorsal end of the vertical articular ridge on each joint-face. Externally, this form of articulation looks very much like a syzygy, as the joints are brought into closer con- nection than when they are united by a pair of muscular bundles. But a glance at their terminal faces is sufficient to show that the plainness of Pentacrinus or Rhizocrinus, or the striation of the Comatula-^jzjfiQS, is altogether absent, and that they are marked by distinct ridges and fossae. According to Sir Wyville’s description, there are none of these so-called “ syzygies ” in the arms of B. gracilis beyond that between the first two joints ; while in B. aldrichianus there is a syzygy between the fourth and fifth brachials, and at irregular intervals beyond them ; but the “ alternate syzygies in the arms, which form * “Notice of new living Crinoids belonging to the Apiocrinidee,” Journ. Linn. Soc. Zool., vol. xiii. p. 50. \ Nyt. Mag. for Naturvidskaherne, Bind. 23, p. 4. 360 . Proceedings of the Boy (d Societij so remarkable a character in Rldzocrtnus, are absent.” I find, how- ever, that in both species the grouping of the arm-joints is exactly the same as was observed in B. carpenteri by Danielssen and Keren, if the term “ trifascial articulation ” be substituted for “ syzygy ” in their descriptions. In the nine lowest brachials there are alterna- tions of a pair of joints united trifascially, and a single joint with muscular attachments at each end ; while beyond the ninth brachial the two forms of articulation alternate with great regularity. The presence of this trifascial articulation, and its peculiar distribution may therefore be considered as characteristic of Batliycrinus ; and the “alternate syzygies” in the arms, which are supposed to be absent in this genus, are really present in a modified form. Keither do the arms “resemble in character the pinnules of RMzoerinusf or “show no trace of pinnules” in B. gracilis. Tor one or two of them have little stumps on their terminal joints, which give them the appearance of bifurcation, just as at the growing points of the arms of young Comcdnlidae. and Pentacrinidse ; and I see no reason to doubt that these stumps are the commencing pinnules. : Family Comatulid^e. Genus Antedon.^ Frem. 5. Antedon rosacea, Linck. sp. “ Frequent in water of moderate depth,” * One individual which seems to belong to this species, though certainly representing a rather strongly marked variety, was obtained somewhere in, the Korth Atlantic, but the exact record of its locality has unfortu- nately been lost. Among the numbers of Ant. phalanglum of various ages which were dredged in 1870, at 30 to 120 fathoms, on the Skerki Bank, and at 50 to 120 fathoms, in the Bay of Benzert, on the Tunis coast, were five young specimens certainly not belonging to this type, and probably, therefore, to be referred to the Mediterranean variety of Ant. rosacea. It is impossible to state now the exact depth from which they were collected, but it was probably not below 50 fathoms, as Ant. rosacea has not yet been found in the * Proc. Ptoj. Soc. Eclin., vol. vii. p. 765. of Edinhurgli, Session 1883-84. 361 Mediterranean at a greater depth than 37 fathoms. I am still in doubt whether some of tlie very varied forms usually re- ferred to this type should not be distinguished by the name Ant. milleri, as was done by Muller, and more especially by Sir Wyville Thomson. But I would postpone giving a decided opinion until I have been able to add considerably to my already large series of specimens from widely-separated localities. 6. Antedon pUalangium, Mull. sp. Comatida iDOodwardii, Barrett. Coinatula celtica, Barrett. Antedon celticMs, Wyv. Th. &c. N’on Anted, on celtica of von Marenzeller, and Sladen. H.M.S. “Lightning,” 1868. Station 13. Lat. 59° 5' K, long. 7° 29' W. 189 fathoms. Warm area. H.M.S. “ Porcujhne,” 1869. The Minch, 60 to 80 fathoms. Several specimens. Off Loch Scavaig, Skye. 1870. Station 13. Lat. 40° 16' K, long. 9° 37' W. 220 fathoms. Temp. 52° F. Several specimens. Off Cape Sagres, 45 fathoms. Several specimens. Off Carthagena, 80 fathoms. Several specimens. Bay of Benzert, 50 to 100 fathoms. Abundant. Skerki Bank, 30 to 120 fathoms. Abundant. Remarlcs. — It has been noted elsewhere * that Barrett’s Ant. celtica from Skye is really identical with the Ant. gAialangium of Muller, which was considered until lately as one of the rarities of the Mediterranean, for it inhabits somewhat deeper water than Ant. rosacea. Sir Wyville Thomson noted it as occurring “ in local patches to 150 fathoms off the north coast of Scotland but I have no record of it besides Stat. xiii. of the “Lightning” expedition, and neither the “ Knight Errant ” nor the “ Triton ” ever met with it. The occurrence of this species off' the Spanish and Portuguese coasts is of some interest ; for it had not previously been recorded between the Mediterranean and the Minch. Curiously enough, it seems (until this year) never to have been obtained in any of the ■" “ Note on tlie European ComatulccA ^ool. Anzeiger, Jalirg. \v. p. 520. 362 Proceedings of the Eoycd Society numerous dredgings, both public and private, off the French and British coasts between the parallels of 40° and 57°. One would certainly have expected its appearance during the first cruise of the “ Porcupine ” in the neighbourhood of the 100-fathom line on the west of Ireland ; but no traces of it were met with. It was very abundant off the Tunis coast, both on tlie Skerki Bank and in the Bay of Benzert, specimens of all ages coming up on the tangles in great numbers, though unfortunately in a very much mutilated condition. These were noticed by Sir Wyville Thomson in the following passage : * — Many examples of the form known to Continental naturalists under the name of A. mediterraneus, Lam. sp., were dredged in the Mediterranean off the coast of Africa. I do not feel satisfied that this is identical with Antedon rosaceus of the coast of Britain, though the two specific names are usually regarded as synonyms. There is a great difference between them in habit, a difference which it is difficult to define.” It is curious that the extreme length of the dorsal cirri of these individuals did not lead Sir Wyville to identify them with Ant. ylicdangiwn {celtica^ Barrett), of which this is one of the special marks, as he himself points out. But I am strongly inclined to believe that he is right in differentiating the common Mediterranean type from the British Ant. rosacea. As pointed out above, however, the ‘‘Porcupine” only got a very few young specimens of it on the African coast. It is singular that while no parasitic M yzostoma occurred among the numbers of Ant. phala7igium dredged on the Tunis coast, some of the individuals obtained in the Minch in 1869, and at Station 13 in 1870 (off Mondego) proved to be the hosts of a new species, AI. cdatum, which is briefly described by Professor von Graff further on. A single example of another new species, M. pidvinar, was also found attached to the peristome of one of the Minch specimens of Ant. phalangium, which does not appear to serve as host to the same species of M yzostoma as occur on Ant. rosacea. 7. Antedon dentata, Say, sp. Antedon Sarsii.^ auct. H.M.S. “Porcupine,” 1869. Station 51. Lat. 60° 6' K long., 8* 14' W. 440 fathoms. Temp. 42° F. One specimen. * Pi'oc, Roy, Soc. Edin,, vol, vii. p. 765. 363 of Edinburgh, Session 1883-84. Station 54. Lat. 59° 56' K, long. 6° 27' W. 363 fathoms. Temp. 31° *4 F. One specimen. Station 55. Lat. 60“ 4' N., long. 6° 19' W. 605 fathoms. Temp. 29° -8 F. Two specimens. Station 74. Lat. 60° 39' K, long. 3° 9' W. 203 fathoms. Temp. 47° '6 F. Three specimens. 1870. Station 17 a. Lat. 39° 39' N., long. 9°39' W. 740 fathoms. Tem23. 49° ’3 F. One specimen. Remarks. — This species occurs in profusion at moderate depths off the ISTew England coast, over 10,000 individuals having been ob- tained by the “ Fish Hawk ” at a single haul. It is also abundant at moderate depths off ^s^’ew Jersey, near the locality (Great Egg Harbour, l^.J.) whence Say’s original specimens were obtained ; and it agrees so well with his description of A7it. dentata, that the identity of the two can hardly be doubted.* The adoption of his specific name thus becomes inevitable, however undesirable this may seem to European naturalists, who have been so long accus- tomed to associate the type with the name of a deservedly honoured Norwegian zoologist. Sir Wyville Thomson gave no definite list of stations for this species, though he mentioned the occurrence of more or less com- plete specimens or fragments in nearly every one of the deep hauls of the dredge from the Eaeroe Islands to Gibraltar. So far as I am aware, its southernmost liuiit in the East Atlantic, and also its lowest bathymetrical range are at present united in Station Via of the “Porcupine,” 1870; 740 fathoms. It was obtained at 605 fathoms in the “cold area” in the previous year; but the U.S. Fish Commission have not dredged it below 238 fathoms off the New England coast. Sir Wyville Thomson stated that one or two small examples of the pentacrinoid were procured in the Eaeroe channel. Only one, however, has come into my hands. It is a trifle more advanced than that represented by Sars in figs. 9 and 11 on Tab. Y. of his classical Memolres. The arms are longer, with the first pinnule on about the twelfth joint. There is, however, but one cirrus, which seems to be the only one as yet developed, though it is of considerable size, reaching up to the level of the radial axillaries. * See Verrill, Am. Journ. Set., vol. xxiii. p. 222. 364 Froceedings of the Boycd Society The stem is attached by a slight calcareous expansion at about its 35th joint to one of the rays of a Rhabdammina ahyssorum ; and it then passes on to form two other spreading attachments, with radicular branches sprouting from them on what appears to be a portion of a tubular hydroid. 8. Antedon eschriehti, Mull. sp. H.M.S. ‘Torcupine,” 1869. Station 57. Lat. 60° 14' K, long. 6° 17' W. 632 fathoms. Temp. 30°-5 F. Sir Wyville Thomson stated that considerable numbers of this species were obtained in many of the cold area hauls; and he noted their small size as compared with more northern specimens. JN’o. 57, however, is the only station of which any record has been preserved; and it is interesting as being by far the greatest depth at which this species has yet been met with. Its usual parasite Alyzostoma gigas^ Liitken, MS., was also obtained at this station. Two pentacrinoids besides that of Ant. dentcda were dredged in the cold area ; but I do not think that either of them can be the one referred to by Sir Wyville Thomson in the following- passage : — “A single example of a pentacrinoid in an early stage was found associated with Ajit. escludchtii. It resembled closely the larva of Ant. sarsii but the specimen was not sufficiently perfect for a critical examination.’' Neither of the larvae which I am about to describe is at all like that of Ant. dentata, and I fear, therefore, that the one mentioned by Sir Wyville Thomson has somehow been mislaid. ' No. 1. In this larva there is no trace of cirri, the anal plate separates two of the radials, and the arms are just beginning to sprout from the radial axillaries. There are five discoidal joints at the top of the broken stem, which is much more robust than that of the corresponding stage of Ant. rosacea ; while the head, which exceeds 1 mm. in length, is nearly twice as big as that of the rosacea larva. The orals which rest directly on the radials recall those of Hyocrinus, having a deep median groove, only more marked than in that type, with the lateral edges folded over somewhat strongly. This interesting larva may perhaps belong to Ant. 'phalangium, but I rather doubt such being the case. For that species is almost the nearest ally of Ant. rosacea ; and from what I of Edinhurgh, Session 1883-84. 365 have seen of the condition of the youngest unattached individuals, I should judge that the larva was not very different from that of Ant. rosacea, I think it much more probable, judging from the robust nature of this larva, that it belongs either to one of the Arctic species, Ant. eschrichti, or Ant. qiiadrata, sp. n., or to Ant. liystrix^ sp. n., which is as yet only known from the cold area. It is very likely only a younger stage of the larva next to be described. No. 2. The stem, which is broken some 20 mm. from the calyx, forms an attachment to a hydroid tube at about its 30th joint, and is continued downwards half a dozen joints further. There are five discoid al joints below the rudimentary centrodorsal, which bears the sockets of five short cirri. Only one of them remains, how- ever, reaching up to the top of the basals, which make up about half the height of the cup. The second radials and axillaries are well developed, as are also the arms, which are unfortunately broken at about the tenth joint. But even under these circnmstances the head has a length of 4 mm. A slightly bifid plate, having a some- what worn appearance, stands up in one of the interradii of the disc. It may be one of the orals, or as I am more inclined to think, the anal plate ; for I cannot make out anything correspond- ing to it in the other interradii, which are, however, but imperfectly visible. A striking feature of this very robust larva, and one in which it resembles Ant. dentata rather than Ant. rosacea.^ is the large development of the arms before the appearance of the cirri. The radials and brachials are much larger than those of a recently detached individual of Ant. rosacea. This is also the case in a “ Challenger ” pentacrinoid from Ascension, which has a robust appearance like the one under consideration. The latter must certainly belong to one of the three Antedon species already men- tioned as occurring in the cold area, though further identification is impossible. 9. Antedon liystrix, P. H. Carpenter, 1883. Formula,* A . 10 . ^ ‘ Centrodorsal hemispherical, and thickly covered with numerous * For an explanation of the signs used in these formulae, see F. J, Bell, Proc. Zool. Soc., 1882, pp, 530-535; and P. H. Carpenter, ibid., pp, 731-747. 366 Proceedings of the Royal Society long-jointed cirri, which vary considerably in appearance. One of the largest reaches 36 mm., and consists of forty smooth joints, of which all hut the basal and terminal ones are longer than broad, the fifth to the tenth being especially so. The cirri attached round the upper edge of the centrodorsal are all of this smooth type, and may be observed in every stage of growth. But those attached nearer the dorsal pole are somewhat different in appearance. They are more slender, and their component joints are relatively shorter than in the other type ; while the joints have slightly expanded distal ends, so as to overlap their successors. This is especially marked on the dorsal side, which is produced into a sharp forward project- ing spine. I have reason to believe that these characters gradually disappear as the joints increase in age, and that the mature cirri of the two types are not very different in appearance, especially about what might be called the equator of the centrodorsal. But the smooth young cirri all round its edge are totally different from the spiny ones nearer the dorsal pole. Traces of the first radials may be seen at the angles of the calyx ; but there is no constancy about their appearance even in individual specimens. The second radials are short, even at the sides, and are often not visible at all in the middle line of the ray, owing to their being very deeply incised to receive the strong backward projections of the axillaries. These are quadrate in form, with their sides curved, especially the anterior pair ; and they are distinctly longer than wide, sometimes almost seeming to overlap the centrodorsal ; but much less than half the length is in front of the line joining their lateral angles. The first brachials have long outer sides and very short inner ones, but (like the second radials) are almost invisible in the middle line of the arm, owing to the very strong backward projections of the irregularly triangular second brachials, which nearly reach the axillaries. Both on these joints and on the rudely oblong third brachials, which are much wider than long, the pinnule-socket is placed much nearer the dorsal surface than usual. The next following joints are short and quadrate, with curved proximal and distal edges ; and the pinnule is on the shorter side, the longer being marked by a backward projection. There are syzygies in the 3rd and 8th brachials, and then at intervals of three or four joints throughout the rest of the arm. The of Edinburgh, Session 1883-84. 367 lower brachials are triangular and sliglitly wider than long ; hut they slowly hecome quadrate and finally slightly elongated towards the arm-ends. The first pair of pinnules (on 2 and 3 hr.) are much longer and stouter than the next pair. They reach nearly 15 mm., and consist of some thirty smooth joints, the first six of which are short and nearly square. The second pair have hut eighteen or twenty slender joints, and are only about 6 mm. long. The following pinnules increase gradually, both in length and stoutness, reaching 15 mm, in the outer parts of the arms. The two basal joints become slightly flattened and the succeeding ones elongated. They have a somewhat glassy aspect, especially in the later pinnules, while their ends present the usual dead white appearance. The same dilference presents itself in the joints of the younger and more spiny cirri round the dorsal pole, and also in the pinnules and cirri of Ant. dentata. It recalls the contrast between the hyaline and porcellanous types of Fora minif era, though due to entirely dif- ferent causes. The ovaries are long and fusiform, extending over the greater part of the length of the lower pinnules ; and the disc is naked, or rather closely covered with irregular polygonal plates. Diameter of centrodorsal 5 mm. ; spread about 170 mm. H.M.S. “Porcupine,” 1869. Cold area? Two specimens, bear- ing seven individuals of Myzostoma cirriferum, F. S. Leuckart. Remarks. — The foregoing description is based upon the characters presented by three examples of the type, two obtained by the “Porcupine” and one by the “Triton.” They all agree very closely in their general features, and especially in the curious dimorphism of the cirri, which recalls that already noticed in Eudiocrinus variansA The shape of the axillaries and of the second brachials is very striking, the great length of the former being much more marked than in Ant. eschricliti. It is the characters of the radials and three lowest brachials which principally dis- tinguish Ant. hystrix from Ant. prolixa, Sladen.f Both species are remarkable for the small size of the second, as compared with the * Journ. Linn. Soc. ZooL, vol. xvi. pp. 496, 497. t Duncan and Sladen, A Mem.oir on the Echinoderinata of the Arctic Sea to the West of Greenland, p. 77, pi. vi, figs. 7-10. 368 Proceedings of the Royal Society first pair of pinnules; and this peculiarity distinguishes them from Ant. phalangium. l^one of the cirri of Ant. liystrix reach the size of those borne by the smaller examples of Ant. prolixa. Many of these have a short dorsal spine on the distal edge which projects forwards over the base of the next joint, just as in the more centrally placed cirri of Ant. liystrix. Ant. eschrichti is described in the “Porcupine” reports as abundant in the cold area. The only record which I have of its occurrence, however, is Station 57 (1869), 632 fathoms. But whether^?^f. liystrix occurred here or not, we may assume with tolerable certainty that it is a “ cold area ” species ; for the “ Triton ” specimen was obtained at a station where the temperature was below 0° C. 10. Antedon lusitanica^ P. H. Carpenter, 1883. Formula, A. 10. (2). “ . c Centrodorsal hemispherical, roughened at the dorsal pole, and bearing about a dozen slender cirri which reach nearly 30 mm. in length. They have about fifty joints, of which the first three or four are quite short, the next three much longer, and the following ones longer than wide, but gradii ally diminishing up to the fifteenth or twentieth joint. From this point (or earlier) to the end of the cirrus the joints have a well-marked dorsal spine, which is slightly less distinct in those just preceding the terminal claw. Ten arms, or (rarely) two distichals not united by syzygy. First radials scarcely visible except sometimes at the angles of the calyx. The second short and trapezoidal, with a strong median ridge, which is continued on to the axillaries. These are just pentagonal with slight backward projections into the second radials, and their sides are much flattened. This is still more marked on the outer sides of the first brachials, which are longer than their inner sides. The second brachials project more or less backwards into the first, and the third is a syzygial joint, the next three squarish, and the following ones more elongated with very oblique ends. The second brachials bear moderately long pinnules of about fifteen broad joints. The lowest have very prominent dorsal keels which are 369 of Edinhurgh, Session 1883-84. continued, thongh less marked, on to tlie later joints. The next following pinnules are altogether smaller, consisting of hut a few slender joints. Disc 5 mm. in diameter, thickly covered with numerous small plates, those at the sides of the ambulacra being rather more regu- larly arranged than the rest. Colour, in spirit, brownish- white or greenish- white. H.M.S. “Porcupine,” 1870. Station 17a. Lat. 39° 39' PT., long. 9° 39' W. 740 fathoms. Temp. 49°*3 P. Ten mutilated specimens. Remarks, — Nearly all the individuals obtained had the arms broken at the syzygy in the third joint beyond the radial axillaries j and it is therefore quite possible that the epizygal of this joint might sometimes have been a distichal axillary. In one example, at any rate, there are two distichal series, each consisting of two joints, the second of which is axillary. This species, therefore, seems to be dimorphic like Actinometra pidchella, and to constitute another exception to the general rule that ten-armed types are sharply distinguished from those in which the primary arms divide. The length and spiny character of its cirri, and the peculiarities of its pinnules, readily distinguish it from all the species of Antedon hitherto described. But it has many points of resemblance to some of those dredged by the “ Blake ” in the Caribbean Sea. It is a type of some interest for two reasons : it is the only European Comatida which is in the condition of the so called recent Cystid, Hiyponome sarsiij i.e., with a plated disc and the ambulacra converted into tunnels by the folding down of the plates at their sides ; and it is the only European Antedon with more than ten arms. 11. Actinometra pidchella, Pourtales, sp. Antedon pidchella, Pourtales, 1878. Actinometra y)ulchella, P. H. Carpenter, 1881. H.M.S. “Porcupine,” 1870. Station 31. Lat. 35° 56' N., long. 7° 6' W. 477 fathoms. Temp. 50° '5 E. Clay. One mutilated specimen. Remarks. — I cannot distinguish this form from the smoother variety of that singularly protean species. Act. pidchellaj of the 370 Proceedings of the Royal Society Caribbean Sea. It was dredged by tbe “ Blake ” at a very large number of stations ; but tbe depth was nowhere over 300 fathoms, and rarely exceeded 200 fathoms; so that its discovery in the “ Porcupine ” collection increases both its bathymetrical and its geo- graphical range. Excej^t the two species of Rhizocrinus, it is the only Crinoid common to the European and Caribbean seas ; while it is the only European species of Actinornetra. This is an essen- tially tropical genus, a few species only ranging to the parallels of 35°, such as those at the Cape of Good Hope, Yeddo, and this Gibraltar specimen. The depth too, 477 fathoms, is much greater than that at which the genus usually occurs ; so that this “ Porcu- pine ” specimen which, like Rliizocrinus rawsoni, was obtained in European seas long before its discovery on the other side of the Atlantic, is of interest in every way. The “Porcupine’s” discovery of Actinornetra 'pidcliella in the East Atlantic has been recently confirmed and extended by the dredgings of the telegraph-ship “ Dacia,” a few dismembered individuals having been obtained in lat. 34° 57' H., long. 11° 57' W., at a depth of 533 fathoms. All the primary arms divide except one ; but the number 20 is kept up by the fact that a palmar axillary is present on one of the secondary arms, a point which I do not remember to have met with in any of the “Blake” speciuiens. This involves a slight addition to the second of the two formulae which I have given for this dimorphic type,"^ so that they become a.lO.X; anda.2.(2).^ , . In the following list of stations at which Crinoids were dredged by the “Lightning” and “ Porcupine,” the forms which are now noticed for the first time are distinguished by an Station List of Crinoids and Myzostomida, 1868-70. H.M.S. “ Lightning.” 1868. Station 12. Lat. 59° 36' K, long. 7° 20' W. 530 fathoms. Temp. 47° "3 E. Globigerina ooze. Rliizocrinus lofotensis. * Proc. Zool. Soc., 1882, p. 745. of Edinburgh, Sessson 188 3-84. 371 Station 13. Lat. 59° 5' N., loner. 7° 27' W. 189 fathoms. y o Temp. 49°-3 F. Antedon pli cdangiiim. Station 16. Lat. 61° 2' lA., long. 12° 4' W. 650 fathoms. Globigerina ooze. lihizocrinus lofotensis. H.M.S. “Porcupine.” 1869. Station 37. Lat. 47° 38' N., long. 12° 8' W. 2435 fathoms. Temp. 36°*5 F. Globigerina ooze. Bathycrimis gracilis. Station 42. Lat. 49° 12' K, long. 12° 52' W. 862 fathoms. Temp. 39° *7' F. Ooze, with sand and shells. * Rhizocrinus rawsoni. Station 43. Lat. 50° V FT., long. 12° 26' W. 1207 fathoms. Temp. 37° *7 F. Globigerina ooze. * Rhizocrinus rawsoni. The Minch, 60 to 80 fathoms ; and off Loch Scavaig, Skye. / Antedon phalangiimi. < Myzostoma alatum. V M. pulvinar. Station 51. Lat. 60° 6' N., long. 8° 14' W. 440 fathoms. Temp. 42° F. Antedon dentata. Station 54. Lat. 59° 56' K, long. 6° 27' W. 363 fathoms. Temp. 31°'4 F. Antedon dentata. Station 55. Lat. 60° 4' K, long. 6° 19' W. 605 fathoms. Temp. 29° -8 F. Antedon dentata. Station 57. Lat. 60° 14' K, long. 6° 17' W. 632 fathoms. 30°*5 F. ( Antedon eschrichti. 1 Myzostoma gig as. Station 74. Lat. 60° 39' K, long. 3° 9' W. 203 fathoms. Temp. 47° '6 F. Antedon dentata. 372 Proceedings of the Royal Society Stations unknown. Antedon rosacea^ var. I Antedon liystrix. ( Myzostoma cirrifermn. H.M.S. ‘‘Porcupine.” 1870. Station 13. Lat. 40° 16' N., long. 9° 37' W. 220 fathoms. Temp. 52° F. ( Antedon phalangium. 1 Myzostoma alaUim. Station 17. Lat. 39° 42' K, long. 9° 43' W. 1095 fathoms. Temp. 39° -7 F. Ooze. Pentacrinus ivyville-thomsoni. Station 17a. Lat. 39° 39' K, long. 9° 39' W. 740 fathoms. Temp. 49° *3 F. Antedon dentata. "^Antedon lusitanica. Station 31. Lat. 35° 56' K, long. 7° 6' W. 477 fathoms. Temp. 50°-5 F. Clay. Act inometr a pidchella. Off Cape Sagres. 45 fathoms. "^Antedon phalangium. Off Carthagena. 80 fathoms. "^Antedon phalangium. Bay of Benzert. 50 to 100 fathoms. Antedon phalangium. Antedon rosacea (young). Skerki Bank. 30 to 120 fathoms. Antedon plialangium. Antedon rosacea (young). II. The Grinoids obtained hy H.M.SS. Knight Errant '' and “ Triton f 1880-82. 1. Rhizoerinus lofotensis, M. Sars. H.M.S. “Knight Errant,” 1880. Station 5. Lat. 59° 26' K., of Eclinbiirgh, Session 1883-84. 373 long. 7° 19' W. 515 fathoms. Temp. 45 •4° E. Mud. Two young S2:)ecimens without arms. Station 6. Lat. 59° 37' T4., long. 7° 19' W. 530 fathoms. Temp. 46°‘5 E. Grey mud. A fragment only. 2. Antedon rosacea, Linck, sp. H.M.S. “Knight Errant,” 1880. In 53 fathoms on the plateau N.N.W. of Korth Eona. Lat. 59° 12' K., long. 5° 57' W. Eough ground. One mutilated individual was obtained here. It closely resembles the “ Porcupine ” variety from an unknown locality, both of them having the first brachials shorter than usual and a better developed backward projection of the second brachials. The “Porcujjine” specimen, which is the better preserved, has a somewhat more robust appearance than is generally presented by this species, and looks altogether as if its habitat were in the cold area. 3. Antedon petasus, Dub. and Kor., sp. A single but tolerably perfect example of this well-known Scandi- navian type was obtained by the “ Triton ” at a depth of 87 fathoms on the Eaeroe Banks (Dredging Station Ko. 3. Lat. 60° 39' 30'' W., long. 9° 6' W. Sand and shells. Temp. 49° E.). It was officiat- ing as host to no less than eighteen individuals of Myzostoma cirri- ferum, E. S. Leuckart. 4. Antedon dentata, Say, sp. H.M.S. “Triton,” 1882. Station 2. Lat. 59° 37' 30” K., long. 6° 49' W. 530 fathoms. Temp. 46°’2 E. Mud. Eive mutilated specimens, the disc varying in diameter from 2 '5 to 4 mm. Station 5. Lat. 60° 11' 45” K., and 60° 20' 15'' K., long. 8° 15' AY. and 8° 8' W. 433-285 fathoms. Hard ground; stones. Temp. 43° -5 to 40° -8 E. The calices and arm-bases of two individuals were obtained here. The larger one, with a disc 6 '5 mm. in diameter, does not reach the size of some of the specimens dredged by the “Blake” off the coast of Kew England. Attached to the disc of each was an example of von GralEs new 2 B VOL. XII. Proceedings of the Roycd Society :^>74 species Myzostoma carpenteri. That on the smaller individual was the larger of the two (2 '3 mm.), almost rivalling its host in diameter. Even the smallest of these seven individuals has fully developed ovaries ; but it is only in the largest that the cirri exceed 10 mm. in length, and are composed of more than twenty joints. This species was taken by the “ Porcupine ” both in the warm and in the cold areas. 5. Antedon eschrichti, Miill. sp. H.M.S. “Triton,” 1882. Station 4. Lat. 60° 22' 40" N. and 60° 31' 15" K, long. 8° 21' W. and 8° 14' W. 327 to 430 fathoms. Temp. 31°-5 to 30° F. Stones; mud. A small but singularly interesting example of this well-known Arctic type. The cirri are small and comparatively delicate, not exceeding 20 mm. in length ; and the arm-bases are but slightly tubercular. All the arms have been broken either at the second (8th) or third syzygy (12th or 13th brachial). One can therefore study the appearance presented by the new arm-joints in various stages of growth. The lowest and therefore oldest of these new joints are most like those of the corresponding part of the arm in the adult, ^.e., triangular or very slightly quad- rate, but relatively long in proportion to their width. These characters, however, do not disaj^pear as they do in the adult, where the joints gradually become shorter and shorter, with a markedly triangular outline. But throughout the remainder of the restored arms the joints are quadrate and relatively long ; while the two lowest pinnule-joints show but few traces of the flattening and peculiarities of outline wliich are so characteristic of the adult. It is just in these characters (besides the smaller size of the third pair of pinnules) that Antedon quadrata (No. 7) differs from Ant. eschriehti ; and it is therefore to be regarded as a permanently immature form of the latter species. 6. Antedon hystrix, sp. n. H.M.S. “Triton,” 1882. Station 4. Lat. 60° 22' 40" N. and 60° 31' 15" N., long. 8° 21' W. and 8° 14' W. 327 to 430 fathoms. Temp. 31° “5 to 30° F. Stones: mud. of JEclinhurgh, Sesdo7i 1883-84. 375 The single individual obtained here has been already described together with those previously dredged by the ‘‘ Porcupine ” {ante, p. 365). 7. Antedon quadrata, P. H. Carpenter, 1883. Formula, A . 10 . ^ • 0 1877. Antedon celtieus, von Marenzeller, Wiener Denksclir., Bd. XXXV. p. 24 (separate copy). 1881. Antedon celtica, Sladen, Mem. Arct. Echinod., p. 75. 1881. Antedon celtica, P. H. Carpenter, Zool. Anzeig., Jahrg. iv. p. 520. Non Antedon celtieus of Barrett, Norman, Wyv. Thomson, &c. Special Marks. — The lower arm-joints (after the twelfth) as long or slightly longer than wide and slightly quadrate in outline, though som^etimes triangular. Tiiose in the middle of the arm are distinctly quadrate, the length bearing a large proportion to the breadth ; ami the later ones are somewhat elongated. But none of the joints are shaped like an isosceles triangle, and much shorter than wide. The third pair of pinnules (on 6 and 7 br.) are little more than half as long as the second pair ; and the basal joints of the lower pinnules have their dorsal edges more or less produced into sharp flattened processes. Pl.M.S. ‘‘Triton,” 1882. Station 4. Lat. 60° 22' 40" N. and 60° 3P 15" N., long. 8° 2P W. and 8° 14' W. 327 to 430 fathoms. Stones; mud. Temp. 31°-5 to 30°. One good specimen. Station 6. Lat. 60° 9' N., long. 7° 16' 30" W. 466 fathoms. Stones. Temp. 29° ’5 F. Two mutilated individuals and one fragment. Remarks. — This species has caused me no little trouble. The first example of it known to science was dredged in 1872 by the ill-fated “Tegetthof” 5° west of Nova Zembla. It was minutely described by von Marenzeller"^ five years afterwards and referred to * “Die Coelenterateii, Ecliinodemien, mid Wiimier dci k. k. osterreidiiscli- uiigaiischen Nord])ol-cxpedition,” Denksch. d. Wien. Akad., Bd. xxxv. p. 25 (of separate copy). 376 Proceedings of the Royal Society Antedon eelticus, Barrett sp., of which only a very poor description had ever been published. In the meantime I had met with a specimen off Disco, when in the ‘‘Valorous” with Dr Gwyn Jeffreys (1875), and I recognised it at once as distinct from an Ant. esehriehti obtained during the same cruise. Three other examples were dredged by Fielden in the “ Alert ” a few months later, two at Discovery Bay (lat. 81° 41' N.), and one at Franklin Pierce Bay (lat. 79° 25' hi.); and when the “ Challenger” Comatuloe came into my hands I found the same type among a quantity of individuals of Ant. esehriehti, from a dredging in 51 fathoms a little to the south of Halifax. I have little doubt that it was also obtained by the “Vega.” The “Willem Barents” met with it in 1880 near the locality of the Tegetthof dredging. Fielden’s speci- mens were well and carefully described by Sladen,* who identified them with that dredged by the “ Tegetthof,” so far as he could judge from von Marenzeller’s description of the latter. Thanks to the kindness of Dr von Marenzeller, I have been enabled to examine his type for myself, and I am satisfied that S laden was right in identifying it with those dredged by the “ Alert.” After writing his description of them Sladen saw for the first time some examples of Ant. eeltiea, Barrett sp., and recognising that these were totally different from the Arctic specimens, he inserted a note to that effect, but did not rename the latter. Barrett’s type now turns out to be the long but little known Antedon phalangium of the Mediterranean ; and the specific desig- nation eeltiea being therefore unoccupied, I thought at first that it might conveniently be retained for the type described under this name by von Marenzeller and Sladen respectively.! This, however, has seemed undesirable for many reasons ; and in compliance with the wishes of both the above named naturalists, I propose to give it a new name altogether. I have, therefore, chosen one indicative of the character by which the species is most easily distinguished from Ant. esehriehti, viz., the markedly quadrate shape of the middle and outer arm-joints, as has been noted above among the “ special marks ” of Ant. quadrata. * A Memoir on the Ecliinodennata of the Arctic Sea to the IVest of Greenland i London, 1881, p. 75, pi. vi. tigs. 5, 6. t “Note on the European Comatidacf Zool. Anzeiger, Jahrg. iv; p. 520. of Ediiiburgh, Session 1883-84. 377 This type was doubtless met with by the “Porcupine” in 1869, somewhere or other in the cold area. But there were no examples of it in the remains of the collection of Comatulce. which have come into my hands. The “ Triton ” dredgings increase its bathy- metrical range down to 466 fathoms, the “ Valorous ” Station in Davis Strait (410 fathoms), having been the deepest hitherto known. The three “ Triton ” specimens are all of them small, like those of the “Tegetthof” and “Valorous”; while they have a stifFer and less feathery appearance than the larger ones obtained farther north by the “ Alert ” and “ Willem Barents.” In fact, they more nearly resemble the small individual figured by Sladen ^ in their general characters. The dorsal processes on the lower joints of the basal pinnules are less prominent than usual ; while the peculiar characters of the first two pinnule-joints in the outer parts of the arms are by no means so marked as in larger individuals. This feature is one which is more or less visible in all the Arctic species, reaching its best development in Ant. eschrichti. Station List of Crinoids and Myzostomida,., 1880-82. H.M.S. “ Knight Errant.” 1880. Station 5. Lat. 59° 26' N., long. 7° 19' AV. 515 fathoms. Mud. Temp. 45°-4 F. Rhizocrinus lofotensis. Station 6. Lat. 59° 37' K., long. 7° 19' W. 530 fathoms. Grey mud. Temp. 46° *5 F. (Fragment only.) Rhizocrinus lofotensis. Aug. 4. On the plateau K.N.W. of Korth Eona. Lat. 59° 12' K., long. 5° 57' W. Rough ground. Antedon rosacea, var. H.M.S. “Triton.” 1882. Station 2. Lat. 59° 37' 30'' N., long. 6° 19' W. 530 fathoms. Mud. Temp. 46° ‘2 F. Antedon dentata. Station 3. August 8, on the Faeroe Banks. Lat. 60° 39' 30” N., long. 9° 6' W. 87 fathoms. Sand and shells. Temp. 49° F. I Antedon petasus. ) Myzostoma cirriferum. * Mem. Arct. Ecliinod. , pi. vi. figs. 5, 6. 378 Proceedings of the Royal Soeiety Station 4. Lat. 60° 22' 40" N. and 60° 31' 15" N., long. 8° 21' W. and 8° 14' W. 327 to 430 fathoms. Stones ; innd. Temp. 31° 5' to 30° F. Antedoii quadrata. Antedon eschrichti. Antedon hystrix. Station 5. Lat. 60° 11' 25" N. and 60° 20' 15" 1ST., long. 8° 15' W. and 8° 8' W. 433 to 285 fathoms. Hard ground ; stones. Temp. 43° -5 to 40° *8 F. ( Antedon dentata. ( Myzostoma carpenteri. Station 6. Lat. 60° 9' H., long. 7° 26' 30" W. 466 fathoms. Stones. Temp. 29° -5 F. Antedon quadrata. ITT. On the Myzostoinida of the “ Porcupine ” and, ‘‘ Triton ” Dredgings. By Prof. L. von Graff, Iffi.D. A. Porcupine” Specimens. 1. ATyzostoma cirriferum, F. S. Leuck. Seven individuals were found on two examples of Antedon hystrix, P. H. Carpenter, probably from the cold area. This is a new host, the species having been hitherto met with only on Ant, rosacea. It has since been found on Ant. petasus as well. 2. Myzostoma gigas, Liitken, MS. Hab. Antedon eschrichti. Station 57. Lat. 60° 14' FT., long. 6° 17' W. 632 fathoms. Temp. 30°-5 F. Two individuals were obtained, but in such a distorted condition that they cannot be accurately determined. As, however, the numerous Myzostoinida infesting Ant. eschrichti at the most widely separated localities invariably belong to this species, those obtained by the “ Porcupine ” are probably of the same type. It will be fully described in the “ Challenger ” Keport. of Edinhirgh, Session 1883-84. 379 3. Myzostoma alatum, sp. n. Hab. Antedon phalangium. The Minch. August 14, 1869. 60 to 80 fathoms. Station 13, 1870. Lat. 40° 16' K, long. 9° 37' W. 220 fathoms. Temp. 52° F. A species belonging to the type of Myzostoma glahrum. Dorsal surface arched and the ventral one hollowed, with a small muscular prominence in the centre. It is unprovided with cirri, and not transparent at the margin. Mouth ventral and cloacal papilla dorsal as in M. glahrum. Colour dirty yellow. Parapodia ex- tremely short and reduced to annular folds, from the middle of which there project the brownish-black points of well-developed booklets. These are closely grouped around the central muscular prominence ; while the round suckers lie near the edge of the ventral surface. A fully grown individual, 4 mm. in diameter, was so firmly attached to the disc of its host near the mouth that the booklets remained in the perisome when it was removed. On its back was a young one measuring 1 mm. in its longer diameter. This differs from the adult in the presence of distinct papillae on the dorsal surface, separated from one another by considerable intervals. 4. Myostoma pulvinar, sp. n. Hab. Antedon phalangmm. The Minch. August 14, 1869. 60 to 80 fathoms. This species has a very singular form. It is transversely oval, 3*2 mm. wide and 2*7 mm. long; and it is thicker than any other free-living species. The dorsal surface is flat, while the ventral one is raised like a cushion, with the parapodia projecting round its edge at equal distances apart, as wide and blunt processes, at the points of which powerful booklets are protruded for some distance. There are no suckers ; while the mouth and cloacal openings, usually situated on the same side as the parapodia, are placed on the dorsal surface. Both this and the ventral surface are of a strong yellow brown colour. The only specimen obtained was closely attached to the perisome of its host. No other Myzostomida but M. pidvinar and M. alatum are known to infest Antedon plialangium. 380 Proceedings of the Boycd Society B. Triton specimens. 1. Myzostorna cirriferum^ T. S. Lenckart. Hab. Antedon 'petasus. Station 3. Lat. 60° 39' 30" N., long. 9° 6' W. 87 fathoms. Sand and shells. Temp. 49° F. The single individual of Ant. petasus obtained at this station was harbouring no less than eighteen examples of this species, some adult and some young. It may have therefore yet another host besides Ant rosacea and the new Ant. hystrix of the “ Porcupine ” dredgings. It has also been found on a specimen of Ant. petasus from Norway, in P. H. Carpenter’s own collection ; and likewise on another Norwegian example (from Arendal) in the University Museum at Kiel. No other species of Myzostorna is as yet known to infest Ant. petasus. 2. Myzostorna carpenter i., sp. n. Hab. Antedon dentata. Station 5. Lat. 60° IP 45" N. and 60° 20' 15" N., long. 8° 15' W. and 8° 8' W. 433 to 285 fathoms. Hard ground ; stones. Temp. 43° *5 to 40° *8 F. I have dedicated this species to my friend Dr P. H. Carpenter. It is of a dirty yellow colour, 2*3 mm. long, and of slightly greater width. Twenty short cirri appear at its margin, which is without a transparent rim. In fact, the whole disc is firm and opaque. The form of the ventral surface is most unusual, and there is no trace of the muscular prominence which is so generally present in its centre. This would indicate that the parapodial musculature is very weak. The parapodia themselves are extremely slender and short, being lodged in shallow pits close to the edge of the ventral side, and almost on the same level with the equally feeble suckers. Both month and cloacal opening are terminal. Attached to the dorsal surface of one of the two adults was an immature individual •46 mm. long. The very characteristic differences betw en the two will be given in the “ Challenger" Eeport, together with the specific diagnoses. This is the only species of Myzostorna which has yet been found infesting Antedon dentata, better known as Antedon sarsii ; and it is as yet only known from the “Triton" dredgings. of Ediiihitrgli, Sessiori 1883-84. 381 5. On the Structure of the Pitcher in the Seedling of Negmi- tlics, as compared with that in the Adult Plant. By Ih^o- fessor Alexander Dickson, M.D. Preliminary Note. The only observations, so far as I am aware, that have been made on the pitchers of Nepe7ithes seedlings, are those by Sir J. D. Hooker, who, in 1859, described their external configuration in his paper On the Origin and Development of the Pitchers of Nepen- thes, &c.,” in voL xxii. of the Linnean Society’s Transactions, and afterwards added a few details of anatomical structure, in his admir- able address on Insectivorous Plants, delivered at the Belfast meeting of the British Association in 1874. This year I have had opportunitiy of examining Nepenthes seed- lings from a large crop which our Botanic Garden Curator, Mr Lindsay, has raised from seeds of a female plant of N. rafflesiana, fertilised by pollen from N. Clielsoni (itself a hybrid). In these seedlings the small lanceolate cotyledons are immediately succeeded by pitcher-leaves, which in form, as ]3ointed out by Hooker, on the whole more closely resemble the pitchers of Sarra- cenia, than those of the adult Nepenthes. We have the entire leaf hollowed out into a funnel-shaped pitcher, with two largely de- veloped wung-like exjDansions, and vdth a remarkably ciliated lid, whose base extends round fully one half of the orifice of the pitcher, very much as in Sa7'racenia, and very unlike the condition in the adult Nepe7ithes, where the ammlus occupies almost the whole of the pitcher-orifice, the base of the lid being narrowed into a very small space. Our seedlings also exhibit, what Hooker has described, the convergence of the lateral wings towards each other above, and their union in the middle line, forming a transverse ciliated mem- brane below the orifice of the pitcher. As regards further details, our seedlings differ somewhat from those described by Hooker. In the first place, Hooker describes (Belfast address) the inner surface of the pitcher as wholly gland- ular, while in our plants its upper half, or so, is eglandular and conducting, being thickly studded with the characteristic down- wardly directed crescentic ledges. This difference between the two 382 Proceedings of the Poyal Society seedlings may be easily accounted for, inasmuch as there are some species of Nepenthes in which the entire inner surface of the pitcher is glandular (c.p., N. amp)ullaria and N. Hookeri), and his seedlings may have belonged to some such species. The occurrence, indeed, of such a large conducting surface in the pitchers of our hybrid, is somewhat surprising when its origin is considered. In the female parent, N. raflesiana, the conducting surface is limited to an incon- siderable area below the hinge of the lid ; which area, when traced round the upper part of the pitcher, is seen to be reduced to a very narrow stripe, just below the line of inflexion of the annulus ; while in the male parent, N. Chelsoni, there is practically no conducting surface at all, there being nothing left of it but the merest trace, running along below the said line of inflexion. The only sugges- tion I can make on the subject is that there may here be a reversion to some ancestor of the cross-bred N. Chelsoni. The following table represents the rather complicated genealogy of our seedlings, so far as ascertained : — Nepenthes rafflesktna x Nepenthes sp. I I N. Dominii | x N. Hookeri I N. ra.fflesiana x | N. Chelsoni J ■ I I Our Hybrid. | It will be observed that the male parent of N. Dominii has not been recorded. On examining this form (which closely resembles N. rafflesiana in the limitation of its conducting surface), I have been struck with the great breadth and almost horizontal expansion of the reflexed portion of the annulus ; and I would suggest that perhaps N. Veitchii^ which seems (I only know of tliis plant by figure) to exhibit this character to a still more marked degree, may have been the parent in question. In the second place. Hooker describes the first developed pitchers of his seedlings as destitute of annulus {Linn. Soc. Tra?is., xxii. p. 418, footnote) ; while in ours this structure is very readily recog- nised, even in the leaf immediately succeeding the cotyledons, by its epidermis of imbricately disposed glassy cells, and its inflexion within the pitcher-orifice. As to this, I should almost be inclined of Edinhurgh, Session 1883-84. 383 to believe that the supposed absence of annulus was the result of an oversight, so distinctly developed is it in my specimens ; not to speak of its universal occurrence in the adult Nepenthes plant. Eegarding the anatomical structure of these pitchers, there are several interesting points to note. A. The Pitcher-lid. — This exhibits ciliary processes each tipped with a cell-group resembling that of a glandular hair. These pro- cesses, however, seem to be somewhat more than mere epidermal ap- pendages, at least containing ground-tissue, as evidenced by the occurrence of the curious spiral cells which are developed so exten- sively in the ground tissue of these plants ; and possibly they may represent prolongations of the entire leaf substance, like the tentacles of Drosera. Furthermore, there is no trace of the honey-glands which are to be seen on the lid of the adult form in both its parents ; and in connection with this, it is interesting to note the absence of lid -glands in the adult of N. ampidlaria, which species may thus be considered as exhibiting the undifferentiated or embryonic character. B. The Annidus. — This is quite distinctly marked, and may be traced by its characteristically imbricate epidermis from just above the transverse membrane joining the wings up to the pitcher-orifice, where it is inflected as a slightly crenated margin. The most inter- esting feature of the annidus., however, is the presence, just within the inflexed margin, of small cushion- or button-like glands, resem- bling in general character the glands of the secreting surface in the lower part of the pitcher-cavity. In the first leaf and those imme- diately succeeding it, these glands are usually three in number (in one specimen I have seen only two). In the subsequently developed leaves they become more numerous, and in our seedlings now about a year old, as many as twenty of these glands may be counted along the margin of a pitcher about an inch long. They form a very pretty circlet — or rather semi-circlet — reminding one of the row of ocelli in an Actinia. The presence of these glands in the annulus, coupled with the absence of lid-glands, at once arrested my atten- tion, and led me to suppose that here we probably had structures of greater morphological significance and of more universal occurrence than the glands of the lid, since these glands — physiologically im- portant as they undoubtedly are — are not necessarily present in the adult plant. I have accordingly examined the annulus of a number 384 Proceedings of the Royal Society of adult forms, and in this I have to acknowledge much valuable co-operation from my assistant, Dr J. M. Macfarlane. The result has almost surpassed my expectations. In all the species examined there is to be seen, immediately above the edge of the inflexed margin, a single line of small orifices alternating with the ridges of the corrugated annulus, and with their tooth-like prolongations when these are present. These orifices are the openings of canal-like fossse, from the bottom of each of wdiich a cellular nipple-like pro- cess or mammilla projects. These mammillae are the apices of what may be termed the Marginal Glands. The glands are of very large size ; the smallest I have seen — those of N. ampidlaria — being -Jy of an inch in length, while in some other forms — e.g., N. destillatoria, N. pliyllampliora, and an undetermined form (apparently allied to the hybrid N. Dominii), for which our Garden was indebted to the late Miss Hope of Wardie, they may reach the enormous length of yV of an inch. The nipple-like apex just men- tioned is never more than about 2^0 of an inch in length, and is the only portion of the gland which is free, all the rest being immersed in the parenchymatous substance of the annulus. The cells composing these glands are of somewhat small size, and are very numerous. Those in the immersed portion are, in a general way, disposed in lines which pass obliquely inwards and tow^ards the apex, the peripheral cells having a more or less transverse direction, wliile the central ones are longitudinally disposed. The superficial cells of the mammilla exhibit a beautiful columnar arrangement, being elongated at right angles to the surface. In some cases, especially in the larger forms, there seems to be a tendency to the formation of a central cavity from disruption from each other of the longitudinally disposed cells in the axis ; but I should not be inclined to attach any physiological significance to this circumstance. In shape the marginal glands vary somewhat. In N. awpidlarla the shape is ampullate, the nipple-like apex representing the neck, while the immersed portion, somewhat pointed at the base, and broadening upwards, represents the body of the ampulla. In the more elongated forms the shape is more or less cylindrical or sausage-like. The marginal glands, it will be seen, are remarkable not only for their large size, but still more for their immersed condition — the of Eclinhurgli, Session 1883-84. 385 other glands of Nepenthes (lid-glauds as well as peptic ones) 2^ro- jecting entirely free from the surface, covered in though they may be by a pocketdike flap, or sunk at the bottom of a surface depres- sion. In their immersed character, the marginal glands are perfectly comparable to the immersed glands of the secreting surface of the pitcher of Ceplialotus. As to the function of these marginal glands, I cannot as yet speak definitely. Sir Joseph Hooker says (Belfast Address) that the pitcher-margins of Nepenthes always secrete honey; but from his making no allusion to these very remarkable glands, I am doubtful whether he refers to them or not. Probably, however, they are honey-secreting, and afford to the insect the last drops, just as it is on the brink of destruction. C. The Conducting surface. — This agrees essentially with that in the adult forms. I have here to note that each crescentic ledge consists of a single semilunar cell, which overlaps a lower and smaller cell. Occasionally these two cells somewhat puzzlingly resemble deformed stomata, but I have not as yet been able to trace a more definite relation in this direction. D. The Secreting or Digestive surface. — The e23idermis cells here are remarkable for their wavy outlines, differing from the more angular form exhibited in the adult plants of the parent forms. The glands, moreover, are in the first-formed leaves entirely exposed, although in the later ones the rudiment of the protective pocket-like flap may be seen. In this connection Dr Macfarlane has pointed out to me that in N. phyllamxjhora the ^^eptic glands are only to a very slight extent covered by flaps, so that in this plant we have the persistence of an embryonic character. In the first pitchers of the seedling the peptic glands are few in number — about ten ; but in the later developed ones they become very numerous. PEOCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. Monday, ^th January 1884, THOMAS STEVENSON, Esq., Vice-President, in the Chair, The following Communications were read : — 1 Approximation to the Boots of Cubic Equations by help of Eecurring Chain Tractions. By Edward Sang. {Ahstract)\ In the progression of fractions here used, each new term is got by corresponding multiples of the three preceding terms, thus : this mode of formation being applied separately to the numerators and denominators of the fractions. For the cube root of 2 there is given the progression for which the multipliers are r=l, <1 = ^ , p = 3, and also a more rapidly converging series VOL. XII. 1883-84. No. 116. rA -1- gB +pC = I) , rB + gC + pH = E , rC + gH +pE = F , and so on, 1 0 1 4 15 58 223 0 ^ 0'^ I ^ 3 ' 12^ 46’ 177’ = - 1 0 5 286 16287 ~d’ 0 ’ 4 ’ 227 ’ 12927 ’ having the multipliers 1 , - 3 and 57. VOL. XII. 388 Proceedings of the Boy at Society The cube root of 7 is given by the progression - 2 0 U 66658 100986738 ^ 3 , 0 ^ 23’ 34846’ 52791621 ’ “ V7 formed by the multipliers 1 , - 3 , 1515. And, in general, the ratio sub-triplicate of that expressed by any two integer numbers K and L, is shown to be the asymptote of the progression formed by the multipliers r = (L-K)6; q = 3(L-K)^; = 3L2 -f 21KL-P 3K^ ; from the initials + (L-K)-^ 0 K+2L -(L-K)-s’ 0’ 2K4-L ■ The asymptote of every progression of this kind is shown to be the root of a cubic equation ; while, for every cubic equation with integer coefficients, such progressions may be found. Thus the corresponding theorem in quadratics, which was thought to exclude periodicity from all higher equations, becomes only one case of a general law. In addition to the progression for the ratio of the long diagonal to the side of a regular heptagon, given in a former paper, that having the multipliers 1 , 4 , 3 is given thus, 1 0 2 7 29 117 474 o 0 ’ 0 ’ 1 ’ 3 ’ 13’ 52 ’ 211 ’ and for the corresponding ratio in the case of the enneagon, - 1 0 3 26 216 1791 o 0 ’ 0 ’ 1 ’ 9 ’ 75 ’ 622 ’ having the multipliers 1 , - 6 , 9. It is also shown that terms placed at equal intervals in such pro- gressions form separate progressions of the same kind; this law applying also to the ordinary periodic continued fractions approxi- mating to the roots of quadratics of Ediiiburgli, Session 1883-84. 389 2. The Eesearches of M. E. de Jonqui^res on Periodic Continued Fractions. By Thomas Muir, M.A. 1. During the present year there has appeared at intervals, in the Comptes Rendus of the French Academy, quite a series of com- munications by M. E. de Jonquim’es, on the subject of those periodic continued fractions which are the equivalents of the square roots of integers. These communications have attracted attention, both on account of the number of results given in them, and because, as a writer in the Bulletin des Sciences Matliematiques says, of their interesting and profound character. To any one really intimate with the bibliography of the subject, this cannot but be a little sur- prising. It is true that the number of so-called theorems is great ; but the very special character of a number of them, the fact that they are just such theorems as may be obtained by experiment and induction, and the want of demonstrations of them as evidence that the author was in possession of a mathematical theory of the subject, are points that have been too much overlooked. Further, and what is more important, many of the theorems are not new, and there is a sense in which the epithet “ new ” cannot fairly be applied to any of the earlier ones, because of the existence of a widely general theorem in which they are directly included, or from which they may with readiness be deduced, 2. It is to this general theorem I now wish to direct attention, making use of it for the purpose indicated, viz., of giving scientific order and unity to M. de Jonquieres’ work. The theorem iras given in the year 1873, in the first paper I had the honour of communi- cating to this Society, and is to be found at p. 234 of vol, viii. of the Proceedings. It, as well as several other theorems given in the paper, was originally accompanied by a good deal of detail of the same nature as M. de Jonquikns’ theorems ; these special proposi- tions, however, were struck out, when by request an abstract of the paper was prepared for printing. A special case of the theorem has been rediscovered twice at least since 1873 ; the latest appearance being in Grunert’s Archiv^ Ixix. pp, 205-13, where the writer, K. E. Hoffmann, says regarding it:— ‘‘Diese allgemeine Formel enthalt nun alle in der Stern’schen Tabelle gegebenen als specielle Falle in sich, welche durch passende Wahl der etc, aus der 390 Proceedings of the Boy at Society hier gegebenen abgeleitet werden konnen.” When it is recalled that Stern’s memoir extends to 102 pages of Crelle’s Journal, the magnitude of the generalisation will be appreciated. 3. The statement of the special case referred to (which is all that is needed for our present purpose) is as follows : — “ The general expression for every integer whose square root, when expressed as a continued fraction with unit numerators, has , q2, qi ? for the symmetric portion of its cycle of partial denominators is fe,. . q^'K.{q^, . . . , Jj) ^ I being the number of elements in the cycle J The functional symbol K( ) is explained by the example K(a, b, c, d)^ a 1 0 -1 & 1 0-1 c 0 0-1 0 0 1 d 4. Taking the case then of this theorem where 1 = 2, we have 1 ^ (m>1) the asterisks indicating the beginning and end of the cycle. This is M. de Jonquieres’ first theorem. It is desirable to state it in two parts, viz., (1) where q is even = 2k say, (2) where m is even, = 2n say. These give * * V(2n)2 + 2n = 2N+ + * * By giving all possible integral values to k, M, q, n here, we obtain every number whose square root has a cycle of two terms, and at the same time we obtain the said cycle. The condition, m>1, is necessary to prevent degeneration of the cycle; if m = 1, the cycle is of Edinburgh, Session 1883-84. 391 2k + 2k+-' * * * 5. When Z = 4 the general theorem gives us V{ Wm + 2g'i)M -- + 1)^2 1 1 1 = { } + 1 2'i+ ^2+ } + * * (IF) where for shortness there is pat { } for {|(?fe + 2g'i)^-2fe2'2 + f)2'2}- Here again a little consideration, based on the knowledge that the number under the root-sign must be integral, serves to show that there are two distinct cases, viz., (1) when ^2 is even, (2) when is odd, odd, and m even. Putting therefore in the first case ^2= and in the second case ^2 = 2s - 1, q-^ = 2r-\, M = 2n, we have as our pair of identities J { (%" + ?)M - (2Z^-h 1 )^ } " + + 1 )M - 4^3 111 + w q + 2k + q +2| j + 2/1' M>-- (II.)/ I (8r2s-8r5- 4r2 + 8r-l2s-3)N - (2r5-r-s + l)(2s - 1) j- -}-2(2'F5-r-54-l)N - (2s- 1)- f ) _i 1 w 1 = \ f +2r-l4-2s-l + 2r-l-F2{ } + -:^ These give every integer whose square root has a four-termed cycle, and make known the cycle as well Returning now to (II') and putting g'i = 1, we have \/{i(2 + 2)m - 1(2 + l)s}2 + (2+ 1)M - 2^ or ^{2(2 + 2)“- 4(2+ 1)2+ 1}^-(m-2+1) V{i(2 + 2)(M-2 + l)F-(M-2 + l) ( 1 2 1 1 1 1 = I J(2 + 2)(m - 2 + l)-l I +Y+^+i+2{ }+... or 392 Proceedings of the Boyal Society where, to prevent degeneration of the cycle, we must have ie., {q 4- 2)m - + 1)^'> 2^' and M>g. Writing N for m - 1, this special result becomes sj { 5(«+2)N }"-N= I ife+2)N-l |"+- wliicb is the accurate form of M, de Jonquieres’ second theorem. M. de Jonquieres’ oversight consists in omitting to notice that the g in his statement mu-st be less than <2 + 1, 6. Theorem III. is avowedly a combination of theorems I. and II. ; it is carefully stated, however, in such a way as to seem to support M. de Jonquieres’ theory that the number of terms in the cycle of the continued fraction for is dependent upon the ratio of : d, 7. Theorem IV, there is no accounting for ; it is but a case of theorem II., viz., where & = 2a + 4 and e == 4. hleither is there any accounting for the remark following it — ‘‘Le nombre 12, qui devrait figurer en tete de la serie, fait seul exception, parce qu’il rentre dans le groupe defini par le theoreme I, a cause de 12 ^3^ + 3”; for 12 is the case where ?2 = 0, and there could be no continued fraction with the cycle 1, 0, 1, 2a. If it be an excep- tion, then a whole class of exceptions to theorem II. has been overlooked, viz,, where q~2, 8. When Z ~ 5, the general theorem gives mJ { + ‘2m +i>^ + 1)M + 4- g)(g2 + 1) j. ^ 4.^ + g)]V[ + (^2 + 1 )2 (III.) of Edinhurgli, Session 1883-84. 393 Here also there are two cases, viz,, (1) q odd, M even, =2A:4- 1, 2n say, (2) q even, p even, m even, = 2r, 2s, 2n say, the corresponding identities being + 2^ + 1 )N + + 4jiA: + + 2^ + + 2A: + 1 ) } ‘ + (4^7c2 + ipk + 2p + 2k+l )2N + (47:2 + 47: + 2f] _( I 1 111 “i / + ^ +27:+l + 27:+l+^? +2{ }+... ^[ { (1 6r2s2 + 8rs+4r2 + 1 )N + (4rs2 + r + 5) (4s2 + 1 ) j 2 + (4rs2 + r + 5)4N + (4s2 + 1 )2] = 1 Ui- 1- ^ i- I ) 2r + 2s+ 2s+ 2r+2| |+... Putting in the first of these k = 0, we have J{2p^ + 2p + 1)n 4- 2p+ 1}^ + {2p + 1)2n + 4 f ] 1 i_ 1 I_ 1 j’^i9+l + l-'rJ9+2{ }+... Specialising still further by taking n = 0, we have sl{^P^^f + ^ = ifP+^)^J^T+T+J+2{2p + l)+ ... * which is M. de Jonquieres’ theorem V., and which is to be found given as an example at page 31 of my pamphlet on The Expression of a Quadratic Surd as a Continued Fraction, Glasgow, 1874. 9. Considerable interest attaches to the above identity deduced from (III.) by putting A; = 0. Written in the unexpanded form of the general theorem, it is J I K(j9,l,l,i^N + iK(p,l,l)K(l,l) |2 + K(^,1,1)2n + K^^ _ i I Jl i_ i_ 1 1 \ ]'^p+l^l+p+2{ )+... How K(p,l,l,^’)N + JK(^D,l,l)K(l,l) = K(p,1,1^)n + K(p,1,1) = K(p,1,1,^,n); 394 and Proceedings of the Royal Society Kfel,l)2N + K(l,l)^ = 2[K(p,1,1)n + K(1,1)} The identity may therefore he put in the form — _ 1 1 1 s/K(p,1,1,p,n)2 + 2K(1,1,p,n) = ■^p + l + l+ p+2{} + ... * * But -f K(l, 1,p,n) =i'+y + y + y+ 4' and thus we have the curious theorem,— If the periodic continued fraction for + %i (d prime to A) he loanted and the continued fraction equivalent to A-~d he found to he 1111 of the form ^ + ^hen the periodic continued .,..1111 1 fraction required ^«A+— — Example — V338= = + __ * * f 18 9,4 for y-=^ + y . „ 1 1 1 = ^ + Y + T+ 3 ’ _2 + l 1 1 J . 1 + 1 + 2 + 1 10. Taking the case of the general theorem where Z = 6, we have ^\{\{pP‘h‘^c + 2ahc + ^a% + 2a + c)m - ^{ah^^c + hc + 2ah + \)(fi^c + 2&)}2 + {ab^c + 6c + 2a& + 1)m - {h'^c + 26)2] :r.n+Ll.J__LJL _L a+6 + c + 6 + a+ 2| | * Here the only case which is not possible is a, 6, c, all odd : that is to say, we may have of Edinburgh, Session 1883-84. 395 (1) a odd, c even. (2) h even, c odd. (3) a even, c even, m even. (4) a even, b odd, c odd, m even. As a particular case of the first of these particular cases, let us take a = 1, c = 2, m - 25^ -j. l. Then This is M. de Jonqui^res’ Theorem VI., and was given by me as a chance example in 1874 (see p. 31 of The Expression of a Quadratic Surd, ^'c.). 11. Having enunciated these six theorems, M. de Jonquim^es adds : — “ Les theoremes I, II et III montrent, comme je I’avais aiinonce, que la longueur et la composition de la p^riode dependent principalement de la valeur du rapport 2a -~d quand cette valeur est entiere, et tons mettent en evidence ce fait que, dans une meme famille de nombres, ceux des termes de la periode qui changent d’un nombre k I’autre sont de la seule variable.” This mode of reasoning is somewhat perplexing. Being concerned with functions of any number of variables, M. de Jonquieres takes the functions in the ultimate or penultimate stage of specialisation, and tries to draw general conclusions from the results thus obtained. Such a course could not but be futile. Knowing, as we do, that, g2» • • • » S'a? 9i being the terms of the symmetric portion of the cycle, the expres- sion for M. de Jonquieres’ 2a is K(gi,g2» • • • » ^ ?3^^2)K(g2» • • • ^^2) > and for his d, we have instantaneously forced on us the conclusion that for the solution of our problem something besides the ratio of 2a to d must be taken into account. Hot only, however, does M. de Jonquieres merely direct his attention to very special cases, but these special cases are specially selected ; special cases that tell a different story are ignored. What simple peculiarity, we may ask, of the ratio 2a ; d exists fnr the infinite number of other special cases of our 1111 1 l + ^+ 2-}-6-l-l-{- 4(6 + 1) -j- . .. K(?1, . . . ,?2)“ - ( - • • • >?2)^ . 396 Proceedings of the Royal Society identity (II.) besides M. de Jonquieres’ special case ? And when tbe ratio 2a : cZ remains constant, because of a varying as fZ, is no altera- tion made in tbe extent of the cycle? Surely M. de Jonquieres, from actual observation, knows as well as any one that if merely 2a cZ be constant, the general ride is that the cycle varies in extent, and that the case where it does not vary (M. de Jonquieres’ theorem I.), instead of being the rule^ is the exception. Then, again, M. de Jonquieres forces into his service facts which are manifestly against him. He says theorems I., II., III. bear out a certain conclusion. How III., as we have seen, shows nothing that I. and II. do not show, and need not therefore have been referred to ; and Theorem II. shows something totally different from Theorem I. In Theorem IL the ratio considered is not 2a : tZ, but 2Z> : e, Z.e., 2(a + 1) : 2a - cZ -i- 1. This theorem is, therefore, not a support to M. de Jonquieres’ theory, but the opposite. As for M. de Jonquieres’ second fact, which, as he says, all his six theorems bear out, we can only meet it by asking in wdiat sense it is possible seriously to talk of or q^ as being functions of 1%). 22. •• • . 22. 2i)m-( - 22. ■ • • . 22W22. • 22)- Had M. de JonquiOTes confined himself to refuting Lagrange’s statement that the extent of the cycle in the expansion of depends only on the value of E, he would have been on safe ground, for the incorrectness of the statement has long been known, and indeed must have been known, one would think, to Lagrange him- self; the only conclusion, however, beyond this, to which his researches entitle him, is the vague one that it depends somehow, as Lagrange also said, “ de la nature du nombre E.” 12. Having, in order to follow M. de Jonquieres, considered the cases of the general theorem where Z = 2, 4, 5, 6, it seems desirable for the sake of continuity to put on record the details of the omitted case, viz., where I = 3. The theorem then becomes x/{2(2^ + l)M + i2}^ + 2M + l = { }+^+2 + 2{^+ ... * * It is readily seen, however, that in order to avoid fractions, q and 397 of JEdinlurgh, Session 1883-84. M must both be even : putting therefore q—^'p and m = 2n, we have as our final result for the case ^|(4^2+l)N+J,p + 4i.N + l={ }+Yp+Y^ + f-}+ .. * * This furnishes a theorem closely resembling that in § 9. here M. de Jonquieres’ ratio — 2(4p2 ^ 2p ~ 4pN + 1 2n For ^2J9 + Hence, 4pN + 1 1 2n If the periodic continued fraction for JAd' + d^ (d prime to A), he wanted, and the continued fraction equivalent to 2 A -^d he found to he of the form 2p + 2^^ the periodic continued fraction . ^ . A 1 1 1 required A + ^ - — -~ ^ 2j9 + 2j9 + 2A + . . . * * 13. These two theorems, as might be inferred, are not isolated from the main subject ; and it is of importance to see their exact position in the theory, not merely on their own account, but because this can be done by establishing a general theorem, which affords a complete solution of the problem M. de Jonquieres set himself, viz., to find what relation exists between the ratio 2a : d and the terms of the cycle. We have seen that 2a = K(gi,22, . . . , ?> - ( - ri%i , gj, ■ • . S2) and writing c for ( - 1)'+^K(^2 ? • • • > ^'2) MK(gj , . .. , gi) + cK(g,, . A 1 0 ... 0 0 0 -1 $2 1 . . . 0 0 0 0- ■ 1 ^3. .. 0 0 0 0 0 0 ... 9.2 1 0 0 0 0 ... -1 9x c 0 0 0 ... 0-1 M 398 Froceedings of the Royal Society Similarly d = , . . . , - ( - 1)*K(2'2 , . • . , ^2)^ * , . . . > 22) + ' I2 1 . .. 0 0 0 -1 ?3* , . 0 0 0 0 0 . • • I2 1 0 0 0 . ..-1 h c 0 0 . ., 0-^ 1 M But this determinant is the complementary minor of the element in the place (1, 1) of the former determinant: hence by the funda- mental application of continuants, 2« ^ 1 T ^^i + - 1_ + 2, + i • • . 22) M Our theorem thus is — - If sja‘^-)rd== aF i + ^2 + * lii_ • • + ^'2 d" S'! “t 2a 4- • • • * then 2^^ 1 1 i (~l)‘"Kfa,...,g,) d ^ q^-\ H g-g + S'! + M where I is the number of terms of the cycle and m some integer or zero. When I is odd and ^{q^ » • • • ? ^2) certain special values, a converse of this is possible : and it is thus that the theorems in §§ 9, 12 originate. Additional Note. (Ordered by the Coimcil to be printed in sequence to Mr Muir’s former Note.) On the 3d April 1883, M. Catalan presented to the Belgian Boyal Academy a paper on continued fractions and certain series. of Edinhurgli, Session 1883-84. 399 At the end of the abstract of it published in the Academy’s Bulletin (p. 612-618) there is the following “ Addition. Un G4om^tre hien conn a, M. de Jonquieres, vient de presenter, a TAcaddinie des sciences, nn travail intitule : Note sur un point de la tlieorie des fractions continues periodiques. Les theor^mes, tres interessants, auxquels I’honorahle auteur est parvenu, m’ont fait revenir sur mes precedentes recherches. Malheureusement, je n’ai pu r^diger encore cette Addition : le temps m’a fait d4faut. Afin de prendre date, j’4nonce le th^oreme suivant, qui contient, comme cas particuliers, quelques-uns des r^sultats obtenus par M. de Jonquieres. P' Q Soient — , ^ les deux dernier es reduites de la fraction continue, symUrique : h, c, d, . . . , d, c, h, Soient a, a, deux nomhres entiers, satisfaisant aux conditions : Qa-2Pa=^P’, (a<2a). Si Von fait A = + a les racines carrees de tons les nomhres A {il y en a une infinite) sont donnees par la formide slA. — a{h, c, d, ...yd, c, b, 2a)S I desire to point out that this theorem also is not new, and that, indeed, when pushed to its proper conclusion it gives the theorem above referred to as having been rediscovered by Hoffmann. When asked for an expression giving all the integers whose square roots have the cycle b, c, d, * . . , d, c, b, M» Catalan re- plies that the expression is a, where a and a are integral solutions of the indeterminate equation Qa - 2Va = Y, Q standing for {b, c, . . ., c, b), P for {b, c, . . .c) and P' for (c, . . ., c). How there is no need for giving the answer in this imperfect and 400 Proceedings of the Royal Society roundabout fashion : the equation referred to can readily bo solved. For it is clear that must be integral : and as P is prime to Q, this is the same as saying that 2P2a + PP' . . I — must be integral. Q But P^ = QP' + (-l)* if I be the number of terms in the cycle (6, Cf ... 7 c, b). Hence 2aQF + 2a(-l)' + PF Q = an integer. (-iy2a + PF 7^; = an integer = m say H a = (-l)'HQM-PP'}. By substitution now in the original equation we find a = (-iy{PM-F2}. Hence the required expression is J{Qm-PF}2+(-1)^(Fm-P'2). M. Catalan’s equation, the solution of it here given, and this final result, are to be found in the The Expression of a Quadratic Surd^ &c., p. 30. o. New Forms of Nerve Terminations in the Bkin of Mammals. By George Hoggan, M.B, (Edin.), Com- municated by Professor Turner. {Abstract.) The new forms have been found in the palms of the raccoon, the Procyon lotoi\ so named from its habit of dipping its morsels in water before eating them. These forms are three in number, and, in order to prevent any morphological or physiological appellation being applied to them, they have been named, for purposes of description and differentiation, after three ladies respectively, the Browne, the Hoggan, and the Blackwell bodies. The Browne bodies occupy the apices of the dermic papillse, exactly where the 401 of Edinburgh, Session 1883-84 Meissner bodies are found in man, monkeys, and marsupials ; otherwise they have no resemblance to these bodies. Properly speaking, they are not bodies, but only forked terminations of the nerves, formed generally of two or three prongs, and these are twisted and intertwined in an intricate manner. Nor do they possess any capsular envelopes, the presence of which differentiates them from the Hoggan bodies, that being the only distinct differ- ence between the two. The Hoggan bodies in their external aspect resemble the Pacinian bodies, being provided with a greater or less number of capsular layers, according to the greater or less depth at which they lie in the dermis. The nerve terminations within the body are, however, quite distinct from anything yet found in the Mammalia, being in general branched immediately after the nerve has become enveloped in the capsules. In their branched and contorted form the nerve terminations resemble the Browne bodies plus the capsules they have received. It is probable that the Browme bodies are formed by rupture of some of the non-medullated nerve fibres forming the subepidermic plexus, a little beyond the point where a medullated nerve has joined the plexus. These ruptured fibres contract upon themselves, and thus form the Browne body. As the Browne body sinks more deeply into the dermis it seems to receive the cellular envelopes which characterise the Hoggan body. The Blackwell body is a modified subepidermic nerve ganglion, still attached to the epidermis, but of which all the cells get com- pressed into a more or less globular or oval form, and are all in connection with a very thick medullated nerve. It is indeed a modified Meissner body within the epidermis in its most complete form, but a subepidermic ganglion in its simplest forms. It is a midway link between these two organs. The Browne and Hoggan bodies seem to be homologous with the forked nerve endings on the hair follicles, and so far they support the author’s previously published views that the Pacinian bodies are only modifications of the forked endings. In most of the sections the sweat glands seem to be greatly deficient in number, and as the author has in other animals, especially rodents, observed Meissner bodies to be only developed where the sweat glands were enormous in size and number, he argues from 402 Proceedings of the Boyal Society this — first, that moisture is necessary to give proper sensation ; second, that the deficiency of sweat makes the animal dip its morsels in water ; and third, that this continual wetting of the hands has modified the nerve terminations. 4. Diagnoses plantarum no varum Phanerogamarum Socotren- sium, etc.; quas elaboravit Bayley Balfour, Scientise Doctor et in Universitate Glascuensi rerum botanicarum regius Professor. Pars quarta (Supplementum). CEUCIFEK.dE. Brassica rostrata, Balf. fit., var. hirsUta, Balf fit. : omnino hirsuta foliisque arete dentato-serratis. Socotra, in montibus crescens. B.C.S. FTo. 555. CAPPAEIDE^. CleoMe brachycarpa, Vahl, var. filicaulis, Schweinf. : minuta eglandulosa inodora filicaulis. Socotra, prope Tamarida. Schweinf. Uo. 289. M^rua angolensis, DC., var. socotrana, Schweinf. : arbor mediocris vel frutex ramis effuso-dependentibUs dense foliosis ; foliis tenuiter carnosulis vel (perennantibus) crassis suberosis, petiolo duplo vel ad J lamina breviore flaccido hand recurve, lamina basi cuneata ovali-obovata v. oblongo-lineari ad apicem rotundata v. emarginata semper mucronata ; floribus paucis mediocribus apetalis ; fruct. ignot. Uom. vern. Eschab. ’Eschab. Eshaib. Socotra, in campis montibusque. B.C.S. Uos. 193, 588. Schweinf. Uos. 251, 457, 603. YIOLARIE^. Alsodbia socotrana, Balf. fil. : herbacea ramosissima humilis glabra ; foliis parvis ellipticis v. subohovatis brevissime petiolatis obscure remoteque serrulatis subtus glanduloso-puberulis ; floribus solitariis : filamentis brevissimis. Socotra, prope Tamarida. B.C.S. No. 26. of Edinburgh, Session 1883-84. 403 CAEYOPHYLLE^. Gypsophila MONTANA, Bolf. fit, vai\ visciDA, Bolf. fil.: robustior iij florescenti80 ramis ulfcimis brevioribus et omnino pilis glandulosis vestita, Socotra, in montibus. B.C.S. l^o. 554. Schweinf. No. 658. Distrib. Somali Land. PoLYCARPiEA SPICATA, Am., var. CAPiLLARis, BoLf. fil. : tenuior pauciramosa ; folds panels filifonuibus ; bracteolis siccis rufis marginibus vix scariosis. Socotra, prope Galonsir, B.C.S. No. 211. Schweinf. No. 239. ZYGOPHYLLE^. Eagonia ORETiCA, Linii., var. socotrana, Balf. fil. : omnino inarmata glauca ramis striatis scabrido-hispidis ; folds unifoliatis crassis ovato-ellipticis v, ellipticis v. rotund atis v. suborbicnlaribns |-1J poll, longis pod- latis; stipnlis minutis — P^d. longis subulatis submembranaceis ; pedunculis sub capsnlis dilatatis et eis subaequdongis ; sepalis snbpapidosis ; petalis albidis v. piirpnreis } capsnlis pnbescentibns ; seminibus obsolete pnnctnlatis. Socotra, abnndans. B.C.S. No. 202. GERANIACE.E. Dirachma, Schweinf, Elores regnlares. Calyx 8-partitns, lobis valvatis. Petala 8, perigyna, imbricata. Glandnlse disci inconspienm. Stamina 8, libera, petalis opposita, omnia antherifera ; antheree magnae, oblongse. Ovarium Sdobuin, Sdocnlare, rostratnin ; stylus centralis, integer, obtusns ; ovula in loculis solitaria, adscendentia. Capsnla 84oba, in carpeda 8 ventral! ter dehiscentia intns ianata secedentia. Semina compressa, in loculis solitaria ; testa nitida ; albumen sparsum. — Frutex ramosus, plusminusve pubescens. Folia alterna, dentato-serrata, paudo revoluta, stipulata. Pedunculi axidares, 1-fiori. Flores albi. Calyx 4-bracteatus. Genus monotypicum generibus Wendtise Balbisias et Vivianice Americanibus austral ibus maxime affine. 2 D VOL. XII. 404 Proceedings of the Royal Society D. soooTRANA, Scliweinf. : species unica in montibus Hagliier crescens. B.C.S. Nos. 285, 344. Scbweinf. No. 528. LEGUMINOSJE. Tephrosia (Brissonia) odorata, Bcdf. fit. : herbacea parva plus- minusve strigosa ; foliis digitatim trifoliatis ; foliolis vix J poll, longis oblanceolatis ; stipulis minntis ; lloribus solitariis axillaribus odoratis purpureis. Socotra, in montibus calcareis prope Galonsir. B.C.S. No. 180. Acacia pbnnivenia, Schiocinf. : arbor rainis glabris fuscis ; foliis glaberrimis 2-3-pinnatis glandulis nullis, foliolis laxe 7-9-jugis oblongo-obovatis nervo fusco medio dimidiatis venis utrinqiie 3-4- pinnatis ; fioribus albis in capitula racemum laxum formantia v. subpaniculata dispositis, involucello infra medium basin versus pedunculi griseo-tomentosi subcaduco ; caljcis lobis rotundato- ciiiatis ; corolla calyce dimidio longiore ; staminibus exsertis ; legumine ignoto. Nom. vern. Tamlior. Socotra, in montibus crescens. B.C.S. Nos. 212, 345. Scbweinf. Nos. 459, 519. Hunt. No. 17. CUCURBITACEJa. Eureiandra Balfourii, Gogn. : caule glabro ; petiolo brevissime sparseque puberulo demum glabro ; foliis utrinque breviter sparseque asperis demum albo-callosis, plerumque leviter 3-5-lobatis, lobis saepius triangularibus, apice subacutis ; lloribus pro genere parvis, masculis brevissime racemosis subfasciculatis ; calycis tubo late infundibuliformi subcampanulato ; staminum lilamentis glabris ; ovario oblongo ; fructu ovoideo-subfusiformi, apice longiuscule acuteque rostrato. Nom. vern. Dacbsliana v. Diclisbani. Socotra, per iosulam crescens. B.C.S. No. 281. Scbweinf. Nos. 502, 541, 640, 647. eicoideh:. Tetragon I A pentandra, Balf. fit. : glabra ramis longe patentibus j foliis deltoideo-ovatis remotis ; lloribus binis axillaribus ; staminibus quot tot calycis lobis ; nucamento pentagono obconoideo. Socotra, prope Galonsir. B.C.S. No. 37. of Edinburgh, Session 1883-84. 405 EITBIACE^. Dirichletia obovata, Balf. var. albescens, Balf. fit. ; ramis albescentibus ; foliis ad ramulos laterales contractos plurimis con- fertis lanceolatis v. oblanceolatis acutis valde revolutis crassiusculis j floribus ssepe solitariis ; pedicellis longissimis tenuibus ; calyce in fructu plerumque concavo. Nom. vern. Sehat. Socotra, in campis prope Galonsir. B.C.S. No. 592. Schweinf. No. 250. Placopoda viRGATA, Balf. fit., var. nan a, Balf. fil. : nana ramis validioribus et ramulis brevibus prostratis ; foliis plerumque minoribus paucioribus et solum 2-5 in quoque fasciculo obovatis crassiusculis. Socotra, in campis. B.C.S. No. 86, Hedyotis pulvinata, Balf. fil. : pulvinata congesta ; foliis parvis anguste acinaciformibus crassis triquetris imbricatis ; stipulls connatis fimbriatis ; floribus sessilibus axillaribus solitariis ; stylo bifido. Socotra, prope Galonsir abundans. B.C.S, Nos. 15, 719. Scbweinf. No. 716. Hedyotis bioornuta, Balf. fil. ; annua minuta plantaginea ; foliis aggregatis linearibus basi in stipulas connatas paucifimbriatas expansis revolutis minute papillosis ; floribus axillaribus sessilibus solitariis ; stylo bifido ; fructu compresso vertice bifido bicornuto septicide dehiscente ; seminibus foveolatis angulatis. Socotra, prope Galonsir. B.C.S. No. 178. COMPOSITE. Helichrysum graciliBes, Oliv. ^ Hiern, var. lanaTum, Balf. fil, : dense lanatum, pedunculis brevibus, acbeniis glabris Socotra, prope Tamarida. Schweinf. No. 327 Helichrysum gracilifes, Oliv, ^ Hiern, var. profusum, Balf. fil. : foliis submembranaceis, capitulis parvis paucifloris in paniculas ramosas dispositis, pedicellis erectis. Socotra, apud Keregnigiti. Schweinf. No. 470. 406 Proceedings of the Royal Society Helichrysum gracilipes, Oliv. ^ Hiern, var. stoloniferum, Balf. fil. : stoloniferiim capitulis majoribus multifloris solitariis, phyllariis exterioribus brevibus ovatis, interioribus longis spatliulatis acutis. Socotra, in montibus prope Galonsir. B.C.S. No. 238. Nimuio. Tripteris Lordii, Oliv. ^ Hiern, var. racemosa, Balf. fil. ; a basi multiramosa ; foliis plerumque oblanceolatis angustis ; capitulis ininoribus \ poll, longis ; involucri bracteis oblongo-ellipticis acutis ^ poll, longis • floribus flavis radii ligula poll, longa ; acheniis ^ poll, longis. Socotra, prope Galonsir atque Tamarida abundans. B.C.S. No. 74. Schweinf. No. 443. PLUMBAGINE^. Yogelia INDIO a, Gibs., var. socotrana, Balf. fil. : omnino tenuior ; foliis niinoribus ssepe vix perfoliatis et retusis ; infloresc- entia multo pseudo-furcatiin ramosissima, racemis ultiniis 1-2 poll, longis ; bracteolis lanceolatis ; sepalis anguste lanceolatis margine membranaceis superne obscure transverse bullato-undulatis, inferne truncatis ; corollse limbo sinu apicali vix mucronulato. Nom. vern. Salepho. Socotra in montibus Hagbier. B.C.S. No. 416. Schweinf. Nos. 406 in lit., 523. EBENACEiE, Euclea laurina, Hiern: fruticosa j foliis ellipticis v. obovatis suboppositis V. oppositis apice plus minusve rotundatis basi cuneatis breviter petiolatis supra intense viridibus ; racemis axillaribus ; floribus 4- rarissime 3-meris ; corolla anguste cylindrata breviter lobata. Socotra, in montibus Hagbier et apud Galonsir. B.C.S. Nos. 166? 383. Euclea Balfourii, Hiern : fruticosa ; foliis ovalibus v. obovatis oppositis V. suboppositis apice rotundatis basi plus minusve angus- tatis demum plerisque obtusis undulatis supra viridibus infra of Edinhurgh, Session 1883-84. 407 rubentibus resiiioso-lepidotis ] racemis masculis axillaribus ; fioribus 4-meris ; corolla lata campanulata. Socotra, in montibus Haghier. B.C.S. No. 167. Scbweinf. No. 644. ACANTHACEiE. Euellia PATULA,/ac^., var. PUBESCENS,Ea//. dense piibescens, foliis obtusis subrotundis. Socotra. B.C.S. No. 579. Scbweinf. No. 614. Distrib. Nile Land. Epellia PATULA, Jacq., var. minor, Balf, fiL: nana canescens, foliis doribusqiie parvulis ; corolla vix J poll, longa ; fructn \ poll, longo ; seminibus J poll, diam. Socotra. B.C.S. Nos. 270, 728. Anisotes DiVERSiFOLius, Ea//. fiL, var. brevicalyx, Balf. foliis apice angustatis, calycis lobis brevibus ~ poll, longis. Socotra, in montibus Haghier, B.C.S. No. 479. LABIATH^. Teucrium petiolare, Balf fiL, var, pubescens, Balf fill pubescens non incanum ramis folia majora gerentibus. Socotra, in montibus Haghier. Scbweinf. No. 578. GENUS ANOMALUM. Wellstedia, BalffiL Elores bermapbroditi regulares. Calyx alte 4-parti tus, persistens, tubo basi ovario adnato, lobis angustis acutis sequalibus extus ad- presse rigide pilosis. Corolla bypocrateriforniis, tubo cylindraceo extus intusque glabro sub fructu a basi sursum in segnienta 4 rum- pente, limbi lobis 4 ovatis v. deltoideo-ovatis sequalibus extus adpresse pilosis imbricatis. Stamina 4, sequalia, angulis corollm loborum inserta, filamentis liberis subulatis incurvis corollse lobis paulum brevioribus; antberse cordato-rotundatae v. suborbiculares, 408 Proceedings of the Royal Society 2-loculares, lociilis parallelis introrsis rima longitudinali, dorso affixse. Discus 0. Ovarium 2-carpellatum, 2-loculare, compres- sum, integrum, parte triente inf era, inf erne glabrum, superne basin styli circum dense albido-setosum; stylus validus, calycis lobis subsequilongus, adpresse rigide pilosus, bifidus, stigmatibus parvis terminalibus ; ovula anatropa, in loculo quoque solitaria (plerumque in uno abortivum?), ab placentis sub apice septi medii affixis pendula, funiculo brevi. Capsula oblique subobcordata, inaequaliter bilobata, complanata, bilocularia, loculo majore vacuo, angusti-septata, loculicide dehiscentia, valvis coriaceis a septo crustaceo tenui uninervio in loculum vacuum convexo semenque amplectente secedentibus, extus adpressis rigidis pilis vestita. Semen solitarium, septo pendulum, complanatum, obliquum, superne truncatum, inferne acutum, testa tenui comosa; embryo magnus, cotyledonibus carnosis ovatis plano-convexis accum- bentibus radicula longioribus, radicula supera tereti, albumine nullo.— Suffrutex pulvinatus, parvus, ramis congestis, omnino pilis rigidis adpressis vestitus. Dolia alterna, subimbricata, anguste spatbulata v. obovata, obtusa. Stipulse 0. Flores in axillis sessiles, spicas unilaterales breves formantes. Genus monotypicum anomalum pluribus notis Boragineis et Ver- benaceis maxime affine, ab illis fructu capsulari ovuloque pendulo differt, ab his ob cotyledones accumbentes, radiculam superam, foliorum cbaracteres babitumque exclusum. W, socoTRANA, Balf, fit. : species unica in campis Socotrse Insulae crescens. B.C.S. No. 569. Hunter. ILLECEBRACE^. Haya, Balf. fil. Flores hermapbroditi, parvi, ad nodes glomerati, bracteis scariosis stipuliformibus involucrati. Periantbium 5-partitum, album; seg- menta aequalia, oblonga, obtusa, mutica, erosa v. emarginata, tenuia, enervia, basi subcrassa. Stamina 5, basi segmentorum inserta, Btamiuodiis minutissimis alternantia, filamentis subulatis ; antlierae of Edinburgh, Session 1883-84. 409 biloculares. Ovarium parvum, trigonum, membranaceum ; stylus filiformis, elongatus, stigmate capitellato ; ovuluin solitarium, basilare, erectum, anatropum, funiculo longo teretL Fructus tenuis, basim versus in valvas tres debiscens. Semen erectum, ellipsoideum, testa Crustacea; embryo dorsalis, albumine farinaceo applicitus, leviter curvatus, radicula inf era. — Herba, diffuse divari- catim ramosa, glabra. Folia sessilia, 3-verticellata, obovata, apicu- lata, integerrima ; stipulie minutse, ovatse, acuminatse, scariosee. Flores sessiles in dicbasia brevia secunda oppositifolia et axillaria conferti. Bractese parvse, fusco-brunnese, scariosee. Genus monotypicum, Illecebro ipso affine. H. OBOVATA, Balf ill, : species unica in montibus Socotrae fre- quens. B.C.S. No. 250. Schweinf, No. 554. Lochia, Bcdf. fil Flores consimiles bracteis scariosis noninvolucratis. Perianthium herbaceum, demuni induratum, 5-lobum, tubo brevissimo obconico angulato fauee disco tenui annulari instructa ; lobi conniventes, ovato-oblongi, firmi, dorso infra apicem mucronati. Stamina 5, perigyna, cum staminodiis setosis alternantia, filamentis brevibus ; antberse parvae oblongse. Ovarium ellipsoideum, liberum ; stylus filiformis apice bifidus ; ovulum ampiiitropum, funiculo basilari erecto longiuscalo complanato suspensum. Utriculus niembranacens, demum basi ruptus. Semen ab apice funiculi suspensum, inversum, compressum, testa membranacea. — Fruticulus rigidus, salsoloideus, diffusus, caulibus tortis, ramulis intricatis nodosis. Folia opposita et in axillis fasciculata, sessilia, anguste lanceolata v. spiculiformia, integerrima, crassa ; stipulse breves, interpetiolares coniiatse, byalinae. Flores parvi, in dicbasia breviter ramosa terminalia bracteis ob- tegentibus majoribus membranaceis brunneis dispositi, sessiles. Genus monotypicum in sectione Paronycbiearum positum et generi Gymnocarpos affine. L. beagteata, Balf. fil.\ species unica in montibus Socotrse in- frequens. B.C.^. No. 429. 410 Proceedings of the Boyal Society AMAEANTACE^. ^RUA LANATA, Juss., var. ROBUSTA, BoLf.fil.: dense lanata, caulibus robustis ; foliis crassis magnis apice rotimdatis ; spicis elongatis. Socotra, in campis. B.C.S. No, 517. Scbweinf. No. 219. EUPHOEBIAC^. Euphorbia (Anisopbyilum) leptoclada, Balf. fil.: fruticosa, ramulis iiltimis delicatulis articulatis glabrisj foliis omnibus op- positis parvis petiolatis ellipticis ; capitulis miniitis terminalibus solitariis pedicellatis ; involucri glandulis inappendiculatis ; stamini- bus paucis. Socotra, prope Kiscben. Scbweinf. No. 615 partini. Euphorbia (Tirucalli) Schweinfurthii, Balf. fil.: fruticosa, ramis juvenilibus glabris ; foliis sessilibus elongatis linearibus ; cyniis solitariis terminalibus monocepbalis ; involucro extus pubescente, bracteis fimbriatis, glandulis albis ; staminibus paucis. Socotra, prope Kiscben. Scbweinf. No, 650. Euphorbia (Tirucalli) arbuscula, Balf fil., var, Montana, Balf fit.: irregulariter ramosa ramis ultimis brevibus validis, articulis brevi- bus ; capsulis ^ poll, longis J poll, latis, pedicello \ poll, longo tenui ; stylo in fructu brevi poll, longo ; seminibus ~ poll, longis, Socotra, in montibus altioribus. B.C.S. No. 347. Scbweinf. No. 643. Euphorbia (Diacantbium) spiralis, Balf fit.: fruticosa carnosa candelabriforinis a basi pauciramosa 1-2-pedalis, caule ramisque acute 5-7-angulatis sulcatis, angulis compressis subalatis spiraliter tortis rarius rectis lobatis lobis rotimdatis parvis arete positis, aculeis stipularibus binis brevibus -J-i poll, longis ab pulvino basali glauco divaricatis demum frequenter demissis, podariis distinctis. Socotra, in campis freqiiens. B.C.S. No. 729. of EclinhurgJi^ Session 1883-84 411 Securinega Schweinfurthii, Balf. fil.: fmticosa, ramulis sub- tetragonis nonspiiiescentibus j foliis crassiusculis obovatis ; pedic- ellis masculis solitariis. Socotra, prope Wadi Digal Schweinf. I^o. 562. LILIACEiE. Asparagus africanus, AcmA, var, microcarpus, ^a//. : suf- fruticosus, intricate- ramosus, cortice griseo nitido levi, ramulis anfractuosis ; foliis spinosis brevibus poll, longis recurvis ; floribus in umbellis, interdum paucis ; baccis parvis poll. diam. pedicello brevi. Socotra, in campis. B.C.S. E"o. 16. Schweinf. N'o. 374 Urginea porphyrostachys, : bulbo ovoideo ; foliis hyster- antbiis ignotis ; scapo tereti fragili ; racemo laxo elongate, pedicellis solitariis elongatis strictis erecto-patentibus, bracteis minutis lanceo- latis calcaratis ; perianthii parvi segmentis lanceolatis uninervatis albidis dorso late purpureo-vittatis ; staminibus inclusis, filamentis glabris, antheris parvis oblongis ; fructu acute angulato ; seininibus in loculo 2-3 magnis nigris discoideis. Socotra, prope Kischeii. Schweinf. No. 678. CYPERACEEE. Cyperus conglomerates, Bottb., var. socotranus, Balf. fil.: culinus rigidus erectus vix pollicaris subcompressus striatus ; foliis poll, longis culmo longioribus substrictiusculis a basi canaliculatis apice supra subplanis subtus carinatis ; fascicule spicarum solitario apicali sessili tribracteato 2-6-stachyo, bracteis insequalibus spicis brevioribus ; spicis teretibus poll, longis poll, latis, squamis arete imbricatis ellipticis obtusis niucronatis paullo convexis superne carinulatis nmltinerviis basi fuscis. Socotra, prope Galonsir. B.C.S. No. 91. GEAMINE^. Ehynchelytrum microstachyum, Balf. fil., var. albicomum, Balf. fil.: spiculis paullo majoribus glumisque tribus exterioribus dense pilis albis sericeo-piloso-villosis. Socotra, prope Galonsir et Tam arida. B.C.S. No. 124. Schweinf. No. 467. 412 Proceedings of the Poycd Society 5. Abstract of Eeport on the “ Porcupine ” Tunicata. By Professor W. A. Herdman. This paper deals only with the Ascidioe Simpliees collected during the cruises of the “Porcupine” in the summers of 1868- 1870. The Asciidce Compositoe will be worked up along with the “ Challenger ” forms, and will appear in the second part of the Eeport upon the Tunicata of that expedition. Eleven species of simple Ascidians were found in the “ Por- cupine” collection. There are no Clavelinidse, but the other three families are represented — the Ascidiidse by three species, the Cynthiidae by five species, and the Molgulidae by three species. Three species (all belonging to the genus Polycarpa) seem new to science ; the remaining eight are most of them common British species. Some of them, however, possess an interest apart from their morphological peculiarities on account of the localities and depths from which they were obtained. For example, several of the stations are in localities of which the Ascidian fauna had never been investigated, and the depths of which exceed 100 fathoms. Styela grossularia, van Beneden, a common British species, which is usually regarded as a littoral or shallow-water form, was obtained in the North Atlantic between Lewis and the Faroe Islands (Station 54), at a depth of 363 fathoms ! 6. Arrangement of the Metals in an Electro-Frictional Scale. By A. Macfarlane, D.Sc. While, in recent years, the progress of the science of electricity has been very rapid, few investigations have been made in the old province of frictional electricity. It cannot be doubted, however, that the laws connecting electricity with friction, and with the nature of the substances rubbed, are of great importance j and the acquisition of more detailed knowledge in this department may throw some light on the still imperfect theory of the voltaic cell. Several electricians have expressed an opinion that the development of electricity by friction is only a modification of the develupmei.t of electricity by contact — that friction is contact in which the of Eclmhurgli, Session 1883-84. 413 number of points which come together is increased by sliding the one substance over the other. But whether friction is a form of contact, or contact a form of friction, or the two co-ordinate to one another, it is interesting to inquire whether the metals can be arranged in an electro-frictional series similar to the electro-contact series ; and if so, to observe the relation of the former to the latter. What is the present state of our knowledge on this subject ? Experimenters have used one or other of two methods, either rub- bing the metal with an insulating substance, or brushing it with a metallic powder. Observations cannot be made, or at least have not as yet been made with success, by rubbing two metals directly against one another, as their high conductivity allows the generated electricities to combine too quickly. Information on this subject is contained in the treatises of Reiss and Mascart. Haiiy,* rubbing with a woollen cloth, found that the following metals became positively electrified — Silver, lead, copper, zinc, brass, bismuth ; while the following became negatively electrified — Platinum, palladium, gold, nickel, iron, tin, arsenic, antimony. Faraday,! oii contrary, using the same material for a rubber, found that silver and copper became negatively electrified. When these two are taken out of the former list, the four left — lead, zinc, brass, bismuth — are metals which are easily disintegrated ; and that we shall find is the reason why they become electrified in the oppo- site manner from the others. Dessaignes,! also rubbing with a woollen stuff, gives a wholly indefinite result, — that gold, platinum, silver, copper, iron, bismuth, zinc, tin, antimony, lead, are sometimes positive, sometimes nega- tive, and sometimes neutral. He considered that the season of the year, the prevailing wind, the barometer, and the thermometer, all had an infiuence on the result. Fortunately, the subject is not so complex as this experimenter would have us believe; I have found that, provided the insulation and the state of the surfaces be attended to, the season of the year, the barometer, the thermo- meter, and the prevailing wind may be left out of account. It is * Ann. de Chim., vol. viii. (1818). t Exp. lies., art. 2141. + Journal de Physique (1811). 414 Proceedings of the Royal Society possible, however, that the state of the air as regards moisture may have some influence. If the surface of the metal is moist, or the rubber moist, the amount of electricity produced by a rub is not so great as when both are dry. This difference is due, in part at least, and it may be entirely, to the worse insulating power of the moist or moistened rubber. Cavallo,'^ with sealing-wax as the rubbing material, found all the metals he tried negative ; but Singerf found iron, steel, graphite, lead, and bismuth positive, the others negative. The iron, how- ever, was positive only when rubbed with smooth wax; it was negative when rubbed v/ith tarnished (soft '?) wax. WilsonJ found Avith a silver plate, that when he rubbed the Avax on the surface the plate became positive, but Avhen he rubbed it on the edge the plate became negative. Some experiments which I have made throw light on these anomalies. With sulphur as the rubbing material, Davy§ found that lead having a fresh surface became negative, but when it had a tarnished surface became positive. While Wilcke found all the metals nega- tive excepting lead, Faraday found iron, copper, brass, tin, silver, and platinum positive. The contradictory results in the case of sulphur appear to be due to the presence or absence of abrasion in the rubbing, and to the presence or absence of a charge on the sulphur. De la Five, II using a variety of rubbers — the hand, ivory, horn, cork, caoutchouc, resin — found the following metals always nega- tive— Fhodium, platinum, palladium, gold, tellurium, cobalt, nickel; the following mostly negative — Silver, copper, brass ; and the folloAving negative or positive — Antimony, bismuth, lead, zinc, tin, iron. He found great difflculty with his mode of friction in getting either * Treat, of El., i. 21. f Elem. d. Elekt., 21 X Vrieatley'’& Hist, of EL, 144. § Gilbert’s 28 168. 11 Bihliothique universetle, 59, 13. of Edinburgh, Session 1883-84. 415 lead or bismuth to become positive. Hard rubbing was doubtless the cause of his anomalies also. The method by metallic powder was employed by Singer* and Becquerel. The former experimenter allowed the powder to fall through a sieve of haircloth, flannel, or muslin. He found the powder always negative, whether it was of copper, iron, zinc, tin, bismuth, antimony, nickel, or graphite. Here the friction was gentle, and in consequence no anomaly. Becquerelf experimented with filings of copper and of zinc. He allowed the filings to fall on a slant plate (in connection with the earth), and to drop into a metallic receiver attached to the knob of an electroscope. He found that the copper filings were positive, when the plate was of Copper, zinc, lead, tin, iron, bismuth, antimon}^ ; and without any sensible charge when the plate was of Platinum, gold, silver. With zinc filings, the following were negative — Platinum, gold, silver, copper, graphite ; and the following positive— Zinc, iron, bismuth, antimony. These results, so far as they go, agree very well with those I have obtained, and that agreement proves that the metals may be com- pared by rubbing them all with one suitable substance. Hone of the investigators mentioned place the metals in a scale ; Becquereks results place them in three groups. The only scale which I have found published is a qualitative one by Gaugain. He experimented with discs of about 7 cm. diameter, formed of gutta percha, and gutta percha rubbed for a greater or less time with sulphur. He rubbed such an insulating disc with wires of the different metals ; and the place of the metal was determined by the kind of electricity produced and retained on the disc. The scale or rather classification is as follows — Aluminium — Gutta percha. Ho. 1. Elem. de Elekt., 1819, 199. + Ann de Chim. et de Phys., 47, 116. 416 Proceedings of the Royal Society Lead, cadmium, zinc — Gutta percha, l^’o. 2. Iron, tin — Gutta percha, No. 3. Copper, bismuth — Gutta percha, No. 4. Antimony — Vulcanised caoutchouc. Silver — Gutta percha. No. 5. Platinum — Gutta percha. No. 6. Mercury, gold, palladium. The upper end of the scale is the positive, and the lower end the negative. This arrangement of the metals differs from that which results from my experiments chiefly in the position of tin, bismuth, and antimony. The positions of the latter two are contradictory to Becquerel’s results. In the experiments which I have made I have aimed at getting quantitative results. With an electroscope to scrutinise the electri- city produced, only qualitative results could be looked for ; but with an electrometer to scrutinise the electricity, more definite in- formation is possible. I had the advantage of the use of a Thomson quadrant electrometer, and not only so, but of all the scientific con- veniences of Professor Tait’s laboratory. The metal to be rubbed was constructed in the form of a circular disc (fig. 1), with a projecting tongue for allowing it to be screwed on to the brass top (s) of a glass insulator {g) (fig. 2). The diameter of the disc was in each case 2*5 inch (6 ‘3 cm.), and the thickness two-tenths of an inch (5 mm.). Some of the discs varied slightly from that thickness ; but a small difference in thickness does not affect the capacity of the disc, for the capacity of a disc depends only on the diameter (Clerk-Maxwell, El. and Mag.^ vol. i. p. 222). A of Edinlurgli, Session 1883-84 417 small pin (h') in the brass top passed through the smaller hole (li) in the tongue of the plate, so that when the disc and top were screwed together by a screw passing through (s), the disc was prevented from rotating when brushed. The end of the wire {lo) (fig. 3), connecting the disc with the electrode of the electrometer, was screwed in between the head of the screw and the disc. To obtain quantitative results, it is necessary to be able to give the disc a constant rub. I found that a small camel’s-hair brush forms a very convenient rub- ber. The hair is a snfhciently good insu- lator, not very difficult to discharge after a whisk across the metal, and it does not scratch the metal — a most import- ant consideration. I always gave the disc a single whisk — never a plurality — for one read- ing. I drew the brush across the middle zone {z) (fig. 3), exerting 'as 418 Proceedings of the Royal Society far as possible the same pressure each time, and moving with the same velocity. Variation in velocity produces very considerable variation in the amount of electricity produced, or at least left after the operation. It is also necessary that the brush be spread out to an equal extent in the successive whisks. I found that by first placing the brush in position at the side at a constant angle to the disc, and then moving it across with due regard to pressure and velocity, that a set of successive readings has very considerable constancy. Tor example, the following for copper, taken at random from my note-book AVhisk.. heading. Difference from Ho, 1. no + 2-5 2, 100 - 7‘5 3. 110 -p 2*5 L 90 --17-5 5, 125 + 17-5 6, 110 -f 2-5 7, 90 - 7-5 8. no -f- 2-5 9. 115 + 7-5 10. 115 4- 7-5 Mean, 107 '5 The differences are fairly alternate in sign, and the mean of the readings may with reason be assumed as giving the effect of the rub aimed at in the ten trials. However, I found later on that the readings tend to increase as the succession of whisks goes om It may be asked, Does the brush change in power after making a considerable number of whisksT De la Eive in his memoir cautions us when rubbing with a stick of wood to use a new stick each time, or else to scrape the surface used with a bit of glass. Were it necessary to use a new brush each time, then to make the thousand and half observations which I have made would be a matter of expense. When the brush is heated slightly before the fire, it produces a larger deflection than when it is not heated. For example, after I had finished the series of readings for copper, given above, and similar series for zinc, tiu, iron, and lead, I held the brush of Edinhurgli, Session 1883-84. 419 for a minute before a strong fire, and then took three readings. The deflections were — 195, 215, 220, giving an average of 210, which is nearly double the previous average. Hair is known to be highly hygroscopic ; the heating drives off the moisture, and the brush, when brought to the electro- meter, is found to be electrified positively. Flannel, after being warmed before the fire, is also electrified positively. These facts seem to favour the idea that electricity is produced by evaporation. It is not advisable to have the brush very dry, for it is then more troublesome to take away the charge from it before using it a second time. In the record of results appended (Table I.) I have entered all the average readings obtained. Each entry is the average generally of ten deflections, sometimes of fifteen and of five. The number of single observations made is upwards of one thousand. The course of the experiments breaks up into four series. In the case of the first series I experimented with a disc of copper and a disc of zinc, each of which had one side highly polished. The two averages for zinc obtained on the 26th Novem- ber are nearly equal to one another, and to the average of all the average readings. It is necessary to choose a standard number for one of the metals, and to compare the others with it ; hence copper is always taken as 100. The electrometer was duly replenished each morning, and all the conditions were preserved constant as far as possible ; but various circumstances caused the magnitude of the deflections to vary considerably from day to day. The first entry of 26th November was got by observing the first swing of the electro- meter, the second by observing the permanent deflection. In all the subsequent observations it was the permanent deflection which was noted. One side of the copper disc was not so highly polished as the other; the rougher side gave an average of 123; the more polished taken subsequently gave an average of 126. I do not con- sider this comparison as conclusive ; for I afterwards found that a disc of copper gave a decidedly larger deflection than a disc of brass copper-plated; and one of the differences between the two discs was, that the latter had a much smoother surface. Another expe- 2 E VOL. XII. Table L — Record of Mean Results, 420 Proceedings of the Poycd Society German Silver. 32 32 1 Magne- sium. 49 41 45 Alu- minium. (M CO O 50 Anti- mony. CO CO aj oa xo 38 Bis- muth. CO 1-^ OJ rH (M 22 Platinum 136 136 Nickel. • . lO ^ ^ 59 Silver. i-HOiO- l(OOCO.oot cicaoocoo i-H r-^ 1 — ^ oa o Gold. 1 CO • CO - CO o ; oi ^ 05 CO I— I o rH rH r-( r-l rH (M (OS I— 1 OO CQ CC • * • • (05 -(j< io ; : : : : . . . CO lO lO ..... 05 iO .s • * • *00^1—1 t^OOO-H UOCO(35»-H • • • -CO r ; : :coo(os r-i oo i~i a> oo oo : ^ r-lrHr-(r-lr-(rH r-( ^ 126 Iron. • • -OOOOiO t-I.-HC rH ^ 100 4^ c coco •'05 «-ch O CO •'CM -CO -cH -(^CRO -rH OO cj ........................................ ‘I soriog -j]; soiiog -jj;j sapiog souog Final Mean of Edinburgh, Session 1883-84. 421 riment was made with the copper disc with the view of ascertaining whether an increase of temperature had an effect upon the amount of electricity produced by the whisk. The disc was heated to such a temperature that it could not he held in the hand with any degree of comfort ; the deflections were — 100, 100, 120, 85, 170, 170, 105, 115, 155, 165, 180, 145, 120, 180, 200, giving an average of 140, compared with 126 before heating. When a brass disc was heated in a similar manner, the average deflection was increased in much the same proportion. It is not improbable that the effect is due to the heat of the disc increasing the insulation of the brush (see p. 428). On the 29th hTovember the surfaces of the discs were polished with a fine sand paper. The several observations were — Copper, 215, 220, 210, 150, 167, 165, 140, 165, 165, 215, 145, 180, 215, 185, 140. Zinc, 35, 70, 80, 70, 90, 40, 110, 75, 45, 110, 70, 85, 90, 65, 75, 110. The average for the copper is 178 ; for the zinc 45, if the first read- ing is not taken into account and the last is, and 42 if the first is and the last is not. The smallness of the first deflection is to be attributed, I believe, to a few of the minute particles of zinc or of sand produced in the cleaning process still remaining on the surface of the metal. Many of the subsequent experiments were made with the view of clearing up this effect, and the still greater effect gene- rally produced when zinc is polished with emery paper. The second series of observations were made with coins and a platinum capsule, while discs of other metals were being prepared. A half-sovereign (11/12 fine gold), a sixpence (37/40 fine silver), and a cent (88 Cu to 12 Ni), are of nearly equal diameter, and therefore of nearly equal capacity. If the cent be taken as 100, the sovereign is 123, and the sixpence 71. The second comparison was obtained by taking a florin and a penny (95 Cu to 4 Sn and 1 Zn) ; the result obtained by supposing the bronze equivalent to copper gives a result for silver (109), which agrees well with the best strict com- parison (107). The result of 4th December, gold to silver as 193 to 422 Proceedings of the Royal Society 100, was obtained by comparing a sovereign and a shilling; it agrees well with the ratio obtained afterwards. The surfaces of the coins were cleaned with hath-brick and wiped against flannel; in no case were the readings anomalous at the beginning. The com parison obtained for platinum is only an approximation. It was obtained by comparing a small platinum capsule, kindly lent me by Mr H. K. Mill, with a florin and a penny. The true value is pro- bably nearer to that for gold. In the third series of observations I made many comparisons with discs of copper, zinc, lead, iron, tin, and brass. The reason why so many comparisons were made was to clear up an anomaly which appeared when the surfaces were polished with emery paper. In the case of the observations of 6th December, one side of each disc was rubbed with emery paper, and then wiped with a dry flannel cloth. The copper disc was first tried ; it gave readings none of which differed greatly from the average, namely, 147. But the zinc disc when taken gave on the first whisk + 110,* on the second + 45 ; after a few whisks the deflection vanished, then became negative, and gave a series of ten readings agreeing closely with their average, 95. The iron disc also gave a positive deflection at first -f 80; it likewise changed after a slight brushing, and gave ten readings agreeing pretty well with their average, 71. When a fresh part of either of these discs was rubbed, the deflection became positive. In the case of the lead disc the deflection was considerably smaller than the average at the beginning. In the ct "e of the copper and the tin discs there was no such marked irregularity ; but the average of a series for copper taken at the end, 187, was greater than the average of the series taken at the beginning of the observations, 147. The values entered in the upper line for the 6th are obtained by giving copper its initial average, and those in the lower line by giving it the final average. Next morning, 7th December, no emery paper was used; the sur- faces were merely rubbed with a piece of white flannel which had been well dried. The copper disc gave regular negative deflections as before, but the zinc disc gave a positive deflection at first. After a few brushings across the middle zone of the disc, the deflection became negative, and remained about an average. The first read- 'When no sign is put before a number, the sign - is to be understood. of Edinhurgli, Session 1883-84. 423 ing for tin was smaller than any of ten subsequent, and such was the case also with the brass ; they were noted, but not included in the average. Two series were taken for lead, the former for the side which had been roughened by polishing, the latter for the side which had not been interfered with : in both cases the first whisk gave a nearly null deflection, but the deflection afterwards became pretty steady about an average. To further elucidate the cause of this initial phenomenon, I rubbed each disc several times with a piece of flannel stretched over my forefinger. The electricity was not discharged after each rub, but was allowed to accumulate : — Disc. Electricity. Lead (rougher side), . positive. Copper, negative. Zinc, • • T> Tin, ' V) Iron, " J? Brass, . negative, with trace of positive at first. The lead disc was tried again, using the same side, and rubbing with what was noted to be a specially clean part of the flannel. It became negative at first, then positive after several rubs with considerable pressure. The same operation was repeated, and with the same result. The more polished side was then tried ; it was negative at first, and greater pressure in rubbing was required to produce positive. Hence, the anomalous electricity produced on the lead is undoubtedly due to the fact that the rubbing with the flannel cloth abraded the lead (or the oxide of lead), as was indeed evident from an inspection of the cloth after the operation. And these trials also show why lead and bismuth and graphite wmre so prone to become positive under the friction to which they were sub- jected by De la Eive and the other experimenters. The ease with which these substances make a mark on paper shows that they can be easily abraded ; and when the rubbing is so violent as to cause abrasion, anomaly may very well be expected. The camel’s-hair brush changes the electricity not from nega- tive to positive, but from positive to negative. It certainly does not abrade the surface. Does the explanation of the anomaly con- 424 Proceedings of the Royal Society sist in this, that the brush sweeps away abraded particles which have been left by rubbing with emery paper and flannel cloth, or with flannel cloth alone, that so long as any of these particles are in its course the deflection is more or less altered in the positive direction; and that after they have all been swept off by a few whisks we get the true unimpaired reading ? I believe that that is the proper ex- planation. On 12th December the surfaces were prepared by rubbing with dry bath brick and flannel, Zinc, iron, and lead were positive at first ; the zinc most, the iron next, and the lead least, and the zinc required the greatest amount of whisking to change it to negative. In case of 13th December the discs were merely brushed with a large soft brush before beginning. The zinc was at first slightly positive. The readings were not so satisfactory as usual on account of imperfect insulation due to very moist weather. On 14th December the discs were rubbed with warm flannel. Only the zinc and lead gave positive deflections, the former more persistently than the latter. The copper disc was then rubbed with sand paper, and the following series of observations taken, the first before the disc had been brushed in any way : — Eepeated Brushing. 60 no 50 115 115 120 Mean 55 Mean 115 Eepeated Brushing. Repeated Brushing. 105 125 105 116 no 118 106 125 Mean 106 Mean 121 The brushing was done by the brush used to make the readings. The first brushing has much more effect than any of the subsequent ones ; and this favours the idea that free particles of the metal are of Edinburgh, Session 1883-84. 425 removed by it. When the zinc disc was rubbed with sand paper and treated similarly, the following series of observations was obtained : — Eepeated Brushing. Eepeated Brushing. + 10 +23 0 + 28 +12 10 + 27 0 + 15 0 Mean +19 +19 2-5 The observations of 17th December, given in full in Table II., may be taken as illustrative of the other sets of observations. The morning was frosty, the stem insulated without being dried, the brush was heated slightly before beginning* The former series was taken with the discs as found ; and the latter, after the discs had been polished with emery paper and cleaned with flannel. The order of entry is the order in which the observations were made. It will be observed that the initial and final readings for zinc in the first series are nearly equal, showing that the state of the brush was practically constant throughout. In the case of the second series, four readings were first taken, then the disc was whisked with the brush backwards and forwards across the middle zone about a dozen times, and then six more readings were taken. The order of the metals is the same, whether the former or latter mean of the second series is taken — zinc, lead, iron, copper, tin, — and this order agrees with that deduced from the entire collection of observations, except- ing that lead is more negative than iron. The comparisons entered for 18th December were obtained without rubbing the discs previously. The order is the same as the latter order of the previous days, excepting that tin comes out less than copper, which I believe to be erroneous. On the 19th the discs were previously rubbed with chamois leather. Zinc and lead were at first positive. On these two days an experi- ment was made with the zinc disc. On the former day it was rubbed with emery paper and chamois leather, and the mean of the first four readings was +111. By repeated whisking it was brought down to zero, and changed to negative. The disc was again rubbed with emery paper and chamois leather, tested once, and found to 426 Proceedings of the Royal Society Table II. — Observations of \lth December, First Series. — Discs without being polished. Zinc. Copper. Iron. Tin. Lead. 105 330 35 175 + 25 100 238 45 160 38 103 256 82 160 70 112 345 80 190 Whisked 125 260 65 165 with brush. 107 245 70 170 160 127 280 70 150 155 105 213 95 190 170 125 265 65 140 220 115 210 90 155 138 178 115 200 140 130 Mean 112 ‘4 264-2 69-7 165-5 160-6 Tin again, whisked repeatedly with brush before beginning. Iron again, wliisked repeatedly with brush before beginning. Zinc again. 185 80 110 225 78 125 210 90 110 210 90 148 180 120 127 175 98 132 195 105 95 170 105 100 215 90 115 205 95 120 Mean 197 95-1 118-4 Second Series. — Discs after being polished. Zinc. Copper. . Tin. Iron. Lead. + 190 150 195 50 0 + 125 180 245 110 25 + 85 187 195 88 40 + 70 160 188 85 35 Mean + 118 169 206 83 25 Whisked. Whisked. Whisked. Whisked. Whisked. 100 180 210 88 110 80 195 160 145 120 78 240 220 140 110 90 217 245 145 80 105 220 210 120 115 80 185 240 110 100 Mean 89 206 214 125 106 of Edinburgh, Session 1833-84. 427 give a positive deflection about the magnitude of the above, and left untouched till next day. When tested next day it gave a read- ing about +52, and after considerable whisking the positive deflection vanished and changed to negative. The result of this experiment favours the idea that the positive electricity is due to the existence of minute particles on the surface of the disc. On 20th December further experiments were made to elucidate the effect of rubbing with emery paper and with sand paper. The rubbing paper was attached to the end of a glass rod. Emery Paper. 1 Sand Paper. 1 Copper, + very slight. + more than with emery. Tin, . 0 - Iron, . + more than copper, less than zinc. 0 Zinc, . + 0 Lead, + less than zinc. + more than with emery. I scratched the surface of the zinc disc with emery paper ; when the scratch was rubbed with the brush positive electricity was ob- tained, but after the scratches were rubbed a few times the electricity became negative. This experiment indicates with what care ob- servations must be made in this subject in order to obtain definite results. The fourth series of observations were taken up with gold, silver, nickel, bismuth, antimony, aluminium, magnesium, German silver. The first three are in the form of discs of brass electro plated. The aluminium and magnesium are cut out of thin sheet metal, and are screwed on to a disc of brass. The electro^plates were on the 20th, 21st, and 27th compared with the disc of copper, but on the 28th with a similar electro-plate of copper. It was found that the copper electro-plate gave only two-thirds of the deflection given by the copper disc ; the entries for the previous days have been corrected by multiplying by |, the other discs are compared with the disc of copper. On 20th December the electro-plates were rubbed with clean chamois leather before beginning, and they were whisked a few 428 Froceedings of the Royal Society times with the brush before any readings were noted, as the deflec- tions appeared too small. A new brush was used. Two series of observations were taken; in the former case the copper was observed before the electro-plates, in the latter after the electro-plates. On 21st each disc was rubbed with chamois leather beforehand. The bismuth was null at the first whisk, the antimony was negative. On 27 th December an elaborate system of readings was taken. The entries in Table I. are deduced from the following four series of means : — 1st Series, after being rubbed with chamois leather. 2nd Series, after brush was heated slightly before the fire. 3rd Series, after being rubbed with warm flannel. 4 th Series, after being heated before the fire. Copper (disc), 101 309 319 Gold, . 79 228 192 212 Silver, 36-6 83 129 184 Nickel, 3 39 50 56 Antimony, . + 38 70 Bismuth, + 20 56-5 + 2 48 Aluminium, 35-3 119 Magnesium, German Silver, 49-6 + 77 28 109 The electro-plates had been lying in a cold room since the 21st, and they were very moist when first taken up. This moisture on the surface probably explains why the ratio of silver to copper and of nickel to copper, changes so considerably. The other discs were brought from a warm room. I consider that the positive values entered are due to the existence of small particles of some kind on the metal. The observations taken on the 28th are given in full in the accompanying table (Table III.). After the first five readings the disc was commonly whisked half a dozen times or so with the brush used. I have marked when this wms done. It had the efifect of increasing the reading. All the discs were brought from home, and a new brush was used. It will be observed that the mean for the copper electro-plate is less than for the copper disc ; the result deduced from the different ratios is 2 to 3. In the second series only bismuth gave positive deflections, and these were soon changed to negative. Zinc was negative from tlm first, and repeated whisk- 429 of Edinhiirgh, Session 1883-84. ing by the brush did not alter the mean very much. The value obtained, 42, does not differ much from the final mean, 45. This result gives strong support to the explanation given in this paper of the occasional positive electricity produced in zinc and some other metals. Table III. — Observations of 2^tli December. First Series. — After being rubbed with warmed chamois leather. Copper (disc). Gold. Copper (el. -pL). Silver. ISTickel. 105 128 60 70 48 105 130 70 68 44 105 145 80 75 48 128 180 75 80 45 138 170 70 85 44 Mean 116 151 71 76 46 Whisked. Whisked. Whisked. 145 230 110 120 78 165 200 117 105 87 157 225 100 110 75 140 200 105 115 73 175 228 105 115 80 Mean 156 216 107 113 79 Second Series. — After being cleaned again. Copper (disc), Copper (el.-ph), Tin, Antimony 1 with emery with warm with emery and flannel. flannel. and flannel. by hand. 76 80 210 65 103 90 190 60 130 83 188 78 130 88 190 80 145 100 200 78 Mean 117 88 196 72 Whisked. Whisked. Whisked. 200 105 210 180 108 170 Aluminium, 200 115 200 chamois leather 190 104 and hand. 150 103 Mean 193 95 Mean 184 107 Reverse Side. 73 240 78 315 84 240 90 1 Mean 265 Mean 84 430 Proceedings of the Royal Society Table III. — Second Series — continued. " Bismuth, flannel and hand. Magnesium, emery, flannel, hand. Zinc, emery, flannel, hand. + 20 28 55 + 46 45 54 + 35 53 30 + 32 40 50 + 15 58 80 70 Mean +30 80 Mean 54 76 1 Whisked, gave Whisked . negative electricity. Mean 56 60 28 50 SO 44 18 30 0 Mean 46 + 20 .^10 Whisked. 60 70 30 60 60 Mean 36 50 1 1 1 Mean 60 On the 27th the following observations were taken (Table IV.). With flannel for the rubber only lead and bismuth were positive, Table IV. Flan- nel. Hand. Sub phur. Caout- chouc. Sealing Wax. State of Metal. Gold, . + No scratches. Tin, - - + + + Wax and other. Copper, . - - + + + Wax. Silver, . - - + + - Few wax. Lead, + - + + + Wax and other. Brass, . - - + + - Wax. Iron, - - + + + Many, mostly wax. Zinc, Nickel, . - - -!■ + + Wax and other. - or + (very small) + + + None. Antimony, - - + + - N one. Bismuth, + + + + + Wax and other. Aluminium, . - - + + + Wax and other. Magnesium, . - - + + + Wax and other. German Silver, ~ + + None. with the hand only bismuth. These are undoubtedly anomalies, caused, I believe, by the abrasion of the metal. The exceptional of Edinburgh, Session 1883-84. 431 result for gold, when caoutchouc was the rubber, is doubtless due to an error in entering the result. But with sealing wax as the rubber we have varying signs. When the electricity of the rnetal was negative, there was no red scratch (a very little in the case of silver) left on the metal ; when the electricity of the metal was positive, there was a red scratch, excepting in the case of nickel. I conclude that the electricity of the metal is normally negative, but that when the wax is abraded it is changed to positive. By taking the average of all the averages, we get the values in the bottom row of Table I. ; they are exhibited graphically on the accompany- ing scale. The order of the metals here exhibited is not an arbitrary order ; it agrees pretty well with the order in which the chemists arrange them, with respect to their affinity for oxygen. This was observed by Professor Tait at an early stage of the experiments. The metals of the iron group are found close together, and their order among them- selves is also significant. The metals of the copper group are found together, but of these lead is at a considerable distance from the others; the entries for that metal, however, vary consider- ably. Platinum and gold are next one another ; the value for the former is as yet only approximate. The chemist classes tin along with antimony and bismuth; the two latter are found to- { 181 All - l=S O fH o g .S 136 Pt-- 126 Sn-- 102 100 p p O O) jp Ph O Q Ag-- Cu-- I 62 Pb - f 59 Ni- 56 Fe- o 50 Al- I 45 Zn - L 42 Mg - r 38 Sb- S ^ 1 .g p ^ 32 to I <1 L 22 Bi- - Brass. -G.S. 0 ELECTEO-FRICTIONAL SCALE. 432 Proceedings of the Royal Society gether and at the positive end of the scale, while tin is nearly at the negative end of the scale. The results of Becquerel may be deduced from this scale, with the exception of the position of tin and of iron. He agrees in making antimony and bismuth positive to zinc. For the sake of comparison, I exhibit the electro-frictional series, deduced from this scale alongside of three other series which we should expect to have an intimate resemblance. Table Y. Electro-Frictional Series. Electro-Chemical Series, by Berzelius. Electro-Contact Series, by Hankel. Electro-Contact Series in Air, by Ayrton and Perry.* Gold. Antimony. Platinum. Platinum. Platinum. Gold. Silver. Copper. Tin. Platinum. Gold. Brass. Silver. Silver. Copper. Iron. Copper. Copper. Iron. Tin. Lead. Bismuth. Bismuth. Lead. Brass. Tin. Antimony. Zinc. Mckel. Lead. Lead. Iron. ISTickel. Tin. Aluminium. Iron. Zinc. Zinc. Magnesium. Antimony. Bismuth. Zinc. Aluminium. Magnesium. Aluminium. It will be observed that the principal diversity consists in the positions of antimony, bismuth, and tin — all metals of the antimony group. As regards crystalline form, tin differs from the other metals comprised in the electro- frictional series; it belongs to the quadratic system. Silver, gold, copper, iron, lead, which are found together in the series, belong to the regular system of crystals ; while antimony, bismuth, zinc, magnesium, which ai’e also found together, belong to the rhombic system. The last four metals also agreed in exhibiting the greatest tendency to be positive at first. BUSINESS. Dr Francis T. Bond was balloted for, and declared duly elected a Fellow of the Society. Trans. Roy. Soc., vol, clxxi, p. 34. of Edinbitrgh, Session 1883-84. 433 Monday, 21st January 1884. EOBEKT GEAY, Esq., Vice-President, in the Chair. The following Communications were read : — 1. On Distant Vision. By E. E. Maddox, M.B., C.M. Communicated by Prof. Crum Brown. I believe it is universally assumed by English physiologists that the zero of accommodation is naturally associated with parallel visual axes as in the “ Primary Position ” of Helmholtz, Listing, &c.* It is self-evident that when even in actual life a body is viewed at infinite distance the visual axes must be parallel. It is also well known that the nervous connection between convergence and accommodation is a most delicate and susceptible one, and is none the less so naturally because it is capable of being overcome for a time by various conditions. It is therefore quite reasonable to suppose that when the ciliary muscle is at rest the converging mechanism should be so likewise ; and to expect that the invariable association of the visual actions of a life-time should be impressed, if not at birth, as Porterfield suggested, “ by an original, connate, and immutable law,” at least by “ dint of habit,” upon the very constitution of the governing ganglia. That this is not the case will be evident from the following experiment : — Let two small round holes be made through a piece of paper, nearly two and a half inches apart. Hold them hori- zontally about six inches before the face, and look through the left hole with the left eye at some very distant object. Four images now, of course, appear as shown in fig. 1. Each hole throws a direct image nearly upon the macula of its corresponding eye, and another image obliquely upon the outer part of the retina of the opposite eye. The appearance which results is represented in fig. 2. The two * “In investigating the movements of the eyes, we take as a normal point of departure a position of the eyes which corresponds to a minimum of inner- vation of their muscles. In this position, which is called the 'primary position, i the visual lines are directed straight in front, parallel to each other, and in ' the same horizontal plane.” — Landolt. 434 Proceedings of the Royal Society direct images wliich fall nearly upon the retinal extremities of the visual axes are mentally referred close to the middle line in obedience to Bering’s law (quoted and supported hy Helmholtz), that points looked at in space are referred to a line drawn from the root of the nose to the junction of the visual lines. Thus the hole A may be referred to c, and the hole B to d. The two indirect images are referred to the outer side of the hole which gives rise to them. Thus the image of the left hole A, upon the retina of the right t Fig. 1. eye, is mentally referred to e, and the image of B to /. Heglecting for the present the lateral false images, it is easy to make the holes at such a distance that the two central false images c and d either coincide as in fig. 3, or appear in the same vertical line as in fig. 4, in which case a slight obliquity is given to the paper, though it remains in the same plane. Each hole is now exactly in the visual axis of its corresponding eye, and were these axes parallel, this would he a simple method of obtaining what Bonders has called of EdinhuTgli, Session 1883-84. 435 viie “ interaxial distance.” This, indeed, was my purpose in trying it. With parallel axes, moreover, the position of the false images should be unaffected by making the paper approach or recede, for accommodation is still negative, and the left eye looking at a distant object. In reality, however, if the distance of the paper be either increased or diminished, the two central false images separate in proportion. A piece of red glass held in front of the right hole e c d f Fig. 2. e cd f ® # S Fig. 3. / d Fig. 4. e d f e ® o 0 c Fig. 5, fe d f ® ® O o c Fig. 6. colours the right lateral image and one of the median ones, and shows that when the paper is made to recede, the red image travels to the right of the other, as in fig. 5, and when it is made to approach the red one travels to the left, as in fig, 6. From this it is clear that the visual axes are convergent. It may be objected that the 9 VOL. XII. F 436 Proceedings of the Royal Society left eye only is looking at a distant object, and accommodation may not be entirely suspended in tbe right eye, in spite of the assertion of Bonders that accommodative effort is always the same in each eye. This objection would be met by the fact, that when the two central images are in the same vertical line as in fig. 4, distant objects are seen in each which are really separated by an appreciable horizontal interval. It is difficult to represent natural objects diagrammatically in the holes ; but if we let them be repre- sented hypothetically by two vertical parallel lines at infinite dis- tance, one red and the other blue, the red line would appear in one hole and the blue one in the other, as in fig. 7. In this both eyes c © © d f Fig. 7. Different objects are seen in c and d. Blue. 1 Red. Two hypothetical lines at infinite distance. e c d f % ©© ® Fig. 8. The same object is seen in c and d. are fixing distant objects. Again, when the images of the holes appear to be separated, as in fig. 8, the same object may be seen in each. The distance between the holes in this case repre- sents nearly what would be the true interaxial distance when the axes are parallel (fig. 9). It is even possible for the two holes to continue separate for a little time when made exactly level, though usually they rush together without much delay. The simple ex- periment, with modification, is also available to determine the obliquity of the intercentral line, and the slight obliquities of the respective meridians of the two retinae with the eyes at rest. For this purpose I make the holes through a piece of cardboard. of Edinburgh^ Session 1883-84 437 and fix a small spirit-level parallel to tlie line which joins them. The results of these experiments I must defer. It remains to Fig. 9. Position of two eyes when looking at the two holes, as in fig, 8 (exaggeruted). V = visual axis of each eye. The left eye is looking direct at the left hole, hut the right is somewhat convergent, so the image falls on x instead of on z, and is referred in consequence outwards. Centre of Eotation, c. 177 mm. behind centre of optic axis (Bonders), Principal optical centre p. The optic axis o” (left eye) is seen not to coincide with the visual axis V. estimate the exact degree of convergence which is naturally asso- ciated with negative accommodation. To this end I have made use of a kind of camera devised for another purpose, and find with my own eyes that convergence 438 Proceedings of the Royal Soeiety occurs to 1°, so that while accommodated for infinity^ the eyes direct their visual axes to a point nearly 12 feet distant. Suppose, now, the eyes are accommodated for an object at the distance of 12 feet. Surely now the accommodation and convergence will coincide ! No ; the right eye rolls inwards another 40'. The optic angle is therefore 1° 40'. It is easy to calculate trigonome- trically, knowing ray own intercentral distance, that the visual axes must now intersect rather more than 7 feet from the eyes, while accommodation takes place for nearly 12 feet (11 feet 8). The slightest increase of accommodation is associated with a sympathetic advance of convergence, and there is a decreasing interval between the two. The excess of convergence over accom- modation diminishes as the object of view approaches till a certain point, when they both coincide. This point in my own case* is 56 inches distant. As the visual object approaches still nearer, convergence fails to keep pace with accommodation. With each increment of accommodation throughout there is a corresponding increment of convergence, but a smaller one. It is like a long- legged and a short-legged competitor in a race, in which both are bound to keep step, the shortdegged having a start, but the long- legged winning in the end. Being somewhat hypermetropic, my convergence would be expected to exceed my accommodation when the latter is negative, but strangely I have found the excess greater in most normal eyes I have tried than in my case, and to vary from 4° to I have not been able to experiment on many, but I have found it quite as much in one or two myopic patients. It raises the question, What is the position of rest of the eyes which they would assume in sleep ? I think it may be accepted as extremely probable that it is the natural condition of brain centres, at least those connected with the eye, to evolve some nerve energy, even in sleep. It is impossible for most people to relax their ciliary muscle completely without a distant object to look at, and even the faculty claimed by some oculists to be acquired by training, is received by their brethren with much incredulity. Evidently the degree of convergence, though it does not coincide with accommodation, is closely affected * I am unable to continue experiments on myself. of EdinhuTfjh, Session 1883-84. 439 by the latter. It may altogether he laid aside that the primary position of the eyes is that of rest. Landolt says — “ It is impossible for any one who has not practised to that end to give his eyes a direction absolutely parallel, especially in strabismus.” How he arrived at this result I do not know, but probably with the inge- nious apparatus of Javal, which requires a candle near the patient’s face and a dark room. Convergence without any definite point of view, therefore, must probably be considerable. Even the centre for the contraction of the pupil by light, which is regarded as a typical example of a reflex instead of a tonic ganglion during waking hours, is not improbably a tonic one naturally, for the pupil is semi-contracted during sleep, and dilates the moment a person wakes up. Whenever a distant object is viewed, impulses must ascend from the retina to inhibit reflexly the ciliary muscle, for it has no antagonist. It is just as easy to extend the process to the centre for the contraction of the iris, and suppose that the activity of some other centre exerts, during waking hours, an inhibition over the tonic moiety of nervous energy for the sphincter pupiili. This indeed might throw light upon the Argyll Robertson symptom of locomotorataxia and spinal myosis in general. It is impossible at present to decide, but I am inclined to believe that the position of rest for each person is that point of space for which accommodation and convergence are equal. Opinions, however, will probably vary between this point and others at a greater distance, but none will entertain parallelism. These facts increase the difficulty of ascertaining the exact inter- axial distance between the two eyes ; indeed, the name would be better changed to intercentral distance, as I have taken the liberty of doing in this paper. A glance at fig. 8 will show that the condi- tions would not be altered in the least, if the holes were drawn out into two parallel tubes, since the object is at practically infinite distance. If a screw were adapted to these tubes for their mutual approximation, or the reverse, they would resemble the visuometer for determining the interaxial distance. It is conceivable that many subjects might aver that they saw the same object through both tubes, when in reality the objects were not completely fused. The error introduced is due to the fact 440 Proceedings of the Royal Society tliat tlie principal optical centre of the dioptric apparatus is more than 7 mm. anterior to the centre of rotation. In the following table I have estimated the degree of error for each of conver- gence with distant vision. It is seen to be very trifling, and to reach half a millimetre only with 4° of convergence in emmetropia. In myopia the error would he greater. 0° 30' ‘06465 mm. 3° 30' ■4221 mm. r '12635 mm. 4° ■5050 mm. r 30' T895 mm. 4° 30' *568 mm. 2° '2527 mm. 5° •631 mm. 2° 30' '3158 mm. 7° 56' 1 mm. 3° ■3789 mm. error is avoided by the practice of shutting each eye in It may be suggested that the eyes tend to take the position in which their optic axes are parallel, rather than their visual axes, but this would not account for the convergence of myopes in which the two axes coincide ; and in my own case, convergence in spite of hyper- metropia is almost certainly less than the angle between the visual axes by two or three degrees at least. The two conditions so far seem to be quite independent. 2. On the Formation of Small Clear Spaces in Dusty Air. By Mr John Aitken. {Abstract ) In the introduction a few remarks are made on the growing interest in everything connected with dust, whether it be the organic germs floating in the air, or the inorganic particles that pollute our atmosphere. Professor Tyndall’s observations on the dark plane seen over a hot wire"^ are referred to. Lord Eayleigh’s recent discovery of the dark plane formed under a cold bodyf is described, and attention called to Dr Lodge’s experiments, detailed in a letter to Nature, vol, xxviii. p. 297. * Essays on the Floating Matter in the Air, p. 5, Longmans, Green, & C 1831, i Nature, vol, xxviii. p. 13^ . 441 oj Edinhurglb, Session 1883-84. The experiments described in this paper were made in a small dust-box, blackened inside, glazed in front, and provided with a window at one side. For illumination two jets of gas enclosed in a dark lantern were used. The light entered the dust-box by the side window, and could be condensed on any part of the inside of the box, by means of two lenses fixed in a short tube, and loosely attached to the front of the lantern. Magnifying glasses of different powers were used for observation. The dusts experimented on were made, some of hydrochloric acid and ammonia ; some by burning sulphur and adding ammonia ; others by burning paper, magnesium, or sodium. Calcined magnesia and lime were also used, as well as ground charcoal. These three last substances were stirred up by means of a jet of air. For testing the effects of slight differences of temperature, tubes in some form or other were generally used. These tubes were closed at the front, projected through the back of the dust-box, and were brought close to the glass front, for observation under strong magnifying power. The tubes were heated or cooled by circu- lating water through them in a small tube passing through their interior. Suppose the experiments to be begun by introducing a round tube into its place in the dust-box, and filling the box with any dust, everything being then left for some time, so that all the apparatus may acquire the same temperature. If the light be now allowed to fall on the box, and be quickly brought to a focus on the tube, it will be found that the dust is in close contact with it, on the top and sides, but underneath a clear space will be observed i close examination will show that the particles are falling on the upper surface of the tube, and coming into contact with it, while under- neath a clear space is formed by the particles falling away from it. If the tube is now slightly cooled, a downward current is formed, and the currents of dustless air from below the tube meet under it, and form a dark plane in the centre of the descending current. It is shown that gravitation can, under favourable conditions, produce this separation of the dust quickly enough to keep up a constant supply of dustless air. Ho increase of effect is produced by a lower temperature. A temperature of - 10° C. makes the dark plane 442 Proceedings of the Royal Society thinner, because it increases the rate of the descending current, and carries away the purified air more quickly. A form of apparatus was arranged to get rid of this separating effect of gravitation. It consisted of an extremely thin and flat piece of metal. This test-surface was placed vertically in the dust-box. The air in passing over this piece of metal did not take up a horizontal movement at any part of its passage. The result was that even with a temperature - 10° C. the dust kept close to its surface, and no dark plane was formed in the descending current. The dark plane in the cold descending current seems, therefore, not to be an effect of temperature, but is the result of the action of gravi- tation on the particles under the body. A dark plane was, however, observed when working with this flat surface, when cooled \ but it was not formed in dusty, but in foggy air, and was found to be due to the evaporation of the fog particles when they approached the cold surface. If a very little heat, instead of cold, as in the previous experiment, is applied to the round tube, then the dark space under the tube rises and encircles the tube, and the two currents of clear air unite over the tube, and form the dark plane in the upward current. But in addition to this, heat has been found to evert a repelling effect on the dust. This was proved by putting the thin vertical test-surface in the dust-box, and heating it ; when it was found that the dust was repelled from its surface, and a dark plane formed in the ascending current ; neither of which effects was obtained with cold. The dust begins to be repelled with the slightest rise of temperature, and the dark space in front of the test-surface becomes thicker as the temperature rises. An experiment is then described in which the dust particles in the air flowing up between two parallel glass plates is caused to pass from side to side of the channel by the repelling action of heat at different points. For testing the effects of higher temperatures a platinum wire lieated by means of a battery was used. The platinum wire was bent into a U-shape, the two legs being brought close together. This wire was fixed in the dust-box with the bend to the front, and the legs in the same horizontal plane, the two copper wires to which it was attaclied being carried backwards and out of the box. of Ediiiburgh, Session 1883-84. 443 By this arrangement a clear view was obtained all round the wire, and other advantages secured. Experimenting with this apparatus, it was found that different kinds of dusts had different sized dark planes. With magnesia and other indestructible dusts, it was very thin j with the sulphate dust, it was much thicker; and with the sal- ammoniac dust, thicker still. So thick was it with the two latter kinds of dust, that the dark planes over the two legs expanded and formed one plane. As the particles could be seen streaming into the dark space under the wires, it was obvious that these large dark planes were not caused by repulsion, but by the evaporation or by the disintegration of the dust particles. When making the experiment in a mixture of different kinds of dusts, the hot wire was surrounded by a series of zones of different brightness, and having sharp outlines. The size of the different zones was determined by the temperature necessary to evaporate the different kinds of dust present, and out- side these zones was another caused by the evaporation of the water from the particles. The conclusions arrived at from these experiments are, that the downward dark plane is produced by the separating action of gravi- tation, in the space under the cold body, and that the upward dark plane is produced — 1st, by the separating action of gravitation ; 2nd, by the repulsion due to heat ; 3rd, by evaporation ; and 4th, by disintegration. The effect of centrifugal force is considered. It is pointed out that as the air in its passage over a body such as a tube, curves as much in one direction as it does in another, therefore any centrifugal effect produced in the one part will be reversed in the other. An experiment is described in which an air current is caused to curve through 180 degrees in its passage round the edge of a thin plate, and without any curving in the opposite direction, but no decided centrifugal action could be detected. The motions of the dust particles produced by the repulsion of the hot surface suggested that electricity might play some part in these phenomena. Experiments were made to test this : the hot body was insulated, and connected with an electroscope, but no electrical disturbance was observed, nor could any electrification be got from the dust and hot air streaming up fiom the hot wires. The effects 444 Proceedings of the Royal Society of electrification were studied by insulating and charging the hot surface. The effect was found to he the opposite of the heat effect. If the potential is slight and the temperature high, the heat is able to keep the dust off the surface of the body, and the dark plane distinct ; but if the temperature falls, or the potential is increased, a point is reached when the electrical attraction overcomes the heat effect, and the dust particles break in upon and destroy the dark space. It was observed that after tlie dust particles were electrified they tended to deposit themselves on any surface near them, and experi- ments were made to determine the best conditions for purifying air in this manner. It was found to be best done by causing as rapid a discharge of electricity as possible, by means of points, surfaces being placed near them to increase the electrification of the dust, and to augment the rate of the currents of air which were driven from the points. These surfaces became places on which the dust deposited itself before losing its charge. A large flask was found to be rapidly cleared of a cloud of dust by means of a point, the dust being almost entirely deposited on the inside surface of the flask. If the end of the conductor in the flask terminated in a sphere, but little effect was produced. Electricity has also been found capable of depositing the very fine dust of the atmosphere. The air in a large flask was purified much more quickly by means of the electric discharge than it could have been by means of an air-pump and cotton-wool filter. It is shown that a wet and hot surface repels dust much more powerfully than a hot dry one. From this it is concluded that the heat and moisture in our lungs exert a protecting influence on the surfaces of the bronchial tubes, and tend to keep the dust in the air, which is ebbing and flowing through them, from coming into contact with their surfaces. This was illustrated by placing a hot and wet surface in a current of dense smoke, where it remained some time without receiving a speck of soot, while a similar surface, but cold, was blackened with the smoke. It is pointed out, that on account of the irregularities on the surface of the tubes and of the more violent movements of the air in the lungs, and on accou ' 1of curves and projecting edges, the protection in the lungs of Edinhurgli, Session 1883-84. 445 is not perfect. Still it is thought that this repelling action at these surfaces must have some influence, and it seems possible it may explain some climatic effects, as it is evident that the lungs will he much better protected in such places as Davos Platz, where the air is cold and dry, and the repelling forces at a maximum, than at places like Madeira, where the air is warm and moist, and these forces are at a minimum. This point can, however, only be determined satisfactorily by anatomical examinations of lungs which have lived under the different conditions. In the experiments it was observed that dust not only tended to move away from hot surfaces, but also that it was attracted by cold ones, and attached itself to them. To study this effect, glass plates were put in different positions near the hot platinum wire. Very beautiful impressions of the dark plane can be obtained by placing a piece of glass vertically and transversely over the hot wire. The hot air in flowing over the glass deposits its dust on the surface of the plate, leaving a clear line in the middle, indicating where the dustless air of the dark plane had passed. In this way the dust is trapped on the glass to which it adheres with some firmness, and not only the impressions, but the dark planes themselves, may thus be preserved.* Other experiments, to study the repulsion and attraction of hot and cold surfaces, were made by placing glass plates on both sides of the hot wire. An interesting result was obtained when the plates were about 1 mm. apart. Using magnesia powder, the particles could be seen rising in the current and approaching the hot wire ; they were then observed to be violently repelled towards the cold surfaces, to which they adhered. If there was sufficient difference of temperature, not a single particle of dust was carried by the current past the hot wire. A thermic filter is then described. In this filter the air is passed through the space formed between two concentric tubes. One tube is kept cold by a stream of water, and the other heated by means of steam or a flame. This instrument was shown in action. One end * Specimens of these trapped dark planes were shown at the meeting. Some of them made of white powder deposited on blackened glass, others of charcoal deposited on opal glass. 446 Proceedings of the Poycd Society of the filter was connected with a glass flask, in which the condition of the air was tested. So long as the difference of temperature was kept up, and the current not too rapid, the air passing through the apparatus showed no signs of producing cloudy condensation on the pressure being reduced, showing that the filter had trapped all, even the invisible dust particles. Some experiments on the effect of diffusion on the distribution of dust at the surface of a diaphragm are described. Where carbonic acid diffuses into a space, the dust comes close to the diffusing surface ; but if hydrogen is the diffusing gas, a clear space is formed in front of the diaphragm. An explanation is then offered of the repulsion of dust by hot surfaces, and its attraction by cold ones. It seemed possible that the dust might be repelled in the same way as the vanes of a Crooke’s radiometer, by a radiation effect. That this is not the true explanation was, however, proved by placing in the dust-box a polished silver flat test-surface, one half of which was coated with lamp black, when it was found that the dark space in front of the lamp black was no thicker than that in front of the polished metal. It is thought that the repulsion is due to the diffusion of the hot and cold air molecules. The hot surface repels, because the outward diffusing molecules are hot, and have greater kinetic energy than the inward moving ones ; and as the side of the dust particle next the hot surface is bombarded by a larger number of hot molecules than the other side, it is driven away from the hot surface. The attraction of a cold surface is explained by the less kinetic energy of the outward than of the inward diffusing molecules. Some experiments are referred to, to show that the rate at which gas molecules diffuse indicate that tliis diffusion effect is sufficient to account for the repulsion and attraction of the dust. If the explanation here given is correct, then the dust is repelled in the same way as the vanes of a radiometer when placed in front of a surface fixed inside the radiometer bulb, and hotter than the residual gas, — the principal part of the energy producing the motion being transferred from the hot surface to the repelled surface by the kinetic energy of the molecules, and not by radiation. Ill illustration of the tendency of dust to move from hot, and to of Edinhurgli, Session 1883-84. 447 deposit itself on cold surfaces, the following experiments were made. Two mirrors, one hot the other cold, fixed face to face and at a distance of two or three millimetres from each other, were placed in a vessel filled with a dense cloud of magnesia, made by burning magnesium wire. After a short time the mirrors were taken out and examined. The hot one was quite clean, while the cold one was white with magnesia dust. In another experiment a cold metal rod was dipped into some hot magnesia powder ; when taken out it had a club-shaped mass of magnesia adhering to its end, while a hot rod attracted none. This tendency of dust to leave hot surfaces and attach itself to cold ones, explains a number of familiar things, among others it tells us why the walls and furniture of a stove-heated room are always dirtier than those of a fire-warmed one. In the one case the air is warmer than the surfaces, and in the other the sur- faces are warmer than the air. This effect of temperature is even necessary to explain why so much soot collects in a chimney. It explains something of the peculiar liquid-like movements of hot powders, and perhaps something of the spheroidal condition. For practical application, it is suggested that this effect of temperature might be made available in many chemical works for the condensation of fumes, and that it might also be used for trapping soot in chimneys. A small trap of this kind was shown. It consisted of a tall metal tube or chimney, surrounded by another tube slightly larger. The products of combustion are taken up the centre tube, and down the intervening space. The heat of the gases is thus made to do its own filtering. This apparatus being placed over a smoky lamp, it trapped out most of the soot, and deposited it in the inside of the outer tube. This arrangement of apparatus is too delicate and troublesome for general use, and it is suggested that as by simply cooling gases in presence of plenty of surface, much of its dust is deposited, it might be possible and advantageous under certain conditions to purify air by heating and cooling it a number of times, which could be done at a small expense by means of regenerators. Experiments were also made by discharging electricity into the smoke in a chimney. This also produced a marked diminution in 448 Proceedings of the Roycd Society the blackness of the escaping smoke. The supply of electricity of sufficiently high potential is, however, a difficulty for the present. 3. The Eemarkable Sunsets. By Mr John Aitken. The very remarkable and beautiful sunsets which have been so frequent of late, in which the sky has been lit up with a wondrous wealth of colouring, and with a splendour more than earthly, has given rise to much interest and speculation as to the cause of the brilliant colouring. According to one explanation, the effect is pro- duced by the light becoming coloured in its passage through the atmosphere by an excess of water vapour, or other absorbing medium, at present in the air. The other explanation is, that the effects are the result of a superabundance of atmospheric dust, probably due to the late eruptions of Krakatoa and other volcanic mountains. There seems to be a possibility of determining by observations which of these theories is the more probable. In all the descrip- tions of the sunsets the point which is most generally remarked on is the immense wealth of the various shades and tints of red. Now, if dust is the cause of these glowing sunset colours, then there must be somewhere a display of the colours complementary to the reds ; because the dust acts, not by the selective absorption, and destruction of the colours, but by a selective dispersion of them. The very small particles of dust in the atmosphere stop the direct course of the rays and reflect them in all directions ; but the dust particles are so very small, especially in the upper regions, that they are only capable of stopping, and reflecting, or scattering the rays of the blue end of the spectrum, while the red rays pass on unchecked. There therefore ought to be somewhere in the sky a display of the colours of the blue end of the spectrum. From the observations I have been able to make since this suggestion presented itself, I find that the display of blue and green colours is quite as prominent a feature of the late sunsets as the reds. Overhead the display of blue is fuller than I have ever seen it before; and as the sun passes below the horizon, and the lower stratum of air with its larger particles, which reflect white light. 449 of Edinhurgli, Session 1883-84. cease to be illuminated, the depth and fulness of the blue increases in a very marked degree. While the sky is deep blue overhead it will be observed that lower down the blue changes to blue-green, and in some cases to green, the wonderful greenness sometimes seen in a clear space in the sky being occasionally intensified by contrast with a rose-coloured cloud or haze alongside of it. These considerations seem to point to dust as the cause of the glowing colours of our late sunsets, as none of the colours are de- stroyed, but are simply sifted out and assorted, and the sunset colours seem to be produced in the following way : When we look into the clear blue sky overhead, we see the light selectively reflected from the small particles capable of scattering only the colours of short wave-lengths, and we see only blue. If in the evening we gradu- ally lower our gaze, and look into the clear sky in any direction not towards the sun, we will then see that the blue gradually changes to blue-green, and sometimes even to green, and lower down it passes into white or rose-colour near the horizon, according to the circumstances. This green would seem to be produced in the fol- lowing way : Suppose we are looking northwards, then the light which enters our atmosphere from the west has, before it arrives at the part of the sky into which we are looking, had much of its blue thrown out by reflection, and is therefore deficient in blue light ; and the particles at that elevation are not large enough to reflect the red, so only green is reflected by the sky, and the red passes on. When we look overhead, we also look through this green stratum, so to speak, but the green is overpowered by the greater brilliancy of the blue. And, further, when looking upwards at only a slight angle, we see the light reflected from a far greater amount of the green stratum than when looking through it towards the zenith. The fine particles of dust having thus scattered the blue and the green rays, only the red rays are allowed to pass on, and we see them reflected on the clouds far to the east of us, as well as to the south and north. Some of the most beautiful and delicate rose tints are formed by the air cooling and depositing its moisture on the dust, increasing the size of the particles till they are able to stop and reflect the rays of the red end of the spectrum, when the haze glows with a strange aurora-like light. 450 Proceedings of the Pvoycd Society Another peculiar feature of these sunsets is the very remarkable amount of after-glow which has sometimes been observed. So brilliant is this after-light that to many it has seemed as if the liglit had returned and increased in brilliancy. This im- pression is, however, only subjective. If we watch the moon, it will be seen to become more and more brilliant, as the colour phenomena change, which would not be the case if the after- glow increased the light. The apparent increase seems to be due to the sensitiveness of the eye becoming restored, after being fatigued by the bright light of day, and part of the apparent increased brightness is due to the increased sensitiveness of the eye, and part is due to the illumination becoming coloured. These remarks are, of course, altogether apart from the wonderful increase of twilight lately enjoyed, which has lengthened the day by nearly an hour, and refer only to the apparent increase and return of the light. The increased amount of red light which fell on the earth at and after sunset produced some very remarkable changes in the appear- ance of surrounding objects, causing all red or reddish-coloured objects to glow with a strange brightness, and destroyed the relation of the colours of the different objects to which we are accustomed. Dead beech leaves, for instance, which under ordinary conditions of light are not conspicuous, shone out brightly. But perhaps the most remarkable effect was observed when looking down on a town. Most of the houses were bathed in a uniform grey light; but all the tiled roofs shone out brilliantly, and looked very much as if they had just been painted with vermilion. of Edinburgh, Session 1883-84. 451 Monday, 4zth February 1884. The Eight Hon. LOED MONCEEIFF, President, in tlie Chair. 1. The President delivered the following Address, giving a Eeview of the Hundred Years’ History of the Society. At the close of our last Session, I undertook to call the attention of the Fellows at the commencement of the present to the history of the Eoyal Society, taking as my theme the completion of its hundredth anniversary. Circumstances have accidentally delayed for a month or two the fulfdment of that engagement ; hut I now proceed, to the best of my power, to discharge it. It is a very wide theme, and it will at once occur to you that a review of the topics which have engaged the attention of the Society during that period, rightly performed, would be equally beyond my ability and your patience. I should have to speak an encyclopaedia, in many volumes. I can, however, but attempt some desultory and frag- mentary reflections, which may not be devoid of interest, on “ the Foundation and the Founders of the Eoyal Society of Edinburgh,” as they appear to us in retrospect through a vista of a hundred years. There is no doubt now of our right to claim our centenarian honours. The Charter which we hold is dated on the 29th of March 1783. Several preliminary meetings were held for the election of offlce-bearers and the enactment of bye-laws, but the first meeting for the transaction of business was held on the 8th of December 1783. So that, had I been able to accomplish my task as I had intended, on the 4th of December 1883, I should have invited your attention to the proposed review, as nearly as might be, on the completion of a century of operative life on the part of the Eoyal Society. I think we may look back on that long history with pride, with pleasure, and with profit. The attainment of this centenarian mile- stone in the life of man, or of nations, or of institutions, always brings with it an element of sentiment — a suggestion both of per- VOL. XII. 2 G 452 Proceedings of the Royal Society liianence and of change, which surrounds it with interest. It points to a commencement which probably no survivor recollects, and even in periods the least eventful, its long roll of expectations, efforts, and vicissitudes cannot be regarded without a share of emotion. But the century along which I invite you to look back to-night is BO crowded with events in the political and social history of the world, that its commencement shades obscurely away into the past. Since that day in dim December, when our great predecessors first gathered together, under the shadow of their new Charter, all that was greatest and brightest in Scottish intellect at that time, what a marvellous wave of change has swept over the civilised world. The echoes of 1783 come to us as from the distant past, and range with the historic, not with the present. We think of the Mirror and the Lounger, rather as the contemporaries of the Spectator and the T after, than of ourselves, as though they had been the in- habitants of a different sphere from that in which we find ourselves to-day. Such is the instinctive feeling which first arises in the mind when we try to span in thought the interval between then and now ; and 80 I felt when I began my preparation for my duty to-night. I have in the course of it been living with the great men of former days, as I find their thoughts recorded in our annals. I have gone over our Transactions for the first fifty years of the existence of the Society, and have risen from my task deeply impressed by the wealth of Cultivated ability which that repertory contains. I mean to ask you to-night to accompany me in rather a rapid journey over that period, along with some of the best travelling companions which Scotland ever saw. As I became familiar with details, and the actual personality of the men, I found the apparent distance percep- tibly diminish, and began to think the century not so wide a chasm after all. This impression was heightened by finding, when I took my leave of our office-bearers at the comparatively modern half-way house of 1830, that three of them, at least, had accompanied me all the way. They were Henry Mackenzie^ Baron Hume, and Sir William Miller of Glenlee. Long or short, however, as it may seem to us in reflection, the century has witnessed signal changes, and many momentous events have been crowded into it. Many stormy days and nights must have of Edinlurgh, Session 1883-84. 453 been witnessed by our founders. The Fellows of the Eoyal Society, no doubt, in its philosophic retreat, know nothing of politics — ‘ ‘ Quid Tiridatem terreat unice Securi. ” IS^evertheless, since its meetings Commenced, the changes on the world’s chess-board have been numberless, and there is something impressive, if perhaps almost incongruous, in finding the Eoyal Society meeting quietly month after month in those first days of palpitation and alarm, as if utterly unconscious of the tempest which was raging without. The end of their first decade brought them to the deepest horrors of the first French Eevolution. The end of the second, in 1803, saw the whole country armed to the teeth on the rupture of the Peace of Amiens. At the end of the third, Europe, after ten years of warfare and bloodshed, had not reached, although it approached, the crisis of Waterloo. Yet we could not have discovered from these records of learning what start- ling events were passing outside, while our forefathers discussed a geometrical problem, or pondered and disputed over the topography of the Troad. Yet, regarding this long interval from the vratch- tower of the Eoyal Society, I can trace within the century a revolution more wonderful and more extensive than monarchies^ or empires, or republics can display. Since this Society held its first meetingj how great to the community has been the fruit gathered from those branches of knowledge which it was incorporated to prosecute 1 During that interval, what has science not done for human comfort and happiness ? What interest so great, what dwelling so humble, as not to have felt its beneficent influence ^ Since the invention of the art of printing, no such advance in material comfort, prosperity, and intellgence has ever been made within a similar period as this century has witnessed. Its triumphs have not been Confined to the more abstruse fields of thought and study^ but have come straight to the world of everyday life. I need not go over the familiar cata- logue ; but one homely illustration meets me on the threshold of the opening night j and homely things go deep into the foundations of human life. I picture to myself our founders wending their way to the College Library, through close and wynd, in mid- winter 1783, 454 Proceedings of the Royal Society while flickering oil-lamps made the darkness visible without, and a detestable tallow candle made the student miserable within doors. Those who cannot recollect the universal reign of tallow candles and their snuffers cannot appreciate how much the sum of human enjoy- ment has been enhanced, and the tranquillity of human temper in- creased, by the transmutation — partial, we must admit — of darkness into light. There has been, I believe, no more potent agent in humanising the denizens of our large cities than the flood of light which chemical science has in our day poured into their recesses. The ingenious author of the diverting volume on the Miseries of Human Life, published, T think, about 1812 or 1814, was quite Tight in uttering one of his deepest groans over the illuminating horrors of that age of darkness. It does not detract from the pic- ture that, great as have been the triumphs of gas light, it is said even now to totter on its throne, and prophets tell us that before the end of the century which we now begin, it will probably have followed the tallow candles into the same unlamented obscurity. Prophets ■are not agreed about this ; but even should this be so, history will 'Carry to its credit the vast amount of public utility, and the many hours of useful employment or comfort in the factory, the study, or the sick room, which this simple application of chemical science gained in its day for the nineteenth century. But the dispersion of material darkness is but a slender illustra- tion of the triumphs of scientific discovery. Time and space are no longer the tyrants they were in 1783. I rather think that when our founders first met, they could hardly hope to hear by post from London under ten days, as Palmer’s mail coaches had not begun to Tun until 1789. It would be an interesting inquiry, if my limits permitted, to trace the moral and social effects of the change from the days when a London letter took even three days to reach Edin- burgh, and cost 13Jd Lord Cockburn lamented over the prospect of London being within fifteen hours of Edinburgh, as endangering the characteristics of our socialj community. His sagacity was not altogether at fault, but even that time has been reduced by a third, and I rather think we and the world are all the better of the change. But although larger victories were in store for the century, they came slowly. Both Boulton and James Watt were original mem- bers of the Eoyal Society, but it was more than thirty years before of Edinhurgli, Session 1883-84. 455 steam navigation became general, and more than fifty before the first passenger railway train ran in Scotland. No doubt, in 1791, Erasmus Darwin, in bis Botanic Gard&n,” a poem too little read, bad exclaimed in tire welbknown lines, — “ Soon sliall thy arm, imconquered steam, afar Drag the slow barge, and urge the flying car.” The fame of the elder Darwin has been eclipsed by his younger relative ; but he deserves to be remembered if it were only for the fact that he was the companion, friend, and adviser of James Watt, in whose genius he was an enthusiastic believer, and from whom he probably drew the inspiration which prompted the lines. The genius of James Watt and George Stephenson has changed all this, and, in changing it, altered the conditions both of public and of private life throughout the world. Darwin was not the only man of that time who looked forward with confidence to the ultimate victories of steam. Godwin, in his work, published in 1793, em titled Political Justice, a book full of bold, if very doubtful specu- lation, argues that since the discovery of the steam engine, the amount of manual labour required for the cultivation of the land was certain to be diminished. He says, in a passage which has been often referred to — Hereafter, it is by no means clear that the most extensive operations will not be within the reach of one man ; or, to make use of a familiar instance, that a plough may not be turned into a field and perform its office without the need of super- intendence. It was in this sense,” he continues, ‘‘that the cele- brated Franklin conjectured that mind would one day become omnipotent over matter,” and now that the locomotive carries mankind to all ends of the earth, Godwin’s sanguine suggestion has been all but realised. There has been during this interval a still more powerful magician at work. To this audience I need not dwell on the triumphs of the future ruler of the world of science — electricity. But one illustra- tion I may be permitted. Franklin was one of the first of the non- resident members elected by the Royal Society of Edinburgh. How little he thought when many years before he drew the electric spark from the cloud, that before a hundred years had sped, his experi- ment, but slightly modified, might convey a message from a meeting 456 Proceedings of the Royal Soeiety of the Society in Edinburgh to one of its Fellows in ^N'ew York, and bring back an answer before the meeting separated. In slightly alluding to this scientific revolution, my object has been partly to illustrate the surroundings of 1783, and also to re- mind my hearers that of all the changes the century has seen, far the most important, and the deepest, have been the work of science. Increased facilities for inter-communication carry with them a com- plete change in the economical and social condition of the communi- ties they affect. Hew wants, new customers, new ambitions, new possibilities, follow in their train by the operation of inevitable laws. YHiat was a luxury before becomes an ordinary necessity thereafter. What was in fashion is obsolete, and what seemed chimerical may be accomplished. By this talisman we have seen, perhaps sometimes without due appreciation, many a social problem solved which had before seemed hopeless ; and although in the pro- cess of transition some period of adaptation may be necessary, and some temporary hardship endured, the result in all cases must be beneficent, and is at all events beyond the power of lawgivers to control or to resist. These last remarks are not without an application to that circle of remarkable Scotsmen who constituted the Founders of the Koyal Society, They were not only prominent by intellect and cultiva- tion, but they were each characteristic and distinctive. It would be as impossible to reproduce that circle now, as to restore the ancient lineaments, and Continental aspect, and Continental usages of the ancestral city where they flourished. Although the exodus to the North had already commenced, we do not associate the Founders of the Eoyal Society of Edinburgh with the Edinburgh of toEay, but with the tall tenements, the wynds and closes, the densely packed hive of educated and learned Scotsmen, as Gold- smith or Johnson found it ; as it was in the early days of Karnes and Monboddo, with its afternoon tea-drinkings and club suppers. The century which has changed so much has changed these things also. As far as external conditions go, no revolution could be more complete. It has been a change from cultivated homeliness to splendour, from frugal although dignified economy to as much domestic luxury as any community in Europe enjoys. While in 1801 the whole population of Edinburgh was little over 60,000, it of Edinburgh, Session 1883-84. 457 amounted by the census of 1881 to 230,000, spread over an area nearly ten times the former in superficial extent, and furnishing in every quarter splendid examples of urban architecture. The Eoyal Society itself was the culmination of that signal reviviscence of literary enthusiasm and power, which, to her own astonishment and that of the world, took place in Scotland in the second half of the eighteenth century. Stunned at its commence- ment by the removal of the legislature, and all the social prestige which the seat of a legislature enjoys, speaking a language which ultra-patriotic Scotsmen still think the more classic of the two, but still barbarous in Southern ears, the educated Scot set himself with the energy of a Border chief to try if he could not invade the territory of his neighbour across the Tweed in the world of letters. With what measure of rapid success the daring attempt was crowned the names of David Hume, Adam Smith, and William Robertson attest to this day. How it came that a knot of Scots philosophers, who used their own vernacular in familiar intercourse, should have become examples, not of thought only, but of style, to Englishmen, might admit of more detailed illustration than I can give it here. But very soon these literary chiefs from the North became famous and popular among London men of letters, as well as with the public. I find David Hume writing from London to Adam Smith on the publication of his Theory of Moral Sentiments in 1759, “ that he had sent a copy of the book to some of his acquaintances, and among the rest to Lord Lyttleton and Horace Walpole and to Mr Burke, an Irish gentleman, he says, “ who has lately written a very pretty treatise on the Sublime.” On the other hand, in Mr Cosmo Innes’ pleasant Memoir of Professor Dalzel, who, as we shall see, was a member, and one of the secretaries of the Royal Society at its foun- dation, he quotes a letter from the Professor to Sir Robert Liston in 1776, in which he says — “There is published also a first volume, quarto, of a History of the Decline and Fall of the Roman Empire, by Edward Gibbon, Esq., a member of Parliament,” an expression which may well be placed alongside of Hume’s reference to “ Mr Burke as an Irish gentleman.” A month before, in April 1776, this same Mr Gibbon wrote to Dr Adam Ferguson from London — “ I have always looked up with the most sincere respect towards the northern part of our island, whither taste and philosophy seemed to 458 Proceedings of the Royal Society have retired from the smoke and hurry of this immense capital.” He goes on to say, “ What an excellent work is that with which our common friend, Mr Adam Smith, has enriched the public — an extensive science in a single hook, and the most profound ideas ex- pressed in the most perspicuous language.” In 1776 we find Adam Smith a member of the “Club,” founded in London by Johnson and Goldsmith ; and the following lines by Hr Barnard (I quote from Hugald Stewart’s Life of Smith, read to the Koyal Society) indicate a position of respect in that circle ; — “ If I have thoughts, and can’t express ’em, Gibbon shall teach me how to dress ’em , In words select and terse. Jones teach me modesty and Greek, Smith how to think, Burke how to speak. And Beauclerk to converse.” I was amused to find that the admission of Smith to the “ Club ” excited the intense jealousy of James Boswell, who, in a letter to Mr Temple, one of those published a few years ago — says loftily, “ Smith too is now of our Club. It has lost its select merit.” It is, however, to Hr Eobertson and Lord Karnes that we are mainly indebted for the idea of the Eoyal Society, and for the successful issue of the project. It sprung partly, of course, out of the example of the Eoyal Society of London. But its immediate antecedent was the Philosophical Society, which had been founded nearly fifty years before by the celebrated MHaurin, and contained many distinguished names. Lord Karnes became its president, and raised it to considerable distinction, both in science and literature, although that vigorous and versatile thinker and writer did not live to witness the commencement of the new institution. Hr Eobert- son’s plan w^as to absorb this Society and all its members in a new Institute, on the model of the Berlin Academy of Sciences, for the prosecution both of Physical Science and of Literature. I find from the minutes of the first meeting that the Society were of opinion that the College Library was an inconvenient place for their usual meetings, and a committee was appointed to find one more suitable, apparently without success, for they continued to be held in the library for twenty-three years, when the Society migrated to the Physicians’ Hall in George Street in 1807. They afterwards of Edinhurgh, Session 1883-84. 459 purcliased ]STo. 40 George Street, in wMch the meetings were held until they obtained their present rooms in the Eoyal Institution. At a subsequent meeting, held on the 4th of August 1783, it was resolved that the Society should be divided into two classes, which should meet and deliberate separately, to be called the Physical Class, and the Literary class, with separate office-bearers. But I have detained you too long on the threshold by this desultory exordium. Let us now draw up the curtain, and display the Pounders of the Eoyal Society. The first President was Henry, Duke of Buccleuch, who had rendered great assistance in obtaining the Charter. The Vice- Presidents were the Eight Hon. Henry Dundas, and Sir Thomas Miller, the Lord J ustice-Clerk. I forbear to go over the names of what may be called the original members of the Society. I include in that term all who were elected within the first ten years. All the members of the Philo- sophical were assumed without ballot ; the rest, to the number of more than a hundred, were elected by ballot, and a general invita- tion was made to the Lords of Session to join. These were the ordinary resident members. There was also a list of non-resident members, which comprised nearly as many. Of the ordinary resident members there is hardly a name which is not known — I might say conspicuous, in the annals of Scotland at that time. Twelve of the Lords of Session accepted the invitation, including the Lord- President, the Lord Justice-Clerk, and the Lord Chief Baron of the day; upwards of twenty professors, with Principal Eobertson at their head ; twenty-two members of the Bar, including Sir Hay Camp- bell, the Lord Advocate — and of these at least fourteen rose after- wards to the bench; the medical contingent included Monro, Gregory, Cullen, and Home ; and the non-resident list contained the names of the Duke of Buccleuch, the Earl of Morton, the Earl of Bute, the Earl of Selkirk, Lord Daer, James Stuart Mackenzie, the Lord Privy Seal, Sir George Clerk Maxwell of Penicuick, Sir James Hall of Dunglass, and many other familiar names. But 1 select from the list those of the members on whom fell the burden of the real work ; and I venture to say that no city in Europe could have brought together a more distinguished circle. They were — Hay Campbell, Henry Dundas, Joseph Black, James Hutton, John Play- 460 Proceedings of the Boyal Society fair, Adam Smith, William Robertson, Dugald Stewart, Adam Rergusson, Alexander Monro {seciindus), James Gregory, Henry Mac- kenzie, Allan Maconochie, and William Miller of Glenlee. I ought to add to these Sir James Hall of Dunglass and Sir George Maxwell of Penicuick. Some of these names are European, all are celebrated, and these were men who for the most part did not merely contribute the lustre of their names to the infant association, but lent the practical vigour of their great intellectual power to aid in the first steps of its progress. And very soon the impress thus stamped on the Society began to establish its reputation in the world, and it took no undistinguished place among the learned societies of Europe. I find the names of Goethe and Buffon among the original foreign members ; and although the events of the next twenty years inter- rupted our relations with the Continent, by the time the Society had completed the half century, there was scarcely a distinguished savant in Europe who had not joined or been invited into our ranks. In the physical class were four men who rose to great positions in the scientific world, and to whom the Society were greatly indebted for its general reputation, and for the vigour and efficiency with which their proceedings commenced. They were James Hutton, Joseph Black, John Playfair, and Dugald Stewart. Hutton and Black were then in the zenith of their fame, and have left a strong impress on the first years of our Society. Hutton was a most assiduous and energetic member. He had the distinction in the very first volume of the Transactions of lighting up two scientific conflagrations which blazed fiercely throughout Europe for many years afterwards. One was his theory of the earth, over which the Neptunists and Yulcanists fought with much fury, and the flames of which are perhaps not altogether extinct. Much has been learned on these subjects since that time. Whether the world of geology has been fused into a coherent mass by reason of this combustion I need not inquire. There have been theories of the earth since then, and possibly the slumbering embers may be re- kindled. The other controversy was of narrower dimensions, and related to a paper of Hutton’s on the “ Theory of Rain,” which was strongly attacked by M. de Luc, a Erench philosopher, and de- fended by Hutton in the Transactions with not a little asperity. That Hutton should have succeeded in the very outset of the of Edinhurgli, Session 1883-84. 461 Society’s labours in setting the philosophers of Europe by the ears, first about the fires beneath the earth, and secondly about the rain which falls from the heavens, is creditable at least to his energy. Into the merits of these controversies it is no part of my province to inquire ; but I am desirous, in this review of the Society’s early days, to revert with gratitude and respect to the memory of one whose labours on behalf of the Society were invaluable. Erom 1783 until his death in 1797 not a year went by in which our Transactions were not enriched by his vigorous conceptions. Hutton was an observer and a thinker of remarkable originality and power. He had been a lawyer, a medical practitioner, a farmer, and an agriculturist, before he became known as a natural philo- sopher. Vigorous in thought and full of enthusiasm, he is said to have been as brilliant in conversation as he was obscure in his written style. Professor Playfair did for Hutton’s theory of the earth what Dumont did for Bentham, and rendered his strong but obscurely expressed reasoning into clear and pellucid language. I ought, in justice to his great services to the Society, and his undoubted ability, to have coupled with the name of Hutton that of Sir James Hall of Dunglass, who was one of our most energetic members, and held the position of President for many years. He was a friend and admirer of Hutton’s, but, as he tells us, was at first entirely incredulous as to his theory of the earth, and it was only by the charm of his conversation, and verbal explanations far more lucid than his written style, that he at last adopted his views. It, however, occurred to Hall that if heat and pressure had pro- duced the effects attributed to them by Hutton, the truth of the theory might be tested by actual experiment. Hutton discouraged this view, thinking that the heat to which these appearances were due must have been so much more intense than any which could be artificially produced, that no satisfactory results could be hoped for. Hall had so much respect for his friend that he refrained from any public notice of his experiments during Hutton’s life; but after Hutton’s death in 1797 resumed them with great ardour, and com- municated the results in two papers read to the Society — one on the composition of Whinstone and Lava, read in 1798, and a second most elaborate account of upwards of five hundred experiments, read in 1805. These experiments were conducted with immense perse- 462 Proceedings of the Boyal Society verance, considerable expense, and varying results. They have, however, not been without fame and favour in the scientific world, for I found, in the library of the Society, thanks to the attention of our Librarian, a work and an accompanying letter which indicate more powerfully than any words of mine could do, what interest and importance is still attached to the results of his experiments by men of science on the Continent. The letter is addressed to the President of the Eoyal Society of Edinburgh by M. Daubree, who therein mentions that he is President of the Academy of Sciences of the Institute of Prance; it is dated in June 1879, and was received by my predecessor in the chair. It is in the following terms (I translate the substance of it). He requests the President to beg of the Society to accept from him a copy of a work which he is in the course of publishing, entitled Synthetic Studies in Experimental Geology. He proceeds — It was on the soil of Scot- land that the powerful and fertile genius of Hutton was inspired, and it was in the Transactions of your celebrated Society that James Hall published in the beginning of the century two papers of high importance to experimental geology. My expression of gratitude (liommage) is thus not without good reason.” The work itself is a record of a series of most elaborate experi- ments, proceeding avowedly on Hutton’s theory, and on the lines of Hall, accompanied by illustrative drawings, and intended to ex- hibit the effects of various mechanical agents in combination with heat or fusion on the materials of the crust of the earth. The scientific merit of these views I do not pretend to judge ; but it is at least a striking tribute to our Pounders to find that their labours at the commencement of the century should be so highly appreciated by the world at large close on the end of it. Black, again, was a Frenchman by birth, although his parents were British, and he was nearly related to Adam Smith and to Adam Ferguson. He came to Scotland when he was about twelve years old, and long before the institution of the Eoyal Society he had risen to the front rank of European chemists ; his discoveries on pneumatic chemistry and latent heat having laid the foundation of much that is valuable in subsequent investigations, and opened a course of inquiry pursued with great ability in our own Transac- tions by Leslie, and Brewster, and Forbes. He took a great interest 463 of Edinhnrgh, Session 1883-84. in the Society, although he only contributed one paper of importance, on “ The Hot Springs of Iceland.” But no man has left a greater reputation behind him. I have said that Black was a relative of Adam Smith, who was on terms of the greatest intimacy with him and Hutton, and loved nothing so much as to get the philosophers together at what he called an Oyster Club, and listen to their talk. He appointed Black and Hutton as his joint-executors. Ferguson was also a relative, and Cockburn sketches what he recollects of each. He says of Ferguson— “ I never heard of his dining out except at his relative Joseph Black’s, where his son. Sir Adam (the friend of Scott) used to say it was delightful to see the two philo- sophers rioting over a boiled turnip.” Cockburn used to watch Joseph Black from his father’s house in George Square, and thus describes him ; — “ He was a striking and beautiful person ; tall, very thin, and cadaverously pale ; his hair carefully powdered, although there was little of it, excepting what was collected into a long thin queue ; his eyes dark, clear, and large, like deep pools of pure water. He wore black speckless clothes, silk stockings, silver buckles, and either a slim green silk umbrella or a genteel brown cane. The general air and frame were feeble and slender. The wildest boy respected Black. No boy could be irreverent towards a man so pale, so ele- gant, and so illustrious. So he glided like a spirit through our rather mischievous sportivencss unharmed.” The two others I have mentioned were too famous in their day, and are so still, to require to be, or to admit of being, described here. John Playfair and Dugald Stewart were men who by them- selves could have raised to distinction any circle to which they belonged. Both of them were men of great versatility, and within the walls of the Eoyal Society capable of filling a foremost place, whether in the fields of exact science or in those of literature or mental philosophy. Dugald Stewart’s contributions to the Transactions are not so numerous as those of Playfair, but no man had more influence in moulding the tone and cast of thought prevalent amongst the culti- vated class of his countrymen than that most popular and most eloquent instructor of youth. 464 Proceedings of the Royal Soeiety But no one can study these volumes of the Transactions^ as I have done, without feeling that for the first two decades of the existence of the Eoyal Society Playfair was the soul and life of the institution. His versatility and power have impressed me exceed- ingly, high as was the estimate I had previously formed of him. Profound and transparently clear, whatever might be the topic, he hears about him a far-reaching vigour which never flags. Whether it be the Origin and Investigation of Porisms, or the Astronomy of the Brahmins, or their Trigonometrical Calculations or Meteorological Tables, or a Double Eainbow, nothing seems too great or too small for him. Some of his obituary notices are fine pieces of English com- position ; in particular, his notice of Dr William Stewart and of Hutton, and his fragment on John Clerk of Eldin, which is printed in the ninth volume of the Transactions. In looking through the list of members towards the commence- ment of the Society, two attracted my attention^from no special connection between them, excepting that they both were members of Johnson’s Club, and both were celebrated in Goldsmith’s poem of “ Eetaliation.” The first was one which, by itself, was sufficient to confer distinction on any assembly, however distinguished, that of Edmund Burke, who, according to Goldsmith’s cynical lines — ‘ ^ Born for the tmiverse, narrowed his mind, And so partly gave np wEat was meant for mankind.” When I first observed the name, I wmndered through what channel the great Irishman came into that company. Dalzel’s Memoirs, however, make that clear. Burke was that year (1784) Lord Eector of Glasgow University, and on his return from his installation paid a visit to Lord Maitland at Hatton House, and there Dalzel met him, was charmed by his conversation, and recruited him for the Eoyal Society. I am not aware that he was in Edinburgh on any other occasion. Dalzel writes to Sir Eobert Liston on the 20th of April 1784 — “Our Eoyal Society is going on extremely well. I have proposed Mr Burke and you as new members.” Next month he informs Liston that he was unanimously chosen a member, “ which,” he says, “ was not the case with Mr Burke. He was chosen, but not unanimously — there were several black balls j ” and the Professor proceeds to moralise on the occasion. There is no of Edinhurgli, Session 1883-84. 465 need that we should do so. It is not in the least surprising that in those days the very fact of his renown should have induced one or two men in any assemblage to doubt whether, born for the universe or no, he was specially born for the Royal Society ; and had the event occurred ten years later, the discontented might have been as numerous, but it is possible they might not have been the same. The other name, although well entitled to remembrance on ac- count of its owner’s accomplishments and learning, owes its principal notoriety now to Goldsmith’s gibe. It was that of Caleb Whit- foord — the merry Whitefoord of the ‘‘ Retaliation” — -of whom the author says — ^ “For thy sake I’ll admits That a Scot may have hnmour, I had almost said wit.” ’ Now, Goldsmith had a very genuine vein of wit and humour him- self, as all the world knowsj and was a Very good judge of it in others. It must not be supposed that his knowledge of Scotsmen was confined to those he encountered south of the Tweed, for he spent one year at least, I rather think two, in 1752, as a medical student in Edinburgh, attended Dr Monro secundus, and was, as Mr Forster in his Life tell us, a friend of Joseph Black’s. If so, I cannot help thinking he must have neglected his opportunities, if he found no humour in the circle in which Black moved. I have not time to unravel the mystery of Goldsmith’s life in Edinburgh farther, for what he did while there, or when or why he quitted it, is left in great obscurity; but at least the Royal Society need not wince, for although wit and humour cannot be said to be the characteristic of our Transactions, there was one Scotsman who spread the fame of Scottish humour as widely as that of the Vicar of Wakefield — -he was President of the Royal Society, and his name was Walter Scott. There are many curious and interesting bypaths, both of science and literature, traversed in these earlier volumes. In 1787 Mr George Wallace read a paper, which he did not incline to have printed in the Transactions^ which I regret, for it related to a sub- ject the interest of which has not ceased by the lapse of nearly a century. Its title was “ On the Causes of the Disagreeableness and Coldness of the East Winds.” As I fear there is little reason 466 Proceedings of the Royal Soeiety to think that the east wind has become less disagreeable or cold since that date, it might have been consolatory to know to what these attributes were due. At all events the question remains un- fortunately as prominently for determination in 1884 as it existed in 1787. In the first volume of the Transactions a very singular problem was presented through Mr Adam Smith to the Society, along with other learned bodies in Europe, by a Hungarian nobleman, Count Windischgratz, and a prize was offered by him of 1000 ducats for the best solution of it, and of 500 ducats for an approximation to a solution. It M^as a bold effort of philanthropy, for its object was the abolition of lawyers for the future. The problem was addressed to the learned of all nations. It was couched in Latin, but was in substance this : — “ To find formulte by which any person might bind himself, or transfer any property to another, from any motive, or under any conditions, the formulae to be such as should fit every possible case, and be as free from doubt, and as little liable to con- troversy, as the terms used in mathematics.” I suppose that the prospect here held out of dispensing for the future with the least popular of the learned professions, inclined the Society to entertain it favourably, for they proceeded to invite solutions of the problem, and three were received by them. In 1788 we find it recorded in the minutes that Mr Commissioner Smith (for so the author of the Wealth of Nations was designed) reported the opinion of the com- mittee that none of the three dissertations amounted to a solution, or an approximation to a solution of that problem ; but that one of these, with a certain motto, although neither a solution or an approximation to a solution, was a work of great merit ; and Mr Fraser Tytler was instructed to inform Count Windischgratz of their opinion. Whether this meritorious dissertation obtained the 500 ducats or no, we are not informed ; but as lawyers continue to flourish, and legal terminology to produce disputes as prolifically as ever, it seems clear that the author had not earned them. How that we have an observatory on Ben Hevis, our successors at the end of next century will know accurately the conditions of the climate under which the hundred years have been spent. There are, however, some details scattered over these volumes which are sufficiently interesting, although whether they show any material of EcUnltirgh, Session 1883-84. 4G7 alteration on our seasons, may be doubtful. The only cheering fact which they disclose is that the first set of returns do not support the idea that the mean temperature in the olden time was higher than it is now. There are two sets of returns printed in the first volume of the Transactions^ one kept at Branxholm, from 1773 to 1783, communicated by the Duke of Buccleuch, who was the first Presi- dent of the Society, and the second by Mr Macgowan, kept at Hawkhill, near Edinburgh, from 1770 to 1776. In the first, the mean temperature of the ten years is 44°, in the second 45° — not a very genial retrospect. Things must have been somewhat dis- couraging for the farmers in 1782, for a paper is noticed in the second volume of the Transactions^ by Dr Bpebuck of Sheffield, who was the manager of the Carron Iron Works, recommending farmers not to cut their corn green in October, although there was ice three quarters of an inch thick at Borrowstounness, because corn would fill at a temperature of 43°. Things looked brighter from 1794 to 1799, for which years we have results furnished by Play- fair. For the first three years, 1794, 1795, and 1796, the niean temperature was 48° ; and that although 1795 was one of the most severe winters on record, the thermometer having stood frequently several degrees below zero, and a continuous frost having lasted for fifty-three days. The mean temperature in 1794, however, was 50°. The account of the great frost of 1795, which is given in the Transactions, is well worth referring to. In the next three years the mean temperature Avas 48°, that of 1798 being 49°-28°. Of this year (1798) Playfair says that the climate of this part of the island hardly admits of a finer season. bio tables were furnished to the Society in continuation of those of Professor Playfair until 1830, Avhen fortunately Dr Barnes of Carlisle communicated to the Society a series of meteorological tables kept at Carlisle for the first twenty -four years of the century. The results seem mainly to concur with those of Professor Playfair. The mean temperature for the twenty-four years being 47°, being 3 degrees higher than the average of the ten years from 1773 to 1783 at Branxholm, and 2 degrees higher than the mean temper- ature of the years from 1770 to 1776 at Hawkhill. The highest temperature I have noted in these returns is that of May 1807, when the thermometer stood at 85° at Carlisle, and the heat on the 5th of August 1770, when the theimometer at Hawkhill Avas A^OL. XII. 2 H 468 Proceedings of the Pioycd Soeiety at 81°. The two years of this century in which the mean temper- ature was the highest were 1811 and 1822, in both of which years it was 49°. Of the purely scientific part of the Koyal Society’s work for the first fifteen years of its labours, while Hutton and Black and Play- fair and Stewart were in full vigour, it is not too much to say it was brilliant, full of interest, full of power, and full of enthusiasm. The first great Founders, of course, gradually waned, and all such associations are necessarily subjected to alternations of the tide; but as the tale goes on, the mathematical papers begin to bear the names of John Leslie and William Wallace. We encounter Walter Scott in 1800, in 1808 the name of David Brewster, and in 1811 that of Sir Thomas Makdougall Brisbane, whose names adorned and whose labours were in the future the prop and stay of the Society. Of Scott I need not speak, but of the services rendered by Brewster it is impossible to express myself too strongly. He too, like Playfair, had a mind of a rare versatility ; he could observe as well as draw from his own resources. He could reason as well as describe. He could build a framework of sound deduction from the most unpro- mising hypothesis, and work out with unflagging spirit the thread of demonstration, however slender. In some respects he differed from some of his contemporaries or predecessors. He did not for the most part shrink from giving the Society the benefit of his present thoughts and current experiments. Sometimes they were imperfect, sometimes perhaps even crude, but always full of acuteness, novelty, and genius. Had I had the scientific knowledge essential to the task, nothing I think could have been more interesting than to have traced Sir David Brewster’s first speculations on light and heat con- tributed to the Society to the end of his career, and to mark and observe how great results gradually crowded on his canvas, to fill in the first slight and imperfect sketch. He was the most prolific con- tributor of his day ; nor do I think that any one but himself in those times could have kept the fire lighted by Hutton and Playfair burning so brilliantly. For it is not to be disguised that in the heat of the continental struggle an air of languor creeps over the pro- ceedings. The joyous enthusiasm of 1783 refuses to be invoked, and is solicited in vain. Hor is it wonderful, when the Gauls were so nearly at our gates, the safety of our own commonwealth should have been comparatively our only care. But when 1815 had arrived. of Eclinhurgli, Session 469 and men’s minds, set free from tlie long anxiety, had again tranquillity to cultivate the arts of peace, the energy of the rebound was great, and the history of British science has been one continued triumph ever since. By the exertions of Brewster and Brisbane, and many other Associates, our Society again began to flourish, both leading and following, the course of discovery as the stream flowed on. Both of these men continued to be the pride and ornament of the Society long after the expiration of that half century which I have assigned to myself as my limit. Sir Thomas Brisbane succeeded Sir Walter Scott as President in 1832, and survived until 1860. Long before that a new generation had surrounded the veteran philosophers, and their destiny has been to recount and carry forward discoveries of which even Brewster and Brisbane hardly dreamt. But the merits and successes of these later heroes must be the theme of some future historian, for at present, although posterity may think them braver sons of brave sires, they and their reputation are too close at hand to be properly treated of. Some names, indeed, contemporary with onrselves, but too early lost, I should like to have mentioned with a word of commemoration ; but, on the whole, I have thought it better to adhere to my original programme. I mentioned in the outset of these remarks that the Society, as originally constituted, was divided into two classes, — the Physical and the Literary, — and that these classes were to meet separately. I do not think this separation was politic ; a'nd it is impossible to deny that it very early proved a failure. Por some years the lite- rary side of the Society was maintained with considerable spirit and vigour, and some of the papers printed in the Transactions will repay perusal. Mr Maclaurin’s paper, to prove that Troy was not taken by the Greeks, is a bold, learned, and not unsuccessful chal- lenge of Homer’s historical accuracy j and since Schlieman’s recent explanations, perhaps more reason has been shown for his doubts. M. Chevalier contributed an elaborate paper on the Plain of Troy, in French, which attracted attention, and obtained some reputation on the Continent. One of the most important contributions to this department of the Society’s labours is a paper by Henry Mackenzie on the German Stage, written at a period when German literature was little known or appreciated in this country, and composed in the light, elegant style characteristic of the author. There is also in the second volume of the Transactions a scholarly and interesting 470 Proceedings oj ilic Pioyal Society paper by Dr Beattie on the Sixth Book of Virgil’s Euclid, read in 1787. Altogether, however, this class or section of the Society did not command the success which attended the physical. As time went on, there seemed to be a want of material, and the papers dwindled down to somewhat pedantic dissertations on grammar, on moods of verbs, on pronouns, on the Greek letter sigma, on the Greek Ae, on the necessity for defining synonymous terms, and topics of this class, which although valued by and probably interest- ing to a limited class of philologists, were not animated in them- selves, nor likely to excite enthusiasm on a general audience. I was quite prepared, accordingly, to find that the result occurred which circumstances foreshadowed. The following entries occur in the Minutes : — “ 1793. — There being no business for the stated days of meeting in April, June, July, and November, no meetings were then held.” The same entry occurs in 1794; and the Literary class thus practically perished of inanition ten years after the foundation of the Society; and in 1808 the minute-book of that class ceases altogether. There has been no separate Literary class since the new rules passed in 1811. It is not difficult to trace the causes which led to the continuance of this. In 1783 there had been a wave of literary revival passing over Scotland ever since the middle of the century, and our prose writers, Hume, Eobertson, Blair, and others of that circle, including specially Henry Mackenzie, had raised a spirit of enthusiasm for such pursuits. But such fashions rapidly change. The immense effects produced on human thought by the French Revolution gave a fresh impulse and a new direction to literary taste. New outlets, more profitable than the supply of our Transactions, soon afterwards opened to the literary world. The Edmhurgh and Quarterly Reviews ; Byron, Scott, Wordsworth, Coleridge, and Campbell in- augurated a new era, under which the old ways became unfashion- able, and the old taste obsolete. Matters stood quite differently with the Physical class. In that opinions may grow obsolete, but the theme never. Fresh ground is always to be found. So men turned out with alacrity to hear about the Vulcanists and Neptunists, or latent heat or the latest geometrical problem, who would not stir from their homes to be told the use of a subjunctive, or Dr Parr’s derivation of the word “ suhlimisT 4'71 of Edinburgh, Session 1883-84. In its former shape it would he impossible to revive the Literary class. Still I think 'it would lighten and enliven our meetings here if the graver matters of the physical class w'ere sometimes inter- spersed with contributions of a literary nature. This I see plainly cannot be done without some labour, and some concert among the Fellows. If I can aid in any such scheme, I need not say that any assistance I can give would be willingly rendered. Before quitting this subject of the Literary class, I would remark tliat the most valuable papers of this class are the Obituary Notices, which in general are good examples of vigorous and elegant writing, and are interesting as authentic records of celebrated men. The three notices by Dugald Stewart of Adam Smith, Principal Eobertson, and Thomas Eeid are printed in Stewart’s Life by Sir W. Hamilton, and are masterpieces of biography. Two others in particular arrested my attention. The first, a very remarkable paper by the Eev. Mr Alison on Lord Woodhouselee, and the other, a charming bio- graphy of Lord Abercroniby by Henry Mackenzie. One class of our Founders I feel I have treated with scant justice- — I mean those of the legal profession. The truth is they furnished a large and available contingent, more perhaps in the way of influence than in that of contribution. But I have not done so from under- valuing the aid they gave, but because to estimate properly their assistance would have led me into inquiries which would have swelled this paper — already, I fear, too prolix — beyond reasonable dimensions. It'would have involved a dissertation on the Mirror and the Lounger, and the state of periodical literature in Scotland at the close of last century. The men whom Henry Mackenzie gathered round him were almost all lawyers, and lawyers of note — Lord Abercromby, Lord Craig, Lord Dreghorn, and Lord Banna- tyne were men well deserving of commemoration. It is true, our Transactions contain few contributions from their pen ; but the true value of such institutions as the Koyal Society is found mainly not in the contributions to the evening’s interest, but in the enthusiasm they foster and the inquiries they excite. One man who indicates earnestness in the prosecution of a science or an experiment, may do more to encourage the spirit and love of investigation than the more constant contributor. It is the social tribunal in which, after all, such institutious as ours must depend; and to excite general atten- tion, and stimulate rivalry, and inspire the generous emulation to 472 Proceedings of the Royal Society walk in the footsteps of our predecessors, and to keep the torch which they have handed down to us burning brightly, is to show ourselves worthy of our great inheritance. I cannot finish my remarks without a tribute of respect to the able and vigorous intellect of the man I just now mentioned — I mean Henry Mackenzie. The Society owes him many obligations ; so does his country. He created a style of periodical literature in Scotland which has borne rich fruit ; and although even he could not prolong the life of the literary class, his own extended to a patriarchal age, in which he saw the lessons he had taught produce an exuberant harvest. As a pendant to some of Cockburn’s sketches of the olden time, I finish these desultory outlines by a quotation from another writer. The author of Peter’s Letters — I suppose I may say John Gibson Lockhart — describes a dinner party about 1818, at the house of Henry Mackenzie, at which the only other guest was another of our founders Adam Pollan d, who, if he only lived on Raeburn’s canvas, could not have been forgotten. He says — “ The only visitor besides myself was an old friend, and indeed contemporary with Mackenzie, a Mr Roland, who was in his time at the head of the legal profession in Scotland, but who has now lived for several years in retirement. I have never seen a finer speci- men, both in appearance and manner, of the old Scottish gentleman. “ It was a delightful thing to see these two old men, who rendered themselves eminent in two so different walks of exertion, meeting together in the quiet evening of their days, to enjoy in the company of each other every luxury which intellectual communication can afford, heightened by the yet richer luxury of talking over the feel- ings of times to which they almost alone are not strangers.” “ They are both perfectly men of the world, and there was not the least tinge of professional pedantry in their conversation.” He proceeds — “According to the picture they gave, the style of social intercourse in this city, in their younger days, seems indeed to have been wonder- fully easy and captivating. At that time not one stone of the New Town, in which they and all the fashionable inhabitants of Edin- burgh now reside, had been erected. The whole of the genteel population lived crowded together in those tall citadels of the Old Town. Their houses were small, but abundantly neat and comfort- able, and the labour which it cost to ascend to one of them was sure to be repaid by a hearty welcome from its possessor. The style of of Edinburgh, Session 1883-8 4-. 473 visiting altogether was as different as possible from the ceremonious sort of fashion now in vogue.” He concludes his description by saying, ‘‘ If I were to take the evening I spent in listening to its history as a fair specimen of the ‘ Auld Time,’ I should be almost inclined to reverse the words of the Laureate, and say — Of all places, and all times of earth, Did fate grant choice of time and place to men, Wise choice might be their ‘ Scotland,^ and their ‘ Thcnd ” Enough for the present, this retrospect, and the slender tribute I have attempted to pay to the memory and labours of a masculine and powerful generation. That we have built on their discoveries, and have learned even by their errors, is quite true ; for the history of the second half of the century exhibits science far in advance of 1783, and even of 1833. In 1783 geology was in its infancy. Paleontology was all but unknown. Cuvier was only then com- mencing his pursuits in comparative anatomy, which were to end in reproducing the forms of extinct life. The glacial epoch had not then been elucidated by the research and genius of Forbes and Agassiz, and the dynamic theory of heat was still unproclaimed. The wonders of the photographic art were unknown, even in 1833^ for Talbot and Daguerre did not come on the scene for several years afterwards. In 1833 the apostle and disciples of evolution had not then broken ground on that vast field of inquiry. The ever-increasing development of the mysteries of light and sound, spectrum analysis, and the marvellous results which it has already furnished, and those which, it promises, have in our day only heralded the advent of a new science. But, however far in advance of the Founders of the Royal Society the current philosophy may be, there was a robustness and characteristic individuality about the great men of that generation which we may not hope to see replaced. We may assume, indeed we hope, that the close of the next century will find the progress of knowledge as far advanced beyond its present limits as we think that the science of to-day is beyond the point reached a century ago. We may be assured that before that time arrives, many surmises, still in the region of hypothesis, will have become certainties, and that many supposed certainties will have turned out fallacies. Many errors will have been corrected, many dogmas discredited, many theories confirmed or refuted at the bar of ascertained fact, as those of 1783 have been. 474 Proceedings of the Royal Soeiety Yet even then will our successors, I trust, as we now do, stand reverently before the memory of our Founders. In their very linea- ments, of which, as portrayed by the master hand of Eaeburn, we saw many not far from this spot a few years ago, the vigour and originality of the men are written in characters not to be mistaken. Happy is the institution which can show such a muster-roll, and happy the country which can boast such sons. I take leave of my theme with the fervent hope and firm conviction that, in the century which we now inaugurate, the Eoyal Society will continue with like success the noble task to which by its Charter it is devoted, of in- vestigating the hidden treasures of nature, and appropriating them to the benefit and happiness of mankind. On the motion of the Hon. Lord McLaren, a vote of thanks was accorded to the President for his address. The following Communications were read: — 2. On the Microscopic Characters of Volcanic Ashes and Cosmic Dust, and their Distribution in the Deep Sea Deposits. By Mr John Murray and Mons. A. Eenard. Communicated by Mr John Murray. In the Session of 1876, Mr John Murray communicated to this Society a paper on the distribution of volcanic debris over the floor of the ocean,* and in it announced the discovery of cosmic dust in deep sea deposits. It was shown that at points, v/here neither the action of waves, rivers, or currents can transport the debris of continents, volcanic materials play the most important role in the formation of the mineral constituents of the deep sea deposits. It was pointed out that pumice, on account of its structure, was able to float to great distances, but in time became waterlogged and sank to the bottom, there to decompose. On the other hand, inco- herent volcanic matters, ejected in the form of lapilli, sand, and ashes, into the higher regions of the atmosphere, may, ceteris jparihus, be conveyed, in consequence of their small dimensions and struc- ture, to greater distances than other mineral particles derived fi'om the continents. The possibility was also admitted that submarine volcanic eruptions might also contribute to the accumulation of * Ptoc, Roy. Soc. Edm., 1876-77. of Edinhurgh, Session 1883-84. 475 those silicates and pyrogenons minerals and rocks, whose microscopic characters and distribution at the bottom of the sea we shall presently point out. During the past few years we have added greatly to the observa- tions which were the subject of Mr Murray’s communication. The present paper has been suggested by the striking analogy which exists between the volcanic products we have found in all deep sea sediments and the ashes and incoherent products of a recent cele- brated eruption, — that of Krakatoa. The remarkable meteorological phenomena we have recently witnessed have been attributed by some to the presence in the atmosphere of mineral particles derived from this volcanic eruption, and by others to that of cosmic dust. It is said that in several places in America, and even in Europe, matters have been collected which must be regarded as the ashes from Krakatoa, which have been suspended for several months in the upper currents of the atmosphere. The importance of this matter has been recognised by the Royal Society of London, which has appointed a committee of its members to collect all the documents and observations relative to the distribution of these ashes. The present state of the question induces us to make known some results of the detailed researches which we have undertaken upon similar subjects. We desire to make known to those who wish to study atmospheric dust, the distinctive microscopic characters by the aid of which we have been able to establish the volcanic or cosmic nature of certain particles found in deep sea deposits, and to show at the same time the enormous area of the ocean over which we have been able to detect their distribution. We believe that no better example could be found in support of our interpretations than the microscopic study of the ashes from Krakatoa, whose mineralogical and chemical composition M. Eenard * was the first to make known, and whose observations on this subject have been amply confirmed by the later researches of other minera- logists. On the other hand, the conditions under which floating pumice was found after that eruption agree perfectly with the inter- pretation given eight years ago by Mr Murray, relative to the mode of transport of these vitreous matters, and of the accumulation of their triturated debris on the bottom of the ocean. We shall also * “Les cendres volcaniques de I’eruption du Krakatau” {Bull. Acad. Boy. de Belghiue, ser. 3, t, vi. No. 11 Seance du 3 Nov. 1883). 476 Proceedings of the Royal Society see how the sorting which takes place in the transport of the ashes of a volcano has its analogy in what we find in the deep sea deposits. In the First Part of this communication we shall give the miner- alogical description of the fragmentary products of Krakatoa, and consider generally the observations relative to these ashes. We shall also give the diagnostic characters of this volcanic dust, and of all similar particles which we find in deep sea deposits. In the Second Part, we will treat of the cosmic matters found in the abysmal regions of the ocean, to which Mr Murray was the first to draw attention, and discuss their origin and distribution. First Part. It is unnecessary to refer to the abundance of floating pumice, to its various degrees of alteration, to its conveyance by means of rivers, waves, and currents, and to its universal presence in deep sea deposits, which have been pointed out in some detail in Mr Murray’s paper above referred to ; but we will briefly recapitulate the char- acters of these volcanic matters, in accordance with the examination we have made of a large number of soundings and dredgings. We need not describe in detail the special characters of the lapilli which have been brought up in the dredge and sounding-rod from great depths. These fragments of more or less scoriaceous rocks belong to the same lithological varieties as those derived from terrestrial volcanoes. They consist of fragments of trachyte of various dimen- sions, of basalt, and, above all, of augite-andesite ; the most remark- able, beyond all question, being lapilli of sideromelan, which are often entirely transformed into palagonite, and pass into the clay which is found so widely distributed, especially in the Pacific. We do not propose here to take up in detail the wide distribution of the materials ejected from Krakatoa; we are engaged in collect- ing these, and will place the observations on maps along with those of Mr Buchan on the upper currents of the atmosphere, which will be published in the ‘‘Challenger” Beports. Before, however, passing to the description of the ashes themselves we will briefly refer to some points touched upon by Mr Murray in his paper. It is there pointed out that, in regions far removed from coasts, rounded fragments of pumice were collected on the surface of the sea by means of the tow-net, and that, at certain points on the bottom of the ocean, the greater part of the deposit is composed of Edinhurgli, Session 1883-84. 477 of vitreous splinters derived from the trituration of pumice stones. The description of the phenomena connected with the Krakatoa eruption gives us a complete explanation of these observations. The specimens of pumice from Krakatoa, which have been collected floating on the sea and which we have examined, are in like manner rounded. The angular surfaces are all worn away just as in pebbles ; the only asperities to be observed consist of crystals and fragments of crystals, which project beyond the general surface of the vitreous matter, which last, on account of its structure, presents less resistance to wear and tear than the minerals which are embedded in it. We may recall the fact that the Bay of Lampoung, in the Straits of Sunda, was blocked by the vast accumulation of pumice, formed in a few hours by the eruption of Krakatoa, which completely filled the bay. This floating bar of pumice stones was about 30 kilometres long, 1 kilometre broad, and 3 to 4 metres in depth, 2 or 3 metres of which were below the surface of the water, and 1 metre above. These numbers give about 150 millions of cubic metres of ejected matter. This moving elastic wall rose and fell with the waves and tide,* and was carried by currents thousands of miles from the point of eruption over the surface of the ocean. The rounded form of blocks of pumice met with everywhere floating on the surface of the sea, as well as of those samples which, after having floated some time, became waterlogged and sank to the bottom, may be perfectly explained if we remember the friability of this rock, and, at the same time, the agitation to which it is submitted by the waves, through which the pieces are continually being knocked against each other. We understand also how this wear and tear gives rise to an immense quantity of pulverulent pumice fragments, which contribute in a great measure to the formation of oceanic deposits. As a matter of fact, rounded fragments of pumice have been met with floating on the surface of every ocean, and during the last few years many samples have been sent to us by captains of ships and missionaries. As has been already pointed out, they are universally distributed in oceanic deposits, although frequently highly altered. If it be easy to pronounce upon the volcanic nature of these larger fragments, it becomes, on the other hand, exceedingly difficult when we have to deal with particles reduced to powder, and when * Comptcs rendus d& V Academie des Sciences, 19 Nov. 1883, p. 1101. 478 Proceedings of the Royal Society recourse must be bad to tbe microscope. Let us see what are tbe microscopic characters by which we recognise the particles of this dust. We may here point out that it is not so much the presence of volcanic minerals which enables us in a marine sediment, as well as in an atmospheric dust like the ashes of Krakatoa, to recognise that the small fragments have an eruptive origin, as the microscopic structure of the small vitreous particles. It is well known that minerals reduced to small dimensions and irregularly fractured, as in the case of volcanic ashes, often lose their distinctive characters. Their size does not allow us to judge of their optical properties ; their form, irregular and fragmentary, renders it difficult to de- termine the characteristic extinction of the species ; the phenomena of coloration, of pleochroism, and the tint peculiar to the mineral, all lose so much of their intensity, that they no longer serve for the identification of isolated minerals like those of the volcanic ashes which we have to study. As a result of our observations, we believe that in most cases where a mineral, under the conditions we have just described, reaches dimensions less than 0'05 mm., its deter- mination with certainty is no longer possible, and consequently its origin can no longer be established ; whilst a vitreous fragment, like those of volcanic ashes or triturated pumice, continues to be dis- cernible when its dimensions are less than 0’005 mm. A reason for showing that the absence or rarity of crystals, or of fragments of volcanic crystals, ought not to be taken as a proof that a sedimentary matter, either from the atmosphere or from the deep sea, is not of volcanic origin, is the sorting process to which these matters are subjected in the air and in the water, a phenomenon to which we shall presently recur. The most reliable distinctive character is always found in the structure of the small vitreous particles which are derived from the trituration of pumice or have an analogous origin, inasmuch as they have been ejected from the volcano in the state of ash. The struc- ture peculiar to these materials is seen in their fracture, which leaves its impress upon the smallest fragments of debris, in which the microscope can decipher no characteristic properties except such as have relation to form. In order to assure ourselves that these characters of pumice remain constant to the extreme limits of pul- verisation, such as are employed in tlie preparation of silicates for oj Edinhurgli, Session 1883-84. 479 clieajical analysis, Ave pounded in an agate mortar several varieties of pumice, and the powder thus produced clearly showed itself to be composed of particles in Avhich were recognisable, with little trouble, the characters of the pumice-like material which is constantly met with in the sediments, and of which the ashes of Krakatoa give us beautiful examples. The diagnostic character to which we here make allusion rests on the distinctive peculiarities of incoherent volcanic products. What distinguishes them from lavas is not merely the extraordinary abundance of vitreous matters, but also the prodigious number of gas-bubbles which are enclosed by the pumice and vitreous volcanic sands and ashes. These bubbles are due to the expansion of the gases dissolved in the magma, Avhich also determine the eruption. If we admit, as everything seems to show, that these incoherent volcanic matters are the products of the pulverisation of a fluid magma, Ave can understand that these particles, on cooling rapidly, will remain in the vitreous state, and, on the other hand, that the dissolved gases, yielding to the expansion, Avill form numerous pores which will become elongated owing to the mode of projection. It is the existence of these bubbles, or of such a filamentous structure, AAdiich points out to us the vitreous volcanic materials in spite of the great fineness of subdivision. It is also this structure which allows these bodies to be carried to such great distances from the scene of eruption. The examination of the Krakatoa ashes, and of the dust resulting from the pulverisation of the pumice of that volcano, shoAVs markedly the peculiarity due to the bullous structure. If this grey-green pulverulent matter be placed under the microscope it is seen to be composed of almost impalpable grains, with a mean diameter of 04 mm., Avhich are almost exclusively colourless or broAvnish vitreous particles permeated by bubbles. The bubbles are rarely globular, but often elongated, as we have just pointed out, and they give a draAvn-out appearance to the fragments. As often happens, several bubbles are elongated parallel to each other, and in this case, the pore becomes a simple streak ; the fragment then assumes a fibrous texture, Avhich may cause it to resemble at first sight a striated felsiDar or an organic remnant ; but an exa- mination of the outline Avill never allow of this confusion. If Ave examine the terminal contours and lines of these bubble-containing fragments, we never find that they are straight lines, but that 480 Proceedings of the Royal Society they show a ragged appearance, all the sinuosities being curvilinear This mode of fracture is in correspondence with the vacuolated structure, and, just as in the porous pumice, the vitreous volcanic ashes are permeated by vacuoles ; besides, everything goes to show that the fragmentary condition and the fresh fractures are due to a tension phenomenon which alfects these vitreous matters in a manner analogous to what is observed in the “Eupert’s drops.” Fig. 1. — Yitreous particles of the Ashes of Krakatoa, which fell at Batavia, 27th August 1883 AYe have pointed out that brown vitreous fragments are rare in the ashes of Krakatoa. These, however, contain skeletons of magnetic iron, and are de vitrified by microliths.^- It is scarcely necessary to add that the particles, whose form we have indicated, are isotropic. If under crossed nicols we sometimes see the field illuminated, this is due to crystals in the vitreous matter, or to phenomena of tension, which are sometimes observed in the neigh- bourhood of the bubbles. These details on the microstructure of the vitreous particles from Krakatoa can be applied with most perfect exactitude to the vol- canic dusts, which we have determined as such, in the deep sea deposits. In virtue of their bulbous structure, their dimensions, and their mode of projection, they are capable of being widely transported from the point of eruption by aerial currents. It must be admitted, * Just as we can divide pumice microscopically according as it is acid or basic, so the products of its trituration may be recognised under the microscope, inasmuch as the former often give colourless and more elongated particles, while the fragments of basic pumice have a more pronounced tint and more rounded pores. of Edinhurgh, Session 1883-84. 481 however, that in the deep sea sediments a very large part of these vitreous splinters has not been derived from the pulverised ejections from a volcano, but from the trituration of floating pumice, of which we have given above a striking example. It will be understood that it is scarcely possible to trace the difference between volcanic ashes, properly so called, and the products resulting from the pulverisation of floating pumice which we have just indicated. As in the inco- herent products of Krakatoa, so we find spread out on the bottom of the sea many more vitreous particles, similar to those we have just described, than of true volcanic minerals. This is easily explained, however, when we remember how the distribution of volcanic dust takes place. Let us now point out the minerals which can be determined with certainty in the ashes of this great eruption ; and we may at once remark that they are the same which we have almost always found associated in the deposits with the splinters of glass. In general all the crystals are fractured, except those which are still embedded in a vitreous layer ; this vitreous coating is often crackled and bullous. In the ashes of Krakatoa, however, we have not remarked the globules of glass which are often described as glued to the minerals of volcanic ashes, nor have we seen the drawn-out vitreous filaments resembling Peles hair. The minerals of the Krakatoa ashes which are susceptible of a rigorous determination belong to plagioclase, augite, rhombic pyroxene, and magnetite.* We shall presently see the peculiarity which distinguishes each of these species in the ashes. Among the most frequent minerals, but poorly represented in comparison with the vitreous matter, plagioclase felspar comes first. This mineral has about the same dimensions as the vitreous frag- ments, and, with the exception of the crystals entirely enclosed in the pumice matter, is in the form of debris. Sometimes twins on the albite plan can be distinguished, and the results of analysis clearly indicate that it is triclinic felspar which should almost exclusively be found in this ash. But the most interesting crystals of plagio- * Lately the works on these same ashes have made known as accidental elements pyrites, apatite, and perhaps biotite (?). It is to be remarked, how- ever, that these minerals must be extremely rare in comparison with the vitreous matters and mineral species above-mentioned. 482 Proceedings of the Royal Society clase, and the most characteristic of this ash, although represented very rarely, are in the form of rhombic tables, extremely thin, and covered with a fine lacework of vitreous matter. We know that the crystals described by Penck * in a great number of lapilli and of volcanic ashes, upon the nature of which doubts have been expressed, belong incontestibly to the plagioclases, and represent an isomorphic mixture analagous to that of bytownite. It is to Mr Max Schuster t that we owe this specific determination. Having found in numerous sediments of the Pacific these same crystals in the form of rhombic tables, and possessing preparations which would be of great interest to him in his remarkable optical studies on the felspars, we submitted them to this ingenious mineralogist in order to confirm our determination. We believe it will be interesting to give a resume here of the results of the observations of Mr Schuster, which are perfectly applicable to the characteristic crystals of felspar from Krakatoa, as well as to those which we have discovered in a great number of deep sea soundings. This plagioclase occurs for the most part in flat tabular crystals with the clinopinakoid especially developed. Individuals of the columnar type, elongated in the direction of the edge P/M, are rare. These tabular crystals consist essentially of a combination of the clinopinakoid with P and x, more rarely with P, u, and y, and occasionally x and y appear together. In the first case the crystals have the form of a rhomb, in the second case they are elongated through the predominance of either x or P. The dimensions of those crystals which were examined and measured, lie between the line 0-61 mm. broad and 1 mm. long as maximum, and 0’015 mm. broad and 0'042 mm. long as minimum. The extinction of the plagioclase is negative. Its value was found to vary between 22° and 32° on the clinopinakoid, and between 8° and 16° on the basal plane. The average values of many measurements made on good crystals are as follows: — 24° 12', 25° 6', and 29° 6' on the clinopinakoid, 10° 42' on the one side, and 10° 18' on the other side of the twinning line, as this is shown on the basal plane. * Penck, “Studien iiber lockere vulkanische Auswiirflinge,” Zeitsclir. d. dcutsch. geol. Gesellscli., 1878. 4 Schuster, “ Bemerkungen zu E. Mallard’s Abhandlung sur risomorpliisme des feldspaths triclinigues, &c.,” Min. petr. Mittli., v. 1882, p. 194. of Edinhurgh, Session 1883-84. 483 Polysyntlietic individuals, made up of repeated twins on the albite plan, were very rarely observed. The felspar in its optical pro- perties is thus seen to lie between lahradorite and hytownite. The twin growths are particularly frequent and interesting on account of the structure of the individuals. In addition to those of the albite type, others were observed in which the edges P/M and P/K could be definitely determined as the axes of twinning, whilst P and K formed the twinning planes. The plane of composi- tion was principally either P or M when penetration twins were not observed. These fragments and crystals of plagioclase contain inclusions of vitreous matter, and sometimes grains of magnetite. Perhaps a small number of felspathic grains may belong to sanidine, the presence of which Is insinuated by the percentage of potass indi- cated by the analysis which follow (K2O — 0*97 per cent.). We have said that the pyroxenic minerals of the ash are augite and a rhombic pyroxene ; we distinguish them by the microscope some- times in the form of fragments— and this is usually the case— some- times in the form of crystals, which we can isolate from the volcanic glass covering them by treating them with hydrofluoric acid. In the crystals of augite we distinguish the faces of a prism, of the brachypinakoid, and indications of the faces of a pyramid. This augite is pleochroic and has a greenish tint, and extinguishes in certain cases obliquely to the prismatic edges. It is this character which often permits it to be distinguished from rhombic pyroxene with which the augite is associated. The crystals of hypersthene are transparent, of a deep brown colour, strongly dichroic, with green and brown tints. They are in rect- angular prisms terminated by a pyramid, and extinguish between crossed nicols parallel to their longitudinal edges. Magnetic iron, which is rather abundant in the ashes, is recognised in the form of grains and octahedrons. We have not been able to detect with certainty either hornblende or olivine. The largest grains of this ash are true microscopic lapilli, where we distinguish in a vitreous mass microlithic crystals of felspar, of magnetite, and more rarely of pyroxene, Finally, we observe with the microscope particles of an organic origin, which are easily recognisable by their fibrous and reticulated structure. These impurities may have been transported 2 I VOL. XII. 484 Proceedings of tlhe Eoyal Society by winds, or may have come from the ground wdiere the ashes were collected. In spite of all the uncertainties which the exact diagnoses of volcanic dust present, we can consider them often, from the point of view of their mineralogical composition, as analogous with the augite-andesites. We know, besides, that it is to these rocks that the lavas of the volcano of Krakatoa should be referred. The ashes which fell at Batavia on the 27th August 1883, and samples of which were sent to Holland by M. Wolf, resident on that island, have been analysed with the following results : — I. 1 T19 grm. of substance dried at 110° C. , and fused with carbonate of soda and potash, gave 07799 grm. of silica, 07754 grm. of alumina, 0’0911 grm. of peroxide of iron, 0*0401 grm. of lime, 0*398 grm. of pyrophosphate of mag- nesia, answering to 0*01434 grm. of magnesia.* II. 1*222 grm. of substance dried at 110° C. gave 0*0335 grm. of loss on igni- tion (water, organic substances, chloride of sodium); the same substance treated with hydrofluoric and sulphuric acids gave 0*1161 grm. of chloride of sodium and potassium, and 0*0118 grm. of chloroplatinate of potassium, answering to 0*0118 grm. of potash and to 0*0188 grm. of chloride of potas- sium; by diff‘erence = 0*0973 grm. of chloride of sodium, answering to 0*05163 of soda. III. 1 *7287 grm. of substance dried at 110° C. was treated in a closed tube with hydrofluoric and sulphuric acid. The oxidation required 2 *3 c. c. of perman- ganate of potash (1 c.c. =0*0212 grm. FeO), answering to 0*047876 grm. of peroxide of iron. I. II. III. SiOa 65*04 65*04 AI2O3 14*63 14*63 FegOg 4*47 4*47 FeO . . . 2*82 2*82 MnO traces traces MgO 1*20 1*20 CaO 3*34 3*34 K^O 0*97 0*97 Ha20 4*23 4*23 Loss 2*74 2*74 99*44 It will be understood that it is barely possible to submit this analysis to discussion. The abundance of vitreous particles in the ashes renders illusory the calculation of the values obtained, and * A recent determination of titanic acid has given 0*62 per cent. TiO.2. 485 of Edinhurgh, Session 1883-84. the distribution of the substances among the different species of constituent minerals. This vitreous matter can indeed contain an indeterminate quantity of the different bases. On the other hand, the difficulties of the calculation are all the greater, as the consti- tuent minerals of the ashes may contain, as isomorphs, the bases which the analysis suggests. It is none the less true, however, that the percentage composition expressed by the analysis supports the preceding mineralogical determinations, without permitting the species to be precisely determined. It agrees with the interpreta- tion that the magma from which the ashes were formed belongs to the augite-andesites. The vitreous and mineral fragments we have just described from the Krakatoa eruption being identical with those which we encounter in deep sea sediments, we may conclude that both have a similar origin. In certain cases, however, we have in place of augite a predominance of hornblende, and sometimes black mica is abundant. Again, we find more or less fragmentary crystals of peridote, of magne- tite, of sanidine, and, more rarely, of leu cite and of hauyne. We can easily understand this variation in composition, following the nature of the magma from which the ashes collected in different regions of the sea were derived. But in all cases it is the predominance of vitreous particles, with their special structure, which indicates most clearly the volcanic nature of the inorganic constituents of a sediment. If now we consider the conditions which govern the distribution of ashes in the atmosphere or at the bottom of the sea, we shall be able to show how it is that there is generally a predominance of vitreous particles in these ashes. In the first place, these are vitreous matters rather than minerals, properly so called, from the moment of ejection from the crater. Moreover, we should, in a general way, not expect to find that incoherent eruptive matters, which are spread out at a distance from the volcano, present a perfectly identical composition with those other loose products such as lapilli, volcanic bombs, and scoriae, which are projected only a short distance from the focus of eruption. Even where there exists a perfect chemical and mineralogical identity, in the crater itself, between the lavas and the pulverulent materials of the same eruption (the supposition being that the ashes arise simply from the trituration of the lavas), we can easily understand that these latter, being carried far and wide 486 Proceedings of the Royal Society by the winds, must undergo a true sorting in their passage through the atmosphere, according to the specific gravity of the amorphous elements or crystalline constituents. It results from this, that according to the points where they are collected, volcanic ashes may, although belonging to the same eruption, present differences not only with respect to the size of the grains, but also with respect to the minerals. In this method of transport it is evident that the vitreous particles, other things being equal, will be transported farthest from the centre. In the first place they are more abundant than the other particles, and again they possess in their chemical nature and in their structure, conditions which permit the aerial currents to take them up and carry them to great distances j they consist of a silicate in which the heavy bases are poorly re- presented as compared with the other constituent elements ; they are filled with gaseous bubbles which lower their specific gravity, and at the same time are capable of being broken up into the minutest particles. The minerals with which they are asso- ciated at the moment of ejection from the crater are not, like them, filled with gaseous bubbles ; they do not break up so easily into impalpable powder, for they are not porous, and are not in the same state of tension as the rapidly-cooled vitreous dust. Finally, many of these species are precisely those whose specific gravity is very high, on account of the bases entering into their composition. These minerals will not then be carried so far from the centre of eruption, and in all cases the vitreous particles are the essential ones in the atmospheric dusts derived from volcanic ashes. We have a beautiful illustration of this in the ashes of Krakatoa. In proportion as the ashes are collected at a greater distance from a volcano, so are they less rich in minerals, and the quantity of vitreous matter predominates. According to a verbal communication from Professor Judd, the ashes collected at Japan contain only a relatively small proportion of pyroxene and magnetite. If we wish to assure ourselves of the nature of an atmospheric dust, and, as has lately been frequently attempted in Europe, to show that the dust is really from the Krakatoa eruption, it is important above all to seek for the presence of vitreous fragments. The characters which we have indicated permit any one to recognise of Edinburgh, Session 1883-84. 487 them easily under the microscope. We would remark, however, that the presence of crystals, either of hypersthene, of augite, or of particles of magnetite in an atmospheric dust collected in Europe, does not prove in a certain manner that the dust belongs to the ashes from Krakatoa; for besides the difficulties of an exact minera- logical determination of the fragmentary elements, it is difficult to understand how these heavy minerals should have been carried by the aerial currents, while the vitreous dust is absent. As we have just shown, it is the contrary which should have taken place. It results as a corollary from these considerations that the chemical composition of an ash may vary according to the point at which it has been collected, and it tends also, other things being equal, to become more acid the further it is removed from the centre of eruption. If we admit, for example, that the magma which gave birth to the ashes of Krakatoa is an augite-andesite, as everything seems to indicate, the percentage of silica (65 per cent.) which our analysis shows appears too high, but if we remember, what we have just said, that the ashes become deprived, during their passage through the atmosphere, of the heavier and more basic elements, it will be understood that the vitreous and felspathic materials, which have a lower specific gravity, and are, at the same time, more acid, will accumulate at points farthest from the volcano. It will be sufficient to have directed the attention to this fact to show how the percentage of silica in the ashes from the same eruption may vary according as they are collected at a variable distance from the crater. The predominance of vitreous splinters in deep sea sediments far removed from coasts is even more pronounced than in volcanic ashes collected on land. This arises, as we indicated at the commence- ment, from the large quantity of pumice carried or projected into the ocean, whose trituration, which takes place so easily, gives origin to vitreous fragments difficult to distinguish from those projected from a volcano in the form of impalpable dust. In addition, we may state that in the distribution of volcanic materials on the bottom of the sea, the ashes are subjected to a mode of sorting having some analogy to that which takes place during transport through the atmosphere. When these ashes fall into the sea a separation takes place in the water; the heaviest particles 488 Proceedings of the Royal Society reach the bottom first, and then the lighter and smaller ones, descending more slowly, are deposited upon the larger and heavier fragments and crystals from the same eruption. We have a fine example of this stratification of submarine tufa in the centre of the South Pacific, lat. 22° 2P S., long. 150° 17' W. This specimen is entirely covered with peroxide of manganese, and at the base of the fragment we see the large crystals of hornblende and particles of magnetite. This lower layer is covered by a deposit in which these minerals and coarser grains are observed to pass gradually into a layer composed of small crystals of felspar, d4bris of pumice, and more or less fine material. We do not propose to occupy ourselves here with the mode of formation of volcanic ashes, and with those of Krakatoa in particular. It will suffice to indicate that in the dust of a volcano we find all the characters supporting the interpreta- tion which regards volcanic ashes as formed by the pulverisa- tion of an igneous fluid mass in which float crystals already formed, and from which, when projected by gases, the pulverised vitreous particles undergo a rapid cooling and decrepitation during their passage through the atmosphere. It is not only the micro- scopic examination of these volcanic matters that leads us to this conclusion, but the prodigious quantity of ashes formed during the eruption of this volcano, which do not agree with the interpretation that regards these ashes as the result of a pulverisation of a rock already solidified in the crater. Indeed one cannot understand how, in two or three days, the immense quantity of ashes ejected from Krakatoa could be formed by this process, as, for instance, on the 26th August 1883 and in the May eruption, which was the prelude to that catastrophe. Second Part. The recent brilliant sunsets have been attributed to the presence in the atmosphere of minute particles of an extra- terrestrial origin, as well as to volcanic dust. This induces us to conclude this brief abstract of our observations by a descrip- tion of the cosmic particles which we have found, along with volcanic ashes and pumice, in those regions of the deep sea far from land, where the sediment accumulates with extreme slowness. 489 of Edinburgh, Session 1883-84. In another memoir * we have pointed out the distribution of these particles on the floor of the ocean, and indicated the conclu- sions which we believe are justifled by their relative abundance in the red clay areas of the Central Paciflc. It is known that the atmosphere holds in suspension an immense number of microscopic particles which are of organic and inorganic origin, and are either dust taken up by aerial currents from the ground or are extra-terrestrial bodies. A large number of scientific men, headed by Ehrenberg, Daubree, Reich enbach, Nordenskiold, and Tissandier, have studied this interesting problem, and have brought forward many facts in support of the cosmic origin of some of the metallic particles found in atmospheric precipitations. It is certain that serious objections may be raised against the origin of a large number of so-called cosmic dusts. In a great many cases it can be shown that these dusts are com- posed of the same minerals as the terrestrial rocks which are to be met with at short distances from the spot where the dust has been collected, and we can attribute a cosmic origin only to the metallic iron in these dusts. It is somewhat astonishing, however, that no trace is ever found in these dusts of meteoric silicates, although in a great many meteorites it might be said that the iron is only accidentally present, while the silicates predominate. On the other hand, having regard to the mineralogical composition of meteorites, it appears strange that the so-called cosmic dusts should present characters so variable, from the point of view of their mineralogical composition, in the different regions where they have been collected. It might also be objected that even the iron, nickel, and cobalt could come from volcanic rocks in decomposition in which these bodies are sometimes present, and this objection would seem quite natural, especially in our particular case, when we remember the numerous volcanic fragments in decomjoosition on the bottom of the sea. Again, according to numerous researches, native iron is found, although rarely, in various rocks and sedimentary layers of the globe. A reduction of the oxide of iron into metal might also be admitted under the influence of organic substances. It might still further be objected in opposition to the cosmic origin of the fine particles of native iron that they might be carried by aerial currents Ptoc. Poy. Soc. Edin. 490 ' Proceedings of the Boy at Society from our furnaces, locomotives, the ashes of our grates, and in the case of the ocean, from steamers. All our materials of combustion furnish considerable quantities of iron dust, and it would not be astonishing to find that this, after having been transported by the winds, should again fall on the surface of the earth at great dis- tances from its source. Such are the objections which present themselves when it is pro- posed to pronounce upon the origin of particles which we are inclined to regard as cosmic, and of which we propose here to give a short description. We shall see that many of these doubts are at once removed by a statement of the circumstances under which cosmic spherules are found in deep sea deposits, and it will be found also that all the objections are disposed of when we show the asso- ciation of metallic spherules with the most characteristic bodies of undoubted meteorites. In the first place, the considerable distance from land at which we find cosmic particles in greatest abundance in deep sea deposits, eliminates at once objections which might be raised with respect to metallic particles found in the neighbourhood of inhabited countries. On the other hand, the form and character of the spherules of extra- terrestrial origin are essentially different from those collected near manufacturing centres. These magnetic spherules have never elongated necks or a cracked surface like those derived from furnaces with which we have carefully compared them. Neither are the magnetic spherules with a metallic centre comparable either in their form or structure to those particles of native iron which have been described in the eruptive rocks, especially in the basaltic rocks of the north of Ireland, of Iceland, &c. Having referred to the objections, let us now see on what we must rely, in support of the hypothesis that many of the magnetic particles from the bottom of the sea which are specially abundant in those regions where the rate of accumulation of the deposit is exceedingly slow, are of cosmic origin. If we plunge a magnet into an oceanic deposit, specially a red clay from the central parts of the Pacific, we extract particles, some of which are magnetite from volcanic rocks, and to which vitreous matters are often attached; others again are quite isolated, and differ in most of their properties from the former. The latter are generally round, of Edinburgh^ Session 1883-84. 491 measuring hardly 0'2 mm., generally they are smaller, their surface is quite covered with a brilliant black coating having all the properties of magnetic oxide of iron, often there may be noticed upon them cup- like depressions clearly marked. If we break down these spherules in an agate mortar, the brilliant black coating easily falls away and reveals white or grey metallic malleable nuclei, which may be beaten out by the pestle into thin lamellse. This metallic centre, when treated with an acidulated solution of sulphate of copper, immediately assumes a coppery coat, thus showing that it consists of native iron. But there are some malleable metallic nuclei extracted from the spherules which do not give this reaction ; they do not take the copper coating. Chemical reaction shows that they contain cobalt and nickel j very probably they constitute an alloy of iron and these two metals, such as is often found in meteorites, and whose presence South Pacific. in large quantities hinders the production of the coppery coating on the iron. G. Eose has shown that this coating of black oxide of iron is found on the periphery of meteorites of native iron, and its presence is readily understood when we admit their cosmic origin. Indeed, these meteoric particles of native iron in their transit through the air must undergo combustion, and, like small portions of iron from a smith’s anvil, be transformed either entirely or at the surface only into magnetic oxide, and in this latter case the nucleus Fig. 2, — Black Spherule with Metallic Nucleus (^). This spherule covered with a coat- ing of black shining mag- netite represents the most frequent shape. The de- pression here shown is often found at the surface of these spherules. From 2375 fins. Fig. 3. — Black Spherule with Metallic Nucleus (^). The black external coating o magnetic oxide has been broken away to show the metallic centre, represented by the clear part at the centre. From 3150 fms. Atlantic. 492 Proceedings of the Eoycd Society is protected from further oxidation by the coating which thus covers it. One may suppose that meteorites in their passage through the atmosphere break into numerous fragments, that incandescent particles of iron are thrown off all round them, and that these eventually fall to the surface of the globe as almost impalpable dust, in the form of magnetic oxide of iron more or less completely fused. The luminous trains of falling stars are probably due to the combustion of these innumerable particles resembling the sparks which fly from a ribbon of iron burnt in oxygen, or the particles of the same metal thrown off when striking a flint. It is easy to show that these particles in burning take a spherical form, and are sur- rounded by a layer of black magnetic oxide. Among the magnetic grains found in the same conditions as these we have just described are other spherules, which we refer to the cliondres, so that if the interpretation of a cosmic origin for the magnetic spherules with a metallic centre were not established in a manner absolutely beyond question, it almost becomes so when we take into account their association with the silicate spherules, of which we have now to speak. It will be seen by the micro- scopic details that these spherules have quite the constitution and structure of chondres so frequent in meteorites of the most ordinary type, and on the other hand they have never been found, as far as we know, in rocks of a terrestrial origin; in short, the presence of these spherules in the deep sea deposits, and their association with the metallic spherules, is a matter of prime importance. Let us see how we distinguish these silicate spherules, and the points upon which we rely in attributing to them a cosmic origin. Among the fragments attracted by the magnet in deep sea deposits we distinguish granules slightly larger than the spherules with the shining black coating above described. These are yellowish- brown, with a bronze-like lustre, and under the microscope, it is noticed that the surface, instead of being quite smooth, is grooved by thin lamellae. In size they never exceed a milli- metre, generally they are about 0'5 mm. in diameter; they are never perfect spheres, as in the case of the black spherules with a metallic centre ; and sometimes a depression more or less marked of Edinburgh, Session 1883-84. 493 is to be observed in the periphery. When examined by the micro- scope we observe that the lamellae which compose them are applied the one against the other, and have a radial eccentric disposition. It is the leafy radial structure {radialhlattrig), like that of the chondres of bronzite, which predominates in our preparations. We have observed much less rarely the serial structure of the chondres with olivine, and indeed there is some doubt about the indications of this last type of structure. Fig. 4 shows the characters and texture of one of these spherules magnified 25 diameters. On account of their small dimensions, as well as of their friability due to their lamellar structure, it is difficult to polish one of these spherules, and we have been obliged to study them with reflected light, or to limit our observations to the study of the broken fragments. These spherules break up following the lamellae, which latter are seen to be extremely fine and perfectly transparent. In rotating Fig. 4. — Spherule of bronzite {—) from 3500 fathoms in the Central South Pacific, showing many of the peculiarities belonging to chondres of bronzite or enstatite. between crossed nicols they have the extinctions of the rhombic system, and in making use of the condenser it is seen that they have one optic axis. It is observed also that when several of these lamellae are attached, they extinguish exactly at the same time, so that everything induces us to believe that they form a single individual. In studying these transparent and very thin fragments with the aid of a high magnifying power, it is observed that they are dotted 494 Proceedings of the Royal Society with brown-black inclusions, disposed with a certain symmetry, and showing somewhat regular contours ; we refer these inclusions to magnetic iron, and their presence explains how these spherules of bronzite are extracted by the magnet. We would observe, however, that they are not so strongly magnetic as those with a metallic nucleus. We designate them under the name of bronzite rather than of enstatite, because of the somewhat deep tint which they present ; they are insoluble in hydrochloric acid. Owing to the small quantity of substance at our disposal, we were obliged to limit ourselves to a qualitative analysis. We have found in them silica, magnesia, and iron. We have limited our remarks at this time to these succinct details, but we believe that we have said enough to show that these spherules in their essential characters are related to the chondres of meteorites, and have the saine mode of formation. In con- clusion, we may state that when the coating of manganese depositions, which surround sharks’ teeth, ear-bones of cetaceans and other nuclei, is broken off and pounded in a mortar to tine dust, and the magnetic particles then extracted by means of a magnet, we find these latter to be composed of silicate spherules, spherules with a metallic centre, and magnetic iron, in all respects similar to those found in the deposits in which the nodules were embedded. We have recently examined the dust collected by melting the snow at the Observatory on Ben l!levis, in order to see whether, in that elevated and isolated region, we should be able to find volcanic ashes or cosmic spherules analogous to those we have described. This atmospheric dust, which we have examined micro- scopically, has not shown any particles which could with certainty be regarded as identical with those substances which are the subject of this paper. Particles of coal, fragments of ashes, and grains of quartz predominated. Besides these, there were fragments of calcite, augite, mica, and grains of rock of all forms and of variable dimensions. These were associated with fibres of cotton, of vegetables, splinters of limonite and of tin — in short, everything indicating a terrestrial origin. In order to give an idea of the facility with which the winds of Edinhurgli, Session 1883-84. 495 may carry these matters even to the summit of the mountain, we may add that Mr Oniond has sent to us fragments of crystalline rocks, some having a diameter of two centimetres, which, he states, were collected on the surface of the snow at the summit after the storm of 26th January 1884. Arrangements are being made to collect the dust at the top of Ben l!4evis during calms with great care. 3. On the Nomenclature, Origin, and Distribution of Deep- Sea Deposits. By John Murray and A, Eenard, Com- municated by John Murray. Introduction. — The sea is unquestionably the most powerful dynamic agent on the surface of the globe, and its effects are deeply imprinted on the external crust of our planet ; but among the sedimentary deposits which are attributed to its action, and among the effects which it has wrought on the surface features of the earth, the attention of geologists has, till wuthin quite recent times, been principally directed to the phenomena which take place in the immediate vicinity of the land. It is incontestable that the action of the sea along coasts and in shallow water has played the largest part in the formation and accumulation of those marine sediments which, so far as we can observe, form the principal strata of the solid crust of the globe ; and it has been from an attentive study of the phenomena which take place along the shores of modern seas that we have been able to reconstruct in some degree the conditions under which the marine deposits of ancient times were laid down. Attention has been paid only in a very limited degree to deposits of the same order and, for the greater part, of the same origin, which differ from the sands and gravels of the shores and shallow waters only by a lesser size of the grains, and by the fact that they are laid down at a greater distance from the land and in deeper water. And still less attention has been paid to those true deep-sea deposits which are only known through systematic submarine investigations. One might well ask what deposits are now taking place, or have in past ages taken place, at the 496 Proceedings of the Royal Soeiety bottom of the great oceans at points far removed from land, and in regions where the erosive and transporting action of water has little or no influence. Without denying that the action of the tidal waves can, under certain special conditions, exert an erosive and transporting power at great depths in the ocean, especially on submerged peaks and barriers, it is none the less certain that these are exceptional cases, and that the action of waves is almost exclusively confined to the coasts of emerged land. There are in the Pacific immense stretches of thousands of miles where we do not encounter any land, and in the Atlantic we have similar conditions. What takes place in these vast regions where the waves exercise no mechanic action on any solid object ? We are about to answer this question by reference to the facts which an examination of deep- sea sediments has furnished. A study of the sediments recentl}^ collected in the deep sea shows that their nature and mode of formation, as well as their geographical and bathymetrical distribution, permit deductions to be made which have a great and increasing importance from a geological point of view. In making known the composition of these deposits and their distribution, the first outlines of a geological map of the bottom of the ocean will be sketched. This is not the place to give a detailed history of the various contributions to our knowledge of the terrigenous deposits in deep water near land, or of those true deep-sea deposits far removed from land, which may be said to form the special subject of this com- munication. From the time of the first expeditions, undertaken with a view of ascertaining the depth of the ocean, small quantities of mud have been collected by the sounding lead and briefly described. We may recall in this connection the experiments of Eoss and the observations of Hooker and Maury. These investiga- tions, made with more or less imperfect appliances, immediately fixed the attention, without, however, giving sufficient information on which to establish any general conclusions as to the nature of the deposits or their distribution in the depths of the sea. When systematic soundings were undertaken with a view of establishing telegraphic communication between Europe and America, the attention of many distinguished men was directed to the im- portance, in a biological and geological sense, of the specimens of of Edinburgh, Session 1883-84. 497 mud brought up from great depths. The observations of Wallich, Huxley, Agassiz, Baily, Pourtal^s, Carpenter, Thomson, and many others, while not neglecting mineralogical and chemical composition, deal with this only in a subordinate manner. The small quantities of each specimen at their command, and the limited areas from which they were collected, did not permit the establishment of any general laws as to their composition or geographical and bathymetrical distribution. These early researches, however, directed attention to the geological importance of deep-sea de- posits, and prepared the way for the expeditions organised with the special object of a scientific exploration of the great ocean basins. The expedition of the Challenger ” takes the first rank in these investigations. During that expedition a large amount of material was collected and brought to England for fuller study under the charge of Mr Murray, who has in several preliminary papers pointed out the composition and varieties of deposits which are now forming over the floor of the great oceans. In order to arrive at results as general as possible, it was resolved to in- vestigate the subject from the biological, mineralogical, and chemical points of view, and M. Kenard was associated with Mr Murray in the work. In addition to the valuable collections and observations made by the “ Challenger,” we have had for examina- tion material collected by other British ships, such as the “Porcupine,” “Bulldog,” “Valorous,” “Nassau,” “Swallow,” “Dove;” and, through Professor Mohn, by the Norwegian North Atlantic Ex- pedition. Again, through the liberality of the United States Coast Survey and Mr A. Agassiz, the material amassed in the splendid series of soundings taken by the American ships “ Tuscarora,” “ Blake,” and “ Gettysburg,” were placed in our hands. The results at which we have arrived may therefore be said to have been derived from a study of all the important available material. The work connected with the examination and description of these large collections is not yet completed, but it is sufficiently advanced to permit some general conclusions to be drawn, which appear to be of considerable importance. In addition to descrip- tions and results, we shall briefly state the methods we have 498 Proceedings of the Royal Society adopted in the study. All the details of our research will be given in the Eeport on the Deep-Sea Deposits in the “ Challenger ’’ series, which will be accompanied by charts indicating the distri- bution, plates showing the principal types of deposits as seen by the microscope, and numerous analyses giving the chemical com- position and its relation to the mineralogical composition. The description of each sediment will be accompanied by an enumera- tion of the organisms dredged with the sample, so as to furnish all the biological and mineralogical information which we possess on deep-sea deposits, and finally, we shall endeavour to establish general conclusions which can only be indicated at present. Before entering on the subject, we believe it right to point out the difficulties which necessarily accompany such a research as the one now under consideration, difficulties which arise often in part from the small quantity of the substance at our disposal, but also from the very nature of the deposit. Since we have endeavoured to determine, with great exactitude, the composition of the deposit at any given point, we have, whenever possible, taken the sample collected in the sounding tube. That procured by the trawl or dredge, although usually much larger, is not considered so satis- factory on account of the washing and sorting to which the deposit has been subjected while being hauled through a great depth of water. We have, however, always examined carefully the contents of these instruments, although we do not think the material gives such a just idea of the deposit as the sample collected by the sounding tube. The material collected by the last named instrument has been taken as the basis of our investigations, although the small quantity often gives to it an inherent diflSculty. It was the small quantity of substance collected by the sounding tube in early expeditions which prevented the first observers from arriv- ing at any definite results ; but when such small samples are sup- plemented by occasional large hauls from the dredge or trawl, they become much more valuable and indicative of the nature of the deposit as a whole. Not only the scantiness of the material, but the small size of the grains, which in most instances make up deep-sea deposits, render the determinations difficult. In spite of the im- provements recently effected in the microscopical examination of minerals, it is impossible to apply all the optical resources of the of Edinburgh, Session 1883-84. 499 instrument to the determination of the species of extremely fine, loose, and fractured particles. Again, the examination of these deposits is rendered difficult by the presence of a large quantity of amorphous mineral matter, and of shells, skeletons, and minute particles of organic origin. It is also to be observed that we have not to deal with pure and unaltered mineral fragments, but with particles upon which the chemical action of the sea has wrought great changes, and more or less destroyed their distinctive characters. What still further complicates these researches is the endeavour to discover the origin of the heterogeneous materials which make up the deposits. These have been subjected to the influence of a great number of agents of some of which our knowledge is to a great extent still in its infancy. We must take into account a large number of agents and processes, such as ocean currents ; the dis- tribution of temperature in the water at the surface and at the bottom; the distribution of organisms as dependent on temperature and specific gravity of the water; the influence of aerial currents; the carrying power of rivers; the limit of transport by waves; the eruptions of aerial and submarine volcanoes ; the effect of glaciers in transporting mineral particles, and, when melting, influencing the specific gravity of the water, which in turn affects the animal and plant life of the surface. It is necessary to study the chemical reactions which take place in great depths ; in short, to call to our aid all the assistance which the physical and biological sciences can furnish. It will thus be understood that the task, like all first attempts in a new field, is one of exceptional difficulty, and de- mands continued effort to carry it to a successful issue. In presenting a short resume of our methods, of the nomen- clature we have adopted, and of the investigation into the origin of the deposits in the deep sea and deeper parts of the littoral zones, we offer it as a sketch of our research, prepared to modify the arrangements in any way which an intelligent criticism may suggest. Before proceeding to a description of methods and of the varieties of deposits, with their distribution in modern oceans, we will briefly enumerate the materials which our examination has shown take part in the formation of these deposits, state the origin of these ,2 K VOL. XII. 500 Proceedings of the Royal Soeiety materials, and the agents concerned in their deposition, distribution, and modification. Materials, — The materials which unite to form the deposits which we have to describe may be divided into two groups, viewed in relation to their origin, viz., mineral and organic. The mineral particles carried into the ocean have a different form and size, according to the agents which have been concerned in their transport. Generally speaking, their size diminishes with distance from the coast, hut here we limit our remarks to the mineralogical character of the particles. We find isolated fragments of rocks and minerals coming from the crystalline and schistomrystalline series, and from the clastic and sedimentary formations ; according to the nature of the nearest coasts they belong to granite, diorite, diabase, porphyry, S^o,, ; crystalline schists, ancient limestones, and the sedi- mentary rocks of all geological ages, with the minerals which come from their disintegration, such as quartz, monoclinic and triclinic felspars, hornblende, augite, rhombic pyroxene, olivine, muscovite, biotite, titanic and magnetic iron, tourmaline, garnet, epidote, and other secondary minerals. The trituration and decomposition of these rocks and minerals give rise to materials more or less amorphous and without distinctive characters, but the origin of which is indi- cated by association with the rocks and minerals just mentioned. Although the debris of continental land to which we have just referred plays the most important role in the immediate vicinity of shores, yet our researches show beyond doubt that when we pass out towards the central parts of the great ocean basins, the debris of continental rocks gradually disappears from the deposits, and its place is taken by materials derived from modern volcanic rocks, such as basalts, trachytes, augitemndesites, and vitreous varieties of these lithological families, for instance, pumice and loose incoherent volcanic particles of recent eruptions, with their characteristic minerals. AU these mineral substances being usually extremely fine or areolar in structure, are easily attacked by the sea water at the place where they are deposited, This chemical action brings about an alteration of the minerals and vitreous fragments, which soon passes into complete decomposition, and in special circum- stances gives rise to the formation of secondary products. In some of Edinburgh, Session 1883-84. 501 places the bottom of the sea is covered with deposits due to this chemical action, principal among which is clayey matter, associated with which there are often concretions composed of manganese and iron. In other regions the reactions which result in the formation of argillaceous matter from volcanic products give rise also to the formation of zeolites. Among other products arising from chemical action, probably combined with the activity of organic matter, may be mentioned the formation of glauconite and phosphatic nodules, witli, in some rare and doubtful examples, the deposition of silica. Tlie decomposition of the tissues, shells, and skeletons of organisms add small quantities of iron, fluorine, and phosphoric acid to the in- organic constituents of the deep-sea deposits. Finally, we must mention extra-terrestrial substances in the form of cosmic dust. We now pass to the consideration of the role played by organisms in the formation of marine deposits. Organisms living at the sur- face of the ocean, along the coasts, and at the bottom of the sea, are continually extracting the lime, magnesia, and silica held in solution in sea water. The shells and skeletons of these, after the death of the animals and plants, accumulate at the bottom and give rise to calcareous and siliceous deposits. The calcareous deposits are made up of the remains of coccosplieres, rhabdospheres, pelagic and deep-sea Foraminifera, pelagic and deep-sea Molluscs, Corals, Alcyonarians, Polyzoa, Echinoderms, Annelids, Fish, and other organisms. The siliceous deposits are formed principally of frustules of Diatoms, skeletons of Eadiolarians, and spicules of Sponges. While the minute pelagic and deep-sea organisms above men- tioned play by far the most important part in the formation of deep-sea deposits, the influence of vertebrates is recognisable only in a very slight degree in some special regions by the presence of large numbers of sharks’ teeth, and the ear bones and a few other bones of whales. The otoliths of fish are usually present in the deposits, but, with the exception of two vertebrae and a scapula, no other bones of fish have been detected in the large amount of material we have examined. Agents. — Having passed in review the various materials which 502 Froceedings of the Royal Society go to the formation of deposits in the deep water immediately surrounding the land and in the truly oceanic areas, attention must now be directed to the agents which are concerned in the transport and distribution of these, and to the sphere of their action. The relations existing between the organic and inorganic elements of deposits to which we have just referred, and the laws which determine their distribution, will be pointed out at the same time. The fluids which envelope the solid crust of the globe are in- cessantly at work disintegrating the materials of the land, which, becoming loose and transportable, are carried away sometimes by the atmosphere, sometimes by water, to lower regions, and are eventu- ally borne to the ocean in the form of solid particles or as matter in solution. The atmosphere when agitated, after having broken up the solid rock, transports the particles from the continents, and in some regions carries them far out to sea, where they form an appreciable portion of the deposit ; as, for instance, off the west coast of Xorth Africa and the south-west coast of Australia. Again, in times of volcanic eruptions, the dust and scoria which are shot into the air, are carried immense distances by winds and atmo- spheric currents, and no small portion eventually falls into the sea. Water is, however, the most powerful agent concerned in the formation and distribution of marine sediments. Running water corrodes the surface of the land, and carries the triturated fragments down into the ocean. The waters of the ocean, in the form of waves and tides, attack the coasts and distribute the debris at a lower level. Independently of the action of waves, there exist along most coasts currents, more or less constant, which have an effect in removing sand, gravel, and pebbles further from their origin. Generally, terrestrial matters appear to be distributed by these means to a distance of one or two hundred miles from the coast. Waves and currents probably have no erosive or transporting power at depths greater than 200 or 300 fathoms, and even at such depths it is necessary that there should be some peculiar configura- tion of the bottom in order that the agitated water may produce any mechanical effect. However, it is not improbable that, by a peculiar configuration of the bottom and ridges among oceanic islands, the deposit on a ridge may be disturbed by the tidal wave even at 1000 fathoms; and this may be the cause of the hard of Edinburgh, Session 1883-84. 503 ground sometime met with in such positions. By observations off the coast of France, it has been shown that fine mud is at times disturbed at a depth of 150 fathoms; but, while admitting that this is the case on exposed coasts, the majority of observations indicate that beyond 100 fathoms it is an oscillation of the water, rather than a movement capable of exerting any geological action, which concerns us in this connection. Although the great oceanic currents have no direct influence upon the bottom, yet they have a very important indirect effect on deposits, because the organisms which live in the warm equatorial currents form a very large part of the sediment being deposited there, and this in consequence differs greatly from the deposits forming in regions where the surface-water is colder. In the same way a high or low specific gravity of the surface-water has an important bearing on the animal and vegetable life of the ocean, and this in its turn affects the character of the deposits. The thermometric observations of the “ Challenger ” show that a slow movement of cold water must take ]3lace in all the greater depths of the ocean from the poles, but particularly from the southern pole, towards the equator. It could be shown from many lines of argu- ment that this extremely slow massive movement of the water can have no direct influence on the distribution of marine sediments. Glaciers which eventually become icebergs, that are carried far out to sea by currents, transport detrital matter from the land to the ocean, and thus modify in the Arctic and Antarctic regions the deposits taking place in the regions affected by them. The detritus from icebergs in the Atlantic can be traced as far south as latitude 36° off the American coast, and in the southern hemisphere as far north as latitude 40°. The fact that sea water retains fine matter in suspension for a much shorter time than fresh water should be referred to here as having an important influence in limiting the distribution of fine argillaceous and other materials borne down to the sea by rivers, thus giving a distinctive character to deposits forming near land. We have pointed out the influence of temperature and salinity upon the distribution of the surface organisms whose skeletons form a large part of some oceanic deposits, and may state also that the bathymetrical distribution of calcareous organisms is influenced by 504 Proceedings of the Royal Society the chemical action of sea water. We will return to these influences presently when describing the distribution of the various kinds of dej^osits and their reciprocal relations, especially in those regions of the deep sea far removed from the mechanical action of rivers, waves, and superficial currents. The action of life as a geological agent has been indicated under the heading Materials. Methods. — We give here an example showing the order followed in describing the deposits examined. Station 338; lat. 21° 15' S., long. 14° 2' W.; 21st March 1876; surface temperature 76° ‘5, bottom temperature 36° ’5, depth 1990 fathoms. Globigerina Ooze, white with slight rosy tinge when wet ; granular, homogeneous, and very slightly coherent when dry ; resembles chalk. i. Carbonate of Calcium, 90 ‘38 per cent., consists of pelagic Foraminifera (80 per cent.) ; coccoliths and rhabdoliths (9 per cent.) ; Miliolas, Dis- corbinas, and other Foraminifera, Ostracode valves, fragments of Echini spines, and one or two small fragments of Pteropods (1‘38 per cent.). ii. Residue, 9'62 per cent., reddish-brown ; consists of 1. Mmerals [F62] m. cli. 0*45 mm., fragments of felspar, hornblende, magnetite, magnetic s];therules,a few small grains of manganese, and pumice. 2. Siliceous Organisms [I'OO], Kadiolarians, spicules of Sponges, and imperfect casts of Foraminifera. 3. Fine TFashings [7’00], Argillaceous matter with small mineral particles and fragments of pumice and siliceous organisms. The description of the deposits has been made upon this plan which was adopted after many trials and much consideration. This is not the place to give the reasons which have guided us in adopting this mode of description, or to give in detail the methods that we have systematically employed for all the sediments which we are engaged in describing. These will be fully given in the intro- duction to our “ Challenger” Keport. We limit ourselves here to explaining the meanings and arrangement of terms and abbreviations, so that the method may be understood and made available for others. The description commences by indicating the kind of deposit (red clay, blue mud, globigerina ooze, &c.), with the microscopic charac- ters of the deposit, when wet or dry. We have always endeavoured to give a complete chemical analysis of the deposit, but when it was impossible to do this we have always determined the amount of Carbonate of Ccdcium. This determination was generally made by estimating the carbonic acid. of Edinburgh, Session 1883-84. 505 We usually took a gramme of a mean sample of the substance for this purpose, using weak and cold hydrochloric acid. However, as the deposits often contain carbonates of magnesia and iron as well, the results calculated by associating the carbonic acid with the lime are not perfectly exact, but these carbonates of magnesia and iron are almost always in very small proportion, and the process is, M^e think, sufficiently accurate, for, owing to the sorting of the 'elements which goes on during collection and carriage, no two samples from the same station give exactly the same percentage. The number which follows the words Carbonate of Calcium ” indi- cates the percentage of CaCOg ; v/e then give the general designa- tions of the principal calcareous organisms in the deposit. The part insoluble in the hydrochloric acid, after the deter- mination of the carbonic acid, is designated in our descriptions “ Residue^ The number placed after this word indicates its per- centage in the deposit; then follow the colour and principal physical properties. This residue is washed and submitted to decantations, which separate the several constituents according to their density; these form three groups — (1) Minerals, (2) Siliceous Organisms, (3) Fine Washings. 1. Minercds. — The number within brackets indicates the percent- age of particular minerals and fragments of rocks. This number is the result of an approximate evaluation, of which we will give the basis in our report. As it is important to determine the dimensions of the grains of minerals which constitute the deposit, we give, after the contraction m. di.^ their mean diameter in millimetres. We give next the form of the grains, if they are rounded or angular, &c. ; then the enumeration of the species of minerals and rocks. In this enumeration we have placed the minerals in the order of the importance of the role which they play in the deposit. The specific determinations have been made with the mineralogical microscope in parallel or convergent polarised light. 2. Siliceous Organisms.~Th.& number between brackets indicates the percentage of siliceous organic remains ; we obtain it in the same manner as that placed after the word Minercds, The siliceous organisms and their fragments are examined with the microscope and determined. We have also placed under this heading the glauconitic casts of the Foraminifera and other calcareous organisms. 506 Froceedings of the Roycd Society 3. Fine Washings. — We designate by this name the particles which, resting in suspension, pass with the first decantation. They are about 0’05 mm. or less in diameter. We have been unable to arrange this microscopic matter under the category of Minerals, for, owing to its minute and fragmentary nature, it is impossible to determine the species. We have always found that the Fine Washings increase in quantity as the deposit passes to a clay, and it is from this point of view that the subdivision has its raison d'etre. We often designate the lightest particles by the name argillaceous matter, but usually there are associated with this very small particles of indeterminable minerals and fragments of siliceous organisms. The number within brackets which follows the words Fine Washings is obtained in the same manner as those placed after Minerals and Siliceous Organisms. These few words will suffice to render the descriptions intelligible. Greater details will be given, as already stated, in the Challenger” Keport. It may be added that in the majority of cases we have solidified the sediments and formed them into thin slides for micro- scopic examination, and that at all times the examination by transmitted light has been carried on at the same time as the exami- nation by reflected light. Each description is followed by notes upon the dredging or sounding, upon the animals collected, and a discussion of the analysis whenever a complete analysis has been made, which is always the case with typical samples of the deposits. Kinds of Deposits. — We now proceed to the description of the various types of deposits into which it is proposed to divide the marine formations that are now taking j)lace in the deeper water of the various oceans and seas. We will speak fi.rst of those which are met with in the deeper water of inland seas, and around the coasts of continents and islands, and afterwards of those which are found in the abysmal regions of the great oceans. Those coast formations which are being laid down on . the shores, or in very shallow water, and which have been somewhat carefully described previous to the recent deep-sea explorations, are here neglected. A study of the collections made by the “ Challenger ” and other expeditions show — (1) That in the deejoer water around continents and islands of EdiThburgli, Session 1883-84. 507 which are neither of volcanic nor coral origin, the sediments are essentially composed of a mixture of sandy and amorphous matter, with a few remains of surface organisms, to which we give the name of muds, and which may be distinguished macroscopically by their colour. We distinguish them by the names, blue, red, and green muds. (2) Around volcanic islands the deposits are chiefly composed of mineral fragments derived from the decomposition of volcanic rocks. These, according to the size of the grains, are called volcanic muds or sands. (3) l!7ear coral islands and along shores fringed by coral reefs, the deposits are calcareous, derived chiefly from the disintegration of the neighbouring reefs, but they receive large additions from shells and skeletons of pelagic organisms, as well as from animals living at the bottom. These are named, according to circumstances, coral or coralline muds and sands. Let us now see what are the chief characteristics of each of these deposits. Blue mud is the most extensive deposit now forming around the great continents and continental islands, and in all enclosed or partially enclosed seas. It is characterised by a slaty colour which passes in most cases into a thin layer of a reddish colour at the upper surface. These deposits are coloured blue by organic matter in a state of decomposition, and frequently give off an odour of sulphuretted hydrogen. When dried, a blue mud is greyish in colour, and rarely or never has the plasticity and compactness of a true clay. It is finely granular, and occasionally contains fragments of rocks 2 centimetres in diameter ; generally, however, the minerals, which are derived from the continents, and are found mixed up with the muddy matter in these deposits, have a diameter of 0*5 mm. and less. Quartz particles, often rounded, play the principal part, next come mica, felspar, augite, hornblende, and all the mineral species which come from the disintegration of the neighbouring lands, or the lands traversed by rivers which enter the sea near the place where the specimens have been collected. These minerals make up the principal and characteristic portion of blue muds, sometimes forming 80 per cent, of the whole deposit. Glauconite, thongh generally present, is never abundant in blue 508 Proceedings of the Royal Society muds. The remains of calcareous organisms are at times quite absent, but occasionally they form over 50 per cent. The latter is the case when the specimen is taken at a considerable distance from the coast and at a moderate depth. These calcareous fragments consist of bottom-living and pelagic Foraminifera, Molluscs, Polyzoa, Serpulse, Echinoderms, Alcyonarian-spicules, Corals, &c. The re- mains of Diatoms and Eadiolarians are usually present. Generally speaking, as we approach the shore the pelagic organisms disappear ; and on the contrary, as we proceed seawards, the size of the mineral grains diminishes, and the remains of shore and coast organisms give place to pelagic ones, till finally a blue mud passes into a true deep- sea deposit. In those regions of the ocean affected with floating ice the colour of these deposits becomes gray rather than blue at great distances from land, and is further modified by the presence of a greater or less abundance of glaciated blocks and fragments of quartz. Green Muds and Sands. — As regards their origin, composition, and distribution near the shores of continental land, these muds and sands resemble the blue muds. They are largely com- posed of argillaceous matter and mineral particles of the same size and nature as in the blue muds. Their chief character- istic is the presence of a considerable quantity of glauconitic grains, either isolated or united into concretions. In the latter case the grains are cemented together by a brown argillaceous matter, and include, besides quartz, felspars, phosphate of lime, and other minerals, more or less altered. The Foraminifera and fragments of Echinoderms and other organisms in these muds are frequently filled with glauconitic substance, and beautiful casts of these organisms remain after treatment with weak acid. At times there are few calcareous organisms in these deposits, and at other times the remains of Diatoms and Eadiolarians are abundant. When these muds are dried they become earthy and of a grey-green colour. They frequently give out a sulphuretted hydrogen odour. The green colour appears sometimes to be due to the presence of organic matter, probably of vegetable origin, and to the reduction of peroxide of iron to protoxide under its influence. The green sands differ from the muds only in the comparative absence of the argillaceous and other amorphous matter, and by the more important part played by of Edinburgh, Session 1883-84. 509 the grains of glauconite, which chiefly give the green colour to these sands. Red Muds. — In some localities, as for instance off the Brazilian coast of America, the deposits differ from blue muds by the large quantity of ochreous matter brought clown by the rivers and deposited along the coast. The ferruginous particles when mixed up with the argillaceous matter give the whole deposit a reddish colour. These deposits, rich in iron in the state of limonite, do not appear to contain any traces of glauconite, and have relatively few remains of siliceous organisms. Volcanic Muds and Sands. — The muds and sands around vol- canic islands are black or grey; when dried they are rarely coherent. The mineral particles are generally fragmentary, and consist of lapilli of the basic and acid series of modern volcanic rocks, which are scoriaceous or compact, vitreous or crystalline, and usually pre- sent traces of alteration. The minerals are sometimes isolated, sometimes surrounded by their matrix, and consist principally of plagioclases, sanidine, amphibole, pyroxene, biotite, olivine, and magnetic iron ; the size of the particles diminishes with distance from the shore, but the mean diameter is generally 0"5 mm. Glau- conite does not appear to be present in these deposits, and quartz is also very rare or absent. The fragments of shells and rocks are frequently covered with a coating of peroxide of manganese. Shells of calcareous organisms are often present in great abundance, and render the deposit of a lighter colour. The remains of Diatoms and Eadiolarians are usually present. Coral Muds. — These muds frequently contain as much as 95 per cent, of carbonate of lime, vt^hich consists of fragments of Corals, cal- careous Algae, Foraminifera, Serpulse, Molluscs, and remains of other lime-secreting organisms. There is a large amount of amorphous calcareous matter, which gives the deposit a sticky and chalky char- acter. The particles may be of all sizes according to the distance from the reefs, the mean diameter being 1 to 2 mm., but occasionally there are large blocks of coral and large calcareous concretions ; the particles are white and red. Eemains of siliceous organisms seldom make up over 2 or 3 per cent, of a typical coral mud. The residue consists usually of a small amount of argillaceous matter, with a few fragments of felspar and other volcanic minerals ; but ofi‘ 510 Proceedings of the Royal Society barrier and fringing reefs facing continents we may bave a great variety of rocks and minerals. Beyond a depth of 1000 fathoms off coral islands the debris of the reefs begins to diminish, and the remains of pelagic organisms to increase ; the deposit becomes more argillaceous, of a reddish or rose colour, and gradually passes into a Globigerina ooze or a red clay. Coral Sands contain much less amorj^hons matter than coral muds, but in other respects they are similar, the sands being usually found nearer the reefs and in shallower water than the muds, except inside lagoons. In some regions the remains of calcareous algse predominate, and in these cases the name coralline mud or sand is employed to point out the distinction. Such is a rapid view of the deposits found in the deeper waters of the littoral zones, where the debris from the neighbouring land plays the most important part in the formation of muds and sands. When, however, we pass heyond a distance of about 200 miles from land, we find that the deposits are characterised by the great abundance of fragmentary volcanic materials which have usually undergone great alteration, and by the enormous abundance of the shells and skeletons of minute pelagic organisms which have fallen to the bottom from the surface waters. These true deep-sea deposits may be divided into those in which the organic elements predominate, and those in which the mineral constituents play the chief part. We commence with the former. Globigerina Ooze. — We designate by this name all those truly pelagic deposits containing over 40 per cent, of carbonate of lime, which consists principally of the dead shells of pelagic Foraminifera — ■ Globigerina^ Orbidina, Pulviimlma, Pidlenia, SphcBroidinay &c. In some localities this deposit contains 95 per cent, of carbonate of lime. The colour is milky white, yellow, brown, or rose, the varieties of colour depending principally on the relative abundance in the deposit of the oxides of iron and manganese. This ooze is fine grained ; in the tropics some of the Foraminifera shells are macroscopic. When dried it is pulverulent. Analyses show that the sediment contains, in addition to carbonate of lime, j^hosphate and sulphate of lime, carbonate of magnesia, oxides of iron and man- ganese, and argillaceous matters. The residue is of a reddish-brown of Edinburgh, Session 1883-84. 511 tinge. Lapilli, pumice, and glassy fragments, often altered into palagonite, seem always to be present, and are frequently very abundant. The mineral particles are generally angular, and rarely exceed 0*08 mm. in diameter; monoclinic and triclinic felspars, augite, olivine, hornblende, and magnetite are the most frequent. When quartz is present, it is in the form of minute, rounded, probably wind-borne grains, often partially covered with oxide of iron. More rarely we have white and black mica, bronzite, actino- lite, chromite, glauconite, and cosmic dust. Siliceous organisms are probably never absent, sometimes forming 20 per cent, of the deposit, at other times they are only recognisable after careful microscopic examination. In some regions the frustules of Diatoms predomi- nate, in others the skeletons of Radiolarians. The fine washings, viewed with the microscope, are not homo- geneous. The greater part consists of argillaceous matter coloured by the oxides of iron and manganese. Mixed with this, we distinguish fragments of minerals with a diameter less than 0'05 mm., and minute particles of pumice can nearly always be detected. Frag- ments of Eadiolarians, Diatoms, and siliceous spicules can always be recognised, and are sometimes very abundant. Pteropod Ooze. — This deposit differs in no way from a Globigerina ooze except in the presence of a greater number and variety of pelagic organisms, and especially in the presence of Pteropod and Heteropod shells, such as Diacria, Atlanta, Styliola, Carinaria, &c., &c. The shells of the more delicate species of pelagic Foraniinifera and young shells are also more abundant in these deposits than in a Globigerina ooze. It must be remembered that the name “ Pteropod ooze ” is not intended to indicate that the deposit is chiefly composed of the shells of these molluscs, but, as their presence in a deposit is characteristic and has an important bearing on geographical and bathymetrical distribution, we think it desirable to emphasise the presence of these shells in any great abundance. It may here be pointed out that there is a very considerable difference between a Globigerina ooze, or a Pteropod ooze situated near continental shores, and deposits bearing the same names situated towards the centres of oceanic areas, both with respect to mineral particles and remains of organisms. Diatom Ooze. — This ooze is of a pale straw colour, and is composed 512 Proceedings of the Royal Society principally of the frustules of Diatoms. When dry it is a dirty white siliceous hour, soft to the touch, taking the impression of the fingers, and contains gritty particles which can be recognised by the touch. It coDtains on an average about 25 per cent, of carbonate of lime, which exists in the deposit in the form of small Glohigerina shells, fragments of Echinoderms and other organisms. The residue is pale white and slightly plastic ; minerals and fragments of rocks are in some cases abundant ; these are volcanic, or, more frequently, fragments and minerals coming from continental rocks and trans- ported by glaciers. T\iq fine washmgs consist essentially of particles of Diatoms along with argillaceous and other amorphous matter. We estimate that the frustules of Diatoms and skeletons of siliceous organisms make up more than 50 per cent, of this deposit. Radiolarian Ooze. — It was stated, when describing a Globigerina ooze, that Eadiolarians were seldom, if ever, completely absent from marine deposits. In some regions they make up a considerable portion of a Globigerina ooze, and are also found in Diatom ooze and in the terrigenous deposits of the deeper water surround- ing, however, the land. In some regions of the Pacific, the skeletons of these organisms make up the principal part of the deposits, and to these we have given the name “ Eadiolarian ooze.” The colour is reddish or deep brown, due to the presence of the oxides of iron and manganese. The mineral goarticles consist of fragments of pumice, lapilli, and volcanic minerals, rarely exceed- incy 0’07 mm. in diameter. There is not a trace of carbonate of O lime in the form of shells in some samples of Eadiolarian ooze, but other specimens contain 20 per cent, of carbonate of lime derived from the shells of pelagic Foraminifera. The clayey matter and mineral particles in this ooze are the same as those found in the red clays, which we will now proceed to describe. Red Clay. — Of all the deep-sea deposits this is the one which is distributed over the largest areas in the modern oceans. It might be said that it exists everywhere in the abysmal regions of the ocean basins, for the residue in the organic deposits which have been described under the names Globigerina, Pteropod, and Eadiolarian ooze, is nothing else than the red clay. However, this deposit only appears in its characteristic form in those areas where the terri- genous minerals and calcareous and siliceous organisms disappear to 513 of Edinhurgli, Session 1883 -84. a greater or less extent from the bottom. It is in the central regions of the Pacific that we meet with the typical examples. Like other marine deposits, this one passes laterally, according to position and depth, into the adjacent kinds of deep-sea ooze or mud. The argillaceous matters are of a more or less deep brown tint from the presence of the oxides of iron and manganese. In the typical examples no mineralogical species can be distinguished by the naked eye, for the grains are exceedingly fine and of nearly uniform dimensions, rarely exceeding 0‘05 mm. in diameter. It is plastic and greasy to the touch ; when dried it coagulates into lumps so coherent that considerable force must be employed to break them. It gives the brilliant streak of clay, and breaks down in water. The pyrognostic properties show that we are not dealing with a pure clay, for it fuses easily before the blow-pipe into a magnetic bead. Under the term red clay are comprised those deposits in which the characters of clay are not well pronounced, but which are mainly com- posed of minute particles of pumice and other volcanic material which, owing to their relatively recent deposition, have not undergone great alteration. If we calculate the analyses of red clay it will be seen, moreover, that the silicate of alumina present as clay (2Si02,Al203 -t- 2H2O) comprises only a relatively small portion of the sediment, the calculation shows always an excess of free silica, which is attributed chiefly to the presence of siliceous organisms. Microscopic examination shows that a red clay consists of argillaceous matter, minute mineral particles, and fragments of siliceous organisms ; in a word, it is in all respects identical with the residue of the organic oozes. The mineral particles are for the greater part of volcanic origin, except in those cases where continental matters are transported by floating ice, or wdiere the sand of deserts has been carried to great distances by winds. These volcanic minerals are the same constituent minerals of modern eruptive rocks, enumerated in the description of volcanic muds and sands; in the great majority of cases they are accom- panied by fragments of lapilli and of pumice more or less altered. Vitreous volcanic matters belonging to the acid and basic series of rocks predominate in the regions where the red clay has its greatest development, and it will be seen presently that the most character- 514 Proceedings of the Royal Society istic decompositions which there take place are associated with pyroxenic lavas. Associated with the red clay are almost always found concretions and microscopic particles of the oxides of iron and manganese, to which the deposit owes its colour. Again, in the typical examples of the deposit, zeolites in the form of crystals and crystalline spherules are present, along with metallic globules and silicates which are regarded as of cosmic origin. Calcareous organisms are so generally absent in the red clay that they cannot he regarded as characteristic ; when present they are chiefly the shells of pelagic Foraminifera, and are usually met with in greater numbers in the surface layers of the deposit, to which they give a lighter colour. On the other hand, the remains of Diatoms, Eadiolarians, and sponge spicules are generally present, and are sometimes very abundant. The ear-bones of various cetaceans, as well as the remnants of other cetacean bones, and the teeth of sharks, are, in some of the typical samples far removed from the continents, ex- ceedingly abundant, and are often deeply impregnated with, or embedded in thick coatings of, oxides of iron and manganese. The remains of these vertebrates have seldom been dredged in the organic oozes, and still more rarely in the terrigenous deposits. The fine washings^ as examined with a power of 450 diameters, are composed of an amorphous matter, fragments of minerals, the remains of siliceous organisms, and colouring substances. What we call amorphous matter may be considered as properly the argillaceous matter, and presents characters essentially vague. It appears as a gelatinous substance, without definite contours, generally colourless, perfectly isotropic, and forms the base which agglutinates the other particles of the washings. As these physical properties are very indefinite, it is difficult to estimate even approxi- mately the quantity present in a deposit. However, it augments in proportion as the deposit becomes more clayey, but we think that only a small quantity of this substance is necessary to give a clayey character to a deposit. Irregular fragments- of minerals, small pieces of vitreous rocks, and remains of siliceous organisms pre- dominate in this fundamental base. These particles probably make up about 50 per cent, of the whole mass of the fine ivasliings^ and this large percentage of foreign substances must necessarily of Edinburgh, Sessio7i 1883-84. 515 mask the character of the clayey matter in which they are em- bedded. The mineral particles are seldom larger than O'Ol mni. in diameter, but descend from this size to the merest points. It is im- possible, on account of their minuteness, to say to what mineral species they belong, their optical reactions are insensible, their outlines too irregular, and all special coloration has disappeared. All that can be reasonably said is that these minute mineral particles probably belong to the same species as the larger particles in the same deposit, such as felspar, hornblende, magnetite, &c. In the case of pumice and siliceous organisms the fragments can, owing to their structure, be recognised when of a much less size than in the case of the above minerals. It can be made out by means of the microscope that the colouring substances are hydrated oxides of iron and manganese. The former is scattered through the mass in a state of very fine division ; in some points, however, it is more localised, the argillaceous matter here appearing with a browner tinge, but these spots are noticed gradually to disappear in the surrounding mass. The coloration given by the manganese is much more distinct ; there are small rounded brownish spots with a diameter of less than 0*01 mm., which disappear under the action of hydrochloric acid with dis- engagement of chlorine. These small round concretions, which are probably a mixture of the oxides of iron and manganese, will be described with more detail in the “ Challenger ” Report. The following table shows the nomenclature we have adopted - f Shore formations, I Blue mud, I Green mud and sand, 1 Found in inland ! seas and along the shores of con- tinents. Terrigenous I Red mud, deposits. ^ , ^ ( ;n-po I miiin Coral mud and sand, Coralline mud and sand, Volcanic mud and sand, 3 Found about • oceanic islands and j along the shores of j continents. " Red clay, I Found in the Pelao-io Globigerina ooze, (leposHs. ^ Pteropod ooze, I abysmal regions I of the ocean basins. J 2 L VOL. XII. 516 Proceedings of the Royal Society Geographical and Bathymetrical Distribution. —in the preceding pages we have confined our remarks essentially to the lithological nature of the deep-sea deposits, including in this term the dead shells and skeletons of organisms. From this point of view it has been possible to define the sediments and to give them distinctive names. We now proceed to consider their geographical and bathy- metrical distribution, and the relations which exist between the mineralogical and organic composition, and the different areas of the ocean in which they are formed. A cursory glance at the geographical distribution shows that the deposits which we have designated muds and sands are situated at various depths at no great distance from the land, while the ORGANIC OOZES and RED CLAYS occupy the abysmal regions of the ocean basins far from land. Leaving out of view the coral and volcanic muds and sands which are found principally around oceanic islands, we notice that our blue muds, green muds and sands, red muds, together with all the coast and shore formations, are situated along the margins of the continents and in enclosed and partially enclosed seas. The chief characteristic of these deposits is the presence in them of continental debris. The blue muds are found in all the deeper parts of the regions just indicated, and especially near the embouchures of rivers. Bed muds do not differ much from blue muds except in colour, due to the presence of ferruginous matter in great abundance, and we find them under the same condi- tions as the blue muds. The green muds and sands occupy, as a rule, portions of the coast where detrital matter from rivers is not apparently accumulating at a rapid rate, viz., on such places as the Agulhas Bank, off the east coast of Australia, off the coast of Spain, and at various points along the coast of America. Let us east a glance at the region occupied by terrigenous deposits, in which we include all truly littoral formations. This region extends from high-water mark down, it may be, to a depth of over four miles, and in a horizontal direction from 60 to per- haps 300 miles seawards, and includes, in the view we take, all inland seas, such as the North Sea, Norwegian Sea, Mediterranean Sea, Bed Sea, China Sea, Japan Sea, Carribean Sea, and many others. It is the region of change and of variety with respect to light, temperature, motion, and biological conditions. In the surface uf Edinburgh, Session 1883-84. 517 waters tlie tempGi\atiire ranges from 80° T'alir. in the tropics, to 28° Fahr. in the polar regions. Below the surface, down to the nearly ice- cold water found at the lower limits of the region in the deep sea, there is in the tropics an equally great range of temperature. Plants and animals are abundant near the shore, and animals extend in relatively great abundance down to the lower limits of this region which is now covered by these terrigenous deposits. The specific gravity of the water varies much, owing to mixture with river water or great local evaporation, and this variation in its turn affects the fauna and flora. In the terrigenous region tides and currents produce their maximum effect, and these influences can in some instances be traced to a depth of 300 fathoms, or nearly 2000 feet. The upper or continental margin of the region is clearly defined by the bigh-water mark of the coast-line, which is constantly changing through breaker action, elevation, and subsidence. The lower or abysmal margin is less clearly marked out. It passes in most cases insensibly into the abysmal region, but may be regarded as ending when the mineral particles from the neighbouring continents begin to disappear from the deposits, which then pass into an organic ooze dr a red clay. Contrast with these those conditions which prevail in the abysmal region in which occur the organic oozes and red clay, the distribution of which will presently be considered. This area comprises vast undulating plains from two to five miles beneath the surface of the sea, the average being about three miles, here and there interrupted by huge volcanic cones (the oceanic islands). No sunlight ever reaches these deep cold tracts. The range of temperature over them is not more than 7°, viz., from 31° to 38° Fahr., and is apparently constant throughout the whole year in each locality. Plant life is absent, and although animals belonging to all the great types are present, there is no great variety of form or abundance of individuals. Change of any kind is exceedingly slow. What is the distribution of deposits in this abysmal region of the earth’s surface ? In the tropical and temperate zones of the great oceans, which occupy about 110° of latitude between the two polar zones, at depths where the action of the waves is not felt, and at points to which the terrigenous materials do not extend, 518 Proceedings of the Royal Society there are now forming vast accumulations of Glohigerina and other pelagic Foraminifera, coccoliths, rhabdoliths, shells of pelagic Mol- luscs, and remains of other organisms. These deposits may perhaps he called the sediments of median depths and of warmer zones, be- cause they diminish in great depths and tend to disappear towards the poles. This fact is evidently in relation with the surface temperature of the ocean, and shows that pelagic Foraminifera and Molluscs live in the superficial waters of the sea, whence their dead shells fall to the bottom. Globigerina ooze is not found in enclosed ^eas nor in polar latitudes. In the Southern Hemisphere it has not been met with beyond the 50th parallel. In the Atlantic it is deposited upon the bottom at a very high latitude belov/ the warm waters of the Gulf Stream, and is not observed under the cold descending polar current which runs south in the same latitude. These facts are readily explained, if we admit that this ooze is formed chiefly by the shells of surface organisms, which require an elevated temperature and a wide expanse of sea. But as long as the conditions of the surface are the same we would expect the deposits at the bottom also to remain the same. In showing that such is not the case, we are led to take into account an agent which is in direct correlation with the depth. We may regard it as established that the majority of the calcareous organ- isms, which make up the Globigerina and Pteropod oozes, live in the surface waters, and we may also take for granted that there is always a specific identity between the calcareous organisms which live at the surface, and the shells of these pelagic creatures found at the bottom. This observation will permit us to place in relation the organic deposits and those which are directly or indirectly the result of the chemical activity of the ocean. Globigerina ooze is found in the tropical ^one at depths which do not exceed 2400 fathoms, but when depths of 3000 fathoms are explored in this zone of the Atlantic and Pacific, there is found an argillaceous deposit without, in many instances, any trace of calcareous organisms. When we descend from the “ submarine plateaux ” to depths which exceed 2250 fathoms the Globigerina ooze gradually disappears, passing into a greyish marl, and finally is wholly replaced by an argillaceous material which covers the bottom at all depths greater than 2900 fathoms. of Edinburgh, Session 519 The transition between the calcareous formations and the argillaceous ones takes place by almost insensible degrees. The thinner and more delicate shells disappear first. The thicker and larger shells lose little by little the sharpness of their contour, and apj3ear to undergo a profound alteration. They assume a brownish colour, and break up in proportion as the calcareous constituent disappears. The red clay predominates more and more as the calcareous element diminishes in the deposit. If we now recollect that the most important elements of the organic deposits have descended from the superficial waters, and that the variations in contour of the bottom of the sea cannot of them- selves prevent the debris of animals and plants from accumulating upon the bottom, their absence in the red clay areas can only be explained by a decomposition, under the action of a cause which we must seek to discoyen Pteropod ooze, ifc will be remembered, is a calcareous organic deposit, in which the remains of Pteropods and other pelagic Mollusca are j)resent, though they do not always form a preponder’^ ating constituent, and it has been found that their presence is in correlation with the bathymetrical distribution. In studying the nature of the calcareous elements Wliicll ate deposited in the pelagic areas, it has been noticed that, like the shells of the Foraminifera, those of the Thecosomatotis Pteropoda, which live everywhere in the superficial waters, especially in the tropics, become fewer in number as the depth from which the sedi- ments are derived increases. We have just observed that the shells of Foraminifera disappear gradually as we' descend alo’ng a series of soundings from a point Where the Globigerina ooze has abtindance of carbonate of lime, towards deeper regions j but We notice also that when the sounding-rod brings up a graduated series of sediments from a declivity descending into deep \Vater, among the calcareous shells those of the Pteropods and Fleteropods disappear first in proportion as the depth increases. At depths less than 1 400 fathoms in the tropics a Pteropod ooze is found with abundant remains of Heteropods and Pteropods ; deeper soundings then giVe a Globigerina ooze without these molhtscan remains; and in still greater depths, as before mentioned, there is a red clay in Which calcareous organisms are nearly, if not quite, absent. 520 ProcGGciings of the Royal Society In this manner, then, it is shown that the remains of calcareous organisms are completely eliminated in the greatest depths of the ocean. For if such he not the case, why do we find all these shells at the bottom in the shallower depths, and not at all in the greater depths, although they are equally abundant on the surface at both places There is reason to thinlv that this solution of calcareous shells is due to the presence of carbonic acid throughout all depths of ocean water. It is well known that this substance, dissolved in water, is an energetic solvent of calcareous matter. The investiga- tions of Buchanan and Dittmar have shown that carbonic acid exists in a free state in sea water, and in the second place, Dittmar’s analyses show that deep-sea water contains more lime than surface water. This is a confirmation of the theory which regards carbonic acid as the agent concerned in the total or partial solution of the surface shells before or immediately after they reach the' bottom of the ocean, and is likewise in relation with the fact, that in high latitudes where fewer calcareous organisms are found at the surface, their remains are removed at lesser depths than where these organisms are in greater abundance. It is not improbable that sea water itself may have some effect in the solution of carbonate of lime, and further, that, the immense pressure to which water is subjected in great depths, may have an influence on its chemical activity. We await the result of further researches on this point, which have been undertaken in connection with the “Challenger” Keports. We are aware that objections have been raised to the explanation here advanced, on account of the alkaliuity of sea water, but we may remark that alkalinity presents no difficulty wdiich need be here considered.* This interpretation permits us to explain how the remains of Diatoms and Eadiolarians (surface organisms like the Foraniinifera) are found in greater abundance in the red clay than in a Globigerina ooze. The action which suffices to dissolve the calcareous matter has little or no effect upon the silica, and so the siliceous shells accu- mulate. Nor is this view of the case opposed to the distribution of the Pteropod ooze. At first we should expect that the Foraminifera shells, being smaller, would disappear from a deposit before the Pteropod shells ; but if we remember that the latter are very thin * Dittmar, Pliys. Chem. CJutU. Exp., Part i., 1884. of Edinburgh, Session 1883-84. 521 and delicate, and, for the quantity of carbonate of lime present, offer a larger surface to the action of the solvent than the thicker, though smaller, Glohigerina shells, we shall see the explanation of this apparent anomaly. It remains now to point out the area occupied by the red clay. We have seen how it passes at its margins into organic calcareous oozes, found in the lesser depths of the abysmal regions, or into the siliceous organic oozes or terrigenous deposits. In its typical form the red clay occupies a larger area than any of the other true deep- sea deposits, covering the bottom in vast regions of the North and South Pacific, Atlantic, and Indian Oceans. As above remarked, this clay may be said to be universally distributed over the floor of the oceanic basins ; but it only appears as a true deposit at points where the siliceous and calcareous organisms do not conceal its proper characters. Having now indicated its distribution, we must consider the mode of its formation, and give, in addition, a concise description of the minerals and of the organic remains which are commonly associated with it. The origin of these vast de]30sits of clay is a problem of the highest interest. It was at first supposed that these sediments were composed of microscopic particles arising from the disintegration of the rocks by rivers and by the waves on the coasts. It was believed that the matters held in suspension were carried far and wide by currents, and gradually fell to the bottom of the sea. But the uni- formity of composition presented by these deposits was a great objec- tion to this view. It could be shown, as we have mentioned above, that mineral particles, even of the smallest dimensions, continually set adrift upon disturbed waters must, owing to a property of sea water, eventually be precipitated at no great distance from land. It has also been supposed that these argillaceous deposits owe their origin to the inorganic residue of the calcareous shells which are dissolved away in deep water, but this view has no foundation in fact. Every- thing seems to show that the formation of the clay is due to the decomposition of fragmentary volcanic products, whose presence can be detected over the whole floor of the ocean. These volcanic materials are derived from floating pumice and volcanic ashes ejected to great distances by terrestrial volcanoes, and carried far by the winds. It is also known that beds of lava and of tufa 522 Proceedings of the Poycd Society are laid down upon the bottom of the sea. This assemblage of pyro- genic rocks, rich in aluminous silicates, decomposes under the chemical action of the water, and gives rise, in the same way as do terrestrial volcanic rocks, to argillaceous matters, according to reactions, which we can always observe on the surface of the globe, and which are too well known to need special mention here. The detailed microscopic examination of hundreds of soundings has shown that we can always demonstrate in the argillaceous matter the presence of pumice, of lapilli, of silicates, and other volcanic minerals in various stages of decomposition. As we have shown in another paper,* the deposit most widely distributed over the bed of modern seas is due to the decomposition of the products of the internal activity of the globe, and the final result of the chemical action of sea water is seen in the formation of this argillaceous matter, which is found everywhere in deep-sea deposits, sometimes concealed by the abundance of siliceous or cal- careous organisms, sometimes appearing with its own proper charac- teristics associated with mineral substances, some of which allow us to appreciate the extreme slowness of its formation, or whose presence corroborates the theory advanced to explain its origin. In the places where this red clay attains its most typical develop- ment, we may follow, step by step, the transformation of the volcanic fragments into argillaceous matter. It may he said to he the direct product of the decomposition of the basic rocks, represented by vol- canic glasses, such as hyalomelan and tachylite. This decomposi- tion, in spite of the temperature approximating to zero (32° P.), gives rise, as an ultimate product, to clearly crystallised minerals, which may he considered the most remarkable products of the chemical action of the sea upon the volcanic matters undergoing decom- position. These microscopic crystals are zeolites lying free in the deposit, and are met with in greatest abundance in the typical red clay areas of the central Pacific. They are simple, twinned, or spheroidal groups which scarcely exceed half a millimetre in diameter. The crystallographic and chemical study of them shows that they must be referred to Christianite. It is known how easily the zeolites crystallise in the pores of eruptive rocks in process of decomposition ] and the crystals of Christianite, which we * “On Cosmic and Volcanic Dust,” Proc. Roy. Soc. Edin., 1883-84. of Edinburgh, Session 1883-84. 523 observe in considerable quantities in the clay of the centre of tbe Pacific, have been formed at the expense of the decomposing vol- canic matters spread out upon the bed of that ocean. In connection with this formation of zeolites, reference may be made to a chemical process whose principal seat is the red clay areas, and which gives rise to nodules of manganiferous iron. This sub- stance is almost universally distributed in oceanic sediments, yet it is not so much of the areas of its abundance that we intend to speak as to the fact of its occurrence in the red clay, because this association tends to show a common relation of origin. It is exactly in those regions where there is an accumulation of pyroxenic lavas in decom- position, containing silicates with a base of manganese and iron, such for example as augite, hornblende, olivine, magnetite, and basic glasses, that manganese nodules occur in greatest numbers. In the regions where the sedimentary action, mechanical and organic, is, as it were, suspended, and where, as will appear in the sequel, every- thing shows an extreme slowness of deposition, — in these calm waters favourable to chemical reactions, ferro-manganiferous substances form concretions around organic and inorganic centres. These concentrations of ferric and manganic oxides, mixed with argillaceous materials, whose form and dimensions are extremely vari- able, belong generally to the earthy variety or wad, but pass some- times, though rarely, into varieties of hydrated oxide of manganese with distinct indications of radially fibrous crystallisation. The in- terpretation to which we are led, in order to explain this formation of manganese nodules, is the same as that which is admitted in explana* tion of the formation of coatings of this material on the surface of terrestrial rocks. These salts of manganese and iron, dissolved in water by carbonic acid, then precipitated in the form of carbonate of protoxide of iron and manganese, become oxidised, and give rise in the calm and deep oceanic regions to more or less pure ferro-man- ganiferous concretions. At the same time it must be admitted that rivers may bring to the ocean a contribution of these same substances. Among the bodies which, in certain regions where red clay predominates, serve as centres for these manganiferous nodules, are the remains of vertebrates. These remains are the hardest parts of the skeleton — tympanic bones of whales, beaks of Ziphius, teeth of 524 Proceedings of the Poyal Society sharks; and just as the calcareous shells are eliminated in the depths, so all the remains of the larger vertebrates are absent except the most resistant portions. These bones often serve as a centre for the manganese-iron concretions, being frequently surrounded by layers several centimetres in thickness. In the same dredgings on the red clay areas, some sharks’ teeth and cetacean ear-bones, some of which belong to extinct species, are surrounded with thick layers of the manganese, and others with merely a slight coating. We will make use of these facts to establish the conclusions which terminate this paper. In these red clays there occur, in addition, the greatest number of cosmic metallic spherules, or chondres, the nature and characters of which we have pointed out elsewhere.* We merely indicate their presence here, as we will support our conclusions by a reference to their distribution. Reviewing, then, the distribution of oceanic deposits, we may summarise thus : — (1) The terrigenous deposits, the blue muds, green muds and sands, red muds, volcanic muds and sands, coral muds and sands, are met with in those regions of the ocean nearest to land. With the exception of the volcanic muds and sands, and coral muds and sands, around oceanic islands, these deposits are found only along the borders of continents and continental islands, and in enclosed and partially enclosed seas. (2) The organic oozes and red clay are confined to the abysmal regions of the ocean basins; a Pteropod ooze is met with in tropical and subtropical regions in depths less than 1500 fathoms, a Globigerina ooze in the same regions between the depths of 500 and 2800 fathoms, a Radiolarian ooze in the central portions of the Pacific at depths greater than 2500 fathoms, a Diatom ooze in the Southern Ocean south of the latitude of 45° South, a red clay anywhere within the latitudes of 45° north and south at depths greater than 2200 fathoms. O Conclusions. — All the facts and details enumerated in the fore- going pages point to certain conclusions which are of considerable geological interest, and which appear to be warranted by the present state of our investigations. * “On Cosmic and Volcanic Dust,” Proc. Hoy. Soc. Edin., 1883-4. of Ediiiburgh, Session 1883-84. 525 Wo have said that the d4bris carried away from the land accumulates at the bottom of the sea before reaching the abysmal regions of the ocean. It is only in exceptional cases that the finest terrigenous materials are transported several hundred miles from the shores. In place of layers formed of pebbles and clastic ele- ments with grains of considerable dimensions, which play so large a part in the composition of emerged lands, the great areas of the ocean basins are covered by the microscopic remains of pelagic organisms, or by the deposits coming from the alteration of volcanic products. The distinctive elements that appear in the river and coast sedi- ments are, properly speaking, wanting in the great depths far distant from the coasts. To such a degree is this the case that in a great number of soundings, from the centre of the Pacific for example, we have not been able to distinguish mineral particles on which the mechanical action of water had left its imprint, and quartz is so rare that it may be said to be absent. It is sufficient to indicate these facts in order to make apparent the profound differences which separate the deposits of the abysmal areas of the ocean basins from the series of rocks in the geological formations. As regards the vast deposits of red clay, with its manganese con- cretions, its zeolites, cosmic dust, and remains of vertebrates, and the organic oozes which are spread out over the bed of the central Pacific, Atlantic, and Indian oceans, have they their analogues in the geological series of rocks If it be proved that in the sedi- mentary strata the pelagic sediments are not represented, it follows that deep and extended oceans like those of the present day cannot formerly have occupied the areas of the present continents, and as a corollary the great lines of the ocean basins and con- tinents must have been marked out from the earliest geological ages. We thus get a new confirmation of the opinion of the per- manence of the continental areas. But without asserting in a positive manner that the terrestrial areas and the areas covered by the waters of the great ocean basins have had their main lines marked out since the commencement of geological history, it is, nevertheless, a fact, proved by the evi- dence derived from a study of the pelagic sediments, that these areas have a great antiquity. The accumulation of sharks’ teeth, of the ear-bones of cetaceans, of manganese concretions, of zeolites, 526 Proceedings of the Royal Society of volcanic material in an advanced state of decomposition, and of cosmic dust, at points far removed from the continents, prove this. There is no reason for supposing that the parts of the ocean where these vertebrate remains are found are more frequented by sharks or cetaceans than other regions where they are never or only rarely dredged from the deposits at the bottom. When we remember also that these ear-bones, teeth of sharks, and volcanic fragments, are sometimes incrusted with two centi- metres of manganese oxide, while others have a mere coating, and that some of the bones and teeth belong to extinct species, we may conclude with great certainty that the clays of these oceanic basins have accumulated with extreme slowness. It is indeed almost beyond question that the red clay regions of the central Pacific con- tain accumulations belonging to geological ages different from our own. The great antiquity of these formations is likewise confirmed in a ^strikmg manner by the presence of cosmic fragments, the nature of which we have described.* In order to account for the accu- mulation of all these substances in such relatively great abundance in the areas where they were dredged, it is necessary to suppose the oceanic basins to have remained the same for a vast period of time. The sharks’ teeth, ear-bones, manganese nodules, altered volcanic fragments, zeolites, and cosmic dust, are met with in greatest abundance in the red clays of the central Pacific, at that point on the earth’s surface farthest removed from continental land. They are less abundant in the Eadiolarian ooze, are rare in the Globi- gerina, Diatom, and Pteropod oozes, and they have been dredged only in a few instances in the terrigenous deposits close to the shore. These substances are present in all the deposits, but owing to the abundance of other matters in the more rapidly forming deposits their presence is masked, and the chance of dredging them is reduced. We may then regard the greater or less abundance of these materials, which are so characteristic of a true red clay, as being a measure of the relative rate of accumula- tion of the marine sediments in which they lie., The terrigenous deposits accumulate most rapidly, then follow in order Pteropod ooze, Globigerina ooze, Diatom ooze, Eadiolarian ooze, and, slowest of all, red clay. * “On Cosmic and Volcanic Dust,” Proc, Roy. Soc. Edin, of Edinburgh, Session 1883-84. 527 From the data now advanced it appears possible to deduce other conclusions important from a geological point of view. In the de- posits due essentially to the action of the ocean, we are at once struck by the great variety of sediments which may accumulate in regions where the external conditions are almost identical. Again marine faunas and floras, at least those of the surface, differ greatly, both with respect to species and to relative abundance of individuals, in different regions of the ocean ; and as their remains determine the character of tbe deposit in many instances, it is legitimate to conclude that the occurrence of organisms of a different nature in several beds is not an argument against the synchronism of the layers which contain them. The small extent occupied by littoral formations, especially those of an arenaceous nature, shown by our investigations, and the relatively slow rate at which such deposits are formed along a stable coast, are matters of importance. In the present state of things there does not appear to be anything to account for the enormous thickness of the clastic sediments making up certain geological formations, unless we consider the exceptional cases of erosion which are brought into play when a coast is undergoing -constant elevation or subsidence. Great move- ments of the laud are doubtless necessary for the formation of thick beds of transported matter like sandstones and conglomerates. In this connection may be noted the fact that in certain regions of the deep sea no appreciable formation is now taking place. Hence the absence, in the sedimentary series, of a layer representing a definite horizon must not always be interpreted as proof either of the emergence of the bottom of the sea during the corresponding period, or of an ulterior erosion. Arenaceous formations of great thickness require seas of no great extent and coasts subject to frequent oscillations, which permit the shores to advance and retire. Along these, through all periods of the earth’s history, the great marine sedimentary phenomena have taken place. The continental geological formations, when compared with marine deposits of modern seas and oceans, present no analogues to the red clays, Radiolarian, Globigerina, Pteropod, and Diatom oozes. On the other hand, the terrigenous deposits of our lakes, shallow seas, enclosed seas, and the shores of the continents, reveal the equivalents 528 Proceedings of the Royal Soeiety of our chalks, greensands, sandstones, conglomerates, shales, marls, and other sedimentary formations. Such formations as certain tertiary deposits of Italy, Kadiolarian earth from Barhadoes, and portions of the Chalk where pelagic conditions are indicated, must he regarded as having been laid down rather along the border of a continent than in a true oceanic area. On the other hand, the argillaceous and calcareous rocks, recently discovered by Dr Guppy, in the upraised coral islands in the Solomon group, are nearly identical with the volcanic muds, and probably also with the Pteropod and Globigerina oozes of the Pacific. Eegions situated similarly to enclosed and shallow seas and the borders of the present continents appear to have been, throughout all geological ages, the theatre of the greatest and most remarkable changes ; in short, all, or nearly all, the sedimentary rocks of the continents would seem to have been built up in areas like those now occupied by the terrigenous deposits, which we may designate ‘‘ the transitional or critical area of the earth's surface." This area occupies, we estimate, .about two-eighths of the earth’s surface, while the continental and abysmal areas occupy each about three- eighths. During each era of the earth’s history, the borders of some lands have sunk beneath the sea and been covered by marine sediments ; while in other parts the terrigenous deposits have been elevated into dry land, and have carried with them a record of the organisms which flourished in the sea of the time. In this transitional area there has been throughout a continuity of geological and biological phenomena. Prom these considerations it will be evident that the character of a deposit is determined much more by distance from the shore of a continent than by actual depth] and the same would appear to be the case with respect to the fauna spread over the floor of the present oceans. Dredgings near the shores of continents, in depths of 1000, 2000, or 3000 fathoms, are more productive both in species and individuals than dredgings at similar depths several hundred miles seawards. Again, among the few species dredged in the abysmal areas furthest removed from land, the majority show archaic characters, or belong to groups which have a wide distribution in time as well as over the floor of the present oceans. Such are the of Edinburgh, Session 1883-84. 529 Hexactinellida, Brachiopoda, Stalked Crinoids and other Ecliino- derms^ &c. As already mentioned, the transitional area is that which now shows the greatest variety in respect to biological and physical conditions, and in past time it has been subject to the most frequent and the greatest amount of change. The animals now living in this area may be regarded as the greatly modified descendants of those which have lived in similar regions in past geological ages, and some of whose ancestors have been preserved in the sedimentary rocks as fossils. On the other hand, many of the animals dredged in the abysmal regions are most probably also the descendants of animals which lived in the shallower waters of former geological periods, but descended into deep water to escape the severe struggle for existence which must always have obtained in those depths affected by light, heat, motion, and other conditions. Having found existence possible in the less favourable and deeper water, they may be regarded as having slowly spread themselves over the floor of the ocean, but without undergoing great modifications, owing to the extreme uniformity of the conditions and the absence of competition. Or we may suppose that in the depressions which have taken place near coasts, some species have been gradually carried down to deep water, have accommodated themselves to the new conditions, and have gradually migrated to the regions far from land. A few species may thus have migrated to the deep sea during each geological period. In this way the origin and distribution of the deep-sea fauna in the present oceans may in some measure be explained. In like manner, the pelagic fauna and flora of the ocean is most probably derived originally from the shore and shallow water. During each period of the earth’s history a few animals and plants have been carried to sea, and have ultimately adopted a pelagic mode of life. Without insisting strongly on the correctness of some of these deductions and conclusions, we present them for the consideration of naturalists and geologists, as the result of a long, careful, but as yet incomplete, investigation. 530 Proceedings of the Boycd Society 4. Note on a large Crystal of Calc-spar, found in Lough Corrib by Professor Tait. By the Abbe Kenard. The crystal of calcite found by Professor Tait presents very large dimensions for a specimen, with very simple, and, at the same time, very definite forms. This crystal shows the faces of the primitive rhombohedron of 105°, and is twinned with parallel axes. The two individuals which compose the crystal show the form of the cleavage rhombohedron P (lOll); they are applied to each other with sym- metrical development with reference to the base oP (0001), and present the appearance of a simple crystal, although formed of two distinct halves, of which the upper belongs to one crystal and the lower to the other, the two individuals being complementary to each other. Along the twinning plane may be noticed a series of very regular grooves, which indicate a repetition of the twinning following the base, It must be noticed that the six faces do not present the same physical characters — two of them, the primitive faces of the crystal, are smooth ; the other four, although having the same crystal- lographic sign, are faces of cleavage more brilliant than the others. They appear to show that the crystal, although found isolated by Professor Tait, was formerly attached. This is further demon- strated by the presence of irregular faces, which are not amenable to any mathematical law. These false faces may be seen on the superior and inferior portions of the crystal ; they are granular, and without lustre, and cannot be confounded either with the crystal faces or with those of cleavage. They have been produced by the pressure exerted upon the crystal by the neighbouring crystals, which were developing at the same time. This consideration explains the anomalies which they show, when regarded from a geometrical poiiit of view. PKIVATE BUSINESS, Mr George M. Low, Dr Frederick Hungerford Bowman, the Eev. Dr J. Gordon Macpherson, M.A. ; Mr Charles Scott Dickson, advo- cate ; and Mr Pobert Traill Omond, were balloted for, and declared duly elected Bellows of the Society. of Edinburgh, Session 1883-84. 531 Monday, IWi February 1884. Sheriff FOEBES IEVIKE, Vice-President, in the Chair. The following Communications were read : — 1. On Eadiation. By Professor Tait. [Abstract.) The first part of this communication was devoted to a recapitulation of the advances in the Theory of Exchanges made by Stewart in 1858, and published in the Transactions of the Society for that year. Such a recapitulation it will he seen is necessary; as Stewart’s papers seem either to have fallen into oblivion or to be deemed unworthy of notice. It was pointed out that Stewart showed in these papers that the radiation within an impervious enclosure containing no source of heat must ultimately become, like the pressure of a non-gravitating fluid at rest, the same at all points and in all directions ; but that this sameness is not, like that of fluid pressure, one of mere total amount ; it extends to the quantity and quality of every one of the infinite series of wave-lengths involved. For, as one or more of the bodies may be blach, the radiation is simply that of a black body at the temperature of the enclosure. Any new body, at the proper temperature, may be inserted in the enclosure without altering this state of things; and must therefore emit precisely the amount and quality which it absorbs. This remark contains all that is yet known on the subject. For we have only to assume for the purpose of reasoning, the existence of a substance partially, or wholly, opaque to one definite wave-length, and perfectly transparent to all others ; or with any other limited properties we choose ; and suppose it to be put (at the proper temperature) into the enclosure. If we next assume that its temperature when put in differs from that of the enclosure, the ex- perimental fact that, in time, equilibrium of temperature is arrived at, shows that the radiation of any particular wave-length by a body increases with rise of temperature, Apd so forth. Yet in the latest authoritative work on the subject, Lehrbuch dev 2 M VOL. XII. 532 Proceedings of the Poyed Society Spektralanalyse^ von Dr H. Kayser (Berlin, 1883), tliougli historical details are freely given, the name of Stewart does not occur even once! There are in the same work other instances of historical error nearly as grave. Thus the physical analogy, by which Stokes in 1852 first explained the basis of spectrum analysis, is given m Ur Kayser’s work ; but it is introduced by the very peculiar phrase wollen wir versuchen, eine meclianische Erkldrung der Erscheinungen zu geben, welche auf unsere Anschauungen fiber das Leuchten begrfindet ist . . . . , ; ” and the name of Stokes is not even mentioned in connection with it ! The second part of the paper deals with the question of the limits of accuracy of the reasoning which led Stewart, and those who have followed him, to results of such vast importance. Ur Kayser, indeed, announces his intention “ in aller Strenge niathematisch zu beweisen ” the equality of emissive and absorptive powers. But the mere fact that phosphorescent bodies, such as luminous paint, give out visible radiations while at ordinary temperatures, shows at once that there are grave exceptions even to the fundamental state- ment that the utmost radiation, both as to quantity and as to quality, at any one temperature, is that of a black body ; — and very simple considerations show that all the reasoning which has been applied to the subject is ultimately based on the Second Laio of Thermody- namics (or Carnot’s principle), and is therefore true only in the sense in which that law is true, ^.e, in the statistical sense. The assumed ultimate uniformity of temperature in an enclosure, which is practically the basis of every demonstration of the extended law of exchanges, is merely an expression for the average of irregularities which are in the majority of cases too regularly spread, and on a scale too minute, to be detected by our senses, even when these are aided by the most delicate instruments. The kinetic theory of gases here furnishes us with something much closer than a mere analogy. For the very essence of what appears to us uniform temperature in a gas is the regularity of distribution of the irregu- larities of speed of the various particles. And, just as in every mass of gas there are a few particles moving with speed far greater than that of mean square, so it is at least probable that a black body at ordinary temperatures emits (though, of course, excessively feebly) radiations of wave-lengths corresponding to those of visible of Edinburgh, Session 1883-84. troo OOO light. Effects apparently or at least conceivably due to this cause have been obtained by various experimenters. If we could realise a dynamical system, analogous to that of a gas on the kinetic theory, but such that none of the particles could have any but one of a certain limited number of definite speeds, and if there were still a tendency to the nearest statistical average, we should have something capable of explaining phosphoresence at ordinary temperatures. 2. On the Need for Decimal Subdivisions in Astronomy and Navigation, and on Tables requisite therefor. By Edward Sang, LL.D. The abstract question as to what number would have been most advantageously taken for the basis of an arithmetical system has been put aside by the universal preference shown for the number ten. All nations having any culture count in tens. In the English language, traces remain of the old numeration by dozens and scores j the French still prefer to say “ quatre-vingt seize,” rather than “ nonante-six.” These vestiges serve to. show that there has been change. But from the old Eastern languages all traces of any but the denary counting have disappeared. It is in vain to argue that the number twelve is divisible by three and by four, or that the perfect number six has the preference ; for, however strong the arguments may be, there is no likelihood that they shall overturn the universally adopted mode. Nay, when, purely as arithmeticians, we come to look into the matter, and consider the needs and capabilities of mankind, we find arguments of no mean weight in favour of the denary mode. But, whatever question there may be about the convenience of one or of another basis, there can be no question as to the principle of uniformity in the plan. To count our money in dozens and scores, our weights in sevens, and our distances in elevens, must necessarily entail trouble and confusion. Our unreasoning adher- ence to the medley of British monies, weights, and measures, is indeed a subject of wonder. If there be fourteen pounds to the stone, why not fourteen ounces to the pound ? Five and a half yards go to a perch, why not five perches and a half to the furlong ? ( 534 Proceedings of the Royal Society We make our pound of seven thousand troy grains, and come down again with sixteen ounces to the pound ! The introduction of the Indian numerals and notation has brought the inconvenience of these haphazard schemes into strong relief. The whole power of this algorithm comes from its uniformity. The old scheme of counting by help of letters had proceeded decimally, its great convenience having led to its use among the Arabs, from whom it passed into Greece. In this scheme the value of the letters depends on their place in the Hebrew Elif Be, which place is fixed in the Arab’s memory by the rhythm “ ebjed hevves hota kelmen,” &c., while the Greeks had to supply two new characters to fit it to their alphabet. The first group of nine letters are taken to signify units, the second group tens, and the third group hundreds. But the marks, in the Indian method, rise in value ten times for each step on the scale, and thus ten characters serve, and much more than serve, for the former twenty-eight. We, who have never had to use the older method, can hardly appreciate the magnitude of the improvement. Adopted at once by men of science, it led to the decimal division of the radius, and to the construction of the canon of sines in its modern form. Passing to commercial men, it greatly facilitated their computations. In every branch of business its influence is felt. Thus Fahrenheit, when arranging his thermometers, divided the capacity of the bottle decimally, and estimated temperature by the expansion of mercury in ten- thousandth parts of its bulk ; while Celsius, proceeding in another direction, placed one hundred degrees between the tempera- tures of freezing and boiling water. The chemist makes his analyses in hundredths ; the banker discounts per cent. \ in every quarter the struggle is in favour of decimals. Gunter contrived his chain of one hundred links in order that there might be one hundred thousand square links in an acre ; the engineer graduates his levelling staff not in feet, inches, and eighths, but in feet and hundredths. There is no doing without decimals ; when, in making a propor- tion, we have to compare twm quantities of one kind, we, as the arithmeticians say, bring them both to one denomination : 2 cwt. 3 qrs. 17 lbs. 11 J oz. must be brought to quarter ounces, of which there are 20 845 in this quantity. That is to say, having found our old system to be unworkable, we have recourse to counting in of Edinhurgli, Session 1883-84. 535 tens ; and, moreover, the trouble of converting our confused measures into decimals exceeds that of the real business in hand. Every such conversion is a protest in favour of uniformity. Of all the affairs to which calculation is applied, trigonometry and astronomy have reaped most copiously the benefits of the Indian algorithm. We have only to compare the laborious process by which Archimedes determined the ratio of the circumference to the diameter of a circle, or the parallax and distance of the moon, to perceive how effectively the new numerals smoothed the rough road of alpha, beta ; iota, kappa. Yet, great as these benefits were, they failed to satisfy the growing needs of science. Each step in exactitude added to the toil of the computer, till, discouraged by the swelling crowd of multiplications and divisions, of proportions among the sines and cosines, the mean distances, excentricities, anomalies, and periodic times, Kepler began to despair of the future of his science. Can we, then, afford to mar these benefits by a slavish adherence to a scheme of subdivision, beautiful in its uni- formity, dignified by its age, but inept to the actual requirements 1 The successive division by sixty, into parts of the first, second, and third degree of minuteness, dates back from before the reach of authentic history ; it speaks of a great advance and subsequent decay of knowledge, for the ancient stadium and the Chinese li agree, within an inch or two, with the third subdivision of the earth’s circumference in this progression. The convenience of its numer- ous divisions has, no doubt, helped to retain it in use. Sixty com- bines, in this respect, the advantages of ten and twelve, but is far" too large for numeration in the ordinary affairs of life. Its reten- tion in the measurement of time and angle is a great hindrance to our progress. In the exceedingly simple applications of trigonometry to land- measuring, we have very little to do even with the addition and subtraction of angles, nothing whatever with their ratios ; and thus the character of the subdivision has, comparatively, little import- ance for the surveyor. Yet even he would be much helped by the centesimal division of the quadrant. It is a long time since the division of the azimuth circle into four quadrants of ninety degrees each was discarded ; the bearings were then read, so many degrees to the east or west of north, so many degrees east or 536 Proceedings of the Royal Society west of sontlij the same number of degrees indicating four different directions. The awkwardness of ' this is obvious to us ; division into two parts of 180° each was substituted, and this again is now superseded by the graduation all round to 360°, so that a number applies to one direction only ; this gives great clearness to the field operations. Having observed, from the station A, the bearings of various signals, among others that of the station B, and having carried the theodolite thither, we wish so to plant it as that it may again indicate the bearings of other signals. For this purpose we so place the azimuth circle as that, on looking back to A, the reading may be exactly the opposite of the previous reading from A to B. As the seamen phrase it, we must box the compass ; we have to add or subtract 180“ as the case may be. In computing the co-ordinates of the stations, by help of the traverse table, or by the logarithmic process, we have to note the change from addition to subtraction at 90°, 180°, 270°, 360°, and have to pass from the top to the bottom of the page at 45°, 135°, 225°, and 315°; changing sine into cosine, difference of latitude into departure. Whereas, wdth the centesimal division of the quadrant, the changes are at the hundreds and fifties, while the opposite directions differ by 200°. The improvement both in comfort and in freedom from mistakes needs not to be insisted on. In astronomical work, the awkwardness of having two numerical systems is conspicuous. We observe a planet’s opposition to the sun, and again another opposition ; the interval of time is noted in days, hours, minutes, seconds ; the change of longitude in signs, degrees, minutes, seconds ; and thence, roughly, to compute the periodic time we have to make a proportion. If we had been habituated to count in sixties, and if the number 24 had not occurred, the calculation in sexagesimals would have been the natural one ; our logarithms would, according to Nepair’s own opinion, have had 60 for their basis, just as now they have 10. As things are, no one can make the calculation. We must turn the times and the angles into decimals, taking the day or the second as the unit of time, the degree perhaps or the second as that of angle ; without decimals we are unable to move a single step. How these divisions are made for the purposes of calculation; intrinsically it is of no moment which way we count, the planetary 537 of Edinhurfjli, Session 1883-84. phenomena are not thereby affected ; the matter is one purely of arithmetical convenience. Had the subdivisions been according to the powers of ten, these conversions and their attendant labour would have been saved. But it is not now and then only that these irksome conversions occur ; they pervade every calculation in geodesy, navigation, astronomy. The estimate is not too high, that they double the labour of computation. In astronomical works there is abundant evidence of the need for a change. While the reckoning of longitude in signs, used sixty years ago, is discarded in favour of the counting in degrees all round, thirds are quite disused, the second is divided into tenths and hundredths. The arguments for the planetary disturbances are given, not in degrees, but in thousandth parts of the entire re- volution. There is no work having greater authority in these matters than that most admirable one, the Nautical Almanac y and every page thereof proclaims the need for decimals. The right ascensions, decli- nations, latitudes, and longitudes are given to decimals of the second. Now, if the division of the second into 100 parts be better than into 60, why should we not adopt, as John Newton did in the Trixfonometria Britannicciy the centesimal division of the degree? There is, and there can be, ho argument in favour of division by 60 down to seconds, that will not hold as well for thirds and for fourths ; and the same instinct for convenience which leads to the decimal division of the second would, if it had its own way, lead to that of the degree, of the quadrant, and of the day. But ease of calculation is not the only consideration. The sun’s daily right-ascensions, to hundredths of a second, are accompanied by a column of variations in one hour ; this, which is really needed for the sake of the inept computer, saves the division by 24. But this column occupies the place of the actual differences, needed by the strict computer for taking into account the variation of the variations. With decimal graduation one column would suffice for all, and the compiler of the almanac v/ould be spared the labour. The same may be said of the sun’s declinations and of the moon’s hourly places, which are accompanied by variations in 10 minutes. In the last-mentioned there is a remarkably strong instance of the awkwardness of sixties. Thus the variation in declination is to be 538 Proceedings of the Royal Society seen written 112''*37, rather than r'*52'''-37 ; it would be difficult to cite a more forcible example. That triumph of skill, patience, and exactitude, the table of Lunar Distances, is a protest even stronger; therein the moon’s distances from a star are given at intervals of three hours. In order to compute the Greenwich time of his observation, the mariner compares his observed distance (corrected for refraction and j^arallax) with those found in the almanac ; he has therefore to make a proportion in sexagesimals. Seamen are understood to be so wedded to the present system, that they of all others would dislike a change ; yet such are the torments of sexagesimals that, for the shunning of them, a column of proportional logarithms is contrived, and a special logarithmic system is arranged. Instead of having to work out a simple proportion, the seaman is drilled to use the proportional logarithm, whose nature, in ninety-nine cases out of a hundred, he does not comprehend. In the higher branches of astronomical calculations, and in the application of trigonometry to mechanical and physical problems, the arcs and their various functions have to be compared, the mode of comparison being suited to the particular cases. When the arcs are homologues of angles measured by help of graduated instruments, their natural unit is the entire circumference ; but their sines and tangents, having reference to rectilineal measure, are most con- veniently compared with the radius. Hence it is that, in ordinary trigonometry, two units are employed ; and hence also the con- venient though somewhat illogical expression, ‘‘ the sine of an angle,” instead of the sine of the arc homologous to an angle.” But in many cases, notably in analytical investigations, the radius of the circle is made the basis of comparison both for arcs and for sines. Also, in computing the anomalies of the planets, the areas passed over by the radius-vector have to be considered, and it is much preferable to measure the sines in parts of the circumference, the areas in parts of the surface of the circle. Thus we have often to pass from one unit of measure to another ; with no system of subdivision can the transitions be made more easily (if at all) than by that of uniform decimal subdivision. From whichever point of view the matter may be studied, the desirability of the change is clear ; but there are difficulties in the of Edinlurgli, Session 1883-84. 639 way ; there are the prejudices of habit, the discomforts of transition, the existing mass of preparatory work suited to the old plan, and, above all, the mass of preparations needed for the new scheme, Here, indeed, the great obstacle lies. Aside from the proposal of a change of system, a new computa- tion of fundamental tables looms in the near future. The precision of modern measurements render it necessary, in astronomical specula- tions, to reckon to hundredths of a second of time, to tenths of a second of arc. How when we determine an arc by help of (say) the seven-place logarithm of its tangent true in the last figure, the uncertainty arising from the omitted parts may amount to the fortieth part of a second; so that, since the logarithm itself is subject to several similar uncertainties, we may, notwithstanding all care, err by the tenth part of a second. But it is a sound principle that the accuracy of the arithmetical work should be clearly beyond that of observation, in order that no perceptible new error may be introduced, and thus the time is not very far distant when eight- place tables may be indispensable. Hence, in designing the canons for the decimal system, we must also look forward to increased precision. Since by far the greater number of computations are done by help of logarithms, our first business is to see to the logarithmic canon. Beginning independently of all previous work, the logarithms of all primes up to 10,000 have been computed to 28 places, that they may be true to 25, each prime being put in relation to, at least, three others. The greatest discrepancy found amounted to unit in the 27th place, so that this fundamental table may be regarded as altogether free from error. The volumes I., II., III., placed on the Society’s table, contain all the articulate steps of the work, with indices to the primes and to the divisors used ; so that, if in any subsequent computation one of these divisors should recur, we are spared the labour of a new division. Thus for the logarithm of 6563, the three equalities were used 32 130 000 001 11-599-743-6563 627 600 001 = 7T9-719-6563 36 930 001 = 17-331-6563 and the agreement furnished presumptive evidence of the accuracy 540 Proceedings of the Royal Society of tlie previous comj3utations (themselves similarly checked) for the above eight primes 11, 599, 742 ; 7, 19, 719; 7, 331, and also for the prime divisors of 3213, 6276, 3693, namely, 17, 523, 1231. In this way the whole work is bound together by an intimate inter- lacing of tests. The search for the appropriate formulae was greatly facilitated by Burckhardt’s admirable “ Table des Diviseurs,” but the recent extensions of that table by Dase and by Glaisher would have been most welcome. By the combination of these primes and by interpolation to second differences, the logarithms, to 15 places, of all numbers from 100 000 to 370 000 have been computed. The actual calculations are contained in the twenty-seven volumes herewith presented, and the transfers in nine. These logarithms are necessarily liable to residual errors, whose amount, however, cannot exceed three units in the fifteenth place. Among a large number of verifications, made for other purposes, no error exceeding two units has been found. They are accompanied by the first and second differences — differences of the third order would only appear in the sixteenth place even at the beginning of the canon. By help of these differences we can interpolate the logarithm of a number of more than six effective figures ; the w'ork consisting of three multiplications. For the converse operation, that of computing the number corresponding to a logarithm not found in the table, we need to resolve an equation of the second degree. jSTow the first differences have teyi, the second difference have five effective figures, and therefore, when the utmost precision is required, either of these interpolations is necessarily laborious. For the purposes of shortening the work, and of avoiding the solution of the quadratic equation, the expedient used by ilepair in the computation of his original canon miri ficus ^ is had recourse in a form modified to suit the present circumstances. To get the logarithm of a number not in the table, it is enough to discover that of the ratio which it bears to the tabulated number immediately below it. ISiow this ratio itself is easily found by division, and, in our present case, is expressed by unit followed at an interval of at least five blanks, by other figures ; its greatest possible value is 1,00001. In the volume marked Auxiliary taible the of Edinburgh, Session 1883-84. 541 logarithms of such ratios are given for each of the ten thousand numbers from 1 000 000 000 to 1 000 010 000. This list serves the purposes of both of Nepair’s Tabulce, iwima et secmida, and gives us, by help of this easy division, the fifteen-place logarithm of any number whatever. Kot only so; it also enables us to solve tlie converse problem, by help of a multiplication as easy. But we may approach to the required result, from the tabulated numbers immediately above. So, in order to supply the means of verification, the auxiliary table is carried, on the other side, to ten thousand numbers below the same 1 000 000 000. This addition to the canon, besides greatly lessening the labour in interpolating, lends itself readily to systematic computation. The fundamental canon for trigonometry is that of sines : these to 25 places for each two thousandth part of the quadrant, and to 15 places for each ten thousandth part, have been computed strictly by second differences, verified at short intervals. In the volumes placed before the Society the actual calculations are con- tained : they are recorded in such a form that each sine may be instantly examined. The manner of the calculation afforded a continuous and complete check, and the table is believed not to contain a single error. From these, the canon of logarithmic sines and the other usual trigonometrical tables may easily be compiled to an exactitude far beyond the requirements of practice. In a paper entitled ‘‘Nouveau Calcul des Mouvements elliptiques,'’ printed in the Memoirs of the Turin Academy for 1879, the mean anomaly of a planet is deduced from its position by taking the sum or the difference of two circular segments. In order to reap the advantage of this exceedingly simple solution of Kepler’s problem, we need first to compute the sines, measured, not in parts of the radius, but in parts of the circumference. The volume marked “Sines measured in Degrees” contains the whole calculation of this canon for each centesimal minute, and to ten decimal places of the quadrant. From this table, that of circular segments, measured in degrees of the surface of the circle, for each of the 40 000 minutes of the entire circumference, has been composed. This table, though designed expressly for astronomical purposes, has its uses in other branches of science. 542 Proceedings of the Roycd Society When the position of a planet in its orbit is given, the mean anomaly is obtained directly and almost by inspection ; but when the mean anomaly is proposed, the position has to be got by the inverse use of the tables, that is by approximation. When the first estimate is reasonably near, the work is scarcely more laborious than an ordinary interpolation ; and when, as in preparing the equations of the centre, the computations are to be made at stated intervals, the labour is insignificant. For the purpose of guiding the first estimate in sporadic cases, the mean anomalies corresponding to each degree of position, and in orbits of every degree of eccentricity, are given in the volume A, titled Mean Anomalies, the results being given to ten decimal places, and in volume B to eight places, with differences and variations. In Kepler’s time the details of only six elliptic orbits needed to be worked out ; now we have forty times as many. The motions of the cloud of specks, so small as to be seen only by help of the telescope, afford an opportunity of verifying and correcting our estimates of the relative masses of the major planets, so much the more valuable that the disturbances exerted by these miniature worlds upon their giant neighbours escape our power of detection. This new mode of calculation vastly reduces the labour of comparing the purely elliptic with the observed motions. For all analytical investigations the arc, as well as its sine, cosine, and tangent, is reckoned in parts of the radius — an arrangement also suited for several other applications of trigonometry. From this point of view, the sine and cosine take their place among functions with recurring derivatives : they are most easily and rapidly com- puted in this connection, without reference to the properties of the circle, being regarded as functions equal to their second derivatives with the signs changed. The volume titled “ Eecurring Functions ” contains their values to twelve decimal places, for each thousandth part of the radius, up to two radii. For facilitating the change from the one unit to the other in the measurement of arcs, a table is here presented of the “ Lengths of Circular Arcs ” both for the ancient and for the modern graduation. The contrast in the arrangement of the two parts of this table affords an excellent exam]3le of the power and conciseness of the decimal system. of Edinburgh, Session 1883-84. 543 The lengths are given for each second of the ancient division up to one degree, in all 3600 values ; thereafter for each degree up to 1 800°, or five complete revolutions ; the values for fractions of a second being got by the transposition of the numbers at the beginning of the table, this facility being due to the adoption of the decimal division for seconds. For the modern division 1000 terms suffice, because by mere transposition the table may be extended indefinitely both ways. In order to pass from the one system of subdivision of the quad- rant to the other, a table of equivalent modern and ancient degrees is given, first from 10^^ to 10® or 9° to 9°; then for centesimal minutes up to 10° (computed for the sake of verification); next for each tenth decimal second up to the same limit; and, lastly, for each hundredth part of a second up to ten seconds. By this table the conversion of ancient into modern or of modern into ancient degrees is easily effected. Similar tables for the conversion of ancient and decimal time are exhibited. In the reduction of astronomical observations we have very often to exchange solar and sidereal time. In 1868 the writer published Time Conversion Tables for each tenth second of the whole day. The counterpart to these is herewith presented ; it is continued from day to day up to 1000 days; and this suffices for minutes, seconds, and fractions by simple transposition. Lastly, there is appended a Traverse Table, for plain and mean latitude sailing, for each of the 400 degrees of azimuth and for dis- tances up to 100. These form at least a beginning in the collection of requisite decimal tables. That which is first wanted beyond them is the canon of logarithmic sines. The preparation of this canon would be greatly facilitated by the extension of the fifteen-place logarithms up to the whole million — that is, for all six-figure numbers. Those of them already prepared need the aid of the auxiliary multipliers 2 and 3 ; had they been carried to the half million, the auxiliary 2 would have sufficed. In conclusion, it may be remarked that five and seven place tables are exact enough for almost all business purposes ; but that, in order to have these true to the last figure, the original calculations 544 Proceedings of the Royal Society must be carried several steps beyond ; also, that while it is easy to abridge the lengthy results, it is impossible to extend those which have proved too short ; then the work must be re-done from the beginning. Hence the great advantage already experienced in this : that Brigg’s computations to fourteen places served for the prepara- tion of Vlacq’s ten-place table, and that again for those in common use, of seven and of five places. All Electro-Magnetic Declinometer. By A. Tanakadate, Assistant to the Professor of Physics in the University of Tokio, Japan. Communicated by Prof. J. A. Ewing, University College, Dundee. The terrestrial magnetic field will in general be disturbed in the neighbourhood of an electric circuit; but if the circuit be a plane set at right angles to the terrestrial lines of force, the direction of the field will remain unchanged at all points in the plane of the circuit. To determine the magnetic meridian, we have only to place a plane circuit in such a direction that, when a current in the circuit is started and stopped, no change takes place in the position of a small magnet hung at a point in the plane of the circuit, and free to turn in azimuth. The plane of the circuit will then lie magnetically east and west. The following method of laying down the magnetic meridian on, say, a laboratory table, will be found very convenient and accurate in practice : — A light rectangular wooden frame is made, about 1 meter long, 15 cm. high, and 3 cm, wide, and its outer surface is recessed slightly, except at the edges, to receive 200 turns of fine insulated wire, which are wound regularly round the frame. Both ends of the coil are led off from the same point, and close together, in order to limit the electro-magnetic influence of the circuit to the portion wound on the frame. The circuit is completed at a con- siderable distance from the frame through a battery, reversing key, and box of resistance coils. A small magnetometer, consisting of the mirror (with attached magnets) of a Thomson’s dead-beat galvanometer, hung in a wood and glass case by a silk fibre 5 cm. long, is placed in the centre of this frame, resting upon a little shelf which projects into the middle 545 of Edinhurgli, Session 1883-84. of tlie frame from an outside stand, so that tlie frame can be moved round or taken out of its place without disturbing the magneto- meter. The displacement of the mirror is observed, as usual, by the motion of the reflected image of an illuminated slit or wire. The whole is shown in fig. 1. To determine the magnetic meridian — 1. Place the frame in a vertical plane, with the magnetometer at its centre, and its length approximately at right angles to the magnetic meridian. 2. Observe the position of the reflected imago on tlm magneto- meter scale before closing the circuit. 3. Make the circuit so that the field due to it has the same sign as the terrestrial field. The image will in general be displaced, and its movements will be quickened on account of the increase of directive force. Turn the frame until the image comes back to its original position. 4. Eeverse the current: unless the adjustment in operation 3 has been correct, the image will again be displaced. The current is to be regulated (by the resistance coil) to prevent the equilibrium from being unstable or too nearly neutral. Turn the frame, if need be, until the image comes to its original position. hTow draw a line on the table, using one edge of the frame as a straight-edge, or in some other way note its position. 5. Break the current ; remove the frame and replace it inverted, and with its former east end now pointing west. Repeat operations 1 to 4 in this position, and take for the magnetic E-W the mean of the two directions so determined. If the edges of the frame are not strictly at right angles to the lines of force at its centre, but are inclined at an angle of ^ -f a to them, the two determinations will differ by 2a, and their mean will be independent of a, provided the edges of the frame are strictly parallel, and the magnetic declination is constant during the operation. Experiments with the above apparatus have shown that the error due to any small excentricity on the part of the magnetometer is inappreciable. The magnetometer was purposely placed 2 mm. away from the centre towards different quarters, but no sensible 546 Proceedings of the Pioycd Society of Edinhurgh, Session 1883-84. 547 difference in the determined directions of the meridian was ob- served. A much more elaborate instrument, based on the same principle, has been constructed for the accurate measurement of magnetic declination. In it the coil is wound in two parts on a bronze frame (the form of which will be described below), of much smaller size than in the simple laboratory apparatus already described. The frame has hollow pivots, and is mounted on the Y’s of an altazi- muth instrument. Fig. 2 is taken from a photograph of the instru- ment. The pivots are made as nearly as possible of the same size as those of the telescope which belongs to the instrument, and the total weight of the frame nearly equals that of the telescope. A light mirror magnetometer stands between the two parts of the coil in the centre of the instrument, and is siq^ported by an inde- pendent tripod, as in fig. 2, or by a central pillar fixed to the base. At the middle of two sides of the frame narrow slits, a a, are pro- vided, through which the edge of the magnetometer mirror is to be sighted to bring it to a central position. It is centred with respect to the other horizontal and the vertical direction by sighting the face of the mirror through one of the hollow pivots, and making the clearance equal all round. The magnetometer is shown separately in tig. 3, The mirror with attached magnets is suspended by a single silk-fibre 40 cm. long. The upper end of the fibre is tied round the middle of a small rod of horn, whose Aveight is nearly equal to that of the mirror and magnets. This rod rests on two small V hooks pro- jecting down from the top of the magnetometer case. The hooks are united at the top, and can be turned or lowered by loosening a jam-nut. At the lower part of the magnetometer case a thin lens is fixed in front of the mirror. A little way above the mirror, a catch, consisting of a pair of inverted hooks, is fixed in the case, so that when the magnetometer is turned upside down, the mirror will be held by the catch, and the horn rod will hang free. This rod is then allowed to turn under the torsion of the fibre until that is completely removed. The V hooks are turned into the same azimuth as the hanging rod, and the magnetometer is then inverted, that is to say, restored to its normal position. It now hangs free, and without sensible initial torsion. It is next 2 N A"OL. XII. 548 Proceedings of the Royal Roddy to be placed in the centre of the coil (the coil being roughly in the magnetic E-W plane), and its position adjusted. The method of observation is the same as in the previous case. 549 of Edinburgh, Session 1883-84. In inverting the coil, it is lifted from the Y’s and ra care being taken not to touch the magnetometer case. ised vertically, i, corresponding 550 Proceedings of the Royal Society to the original and inverted positions of the coil, are to be read on the azimuth circle. To determine the astronomical meridian, the coil and the magneto- meter are to be removed without displacing the base, and the tele- scope mounted. Any of the usual methods of observation can then he applied. An alternative construction is to attach directly to the telescope a frame for the coil. This requires that the tube of the telescope be perforated in its middle to let in the magnetometer. The in- strument becomes somewhat clumsy, but it has the advantage of allowing the same pivots to he used in both the magnetic and astronomical observations. The sensibility of the apparatus (in either its simple or more elaborate form) may be investigated as fol- lows : — Let H he the horizontal component of the terrestrial field. Let F be the field due to the coil alone. Let 6 he the angle between F and H. Let 8 be the angle hetween H and E,, the resultant of H and F. This will he the angle through which the magneto- meter is deflected when the current is made, and ± F sin ^ tan 8 = F cos 0 -f H F having a -f or - sign, according as its direction is the same or opposite to that of H. Since 8 and 0 are small, ±F^ e ±F4-H“-, h from which we see that 8, the deflection of the mirror due to any assigned error in the position of the coil, can be greatly magnified h}^ making F a little less than and of opposite sign to H. This magnification can he roughly measured by turning the frame through a known angle from its determined position, and observing of Edinhuryh, Session 1888-84. 551 the displacement of the image when the current is made. There is no difficulty in detecting an error of V in the position of the coil hy the motion of the reflected image. Evidently this magnification must not be carried so far as to make the initial torsion of the fibre seriously comparable with the magnetic couple. The plan described above of depriving the fibre of initial torsion was introduced for this reason. If the displacement of the mirror he observed with a sufficient degree of optical magnification, the process of giving sensibility hy reversing F may be dispensed with. When F = H, 8 becomes and the angular displacement of the reflected ray is equal to the error in position of the fame. The form of frame (with two parallel coils) shown in fig. 2 has been chosen in order to minimise the error produced by excen tricity on the part of the magnetometer. The proportions of the frame have been calculated as follows : — Let a length of the frame. „ & = J height „ Cj = distance of the nearer face of each coil from the centre. ,, ^2 = distance of the further face of each coil from the centre. Suppose the coil he set with the plane of ah perpendicular to the magnetic meridian. Take the centre of the frame as origin of co- ordinates. As we are only concerned with the direction in azimuth, we shall consider excentricity in the horizontal plane only. From the sym- metry of figure there will be no error, so far as direction is con- cerned, when the centre of the magnet is on either axis NS or EW (see next figure). Let the centre of the magnet he at a point (fa, Sc) from the origin. The angle which the lines of force at {8a, 8c) make with the axis of NS will be the error due to excentricity. Call this angle €, then, _ force in direction WE ^ force in direction NS ’ IL F, say . 552 Proceedings of the Royal Society When € is small, To find F^, which is the deviating force on the magnetometer — Let ABCDA'B'C'D' be a horizontal projection of the frame; and let the centre of the magnetometer be excentrically placed at the point (Sa, 8c). By supposing the frame to be divided into two parts by a vertical plane, c?<;dc'( where Ad = 2Sa = A'd'), and imagining pairs of equal and opposite currents to flow in this plane up and down, we may resolve the circuit into two pairs of coils, dcCD, d'cCT>', and ABcd, A'B'cd'. Fig. 5. The former pair, being symmetrically placed with respect to the assumed position of the magnetometer, will give no deviating force ; and in finding F^ we have only to consider the remaining pair, namely, ABc(i, A'B'c'tl'. Again, suppose two vertical planes, EF and E'F', to be drawn parallel to the planes of the coils, making EB = 8c* = E'B'. In this way the remaining pair is again divided into two pairs, AEFc/, A' E'F'<^', and EBcF, E'B c'F' ; of these the former, being placed symmetrically with regard to the mag- netometer, will give no deviating force. We are thus left with a pair of narrow magnetic shells EBcF and E'B'c'F', the breadth of each shell being 28a, height 25, and thickness * [Evidently this should be 25c, not 5c. The mistake, which I have noticed only in reading the proof, does not affect the accuracy of Mr Tanakadate’s con- clusions as to the proper proportions of the coils ; and the equations which follow, as well as the numerical values given in fig. 8, need not be altered, if we assume the excen tricity of the magnetometer in the direction NS to be |5c instead of 5c as in the text. — J, A. E.]. 553 of Edinburgh, Session 1833-84. 8c* Since 28a and Sc* are supposed to be small compared with the height 2b, these shells may be treated as electromagnetic strips. The two strips we are considering, being on opposite sides of the origin, will produce deviating forces with opposite signs. Hence if the numerical magnitudes of the forces they cause are equal, they will produce no deviating effect on the magnetometer. ISTow it is evident, if such a magnetic strip be placed due east or due west of the magnetometer with its plane at right angles to the magnetic meridian, the deviating force due to it will be zero. But if its position be changed along the magnetic meridian, without any rotation, the deviating force will increase, pass a maximum, and again become insensible when the strip is carried to a very great See note, \\ 552. 554 Proceedings of the Royal Society distance. If the strip be moved in the opposite direction, the same thing will happen with the opposite sign. Hence if we make the frame on which the coils are wound such that the values of the deviating forces due to the two strips EBcF and E'B'c'E' are numerically equal, the former being on the nearer side of the positive maximum and the latter on the further side of the negative maximum, the deviating force on the magnetometer will he insensible. This is illustrated by fig. 6, where the curve shows the deviating force caused by a strip in various positions along the line NS. To find the action of each magnetic strip — Let NS in the annexed figure represent the magnetic meridian. Let the centre of the magnetic strip be on the line ns^ parallel to N S,and let the magnetometer be placed at m. From the preced- ing figure it will be evident that the breadth of the strip is 28a, its thickness Sc, its length 25, and the distance of its centre from N S the point m ; differentiate it with respect to a ] multiply the result by Me, where ^ is the strength of the current, and n the number of turns of wire per unit of length. Since the strip is supposed to be very narrow, we can, without sensible error, project the area perpendicular to the direction of r, and take w subtended by this projected area in finding the potential at the point m due to the strip. To do this we have only to find the solid angle subtended by a rectangle whose height is 25 and breadth 2Sa^, namely, N n is a. Further, let c be the distance of its centre from WE, and r the dis- tance from m. Fig. 7. To find the force in the direction of a, which is the deviating force, we have to find the solid angle o> subtended by the area of the strip at w ~ 4 cos of Edinhiirgh, Session 1883-84. 555 Hence, neglecting terms involving (Sa)^, the potential V = inScI 4cos"^ — - _ OttI . dV da dV (fr dr da , . g 8a abc(Zr‘^ + ^h‘‘) “ ,.4(J2 + ,.2)f > F.= _,4afe(3a-J + 2i2 + 3c2) ,, nhahc {d^ + c^Y{d^ + This result can also be arrived at by finding the solid angle sub- tended by the whole rectangle 2a, 2& at the point m. Multiplying this by mSc we have the potential due to the whole shell 2a, 26, 8c, and differentiating with respect to a we obtain the force at m in the direction of a : this will evidently be zero. But differentiating this again with respect to a, and multiplying the result by 8a, we obtain for the action of the magnetic strip a value which agrees with the above result. Differentiating the coefficient respect (a2 + c2)2(a2 + 62_|_(.2)t ^ to c to find the maximum value of the deviating force, we obtain un equation which is cubic with respect to c^, from which it can be proved that the maximum value of the coefficient lies between c = — and c = 2 n/3 for all real values of h In fig. 8, the values of the above coefficient for various values of c are represented in curves, the length being expressed in centi- meters. Curve I gives the values of the coefficient when a =10 and h = Sb (that is when the strip is indefinitely short). In this case, 12ac (a2 + c2)i inSaSbSc . The curve may be interpreted as a diagram representing the deviat- ing force exerted by a magnetic particle, whose moment is 4 (in C. G. S. units) upon a unit magnetic pole at m. Curve II is for the case a = 10 6 = 2; Curve III „ „ a = 10 6 = ^; Curve IV ,, ,, a=10 6 = qo . Values of Coefficient x 103. 556 Proceedings of the Royal Society This last may be interpreted as a diagram representing the deviating force due to an indefinitely long wire hung vertically and magnet- Values of c in centimeters: Fig 8 ised uniformly in a transverse direction parallel to c, its magnetic moment per unit length being 2 in C. G. S. units. In this case of Edinburgh y Session 1883-84. 557 Fig. 9. nearly equal values at c=10 and c = 2 for curves I, II, and III, 568 Proceedinys of the Royal Society Hence we find that the effect of any small excentricity will be a minimum with practically any value of h between 0 and 3, provided the coils are wound so that the ratio of a : ; C2 is 10:2:10. The frame actually used has the following dimensions: — cm., 5=1.8 cm., Cj = 1 . 8 cm., C2 = 9 cm. [Independently of the above calculation, the deviating effect of a magnetic strip was determined experimentally. Upon a rectangular plate of wood a coil of wire was wound so as practically to represent an electromagnetic strip, with the following dimensions : — Internal width of the strip Internal height „ ,, External width ,, ,, External height „ „ Thickness „ ,, Humber of turns of wire = 0'37 cm. = 9-1 „ = 0-7 „ J. Vy X jy = 0*34 „ = 49 A strong uniform current was supplied by four large gravity cells. The strip stood upright on two round legs in a V groove which was placed along the magnetic meridian, and 30 cm. east of the magnetometer, which hung in a horizontal plane through the bottom of the strip. To increase the sensibility, the directive field was considerably weakened without change of direction by using a permanent magnet. The apparatus is shown in fig. 9. Calling 6 the deflection of the magnetometer. tan 0 — .do) dx H + i jdoi dy with the usual notation. ,doi . dy But since is small compared with H, we may take the deviating force as nearly proportional to tan 6. Fig. 11 gives the curve plotted from this experiment. It will be seen that the fall after passing the maximum is rather rapid compared with that in curve III in fig. 8, which, allowing for change of scale, of Edinhurgli, Session 1883-84. 559 represents the same conditions as those of the experiment, probably because of the neo-lected effect of ”1. dyj With a frame constructed as described, the error due to any small excentric position of tlie magnetometer is insensible. Practically, however, there will be some difference of thickness in the front and rear coils due to imperfect workmanship. We shall make a liberal allowance by supposing that one coil is broader than the other by Value of c in centimeters. Fig. 11. 1 mm. Also let the magnetometer be placed 1 mm. east or west of the centre of the frame. The value of the deviating force will then be the value of the ordinate at c= 10 in curve II., fig. 8, multiplied by in x 0.1 x 0. 1, which is 0.0042 x 0.01 x in = 0.000042 in. This, divided by F,, the force along the axis NS, will give the angle e (page 551). To find in the assumed conditions of excentricity : — Let w be the solid angle subtended at m by a thin shell vLose thickness is 8c, and n= the number of turns per unit length. Then, using the same notation as before, TT-l . d(li . 560 Proceedings of the Royal Society If we take both the front and rear coils this must be doubled, thus — F, = 2m[(u, - wg] Q • r 1 1 ~\ — oin\ cos“^ — QOS — , ■■ L \/(c? + a^){c\ + 52) x/(c| + a2)(c| + 52) J = 8m(<^i - <^2) say. Whena=10; 6- 2 ; = 2 ; ^3= 10, <^i - <^2 = 35°56' or 0.627 radians. Thus Fc = 8zV« X 0. 627 = 5.02m . Hence F„ 0.000042m ~ F^~ 5.02m = 0.0000084 radians = 1".7. In practice there should be no difficulty in keeping Sa and Sc within J mm., in which case the error will be limited to one quarter of the above. The paper has been kindly revised by Professor J. A. Ewing, for whose instructions my obligations are manifold. [Note added August 1884. — In a letter of dated April 27, Mr Tanakadat^ describes how, by the use of spider-thread instead of silk-fibre for the suspension of the magnetometer mirror and magnet, he has succeeded in reducing the error due to initial torsion to an altogether insignificant amount. He also suggests a method of optically magnifying the displacement of the mirror by hanging it in a chamber containing a liquid with a high index of refraction /a. The front of the chamber is of glass, and the mirror hangs parallel to it. If if/ be the angle of incidence, on the outside of the face of the chamber, of the entering ray, then for any small angular dis- placement of the mirror the reflected ray, on leaving the chamber, will be turned through an angle which is 2 - 1) sec^if/ -h 1 times the angle turned through by the mirror. The reflected image will of course form a spectrum, but this is of no consequence when, as here, the method of observation is a md method. — J. A. E.]. of Edinhimjh, Session 1883-84. 561 4. On an Equation in Quaternion Differences. By Professor Tait. {Ahsf7^act.) When the sides of a closed polygon are bisected, and the points of bisection joined in order, a new polygon is formed. It has the same number of sides, and the same meaii point of its corners, as the original polygon. In what cases is it similar to the original polygon ? In what cases will two, three, or more successive opera- tions of this kind produce (for the first time) a polygon similar to the original one ? Take the mean point as origin, and let q^a, . . . be the 71 corners. Here a. is any vector, which, if the polygon be plane, may be taken in that plane ; and q^, . . . q^ are quaternions, which in the special case just mentioned are powers of one quaternion in the same plane. We obviously have, if ^qr = 9^r-\-i for the plane polygon, two conditions: — the first, (1+D + D2 + . . . . + D”~^)g,.a = 0 , depending on our choice of origin; and the second, ^(1 +D)'”g,a = QD*$,a, depending on the similarity of the derived polygon to the original. In this last equation, Q is a scalar multiple of an unknown power of the quaternion of which the qs, are powers, expressing how the original polygon must be turned in its own plane, and how its linear dimensions must be altered, so that it may be superposed on the derived polygon. Also 5 is an unknown integer, but it has (like Q) a definite value or values when the problem admits of solution. r has any value from \ to n inclusive, as may be seen at once by operating by any integral power of D, and remembering that we have necessarily The solution of this case is easily effected, and gives the well-known results : — the general solution involving all equilateral and equi- angular polygons, where m may have any integral value. Besides this, there are special solutions for the triangle, and quadrilateral reduced at one operation to a parallelogram. In the former of these m may have any value ; in the latter (unless the figure be a square) m must be even. 562 Proceedings of the Poyal Society But, when the polygon is gauche, the second of the above con- ditions becomes and the solution is somewhat more difficult. Its interest consists in its leading to a new and curious question in quaternions. 5. On Vortex Motion. By Professor Tait. {Ahstrcict.) This paper contained a discussion of the consequences of the assumption of continuity of motion throughout a perfect fluid ; one of the bases of von Helmholtz’s grand investigation, on which W. Thomson founded his theory of vortex-atoms. It is entirely on the assumed absence of finite slip that von Helmholtz deduces the action of a rotating element on any other element of the fluid, and that Thomson calculates the action of one vortex-atom or part of such an atom on another atom, or on the remainder of itself. The creation of a single vortex-atom, in the sense in which it is defined by Thomson, involves action applied simultaneously to all parts of the fluid mass, not to the rotating portion alone. Monday, Zrd March 1884. Sir william THOMSON, F.E.S., Vice-President, in the Chair. The Council having awarded the Keith Prize for the Biennial Period 1881-83 to Mr Thomas Muir, for his Researches into the Theory of Determinants and Continued Fractions, the most recent instalment of results obtained by him being in a Paper on “ Per- manent Symmetric Functions,” the Chairman presented the prize. Professor Chrystal, in explaining the grounds of the award, said — While it would be easy to give you an idea of the manner of man whom the Society has delighted to honour, I feel that the task imposed upon me by your Council of giving the members at large some idea of the actual work for which the Keith Prize has in this instance been awarded is a difficult one. Were the subject of my discourse a physicist, a geologist, or even a biologist, I might tell you of the mills that would be turned by means of his discoveries, of the kinds of coal or of diamond to of Edinburgh^ Session 1883-84, 563 be explored under bis leadership, or I might take your fancy a promenade on that most fascinating new pleasure-ground of naturalists, the bottom of the sea. But, in the case of a pure mathematician’s work there is, to use the words of one of the greatest living cultivators of the analytic art, no such appeal to the immediate Utilitarianism so dear to the Philistine soul. If, however, the public to whom I can appeal is small, I feel that their judgment is sure ; and, when I have reminded those who represent that public here, of the succession of papers which Mr Muir has contributed to our Transactions and Proceedings^ I am contident that they will sanction with an emphatic approval the decision of the Council of the Koyal Society to confer upon him the Keith Prize. One of the most interesting branches of analysis is the theory of Continued Fractions. The subject has a double interest, because it is connected on the one hand with that most pure of all the branches of pure mathematics, I mean the theory of numbers, a sanctuary into which the profane foot of even the applied mathe- matician scarcely enters; and, on the other, with the theory of forms, for I need scarcely remind my mathematical hearers that the algorithms of the greatest common measure and of the calculation of the convergent to a continued fraction are formally identical ; and that this algorithm is also that by which Sturm deduced the functions which bear his name, and which play so important a part in the theory of equation. Mr Muir has pursued the theory of continued fractions, and has obtained some very important results in both its branches. In the first paper of the series for wdiich the Keith Prize is now awarded him, published in the twenty-seventh volume of our Transactions, he gives a perfectly general solution of the problem of transforming an infinite series into a continued fraction. Special cases of this transformation were known before, but no one had been able to assign the general form of the expression until Mr Muir successfully attacked the problem. . His second paper, in volume xxviii. of the Transactions, is to my mind the most noteworthy of the various pieces of work now under review. He there takes up a number of remarkable transformations of various series into the form of continued fractions, which were 2 0 VOL. XII. 564 Proceedings of the Royal Society given by the great but prematurely removed mathematician Eisenstein. These results of Eisenstein’s were left by him almost entirely without demonstration, and their connection among them- selves or with other known theorems was very obscurely indicated. So much was this the case, that several mathematicians had endea- voured unsuccessfully to prove the truth or falsity of the results. Mr Muir, guided mainly by the general ideas gained in the research just mentioned, takes up these theorems of Eisenstein’s, and succeeds with apparent ease in not only proving them, but in showing their relation to each other and to other known results. There is yet another of Mr Muir’s papers on the subject of con- tinued fractions which deserves especial mention at this moment. I allude to his paper on Continuants, in the eighth volume of the Society’s Proceedings, Passing over the remarkable general theorems regarding the special form of determinants called continu- ants, I would especially direct your attention to the remarkable theorems there arrived at regarding the expression of quadratic surds by means of continued fractions. Mr Muir finds a general expres- sion for any integer whose square root is expressible by means of a continued fraction having unit numerators and a given recurring cycle of denominators. And he finds the general condition, that any given periodic fraction may represent a quadratic surd. Another branch of analysis in which Mr Muir has equally distin- guished himself is the theory of Determinants, which I may call the chief handmaiden of the tlieory of algebraic forms. In this subject Mr Muir may be classed as a worthy follower of our great countrymen, Sylvester and Cayley. I need only allude at present to three of the papers on this subject. The papers in volumes xxix. and xxx. of the Transactions contain two most valuable generalisations in this theory, viz., Mr Muir’s Extension of Lap- lace’s Law, and his Theorem of Extensible Minors. These results are characteristic of Mr Muir’s work, the constant tendency of which is the attainment of that higher kind of simplicity which results from greater generalisation. Concerning the last paper of the series (not, I ani glad to see by the evidence of the billet for to-night, the last from Mr Muir to the Society), On a Class of Permanent Symmetric Functions, I have simply to say, that in it, by the evolution of a few simple general of Edinburgh, Session 1883-84, 565 theorems, Mr Mnir succeeds in drawing together into a compact whole a series of highly interesting but hitherto isolated results. The Council having awarded the Makdougall-Erishane Prize for the period 1880-82 to Professor James Geikie, for his contribu- tions to the Geology of the North-West of Europe, including his Paper on the Geology of the Faroes, published in the Transactions of the Society, 1880-81, the Chairman presented the prize. Lord Maclaren, in explaining the grounds of the award, said — The Council has awarded the Makdougall-Brisbane Prize to Professor James Geikie for his contributions to the geology of the north-west of Europe, including his paper on the “ Geology of the Faroes,” published in the Transactions of this Society. The Society does not need to be informed of Professor Geikie’s contributions to geological literature, because — like the great geolo- gists of the Scottish school — our professor is able to invest his scientific writings with the charm of a flowing and picturesque literary style, and his works descriptive of the Great Ice Age and of the later Prehistoric Period, when man appears upon the scene ii^ the company of the mammoth and cave-bear, have been perhaps as widely read as those of his distinguished compatriots Charles Lyell, Hugh Miller, and Roderick Murchison. But it is not only for their descriptive merits that the writings of our prizeman-elect claim our recognition. In his first and per- haps most important work. Professor Geikie proposed to himself the task of exhibiting the causes of that most remarkable and indubit- able phenomenon, the existence of continuous traces of ice-action throughout an area which extends laterally over all the elevated land of the north-west of Europe, and vertically from the highest moun- tain peaks to the water lines of our European shores and valleys. I will not undertake to say whether the bold conception of an ice-cap or ice-river stretching from the Arctic Circle to the alluvial plains of England and Germany originated in the mind of our distinguished friend, or whether it was suggested by the discoveries in connection with the ice-cap of another planet whose polar surface is said to be already better known to science than that of our own vrorld. But whether the idea of a northern ice-cap was or was not in the air, to Professor Geikie belongs the merit of having siilqected that idea to the test of a rigorous scientific examination, and of hav- 566 Proceedings of the Poyal Society ing collected and marslialled. a most imposing array of facts and logical deductions in support of his theory. I do not need to remind the Society of the confirmation which his views have received from the results of the expedition of last summer to the interior of Greenland, which are the more remarkable that Baron Nordensjold went to Greenland in the design of disproving the existence of a continental ice-cap in that region, and returned con- vinced of its existence by the evidence of his own eyes and the reports of his explorers. Professor Geikie, I suppose, has not penetrated so far north, but we know that he has qualified himself for the exposition of the history of the Glacial Age by a careful study of all its phenomena, not only in Scotland, for which his connection with the Geological Survey offered peculiar facilities, but also on the Continent of Europe, and among the islands of the North Atlantic. Of these studies his published works, as well as his contributions to the transactions of scientific societies, offer ample evidence. His latest contribution is the paper on the Faroes, which appears in the Transaetions of this Society. In estimating the importance of that paper, it may be remarked that the geological interest of a country or group of islands, is not to be measured by their political and commercial importance. In this paper we find evidence that the Faroes have been covered by an ice-cap or mer de glace of 1400 feet in thickness, entirely local in its origin. The fact that ice has accumulated to so great a height in this relatively small area, makes the geological evidence applicable to the greater and more elevated ice-masses of the continent more significant, and perhaps more easy of reception and comprehension. I have no doubt the Society will approve of the nomination of Professor Geikie by the Council for the Makdougall-Brisbane Prize. The Council having awarded the Neill Prize for the Triennial Period 1880-83 to Professor Herdman, for his Papers in the Pro- ceedings and Transactions on the Tunicata — Mr John Murray, in explaining the grounds of the award, said — Professor Herdinan’s principal papers on the Tunicata may be divided into two groups, — 1st, those on British Ascidians, and 2nd, those on the collections made during the “Challenger” ex- j^edition. of Edinhurgh, Session 1883-84. 5G7 In his first paper, “iSTotes on British Tunicata,” published in 1880, a suggestion is made as to the cause of the peculiar relations of the viscera in the genera Ascidia, Ciona, and Corella. Six new species are described, and several old ones are fully described for the first time, and their synonymy cleared uj). In subsequent papers f on British Ascidians, various other species are described, and he deals with individual variations in the Tunicata, traces changes in the branchial sac of Styela grossidaria^ showing the folds becoming obsolete and almost disappearing, discusses the variations of the dorsal tubercle within the limits of species, and tries to show how the various forms are connected, § In the last number of the Transactions there is a paper on the Tunicata of the Faroe Channel,’' in which the anatomy and histology of Doliolum is treated in great detail. The valuable collections made by the ‘‘Challenger” Expedition were placed in Professor Herdman’s hands for examination and description, and the preliminary notices of these were published in the Proceedings of this Society. In the first part of the final Memoir published in the “Challenger” series of Eeports, nine new genera and seventy -four new species are described. If we except the Molgulidge, which Lacaze-Duthiers discussed in 1877, Professor Herdman was the first to fully define the families and sub-families of the Asddice Simplices. The anatomy and histology of the new and more remarkable deep-sea forms are described in great detail, the description of Cideolus murrayi being probably the most minute and detailed description of an Ascidian that has ever been published. In this memoir some remarkable structures are for the first time pointed out, — 1st, a system of branched calcareous spicules in the vessels of the branchial sac and endostyle \ 2nd, a curious modifica- tion of the blood-vessels in the test, which probably converts the outer layer of the latter into a respiratory organ. The family Clavelinidse is removed from the compound to the simple Ascidians, and reasons are given for this change in classification, and the Report concludes with a phylogenetic table. * Journ. Lhm. Soc. ZooL, vol. xv. p. 274. t Ibid., p. 329. t Proc. Lit. and Phil. Soc., Liverpool. § Proc. Roy. Phys. Soc., Ediuburgli, 568 Proceedings of the Pioycd Society In 1881 Julin and E, van Beneden proposed the homology of the neural gland in the Tunicata with the vertebrate pituitary body. Professor Herdnian has suggested a modified theory — that the neural gland, its duct, and the dorsal tubercle (and therefore also the original pituitary body) were formed by the conjunction of a primitive renal organ and a sense organ. Some of Professor Herdmaii’s views have been subjected to con- siderable criticism by continental biologists, but it is universally acknowledged that his remarkable series of papers on the Tunicata are characterised by great ability, and the Council have accordingly adjudged to Professor Plerdman for these papers the Neill Medal. The following Communications were read : — 1. On Efficiency of Clothing for maintaining Temperature. By Sir W. Thomson. 2. On the Law of Inertia ; the Principle of Chronometry ; and the Principle of Absolute Clinural Best, and of Absolute Kotation. By Professor James Thomson, LL.D., D.Sc., C.K There is no distinction known to men among states of existence of a body which can give reason for any one state being regarded as a state of absolute rest in space, and any other being regarded as a state of uniform rectilinear motion. Men have no means of know- ing, nor • even of imagining, any one length rather than any other, as being the distance between the place occupied by the centre of a ball at present, and the place that was occupied by that centre at any past instant ; nor of knowing or imagining any one direction, rather than any other, as being tire direction of the straight line from the former place to the new place, if the ball is supposed to have been moving in space. The point of space that was occupied by the centre of the ball at any specified past moment is utterly lost to iis as soon as that moment is past, or as soon as the centre has moved out of that point, having loft no trace recognisable by us of its past place in the universe of space. There is then an essential difficulty as to our forming a distinct of EdinhimjJi, Session 1883-84 5G9 conception eitlier of rest or of rectilinear motion throngli unmarked space. We have besides no preliminary knowledge of any principle of chronometry, and for this additional reason we are under an essential preliminary difficulty as to attaching any clear meaning to the words uniform rectilinear motion as commonly employed, the uniformity being that of equality of spaces passed over in equal times. If two balls are altering their distance apart, v/e cannot suppose that they are both at rest. One, at least, must be in motion. Men have very good means of knowing in some cases, and of imagining in other cases, th,e distance between the points of space simultaneously occupied by the centres of two balls ; if, at least, we be content to waive the difficulty as to imperfection of our means of ascertaining or specifying, or clearly idealising, simultaneity at distant places. For this we do commonly use signals by sound, by light, by electricity, by connecting wires or bars, and by various other means. The time required in the transmission of the signal involves an imperfection in human powers of ascertaining simul- taneity of occurrences in distant places. It seems, however, pro- bably not to involve any difficulty of idealising or imagining the existence of simultaneity. Probably it may not be felt to involve any difficulty comparable to that of attempting to form a distinct notion of identity of place at successive times in unmarked space. There is, in the nature of things, a real distinction, cognisable by men, between absolute rotation (or absolute clinural motion) and absolute freedom from rotation (or absolute clinural rest).* The only motion of a point that men can know of or can deal with is motion relative to one, two, three, or more other points. Three points marked or indicated on one, two, or three bodies, the centres, for instance, of three balls, whether preserving their dis- tances apart, unchanging or not, are sufficient for enabling us to construct or to imagine a reference frame of any changeless configu- ration desired — three rectangular co-ordinate axes, for instance, or * The word clinural is to be understood as introduced for conveying pre- cisely one out of the various conflicting meanings of the word directional. All straight lines which are mutually parallel are, in this amended mode of nomen- clature, said to be in one same clinurc. In connection with this, it may l)e convenient here to mention that all parallel planes are, in like manner, said to be in one same Closure. 570 Proceedings of the Boyal Society throe rectangular co-ordinate planes — to which the situations, in- stantaneous or successive, of points may be referred. Any arrangement whatever of points, lines, or planes, changeless in mutual configuration, will, for present purposes, be named as a reference frame, or briefly as a frame. The word motion, in ordinary usages, has several varied signi- ficances. 1 . Thus it is often said that a body, or rather some specified point of it, has performed a motion from a point A to a point B, along a straight or curved line of motion AMB. It may be often said that this same motion has been effected slowly on one occasion and quickly on another, speed or velocity of the moving point not being treated as any essential quality or condition of the motion. 2. Again, it is often said that a point, moving along a curve GABH, has a certain motion at the instant of its passing A, and that its motion undergoes change during the passage from A to B, and that at B it has a motion changed from that which it had at A. In this sense the motion at A is regarded as determined by the line of motion specified as being the tangent to the curve at A, and the ward, or way, of the motion along its line at the point of contact A, and the velocity of the motion at that point. The velocity of the motion is usually understood as meaning a true time rate of motion — a rate which may be specified, for instance, as being that of so many feet per second, or the like. For this ordinary *mode of specifying that which is to be called velocity, it is necessary that of Edinburgh, Session 1883-84. 571 true chronometry should have been previously attained to, in idea at least, and approximately in fact. Sometimes it is found convenient to apply, temporarily at least, the name velocity (for want of any other name) to the rate of travel of a point along a line as referred to the progress of something else moving relatively to a frame or to a dial. Thus, for a point moving along a line, the motion at any point of the path may sometimes be said to have a velocity of so many feet per unit of angular space turned by the crank shaft of a steam engine relatively to the framing of the steam engine. What is thus specified might be called a quasi-velocity, not a true velocity, as it is customary to regard true velocity as being referred not to the revolution of a steam engine shaft, nor to the revolution of a hand of a badly-going clock, but to the progress of absolutely true time when once the idea of progress of true time has been arrived at. Before arriving at any principle of absolute chronometry, how- ever, we cannot deal with true velocity at all. We cannot specify a rate of progress of any moving point relatively to progress of true time, or relatively to progress of a clock hand on its dial advancing proportionally to progress of true time. But, without assuming or presupposing any principle of absolute chronometry, we can refer motions of points to an assumed reference frame, jointly with an assumed dial-traveller. The dial-traveller may conveniently be imagined as a clock hand or index travelling continuously along a graduated dial, such as the face of a clock, but without the adapta- tion of any pendulum or balance wheel, or other chronometric arrangement for regulating the motion of the hand. The traveller, for instance, might be kept moving round its dial by a winch handle, such as that of a grindstone, or of a barrel organ, turned by hand. Or it might be an index projecting out radially from the crank shaft of a steam engine, and revolving round a dial fixed to the adjacent frame- work of the engine, so as to surround the shaft. Or the traveller might be an index kept revolving by the shaft of a water wheel, with a motion depending on variable conditions of rain-fall and stream-flow. For purely kinematic considerations as to relative motions of points or bodies we have no essential concern with true time, nor with true velocities, understood as velocities of motions relative to a frame, and specified quantitatively as true time rates. 572 Proceedioigs of the Royal Society ISTow, reverting to the essential difficulty already mentioned as to our forming a distinct conception either of rest or of uniform recti- linear motion, we may go forward to some further considerations and scrutinies as to what inen can imagine or can, really know through observation and experience respecting motions of bodies in the universe of space. We may have a firm persuasion, even without perfect understand- ing, that in the nature of things there niu,st be a reality correspond- ing to our glimmering idea of motion of a body along a straight course with changeless velocity, and that there must be an essential clistinction between such motion and motion along a curved course or motion with varying velocity. We cannot, however, specify such motions relatively to unmarked space and unmeasured passage of time. We cannot specify them as to any condition of absolute rest. We can only specify them as to part of their characters, or conditions, or distinctions. We can do so only in so far as quali- ti,es or distinctions of motions of one or more bodies can be ascer- tained through knowable relations between these motions and the motions of one or more other bodies. Briefly, we can deal only with relative motions or relative rest ; not with absolute motions nor absolute rest. Sir Isaac Newton sets forth, under the designation of the First Law or Motion, the statement that — Every body continues in its state of resting or of moving uniformly in a strciight course, except in so much as, hy applied forces, it is compelled to. change that state. A most important truth in the nature of things, perceived with more or less clearness, is at the root of this enunciation, but the \yords, whether taken by themselves or in connection with Newton’s prefatory and accompanying definitions and illustrations, are inade- quate to give expression to that great natural truth. In attempting to draw from the statement a perfectly intelligible conception, we find ourselves confronted with the preliminary difficulty or im- possibility as to forming any perfectly distinct notion of a meaning- in respect to a single body, for the phrase ‘‘ stgte of resting or of ryoving uniformly, in a straight course.” Newton’s previous assertion tfuit there exists absolute space, which, in its own nature, without reference to anything else, always remains alike ayd immovable, does not clear away the difficulty. It does not do so, because it involves of Edinhurcjh, Session 1883-84. 5 Ho / O in itself the whole difficulty of our inability to form a distinct notion of identical points or places in unmarked space at successive times, or of our inability to conceive any means whatever of recog- nising afterwards in any one point of space, rather than in any ' other, the point of space which, at a particular moment of past time, was occupied by a specified point of a known body. To aid in the apprehension of the underlying truth referred to, and also as an aid to the understanding of the enunciation about to be given in the present paper as The Laio .of Inertia and^ Princijple of Chronometry, some purely kinematic principles will now be . adduced for consideration. Thus the question is to be opened up as to what may be the nature of relative mpfions of various bodies, W’hich can in any sense truly be regarded as uniform rectilinear mutual motions. Explanations are to be given on such motions of •points in unmarked space, as can have a reference frame and reference dial-traveller relatively to ivhich jointly those motions are rectilineanar and are uniform in the sense of being changeless in quasi-velocity. In other words, quite to the same effect — Explana- tions are to be given on such motions of points in unmarked sp>ace as can have a reference frame relatively to loIiicJi those motions are rectilinear and are changeless in mutual rate; or what is the same, are mutucdly proportional in their simultaneous progress. Let us imagine a reference frame, rigid in its configuration, and for simplicity let it be taken as including three rectangular reference planes firmly connected. Let several points or small bodies be kept moving by geared mechanism, such as that o| toothed wheels on variously inclined axles, and toothed straight sliding racks with pinions, all carried or guided in bearings firmly a,ttached to the reference frame, the arrangements being such that those moving points shall be made simultaneously to travel over mutually pro- portional lengths along straight lines fixed in relation to the reference frame. The motion may be given by a w;inch handle like that of a barrel organ, fixed on one of the axles ; and, for help in consideration of the subject, we may imagine a uniformly graduated dial surrounding the winch handle axle, and an ipdex attached to the axle so as to project .radially outwards like a hand of a clock, and to travel round the dial keeping pace in angular motion with the winch handle. Thus fhe simultaneous travels of the various 574 Proceedings of the Royal Society small bodies along their straight courses are to be mutually propor- tional, and they are also to be proportional each of them to the simultaneous travel of the index on the dial. Now, if any other frame of three co-ordinate planes be arranged to exist with the point of their intersection keeping at any one of the moving points, and with the three planes maintaining changeless angles with the original three reference planes, any one of the moving points will either be at rest relatively to the new set of reference planes, or will generate, in relation to them, a straight line, and the simultaneous lengths traversed by the various points relatively to these new reference planes will be mutually proportional. It is convenient to notice, in preparation for subsequent reference of motions to true time or to a truly chronometric clock, that the simultaneous lengths traversed by the various points relatively to the new reference planes, and of the winch handle index relatively to its dial, will be mutually proportional. We may thus see that for the established set of motions of the points, there can exist as many sets of reference planes or frames as we please, differently moving and differently inclined, in reference to each of which every one of the points will generate a straight line with a quasi-velocity (or rate per dial-traveller progress) proportional to the quasi-velocity of every other along its own line. We are now perfectly entitled to speak of the motions of all these points as referred to any one of the frames and the original dial traveller, as being uniform rectilinear motions. The word uniform, it should be noticed, has, neither in its origin nor in its customary employment, any essential connection with progress of time. The notion besides of the dial-traveller as a standard to which the simultaneous travels of the various points may conveniently be referred, or rated, is not at all essential. We would be quite entitled, without knowledge of chrononietry, and without having recourse to the quasi-time indicated by the dial- traveller, to speak of the motions of all the points relatively to all the reference frames, as being uniform rectilinear motions. The uniformity in rate of progress would be in respect to rate of travel of any one of the points per simultaneous travel of any other one of them. In all that has been said in this inatter no assumption has been made as to any particular condition of rest or motion having belonged to the original reference frame. It may have been firmly oj Edinburgh, Session 1883-84. 575 attached to the surface of the earth, or it may have been firmly attached to the floor and side walls of the cabin of a ship sailing in devious courses over the sea and tossing on the waves. ISTotwith- standing any such motions, or any motions whatever, belonging to the original reference frame, the mutual motions of the points will possess the character that they admit of having reference frames, as many as we please, relative to which they will be rectilinear and mutually proportional (or, in other words, they will be uniform rectilinear motions, by mutual reference without reference to time). If the moving points alone were available to us for progressive observation or measurement it might be a difficult, perhaps an extremely difficult, geometrical or Idnematical problem* to find from them a reference frame accomplishing the stated condition ; but this does not hinder us from easily and distinctly understanding that such a frame is geometrically or kinematically possible. On the other hand, for a set of points moving at random like flies in the air, or for a set of points having uniform rectilinear motion as already described, together with others revolving like satellites round some of them, no reference frame to accomplish the condi- tions stated would be possible. For a single fly moving anyhow, reference frames would be possible, relative to any one of which the motion of the fly would be rectilinear, and would be uniform in rate of progress relatively to true time, or to any assumed standard whatever for rate of progress ; but for two flies, or any greater number, no such frame would be possible. Eeasons for this are so obvious as scarcely to require statement. Briefly, however, it may be mentioned that any two flies might in their mutual motions come into contact once and then separate, and then come into con- tact again ; but no second meeting could occur with points moving * Postscript Note, May 1884. — On the evening of the reading of the paper (March 3, 1884), just after the close of the meeting of the Society, the author inquired of Professor Tait whether he could see how the jn-oblem referred to here in the paper as being perhaps extremely difficult, could be solved. Pro- fessor Tait replied that he could solve it very briefly by use of quaternions. The author, not being at all acquainted with quaternions, has since seen his way clearly to the solution by an easy method of mechanical adaptations. The mechanical method is merely for intellectual use, not for practical application. The ideal mechanism can serve as an instrument for use in reasoning, thou«-h friction, and elasticity of materials, &c., might render it incapable of complete practical realisation. B76 Proceedings of the Royal Society straiglitly and mutually proportionally in relation to any frame whatever. Or the two flies might be increasing their distance apart and afterwards diminishing it j but no approach after reces- sion is possible for points moving straiglitly and proportionally in relation to any frame whatever. The explanations now given are sufflcient to show that there can be mutual motions of various bodies, so related as to have a pro- perty of being uniform rectilinear mutual motions, and to explain the nature of that mutual relation. This is quite irrespective of any idea of chronometry, or any idea of absolute rest or motion in the universe, or of any idea of absolute clinural rest or absolute rotation, and of any distinction whereby one body might be said to be in absolute rotation and another devoid of absolute rotation. The mutual relation described has been purely kinematic, and will not be at all altered by the superposition of any new motion whether of translation or of rotation, the meaning of this statement being rendered intelligible by consideration of the attachment of the original reference frame to the floor and side walls of the cabin of a ship at sea, already mentioned. Now, to pass from mere geometric or kinematic motions, governed mutually by connecting mechanism to the motions of bodies existing in space free from any such governance, we are to accept as an established law of nature, established through multitudinous obser- vations and speculations, together with theories confirmed by multi- tudinous agreements, the following, which may be called the law of inertia. The Law of Inertia. For any set of bodies acted on each by any force, a reference FRAME and a reference dial-traveller are kinematically possible, such that relatively to them conjointly, the motion of the mass- centre of each body, undergoes change simultaneously with any infinitely short element of the dial-traveller progress, or with any clement during which the force on the body does not alter in direc- tion nor in magnitude, which change is proportional to the intensity of the force acting on that body, and to the simultaneous progress of the dial-traveller, and is made in the direction of the force. of Edinhunjh, Session 1883-84. 577 Principle of Chronometry. From the foregoing law it is readily deducible, as a corollary by elementary matbeinatical considerations, that — Any dial-traveller which would accomplish the conditions stated would make progress proportionally with any other dial-traveller, obtained likewise from the same set of bodies, or any other set of bodies with the same or any other reference frame. Then, in view of this remarkable agreement, we define as being equal intervals of time, or we assume as being somehow in their own nature intrinsi- cally and necessarily equal intervals of time, the intervals during which any such dial-traveller passes over equal spaces on its dial. Thus, any dial-traveller which would accomplish the conditions stated would constitute a perfect chronometer. This gives us the ideal of a perfect chronometer. It remains for men to aim at ap23roaching as near as they can towards that ideal in the practical realisation of good chronometry. For good and long-enduring realisations of chronometry, astro- nomical methods are alone available, l^one of these present any simple method of procedure. They require hypothetical assump- tions of supposed forces acting on the bodies considered, and, above all, there is involved in them the assumption, and after multitudinous tests, accompanied by multitudinous confirmations, the discovery of the Law of Universal Gravitational Attraction — the grandest of the discoveries of Sir Isaac Uewton. Principle of Absolute Clinural Rest and of Absolute Rotation. Any straight line fixed relatively to any reference frame which accomplishes the conditions specified in the statement of the law of inertia has absolute clinural rest. If another straight line fixed in any other such reference frame be parallel to that former line, the two lines will continue parallel, so that by either of them the one same absolute clinure is permanently preserved. The principle here called that of absolute clinural rest is clearly enunciated in Thomson and Tait’s Natural Philosophy, § 249, under the designa- tion of “ Directional Fixedness.” It is there exhibited by a very simple device, and here by a somewhat different method. 578 Proceedings of the Royal Soeiety Any body wliich lias no rotation relative to a framing wliicli accomjilislies the conditions stated is devoid of absolute rotation, and if a body rotates relatively to any such frame it has the same rotation absolutely. The Law of Inertia here enunciated sets forth all the truth which is either explicitly stated or is suggested by the First and Second Laws in Sir Isaac Newton’s arrangement. By applying the Law of Inertia to the case in which the forces acting on the bodies vanish, the law becomes a remodelled substitute for the statement set forth by Sir Isaac Newton as the First Law of Motion in his arrangement. 3, On a Modification of Gauss’s Method for determining the Horizontal Component of Terrestrial Magnetic Force, and the Magnetic Moments of Bar Magnets, in Absolute Measure. By Sir W. Thomson. 4. On the Phenomenon of “ Greatest Middle ” in the Cycle of a Class of Periodic Continued Fractions. By Thomas Muir, M.A. 1. The highest square in an integer H being A^ and H = A2 + D ; it is a familiar fact that the square root of H when expressed in the ordinary way as a continued fraction with unit-numerators takes the form A + - 1 ^2 • + ^2 2A + - * . . , ^.-i) + tem... J therefore in the case of “greatest middle” we have 2Afa , . . , + 2fe , . . . , q,_i) j. ^ A(2'i,..., 2'.-i) + 2(2'i,.., g,_2) ' Atem..*: q.-l) + ^ql,• •‘,qz-2) The numerator here, however, being less than the denominator, — for even 2(^2 • . • qz-i) is less — must be zero, and therefore te2 ) . . . 5 2'«-i) ~ 2(g'j 5 . . . , qz-2) . Conversely, if we suppose this to be the case, we can by taking the same starting-point show that q^ = A, that is, that the cycle is one of greatest middle. The condition is thus necessary and sufficient. VOL. XII. 9 p 580 Proceedings of the Royal Society 3. If ^A^4-D he expressed as a continued fraction with unit- numerators^ and the middle element of the cycle of partial quotients he equal to A, then tel,. We have already seen that generally (•'^ , * . . , Iz-i) i Iz) } . tei>---» 5^.-i){tei,«..» ^.-2) + tel,..., iz)V and J in the preceding paragraph being shown to be 2, we have in the case of “greatest middle,” (A , 2^1 , . . . , q,-i) = tel , . . . , g ) + tel , • • • , R-^) • Hence = (2'2,...,2'^-i,A) + A%i,...,g^-i) + fe,---,!Z»-iA) H= A2 + 2(g2,-.-,g^-i,A)^ -1) as was to be proved. 4. The condition (q£ , . . . , qz-i) = 2(q^ , . . . , q^-o) being satisfied^ the general expression for all integers lohose square roots have cid- minate cycles is [((Zi, ... ,3'2-i)m - (3'i, ... , 2'2~2)(9'2, ••• ,9'2-2)]^ + ( ~ 1)*{4(3'u jS'a -2)^ “ 2(g'2, ... From § 3 we have T-\ _ ^te2 , * * * , QLz-i , A) (?i, •• • . ?.-i) 2-^((?2 ) * * • . ^a-l) ^(^'2 » • • * » _ 2AQ2_i + 2Qj_3 ^ Alultiplying both sides by P^_2 and using the identity V-iQ.-2-P.-2Q.-1 = (-1)'-' we have „ ^ 2A{P,..Q„3-(-ir'} + 2P.-2Q.-2 ^z-l ^2-1 of Edinburgh, Session 1883-84. 581 Kow as {§ 2) is even, -wliieh is prime to it, is odd 3 hence (-1VA + P,.,Q,_, a-l = an integer = m say. A = (-1)'P,.,M-(-1)T,.,Q,_, .... (a). Substituting this in the expression for P^.^D we have V-=D = ( - lr2P,_,Q,.,M - ( - l)*2P,.,Ql.i + 2m = ( - ir2M{P._,Q,_, + ( - 1)^} - ( - 1) 2P,_,Q^, = (-1)^2mP,_,Q._,-(-1)^2P,_,QL, and.-. D = (-l)^2MQ,.,~(-ir2QL, (P). As H = A® + D it is seen that (a) and (/5) give the desired expression. 5. As an example of the use of the preceding result, let us try to find all the numbers whose square roots have culminate cycles of eight elements. If we denote the symmetric portion of the cycle by a, b, c, d, c, b, a, the initial condition which we have to satisfy is (J,c) = 2(a, h); i.e., bc+1 = ‘lab + 2 ; ■ i.e., b{c - 2a) = 1 j the solution of which in integers is clearly 6=1, and c = 2a+ 1 . We thus have l^a-i = (^5 I5 2a + 1) = 2a^ + 4a + 1 , Pa-2 = («, 1) =a+l, Qz-2 = 1 p SO that the general result desired is x/{(2a2 + 4a -M)m » (a + 1 }2 + 4(a + 1)M - 2 _ f ) 1 1 1 1 1 111 ( / ■*'S+ 1 +2a + l + { } + 2a+l+ l + a + 2{ }+•••’ * * where for shortness there is put { } for {(2a2 + 4a+ 1)m - (a + 1)} . 582 Proceedings of the Boycd Soeiety The only difficulty which lies in the way of finding the correspond- ing result for cycles of a greater number of elements is the solution in integers of the indeterminate equation — (ft - • • • . ft-i) = 2(ft , ft-s). This is the analytical problem we now attack. 6. In a culminate cycle of 2z elements, q2, toe have either qz-i = 2qi, or q,_i = 2qi4-l; and if the latter, then also q2 = 1 • Since q,-i) = g.-ife ? • • • » P-2) + fe » • • • ^ B-s) , and {^1 , . . . , 2.-2) = qi(q2 j • • • > qz-2) + fe 5 • • • » B-2) i therefore from the equation of condition we have (ft-i - 2ft) (ft ft-2) = 2(^3 , . . . , ft_j) - (ft , , ft.3) (a). Now (ft,-",ft-2)>(g2.-'--ft-3). ••• g.-i-2gi <1:0; and (g2.---,g«-2)>(g3>'--.g.-2). g.-i-2ft >> 1. We have thus, as was to he shown, q^- 2q~^^ either = 0 or 1. Further, when q^_^ - 2q^ = 1, our equation (a) becomes ( • • • > ^'2-2 ~ ^2-2 ) ' • • > ^'^4 ) % • When 2'z.. i = 29'j + 1, we know that g'2=lj and therefore, from § 6 (yS), the equation for determining the other elements is fe . • • • ) 5.-2) = (?3 . • • • J (?z-2) “ (g'2 J • • • ? qz-z) i.e.y = (?3 . ■ . • . 2.-3). or fe,.. CO 11 1 • • J ■ •>(?3-2)+((Z4?-- • , 2.. s)' hTow the substitution here of 2'3_2 » 2‘z-s >«•••? > 5's for ^'3 , ^4 , • • . 9’z-3?$’z-2 respectively, changes the second of these continuants into the third, the third into the second, and does not alter the first and fourth ; that is to say, the equation is symmetrical with respect to the two sets of quantities, which proves our theorem. 9. In a cidminate cycle of 2z dements where q^_i = 2q^ + 1 we have either g-3 = l, and g.-g- 1) = 2(3-4, <7^-3), or 2'3 = 2, 3-z-2 = 2, and (^4,... s) = (?4» ••• >^^-4) + fej ••• , ^ or 33=2 + «,3^-2 = 1, and (1 +«,g-4, ... ,gz-d) = 2(g4,..., From § 8 the equation for determining ^'3 , ^4 , &c., is (33,..., 3^-2) = (g3»--M + + This evidently gives 33(34,...,3z-2) + (2'5»---; 9'.s-2) = ?3(9'45---»2'^-3) + (2'55---5(?«-3) + ('Z4.---»^?^-2)+(9'4 V , -j , (go? + (^4? •••>$'^-2) + (g4> 2) (?4? ■••?gz-2) ~ (g4? ••"?g«-3) ^ 2(34,...,3^-3) + (35,..„3^ -3) -(g5...,g^-2) (g4?-*-?g^-2)-(g4? ••?g^-.3) _ ^ 2(g4?-- ?g^-3)~(g.3?---?g.^-2- 1) ^ (g4?--'?g^-2)-(g4?-*-?g^-3) Hence (?3=1, and 2(2'4,...,<7,_3) = (g5v?(Zz-2- 1) is a partial solu- tion. 584 Proceedings of the Royal Society Again, we may write Hence ^3 = 2, and 3(g^,...,^,_3) + (g5,...,^,.3) = (^4,...,^,_2) + (g5,.,.,g'^_2) is a partial solution. The second part of this, how- ever, is advantageously carried farther. Thus we have from it 3{g'4v5 2z-3) + (9'55 •••,^2-3) = gz-2(^4» ••• + (2'4»-*-»9'e -) +^z-^[q5, g2-3)+(g5J ••• > ana .-. q,_ _3(g4-- g^-3) + (g5. •••> g^-3) - (?4 ••• - (gs ^ (g'4 ... 2'z-3) + fe-‘- 2'3-3) How this fraction cannot = 1, for then we should have 2(^4) • • • ) Qz -s) ~ (2'4’ • • • • j S'z-i) + (S'S’ • • • ) which is impossible, for 2(^^, . . . . , g^_3) is greater than either of the continuants on the right. Trying if it may equal 2, we put the result in the form ^ _ 0 , fe • • • » 9z-^) - fe • • • R-s) - (^4 • • • R-i) -(%••• R-i) [/z-2 f - - I - - , 04--'2.-3) + (?5- ••.S.-s) from which it is at once manifest that the only solution is 2,.2=2 and O4 . . . 5.-3) = O4. • . ?.-4) + (?6- • • + -l.-t)- Lastly, let us try if can be equal to 2 + a. We should then have (3 + «) (^4 ... gz-3) + (2s ••• $z-3) = (l + a)(g4 ••• 9'^-2) + (9'5 ••• ^z-l) , = (1 4-a)5'^-2(g'4 ... g'2_3) + (l + oc) {q^...qz-^ + qz-2{q5 qz-2) + {q5 -• qz-^) ; .-. {3 + a-(l + «)^3_2}(g4 ••• gz-3) = (!+«) (g4 ••• ^2-4) + (^z-2-l)(g'g ... qz-z) This necessitates (3+ ) - (1 + a)2'2_2 >0 ; a -f- 3 < < 1 H- a -f 1 a + 1 and g^_2 = l Putting qz-^ = 1, we see that we must further have 2(24. • • • , 2. a) = (1 + “)(24. • • • . 2.-4) + (25. • • • . 2.-4) ^.e., = (1 -f-a, ^4, . . ., as was to be shown. of Edinhurgli, Session 1883-84. 585 10. The theorems of the preceding four paragraphs, or even of §§ 6, 7, 9, afford a complete solution of the equation of condition. The process may be thus described. It depends upon the solution of equations of two types, A and B say ; of which (v, w, X, y, z) = 2(ti, V, IP, X, y) (A) and (v, 10, X, y, z) = {v, to, x, y) + (w, y, z) + {w, x, y) . (B) are examples. The equation of condition, to begin with, is of the type A. We show that this can be made dependent upon an equa- tion of the type A but of lower order, and upon an equation of the type B. Next we show that the equation of type B depends on the solution of another of type B of lower order, and on the solution of two equations of type A. Thus by repeated partial solutions the desired result is obtained. A caution, however, is requsite in regard to the ultimate equations of the two types. In the case of type A the ultimate form may bo either (x, y, z) = x, y) (kz) , or {y, z) = 2{x, y) (A^) . The former has for solutions (1) z=2w,x:=2y, 1 (2) z = 2w+\, x = \,y = 2 ■,] the latter has 2=2.r-l-l,2/ = l • In the case of type B the ultimate form may be either {x, y, z) = {x, y) + [y, z) + y (Bz) or {x,y)= X + y +l (B.^) The solutions of the former are (1) x=l,z=2y+l , -V (2) x = y = z=2, (3) 2y + 1, = 1 : 3 of the latter x = y = 2. 11. The application of the theorem in § 8 effects a considerable simplification of this process. W^henever an equation of type B is reached, it enables us to dispense with the consideration of the last and most troublesome of the three partial solutions given in § 9, For, this solution is 586 Proceedings of the Royal Society and (§ 8) we have already virtually got it from the first of the three, viz., ^3 = 1, and fe , . . . , ^,-3 , - 1) = , . . . , q,_^) , because in the change which is the test of the symmetry of the equation and are interchanged letters. In short, if we con- sider the case where ^3 = 1, we do not require to consider the case where 12. Taking the case of a cycle of 16 elements, a, h, c, d, e,f g, h, g,f c, d, c, b, a , the equation of condition is (b, c, d, e, /, g) = 2{a, b, c, d, ej) . The solution leads to the following “ tree ” : — <5r CM \ II a, 1 , 1 , d , 1 , 2cZ + 2, 2a + 1 , { }, cc j 1l , 2d +2,1, d , 1, 2a+l, { }, cif , 1 , 2 , 2 , 2 , 2, 2a + 1 , { }, where { } indicates the middle of the symmetric portion of the cycle. All of them are shown by the tree except the fourth, which is got from third by the theorem of § 8. The following are the like results for cycles of less than 16 elements : — Elements in cycle. Cycle itself (up to middle element). 2. { },.... 4. impossible. 6. a, 2a, { }, 8. a, 1, 2a+l, { . 10. a , 1 , 2 , 2a + 1 , { }>••• a, 26, 6, 2, { }.••• 12. a, 26 + 1 , 1 , 6, 2a, { },... a, 1, 2, 2, 2a + 1 , { 14. a, 26, c, 2c, 2a + 1 , { },... a , 26 +1,2, 1 , 2a + 1 , { },... a, 1 , 26 + 1 , 6, 1, 2a + 1, { a, 1, 2, 2, 2, 2a + 1 , { },... a , 1 , 1 , 6 , 26 + 1, 2a + 1 , { },... Numbers whose square roots have these cycles: 2. a2 + 2. 4. 6. -j(2a2 + l)M + aj- ^ + 4<2M + 2. 8. |(2a2 + 4a + l)M-(a + l)P + 4(a+l)M-2 . 10. { (6«2 + 8a + 3)m + (9a + 6) + i{Za + 2)m + 18 . I + iah + 2a^ + 1)m - (2«6^ + a + b){2b^ + 1) f ^ - 4(2a62 + a + j)m + 2(262 + 1)2. &c. &c. 588 Proceedings of the Roycd Society 13. The well-known property regarding the quadratic form to which the integers belong whose square roots have culminate cycles, suggests that the coefficient of m in the general expression for these numbers (§ 4) must have the same form. We are thus led to the curious theorem: — -^/ (d2 5 • • • j dz-i) = 2(qj , . . . , q,_2) then (qi , . . . , q„_i) is of the form + 2B^ or according as z is odd or even. This further suggests the inquiry as to how A and B are to be obtained in any particular case, — how, for example, knowing that a, 25, c, 2c, 5, 2a, { } , is a culminate cycle, we can partition (a , 25 , c , 2c , 5 , 2a) into a square and the double of a square. The result is (a, 25, c, 2c, 5, 2a) = 2(a, 25, c)2 + (5, 2a)2, where the element 2c separates the given continuant into two con- tinuants which are B and A. Similarly we have (a, 25 + 1,2, 1,5, 2a) = 2(a, 25+ 1)2 + (1, 5, 2a)2, (a, 1, 25 + 1,5,1, 2a + l) = 2(a, 1)2 + (5, 1 , 2a + 1)2, (a, 1, 2, 2,2, 2a + l) = 2(a, 1, 2)2 +(2, 2a+l)2,' (a, 1, 1, 5, 25 + 1, 2a + l) = 2(a, 1, 1, 52) + (2a + 1)2. 14. Closely associated with culminate cycles are those in which the middle element of the cycle is less by 1 than the unique partial quotient ; for example, , _ 1 1 1 1 1 1 '^107-10 + 2+T+9 + 1 + 2+^ + ... Indeed, the two cases are almost co-extensive with the case where the middle element of the cycle of divisors is 2 : the exact state of matters being that if the middle element of the cycle of divisors be 2 the cycle of partial quotients is culminate or peneculminate, and if the latter cycle be culminate or peneculminate the middle element of the divisors is 2, except in the solitary instance of ^12 where it is 3. The complete theory of peneculminate cycles can be very shortly given after what has preceded. 15. The necessary and sufficient condition that the middle element of Edmlurgli, Session 1883-84. 589 qz of the cycle of partial quotients shall he 1 less than the unique partial quotient is ••• + 5 •••» = ^.-2)- 16. + D he expressed as a continued fraction with unit- numerators, and the middle element of the cycle of partial quotients he equal to A - 1, then D _ fe > • - > 9!z- lA) + (^2 > ♦ ■ • > g.-i ^ A - 1) ^ fej •••5 • • • ?. s)- From § 15 we have 2fe , . . . , ^.-2) = fern • • • , ^0-i) + (^2 ’ • • • j 1) = QzMi j • • • 5 P-2) + fei , . . . , qz-i) + j • • • ) ^70-2) + fe 5 • • • 5 70-3) 7z-i<2 = 1 and . •. (7m • • • j 70-2) = (7m • • • j 70-3) + (72 » • • • 5 70-2) + (72 ^ • > dz-^h 19. As the equation here got for the determination of 7i > 72 5 • • • 5 70-2 the type B formerly investigated in con- nection with culminate cycles, it is evident that having got all possible culminate cycles of 2z elements we can at once write down all possible peneculminate cycles of 2^ — 4 elements. Thus sup- pose it be required to find all the peneculminate cycles of 12 elements. Eepresenting the cycle by a, 5, c, c, { },.... we know that e = 1 and that for the determination of a, h, c, d we have (a, b, c, d) = {a, h, c) + (5, c, d) -i- (5, c). The solutions of this equation, however, have been found in § 12, in considering the culminate cycles of 16 elements, to he a, h, c, d=\ , 5 , 1 , 25 -f 2 = 25 + 2,1,5,1 = 2 ,2,2,2. Thus all the peneculminate cycles of 12 elements are 1 , i, 1 , 25 + 2, 1 , { } . 26 + 2, 1 ,6,1 ,1,1},... 2 ,2,2,2 The connection between the two kinds of cycles may be best formulated thus : — Every culminate cycle of the form fi,l,7r,p,(T,...,a), 2n + 1 , { j , . . . . of Edinlurgli, Session 1883-84. has corresponding to it a penecidminate cycle of the form 591 and there are no other penecidmincde cycles. The equation of condition P2-1 + Q^-i = 2P2_2 is inapplicable when 2: = 2 or 1 : in the former case we have 20. The same considerations which led to the theorem of § 13 give us now the theorem : — If (qi , . . . , q^-i) + (q2 , • • • , 9. i) = 2(qi, . . . , q.-s) (q^ , . . . , qz_i) is of the form + 2B^ or - IW, according as z is odd or even. Also, the expressions for A and B present themselves in the same simple manner as before : thus for the cycles above obtained we have 21. It only remains now to see if we can ascertain how many different kinds of culminate and peneculminate cycles there ought to be with a given number of elements. If the number of elements be 2^, then in the case of culminate cycles what we have to find is the number of solutions of an equation of type A (§ 10) and of the (2 — 2)th degree. Let the said number be denoted by and let p be used in a similar way in connection with equations of type B. Then (§10) we have the pair of difference-equations + 2A - 1 = A + 1 1 +A- 1 + 1 +2A'*' ■ ■ ■ in the latter, the solitary example 592 Proceedings of the Royal Society. and also (§ 10) the initial conditions Ct2 1 } /?2 ~ 1 tts = 2 , ft = 3 . From the two equations by division we have ft-2 - 2 - 4 ”h /^2 - 4 = 1 + «e-4 Therefore when 2 is even a,., = (2, 2, . ^,., = (1, 2, 2, 2,...)s,-, where the suffix afteF the bracket of the continuant is used to indi- cate the number of elements in the continuant ; and when z is odd '^5-2 = (2 5 2 , 2 , . . . ft_,= (l,2,2,2,..ft,_,, Putting z==2r and then z=2r + \ we see that CL.2f — d2r+l Und ft^ = ftr+l and that there is thus no need of stating the two cases separately. Our result may therefore be put thus : The number of different kinds of cidminate cycles having 2z elements is (2,2,2,....), or and the number of different kinds of peneculminatc cycles of the same extent is (2,2,2,....), + (2,2,...),_. toiler e y is the highest integer in - 3) . PEIVATE BUSINESS. Mr G. A. Woods, Dr Eichard Davy, and Dr John Grieve were balloted for, and declared duly elected Fellows of the Society. PKOCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. VOL. XII. 1883-84. No. 117. Monday, March 1884, EOBEET GEAY, Esq., Vice-President, in the Chair. The following Communications were read : — 1. The Old Eed Sandstone Volcanic Eocks of Shetland. By Messrs B. N. Peach and John Horne, of the Geological Survey of Scotland. 2. On the Principles of Economics. Part I., Mathematical. Part II., Physical. By Mr P. Geddes. 3. An Integrating Hygrometer. By Prof. C. Michie Smith. This instrument consists essentially of a cryophoriis, one bulb of which is kept wet by the same arrangement as is used for a wet- bulb thermometer, while the other bulb is left dry. For con- venience, the wet bulb is made spherical, and the dry bulb is made cylindrical, and is graduated. The difference of temperature be- tween the two bulbs produced by evaporation causes a transference of water from the dry bulb to the wet bulb, and the amount of water thus transferred in any period of time, taken along with the mean temperature, will give a measure of the average hygrometric 2 Q VOL. XII. 594 Proceedings of the Royal Society condition during that time. Preliminary observations with this instrument show that even in comparatively moist weather the total evaporation during twenty-four hours is great enough to be easily measured. The instrument is intended primarily to be used for determining the total evaporation from tanks and other free surfaces of water. Por this purpose it will be used first in connection with an atmo- meter, devised by Mr G. K. Winter and myself, by means of which we hope to determine with greater accuracy than has yet been done the total evaporation from the surface of a tank. By this means the constant of the hygrometer will be obtained, and future deter- minations can be made with the hygrometer alone. Other uses of the instruihent will at once suggest themselves, but it is not necessary to go into details till more complete observations have been made. Monday, ^th April 1884. EGBERT GRAY, Esq., Vice-President, in the Chair. The following Communications were read: — 1. On the Philosophy of Language. By Emeritus Professor Blackie. 2. On the Principles of Economics. Part III., Biological and Psychological. By Mr P. Geddes. 3. Note on a New Eorm of Galvanometer. By Professor James Blyth. This instrument consists of a close spiral of insulated copper wire bent into the form of an anchor ring, so as to form an endless solenoid. The spiral is placed in a rectangular groove turned on the 595 of Edinlmrgli, Session 1883-84. edge of a wooden or brass ring of suitable thickness and diameter. Short lengths of wire at both ends of the copper spiral are left straight. These, after being well insulated, are twisted together and led to two terminals, which serve as electrodes. The ring containing the spiral is fixed on a base board with its plane vertical, and at right angles to the magnetic meridian, when the instrument is in use. A short magnet, rigidly attached at right angles to the lower end of a stiff wire, is suspended from a silk fibre, so that its centre is in the circular centre line of the anchor ring. ?Tear the upper end of the wire a long glass fibre pointer is attached, which moves over a horizontal disc graduated to degrees, and the whole is so enclosed so that the magnet, fibre, and pointer are free from currents of air. rig. 1 gives a sketch of the arrangement, showing, however, the convolutions of the wire much too far apart. These are in reality quite close together on the inner side, the spiral being tied tight into the rectangular groove by means of a cord. Let ?z = the number of convolutions in the spiral, r = radius of circular axis of coil = OB, C = current strength ; then, if 6 be the deflection, and H « horizontal intensity of the earth’s magnetism, we have '2nC ^ . cos 6^ = H sin 0 ^ r C = — tan 6 2n From this formula it will be seen that the galvanometer constant can be very easily determined, since it depends only upon r and n. Since the endless coil, when carrying a current, forms a closed 596 Proceedings of the Royal Society magnetic shell, it can exert no magnetic force outside the shell ; and hence the current will have no effect upon any system of permanent magnets that may be employed to produce a stronger magnetic field surrounding the needle. PRIVATE BUSINESS. Mr James Tait Black and Mr E. Peirson Eamsay were balloted for, and declared duly elected Eellows of the Society. Monday, 21st April 1884. Sir william THOMSON, Hon. Vice-President, in the Chair. The following papers were read by Honorary Fellows now in Edinburgh : — 1. On Galvanic Currents passing through a very Thin Stratum of an Electrolyte. By Professor H. von Helmholtz. If one closes a galvanic circuit containing a small battery, the electromotive force of which is not able to decompose water, and a voltameter with two platinum plates dipping into water acidulated with sulphuric acid, the current has a great intensity in the first moment, and diminishes at first very rapidly, afterwards slowly. At last its intensity approaches to zero more and more, but it never ceases completely. The more sensitive the galvanometer by which you measure its intensity, the longer the time during which you are able to observe the deflection of the needle. If the electrolytic fluid is in contact with atmospheric air, it is easy, even with a galvanometer of simple construction and moderate sensibility, to observe that at last a feeble residue of current remains, keeping a nearly constant inten- sity. This intensity, however, is increased by the slightest motion of the fluid, also by feeble motions produced by changes of tempera- ture. Under these conditions, it is nearly impossible to determine by measurement regular relations between the electromotive force. of Edinburgh, Session 1883^84. 597 the resistance, and the intensity of the current. Three years ago I had the honour to describe before the Eoyal Society a little apparatus, hermetically sealed and purified as much as I was able to do from all traces of oxygen and hydrogen. There I thought that the current could be really reduced to zero. But since that time I have applied an extremely delicate galvanometer, and I have found that this cell also lets pass a never-ceasing current even with small electromotive forces. The residual current remaining under such conditions is indeed only the ten thousandth or hundred thousandth part of the current which would be produced by the same electro- motive force in a metallic conductor of the same galvanic resistance, and it goes on decreasing through weeks and weeks before it becomes constant, or rather oscillating about a constant mean value. Lately I have tried to shorten the time through which one has to wait for such observations, and to increase the intensity of the residual current by making the stratum of electrolytic fluid between two plane surfaces of platinum very thin. I have used plane plates of glass lying horizontally and separated by very thin little pieces of clean glass. The two plane plates were platinised along their interior surfaces, and the platinum covering of the superior plate (a rectangle of about 10 and 5 cm. side), which was smaller than the inferior, extended over a part of its upper side in order to fix on the upper sides of both plates two little hollow cylinders of paper con- taining mercury in contact with the platinum. By the mercury the platinum could be connected with the other parts of the circuit. If one brings drops of the electrolytic fluid near to the margin of the upper plate, they are sucked in by capillary force into the fissure between the plates and kept fast there. The galvanic resistance of the little apparatus is only a small fraction of an ohm, and can be neglected when compared with the other parts of the circuit, which contained about 600 ohms. The fluid at the edge of the upper plate was in contact with atmospheric air, and therefore saturated with atmospheric oxygen according to its density in the atmo- sphere. I was able, indeed, with this little apparatus, to get the constant value of the residual current after six or twelve hours, and to 598 Froceeclings of the Boyal Society liave it unusually strong. If one compares the intensity of the residual current with that which would have been produced in a metallic conductor of the same resistance (600 ohms), it was about 0'025 of the latter with an electromotive force of 0-8 Daniell, 0*125 with 1*0 Daniell, 0*4 with 2*0 Daniells. I shall not try to give you more exact numbers, because I hope to get them still more accu- rate than they are at present. But there was not the slightest trace of evolution of gas. And you see that even with two Daniells the current which was kept up required the force of 0*8 Daniells to overcome the resistance of the circuit. Therefore, only 1 *2 Daniells remained for the decomposition of the water, which are insufficient to develop the two gases under atmospheric pressure. By reducing the resistance of the circuit to 300 ohms I could get a decomposing force of 1*36 Daniells. But also this was not sufficient for visible decomposition. The arrangement of the apparatus used hitherto did not admit of going farther. Bor these experiments a very con- stant electromotive force is needed, which is steady through months, and of which well-measured parts can he derived to pass through the electrolyte, and I had not yet had the time to introduce those modifications of the apparatus which are necessary for the employ- ment of higher electromotive force. These experiments show that in this case a current of about 0*002 ampere could pass contantly through acidulated water without developing any visible trace of oxygen and hydrogen. I don’t think, nevertheless, that the electrolytic law of Faraday is violated in this case. I suppose that really oxygen and hydrogen exist separately at the electrodes, only they don’t bubble off, hut remain dissolved in the fluid, where they exist electrically neu- tralised, being no longer subject to electric attraction, and therefore free to migrate through the fluid by diffusion. But when electri- cally neutral oxygen reaches the cathode, where positive electricity is subject to the attraction of the negative electricity of the metal, it will yield its + E far easier to the cathoda than does hydrogen. And the same will happen at the anode. Neutral hydrogen, carried over by diffusion, will yield its - E easier to the positive metal than the anion oxygen will do. This, as you see, produces only a convective current of electricity. At the cathode diffused of Edinhurgh^ Session 1883-84. 599 oxygen^ having given off its + E and now charged with - E, will combine with the kation + H. At the anode diffused hydrogen, after having received a positive charge from the metal, will combine with the anion - 0. So the results of the electrolytic decomposition of water are annihilated continually. Oxygen, charged negatively, migrates as anion from the cathode to the anode, then, neutralised, it is carried back to the cathode. Hydro- gen, charged and discharged, goes in the opposite direction. The work done by the electromotive force of the battery is not chemical decomposition, but it is this migration of the constituents of the fluids by which heat ought to be evolved. That heat, which is evolved by the migration of the ions, falls under the heat evolved by galvanic resistance, but the heat evolved by diffusion ought to be proportional to the intensity of the current. But before this stationary state of the current can be produced, electrolytic decom- position must go on till the required amount of gases is dissolved in the fluid, if there is not already from the beginning a sufficient quantity of one of the gases, viz., oxygen, of the atmosphere in solu- tion. Here the thermodynamic inferences come into play, which I have developed lately from the law of Carnot. They show that a limited quantity of the gases can be produced electrolytically even by very feeble electromotive forces, till a certain value of density of the dissolved gases corresponding to the value of the decomposing force has been reached. Out of these thermodynamic laws one can develop a complete mathematical theory of galvanic polarisation and its effects. As far as the accuracy of my measurements reaches, the facts appear to be in sufficient harmony with such a theory. 2. On Cosmic Dust. By TAbbe Eenard. 3. Esempio del metodo di dedurre una superficie da iina figura piana. By Professor Cremona. Scopo della presente piccolo comunicazione di mostrare con un asempio notevole, ed in connessione colla teoria conosciuta delle 600 Proceedings of the Royal Soeiety rappresentazione piana di una certa classe di superficie, e con qiiella delle trasformazioni razionali nello spazio, come da nn sistema piano di punti, rette e curve si possono dedurre la costruzione e le pro- prieta di superficie situate comunque nello spazio (di quelle che sono rappresentabili punto per punto sul piano). Se sono dati sei punti 123456 in un piano, per essi passano quindici rette e sei coniche. Ciascuno de’ sei punti e doppio per infinite cubiche (curve di 3° ordine) passanti per gli altri cinque, formanti un fascio ; le tangent! nel punto doppio sono percio in involuzione. I sei punti doppi danno cosi sei involuzioni. Allora si puo domandare di costruire una curva Kg di 6° ordine, che abbia sei punti doppi in 123456 e per tangent! altrettante coppie delle sei involuzioni. II problema e risoluto dalle lacobiane delle reti di cubiche passanti per i sei punti dati. Le Kg costituiscono un sistema lineare tre volte infinite, ossia sono combinazioni linear! di quattro Kg fra loro indipendenti. Vi sono altre involuzioni, in ciascuna delle quindici rette e delle sei coniche. L’ involuzione in una retta 12 e determinata dal fascio delle coniche 3456 ; e T in- voluzione in una conica 12345 dal fascio delle rette per 6. Le curve Kg segano ciascuna delle quindici rette — delle sei coniche sempre in coppie di punti dell’ involuzione. Vi sono poi infiniti punti dotati della propriety che tutte le curve Kg passanti per uno di essi ivi si toccano; il loro luogo e una curva Hjg del dodicesimo ordine, aventi sei punti quadrupli in 123456, e tangent! alle quindici rette ed alle sei coniche nei punti doppi delle involuzioni, e nei punti quadrupli ai raggi doppi delle involuzioni risprettive. Possiamo ora prendere le Kg come imagini delle sezioni plane d’una superficie. L’ ordine sara 6*6 - 6 ‘4= 12. Essa ha ventisette rette doppie, le cui imagini sono i sei punti dati, le quindici rette e le sei coniche. Ha inoltre quarantacinque punti tripli n^ quali le ventisette rette nodali concorrono tre a tre. La superficie ha poi una curva cuspidale avente per imagine Hj2 ; e siccome questa e incontrata da ogniKg in 6 ’12 - 6*2*4 = 24 punti, cosi la curva cuspidale e del 24° ordine. Di qual classe e la superficie 1 Ai piani tangent! che passano per un punto 0 dello spazio corrispondono Kg formanti una rete, la cui of Edinburgh, Session 1883-84. 601 lacobiana sara 1’ imagine della curva di contatto della superficie col cono circoscritto. La lacobiana d’ una rete di Kg e dell’ ordine 3 ’5 e passa con 3 ‘2 — 1 = 5 rami per ciascuno de’ punti dati. Ma di essa h evidentemente parte la H^2 ^ dunque la curva residua e una cubica coi punti seniplici 123456 ; e siccome due curve analogbe si segano in altri tre punti, cosi la superficie e della terza classe. Si vede cosi che la superficie e la reciproca della superficie gene- rale di terzo ordine. Monday, ^th May 1884. ROBEET GRAY, Esq., Vice-President, in the Chair. The following Communications were read : — 1. On the Construction of the Canon of Logarithmic Sines. By Edward Sang, LL.D. In setting about the construction of the Canon of Logarithmic Sines, we naturally look for any means of lessening the heavy labour of the undertaking. The very first table of logarithms, that given by Repair in his Canon Mirificus, was one of logarithmic sines, and was made by the actual computation of the logarithms as given in Reinhold’s table of sines (see Constructio, section 39). But, in the modern text-books on trigonometry, we are told that the logarithms may be computed independently of the sines themselves. If this computa- tion be less laborious than, and as trustworthy as, the operation from the already computed sines, it must be adopted. Our canons of sines, and of logarithms to fifteen places, then only serve for occasional verifications. In the introduction to Callet’s admirable collection of Tables Portatives, the investigation of the formulae and the series for the logarithmic sines are given. According to the rule strictly followed in the preceding works, each of our steps must be made indej^end- 602 Proceedings of the Royal Society ently of all previous computations, and tlius we come to revise critically the deduction of the formulse themselves, and of the series resulting from them. It is pointed out that if, in the series for the cosine of an arc, viz. : — cos a = 1 + 1.2 1.2.3.4 1 + &c. we substitute for «, the length g-, of a quadrant, the cosine becomes zero; and that, according to the law for equations, the series is divisible by 1 - — . But the cosine is also zero for a = -q, hence the series being divisible also by 1 + - , is divisible by the product cd 1 — 2 • same way, since the cosine is zero at each odd (P cd o? quadrant, the terms 1 - , 1 - j 1 ~ so on, are all divisors of the series ; whence it is concluded that the cosine is the continued product of all these divisors to infinity, or that cos a cd \ TVV’ By similar arguments it is shown that sin ct = a\ 1 _^Yi __^Yi _ 2VA a Q2g2 Taking now the logarithm of each side of the equation, and using the formula /y» /v»0 vU frO tA/ tA/ log (1 -x)= - J collecting also the terms containing the like powers of a, we get , ^2 f 1 1 1 1 , ) logseca= I p + -+^+^ + &c. I . -;N / 1 1 1 1 , I O-l ■ 2 i + 34 + 5I + 74 + f of EcUnhurgh, Session 1883-84. 603 and so on. and so on. There remains for us the summation of these series of inverse powers. M. Callet says — “ Sommant enfin toutes ces series, nous aurons, en nous hornant a vingt decimales ” (lastly, summing all these series, confining ourselves to twenty places, we shall have), &c. , leaving us to understand that the results are obtained by actual summation. Let us proceed to verify the first coefficient by this method : — we have l-^= 1.00000 00000 00000 00000 3-^= mil mil 11111 mil 5-2 4000 00000 00000 00000 7-2= 2040 81632 65306 12245 9-2= 1234 56790 12345 67901 11-2= 826 44628 09917 35537 101-2= 9 80296 04940 69289 1001-2= 9980 02996 00499 1003-2= 9940 26892 40355 Here the progression is so slow that, after five hundred divisions, which bring us to the divisor 1001, we have got only to the sixth place. The convergence is becoming rapidly less, and we should need to use five thousand million of terms ere our quotient he brought below the twentieth decimal place. Worse than that : — the succeeding terms diminish so very slowly that their sum may 604 Proceedings of the Royal Society reach to a thousand million of units in the twentieth place; that is to say, with five thousand million of terms we shall not he sure of the result in the tenth, place. Thus it is clear that M. Callet did not get his numbers by the summation of the series ; he must have got them elseways. These series, though interesting and valuable, are useless in calculation; they are not even established by the arguments adduced. The logic is as faulty as the logistics. When a polynome consists of a finite number of terms, each a multiple of an integer positive power of some variable x, and when the substitution of a definite value r for x renders that polynome zero, it is easy to show that the expression is divisible by the differ- ence X - r, the quotient being another polynome one degree lower in rank. The proof of this theorem rests essentially on the finitude of the expression; the very idea of divisibility implies a termination. Hence in extending this law to interminate progressions we destroy the foundation on which the argument rests. Granted the use of unending series, we may divide any finite polynome by any binome, the quotient being an endless progression ; there is now no indivisi- bility, and the adjective divisible ceases to have a meaning. It is absurd to say that the progression 1 . . . 6 + &c. is divisible by 1 - ; the result of the division by any binome of the form 1 - ax'^ will be a progression arranged according to the ascending even powers of x. If we divide the quotient by another binome I - px‘^, the new quotient again by 1 - yx^^, and so on, we shall find no obstacle to the divisibility except the labour of the operation. Shall we thence argue that the original series is the continued product of — ax‘^){l - - yxf Truly not, for that would be to omit from consideration the essential item, the quotient resulting from the divisions. It is necessary to show that the successive divisions of the series for the cosine by 1 - of Edinhurgli, Session 1883-84. 605 mate quotient unit. The fallacy of these arguments may he clearly seen from another point of view. A certain curve crosses the line of abscissae at equal intervals extending indefinitely both ways. If we place the origin of the abscissae at the middle of one of the intervals, and denote the ordinate y by the general symbol (fiX, y becomes zero on substituting for X any odd multiple of the half interval ; which half interval we shall denote by q ; that is to say, , <^( ± 3q) , ± 5q) , &c., are all zero. Hence, according to these arguments, the expression for y or (f>x must be the continued product of the factors and thus our curve can be none other than the curve of sines ; or, to state the conclusion in all its absurdity, no curve other than the curve of sines can cross its axis at equal intervals extended inde- finitely both ways ! of all the coefficients a, (3, y ; that of is the sum of the products of each pair of them ; and so on, or, in the usual notation, (1 - ax^)(l - Px^){l - yx^~) . . . = 1 - 4- x^ta(3 - x^ta^y . . . , and thus, in accepting the above arguments, we assume, inad- vertently, that the interminate series amounts exactly to \ ; that is to say, we assume the equality In the continued product of any number of factors of the form 1 - 1 - (3x^, 1 - yx"^ , the coefficient of x^ is the sum 1 1 1 ^2 +952 2523’^ ■■■ or and have accomplished the very difficult problem of summing the 606 Froceeclings of the Royal Society inverse powers of the odd numbers, without having been conscious of the fatigue of the operation. Nay, even in our advanced text books on trigonometry, this gratuitous assumption is used to de- monstrate its own truth. Our taking for granted ” does not cease here ; we have to con- sider the subsequent terms of the progression. The sum of the products, two and two, of all the quantities 1111 g2 ’ 32^2 ’ 52^2 ’ J2^2 ’ must amount exactly to — . Now it is well known that the ^ 24 square of the sum of any quantities exceeds the sum of their squares by twice their product, taken two and two, or that but we have already assumed to be — , we now assume 2 . afi A to be ~ , and the obvious result of the two assumptions is that ^ i . Thus, by this easy process, we find that 6 1 = J- _L J_ 1 6 “ 1 Y ‘‘‘ 3 V 5 V or that 1 1 J_ 0 6 “96“14 ■’'3^ ■‘‘7^ The same line of exposition may be continued indefinitely, and it now becomes clear that M. Callet has not got the numerical values of his coefficients from the impracticable summations of the series (de toutes ces series) ; but that he has deduced the sums by a totally different and manageable process. The following process for computating directly the sum of the inverse second powers of the natural numbers may, perhaps, have some points of novelty and interest. Denoting by the symbol (f)X, a function whose development is of Edinburgh, Session 1883-84. 607 12 + 22 32 42 + 52 /y* /y»2 /y*3 /y»4 /y»5 tA./ cv tA^ tAj */0 + ^ + &c„ we observe that this series is convergent for every value of less than unit, and even so for unit itself ; but that for any value of x greater than unit by however little, its terms ultimately increase so that their sum either is infinite, or represents an unreality. It is thus a moot question whether just at the limit x=\, *= -log(l -*)•“ we substitute 1 - z for a? , we have 8 , -x) = - log X . ^ , whence 8[cf)X-\-cf>{\ -x'^ = - log (1 - cr) . 8 log a? - log . 8 log (1 - a;) ; which, on be integrated, becomes (f>x + (f>{l - ir) = C - log a? . log (1 - a?) . Having made Oe equal to AE or 1 - Xj draw ecf parallel to EOF j then is the surface eOGf the representative of (!- ir) , and EOGF + eOG/+EC.ec = C. Again, if through K , the middle of OA , we draw KHL parallel to AB , the equation takes the form 2.KOGL + KN2 = C, so that the nnmerical value of the constant of integration is easily computed; it is represented by the algebraic symbol C = (log 2)2 + 2 1 + &c. I . Each term of this progression is less than half of the preceding term, so that the convergence is not slow. When the computation is carried to a considerable number of places, the convergence is so nearly by halving, that the sum of the terms beyond the last com- puted one may be held as nearly a repetition thereof. The following is the couiputation to ten places : — of Edinburgh^ Session 1883-84. 609 Computation of 1 . 50000 1 . 50000 00000 00 2 . 25000 6250 00000 00 3 . 12500 1388 88888 89 i 4 . 6250 |i 390 62500 00 ! 5 3125 1 125 00000 00 1 6 1562 50000 43 40277 78 7 781 25000 i| 15 94387 75 8 390 62500 6 10351 56 9 195 31250 2 41126 54 10 97 65625 97656 25 11 48 82812 50 40353 82 12 24 41406 25 16954 21 13 12 20703 12 7223 09 14 6 10350 56 3114 04 15 3 05175 78 i 1356 34 16 1 52587 89 i 596 04 17 76293 95 263 99 18 38146 97 117 74 19 19073 49 52 83 20 9536 74 23 84 21 4768 37 10 81 22 2384 18 1 4 93 23 1192 09 2 25 24 596 05 1 03 25 298 02 48 26 149 01 i 22 27 74 50 1 10 i 1 i Succeeding terms 9 . 58224 05264 62 Hence the value of the constant C is 2.(^1 =1.16448 10529 2 (log 2)2= .48045 30139 2 C = 1.64493 40668 4 On giving to a; a value very little less than unit, the point E VOL. XII. 2 R 610 Froceedings of the Royal Society comes close up to A, and at the same time, e to O. Hence for a? = 1 , the area eOG/ becomes zero, and thus the ultimate area AOG . . . B , has for its value the constant C less the limiting value of the rectangle under the two logarithms ee and EC. How on halving the minute distance eO , we render ec rather less than half ; hut instead of doubling the line EC , when close to AB , we only augment its length by KN , the logarithm of 2. And thus the rectangle EC . ec is almost exactly halved; the halving being more and more nearly exact the more minute AE is made ; hence the limit- ing value of EC . ec is zero, and the constant C is nothing else than the representation of the area AOG . . . B , or of the sum of the series of inverse squares ; that is C = 1 -64493 40668 = {- + ^ ^ ^ + &c. How the square of the number tt is 9.86960 44011, the sixth part of which is exactly C, so that 7t2^L L L L + 52+02+ This process, although it bring out the agreement of the value of the sum of the series with that of the sixth part of the square of tt, is unsatisfactory, because it gives us a mere arithmetical coincidence, without showing why that coincidence should be. 611 of Edinhimjh, Session 1883-84. Taking the fourth part of the above _ 1 1 1 1 24 22 42 62 ”^82 and subtracting, we get for the inverse squares of the old numbers 7r2_l 1 1 1 8 P 32 52 72 thus showing that the term of the series 1 - 1.2 1.-4 1-6 + &c., would be exhausted by the divisors 1 1- 12^2 The successful pursuit of this line of inquiry would show that, in the present case, the extension of the laws of finite equations to equations involving interminate series is admissible ; but it would do so at the expense of previously discovering those coefficients which were thought to have been found by the summation of the series of inverse powers. The expressions for the log cosine and log sine may be developed directly by a process applicable to all series of the general form. 6x=l - G^X + C.2P - C2X^ + &c. If, for shortness, we write A = - C2P + C3P - &c., we have , ^ A A2 A'^ A4 ^ -log 6x= j + -j + j + — + (fee. Here, from the expansions of the various powers of A, we have to collect the terms containing like powers of x. A study of the character of these expansions enables us to write out the details of any one term separately from the rest. Thus, if we wish to get the term involving we have to consider all the combinations giving the tenth power ; from A we have only the one form ; from A2, x^^ is got in as many ways as 10 is decom- posable into two parts, as 5 4- 5, 6 4- 4, 7 + 3, 84-2, 9 4-1; from A^ in as many ways as 10 may be divided into three parts, as 4-1-44-2; 4 4-3-1-3, and so on. Hence, altogether, the number of parts of which the term x^^ is composed agrees with the number of ways in which 10 is decomposable. 612 Proceedings of the Royal Soeiety The following simple scheme shows the decomposition of 10 and of all inferior numbers. The number of parts increases rapidly with the order of the term : for there are 2 ; for 3 ; for x^, 5 ; for 7; for x^, 11; for x’^, 15; for x^, 22; for x^, 30; and for 42 parts. 1+1+1+1+1+1+4 1 + 1 + 1-1-1 + 1 + 2 + 3 1+1+1+1+1+5 1+1+1+1+3+3 1+1+1+1+6 1+1+1+2+2+3 1 + 1-1-1 + 2 + 5 1+1+1+3+4 1+1+1+7 1+1+2+2+2+2 1+1+2+2+4 1+1+2+3+3 1 + 14-2 + 6 1+1+3+5 1+1+4+4 1 + 1+8 l + 2 + 2 + 2-> 3 1 + 2 2 + 5 1+2+3+4 1 + 2 + 7 1 +3+3+3 1 + 3 + 6 1 + 4 + 5 1+9 2+2+2+2+2 2+2+2+4 2+2+3+3 2 + 2 + 6 2 + 3 + 5 2 + 4 + 4 2 + 8 3 + 3 + 4 of Edinburgh, Session 1883-84. 613 3 + 7 4 + 6 5 + 5 10 The order of these parts is thus simple ; their coefficients also are readily found ; thus for the part or cl . ^10 > we observe that the number of its parts is 6, so that it must have come from A®, as belonging to which power, its multiplier must be 1 . 2 . 3 . 4 . 5 . 6 1 . 2 . 3 . 1 . 2 . 1 -60, wherefore as coming from it is 6 ^10 In this way it is a matter of mere labour to write out the parts of the term, and to sum them. In the case of the logarithmic cosine this part becomes 60/ y/ cd y/ y 6 \1 . 2A1 . 2 . 3 . 4/ VI • 2 . 3 . 4 . 5 . 6/ , and for log the corresponding part is 60/ cd y/ y/ cd \ ■'‘TVl . 2 . 3^ 6 • 2. 3.4..V \1 • 2 • 3 . 4 . 5 . 6 . 7A For facilitating the multiplication of these denominators it is con- venient to make a list of the continued products of the natural numbers, thus — (2) = 2 (3) = 2 *3 (4) = 2^ -3 (5) = 23 • -5 (6) = 24 -32 -5 (7) = 24 •32*5 -7 (8) = 27 -32 -5 *7 (9) = 27 -34 -5 -7 (10) = 28 -34 -52 -7 (11) = 28 • 34 -52 • 7 -11 (12) = 2i« • 35 •52-7 • 11 614 PToceedincfs of the Royal Society (13) = 2io-35-52-7 “11 *13 (14) = 211 • 35 » 52 -72 *11 *13 (15) = 2ii-36-53-72-ll “13 (16) = 2i5-36-53-72-ll -13 (17) = 215 -36 -53 -72 -11 .13. 17 (18) = 2i'“38*53»72“ll »13“17 (19) = 2i6-38»53 •72»11 -13 -17 -19 (20) = 31s- 3s -54 “72 “11 -13 ‘17 *19 (21) = 218 -39' 54 -73 . 11 • 13 *17 ' 19 (22) = 219 • 39 • 54 • 78 ' 112 • 13 • 17 • 19 . As an example of tlie manner of carrying on tlie work, the com- putation of the coefficient of ci)-^ (that is od) in the expression for log sec a, is subjoined. Computation of term in log sec a. Denominators. Numerators, 4©’ + 27 _ . 7 + 2^35.52.7 .11.13 ■! -28 .3 -23.3^.52.72.11.13 1 5 5\2j\6) + 28 .3.5 + 23.33.6 .72.11.13 i + 28 .32 + 23.33,52.72.11,13 j -219.32.5.7 -2 .33.5 .7 .11.13 1 12/a2y/ a^y/a^Y - 29 . 32 . 5 -22.3».5 .72.11.13 1 3 /a2\2/aio\i ^ 3(2)-(l0/ + 219. 3A 52, 7 + 2.3. .7.11.13 4 /a2y /<24\3 -219.38 -2 .32.52.72.11.13 \ 6/a2V/a4y/a8\i + 219.38.5.7 1 + 2 .32.5 ,7 .11.13 j 615 of Eclinhurgh, Session 1883-84. common denominator, Denominators. Numerators. + 29 .31.52 + 22.3 . .7 .11.13 -211.35.52.7.11 7 . .13 + 210. 34.5 + 2.3.5 .72.11.13 - 211 . 35 . 52 . 7 7 .11.13 ' - 211 . 31 . 52 . 7 - .3 . . 7 .11.13 + 211.35.52.72.11.13 + 1 211.35.52.72.11. 13 16 216 200 ! j + 45 405 360 - 4 054 050 i + 6 006 - 3 063 060 ! + 84 084 - 91 + 210 210 1 + 22 372 259 1 4 004 + 1 1 + 22 368 256 616 Proceedings of the Royal Society TT ^-u • 22 368 256 i. i . • Hence the term is— — — — — - — — — ^a}^ which, on being sini- 211 . 3^ . 52 . 72 . 11 . 13 » » plified, becomes 2.43.127 10922 35.52.72.11.13“ ~ 42667525“ ' In this way we get the following results : — ^lep. log sec a = 1 9 1 4 1 ¥“ +¥73“ +¥75 a^ + 17 23 . 32 . 5 . 7 -a° + 31 34 . 52 . 7 no 691 ,, 2.43.127 ■*■2.3^52.7.11^ ■*■35.52.72.11.13^ 257.3617 73.43867 ^2*. 36. 53. 72. 11 . 13 ^33. 53. 72. 11 . 13. 17 31.41.283.617 ^ ■*■2.33.54.72.11.13.17.19 Nep. log -A- = sin a ^ a2 + ^. L -a4+ v,7--l— + 1 2.3 ‘ 22 . 32 . 5 34 . 5 . 7 23 . 33 . 52 . 7 1 691 -^10-1 35. 52. 7. 11 ^2. 37. 53. 72. 11 . 13^ 2 ... 3617 /I2 ai4 + ,16 36. 52. 72. 11 . 13 24. 37. 54. 72. 11. 13. 17 43867 283.617 ai3 + 341.53.73.11.13.17.19 2.39.56.72.112.13.1.7.19 a20 + &c. The coefficients in the first series are multiples of the corre- sponding coefficients in the second series, the multiplier for the terms a2” being a2« _ 1 or (a” - l)(a”+ 1). Thus for Cfc2 the multiplier is 1.3; for «4 it is 3.5; for it is 7 . 9, and so on ; which is in accordance with the obvious law, that the sum of the nth. inverse powers of the natural numbers, is 2n times that of the series of even numbers. of Edinhurgh, Session 1883-84. 617 The law of formation of the coefficients in these series may he shown in the following manner. If the polynome designent des polynomes entiers, n r^dx et quand l’int6grale est alg4brique et sans logaritbmes, on a iden- tiquement : <1> = 0 . xdx Envisageons maintenant les int4grales byperelliptique^ Q ’ et distinguant dansle denominateur Q les facteurs simples premiers k R , que je nomme A , B, ; et les facteurs appartenant a R , que je nomme S , T , . . . . ; je ferai encore 644 Proceedings of the Royal Society P_ G H J K Q-^.+1 + Bi.+i +g, •• observant maintenant que A n’ayant que des facteurs simples, et etant preniier avec B, je puis 4crire ; G = MA-aNBA\ Soit encore on Nj est 4videmment un polyn6me entier, on obtient la formule da ri^duction f- Gdx NVB A* (M-N^)dx n/B Faisons ensuite : B = SU ; en admettant, comme on le doit, que B n’ait que des facteurs simples, de sorte que S et US' soient sans diviseurs communs, j’ecrirai : J = MS~(s-J)NUS' et nous aurons Nn/R , /'(M-Ni)rfx s-Vr ■ Cette nouvelle formule de reduction, dans laquelle j’ai fait se v4rifie en differentiant, comme la precedents ; et si I’on remarque qu’elle ne soudre pas d’exceptions, qu'elle est applicable en supposant 6’ = 1 , on parvient a la conclusion suivante. Bosons, en excluant les facteurs S, T, . . . . qui appartiennent a B, F = AB., plus Fi = A«B^ .... S*T‘, .... on aura cette expression de Tint^grale proposes, dans laquelle II et 4> repr4sentent des polynomes entiers, Jl Tdx _n r ^dx Un dernier pas nous reste k faire ; soit la partia entiere de la of Edinburgh^ Session 1883-84. 645 fraction rationelle % j I’integrale C se reduit en posant J \/R et determinant le polynome M de sorte que le degre de N soit I0 plus petit possible. On reconnait ainSi qu’il faut prendre pour M la partie entiere du d4veloppenient, siiivant les puissances descen- dantes de la variable, de I’expression ^ sj JRi K/ sj Commons r le degre de R, et k le degre de N, nous aurons done la condition — -1 • 1 + 1 ; d’ou n = r -2 , Les resultats que je viens d’etablir succiiictement conduisent h la notion importante des forictions de premiere, de seconde, et de troisieme espece. II suffit d’y joindre en effet la substitution lin^aire par laquelle on transforme un polynome E de degre pair, dans Texpression R, (1 + 0^ , oil Ej est de degre impair Admettant done que R soit de degre impair, les fonctions de ’'x^dx premiere espece serolit les quantites /— ^/R ’ ou ^ = 0.1.,.. r-3 , qui sent finies pour x infini, les fonctions de seconde espece celles oil It 1 r+1 . o r - 2 , qtii Sent infinies avec x : dx et les fonctions de troisieme espece, les quantites J (0 (®-«) Vk Une remarque encore en terminant, sur la substitution * = y + t qui fait disparaitre les puissances impaires dans un polynome du 4“® degr4 : R(a:) = A.{x -a) (x- h) (x - c) {x - d). Des equations, donn6es dans mon Cours de la Faeultk^ p. 8 ^ h-~p c-p d-p a -p q-a q-b q q-d 646 Proceedings of the Royal Society j’ai remarque qu’on tire facilement celle-ci : 1 1 = 0 p- a p -h p- c p - d de sorte que Tune de ses racines donne p, et Tautre q. Or on reconnait que cf, 6, c, d, 4tant des quantites reelles rangees par ordre de grandeur, cette equation aurait une racine entre a et &, et une seconde entre c et d. Et si Ton suppose a et reelles, et c et c? imaginaires conjugu4es, on a encore de meme une racine r4elle entre a et h, et par consequent une seconde. Admettons enfin que a et ^ soient aussi imaginaires conjugu4es et representons par f {p) le premier membre. Pour p tres grand on aura f(p) = ^ ^ ^ ~ - ; pz j a + h j,, s a+ b — G — d , on trouve ensuite pour = — - — , f{p)= - — — : et pour c + d j., . p = = - 2 a-\-h - c - d (p-e){p-d) Nous avons par consequent 2 (p-a)Qj-J) encore deux racines reelles en dehors de Tintervalle compris entre a + h , c-\-d __ et 2 2 2. At the request of the Council, Professor Schuster gave an Address on the Discharge of Electricity through Gases, with Experimental Illustrations. Monday, 2nd June 1884. Sheriff FOEBES IEVINE, Vice-President, in the Chair. The Chairman announced that on June 16th, in terms of the Laws, a Ballot would take place for the following proposed Foreign Honorary Fellows : — M. Charles Hermite, Membre de I’lnstitut (Academie des Sciences), Paris ; M. Pierre Van Beneden, Pro- fesseur h TUniversite de Louvain. The following Communications were read t — > 1 . The Enumeration, Description, and Construction of Knots, with fewer than Ten Crossings. By the Eev. T. P. Kirkman, F.E.S. Communicated by Professor Tait. [This Paper will appear in the Transactions.~\ of Edinburgh^ Session 1883-84, 647 2. On Knots, Part II, By Professor Tait. [This Paper will appear in the Transactions. ] 3. Second Kote on the Eemarkable Sunsets^ By Mt John Aitken. When I communicated my first note on this subject on the 21st of January last, the only definite conclusion I had then arrived at was that the very remarkable and brilliant colour effects, lately seen in the heavens at sunrise and sunset^ were due to the presence of an unusual amount of dust at the time floating in our' atmosphere. This atmospheric dust acts as a Sifting medium, breaks up the White light into its components, and reflects all the different colours to us from different parts of the shy. Owing to the cloudy state of our northern Skies, and to the ever- varying condition of our atmosphere, it was found very difficult to follow the successive Colour changes in such a way as to enable me to form anything like a satisfactory explanation of all the phenomena. Since coming, however, to the south of France, and seeing all the different sunset effects repeat themselves evening after evening in cloudless skies, I have been enabled to form a clearer idea of how the different effects are produced ;■ and from the observa- tions made under these more favourable conditions, 1 shall now attempt to give what appears to be the explanation of some of the principal phenomena of these very remarkable and brilliant sunsets. Though it was the month of March before I saw these sunsets under the more favourable conditions,' and the brilliancy of the display had very greatly diminished, yet sufficient remained to enable the different colour changes to be followed, and 1 was still able to detect marked differences in the brilliancy of the effects on different evenings. Briefly stated, the following is something like the order in which the different phenomena followed each other, evening after evening,- in these cloudless skies, the only difference being in the brilliancy of the colours on the different evenings. During the day the sUn was sUrroUnded by an unusual amount of white light or glare. As it descended, this glare gradually in- creased in brilliancy and extent ; but while it was still an hour from setting, no colours, save blue, were anywhere visible in the heavens, and the horizon all round was white. As the sun was 648 Proceedings of the Royal Society about to set, the lower part of the western horizon became tinged with yellow, which deepened to orange as the orb touched the horizon. After it had sunk below the horizon, the band of colour in the west deepened and widened. The yello\^, which when first visible was close to the horizon, after a time rose higher, while the colour on the horizon gradually deepened to orange and at last to red, the upper limit of the colours at the same time rising higher and higher in the heavens. The amount to which the colour deepened, and the height to which it rose, varied from evening to evening. Tor some minutes after the sun had set, nothing very remark- able appeared in the sky. Overhead it was blue, and the blue gradually changed through white to a dull reddish colour on the horizon, in the north, south, and east; in the west the blue changed by imperceptible degrees from blue into white, which melted into yellow, and the yellow in turn deepened into orange and red on the horizon. But on most evenings, within a quarter of an hour after the sun had set, a very remarkable reddish glow made its appearance high up in the western sky. When this aurora-like glow first became visible, its upper edge would be about 40° above the horizon, and extended downwards to about 15° from the horizon. The colours of this glow were quite different from any of those on the horizon^ There the colours varied from yellow through orange to red; but this upper glow was a very different red from that on the horizon — perhaps crimson is the colours to which it most nearly approached. As time progressed, this glow gradually descended, till at last it merged into the sunset colours on the horizon, and the two bands melted into one. This upper glow generally took about 10 or 15 minutes, from the time it was distinctly visible, to descend and become absorbed in the horizon colours* Owing to the perspective, its upper edge seemed to descend more quickly than the lower, which made the glow appear to become narrower as it approached the horizon. After the sun had been from 20 to 30 minutes under the horizon, nothing remarkable was visible ; the upper glow having sunk into the horizon colours, the heavens had again much the same appear- ance they had before the upper glow began, only somewhat darker. But a few minutes after this upper glow had disappeared, a 649 • of Edinburgh, Session 1883-84. second made its appearance. This second upper glow was not, however, confined to the west, but the whole heavens gloWed with a strange reddish light, of very much the same tone of colour as the first upper glow. This second one generally seemed to attain its maximum first in the east, then all over the sky^ a short time after which it died awayi, and the sky took up its usual night appearance. Only a very few observations of this Second glow were obtained, as it was only on a few evenings that its appearance and dis- appearance were sufficiently distinct for the hour to be correctly noted. The time after sunset, when it appeared and disappeared', cannot therefore be given with any accuracy. I may state, how- ever, that it appeared within a few minutes after the first upper glow had vanished, perhaps about 30 or 35 minutes after sunsetj and it did not last long. It is obvious that the times here given of the first and second glows only refer to the particular cases observed. A month or two earlier, when there was more dust in the air, there is every reason for supposing that both the first and second glows would have continued much longer after sunset, as there would then be plenty of dust in the higher regions to sift the rays, also to refiect the red ones, and the sun would thus continue to shine on the dust to a later hour. It is necessary for me to state that the position from which the observations were made was such that the sun did not set on the sea, but over land, and that the land was low, and the position of observation high enough for the sun to be seen down to the true horizon. The conclusions at which I have arrived are — 1st, that the first upper glow is produced by the direct rays of the sun illuminating the particles of matter suspended in the atmosphere j and 2nd, that the brilliant western horizon light is the source of illumination of the second upper glow^ I shall now attempt to state the manner in which all the different successive colour effects are produced. The sun’s rays, in passing through our atmosphere, there encounter innumerable multitudes of very small dust particles. Some of these particles are so ex- tremely small that they can stop and scatter only the rays of small wave length- that is, those of the violet end of the spectrum. The result of this is, that the blue light is stopped and reflected in every direction, -while the rays of the red end of the spectrum are G50 Frocecclinys of the Royal Society allowed to pass on. The amount to wliicli the rays of the violet end are thrown out depends on the number of small particles encountered by them. It is generally supposed that water vapour, by absorbing the rays of the violet end of the spectrum, has a somewhat similar effect on the light passing through it. If so, the water vapour in our atmosphere will tend to deepen the red, and so intensify the effect of the dust. The reason why a great amount of dust in oUr atmosphere should give such brilliant sunset effects, is that it causes a more perfect sifting action on the sun’s rays in the outer strata of our atmosphere, and provides a greater amount of particles in the lower strata large enough to reflect the red rays. If there were no fine particles in the upper strata, the sunset effect would be whiter, and if there were no large particles in either upper or lower strata, then no such sunset effect would be possible. If our atmosphere were perfectly free from dust, the light would simply pass through it into space without revealing itself, and the moment the sun dipped below the horizon total darkness would follow. The length of our twilight, therefore, depends on the amount of dust in some form or other in our atmosphere, and the height to which the dust extends. A great amount of dust in the higher regions of our atmosphere would fully account for the greatly prolonged twilight we enjoyed while these sunset effects were at their brightest. While the sun is still high above the horizon, its rays have to penetrate but little more than the depth of our atmosphere, and they are subjected to but a slight sifting action by the dust, the colour of the light being little changed by the small amount of blue thrown out of it, before it arrives at the surface of the earth. But as the sun approaches the horizon, its light has to pass through a rapidly increasing extent of our atmosphere, and its rays are sub- jected to a proportionate increase in the amount of the sifting action; so that by the time the sun is on the horizon, the sifting action is so great that all the rays of short Wate length are stopped and scattered, and only those of the red end of the spectrum reach the earth ; hence the illumination of any object lighted by the direct rays alone is yellow, orange, or red, according to the amount of sifting that has taken place. After the sun has sunk below the horizon, the amount of air ' 651 of Ecivtibargh, Session 1883-84. through which the rays have to pass, before arriving at our position, still goes on increasing ; and though the rays cannot now come direct to us on the surface of the earth, yet they pass through our atmosphere overhead, and illuminate any particles large enough that may be floating there. But not only do the sun’s rays pass through a greater extent of our atmosphere when the sun is below the horizon, but as the rays are then at a tangent to the earth’s surface, they have to pass through a greater proportion of air near the earth ; and in that region there are, in addition to the large particles, more of the very fine smalbwave-scattering particles, as well as more water vapour, than in the upper regions of our atmosphere. The rays, therefore, that pass have the colours of small wave length more perfectly sifted out of them, and the light tramsmitted is deeper red. When we look towards the north, south, and east soon after sun- set, we see that the sky near the horizon is of a dull reddish colour. This is due to the sun’s rays being deprived of all save their red, in their passage horizontally through so much of the atmosphere, and these red rays falling on the large particles low down in the atmosphere illuminate them with red light. This red light near the horizon would be much redder if it were not for the great amount of blue light reflected to the particles from the sky overhead. As the sun sinks, but before it ceases to shine on our atmosphere, the temperature of the air begins to fall, and its cooling is accompanied by an increase in the size of the particles floating in it, due to water vapour condensing upon them. The particles to the east lose the sun first, and are thus coolest ; and the rays in that direction being best sifted, the red colour is here more distinct than in the north or south. As the sun sinks lower, the particles overhead get larger and better able to reflect the red rays ; and the red colour at first visible in the east slowly rises, passes overhead, and descends in the west. We cannot, however, see it in the zenith with the unassisted eye, and it is not till it forms the first glow that it becomes visible. I have, however, been* able by means of a Mcol prism to detect the presence of the red glow overhead, tracing it from its first appearance in the east, and following it in its passage to the west, long before it became visible to the unassisted eye in the western glow. 652 Proceedings of the Royal Society One reason why the red light is not visible overhead, is that the depth of the red reflecting stratum is not enough to stop out the great quantity of blue light coming from the sunlit air higher up ; and as this blue light is complementary to the red of the afterglow, the two combine, and cause the heavens to appear whitish, both colours being destroyed ; but the I^i'col prism, by cutting out the polarised light, reveals the red to the eye. By examining the sky overhead with the prism, it was always possible to tell, before the first afterglow in the west began, whether it Would be bright or not. If the red glow was not strong overhead When the polarised light was cut out, then the afterglow was sure to be poor. From this we see that the red seen in the east, shortly after sunset, rises and passes overhead unseen, but again becomes visible in the aurora- like glow in the west. Another reason why we see this afterglow in the west, though we cannot see it with the unassisted eye overhead, is, that when viewing it towards the horizon^ we are looking obliquely into the red stratum, and are thus receiving light from a greater depth of it than when looking upwards ; we are therefore receiving a greater amount of red light, and the greater thickness also helps to block out the blue light beyondi It is very evident, however, that this does not explain some of the peculiarities in the visibility of the first glow. If the first glow, as seen in the west, is due to the sifted rays of the sun falling on particles large enough to reflect the red rays^ thus producing in the atmosphere a Stratum of air full of red glowing particles, then we naturally ask ourselves, Why is not this red light visible to the unassisted eye when looking towards the north, South, and east, as well as towards the west ? If at sunset there is formed in the sky a red stratum, we can image it so thin as to be invisible when looked through overhead, but we should expect it to be equally brilliant in all directions, at the same elevation, or if it is more brilliant in one direction than another, we should expect the east, and not the west, to be most brilliant at sunset. Or to put this difflcUlty in another way. Why is it that this brilliant upper glow is visible only when viewed from a certain direction ? To an observer placed to the noHh, south, or west of it, it is quite invisible. We know, for instance, that a short time before this upper glow was visible to us on any evening, there of Edinhurgli, Session 1883-84. 653 was a similar glow to tlie south of us ; and seen by observers to the south-east of us ; and though we were looking into the sky where the glow was, and at the same elevation as they were, yet it was quite invisible to us. Two explanations suggest themselves to account for this peculiarity in the glow. One supposition is, that its brilliancy is dependent in some way on the brightness of the sky behind it ; the other supposition, and by far the more, probable one, is, that it is due to some peculiarity in the reflecting, particles. The glow being visible only on particles situated between us and the ,sun, would seem to. indicate that the particles engaged in producing that glow are not ordinary dust particles, which absorb and radiate the light in all directions, but that this peculiar ef ect is produced by the regular reflection, of the sun’s rays. But it may be asked, Where are the necessary reflectors to come from? Now it is obvious that any small crystals floating in the air will, by the reflection from, their surfaces, produce this result. All examinations of the volcanic dust lately collected from the atmosphere show that a great quantity of it is composed of small glassy crystals. An abundance of such crystals would quite, account for the peculiarity in the visibility of the first glow, as these crystals would shine far more brilliantly when placed between the observer and the sun than in any other position, ft is now simply a question as to whether there is a. quantity of such small crystals sufficient to produce this result. The evidence seems to indicate that there is; if so, then the difficulty vanishes. Mixed with, these crystals there are also large quantities of ordinary kinds of dust, and it is the light reflected by the latter which principally causes the red glow seen in the south, north., and east Both kinds of dust are necessary fully to explain all the phenomena. The first glow looked as if it stood vertically in the western heavens ; this, however, is an effect of perspective. In reality we were looking into what was practically a horizontal, layer of mote-filled air; and as the.sun got lower and lower the part of tflis layer reflecting the red light, gradually moved westwards, which gave it the appear- ance of moving downwards. From the high angle at which this first glow was seen, it could not be far from us, at least when it was first visible— not more than ten or fifteen miles, perhaps much less. 654 Proceedings of the Royal Society On all the evenings on which this first glow was distinct, I ob- served a thin film of silvery cloud, if cloud it could be called, form or become visible over the western sky, just after the sun had dis- appeared, It was rather curious that this filmy cloud seemed to have a definite boundary underneath, its wavings or undulations being quite distinct. The peculiar silvery appearance of this filmy cloud struck me at the time, as it had a strange lustre about it ; but it was not till I considered the necessity for crystalline reflectors fully to explain the peculiarities in the visibility of the first glow, that it struck me these crystals would also explain the peculiar silvery lustre of this haze or cloud. This crystalline dust would also account for the great brilliancy of the mid-day glare, accompanied as it was with comparatively little white light at a distance from the sun, and with fair transparency in the other parts of the sky, the crystals between us and the sun reflecting more light than those situated in other directions. So far as these observations have gone, no relation has been detected between the brilliancy of these after glows and the humidity of the atmosphere, as given either by the spectroscope, or by the wet and dry bifib thermometers. The observations, so far as tliey go, rather indicate a dry atmosphere as favourable to brilliancy, but the observations are too few to settle the point. We shall now suppose that our first glow has sunk down and melted into the horizon colours. The, sky now has little red in it anywhere save in the glowing west. The sky is now very much the same as before the first glow began, only the light from all parts is now much less. With the assistance of these glowing colours in the west, we shall now try to explain the way in which the second glow is produced. Shortly after the first glow dis- appeared, it was observed that the overhead changed in appearance, the blue slowly faded and became a whitish (X)lour. In a short time the white changed, to a redd^h hue, and at last the whole heavens glowed with a fine red light. Though this second glow was only now visible, it had been there, for some time, hut could not he seen by our unassisted eyes. |f, however, we used the polariscope we could see it at any time, after the brilliancy of the first glow had gone. It was not visible to the unassisted eye, for the same reason that the first glow could not he seen overhead, on 655 of Edinbicrghy Session 1883-84. account of the blue light from the sky overhead mixing with the red and making the sky look whitish. Now this second glow I hope to be able to prove is not caused, like the first, by the direct rays of the sun shining on the particles floating in the air, but by the particles engaged in the first glow being now illuminated, not directly by the sun's rays, but by the glowing colours on the western horizon, The clouds, dust, and floating matter to the west of us were so brilliantly illuminated, that they in turn became a source of illumination, reflecting their reddish light in all directions, and illaminating particles suspended in the air in every direction, during last winter, when these sunset effects were at their brightest, I observed one evening, after the sun had set, this red light streaming in from the glowing west with such brilliancy as to light up the smofie of a factory chimney, making it appear of a reddish colour; while all objects in the landscape of a reddish hue shone out with a brilliancy out of all proportion to what we are accustomed to see, This glowing light streaming in from tfie west falls on the particles suspended in the atmosphere, and illuminates them ; and the particles on which the sun shone directly and produced the first glow, are agaifl lit up with a reddish light, The effect of this rod illumination is not at first visible, as the sun is still shining on the upper strata of the atmosphere, and the very fine dust there reflects the blue light, which mi^es with the red and masks ft, As the sun sinks lower, it shines on less and less of the upper air, and soon the brilliancy of the blue is only equal to that of the red ; the heavens then appear whitish, and when at last the sun passes altogether out of the dusty air overhead, the red light becomes visible to the unassisted eye, and the heavens seem filled with a reddish glow. It will be observed that the explanation here offered puts the position of the illuminated particles producing the sunset effects at a much lower elevation than has generally been supposed. It will be necessary, therefore, for me to give my reasons for supposing that the phenomena are really produced by particles floating at com-' paratively low elevations. This explanation supposes that only the first glow is produced by the direct rays of the sun, and the second glow by reflection, or rather radiation from the illuminated / G5-6 Proceedings of the Royal Society particles near the horizion ; it is therefore necessary for me to show how this second glow is produced without the direct rays of the sun. It may be that while the second glow is visible, the sun is still shining in the atmosphere overhead^ but at the time of the second glow it touches only the upper limits, and there are no particles there large enough to reflect red light. Indeed, the second glow is not visible till the rays have passed out of the air in which the particles are large enough to reflect blue light. It is clear, .therefore, that the second glow cannot have its source in direct illumination. There are different ways of satisfying ourselves that the second glow is but a reflection of the sunset colours on the horizon, by the same particles as shone by direct sunlight in the first glow. Before going further, there is a most important fact which requires attention. It is one to which we are so much accustomed that we might not give it its true value. It is, however, so important, in the study of these phenomena, that it is necessary we should constantly keep, it in view. Of course, every one knows that daylight is far brighter than gaslight, but how difficult it is to realise the difference. On any ordinary day at sundown, light the gas ; it has no effect — the. room is not a bit better lighted. Leave the gas liL and as the sun sinks, note how the gas, begins to light up a wider and wider area, and at last the room appears to be brilliantly illuminated by the gas alone, while outside we can atill see our way about, and the last of these sunset effects are still visible. Now, try to realise this enormous scale of brilliancy we. have got to deal with in daylight. We should be more sensible of the difference were it not for the curtain in front of our eyes, which nature draws closer and closer the more brilliant the light is. As only enough, light is admitted to the retina to give distinct vision, and as the amount is regulated by unconscious movements, we are not so. sensible as we. might be of the vast scale of illumination used by nature. Keeping ever in view this vast scale of brilliancy we have to work with at sunset, it is easy to see that what is dark at one time, and under certain con- ditions, may really appear brilliantly illuminated a short time after under different conditions. A cloud, for instance, on a bright sky may look black, but remove the bright sky and. we find the cloud is brilliantly lighted up. of Eclinhurgh, Session 1883-84. 657 When the first glow was formed, and during the time it was descending as well as when it melted into the horizon colours, the glowing west no doubt was radiating a great amount of red light in all directions, but no red glow was visible overhead, on account of the great amount of white and blue light also reflected by the sky, by which the red effect was masked ; as we have seen, however, it was there all the time, but only became visible when the other light ceased to be reflected by the sky. Now, though during the second glow the sky seemed to get lit up with a red light, yet the brilliancy of its total illumination had not increased, it had rather decreased, as we can satisfy ourselves by observing that while all these changes are taking place the stars are becoming more and more numerous, showing that the daylight has been decreasing all the time. It has already been mentioned that immediately after sundown, a thin silvery film of cloud was always seen over the western sky before the first glow became visible. What appeared to be this film has also been detected overhead with the polariscope while the sun was shining on it, and its faintly indicated outlines traced, as it shone as a red filmy cloud when the polarised light was cut off. Now, as it was observed that the second glow took place in these same filmy clouds, and that this second glow was not visible for some time after the first glow, and not till the sunshine had almost left our atmo- sphere, it is evident that the filmy clouds from Avhich these glowing colours proceed are at no great elevation. Another thing which indicates that the second glow is but a reflection of the horizon colours, is that it was always possible to tell whether the second glow would be brilliant or not before it made its appearance. If the horizon colours were high up and brilliant, then there always followed a brilliant second glow ; but if they were low and dark, no second glow followed. There was thus a direct relation between the brilliancy of the sunset colour and the second glow. It may here be asked, Is the horizon glow sufficiently brilliant to light up the floating motes all over the sky, and account for the brightness of the second glow ? This doubt is again suggested by something which, from its very familiarity, we have almost ceased to notice. The amount of light that streams in from the western sky after sunset is much greater than Ave might imagine. It is not 2 VOL. XII. TJ 658 Frocecdings of the Royal Society miich noticed, because it casts but little shadow, on account of the light coining from a wide area. To satisfy ourselves, however, of the brilliancy of the western sky, compared with the north, south, or east, we have only to project, by means of a mirror, a small area of the western sky on to the eastern. Compared with the reflection of the western sky, the eastern looks black, and the pro- jected image contrasts as strongly with the eastern sky as the sun does with the heavens at mid-day. There is another way of studying the illuminating power of the western sky, which I had occasional opportunities of following. On some evenings there were a few small clouds floating about, just enough of them to show the successive illuminations, but not so many as to cast shadows, and interfere with each other. These test reflectors were carefully watched as the sun went down and till it was nearly dark. As the sun touched the horizon, it shone into my room, and painted an image of the window on the ojrposite wall in bright orange light. At the same moment it lighted up the little clouds with the same coloured light. This colour deepened on the clouds as the sun sunk below the horizon, till they glowed with a fine red light. After a little the sun had sunk so low that it ceased to shine on the clouds, their brilliancy died away, and at last they looked black. The sky overhead, however, still remained brilliantly illuminated. After a time a change began to appear ; as the light in the sky died away the clouds lost their dark look, and gradually after a time appeared to be lighted up again; till at last their western edges again glowed ivith a red light, in gene- ral appearance very much the same as the first red illumination. This time obviously the source of the illumination was the western sky, as the clouds were much too low to catch the direct rays of the sun. The boundaries of the illuminated parts were no longer sharp, as when the sun shone on them, but hazy and indefinite on account of the light coming to them from the wide area of the western sky. So far as I have been able to judge, the second glow which illumin- ated the whole heavens was produced in exactly the same way as the second illumination of the clouds as above described. On some evenings thin hazy clouds floating in the sky, a little below the haze that gave the true glow, were brilliantly illuminated with red of Edinhurgh, Session 1883-84. 659 light, and shone more brightly than the true glow ; and on some evenings, these thin clouds and the glow haze seemed to be so near the same elevation, that it was difficult to distinguish the one from the other. It is scarcely necessary to say that the clouds, like the second glow, did not really get lit up with red light. The appearance of lighting up was not a reality, but was due to the other light dying out of the sky more quickly than the red light in the west, and the light now coming from the clouds being more brilliant than that from the sky, the clouds appeared bright on the dark sky. Some interesting colour effects were observed on the second illumination of the clouds. They were not always coloured to the same depth of red at all points where they were exposed to the western glow. The western edge of the cloud, for instance, was generally of a light red; whilst the parts which projected underneath, and were exposed to the western glow, were of a much deeper red. This was caused by the western edge of the cloud being exposed to the illumination of the white and blue sky in the west and overhead ; this light with the red made the exposed edge whitish red, while the parts projecting underneath the clouds were protected from the white and blue, and exposed only to the horizon glow ; they shone therefore with a redder light. It has been said that the colour of the first glow was not the same as the sunset colours of the horizon, but was of a crimson hue. Now this is just what we might expect, because, from the lower strata in which the large particles are, red or reddish light is reflected to us, but this red light is accompanied by a certain amount of blue light from the higher strata, and the combination of a smalt amount of blue with the red gives a crimson tone. The second glow, for the same reason, was of a similar colour. On the horizon the red is combined with the green and yellow, causing it to appear more or less orange. It will be interesting in the future, when all these peculiar sunsets are over, to see if we can find any of this afterglow by means of a polariscope. It is obvious that there may be a con- siderable amount of red afterglow in the west, without its ever being visible to us. The reason for this, as already explained, is, that a mixture of red and blue lights appear white, and as 660 Proceedings of the Poycd Society the red glow comes to ns mixed with a certain amount of blue light from the sky beyond, a certain amount of red light is masked, and it is only when the red is greater than a certain proportion that it becomes visible as red. Any amount less, only changes the blue towards white. If, however, on searching the sky overhead after sunset with the polariscope, we find the red still there, we may be sure it will be follovt^ed by a red glow in the west, though it may not be visible to our eyes. Conclusions. We may sum up our conclusions under the five following heads : — 1. If our atmosphere were perfectly pure, and free from suspended particles, there Avould be no twilight. When the sun sunk under the horizon, its rays would pass through our atmosphere into space, without revealing themselves by illuminating our sky, and the moment the sun disappeared total darkness would follow, almost as quickly as when a candle is extinguished at midnight. 2. The greater the amount of suspended particles — up to a certain quantity — ^there is in the atmosphere, and the greater the height to which they are diffused, the more the western sky will be illuminated at sunset, and the longer will be the twilight. 3. The greater the amount of suspended particles of extremely small size there is in the atmosphere, the more highly coloured will be the transmitted light of the sun and the reflected light of the sky. 4. The western afterglow is caused by the transmitted light being reflected to the earth by small dust crystals floating in the air. 5. When there are plenty of suspended particles in the atmo- sphere, the western sky at sunset becomes so brilliantly luminous that it radiates light in every direction, and illuminates the suspended particles all over the sky, causing them to shine long after the direct rays of the sun have left them. of Edinburgh, Session 1883-84. 661 4. Thermometer Screens. By Mr John Aitken. (Plate VI.) Part I. In meteorological observations the temperature of the air is of the first importance, and it is a subject to which a great deal of attention is given, thousands of temperature observations being made and recorded every day. It is therefore desirable that these observations shall be as correct as possible. At first sight nothing seems more simple than to take the temperature of the air. All that appears necessary is to hang up a correct thermometer of any construction, anywhere out of the sun, and the thermometer will then indicate the temperature of the air where the instrument is placed. We shall presently see that this is very far from being the case ; and not only so, but we shall find that it is difficult to get two thermometers which will give the same readings, when hung near each other in the open air, even though they agree perfectly with each other when placed in water. It has been the custom of most observers to place the thermo- meters in some kind of screen, to protect them from the sun and the rain. Many forms of screens have been devised, but Steven- son’s is the one that has met with the most general approval. This screen consists of a square-shaped box, the sides of which are made of double-louvre boards. In this box the thermometers are protected from radiation, while the air can circulate freely through it. ilo doubt Mr Stevenson’s screen is admirably adapted to our climate, where we scarcely ever have calm weather, and the tem- perature of the air inside the screen is generally nearly the same as that of the air outside it. My attention has, however, been lately directed to certain conditions of climate under which this screen is not suitable. In France and Italy there is frequently a succes- sion of perfectly calm days, in which the sun shines with great brilliancy and strength. Under these circumstances I have seen the Stevenson screen baking in the sunshine, and the thermometers recording temperatures much higher than that of the air outside them. These calm, sunny days are not unknown in this country, though they may occur seldom ; and it seems worth while con- sidering whether something ought not to be done to prevent the 662 P'roceedings of the Royal Society too high readings given on exceptional days in the screens at present in use. To get the true temperature of the air, the simplest plan seems to he to place the thermometer in some sort of box or tube where it will be protected from radiation, and to cause a rapid current of the air to be tested to rush over it. The only difficulty in prac- tically carrying out this method for general meteorological purposes is to get some simple means of keeping up a constant and rapid current of air. There are many ways in which this may be done, but none of them are very satisfactory. We might, for instance, by means of a pipe, connect the box containing the thermometer with a chimney, under which a fire was constantly burning ; or we might keep up the draught by means of a jet of gas burning in a vertical tube placed over the thermometer box ; or we might use a revolving fan and water power, or a water jet, or any other easily applied method of causing a current of air at the place where the observations are to be made. All these plans, however, require special apparatus and constant attention to see they are in working order ; and though some of them might be used in certain conditions, yet none of them are suitable for general adoption. A simpler and self-acting arrangement has therefore been designed, by means of which a current of air is kept con- stantly flowing over the thermometer. This apparatus consists of a screen and a draught tube combined, the draught tube being heated and put into action by the sun’s rays. The screen acts during ordinary dull weather when the wind is blowing, and the draught tube keeps up the air current over the thermometer when the wind falls. This draught tube is always in action when required, and most when most required, always acting more power- fully the stronger the sunshine. Plate VI. fig. 1 shows the theoretical form of a thermometer screen made on this principle. The thermometer t is placed in the lower end of the vertical tube ah. The lower part a of the tube is constructed of some non-conductor, or some other arrangement is made to prevent radiant heat getting to the thermometer. The upper part h of the tube is made of metal, and painted black. Suppose this tube placed vertically anywhere in sunshine, the upper part of the tube will become heated, and will warm the air inside. A rapid current will yoi.ar piaAe.n JoknAitken del. ArcMbaJA &,Fe(dc Edin'.' of Edinburgh, Session 1883-84. 663 thus be formed, and will keep rushing up the tube while there is any sunshine. In this way a current of air will be kept flowing past the thermometer ; and the thermometer being protected from radiation, the correct temj)erature of the air will be obtained during calm and sunny weather. One of the principal difficulties met with in the construction of this screen is to prevent heat getting to the thermometer through the lower part of the tube. If any heat get conducted through the walls of this tube, it will heat the air inside, and the inside surface of the tube will also radiate heat to the thermometer, and the indicated temperature will be too high. In figs. 2, 3, and 4 are shown some of the different forms of this screen which have been made. It will be observed that they differ principally as to the manner in which the lower part of the tube is protected. In the screen represented in section in fig. 2, the thermometer t is placed near the bottom of the long tube ah, which is made of thin metal. To prevent heat getting to the thermometer, the lower part of the tube is surrounded by a second tube c, and the space between the tubes is filled with a non-conductor. But as all non-conductors are far from perfect, still greater protection is necessary, and the lower part of the draught tube is surrounded by two conical -shaped metal sunshades d, e. A space is left between the two shades for the free circulation of air to keep them cool. The screen is supported on three iron legs at the standard height of 4 feet from the ground. In fig. 3 another form of construction is shown. In this instru- ment the lower end of the tube, as in fig. 2, is surrounded by a tube c, and non-conducting covering, but in place of further protecting the lower end with a shade, it is put into a circular box d, made of louvre boards similar to a Stevenson screen. The air which enters the draught tube of this screen comes from. the lower side of the box. As this air has been in contact with the surface of the under side of the box, and may thus have got heated, there are placed inside the tube, and surrounding the thermometer bulb, two concentric tubes / and g, made of non-conducting material, to prevent the heated air from touching the thermometer. By this arrangement the air which flows over the thermometer has the true temperature, as it has never touched the surface of any solid ; and as the only radiation to which 664 Proceedings of the Iloyal Society the thermometer is exposed, is that from a small surface of the ground under the open end of the tube, it has little effect, and the thermometer shows nearly the true temperature of the air. The screen shown in. fig. 2 is also provided with non-conducting con- centric tubes / and g, surrounding the thermometer bulb the same as in fig. 3, as these tubes prevent heat being conducted inwards towards the thermometer. It may be thought that in these screens the thermometer is too well protected, and that it will follow too slowly the changes in the temperature of the air. The changes must no doubt be to a certain degree sluggish. This, however, does not seem practically to interfere with the readings so far as has been observed. This sluggishness will prevent sudden local gusts of hot air from affect- ing the readings. An addition has, however, been made to one of the screens to cause it to act more quickly while the wind is blowing. It is shown in section at at the bottom of the draught tube in fig. 2. It is simply a wind deflector, made of a circular piece of wood shaped as shown in the sketch, and having a number of thin vertical radial plates fixed on it. When the wind blows it enters the radial passages, and has its course deflected upwards and past the thermometer. In this way the wind keeps up a circulation in the draught tube while there is no sunshine. Experiments have also been made to get some satisfactory form of wind-ventilating apparatus, which could be fixed near the to}') of the draught tube, to cause a rapid upward current when the wind is blowing. The advantage of putting the wind circulator near the top of the tube, is that when placed there the air does not come into contact with any surface before it reaches the thermometer, and therefore, theoretically at least, the arrangement is more perfect than the other. The slight heating got by having it underneath the tube is found practically to be of little importance. To combine the full advantage of wind-circulation with that of the draught tube the screen shown in fig. 4 has been devised. As before, ah is the draught tube. To the lower end of this tube is attached a small circular louvre box c, and to protect this box from the sun and rain an umbrella-shaped shade is placed over it. This shade consists of two circular discs of wood d and e, and a metal covering /, all fixed parallel to each other, and with air spaces C65 of Edinburgh, Session 1883-84. between them for the free circulation of air, to keep them cool and to prevent the heat absorbed on the top during sunshine penetrating to the thermometer. When fitted up the discs are placed hori- zontally, that the wind may blow freely between them from any direction. The thermometer is placed with its bulb in the louvre box, and its readings taken through an opening g, in the draught tube, this opening being closed with a glass plate or provided with a door. In this screen the wind blows freely over the thermometer, and when the wind falls and the sun shines the current is kept up by means of the draught tube, so that under all conditions nearly the true temperature is indicated. This screen is the last devised, and seems to possess over the other two forms the advantages of simplicity, cheapness, and convenience. These screens are suitable only for recording maximum tempera- tures. For minimum temperatures the arrangement is similar to that shown in figs. 3 or 4, only inverted, the draught tube being placed underneath the thermometer. A convenient arrangement is to use an L-shaped minimum thermometer, and fix the stem into the top shade. To enable the index to be set this shade is hinged, so that it can be placed vertically to cause the index to drop. Some of these instruments have been tested and found to work satisfactorily, but complete tests continued for some time in all weathers will be made and are required before any practical decision as to their value can be given. Wet Bulb Observations. In meteorology, the next most important point after the tempera- ture, is the humidity of the air. Different methods are in use for determining this most important point, but the one most generally used is the indirect one of simultaneous readings of wet and dry bulb thermometers. These observations are generally made in some kind of screen, the wet and the dry bulbs being placed near each other. Little consideration is necessary to show us that less favourable con- ditions for obtaining the true condition of the air could scarcely be selected, because the amount to which the wet bulb is depressed depends, not only on the dryness of the air, but also on the rate at which the wind circulates through the screen and over the wet surface. The result of this is, that with the same degree of humidity 666 Proceedings of the Royal Soeiety of the air we may have at the same temperature very different read- ings of the wet bulb, according to the rate at which the air may happen at the time to circulate. The quicker the circulation, up to a certain rate, the lower will he the temperature indicated. Now it is evident that if the readings are correct when taken in calm air, they must be incorrect when there is a rapid circula- tion; and as the rate at which the air circulates in screens is constantly varying, the observations made with the arrangements at present in use are of little value. The reason for the difference in the readings taken under the dif- ferent conditions seems to he that, when there is no circulation, the atmosphere round the wet bulb is more moist than the surrounding air, owing to the evaporation, and the wet bulb thus indicates a high humidity ; but when the moist air is removed as quickly as it is formed, the temperature falls lower. In illustration of the effect of the greater or less freeness of the circulation on the readings of the wet bulb, and to show the small value of the indication of some of the instruments at present in use, I will give the readings of a combina- tion of wet and dry bulb thermometers which is now before me. The instrument is one of a kind which is frequently used. The two thermometers are fixed to a piece of boxwood, on which the scales are marked. The bulbs of the thermometers project some distance below the edge of the scale. The thermometer and scale are carried in a metal frame which supports the water bottle for moistening the wet bulb. The observations were made in a room, to get constant conditions of temperature and moisture. The instrument was hung clear of everything, to allow of a free circula- tion at the back. Under these conditions the readings of the thermometers were — dry bulb 62°, wet bulb a little under 59°. The thermometers were now taken out of the frame, and hung up in the same place ; the increased freedom of circulation obtained by removing the frame made the wet bulb fall to 57°. The instrument was now placed in a strong draught of air, produced by a revolving fan, when the wet bulb fell to 56°, the dry one re- maining all the time at 62°. Using this instrument as was in- tended by the maker, it showed a humidity of about 80. When stripped of its frame and the air allowed to get freely at the wet surface, it showed a humidity of 72, and when put in a current of Edinburgh, Session 1888-84. 667 of air it said the humidity was only 67. From these observations we see the necessity of keeping the wet bulb at a distance from all objects which interfere with the free circulation of the air. But even with the very best form of construction,^ the readings taken at different times, and by different instruments, can not be com- pared with each other unless we can control the circulation. For the purpose of getting the true temperature of the air with the dry bulb, the Froude, or sling thermometer has been devised, but its evident inconvenience and risk have prevented its general use. An improved form of this method of observing has been designed by Mr Edwin Clark. In his observations he uses a whirl- ing table, to which the instrument is attached, the table with the thermometer being rotated rapidly before the readings are taken. Mr Clark has also used his whirling table for wet bulb observations. By these means a decided advance has been made, and a nearer approach to correct readings of wet and dry bulb thermometers has been obtained. The practical difficulty in working this apparatus is the impossibility of taking the reading while the air is acting on the instruments ; and as the table requires to be stopped before the readings can be taken, there is time for them to change. To obviate this difficulty, I have arranged for wet and dry bulb observations a simple revolving fan arrangement for keeping up a circulation of air past the thermometers, which brings them quickly to the correct temperature, and allows the readings to be made while the air is rushing over the instruments. This apparatus is shown in figs. 5 and 6. . Fig. 5 is a back eleva- tion, and fig. 6 a side elevation shown in section. The bulbs of the thermometers t, t, are placed in the horizontal tube a ; a vertical division being fixed in the tube between the bulbs. The tube a is placed at a height of 4 feet from the ground, and is supported by the two standards hh, which are firmly fixed in the ground, or otherwise supported. For circulating the air a large fan is used, as it enables us to dispense with all multiplying gear, which is troublesome, and aj)t to get out of order when exposed to the weather. This fan is shown at c ; it is driven by the handle d, which has a small radius to enable us to turn it rapidly.* The * The handle has been coupled by means of a connecting-rod g, with a short lever or treadle /, if we may use the word, which is actuated by the hand. This 668 Proceedings of the Boyal Society tube a and the fan c are connected by means of the pipe e. When the fan is revolved, a rapid current of air is drawn in through the tube a, and over the thermometers, which quickly acquire the correct temperatures. When the fan is turned very slowly the wet bulb falls a little below the dry bulb, and falls further and further as the velocity is increased ; but this fall only goes on till a certain slow velocity is attained, after which any increase in the rate at which the fan can be driven does not alter the temperature, either of the wet or of the dry bulb, but only causes them to acquire the correct tempera^ tures more quickly. With this apparatus we always get the same difference of temperature with the same conditions of atmosphere. It will be noticed that the upper part of the fan is cased in to prevent the air currents put in motion by it from rising and entering the suction pipe a, and coming into contact with the thermometers. When this fan arrangement is put into action, the air drawn into the thermometers does not come into contact with much heated sur- face, and the circulation is sufficiently rapid to keep the sides of the air passage at the temperature of the air, and also quick enough to absorb any heat the thermometers may receive by radiation ; it may therefore be assumed that the readings given by the dry bulb show very nearly the true temperature of the air. This apparatus has accordingly been used in preference to the Froude thermometer for testing the action of the different forms of thermometer screens, their degree of perfection being judged by the nearness with which the readings of the thermometer placed in them agreed with those given by this fan arrangement. The readings were also occasionally checked by means of the sling arrangement; which, however, is very difficult to use, especially when the sun is shining. On the Temperature of different sized Bodies. Before concluding this paper, I wish to record the results of some observations made to test the effect of size on the temperature of bodies placed in the open air, as these results have a direct bearing- on our present subject. Let us first consider the temperature of bodies under the most arrangement has been found much more convenient than the handle, as an impulse can he easily given by means of it to the fan while it is in rapid motion. of Edinhurgli, Session 1883-84. 069 simple conditions for observation. Suppose the sky overcast, with a uniform and thick covering of clouds, that a fresh breeze is blowing, and that the temperature has been constant for some time. Under these conditions, the surfaces of all bodies, large and small, in the open air, have nearly the same temperature. But now suppose the the clouds to clear away, and the sun to shine out brightly. The temperature equilibrium is soon destroyed, and the surfaces of the different bodies quickly take up different temperatures, all becoming more or less warmer than the air. The degree to which the different bodies are heated will depend on — 1st, their exposure to the sun ; 2nd, their exposure to the wind : 3rd, the absorbing power of their surfaces for heat ; 4th, their conducting power ; and 5th, their capacity for heat. But, in addition to these, I find that the size of the body, or ratjier the extent of its surface, has a most important influence. These remarks apply to bodies placed in shade as well as to those exposed to sunshine. Before describing the experiments which show the effect of size on the temperature of bodies, it will be necessary for me to describe the nature of the objects surrounding the spot where these ex- periments were made, as the results in experiments of this kind are determined very much by the surroundings, every position giving a different result according to the objects to which it is exposed. The view from the position of these experiments is bounded on the south and west by trees at a considerable distance, on the east by shrubs close at hand, and backed by a wall which extends south- wards, and closes in the view to the south-east. One half of the north is bounded by a wall at a distance of 6 feet, and the other half by trees at a distance, while the ground is covered with grass in nearly every direction. This site was selected on account of its being sheltered from the wind, and otherwise suited for the experi- ments. When studying the action of the draught tube thermometer screen, the experiments were begun by erecting, in the position above described, a horizontal sunshade made of wood, 3 feet long by 2 feet broad. This shade was erected at a height of about 5 feet from the ground. In the sunshade was made a round opening, into which fitted a tall metal tube. This tube projected 1 foot down- wards into the shade and 2 feet upwards into sunshine. Expori- 670 Proceedings of the Roycd Society ments were now made by testing the readings of a thermometer when placed in different positions. The results with which we are at present concerned were got when the thermometer bulb was pushed up inside the tube, and when it was pulled down clear of it. When the bulb was pulled down and clear of the tube, it always showed about a degree lower than when in the tube. Now, why was this ? The thermometer and the tube were both subjected to the same conditions, and we might have expected that they would have the same temperature, that the thermometer would read the same inside the tube as outside, or we might have ex- pected it to be cooler inside the tube, as it would there have the advantage of the upward current ; yet it showed a higher temperature inside than outside. I now stopped the upward current in the tube to see the effect on the thermometer. When- ever the current was stopped, the temperature began to rise till the thermometer was more than 2° higher than when placed outside the tube. It was thought that the high temperature inside might be partly due to the heat radiated from the hot upper part of the tube. The apparatus was therefore taken within doors, to get a constant temperature, and the draught tube heated by means of a gas flame. No increase of temperature was, however, observed when the upper part of the tube was heated. We may therefore conclude that but little heat is radiated downwards, or at least that all the heat that is radiated to the thermometer is easily carried away by the upward current of air. Another possible explanation is, the difference in the absorbing powers of the surface of the tube and of the thermo- meter bulb. As the tube, however, was polished tin, their absorb- ing powers would not differ greatly. Neither of these explanations, therefore, seem satisfactory. The other explanation which suggested itself was that the difference in temperature was due to the difference in size of the two bodies, the thermometer bulb being about J of an inch in diameter, while the tube was nearly 3 inches. When we consider the conditions under which the thermometer and the tube were placed, we can easily see that the comparative size of these objects would have a most important influence in deter- mining their temperatures. When the sun is shining, all objects exposed to its rays get heated, and they in turn become sources of of Edinhurgh, Session 1883-84. 671 radiation, and radiate heat to all surfaces in every direction within their view. All surfaces, therefore, though shaded from the sun, are receiving a great amount of radiant heat ; and if this heat was not carried away by the air, the surfaces in shade would acquire nearly the same temperature as those in sunshine. But the supply of heat comes in slowly from the sunlit surfaces, and the passing air carries it away nearly as quickly as it is received. We see from this that the temperature of bodies, even in the shade, is greatly determined by the rate at which this radiant heat is carried away. Now, very little consideration is necessary to show us that the air will carry away the heat much more quickly from a small than from a large surface. When a current of air comes into contact with a hot surface, the air where it first touches the surface is rapidly heated, and a film or layer of hot air is formed near that surface. Now, if the body is small, this hot layer is at once swept away, and gives place to another cold layer, which in turn abstracts more heat ; whereas in a large body, the hot film or layer formed where the current first touches the body keeps near the surface in its passage over it, and forms, as it were, a hot j)rotecting coat to all parts of the surface at a small distance to the leeward of the point where the current first touched it. No doubt this hot layer of air will thicken as it passes over a large surface, but the rate at which it thickens is very slow after it has passed over a very small distance. This I have observed in my late experiments on dust. The effects due to the heat in the air in front of a hot flat vertical surface are almost all accomplished at the lower edge of the plate, where con- tact is first made, the upper part of the plate producing but a slight increase in the effect. The result of the air acting in this way is, that a large body parts with its heat to the passing air at a much slower rate per unit of area than a small body does; and as both are receiving heat at the same rate, the temperature of a small body is lower than that of a large one. The protection of large bodies will be far from being so perfect when the currents are rapid and the air ceases to move in stream lines. Experiments were made to see if this reasoning was correct, to determine whether large bodies were really hotter than small ones, and if so, to what extent. For this purpose I pre- pared three tin boxes, all 8 inches long, but of different 672 Proceedings of the Royal Soeiety diameters, being J inch, 2 inches, and 4 inches respectively. These boxes were provided with an opening in the centre of one end, for the purpose of introducing a thermometer to determine their temperatures. Before being used they were painted black, to get a good and a uniform condition of all the absorbing surfaces. After a thermometer was fitted into each box, they were all hung up under the horizontal shade, and perfectly protected from the direct rays of the sun. Alongside of the boxes was hung a thermometer with a clean bulb, also a thermometer having the bulb blackened with the same paint as used for the boxes. After they had hung for some time, no two of the boxes were found to have the same temperature. The larger the box the higher was its temperature. The difference between the temperatures, as might be expected, was not always the same, because on no two days is the amount of radiant heat the same, nor is the rate of circulation of the air the same. The following table shows the readings taken at two different times on the same day ; — Clean Bulb. Blackened Bulb diameter. Box diameter. Box 2" diameter. Box 4" diameter. 67° 68° 69°-5 71°-3 74°-l 71° 72° 74° -2 76° 79° These readings, of course, only show the comparative tempera- tures at the particular place on the day the observations were made. Some days the difference was less, but in spring weather, wdien the sun is hot and the air cold, greater differences may be looked for. The boxes with their thermometers were then hung up under the horizontal sunshade in an open field, clear of all buildings, and surrounded by trees at some distance. The amount to which the different boxes were heated was found to be almost the same as in the more confined place, where the tests were first made ; showing that the amount of heating is not much influenced by the nature of the surrounding objects. The above readings were shade temperatures ; the boxes were now of Edinlmrrjh, Session 1883-84. 673 hung up in sunshine, to see the effect of size on objects exposed to the direct rays of the sun. The following table shows the result : — Clean Bulb. Blackened Bulb T' diameter. Box 2" diameter. Box 2" diameter. Box 4" diameter. 78° 8or 84° 89°-5 95° Objection might be taken to the manner in which the above experiment was made. It might be asked, for instance, Was not part of the difference of temperature due to the heat received on the side of the box next the sun being quickly conducted to the shade side, in the small boxes, and carried away by the wind, while in the large boxes the heat could only be slowly conveyed to the shade side by the hot air in the box To check these results, I filled the large box with a liquid, using turpentine, on account of its small specific heat. Placing this box in sunshine, and alongside of it the half-inch box, in which was fixed a maximum registering thermo- meter, it was found that the large box attained a temperature of 96°, while the thermometer in small one indicated a maximum of 85°, thus confirming the result of the previous experiment. We might look on these boxes with attached thermometers simply as thermometers with very large bulbs. We see from this that the indications of correct thermometers may vary when hung in certain positions, owing to a difference in the size of their bulbs. No doubt these are very extreme sizes, still I find that the size of the bulbs of the thermometers in general use does affect their indications. Selecting two thermometers, one with a large and one with a small bulb, I hung them up beside each other under the shade, and found that the one with the smallest bulb indi- cated a temperature about half a degree lower than the large one. I may say that the precaution was taken of checking the readings of these thermometers in water at the same temperature as the air. It is possible that a difference in the thickness of the walls of ’the bulbs may have caused the large thermometer to absorb more heat than the other, but this can scarcely account for the whole difference. Not only will the size of the bulbs affect the indications in the open air, but the manner in which the thermometer is mounted will 2 X VOL. XII. 674 Proceedings of the Royal Society have an important influence. Anything which prevents the free circulation of the air near a bulb, or which comes in contact with the air before it reaches the thermometer, will cause it to read too high. The system of sinking half of the bulb into a wooden frame cannot but interfere with the correctness of the indications, save when the thermometer is perfectly protected from radiation, and even then it makes the instrument sluggish. All thermometers not protected by proper screens, such as those used in gardens, and for other rough purposes, ought to have the bulb perfectly exposed to the air, and as far away from all surfaces as possible. To illustrate the effect of size and radiation, I may mention that when I found that small bodies were cooler and nearer the tempera- ture of the air than large ones, I repeated my experiment with the horizontal shade and vertical draught tube, but in place of enclosing the thermometer bulb in a three-inch tube, a very small one was employed, just large enough to allow a current of air to flow freely between it and the bulb. The result, however, was that the upward current did not quite compensate for the larger size of even this small tube, and the thermometer was never quite so low in the tube as out of it, and exposed to the wind blowing at the time. No doubt, in a calm day this arrangement would have prevented any great rise in the temperature, and the arrangement would have been better than some screens or than no screen. These experiments, while they indicate certain errors in the construction of thermometers, suggest some possible advances and improvements. We have seen that the temperature of a body exposed to radiation in the open air is colder the smaller it is. The meaning of which is that the smaller a body is, the less effect radiant heat has on it, and the nearer its temperature is to that of the air. Carrying out this line of thought, we see that if we could construct thermometers sufficiently small in the bulb, they would indicate nearly the true temperature of the air, and if small enough they would indicate nearly the true temperature even in the sunshine. A ther- mometer made of a fine wire, for instance, would be well enough protected if simply screened from the direct rays of the sun. At present I am attempting to get a mercury thermometer made with a very fine bulb, which it is hoped will give nearly the true tempera- of EcUnlmrgh, Session 1883-84. 675 ture of the air when placed under a sunshade such as that shown in fig. 4, hut without the louvre box. I regret that the time taken in getting a satisfactory instrument of this kind made prevents me from being able to say how near the indications of such an instru- ment will approach the true temperature of the air. These experiments have also suggested the construction of a cheap and simple radiation thermometer, which has been made in the following way : — An ordinary thermometer, or a registering one by preference, is let into the surface of a thick piece of wood. The best size of this casing has not been determined, but it ought to he at least a foot square, or, better still, large enough to encase the whole stem of the thermometer. The thermometer is let in to such a depth that the bulb is level with the surface of the wood. Cement is then put in to fill up all inequalities and restore perfect smooth- ness to the board. The surface is afterwards blackened. It may be mentioned that, in order to make the instrument act quickly, a large cavity is cut in the wood, into which the bulb of the thermometer is placed, and the cavity is packed with cotton-wool, and covered over with a thin layer of the cement. There have only been two opportunities for making observations with this instrument. On one afternoon it was placed in sunshine, and alongside was hung a thermometer with a blackened bulb, but exposed to the air. The blackened bulb only rose to a tempera- ture of 78°, while the one fitted into surface of the wood rose to 105°. This effect of the size of the surface of a body in determining the amount of the cooling effect of the air will, I hope, help to explain some difficulties. And one cannot help asking here, whether we have not in this a suggestion as to the explanation of why it is that dust in the sun’s rays, focussed by a powerful lens, escapes being burned. It does seem strange to any one accustomed to use a “ burn- ing glass ” to light cigarette or pipe, that the organic dust passes through the focus of his lens without being affected; but the moment the focus falls on the solid tobacco, it at once responds with a cloud of smoke, blow why is this '? Does not the difficulty of heating small bodies by radiant heat suggest the answer? It is true the conditions are not alike. The small bodies we have been experimenting with are comparatively large ; and further, a 676 Proceedings of the Boyal Society necessary condition is that they are fixed, and that the air moves over them, whereas the dust particles move with the air. But may not a precisely similar cooling effect he brought about in another way? In the case of a very small object, like a dust particle, a molecule of air, which has touched it and got heated, passes into the widening space outside, and scarcely never returns to the dust particle; so that every air molecule that touches the particle is cold, and the heat received by the particle is not con- served by the heated molecules keeping near it and protecting it from contact with the cold ones. In this way the molecular movements accomplish for the dust what the mass movements do for fixed bodies. These experiments also suggest some thoughts regarding the thermal experiences of different forms of life. The tiny insect, as it sports in the sunshine, is the one above all others which is generally supposed to have the greatest enjoyment in the warmth of the sun’s rays. From what we have seen, we now however know, that it is the one above all others which has the least reason for gratitude, as it can scarcely receive any heat from the sun. Let the sun shine as brightly as it may, it can scarcely warm to a perceptible degree the tiny limbs of these fluttering insects ; and if it will enjoy the sun’s heat, it must descend to earth. And what a change does it meet with there when it lights on branch or stem of tree ! In a moment it passes into an atmosphere twenty or thirty degrees w^armer than the sunlit air in which it delights. On the other hand, this immunity from the heating effect of the sun makes life possible to these insects under a sunshine that drives the larger animals to seek the shade. .Part II. (Added 23rd August 1884.) Since the first part of this paper was written, there has been some weather suitable for testing the efficiency of the thermometer screens under trying conditions. From the beginning of the month till the 22nd there were a number of warm, bright, and nearly calm days. Under these conditions it is well known that it is difficult to get the true temperature of the air ; advantage was therefore taken of of Edinlnmjh, Session 1883-84. 677 these exceptional conditions for making a number of test observa- tions with the screens. For a standard of comparison, the fan apparatus already described was used. The first thing to be done was to test the action and efficiency of the draught produced by this fan. In this apparatus the vacuum produced is less than ^ of an inch of water, and the current consequently is not very strong. I therefore first compared its action with that of a more powerful instrument, the fan of which is driven by multiplying gear, and which easily gives a vacuum of 1 inch of water, and draws a perfect hurricane of air over the ther- mometer. Working these two instruments alongside of each other in the open air on a bright day, there was not found to be any difference in the readings of their respective thermometers ; showing that for all practical purposes the draught in the simple apparatus gave as correct results as the powerful draught of the more com- plicated fan. The only advantage of the powerful apparatus was, that it brought the thermometer more quickly than the other to the temperature of the air. The readings of the fan apparatus were now compared with those given by the sling thermometer. The result was, that whenever there was any sunshine, the fan thermometer read lower by one degree than the sling, and if the sun was bright the difference was more than one degree, I shall presently show why these two methods of testing the temperature of the air should give different results, and why the sling should read higher than the fan arrange- ment ; also why the lower temperature given by the fan is nearer the true temperature of the air than that given by the other. In the following experiments with the screens the fan apparatus has been used as a standard, as it is, I think, more correct than the sling method, and also because it is much more easily worked. Assuming then the fan apparatus as our standard instrument, it w^as fitted up alongside of the screens on a lawn, in a position well pro- tected from any little wind that might be blowing, so as to get the most trying conditions possible for the screens acting correctly. The amount of wind during most of the experiments was very small, and generally from the east. At times there was scarcely a breath of air, and during the calm periods frequent readings were taken. In conducting the experiments, the fan was kept in constant action, 678 Proceedings of the Poyal Society and whenever the temperature was at all steady, readings were taken of the thermometers in the different screens. The result of these tests has been satisfactory. The thermometer in none of the screens rose much above the standard, even during the most trying conditions of the experiments. The thermometer in screen fig. 3, under many conditions read almost the same as the standard; but on one or two trying occasions, when the wind died away and the sun shone brightly, the error was quite decided, and amounted to an average of a little over half a degree. From my notes on these occasions, I see that it read sometimes exactly the same as the standard, but at other times it was one degree too high; generally, however, the difference was not so great, and gave an average of 0°‘6. It may be objected that we cannot average errors of this kind, because the maximum error may be the true error of the instrument, as the maximum temperature to be registered might happen just when the error was greatest. From the manner in which the experiments were made, it is, however, I think the average, and not the maximmm that is the true error of the screen. The occasions on which the error was greatest was when the temperature was changing. The readings were taken while the tem- perature was falling ; and as the fan thermometer follows the changes more quickly than the screen, it had fallen more than half a degree before almost any change was effected in the screen thermometer ; so that when the readings were taken the screen thermometer was still recording the higher temperature to which it was previously exposed. These tests do not show that the maximum of screen was ever one degree higher than the maximum of the standard. A more correct method of testing would have been to employ maximum registering thermometers, and to take the maximum temperature indicated during a certain time. This method was intended to have been followed, and special registering thermometers were being pre- pared, but they were not ready in time for the experiments, which had to be made before the hot weather was over for the season. The screen shown in fig. 4 has almost exactly the same error as screen fig. 3. Though its indications are nearly as true as those of the other, yet it does not seem so susceptible of improvement. It may be possible to reduce its error by changing the form of the screen at the bottom of the draught tube. It can, however, scarcely 679 of Edinburgh, Session 1883-84. be expected to act as correctly as the other, because the louvre boards of the screen become heated by radiation, and the air passing over them gets warmed before arriving at the thermometer. In the construction of screens it is necessary to shade the thermo- meter as much as possible from all radiation. It ought not to see anything out of its screen. A small amount of exposure even to the grass underneath shows its effect in an increase of temperature. This could be observed when testing the screen fig. 4. If the bottom was taken out of the box, to allow of a freer circulation, the tem- perature always rose a little. On the other hand, if the louvre box was made too close by the addition to it of complicated louvre boards, the flow of the air was retarded, more heated surface was given to warm the air before it arrived at the thermometer, and in this case also the thermometer read too high. The arrangement shown in the sketch is the one which as yet has been found to give the best results. The thermometer is so protected that no radiation from objects outside can fall directly on it, while the free circulation of the air is but little checked. Perhaps an improved form of box for this screen might be made of double louvre boards, but as this would increase the outside diameter of the box, and consequently the amount of surface over which the air has to pass ; it would also greatly reduce the velocity of the air when no wind was blowing, and only the draught tube acting; it is therefore very doubtful whether any advantage would be obtained. Prom the experiments on the temperature of large and small bodies already detailed, we have seen that large bodies become more highly heated than small ones, when exposed either to the direct rays of the sun, or only to diffused radiation. Prom this we get some guidance for the construction of thermometer screens. As large bodies are less cooled by air passing over them than small ones, it follows that the louvre boards in the thermometer box ought to be as large as possible, because the air in passing over large louvres will carry less heat into the box than if it passed over small ones. The large size of the louvres will also prevent heat being conducted to the inside of the box. Again, if we wish to lessen the radiation from any particular area, wq must reduce all objects exposed in that direction to as small dimensions as possible, and coat them with some substance which is a good absorber of radiant heat. Blackened 680 Proceedings of the Boyal Society wire clotli, for instance, freely exposed to the air, will get but little heated even in sunshine, and will neither radiate nor reflect much heat. Attempts have been made to improve the working of the screen (fig. 3) by cutting off all radiation from the ground. First, a small non-conducting screen was fixed horizontally under the tube, but leaving plenty of space for the air to enter freely ; but no decided advantage was obtained. Then a small screen was placed in the tube, just under the thermometer bulb, to check the radiant heat falling on it, but no reduction in temperature was effected. No great advantage can be got from placing a small screen under the bulb. If the effect of the upward radiation from the ground is to be entirely checked, it must be cut off from the inside surface of the tube, as well as from the bulb ; as I find that, to get rid of the last fraction of a degree above the temperature of the air, it is of far more importance to check radiation, than to increase the current past the bulb ; as a very small amount of radiation is equal to a strong current of air, and the changes of temperature in a thermo- meter are far more quickly accomplished by radiation than by con- tact with the air. These considerations show us that the tube surrounding the bulb, in addition to being a non-conductor, ought to be made of some substance that has small capacity for heat, so that its temperature may change quickly with that of the air ; because the changes in the thermometer are caused more by the exchange of heat with the surface of the tube than by contact with the air passing over it. In these instruments the inner concentric tubes are made of blotting paper kept in shape by thin metal tubes. Hair felt, if it could be got of suitable shape, might be better than paper. The screen constructed according to the plan shown in fig. 2 does not give quite such good results as the one made as shown in fig. 3. In the former screen the draught tube is of a less diameter, and the lower part is less protected by non-conducting coats and air passages than the latter. This suggests that the fraction of a degree too high, given by the thermometer in screen fig. 3, is partly caused by heat conducted through the lower end of the tube, and radiated across the air passages. This sup- position has been confirmed by an examination of the air passages by means of a thermometer. The temperature of passage next the of Edinhurgh, ScssioJi 1883-84. 681 centre tube was found to be generally about half a degree higher than in the centre tube, while the outer passage was often more than a degree higher, showing that the lower end of the tube is not properly protected. Another screen is therefore being prepared, with a more perfect screen protection, a larger draught tube, and more concentric non-conducting tubes and air passages, and it is hoped this new screen will have a less error. It will be remembered that the fan thermometer is, under the conditions during the experiments, always about one degree below the sling thermometer, so that screen fig. 3 is nearly half a degree nearer the truth than the sling. It is only within the last few days that I have been in possession of ■ a Stevenson screen, and been able to make comparative trials with it. During these tests its action was compared with the fan apparatus, and readings were taken at the same time of the thermometers in the draught tube screens. These latter, as already stated, had an average error of about 0°*6 too high. The smallest error recorded in more than thirty readings of the thermometer in the Stevenson screen was 1°’3, and it only fell to that on two occasions. The excess error was generally more than 2°, and was as high as 2*8 on two occasions. The morning on which the trials were made was certainly a trying one, but was not so bad as it might have been, for the Stevenson screen. The sun was very strong, and there was but little air moving ; the direction of the wind, however, was favourable, being from the north-east, so that the air entering the screen passed over the cold louvre boards and not over the sun-heated ones. If the wind had been southerly, the error would have been greater, as the entering air would have been heated in its passage over the hot louvres. These tests were made on an exceptional day. On most days, when there is wind, the screen gives a much nearer approach to the truth than it did on that occasion. By a slight addition to this screen, I was able, when the error was high, greatly to reduce it. On those days on which the wind blew from a northerly direction, and the air entering the screen came in from the cool side of the box, I found the high temperature given by the thermometer was due to radiant heat entering the open bottom of the box. Either a solid or a louvred bottom has been found greatly to improve the correctness of this screen, but whether the solid or the louvred bottom is the best has not yet been deter- 682 Proceedings of the Pogal Soeiety mined, and whether this addition will work equally well in all weathers or not remains to be seen. Radiation Thermometers. Some observations have been made with the radiation ther- mometer already described. In addition to this instrument, another has been prepared. In this second instrument a small circular chamber is made in the centre of the black surface, and covered with thin glass let in level with that surface. The thermometer with its bujb blackened is exposed in the middle of this chamber. This instrument always reads higher than the other one in which the bulb forms part of the surface. For this reason, it is perhaps not so satisfactory as the other, as it possesses something of the so-called “bottling up” powers of the black bulb in vacuo. These radiation thermometers were generally exposed in sunshine while the trials with the screens were going on. Their indications, of course, varied from hour to hour and from day to day. The highest temperatures observed were on the afternoon of the 7th August, when the thermometer fixed in the black surface rose to a temperature of 144°, and the one in small chamber in the black surface indicated a temperature of 154°. On the 8th, and on some other days, the temperature was nearly as high. When the observations were made, the instruments were generally placed near the ground with the black surface perpendicular to the sun's rays, and freely exposed to any wind that might be blowing. On dull and sunless days these thermometers often read 10° or 15° higher than the temperature of the air. Thermometers with Protected Bulbs. A short time ago, I received one of the thermometers specially constructed for the experiments with small bulbs, to which refer- ence has been made in the former part of this paper. The directions for the construction of this thermometer were to make the bulb as long as might be necessary to give the desired capacity, but its diameter as small as possible. The bulb of the instrument sent is, however, not by any means so small as desired, nor so small as it might easily have been made. Owing, however, to an unex- of Edinburgh, Session 1883-84. 683 pected change in the manner of working, this defect has not been of importance, and the instrument has been found to be very service- able. The bulb is very long, being 55 mm. or more than 2 inches, and has a diameter at the top of 3 mm. and of 2 mm. at the bottom. It is graduated from 0° to 100° Fabr., and has an expansion at the top of the tube to prevent bursting when heated over 100°. The large capacity of the bulb has given a long and easily read scale, there being almost 2 mm. between each degree. It may be remembered that this thermometer was constructed for the purpose of following up a line of investigation suggested by the experiments on the temperature of large and small bodies exposed to radiation. It bad been found that the smaller a body was, the nearer its temperature was to that of the air surrounding it, because it was more quickly deprived, by the passing air, of the beat received by radiation from surrounding objects ; and there seemed reason for supposing that if the bulb of a thermometer was smaii enough radiation would not beat it to a perceptible degree. This thermometer was therefore constructed with the intention of seeing how nearly a thermometer with a very small bulb would indicate the true temperature of the air. Owing to an unexpected change in the development of this investigation, but few trials were made with this instrument as received from the maker. A few tests were, however, made. In these experiments the thermometer was placed under a horizontal sunshade, which protected it from all sunshine, and from nearly the whole of the sky radiation. The day on which the experiments were made was bright and warm, with a slight air from the east. The radiation thermometer already referred to showed a temperature of 140° in the sun. Under these conditions, the new thermometer always read just about a degree higher than the fan thermometer, and was generally more than half a degree lower than another thermometer with ordinary sized bulb placed alongside of it. It is, therefore, evident that this instrument, though better than an ordinary one, cannot be relied on to give the true tempera- ture of the air when shaded in the manner described ; as it would read correctly only on dull days, and be a degree more or less too high according to the brightness of the day. If the bulb of this thermometer had been made smaller, as ordered, it is possible the 684 Proceedings of the Royal Soeiety error might have been less. Dr Lenz* has recently described an application of the telephone to the measurement of temperatures at a distance. Dr Lenz connects the observer with the distant station by means of a thermo-electric combination of wires, into the circuit of which he introduces a silent interrupter and a telephone. If the temperature of the junction at the distant station is not the same as that of the junction near the observer, a sound is heard in the telephones, which ceases when the observer has made the tem- perature of his junction the same as that of the distant one. This arrangement suggests a method of getting the true temperature of the air, by making the thermo-electric junction or junctions of as fine wire as possible, and exposing them freely to the air under shade at the distant station. In this way we might get as small a sensitive surface as it is possible to construct. On reconsidering the whole matter at this point, it soon became evident that it is hopeless to expect any thermometer of ordinary construction, however small the bulb, to give the true temperature of the air while it is exposed to radiation. When we consider what is taking place it is easy to see why this must be so. When radiant heat falls on the bulb of a thermometer, the heat is absorbed not only at the surface of the bulb, but all through the thickness of the glass, and at the surface of the mercury. The inside of the bulb therefore gets heated, and this heat must be conducted outwards through the glass before it can be carried away by the air. The consequence is, the inside of the bulb is hotter than the outside, and the thermometer while exposed to radiation must always read too high, however strong the current of air may be to which it is exposed. As the absorbed heat requires to be conducted to the outside, the inside of the thermometer must always be considerably hotter than the air, so long as the radiation temperature is higher than the temperature of the air. The natural sequence to these thoughts was — cover the bulb with something through which radiant heat cannot penetrate ; and as it would be necessary to use some substance having a small absorbing power for radiant heat, silver naturally suggested itself as the most suitable material for the purpose. I accordingly coated the bulb and part of the stem of the fine-bulbed thermometer with silver * Nature, voL xxx. p. 345. of Edinhurglh, Session 1883-84. 685 deposited on it, from a solution of the nitrate. By this simple process I had now acquired an extremely interesting and curious instrument. Its powers of repelling radiant heat, if we may use the expression, are very remarkable. My first experiments with this instrument were made in the beginning of this month. I first wished to get the heating effect of the sun’s rays on this silvered thermometer in calm air ; the experiments were therefore made in a room, and only enough of the window opened to allow the sun to shine in on the thermometer, which was placed with its bulb in sunshine. Alongside the silvered thermometer was hung an ordinary thermometer, and readings were taken from time to time of the temperature of the room and of the sun-warmed thermometers. In these tests the silvered thermometer never rose more than one degree abov^e the temperature of the room, and was often only half a degree, and sometimes less, while the other thermometer rose from 4 to 41- degrees above the temperature of the room. In these experiments it was found extremely difficult to get the true temperature of the room with an ordinary thermometer, so much depended on where the thermometer was placed, and the amount of radiation that reached it, but the result given is as correct as I have been able to make it. Another difficulty in making these experiments is the extreme sensitiveness of the fine-bulbed thermometer, it is so constantly rising and falling nearly a degree in little more than a minute. To give an idea of the difficulty of getting the tempera- ture of the room where the experiments were made, I may mention the following, as it at the same time shows how much the indica- tions of ordinary thermometers are affected by radiation. At one stage in the experiments the thermometer employed for giving the temperature of the room was hung alongside the other thermometers, but provided with a shade wffiich protected it from all direct sun- shine. When in this position it was in the same air as the silvered thermometer, yet it always read higher, sometimes by nearly one degree ; that is, the ordinary thermometer was more heated by the radiant heat from the carpet, and other objects in the room on which the sun was shining, than the silvered bulb was by the direct rays of the sun added to the radiation from surrounding objects. The next tests with this instrument were made outside under the 686 Proceedings of the Royal Society ordinary conditions for testing the temperature of the air. The thermometer was placed under a sunshade, similar to that shown in fig. 4, hut without louvre box at bottom, or draught tube at top. The stem of the thermometer passed through the sunshade, the silvered bulb was freely exposed under the shade, while the scale projected through the top of the shade for convenience in reading. The bulb was thus protected only from the direct rays of the sun, and from the greater part of the sky radiation. The fan apparatus was used as a standard as in the test with the screens. It must be confessed that the result surprised me not a little. That the readings of the silvered thermometer would be nearly as low as those of the fan thermometer, I quite expected ; but that they should be almost always lower, was somewhat astonishing, d.'here can be no doubt but that it does read lower, but how much it is very difficult to say. I have made many and continuous observations with it in different conditions of weather, but it always read lower than the thermometer in fan draught, when the silver coating was at all in good order, the weather bright, and the slightest air of wind moving. I have watched the two thermometers for hours under trying con- ditions from calmness and brilliancy of sun, and yet the result was always the same. The difficulty of saying how much lower the exposed silvered thermometer was than the fan thermometer, arises from the extreme sensitiveness of the fine-bulbed silvered thermo- meter to rapid changes of temperature. Sometimes it rises higher than the other by a fraction of a degree, but only for a very short time, and at other times it falls much lower, the changes taking place quickly. The thermometer in the fan, on the other hand, follows these changes more slowly, and never goes to the same extremes. The quickness of this instrument is most interesting, and reveals to us a most curious fluctuating state of the temperature of our atmosphere. The mercury in it is in a constant state of ebb and flow. That these ups and downs really indicate changes in the temperature of the air, or rather differences in temperature in different parts of the passing air, and are not due either to changes in radiation or to variations in the cooling effect of the wind, is I think indicated by the fact, that it was always possible, by watching the silvered thermometer, to tell whether the thermometer in the fan draught was going to rise or to fall, as all its indications 687 of Edinlurgli, Session 1883-84. were predicted by the silvered thermometer. The changes in the fan thermometer are slow compared with the other, owing to the shape of the hulh, and to time being required to alter the temperature of the air passages, which radiate heat to the thermometer. So nearly as I was able to judge from observations made when the temperature was nearly steady, the average reading of the silvered bulb was about a quarter of a degree below the fan readings. It might sometimes be less when the air was calm. The silvered thermometer scarcely rose one degree above the standard when hung in sunshine during a fine calm day, while the radiation thermometer similarly exposed showed a temperature of 131°, or 65° above the temperature of the air. As a great deal of radiant heat is absorbed by the glass of the bulb of an ordinary thermometer, not only at the surface, but all through the body of the glass, it seems probable that part of the lower temperature indicated by the small bulbed thermometers is probably due to this cause ; the small bulbs having a less thick- ness of glass than the large ones, as bulbs with thin walls will absorb less radiant heat than those with thick ones, and will also conduct the absorbed heat more quickly outwards to be carried away by the air. I have frequently referred to the constant fluctuations in tlie temperature of our atmosphere. Now, to prevent any mistake in this matter, it will be as well for me to state more clearly the amount of these fluctuations. With a thermometer having a large bulb, these changes are little noticed ; but after one becomes ac- customed to the careful reading of thermometers with medium-sized bulbs, they become very evident. In the fan apparatus the changes on certain days would amount to half a degree more or less almost every minute, and in the fine-bulbed thermometer they often amounted to a degree or more in the same time. These changes take place whether the wind circulation is strong or slight. It may be as well for us to consider here why the thermometer in the fan draught should read higher than the silvered thermo- meter. No doubt the silvered bulb will be a little higher than the temperature of the air, but why should the fan give a higher reading still '? So far as I understand it, part of this higher read- ing given by the fan apparatus is due to heat conducted inwards G88 Proceedings of the Ployed Society through the indraught tube, and radiated to the thermometer ; and i:>art is due to the air which enters the tube having first touched the outside of the apparatus, and in this way got heated before arriving at the thermometer ; while the silvered thermometer is less heated by diffused radiation when exposed freely to the air than the thermometer in the fan apparatus. All these experiments have been made with the silver coating deposited on the bulb by chemical means. A comparison of man}" different experiments with different thermometers shows a variation in the protecting power of the different coverings due to their greater or less thickness, and also to their greater or less perfection, and freeness from scratches which remove the silver from the glass. In some of the experiments the thermometers had two and three coatings of silver put on them, by placing them in successive baths ; the surfaces of the bulbs being simply washed when taken out of one bath and placed immediately in the next. When taken from the final bath, some of the bulbs looked dull and dusty, but acted quite well, while others were improved by polishing with rouge. These chemically deposited silver coverings being rather delicate for practical purposes, the next thing to be done was to get a silver sheath prepared for the thermometer bulb. This sheath was made of thin sheet silver and fitted easily over the bulb, and it also covered part of the stem. The silver coating being dissolved off the thermometer bulb, the silver sheath was polished, and fitted on, and the thermometer tested as before with the fan apparatus. The result in this case was not so good as with the chemically deposited silver. The readings of the thermometer now almost exactly corresponded with those of the fan thermometer; that is, the silver sheath reduced the readings 1° lower than the clean glass, but gave about 0°‘25 higher than the deposited silver. These higher readings suggested that this sheath was not made of pure silver. On inquiry, I found this to be the case ; so another sheath was prepared, and special precautions taken to have the silver as pure as possible. This second sheath was tried on the morning of the 18th, when there was a bright sun and almost no wind. As in the previous experiments, the thermometer was simply placed under a horizontal of Edinhunjh, Session 1883-84. 689 sunshade. The sheath was found to act almost as well as the chemically deposited silver, hut not quite, its readings being gene- rally about 0°*2 below the fan thermometer. As silver has a tendency to tarnish, it was thought as well to try the efficiency of gold as a protector. Gold is not quite so well suited for the purpose, as it absorbs more radiant heat than silver ; while silver only absorbs 3 per cent., gold absorbs 5 per cent. The first sheath which was prepared for the thermometer, and which was ipade of impure silver, was gilt with gold, and tested under the same conditions as the pure silver sheath. It was found to be not nearly so efficient a protector as the silver, its readings being generally about 0°*2 above the fan thermometer, or nearly 0°*4 higher than the pure silver. The gold gilt sheath, after being very much finger-marked, made the thermometer read nearly 0°‘5 above fan, or about half a degree better than clean glass. As to whether gold or silver is the best for practical purposes can be determined only by continued use. Gold has certain advantages, as it will probably keep its protecting powers longer than silver ; and where frequent cleaning is incon- venient, gold may be the most suitable; but when great accuracy is aimed at, silver must be employed. The action of these silver-coated thermometers is most curious and interesting. They never agree with any other thermometers when hung alongside of each other in a room into which the sun is shining, or in which the gas is lighted ; and even after the windows are closed, and shutters shut, or the gas put out, it is long before they agree with the others. Like captious critics, they always under- estimate the radiations emanating from surrounding bodies, and manage to keep themselves cool amidst the heat exchanges taking place on every side. If we examine the readings of an ordinary thermometer, it is influenced by our presence; and if long in making our observation, the heat radiated from our body may cause the thermometer to indicate a temperature half a degree too high ; but these silvered thermometers are almost indifferent to our presence, while they are sensitive to the temperature of the air. Sling Thermometers. The sling or “ Fronde ” method of taking observations has generally been accepted as the most accurate way of determining 2 y VOL. XIT. 690 Proceedings of the Royal Society tlie true temperature of the air. The result of the preceding experiments seems to indicate that observations taken in this way may not be correct, owing to a fundamental error in the construction of the apparatus. We have seen that radiant heat is absorbed in the thickness of the walls of the bulb, and at the surface of the mercury as well as at the surface of the bulb, and this internally absorbed heat must be conducted outwards to the surface before it can be carried away by the air through which the thermometer is rushing in its circular flight. There will evidently therefore be a heating effect due to radiation, which it is impossible to keep down by the cooling effect of the air, and the only question is, what is the amount of this heating ? Following up the same line of experiment as was previously employed to prevent the internal absorption of heat by the bulb, and to reduce the surface absorption to a minimum, two similar thermometers were selected, the bulb of one being coated with silver and the other kept clean. These thermometers were firmly tied together and slung with as great rapidity as was thought safe. The readings of these thermometers were then compared with each other, and with the fan arrangement. The result of a number of trials was, that when slung in sunshine the silvered bulb always read at least one degree lower than the clean bulb. Compared with the thermometer in the fan draught, the silvered thermometer was a small fraction of a degree higher, while the clean bulb was higher by more than 1”. These figures of course varied with the heat of the sunshine. These experiments show us that the ordinary sling thermometer in a bright day is more than V too high ; probably it is 1 to 2° too high in bright weather, as we must remember that the fan indica- tions are not quite down to the true temperature of the air. These experiments also show us that the silvered sling is nearer the truth by at least 1° than the thermometers generally used. Other experiments made at the same time show that slinging the silvered thermometer has no advantage over simply placing it in shade, even if there is only a slight air of wind moving ; this proves that it takes all the cooling effect of rushing through the air to counteract the heating effect of the sun’s rays. Instead of slinging the two thermometers, they were hung up under a sunshade on a day when a little wind was blowing : the readings then obtained agreed very of Edinhurgh, Session 1883-84, 691 nearly Avith those got by slinging. From other experiments made in different states of the weather, it is found that there is not muoli advantage got by slinging the thermometers, either silvered or clean, in sunshine, unless there is extremely little wind at the time. Almost exactly the same degree of truth can he got by simply shading the thermometer from direct sunshine, and from the sky radiation. Another experiment to test the heating effect of the sun on the sling thermometer was made in the following way : — An ordinary thermometer was placed near the mouth of the suction tube of the powerful fan apparatus. First the thermometer was carefully shaded from all radiation. The thermometer under these conditions agreed with the thermometer in the other fan apparatus. The open mouth of the tube was now directed towards the sky, so as to allow part of the sky radiation to fall on the bulb. The effect was to cause this thermometer to read a little higher than the other, and when the tube was directed so as to allow the sun’s rays to fall on tlie bulb, its indications Avere more than a degree above the other fan thermometer. This shoAvs us that even a poAverful draught of air Avill not compensate for the exposure of the thermometer to the sun, and confirms the conclusion Ave have come to that the readings of the ordinary sling thermometer are at least one degree too high. Temperature Ohservations without Screens. We have seen that, in taking the temperature of the air, there are different methods of operating. First, Ave may surround the ther- mometer with a screen to catch all radiant heat, and prevent it falling on the thermometer, as is done in the Stevenson screen and in the one shown in fig. 4, The disadvantage of this method of Avorking is that the air in passing over the louvre boards gets heated before entering the screen, and coming into contact with the thermometer ; and though in the screen fig. 4 the louvre boards are not heated by direct sunshine, and the circulation is kept up independent of the Avind, still it can scarcely be expected to give correct readings, but must always be a little too high. A second method of operating is to cut off all radiation as far as possible, isolate the thermometer from all conducted heat, and bring to it air which has never been in contact Avith any solid, and has not there- fore got heated. This method has been employed in constructing 692 Proceedings of the Poycd Society the screens shown in figs. 2 and 3. A third method is to reduce the absorbing power of the thermometer bulb, and expose it freely to the air, so that it may absorb as little radiant heat as possible, and make the bulb small, so that the heat received may be carried away by the air as quickly as possible. This plan has been adopted in the thermometer with silvered bulb. In all these different methods of working, the enemy we have been contending with is radiation, and though we may have succeeded in greatly reducing its influence, yet it must be admitted that it has still some power. Seeing then we have been unable thoroughly to vanquish our enemy, perhaps the wisest course now open to us is to see if we cannot make an ally of it, and enlist it in our service. We know that large bodies are more highly heated by radiation than small ones ; we also know that different coloured bodies are heated to different degrees by radiant heat. Here then we have the foundation of a method of estimating the temperature of the air, by observing the difference in temperature, either of different sized or of different coloured bodies. For the obvious reason that the changes of temperature in different sized bodies do not take place at the same time, they evidently are not suitable for our purpose ; but, on the other hand, different coloured bodies are. If we can And out the relation between the absorbing powers of two substances, then we can, by simply coating the bulbs of two thermometers with these and noting their different temperatures, tell what the temperature of the air is. Suppose, for instance, one substance heated the bulb of the thermometer twice as much above the temperature of the air as the other, then we should only require to take the readings of the two thermometers, and subtract the difference between them from the lowest, to get the true temperature of the air during the day, and add the difference to the highest, to get the temperature at night. In practically carrying out this plan and selecting the substances most suitable for coating the bulb, one great object evidently is to get substances which will not change, and which can be easily kept in order. How in these respects no substance is more suitable than glass, and one thermometer ought therefore to be kept with its bulb clean. As for the other bull), something is required of Edinh argil, Session 1883-84. 693 which will heat it twice as much as clean glass when exposed to radiation. Any other relation in the heating ehect would do, but twice is the simplest to work with. Black paint is too powerful ; but I find that coating one half of the bulb with black paint or black varnish works very satisfactorily. The advantage of black varnish is that it is fairly permanent, adheres firmly to glass, and can be easily renewed if required. The black surface ought not to be put all on the same side of the bulb, but should be in at least two sections, opposite each other, as the radiation from all directions may not be equal. I have found the working of these differential radiation thermo- meters very satisfactory, and it is easily done. Suppose, for instance, the blackened bulb reads 69° and the clean one 68°, then the temperature 67° is easily found. With practice the eye becomes quickly accustomed to the working of the instruments, and easily gets the true tenq^erature mentally, even -when dealing with frac- tions. These remarks are true only if the thermometers are correctly graduated. If the thermometers are not correct, most people will require to note down the readings, and make the necessary correc- tions, before adding or subtracting the difference. One point of importance is, to be very particular about the reading of the lowest or clean bulb temperature, in the day observations, as any error in it is doubled in the final result. For night observations, it is the error in the maximum reading that is doubled, and in this case also it is the readings in the clean bulb that have to be most carefully attended to. For experimenting with these differential readings, I selected two thermometers which were nearly correct at the part of their scale corresponding to the temperature at the time of the observa- tions. These differential radiation thermometers were placed under the same sunshade as the thermometer with the silvered bulb. This enabled the comparisons to be quickly made, and prevented the constantly changing temperature of the air from interfering with the results. By watching the differential thermometers till they were nearly steady, then rapidly subtracting the difference in their read- ings from the lowest or clean bulb, the result generally agreed perfectly with the readings of the silvered thermometer, and never differed by more than a small fraction of a degree. 694 Proceedings of the Royal Society 111 workiag with these differential thermometers, it is not neces- sary to screen them from the diffused radiation. If they are simply shaded from the sun, it is enough. The principal point to be attended to is, that they are placed where there is as free a circula- tion of air as possible, and not near any surface on which the air might be heated before coming into contact with them. When permanently fitted up, the screen required for them should be all above the bulbs, and may be of the simplest description sufficient to protect them from the weather. Two pieces of wood fixed parallel to each other, and with an air space between them, to prevent heat descending to the under side of the screen, is quite sufficient, and only requires to be securely fixed in a horizontal position. The thermometers are placed with their bulbs projecting a short distance below the screen, and the scale above it. One of the principal things to be aimed at is to secure a free circulation of air, and to prevent heated air coming to the thermometers, the screen having nothing to do with the diffused radiation, as it is welcomed and allowed for by the instruments. This differential arrangement may be used for maximum and minimum registering thermometers. So far as the experiments go, they seem to give truer readings than most forms of screens ; and as the air can circulate freely over the bulbs without being heated or cooled on louvre boards, the thermometers follow the changes of temperature ciuickly. Further, as the maximum error of a clean glass bulbed thermometer under those simple screens is scarcely ever 2'', and is more generally only about 1°, the amount of correction necessary is not great, and can be easily made. Night Temperatures. But little has been done in observations of night temperatures ; no trials of the minimum screen have as yet been made. A few trials, however, with the silvered bulb were made on the 19th of the month, when the sky was clear and air calm and chilly. The experiments were conducted in the following manner : — The two thermometers used in the sling experiments, the one with bulb silvered and the other clean, were tied firmly together, and prepared for sling observations. The thermometers were first slung, and their readings taken ; then they were hung up freely exposed to the of Edinburgh, Session 1883-84. 695 sky, and clear of all surfaces, and so that air could circulate freely over them. After time was allowed for them to acquire their respective temperatures, their readings were again taken. They were then slung and read, and so on, a number of readings being taken when slung, and when hung up. The result was that the thermometers read almost alike when slung, but the clean bulb always fell more than one degree and sometimes nearly two degrees when hung in the calm air. This fall was always nearly regained when slung ; whereas slinging did not produce any decided effect on the silvered bulb, the effect being so small as to be lost in the changes in the temperature of the air. These experiments show us that the silvered bulb is as suitable for night as for day observa- tions, and that practically it takes up the temperature of the air. radiation having but a small effect on it. The differential radiation bulbs also seem well suited for night observations; but the bulbs require to be coated in a different manner from those used in day experiments, as the quality of the heat is then different. Conchision. For travellers, these differential radiation and silver coated ther- mometers seem to possess special advantages, as they enable the observer to get nearly correct readings without screens, because he can be nearly indifferent to all save direct sunshine, and will be able with confidence to expose his thermometers anywhere, in shade, where there is a free circulation of air. One result of these experiments is to show us that, oven when working with our most accurate methods of observation, we have been regularly overestimating the temperature of our bright days by about one or two degrees, and in some climates this overestimate may be even greater. In recording future observations with the sling thermometer, it will be necessary to say whether the temperatures have been taken with clean or with silvered bulb thermometers, in order that the necessary corrections may be made. It is no very pleasant conclusion to an investigation such as this, to find that it ends in taking a degree or so off the average maximum of our summer temperature. Had it been in my power, it would have been far more pleasant to add to it a degree or two. We may, however, console ourselves with the idea that we have, (596 Proceedings of the Royal Society so to speak, been simply taking stock of the amount of the world’s capital invested in the heat of our atmosphere, and our investiga- tion shows us that we have been overestimating this quantity, and that the produce of the world is obtained by a less expenditure than we supposed. Monday, June 1884. EDWARD SAND, LL.D,, Vice-President, in the Chair. The following Communications were read ; — 1. Abstract of Paper on Micrometrical Measures of Gaseous Spectra. By C. Piazzi Smyth. [Printed in full, with Plates, in tlie Transactions. ] Ever since the Royal Society, Edinburgh, was pleased to accept my paper in 1880, on the general appearance of Gaseous Spectra, as seen on a very small scale ; but complete on that scale from end to end of the visible spectrum, — I have been desirous of presenting them with some very highly-dispersed views of the more intricate portions of those spectra. An example in that direction was finely set by MM. Angstrom and Thalen in the Upsala Transactions in 1875. But though their work was splendid for its day, it is not enough to satisfy the demands of theory now. These demands, too, are so terribly exacting, that I have had to labour for several years at continual cumulative improvements of my private spectroscope, before it attained power and precision enough for the present work. This, however, is the comparative condition lately attained. My spectroscope of 1880 had a dispersion of 3°, with a magni- fying power on the telescope of 10 times ; say for the simple eye = 30° from A to H. The Upsala instrument had a dispersion of 24°, with a magnifying power of about the same ; say = 600° from A to H. But my present spectroscope has 60° of dispersion ; a magnifying power on the telescope rising to 36 ; with a further mechanical magnifying of 5 times. Equal altogether to 9000° from A to II ; of Edinburgh, Session 1883-84. 697 or to the simple dispersive action, as viewed by the unassisted eye, of no less than 1800 prisms of dense flint glass. The result of such an immense prismatic power on a bright con- tinuous kind of light, such as that of incandescent carbon, is to produce a coloured spectrum strip, virtually 120 feet long, or stretching all round the meeting hall of R. S. Ed. And the regions or places of its several successive colours will be the places also of any lines of the same colours which we may meet with in the bright line spectra we are about to observe. CH, or Carbo- Hydro gen, in Flame. Beginning with the compound gas CH, in its Coal-gas form, and burning in a blow-pipe in the open air — very nearly as described to this Society by Professor Swan in 1856 — the new instrument con- firms all his findings, with the addition of further details. There are, for example, 5 bands, widely separated from each other — the orange, the citron, the green, the blue, and the violet. Each of these bands is intense towards the red, vanishingly faint on the violet, side. Each of the first four bands, too, is made up of certain strong lines and much interstitial and following haze. But the new instrument further shows that each of those strong lines is double, and the haze is entirely resolvable into a far minuter class of lines or linelets \ excessively close on the red side, but con- tinually widening towards the violet. With each of those bands I measured between 80 and 90 of such linelets ; and only stopped then, not because any definite termination of them was reached, but because they had then become too broad, faint, and hazy to justify micrometrical measure being expended upon them. A grand constant was however thus obtained, of a useful character, for reference in certain disputed questions in spectroscopy. And if for sharpness of definition and precision of detail it left much to be desired, I endeavoured to supply that by subsequently employing as the illuminant, not flame of any kind, but the well-known electric spark of the induction coil. Even this, however, may be sometimes insufficient for definition purposes, unless appropriately used ; for The simple induction spark, tried on chloride of sodium vapour in the open air, though less hazy than flame, was of a crackly, uncertain 698 Proceedings of the Royal Society nature, touching its power and manner of showing the two D lines of the solar spectrum. The condensed induction spark filled all the field of view with continuous fervid glow, and quaking air-hands almost fearful to behold. But a vacuum tube of Hydrogen, with a trace of sodium chloride, showed of the latter only the two D lines, each of them intensely bright, exactly defined, without any stray light; and, in short, exactly as they should be to serve any case of Micrometical measure. CH again^ hut now in Vacuum Tubes. Trying the vacuum tube method, therefore, on Coal-gas, the first tube, though bright enough, was yet a failure ; for it was not bright with the coal-gas spectrum, but with a variety of impurities and decomposed materials. After this, however, had been got over to a considerable extent by increasing the density of the gas put into these so-called vacuum tubes from OT" to 2 '5 inches of Barometric pressure, the Citron and the Green bands of CH were produced in a condition for examination. They ran quite parallel with their blow-pipe congeners, but were far more refined : the linelets being often like exquisitely thin spider lines, in place of broad hazy threads. But they did not last ; for day after day they grew fainter, more and more of them became first double, then treble, and then faded away, lines of pure Hydrogen coming in their stead. The leading Orange band of the CH spectrum was particularly difficult to observe, on account of the intrusion of these H lines. But after having appealed from Coal-gas to Olefiant gas, and having increased the pressure of that up to 4 Mercurial Inches, the cynosure was obtained at last, resulting in what may be termed a perfect view of the beginning of the CH spectrum, and of that alone. There, for instance, was the Orange band, with its leading lines brilliant, and its linelets clear and distinct, though continually widen- ing in distance apart, but in unbroken series not only to the usual place of vanishing but right up to the strong beginning of the Citron band. The Citron band’s linelets similarly continued in exquisite perfec- tion of gradation right up to the Green band. And the Green band’s linelets continued without a break, or an interference, or of Edinhuryli, Session 1883-84. 699 foreign intrusion of any kind, right up to the Blue band, — save, that shortly before that notable Spectrum milestone was reached, a faint, but extensive grey cloud was passed ! What could that mean ? It proved to be the then broadened or hazy condition of the usually sharp line known as Glaucous Hydrogen. Minute by minute that cloud brightened and narrowed, while the CH linelets continually paled ; and after an hour’s sparking the H, of the once CH, had come out in lines everywhere ; while its C was deposited as a brown glazing on the inside of the tube ; and my beautiful example of a perfect CH spectrum was gone for ever. But if we bear in mind how II behaved with regard to C therein, and compare that presently with the actions of 0 (Oxygen) in the same relation, the experience will be well worth the price paid for it. For the chemical interpretation of those spectra is still under perfectly radical disputation. The CO Spectrum. A CO spectrum is easily procured, and with the smallest charge of either Carbonic Oxide or Carbonic Acid. Moreover, it remains and even improves by use. At first sight, the CO spectrum is superficially much like the CH, inasmuch as it is a spectrum of coloured bands, intense towards the red, vanishing towards the violet. But there are more of them, and they have no leading lines in them like the CH, being composed of linelets only. Moreover, every such linelet is of a different constitution; for while those of CH are weak and semi-transparent like spider-lines, the CO are hard, sharp, and densely metallic. In fact, in place of both of them being spectra of one and the same simple element C (Carbon) as usually held in London, I may rather say that we are in presence, before them, of two most opposite principles of the physical world. The H, in CH, always trying to free itself from contaminations of every earthy matter ; but the 0, in CO, taking hold of everything near it, and of C most particularly. Whence it comes that CH tubes generally end in showing only II ; whereas some other tubes, begun with a different gas, end in showing nothing but CO. Or if that is a petty scale on which to allude to the actions of 700 Proceedings of the Pioijal Society universal Nature, let us say with the American Astronomers, that if this earth were touched by the Sun, and so sublimated by its terrific heat, that in a moment nothing of terrestrial substance would he left, except molecules and atoms vibrating in the intense light and temperature, — the H lines would be seen above, like a Solar red prominence, while the CO would be increasing its domain below. But would such a reproduction of Nebular haze bring hack the Chaos of the Greeks, or a reign of law and numerical order 1 Let the last Plate of this paper (see Trans, vol. xxxii. part ii.), and its view of the beginning of the Green hand of CO now declare ; for Avhat was mere haze to smaller instruments is here proved by higher dispersion, conjoined with improved definition, to be a most curious and exact mathematical arrangement of lines, without one missing one. Op Elemental Gases. HYDROGEN. But if H, in CH, makes the carbon element behave so very differently to what it does when in the power of O, as CO, — how do H and 0 behave when single and separate'? Let us begin with H. Tubes of H vacuum are very bright to the naked eye, and to the spectroscope are multi-linear all the way along from Ultra Red to Violet. I have measured the places of 1625 of them. They form generally an open kind of groupings, occasionally exhibiting exqui- site specimens of close sharp doubles and trebles, but never enlisted into a rigid band system. It is rather a most free and aerial kind of atom dance from one end of the spectrum to the other in a pure H tube. OXYGEN, Oxygen, on the other hand, is a poor lighter up; and was declared by the British Association’s Committee’s Report in 1880 to have only 4 lines in its spectrum, and those very faint. Those 4 so-called lines I have identified readily enough by place, and they are the brightest of the faint appearances in that spectrum, but there are many others to be noted. Three also of the first 4 are triples of a very peculiar and uniform formation. They join too with three others which I have since discovered, in making a of EdinljUTgli, Session 1883-84. 701 long connected system of rigidly similar triplets, extending all across the spectrum from Scarlet to Glaucous. Besides which, the whole spectrum commences with a notable Ultra Bed line which outflanks, or is further towards the invisible red than any line in any other gas. NITROGEN. Nitrogen in vacuum tubes must come in here, for though I may have some suspicions that it will be found eventually not to be a simple gas, it is practically so to all present science. Nitrogen’s tube spectrum then begins only a very little short of the Ultra Red line of 0 ; and rapidly rises to remarkable and almost continual brilliance in five long and successive groupings of 10 or 11 bands each. This, in a general way, has long been known ; but what I have now to add, besides the discovery of the earliest or most Ultra Red group, is the resolution of these bands into lines; into hundreds and thousands of lines finer, sharper, and set more closely together than the lines of any other gas. A good idea is given of them in the Plates of Orange and Green “ N,” now presented to the Society, and like all the other plates are reduced copies of my original measures and drawings, lately executed for me by Mr T. Heath, the first Assistant in the Observatory, and who has remarkable skill and understanding for such work. Of Elemental Gases Generally. If an elemented gas, such as that of Carbon, or of Iron, can only exist as a permanent gas at the temperature of the condensed electric spark, it can pretty evidently have for us only the one gaseous spectrum due to that temperature ; for man knows no other higher stage. But if it be the case of a gas permanent at all temperatures from the lowest to the highest, it may have besides the condensed spark spectrum, the simple electric spark spectrum, and also what we may call the cold spark, or the auroral spectrum. Each of these three spectra too, of one element, must, under appro- priate circumstances, have its reversal or double ; as from bright lines in a dark field to dark lines in a bright field. 702 Proceedings of the Roycd Society. There are thus 6 conditions under which the spectrum of a per- manent elementary gas may be viewed ; but seldom more than two or three or these have been observed by any one. Thus with Oxygen, the most advanced of all the gases, — (1) Its condensed-spark bright-line spectrum has been much written on by Angstrom, Thalen, Kirchoff, Bunsen, Hoggins ; and the dark reversal of some of these lines is now being worked at by Professors Liveing and Dewar. (2) Its simple-spark bright-line spectrum is what has been described in this paper ; but the dark reversal of these lines, either single or triple, has not yet been accomplished by any one. (3) Finally its Auroral, or cold-spark spectrum, though never yet seen in the bright form, has been long witnessed unconsciously in the dark variety by every one who has ever noted the huge telluric black lines in the Solar Spectrum known as A, B, and Alpha ; the identification of the first two of these lines with Oxygen having been recently established by M. Egoroff of St Petersburg, by looking through a tube of condensed Oxygen 66 feet long, at a bright con- tinuous spectrum of the lime light ; and the structural identity of the 3rd, with the 1st and 2nd, having been since then most ingeniously worked out by M. Cornu in Paris. OF HYDROGEN. (1) At condensed-spark temperature, and also in the Sun, H’s three grand lines are well known, both in the bright and the dark conditions. (2) Its simple-spark multilinear spectrum, in the bright state, has been described here ; but the reversal is unknown. (3) And of its cold-spark, or Auroral spectrum, nothing I believe is known either in the bright or dark variety. AND OF NITROGEN. (1) At condensed-spark temperature, the report is the same as for Oxygen. (2) At simple-spark temperature, the bright line form has been described in the preceding pages ; but its reversal is unknown. (3) And of its cold-spark, or Auroral spectrum, nothing I believe has yet been positively ascertained either for bright or dark lines. of Edinhurgli, Session 1883-84. 703 2. On the Computation of Eecurring Functions, by the Aid of Chain-Fractions. By Edward Sang, LL.D. 3. On Extensions of Euclid I. 47. By A. H. Anglin, Esq. In Euclid I. 47, it is proved that if regular tetragons be described on the sides of a right-angled triangle, that described on the hypo- tenuse is equal to the sum of those on the sides containing the right angle. This proposition, as is shown in Euclid VI. 31, is only a particular case of a more general one ; and the object of this Paper is to establish the corresponding result in the case of regular trigons, pentagons, hexagons, and generally regular figures of any number of sides, and finally, in the case of any similar rectilineal figures, without the use of ratio and proportioyi. 1. The case of regular trigons or equilateral' triangles admits of an easy and independent proof, somewhat like that of squares as given in Euclid ; but the following general proposition will enable us to establish the case of regular polygons of any number of sides, including of course these two particular cases : — If isosceles triangles of the same vertical angle he described on the sides of a right-angled triangle as bases, that one on the hypotenuse is ecpted to the sum of the other two. (A.) Let G, H, P (fig, 1) be the vertices of isosceles triangles of the same vertical angle described on the sides of the right-angled triangle CAB; then if D, E, F be the middle points of the sides, GD and PE will meet at F, since the line drawn through the middle point of the side of a triangle parallel to the base bisects the other side. Through H draw HK parallel to GFD, or perpendicular to CB. Join FK and GK, and pro- duce them to meet BG and AB in M and L respectively. Then shall GKL be perpendicular to AB. 704 Proceedings of the Boycd Society For a circle may be described about the figure HFKB ; therefore the angle KHB is equal to the angle KFB. But the angle HBK is equal to the angle FBM, since the isosceles triangles are equi- angular; therefore the remaining angle FMB is equal to the remaining angle HKB, and is a right angle. Thus K is the ortho- centre of the triangle GFB, and the line GKL is perpendicular to FB. Hence the figure FGKH is a parallelogram, and FG = KH, and therefore the triangle GFB is equal to the triangle BHD, since the rectangle whose sides are FG and DB is equal to the rectangle whose sides are HK and DB. Thus the whole figure GCFB is equal to the whole triangle HOB ; that is, denoting the isosceles triangles by A, C respectively, A -f GFB = HHB + CHF + GFB , or ^=HNB^-GHF. Similarly B + CFA==HNA + CNA, or i5-t-GHF = HNA. Thus A + B=0. Now let regular polygons of the same number of sides be described on the sides of the right-angled triangle, and suppose B, S, T to be the centres of the polygons. By joining K, S, T to the angular points of the respective figures of which they are centres, the poly- gons will be divided into the same number of isosceles triangles which are equal to one another in each polygon. But, since these triangles have the same vertical angle, by what precedes ATAB= ARBG+ ASGA. Hence the regular polygon described on AB is equal to the sum of the regular polygons of same number of sides described on BG and GA. (B.) 2. Since the sides of the triangle GDK or of HFI are equal to FH, DG and PE respectively, it follows that HF2 = DG2 + PE2, But FB2 =DB2-fGE2, Therefore HB2 = BG^ -i- PC^ , of Edinhurgli, Session 1883-84, 705 and thus the equal sides of the isosceles triangles are also the sides of a right-angled triangle. Now draAv a line from B at right angles to CB, and let it meet CG produced in J ; then the triangle BGJ is isosceles, BG being equal to GJ, and is equal to the triangle GCB. The same being true in the case of corresponding triangles BHO and CPQ described on the other side, it follows that ABHO= ABGJ+ A CPQ, But HB, BG, and CP are the sides of a right-angled triangle ; and this triangle being equiangular to the triangle ABO, the triangle BGJ is any isosceles triangle described on BG. Hence the propo- sition follows in the case of equiangular isosceles triangles^ one of their equal sides being respectively a sid.eof the right-a.ngled triangle, (C.) The case of similar segments of circles described on the sides may be deduced either by the application of result {A) or of (G), The latter may be employed by inscribing in the circles, of which the described segments are parts, regular polygons of the same number of sides, and joining their centres to the angular points of the polygons which are external to the sides of the triangle. These joining lines being the sides of a right-angled triangle, it may be, shown by (G) that the figure external to AB is equal to the sum of the corresponding figures for BG and CA, and therefore, in the limit, the proposition follows in the case of the segments. It may, however, be more simply shown by the application of (A) directly. Let AB (fig. 2) be the hypotenuse of the right-angled triangle ABC^ and ADEB any segment of a circle described on it. If D be the middle point of the arc, the tri- angle ADB = sum of the corresponding tri- angles by (A). Again, if E be the middle point of arc DEB, since DB and the cor- responding lines are sides of a right-angled triangle, the triangle DEB = sum of corresponding triangles. Pro- ceeding in like manner with the arcs DE and EB, it follows finally that the segment DEB = sum of corresponding segments. The same being true of the segment AFD, therefore the whole segment AEDEB = sum of similar segments on CA and BC. (D.) VOL, XII. 2 z D ‘roe Proceedings of the Royal Society 3. The cases of certain irregular figures, in addition to those of isosceles triangles, are then deduced. If in fig. 1 a line he drawn from B at right angles to CB, and meet CG produced in J, the triangle OBJ is double of the triangle CBG. Hence the proposition follows in the case of equiangular right-angled triangles, one of the sides containing the right angle being a side of the given triangle j and hence also in the case of similar rectangles described on the sides. [E.) Again, it follows from (G), since the perpendicular from the vertex of an isosceles triangle on the base bisects the triangle, that the proposition is true in the case of equiangular right-angled triangles, the hypotenuses being respectively a side of the given triangle ; and also, by doubling the triangles in result (G), it follows in the case of rhombuses of the same angle, described on the sides. {F.) By combining these results we may show the proposition true in the case of any similar triangles described on the sides. For, since CJ, the hypotenuse of the triangle CBJ, is double of CG, and since CG, and corresponding lines HB, CP, have been shown to be the sides of a right-angled triangle equiangular to ABC, so also will CJ and its corresponding lines be the sides of a similar right-angled triangle. Again, the corresponding sides in the class of right-angled tri- angle in {F) are also the sides of a right-angled triangle. For, if GU be drawn at right angles to BJ-, GUB is such a triangle by what precedes. But GU is half of CB. Thus GU and corre- sponding lines are sides of a triangle similar to ABC, How, let AB (fig. 3) be the hypotenuse of the given triangle ABC, and let the triangle ADB, right- angled at D, be described upon it. By result (i^) the triangle ADB = sum of corresponding triangles on other sides of ABC, Produce D, and draw any line AE to meet it at E. Then, since AD and corresponding lines are the sides of a right-angled triangle, we have, by {E)^ the triangle ADE = sum of corre- the whole triangle ABE is equal to the Proc. Roy. Soc. Edin., Vol.Xl I Pl.VII. W.E. Hoyle, Del, Figs. 1“S. Ampliiura bellis var. tritonis nov „ 4-8. Ophioglyplia signata, VerriU. of Edinhurgli, Session 1883-84, 707 sum of the similar triangles on CA and CB— and this is any tri- angle on AB, ((7.) Finally, if any triangle, AEF, he described on AE, since AE and corresponding lines are sides of a right-angled triangle, it follows, by the result last proved, that the triangle AEE = sum of corresponding triangles ; and in like manner for any triangle described on AF, Thus the whole .rectilineal figure BEF . . . . A is equal to the similar and similarly described figures on CA and BCj lohicli is Prop. 31 of Euclid, Bk, YL (H.) It may be remarked that the following two interesting results, proved in the case of isosceles triangleSj are true for any similar triangles described on the sides of ABC. (1) If perpendiculars be drawn from the vertices G and P (fig, 1) on the hypotenuse AB, the parts of them intercepted by the sides BC and CA resj^ectively are each equal to the altitude HF of the triangle on AB. (2) If CH meet AB in and HF be perpendicular to AB, then ACGB= AHYB+ ACNF, and ACPA= AHHA- ACYF, so that ACGB-i- ACTA = AAHB, When ABC is isosceles, the triangle CHF disappears.- 3. Eeport on the OphiueoiIjEA of the Faroe Chanhei, mainly collected by HAI.-S, “Triton” in Aiigtist 1882, with some Eemarks on the Distribution of the Order, By W. E, Hoyle, M.A, (Oxon,), M.E.C.S,, Haturalist to the “ Challenger ” Commission. (Plate YII,) Some time ago Mr John Murray kindly placed in my hands the Ophiuroidea collected by H.M.S, “ Triton” in the Faroe Channel, with the request that 1 would draw up a report upon them, and the object of the present paper is to communicate to the Society the results of my investigations,- The collection contains no new species, but one specimen appears to be a well-marked variety of Amphiura hellis, Lyman, a species 708 Proceedings of the Boyal Society discovered by H.M.S, “Challenger” in the North Pacific. This small number of novelties does not, however, imply that the collec- tion is deficient in importance, for, owing to the peculiar configura- tion of the sea-bed in this region, every dredging in it is of value ; and when, as in this case, the physical conditions are carefully de- termined at each station, the result possesses a very great interest for students of the distribution of animal life upon the globe. Before proceeding further, I give a list of the species collected by H.M.S. “Triton,” arranged according to the stations at which they were obtained. I have also had the opportunity afforded me by Mr Murray of examining the Ophiurids obtained by H.M.S. “Knight Errant,” already recorded in the Proceedings of this Society,* and also a large proportion of those collected by H.M.S. “Porcupine.” These last have been named by Mr Theodore Lyman, but as no list of them has yet been published, and as reference will be made to them in what follows, I think it well to enumerate them here, although the list will be far from complete, for the collection to which I have had access does not contain all the specimens collected by the “ Por- cupine,” and especially is it deficient as regards the cruise in the Mediterranean in 1870. In a few instances the list has been supple- mented by information derived from the published accounts of the “ Porcupine ” inv3stigations. f The figures f olio vu'ng .each name indicate the number of speci- mens caught. The First Cruise of H.M.S. “ Porcupine,” 1864. Off Valentia.J May 24th. Depth, 110 fathoms. Ophiothrix pento,pliyllum (Pennant), . . .20 Ophioglyplia alhida (Forbes), . . . . .5 Lough Swilley. June 10th. Depths 13 fathoms. Ophioglypha lacertosa (Pennant), . . . . 9 * Proc. Roy. Soc. Edin., vol. xi. p. 707, 1882. t Carpenter, Jeffreys, and Thomson, Proc. Roy. Soc, Lond,, vol. xviii. pp. 397-492, 1870 ; AVyville Thomson, Depths of the Sea, London, 1874. + The bottles containing these specimens are labelled, “ ‘ Lightning,’ off Valentia,” but there must be some error in this, for no dredgings were made by that vessel in this locality. of Edinburgh^ Session 1883-84. 709 The Second Cruise of H.M.S. “Porcupine,” 1869. Off Cape Clear.* Ophioglypha lacertosa (Pennant), , . . . 5 Station 34. Lat, 49° 5,1' K, long. 10° 12' W. Depth, 75 fathoms. Bottom temperature, 49° ‘6 F. (9°"8 C.), Mud, gravel, shells. Amphiura CMojil, Forbes, . . . . .5 Ophioglypha Sarsiil (Liitken) (^wy.), . , ,1 Ophiopdiolis aculeata (0. F. Muller), , , I Station 37. Lat. 48° 38' K, long. 12° 8' W. Depth, 2435 fathoms. Bottom temperature, 36°*5 F. (2°-5 C.). Glohigerina ooze. Ophiacantha hidentata (Eetzius), . . . . ? Ophiocten sericeum (Forbes), , .... .5 Stations 39-41. f Lat. 35° 59'-35° 57' K, long. 5° 27'-4° 12' W. Depth, 517-730 fathoms. Bottom temperature, 47°‘0-46°'5 F. (13°-3-13°‘4 C.). Ooze, sand, shells,, Ophiaetis Ballii (Thompson), . . ... .1 Ophiamntha hidentata (Eetzius), , 1 Ophiothrix fragilis (0. F. Muller), . % Station 42. Lat. 49° 12' K, long. 12° 52' W. Depth, 862 fathoms. Bottom temperature, 39° '7 F. (4° ‘3 C.). Ooze, sand, shells. Ophiochiton tenuispinuSy Lyman, . . . .1 Station 43. Lat, 50° 1' N., long. 12° 26' W. Depth, 1207 fathoms. Bottom temperature, 37°*7 F. (3°-2C.). Glohigerina ooze. Ophiocten sericeum (Forbes), ... . . 1 Station 45a.. Lat. 51° 1' K, long. 11° 2P W. Depth, 180 fathoms. Ophiomusimn Lymaniy Wyv. Thoms., . . * One of the following stations; — 33 (Lat. SO® 38' N., long. 9° 27' W, Depth, 74 fathoms. Bottom temperature, 65°'2 F. [9°‘8 C.]), 34 or 45 a. t Proc. Roy. Soc. Lond., vol. xviii. p. 431, 1870. 710 Proceedings of the Boijal Society Ophiothrix Lilikeni^ Wyv. Thoms,, . . . 5 Opliioglyplia laeertosa (Pennant), , , . (many) The Third Cruise op H,M.S, ^‘Porcupine,” 1869. Station 46. Lat. 59° 23' K, long, 7° 4' W, Depth, 374 fathoms. Bottom temperature, 46° ‘0 F. (7°“7 C,). Ophiothrix fragilis (O. F. Muller), , , , , 1 * Station 47. Lat. 59° 34' K, long. 7° 18' W. Depth, 542 fathoms. Bottom temperature, 43° *8 F. (6° *5 C.), Glohigerina ooze, sand. Ophiactis abyssicola (Sars), , , , , .22 Ophiocten seficeum (Forbes), , , , , .2 Station 51. Lat. 60° 6'N,, long. 8° 14' W. Depth, 440 fathoms. Bottom temperature, 42° 0' F. (5°'5 C,), Ophiactis abyssicola (Sars), , ? « » .7 Ophiacantha hidentata (Betzius), , , , *11 Station 52. Lat. 60° 25' N„ long, 8° 10' W. Depth, 384 fathoms, Bottom temperature, 30° ’6 F. (~0°‘8 C,). Ophiopus arcticus^ Ljungnian, , , , . ,6 Ophiacantha hidentata (Betzius), , , . . 1 Ophiaxtis abyssicola (Sars), , , , . ,28 Station 54- Lat. 59° 56' 1^,, long, 6° 27' W. Depth, 363 fathoms. Bottom temperature, 31°‘4 F, (-0°-3 C,). Ophiacantha hidentata, (Betzius), „ abyssicola^ Sars, , Ophiactis Ballii (Thompson), , Ophiomyxa serpentaria, Lyman, Opliiopholis aculeata (0. F. Muller), Ophioscolex purptireus, Dub. and Kor„ 1 t 1 1 1 4 2 ^ Possibly the young of 0. Liltkeni, t These specimens have six arms. of Edinburgh^ Session 1883-84. 7H Station 57. Lat. 60° 14' N., long. 6° 17' W. fathoms. Bottom temperature, 30° '5 F. (-0°'8 C.) Depth, 632 Opliioscolex piirpiireuSj Diib. and Kor., . 2 Station 60. Lat. 61° 3' K, long. 5° 58' W. Depth, 167 fathoms. Bottom temperature, 44° '3 F. (6° *9 C.). Ophiopholis acideata (0. F. Muller), . 3 Station 61. Lat. 62° 1' K, long., 5° 19' W. fathoms. Bottom temperature, 45° -0 F. (7° *2 C.). Depth, 114 Ophiopholis acideata (O. F. Muller), . 1 On the Faroe Bank.* Opliiothrix pentaphyllum (Pennant), 2 „ fragilis (0. F,. Muller), , 7 Station 65. Lat. 61° 10' K, long. 2° 2V W. fathoms. Bottom temperature, 20°‘8 F. ( - 1°*1 C.). Depth, 345 Gorgonocephaliis eucnemis (Miill. and Tr.) , . 4 Ophiacantha abyssicola, Sars, ..... . 3 Ophiactis abyssicola (Sars),. .. .. . 3 Ophiobyrsa hijstricis, Lyman, .... . 1 Opliioglypha Sarsii (Lutken), . ... . 2 Ophiopholis acideata. (Oi F. Muller), . . 12 Station 67. Lat. 60° 32' N., long. 0° 29' W. Depth, 64 fathoms. Bottom temperature, 49° ‘1 F. (9° *5 C.). Ophiopholis acideata (0.. F. Muller),. . . . .12 (Amphmra CMajii, Forbes, . . . . . 1 OphiacUs abyssicola (Sars), . . . . . 2 ^ j OphioglypTia Sarsii (Liitken), . . , . .6 \OphiophoUs aculeata (0. F. Muller), ... .4 * Either Station 61, or Station 62. (Lat. 61° 59' K., long. 4° 38' W. Depth, 125 fathoms. Bottom temperature, 44° ‘6 F. [7°'0 0.]). t The specimens bracketed were contained in a bottle labelled “Stations 67 and 68.” The bottom temperature of the latter is 44° F. Depth, 75 fathoms. 712 Proceedings of the Royal Society Station 74. Lat. 60° 39' long. 3° 9' W. Depth, 203 fathoms. Bottom temperature, 47° *6 F. (8° *7 C.). Amphiiira borealis (Sars), , , , , . 1 OpMacantlia ahyssicola, Sars, .... . 12 „ hidentata (Eetzius), . 15 Opliiactis ahyssicola (Sars), , ^ , . 10 „ Ballii (Thompson), , , , . p 4 Ophiopholis aculeata (0. F, Muller), . . 17 OpMoseolex puTpureus^ Diib. and Kor,, , , p 3 Ophiothrix fragilis * (0. F. Mtiller), , p 2 Station 77. Lat. 60° 3F K, long. 4° 40' W. fathoms. Bottom temperature, 29°'8 F. ( - 1°*2 D). Depth, 560 OpluQcten sericeum (Forbes), , , , . p 16 Ophiopholis aculeata (0. F, Muller), , , p 2 Station 78. Lat. 60° 14' N., long. 4° 30' W. fathoms. Bottom temperature, 41° -5 F. (5° *3 C,). Depth, 290 Ophiacantha ahyssicola^ Sars, .... , 10 OpMoglyplia Sarsii (Liitken), .... , 1 OphiopAiolis aculeata (0. F. Muller), . , . 10 Ophioscolex glacialis^ Miill. and Tr., , . , p 1 Station 82, Lat, 60° 0' N., long. 5° 13' W, fathoms. Bottom temperature, 41°‘4 F. (5°‘2 C.). Depth, 312 Ophiacantha ahyssicola^ Sars, .... . 9 Ophioglyplia Sarsii (Liitken), .... . 8 Ophiopholis aculeata (0, F. Muller), . . . , 30 Ophioscolex glacicdis, Mull, and Tr., . . 2 j, purpureuSi Dub. and Kor., . , p 16 Station 87. Lat, 59° 35' FT., long. 9° 11' W. fathoms. Bottom temperature, 41°'4 F. (5°-2 C.). Depth, 767 Ophioscolex purpureus^ Diib. and Kor., . 4 * Possibly the young of 0. Liitlceni, of Ediiiburgli^ Session 1883-84. 713 Depth, 705 Station 88. Lat. 59° 26' K, long. 8° 23' W. fathoms. Bottom temperature, 42° *6 F. (5° *9 C.). Opliiocten sericeum (Forbes), {jtivf , . .20 Station 89? Lat. 59° 38' K, long. 7° 46' W. Depth, 445 fathoms. Bottom temperature, 45° '5 F. (7° -5 C.), Aster onyx Loven% Miill. nnd Tn, . , . . ? Station 90. Lat. 59° 41' N., long. 7° 34' W. Depth, 458 fathoms. Bottom temperature, 45° *2 F. (7°*3 C.), Amphiura filiformis (0. F, Muller), . Qpliiacantha ahyssicola, Sars (juv.), Opliiactis ahyssicola (Sars), (juv.), Ophioglypha alhida (Forbes), . , Ophiothrix fragilis (0. F. Muller), , The Minch, Depth, 60-80 fathoms, Amphiura Ghiajii^ Forbes, . , Ophiothrix pentaphyllum (Pennant), Aster onyx Lovmi, MiilL and Tr^, , The Cruise of H.M.S. “Porcupine” in the Mediterranean, 1870, Station 13. Vigo Bay, Depth, 220 fathoms, Bottom tempe- rature, 52° F. (11° C.). Amphiura filiformis (0. F. Muller), . , . .45 Adventure Bank, South of Sicily. Depth, 30-250 fathoms. Ophioglypha lacertosa (Pennant), . , , , 1 The Cruise of H.M.S. “Triton.” Station 1. August 4, 1882. Lat. 59° 51' 30'' N., long. 6° 21' W. Depth, 240 fathoms. Bottom, sand and gravel. Bottom tempera- ture, 47°-5 F. (8°*7 C.). Dredge. Ophiactis Ballii (Thompson), . , . . .1 2 1 31 1 3 714 Proceedings of the Royal Society Station 2. August 5, 1882. Lat. 59° 37' 30" N., long. 6° 49' W. Depth, 530 fathoms. Bottom, mud. Bottom temperature, 46° -2 F. (8°-0 C.). Trawl OpMopholis aculeata {O. F. Muller), . , .2 Station 3. August 8, 1882. Lat. 60° 39' 30" K, long. 9° 6' W. Depth, 87 fathoms. Bottom, sand and shells. Bottom tempera- ture, 49°-25 F; (9°”6 C.). Dredge. OpliiocomfL nigra (0, F. Muller), , 9 Ophioglypha lacertosa (Pennant), . 3 Opliiopliolis aculeata (0. F. Muller), . 51 Ophiothrix fragilis (0. F, Mullei), . , 74 Station 4. August 8, 1882. Lat. 60° 20' 15" N., long. 8° 25' 30" W. Depth, 327' fathoms. Bottom, stones. 3r-75 F. (-0°-7 c.). Trawl, ^ Bottom temperature, Ophiactis ahyssicola (Sars), . . 4 Station 5. August 9, 1882. Lat. 60° 11' 45" N., long. 8° 15' W. Depth, 433 fathoms. Bottom, hard ground. Bottom tern- perature, 43°-5 F. (6°-5 C.). Trawl, GorgonocepJialus eucnemis (Mlill and Tn), , , 7 Ophiacantha spectahilis, Sars, . ... ,2 Ophiactis ahyssicola (Sars), . 5 Ophioglypha signata^ Verrill, . , 3 Opliiopholis aculeata (0. F. Muller), . 16 Opkioscolex purpureuSy Dilb. and Kor^, . 14 Station 6. August 17, 1882. Lat. 60° 9' K, long. 7° 16' 30" W. Depth, 466 fathoms. Bottom, stones. 29°“75 F. (-l°-2 C.). Dredge. Bottom temperature. Ophioglypha signata^ Verrill, . 35 Station 8. August 22, 1882, Lat. 60° 18' IST., long. 6° 15' W. of Edinburgh, Session 1883-84. 715 Depth, 640 fathoms. Bottom, mud. Bottom temperature, 30° F, ( - 1°‘0 C.). Trawl twice, Ophioglypha signata, Verrillj , . . * 27 Station 9. August 23, 1882. Lat. 60° 5' N,, long. 6° 2T W. Depth, 608 fathoms, Bottom, mud, Bottom temperature, 30° F. (-1°-0C.). Trawl, Ophioglypha signata, Verrill, , , , ,15 Olf Castle Walker, Loch Linnhe, 35-37 fathoms. Amphiura Chiajii,YoxhQB, , , , , ,11. Station 10. August 24, 1882. Lat, 59° 40' N,, long. 7° 2L W. Depth, 516 fathoms. Bottom, mud. Bottom temperature, 56°*25 F, (13°*55 C.), Trawl, Amphiura hellis, Lyman, var. tritonis, noY.,, , , 1 Ophiactis abyssicola (Sars), , , , . ,3 Ophioglypha aurantiaca, Verrill, , , , ,35 Ophiothrix fragilis (0. F. Muller), . . . , 2 Young specimens undetermined, . . , ,3 Station 11. August 28, 1882. Lat. 59° 29' 30'' K, long, 7° 13' W. Depth, 555 fathoins. Bottom, ooze. Bottom, temperature, 45° 5' F. (7° ”6 C.). Dredge and trawl. Arriphmra fiUformis {0, F, Muller), Ophiactis abyssicola (Sars), Ophioglypha aurantiaca, Verrill, 1 1 6 Station 13, August 31, 1882. Lat. 59° 51" 2" K, long. 8° 18' W, Depth, 570 fathoms. Bottom, ooze. Bottom temperature, 45° '7 F. (7° ’7 C.)., Dredge and Trawl, Ophioglypha aurantiaca, Verrill, . . . , 3 Young specimen undetermined, , , , . 1 716 Froceeclings of the Boyal Society A description of the one new form may he conveniently appended here, along with a few notes upon one or two other species. AmyihiuTa hellis, Lym., var. tritonis. (Ph VII. figs. 1-3.) Diameter of disk, 12 mm. Arms, long and slender, 11 cm. Width of arm close to disk, without spines, 2 mm. Two mouth papillae on either side ; one large trapezoidal at the apex of the mouth angle, one of its sides coinciding with the corresponding margin of its fellow, the ten papillae almost enclosing the circle of the mouth ; the other mouth papilla is at the commencement of the oral process ; is acutely pointed and triangular, and is succeeded immediately by a diamond-shaped scale, which covers the opening of the first tentacle. A supplementary scale was noticed at one mouth-angle (fig. 1). Mouth shields heart-shaped, one subpentagonal. Side mouth shields appear to be triangular; they do not project inwards be- yond the median shields, and they meet each other in the position usually occupied by the first under-arm plate, which is absent. The other arm-plates are rectangular, vrith the inner and outer margins somewhat rounded ; farther out on the arms they form an angle, so that the plate is hexagonal ; the lateral margins straight and coin- cident with the attached margin of one of the tentacle scales. Side arm-plates slightly prominent where the spines are attached, not meeting in the middle line either above or below. Upper arm- plates transversely oval, but the proximal margin, instead of being evenly curved, forms an angle. Disk flat, thin, covered with small swollen overlapping scales, which are coarser and radially elongated near the radial shields. Eadial. shields, wedge-shaped, very long, about four times as long as wide, pointed at the proximal extremity, truncated distally, completely separated from each other, except perhaps at the ex- treme outer end, by a median and one or two lateral rows of elongated scales. Interbrachial spaces in the under surface covered with similar small scales.; three, or sometimes at the proximal end of the arm four, straight tapering bluntly-pointed arm-spines.. Two tentacle scales, one towards the axis of the arm, elongated, semi-oval ; one on the proximal margin of the aperture, shorter and more nearly circular. 717 of Edinburgh, Session 1883-84. Colour, yellowish-grey, with five rather indefinite radial markings on the dorsal surface of the disk. The typical Amghiura bellis differs from this in having one short stout blunt papilla on either side of the base of the mouth angle. It has also suhtriangular mouth shields, and the lateral mouth shields do not meet each other in the middle line. The mouth papillae are of a different shape. A first under arm bone is present, and the tentacle scales of the first pair are spini- form and rather conspicuous. This single specimen is worthy of special notice, because the species has been only known hitherto from specimens collected by the “Challenger” at Stations 174, near the Fiji Islands, and 232 and 236, off Japan. It is interesting to notice that Aster onyx Loveni is also common to the north European seas and those of Japan, and a relation has been traced by Drs Gwyn Jeffreys, and Gunther between the mollusca and fishes of Japan and the North Atlantic and Mediterranean.* OjAiioglypha aurantiaca, Verrill. Ophioglypha aurantiaca, Verrill, Amer. Jour. Set. and Arts, vol. xxiii. p. 141, 1882. Lyman, Bull. Mus. Comp. Zool., vol. x. No. 6, p. 240 (with fig.), 1883. The mouth shield has the inner angle almost a right angle ; the outer edge is not nearly straight, but with a re-entering angle. The teeth papillae are usually four. As in Professor VerrilFs specimens, the arms have all been broken ; the longest measured twice the diameter of the disk. The arm-spines are three ; the uppermost is the longest, and is a little longer than the arm-joints, and the second is about two-thirds the length of the first; the third is still shorter ; the tentacle-scale is close to the arm-spines, and appears to form part of the same series with them ; there is only one tentacle-scale, except in the proximal portion of the arm, where there are two ; where this is the case, the outer is spiniform, the inner scale like. The margin of the genital slit is finely serrated. The two or three proximal tentacle pores have some- times three tentacle scales, close beside which are two small spines, about equal to them in size. Journ. Linn. Soc. Land., vol. xii. pp. 100-109, 1874. 718 Proceedings of the Poyal Society Average dimensions, — diameter of disk, 12-15 mm. ; thickness rarely more than 5 mm. Ophiactis Bcdlii> The bathymetrical range of this species is ex- tended to 730 fathoms. Ophiocten sericeimi dredged by ITM.S. “Porcupine” at six stations, the depths varying from 542 to 2435 fathoms, its bathy- metrical range being thereby greatly extended. Ophiopholis aculeata. Bathymetrical range extended to 560 fathoms. Ophiothrix fragilis. Bathymetrical range extended to 516 fathoms. Gorgonocephdlm eiicnemis and Ophiacantha spectabilis are new to British seas. Ophiactis ahyssicola. This species has not been previously ob- tained in British seas, and its bathymetrical range is extended from 400 to 767 fathoms. Opliioscolex piirpurmis. This species is also an addition to the British fauna, and its bathymetrical range is extended from 200 to 767 fathoms. Ophioglypha signata^^ Verrill (Pi. Vll. figs. 4-8), was first dis- covered by Professor Verrill off the north-eastern coast of the United States (100-258 fathoms),^ and has again been recorded by Mr Lyman in the Proceedings of this Society (vol. xi. p. 707). As no figure of it has yet been published, I have given one on the accompanying plate. Amphiufa filiformis. Bathymetrical range extended to 555 fathoms. These few matters of systematic aiid descriptive interest being disposed of, we may proceed td discuss the distributional problems suggested by the material in hand. The importance of the Faroe Channel as a field for zoological investigation lies, as is well known, in the fact that there are here two areas not far separated, and resembling each other in depth and physical conditions generally, save only that in one the average temperature of the bottom water * AmeTi Joilr Sci. and Arts^ vol.- cxxiii. pp. 218, 220, 1882. of Edinburgh, Session 1883“84. 719 is some 10-15° F. higher than in the other. We have thus two areas in which all factors influencing the distribution of animals are approximately eliminated, save and excepting that of tempera- ture, so that here, if anywhere, we may hope for an opportunity of determining the influence due to this important factor. With the view of investigating this matter, so far as the Ophiu- roids are concerned, the table on the next page has been drawn up, which includes all the results obtained by Porcupine,” “Knight Errant,” and “Triton” which are applicable to the problem under discussion. In order to render the results strictly comparable, only those stations are considered v^hich are clearly within one area or the other, none, of course, being admitted which are at a less depth than the top of the Wyville-Thomson Ridge, that is, about 300 fathoms. The depth and bottom temperature of each station are given, and the number of specimens obtained at each is shown by the figures in the several columns. It will be obvious that in attempting to draw conclusions from such a table, the utmost caution must be observed ; the numbers are so small, that any extensive series of dredgings will be sure to alter them very considerably. For instance, the whole of the expeditions together, prior to the “ Triton,” only obtained one specimen of Ophioglyylia mirantiaca, while only three dredgings on that cruise yielded together forty-five specimens. Still as no further data are at present available, the best use possible must be made of these, it being understood that the results are only provisional. It appears then, that while eight species were found both in the warm and cold areas, six were peculiar to the latter and six to the formen These facts suggest that there are certain forms which flourish in warmer, whilst others are better adapted to colder waters ; but in order to confirm this view, it will be well to state what is known of the distribution, with respect to temperature, of each of the species in question in other localities ; unfortunately our knowledge upon this point is very fragmentary, because it is only of recent years that dredgings have been made, while, at the same time, accurate physical observations have been taken, but such facts as I have been able to collect are given in the following paragraphs. Amphiiira hellis, Lym,, has previously been found only at three 720 Proceedings of the Royal Society Table showicg the Distribution of the WARM AREA. Porcupine, 1869. Knight Errant. 1880. Triton. 1882. Station, . . i . 46 47 51 87 90 1 7 2 6 10 11 13 Depth, . . * * 374 542 440 767 458 1 515 530 S30 433 516 555 570 Bottom Temperature (C), | 7° 7 6°-5 ; 5°’5 S°-2 ' 7° ‘3 Cp H 0 c VO 00 ; 8°'i 00 00 d d 6^-5 6 -5 i 7° ‘8 . 8"-i 1 7“-6 7" -6 Amphiura bellis var tritonis, . 1 ! 4 1 „ filiformis, 2 : 4 4 1 o Ophiacantba spectabilis, • 2 -S Ophioglypba albida, 4 .4 1 a a „ aurantiaca, i . 1 35 6 3 Ophiothrix fragilis, 4 1 3 2 Gorgonocepbalus eucnemis, , 7 Ophiacantha abyssicola 1 . ,, biclentata, ; 1 2 o rQ Ophiactis abyssicola, 22 7 31 2 10 5 3 1 O Opbiocten sericeum. 2 ! ‘ o g § Ophioglypba signata. • 3 o Ophiopholis aculeata, ; 2 16 . Ophioscolex purpureus, 4 14 Ophiobyrsa hystricis, , i 4 4 Opliiomyxa serpentaria, 4 0 cS 01 Opbiopus arcticus, 4 i (h Ophiactis Ballii, . 4 Q Ophioglypba Sarsii, Ophioscolex glacialis, . of Edinhiirgh, Session 1883-84, 721 OPaiuRoiDEA in the Faroe ClianiieL 3 A VOL. Xlt. 720 Proceedings of the Royal Society Table showing the Distribution of the WARM AREA. Porcupine. Knight Errant. 1880. Triton. 1882. Station, .... 46 47 51 87 00 5 7 2 s 10 11 13 Depth 374 S42 440 767 458 515 S30 S30 433 SI6 S5S 570 Bottom Temperature (C), | 7° '7 6°‘S 5“-S S°-2 f'S 6° -8 8"-t 8°-i 8“-o 8°-o 6“ -5 8"-i 7“-6 7"-6 7" 7 7’’7 Ampbiura bellis var tritonis, T „ filiformis, 2 1 Opbiacantba spectabilis, 2 Ophioglypha albida, * 1 s „ aurantiaca, 1 35 6 3 Opbiotbrix fragilis, ; 1 3 2 Gorgonocepbalus eucnemis, . 7 I Opbiacantba abysslcola 1 4 ,, bidentata, 1 2 1 Ophiactis abyssicola, 22 7 31 2 10 5 3 1 ■2 Opbiocten sericeum, 2 1 Ophioglypha signata, . 3 Opbiopholis aculeata, . 2 16 Ophioscolex purpnreus, 4 14 Opbiobyraa hystricis, . i Opbiomyxa serpentaria, Opbiopus arcticus, . Let us imagine the original triangular plane ACB as having one of its two faces red and the other blue ; and imagine its face which at the point A is anterior in its motion relative to the vice-original frame to be red, and the one which at that point is posterior to be blue. In respect to this it is to be noticed that the red face thus specified though anterior at A may happen to be the posterior one at B : but this need not give us trouble, and for brevity we may speak of the red face which at A is anterior as being the anterior face. Let the faces of all the templet triangles be coloured red and blue correspondingly. By going forward with considerations readily suggested by what has just been set forth, we may obviously find that the process of solv- of Edinburgh, Session 1883-84. 741 ing the stated problem for the case of only three original points by the kinematical mechanism can bring out two straight lines AA and BB really at rest relatively to the vice-original frame, and consequently having all their points either at rest or moving rectilinearly and mutuo-proportionally in relation to the original secret frame : and further that the same process of solving the stated problem can bring out another real true solution in finding two straight lines which we may call A' A' and B'B' which will be the images of AA and BB in a plane mirror whose plane always passes through the three points A, B, and C. The two straight lines A' A' , B'B' so found may be taken as lines fixed in a frame which we may designate as and which will rotate relatively to the vice- original frame , as also relatively to the original secret frame. Now, as the motion of the original points goes on making their distances apart increase unlimitedly, this relative rotation between the frames ' approaches ultimately to identification with that which brings out the frame ^ which is in agreement with the original secret frame. If now instead of using the three points C, A, and B, we use a different group of three points C, A, and D, these will bring out for us as solutions two frames $ and ^>", of which the one will be identical with the frame ^ already found by the three points C, A, and B. It follows from this (and it seems very obvious that it could be brought out in various other ways), that for four original points no frame in general could be brought out as a solution except one in agreement with the original secret frame ; that is to say, a frame either at rest relatively to that original frame, or having all its points moving rectilinearly and mutuo-proportionally relatively to that original frame. One reason which seems very decisive in favour of this conclusion is : — that if any three of all the original points be retaining their distances apart unchanging, then these three will themselves constitute a frame <1> which will be in agree- ment with the original secret frame : and then for any other one or more of the original points taken along with these three, no frame will be possible to serve as a solution except such as shall be in agreement with that one. 742 Proceedings of the Boyal Society Postscript. The ideas noted in what follows had not completely occurred to me till after the evening of the meeting of the Society when the paper was read, and a suggestion towards their development came from Professor Tait’s paper of the same evening On Reference Frames.” Thus it seems suitable to annex them here as a postscript. It may be noticed that in the case referred to in the last sentence of the paper just before this postscript — the case of three original movingpoints retaining their distances apart unchanging — the method of procedure employed throughout the paper would collapse because the points A and B would be at rest relatively to the vice-original frame, and so the straight lines of motion AA and BB previously used would become only two points. Yet a solution is in this case even more readily available than in the previously considered cases. It thus becomes desirable to find some way of harmonising the two modes of thought or of procedure so as to bring them into connec- tion ; rather than to be content to suppose that, in passing from one to the other, we should have quite to abandon the one mode of thought, and take up another and quite unallied mode instead. A satisfactory connection between the two presents itself, if, instead of taking frorn the kinematic model only the lines of motion AA and BB, as the basis for our desired frame, we take from that model also the points A^ and B^ on those lines, getting them known by measurement of their distances from any future points A„ and B;i , so that when, among the three original points A, B, and C, the particular configuration A,iCB,j found in anticipation from the model shall come to exist, the old triangular frame A^CB^ shall become known to us relatively to the then existing frame A„CB„ . In this way of procedure, the solution, for the case of A and B being, as well as C, at rest in the vice-original frame, will come out simply by the distances and B,^Bj being each zero in length, and by the concomitant of this, that the old frame A^CB^ is to be found as being coincident with the new momentarily existing and known frame A??CB^ , of Edinlurgh, Session 1883-84. 743 2. Note on Eeference Frames. By Professor Tait. As I understand Prof. J. Thomson’s problem (anUy p. 568) it is equivalent to the following : — A set of points move, Galilei-wise, with reference to a system of co-ordinate axes; which may, itself, have any motion whatever. From observations of the relative positions of the points, merely, to find such co-ordinate axes. It is obvious that there is an infinitely infinite number of possible solutions ; because, if one origin moves Galilei-wise with respect to another, and the axes drawn from the two origins have no relative rotation, any point moving Galilei-wise with respect to either set of axes will necessarily move Galilei-wise with respect to the other. Hence any one solution suffices, for all the others can be deduced from it by the above consideration. Keferred to any one set of axes which satisfy the conditions, the positions of the points are, at time f, given by the vectors ttj + fS^t for A , -f p^t for B , &c., &c. But it is clear, from what is stated above, that we may look on the pair of vectors for any one of the points, say and /Sj for A, as being absolutely arbitrary : — though, of course, constant. We will, therefore, make each of them vanish. This amounts to taking A as the origin of the co-ordinate system. The other expressions, above, will then represent the relative positions of B, C, &c., with regard to A. The observer on A is supposed to be able to measure, at any moment, the lengths AB, AC, AD, &c. ; the angles BAG, BAD, CAD, &c. ; and also to be able to recognise whether a triangle, such as BCD, is gone round positively or negatively when its corners are passed through in the order named. What this leaves undetermined, at any particular instant, is merely the absolute direction of any one line (as AB), and the aspect of any one plane (as ABC) passing through that line. These being assumed at random, the simul- taneous positions of all the points can be constructed from the per- missible observations. But it is interesting to inquire how many observations are necessary; and how the ^s depend on the as. 744 Proceedings of the Poiyiil Society Tims, at time t^ whatever be the mode of measurement of time, we have equations such as follows:— ^a-al + 2Sa2/g2' ^ + - & = Sa2tt3 S(a2/?g + ^2^3) • ^ + S^2^3 - ^^ = o| + 2Sa3/33,if + ^P^ For any one value of t we have n equations of each of the 1st and 3rd of these types, and n{n l)/2 of the 2nd, w + 1 being the whole number of points. In all, n{n+ l)/2 equations. The scalar unknowns involved in these equations are (1) the values of f ; (2) a|, ag, &c. j (3) &c.; (4) &c.; (5) (®) Sa2^2, S«3^3, &c.; and (7) S{a^s + ^^a^), &c. Their numbers are, for (2), (3), (6), each ; for (4), {5), (7), n{n-l)/2 each; in all 3?z(?z + 1)2. Suppose that observations are made on m successive occasions. Since our origin, and our unit, of time are alike arbitrary, we may put ^ = 0 for the first observation, and merge the value of t at the second observation in the tensors of /?2j &c. This amounts to taking the interval between the first two sets of observations as unit of time. Thus the unknowns of the form (1) are m - 2 in number. There are therefore mn{n + l)/2 equations and 2>n{n + l)/2 + m- 2 unknowns. Thus TO = 3 gives an insufficient amount of information, but to = 4 gives a superfluity. In particular, if there be three points only, which is in general sufficient, 3 complete observations give 9 equations with 10 unknowns; while 4 complete observations give 12 equations with 11 unknowns. Thus we need take only two of the three possible measurements, at the fourth instant of observation. The solution of the equations, supposed to be efiected, gives us among other things, a| , ug , and Sa2a3. Any direction may be assumed for and any plane as that of and a^. Fom these assumptions, and the three numerical quantities just named, the co-ordinate system required can be at once deduced. of Eclinhurgh, Session 1883-84. 745 This solution fails if (Sa2a3)2 - , or TVa2a3 = 0; for then the three points A,B,C, are in one line at starting. But this, and similar cases of failure (when they are really cases of failure) are due to an improper selection of three of the points. We need not further discuss them. But it is interesting to consider how the vectors P can he found when one position of the reference frame has been obtained. Keep- ing, for simplicity, to the system of three points, we have by the solution of the equations above the following data : — = ^ Sa^3 = e', + =f , = = where e, e\ /, y, g\ li are known numbers ; which, as the equations from which they were derived were not linear, have in general more than one system of values. The second, third, and sixth of these equations give ^38 . a2tt3^2 “ 'b (/“ b ^ ^ (^2^2 * Provided coplanar with a2,a3 , this equation gives, by the help of the fifth above, a surface of the 4th order of which is a vector. But is also a vector of the plane ^a.^P2 = e, and of the sphere T^2 =" 9^ Hence it is determined by the intersections of those three surfaces. But if S . a2a^P2 vanishes, the equation above gives (by operating with S . Va2tt3) 0 = h(Ya^a^)^ - (/- S^2«3)S . P2Y. e'S . a2Va2tt3 , which gives a surface of the second order (a hyperbolic cylinder) in place of the surface of the fourth order above mentioned. This may, however, be dispensed with : — for P^ is in this case deter- mined by the planes Sag/?^ = e and S . agag/Jg = 0, together with the sphere T/Sg = g. 3. Note on the Occurrence of Drifted Trees in Beds of Sand and Gravel at Musselburgh. By James Geikie, LL.D., F.E.S. 1 am indebted to Mr William Robertson for calling my attention to the interesting phenomena which form the subject of this 746 Proceedings of the Royal Society communication. Some months ago he showed me at his works, Haymarket, the trunk of a large oak which had been obtained from beds of sand- and gravel in his property at Olive Bank, Musseh burgh. The wood was very dark in colour, and in a fine state of preservation. It was, in fact, in process of being sawn into planks, from which a number of useful and ornamental articles have since been made. The trunk was perfectly straight, showing no appear- ance of branches, and when first uncovered measured 31 feet in length, having a diameter of 2 feet at the butt end close to the roots, from which it tapered upwards very gradually. The portion seen by me in Mr Kobertson’s premises had been more or less scraped by his workmen, and the bark was almost entirely wanting ; but I was informed that very little bark appeared when the tree was disinterred. The roots were somewhat rounded, and looked as if they had been rubbed and abraded. Shortly afterwards I visited the sand-pit, and saw the trunk of another large oak in situ. It was only partially uncovered, the portion concealed being buried under some 10 feet of sand and gravel. The trunk was hollow and filled with wet sand, and the wood was so soft that it could be cut in most places with a spade. The greatest diameter of the exposed portion was 3 feet 9 inches, and when the trunk was finally dug out it was found to measure 18 feet in length. But Mr Eobertson informs me that, before the time of my first visit to the sand-pit, the workmen had dug away a considerable portion of the dark brown soft woody matter, under the impression that this was merely “ peat,” and he estimates the length of the part so removed as not less than 30 feet, and thinks the trunk at its butt end could not be less than 5 feet in diameter. This would give a total length for the trunk of 48 feet. It was not so straight as E"o. 1 tree, and unlike it, it had several branches. Most of the bark had been removed from the tree before the time of its entombment, but some still adhered in places, and was covered with a foliaceous lichen. Here and there also the trunk was thickly set with the stems of a clinging or climbing plant, wEich may have been ivy. I did not, however, detect any leaves of that plant ; but in the hollow of the trunk I picked out a few leaves of holly, and other vegetable matter which was too decayed to allow of identification. Since this tree was exposed, other two have been extracted. One of these of Edinburgh, Session 1883-84. 747 resembled Xo. 1 tree in the soundness of the wood, but the trunk was hardly so straight, and it had several branches. At 1 foot above the roots it measured 20 inches in diameter, from w^hich it tapered upwards for 26 feet to a diameter of 1 foot, after which it bifurcated, the two branches measuring 16 feet 6 inches and 6 feet 6 inches respectively. There were smaller branches also both on the main trunk and on the two principal branches. The fourth tree I did not see in situ, but in Mr Kobertson’s premises. It measured 2 feet 7 inches in diameter near the root, but bifurcated at about 4 feet 6 inches. Only one of the two limbs, however, remains, and it measures 18 feet 4 inches in length. It also bifurcates, the branches measuring 18 feet and 15 feet, with diameters of 9 inches and 7 inches respectively. All the trees were more or less soft and spongy externally, the soft wood being readily removed by a spade to the depth of an inch or more. They seem to have been for the most part deprived of their bark before they became buried in the sand, and the worn and abraded character of the roots and branches was just such as we see in trees which have been drifted some distance in water. It remains only to add that the trees were lying with their butt ends directed inland. Nos. 1 and 4 I did not see in situ, but the others I took the direction of, and found that the top of No. 2 pointed E. 20 N.; and Mr Eobertson informed me that No. 1 had the same direction. No. 3 tree lay N. 5 W. or nearly north and south, the top being directed seawards. No. 4, again, appears to have had very much the same direction, the top being directed a few degrees more to west of north. I may add, that the four trees now referred to occurred within a dozen yards or so of each other, one of the branches of the great hollow trunk (No. 2) lying across No. 3 tree. Scattered through the sand in the neighbourhood of the trees, many twigs and branches were seen, some of which may have belonged to those particular trees ; it is quite possible, however, that a portion of the vegetable d4bris may have become entangled in the roots and branches of the snags as it drifted seawards. The succession of deposits seen in the sand-pit is in descending series, as follows (see fig. 1) : — {a) Soil, &c. (6) Sand, white and yellow, about 1 foot 6 inches. 748 Proceedings of the Royal Society (c) Peat, about 9 or 10 inches. (d) Gravel and Sand, excavated to a depth of 8 or 9 feet. ,c a Fig. 1. Section in Sand Pit, Olive Bank, Musselburgh, a, Soil, &c. ; h, sand ; c, peat ; d, sand and gravel. + Position of drifted trees. The Sand (a) is a moderately fine-grained siliceous sand, seen only in the north part of the sand-pit. It dies out rapidly to the south. The granules are often coated with hydrous ferric oxide, and the bed becomes quite ochreous towards the north. No fossils seem to occur. The bed is overlaid by a mass of “made ground,” consisting of sandy soil, in which fragments of very recent pottery and glass are seen. The thin bed of peat underlying this sand is in like manner restricted to the north end of the pit. It occupies a hollow, and dies out rapidly to north and south. Both it and the overlying sand abut against the subjacent gravel and sand in such a way as to show that the latter had been considerably denuded before the accumulation of the peat and upper sand-bed had commenced. There is nothing particularly noteworthy about this peat, save that it seems to be made up to a considerable extent of the remains of trees, such as birch, elm, Scots fir, (fcc. Here and there I detected the wing-cases of beetles, and possibly other organic remains may occur, for I made no special search. Both this peat and the overlying sand-bed are evidently of much more recent date than the gravel and sand below, and it is to these specially that attention is at present directed. The deposits in question have been excavated to a depth of 8 or 9 feet, and how much thicker they may be I cannot say, but the boulder-clay will probably be met with at no great distance from the bottom of the sand-pit ; and possibly the sand and gravel do not attain a greater thickness than 20 or 30 feet. The beds of Edinhiiryh, Session 1883—84. 749 exposed in section are somewhat variable, and show a good deal of diagonal bedding, pointing to somewhat persistent current action from the south ; in a few places, however, there is evidence of a movement in quite the opposite direction. Although the deposits show so much false-bedding, the inclination of all the various lenticular beds and sheets of gravel and sand is towards the north at a low angle, between 2° and 3°. The sand is chiefly siliceous, and remarkably “ sharp ” or clean, and it greatly predominates over the gravel. Some layers are very fine, others are less so, passing into a grit. The gravel consists of well water-worn stones, varying in size from mere grit up to fragments several inches in diameter. Coarser and finer gravels alternate in lenticular or irregular layers and beds, which interosculate with lines and sheets of sand. So far as I have observed, there are no rock-fragments in the gravel which do not also occur in the boulder-clay of the same district, and very few, if any, that might not have been derived fi-om the drainage-area of the Kiver Esk, which enters the sea about half a mile to the east of our section. It is in these gravel and sand beds that the drifted trees occur. They were met with at or about the bottom of the section in the sand-pit, and all within a distance of 40 feet of each other. The absence of any trace of marine organisms in the beds, taken in connection with the presence of the drifted trees, branches, twigs, &c., suggests the fluviatile origin of the deposits, and the same might be inferred from the general appearance of the deposits them- selves. All the evidence points to a flow of water from south to north. The inclination of the various layers, the “ pitch ” of the diagonal bedding, the shape of the gravel stones (well water-worn, but not generally so well rounded as marine gravel), the manner in which the stones often overlap, and the general disposition of the materials precisely resemble what we see in the recent alluvial accumulations of our larger rivers, and in certain older valley-terraces laid down by many of our streams at a time when these flowed in greater volume than at present. The deposits at Musselburgh occur some 30 feet above Ordnance datum-line, and form part of a broad terrace which slopes gradually inland to a height of as near as may be 45 feet. Indeed, the 50 feet contour line may be taken as the bouudary of the gravel and sand, the terrace formed by which 750 Proceedings of the Eoyal Society abuts against a well-defined bank of boulder-clay. This bank and terrace may be followed more or less clearly from the site of St- Mary Magdalene’s Chapel near Pinkie Salt Pans, south-east by the municipal boundary and Stoneyhill to Stoneyparkj where they are truncated by the modern “ cut ” of the Esk (see fig. 2). At Monk- tonhall they again come on, forming well-marked features — the terrace sloping gradually down to the more recent alluvium of the Shire Haugh opposite Inveresk. The counterparts of this sloping bank and broad terrace are also met with on the east side of the Esk, Thus, they are well seen between the river and Inveresk, from which they may be followed down to a little beyond the Waukmill, after which the bank sweeps away to the east by Inveresk House and Pinkiehill Colliery, until eventually it turns north by Pinkie Brae, and is at last truncated by the 25 to 30 feet beach, to; the east of Fig. 3. Section across superficial Deposits at Musselburgh. 1, Glacial Deposits | 2, 45-50 feet terrace ; 3, 25 feet terrace ; 4, sea. Musselburgh Links. It may be added that this last-named beach has been excavated in our old terrace, across its whole breadth from west to east, so that in descending seawards from the bank which forms the margin of the 45 to 50 terrace, we first traverse 751 of Edinhurgh, Session 1883—84. that terrace, and then reach the short slope or bank that overlooks the 25 feet beach and the modern alluvia (see fig. 3). And just as the deposits of the 25 feet beach pass up the valley of the Esk into well-marked haughs of river alluvia, which gradually ascend with the slope of the valley ; so, when we follow the deposits of the older terrace inland we find them in like manner rising to a gradu- ally higher level, and behaving in every respect like ordinary river alluvia. There cannot, therefore, be any doubt, I believe, that the sand and gravel which contain the drifted trees are of fluviatile origin — accumulations formed by the Esk, at a time when that river flowed at a higher level and in considerably greater volume than at present. Since the upper or 45-50 feet terrace was formed the River Esk has cut its way down through that terrace and the boulder- clay and carboniferous strata to a depth of some 30 feet ; and the greater size of the Esk when flowing at the 45-50 feet level is indicated not only by the character and bulk of the deposits then laid down but by the much wider area over which these extend. I think it is also suggested by the great size of the drifted trees, which could hardly have been floated seawards by such a stream as the modern river. It is of some interest now to inquire what relation this ancient alluvial terrace bears to the raised beaches which occur at so many different places on both sides of the Firth of Forth. From what I have seen of those old sea-beaches I have little doubt that the tree- bearing beds referred to in this communication are on approximately the same geological horizon as the well-known 45-50 feet beach ; that, in short, the sand and gravel in which the great trees occur were deposited at or near the mouth of the Esk, when the sea-level stood some 45 feet higher than it now does. This appears to be shown by the fact that the upper limit of the terrace at Musselburgh preserves the same level when followed from west to east across the valley of the Esk, and hardly begins to show any rise when traced up that valley until we reach Inveresk. In short, the deposits at Musselburgh seem to me to resemble the delta accumulations of a very considerable river, and it is just possible that some of the current-bedding seen in the sand-pit at Olive Bank may be the result of tidal action. But the body of fresh water flowing seaward would be sufficiently great to prevent the incursion 752 Proceedings of the Royal Society of marine organisms, and the absence of any trace of these is no proof that the land may not then have stood, relatively to the sea, some 45 or 50 feet lower than it does at present. It is in the upper reaches of the Firth of Forth that the 45-50 feet beach is best developed. In the neighbourhood of Falkirk and Stirling the deposits of this level form the well-known Carse-lands — extensive sheets of mud, silt, clay, and sand, containing in many places recent sea-shells, such as Gardium edule, Ostrea. edulis, Cyprina islandica, Littorina litorea, Trophon clathratus, Buccinum undatum, &c. The upper limits of this great fiat are well marked out by bluffs and banks — the old coast-lines. Of its marine origin, therefore, there can be no doubt. Now, throughout the Carse- deposits there occurs at various levels much drifted vegetable debris, consisting of the trunks, branches, and twigs of such trees as birch, hazel, pine, and oak, and associated with these oyster-shells often appear in abundance. Eemains of the whale,* dug-out canoes, and rude implements and weapons have likewise been discovered in the same deposits, while along what was the old shore-line kitchen- middens are frequently met with. Ail the middens, as Mr Peach observes, “ occur on the bluff itself or just at its base, as if when it was the limit of high-water, the people who formed the middens, after searching the shores during low-^water, had retreated thither to enjoy their feast while the tide covered their hunting-ground.” It is noteworthy that when those Carse-deposits are followed up the valley, they are found rising with a gentle gradient, until eventually they pass into fresh- water alluvial deposits of sand and gravel of fluviatile origin. Here, then, at the head of the Firth of Forth, we meet with the counterparts of the Musselburgh beds. The evidence shows that at a time when the sea washed the 45-50 feet level the Eiver Forth, flowing in much greater volume than at present, carried down to its estuary enormous quantities of drift-wood, some of which got bedded in the sand of the lower reaches of the river, .some in the silt and mud of the estuary, while much no doubt found its way eventually out to the open sea. The Musselburgh * Professor Turner informs me that the skeletons of large whales, which from time to time have been found embedded in the Carse-deposits of the Forth valley, so far as they have been critically examined, have been determined to belong to the genus Balcenoptera, and are not examples of the Balcena mysticetus, or Greenland whale, as is generally believed. of Edinburgh, Session 1883—84. 753 beds, then, I take to be of the same age, and to betoken the same conditions, as are shown by the old fluviatile accumulations of the Forth at the point where these merge into the estuarine-marine beds of the Carse-lands. It is remarkable that precisely the same phenomena are met with in the lower reaches of the Tay valley. In that district, however, the succession of changes evinced by the Carse-deposits and the correlative fluviatile accumulations of the Tay and Earn, is even more clearly read. In the Carse of Gowrie, for example, we detect underneath the clay of the Carse the remains of an ancient buried forest. The lower portions of the Carse-deposits are often abund- antly charged with drifted vegetation, and here and there marine shells occur. I got oyster-shells and drifted wood in the Carse-beds a few years ago, during some excavations that were being made within the grounds of the Perth Penitentiary. But no marine remains have been met with higher up the valley, for as the deposits are traced further in that direction they pass gradually into fluviatile gravel and sand. That the Carse of Gowrie, &c., is of the same age as that of Falkirk, may be inferred from the fact that its upper limits reach the same elevation, viz., 45 feet. I may add that underlying the buried forest of the Tay and Earn valleys fluviatile gravel, sand, &c., are seen in some places. These phenomena, which I have described at length elsewhere,* seem to me to indicate the following succession of changes : — Taking first the fluviatile beds under the buried forest, these point to a time when the Tay flowed at a lower level than at present — for the old fluviatile beds referred to occur underneath the present mean tide-mark at and below Perth. Hence we may further assume that the land stood relatively to the sea somewhat higher then than it does now. Next in succession comes the buried forest. This, as I have shown, represents an old land surface which extends out seaward, and consequently proves that the Scottish shores formerly stretched much further to the east. I need not recapitulate the evidence which has led me to believe that the buried forest of the Tay valley finds its counter- parts in the so-called submerged forests which are met with at many points along the shores of these islands and the opposite coasts of the Continent ; and that the evidence furnished by these * See Prehistoric Europe, p. 385. 3 0 VOL. XII. 754 Proceedings of the Royal Society leads to the conclusion that at the time those forests flourished, the British area formed a portion of the European Continent, and enjoyed a more genial climate than at present. The buried forest of the Tay is covered by the Carse-clays which are indubitably of estuarine or estuarine-marine formation. Consequently they show us that the continental conditions during which the great forests extended themselves had now passed away ; more than this, we may infer from the appearances presented by the Carse-clays and correlative river deposits of the Tay and the Earn that the climate had now become less genial. The river-gravels referred to are more or less coarse tumultuous deposits extending over broad areas, and when they are followed into the Highlands they are actually found in close association with torrential debris and morainic accumula- tions. Again, the Carse-clays have all the appearance of those flood-loams and clays which are deposited by water bowing from snowfields and glaciers; and now and again they contain isolated stones and boulders which could only have been carried down to sea by river-ice. So that, at the time the clays of the Carse of Cowrie were accumulated, it would appear that local glaciers occupied some of the Highland glens, while our rivers had often a torrential character, and swept down to their estuaries immense quantities of fine silt, “the flour of rocks.” Thus, as it seems to me, we have more or less distinct evidence in the Carse-deposits of the Tay and Earn of marked geographical and climatic changes. Eeturning now to the Carse-accumulations of the Forth, we encounter very much the same appearances, but certain evidence is wanting. Thus we have not yet encountered any ancient buried forest underlying the Carse-clays of Ealkirk and Stirling, which can be considered as the equivalent of the buried forest of the Tay valley . But we have every evidence to show that an arboreal vegetation similar to that which now forms our forests, clothed the hill-slopes and valley-bottoms in the region drained by the Forth, at the time the Carse-clays began to form. We have proof also of torrential and flooded rivers, and of the wholesale destruction of trees. No geologist who has studied the Carse-beds of the Forth can doubt that those accumulations occupy an old valley, the bottom of which is under the present level of the sea. Nor does it take much imagination to picture to one’s self the conditions which must have of Edinhurgli, Session 1883-84. 755 obtained in the Forth district at the time when the buried forest of the Tay stretched away out to sea. In place of the flats of the Stirling and Falkirk Carse and the waters of the estuary of the Forth, we see a broad and gently sloping valley clothed with thick forests, through which the ancient Eiver Forth winds far away to the east, to mingle its waters in all probability with those of the Ehine, which at that time flowed northward through the area now covered by the North Sea. How long those conditions obtained we have no means of estimating, all one can say is that it was probably at or about that time that Neolithic man entered Britain. These geogra- phical and climatic conditions eventually become changed. Britain is insulated, and a cold, wet, and ungenial climate supervenes. The forests decay more or less rapidly, while marshes and bogs extend their boundaries. Local glaciers exist in some of our mountain glens, and flooded rivers carry seaward the trunks and branches of many a fallen monarch of the forest. The sea at this time washes the 45-50 feet level, and along the shores live Neolithic fishermen who revel in a molluscan diet, and now and again succeed in capturing a whale. Such, I believe, were the general conditions that obtained during the accumulation of the gravel and sand with drifted trees at Musselburgh. The peat and sand which overlie the tree-bearing beds belong to a much more recent time ; but whether they are older or younger than the 25 feet beach there is no evidence to show. I need hardly add that the deposits of the 45-50 feet beach are of post-glacial age, — being younger than the estuarine-marine deposits of the 100 feet terrace, — which latter, as I have shown elsewhere, must be classed as of late glacial age. 4. On a Special Class of Partitions. By Professor Tait. 5. Observations on a Green Sun, and Associated Phenomena. By Professor C. Michie Smith. 6. Analysis of the Principles of Economics. Part Y. — Psychological. By Mr P. Geddes. 756 Proceedings of the Royal Society 7. On a Singular Electrical Eesult. By Mr Harry Rainy. Commnnicated by Professor Tait. In order to observe the spectrum of coal gas at atmospheric pressure, I passed a stream of the gas through a tube open at both ends, and into the sides of which the platinum electrodes of an induction coil were inserted. I noticed that the spectrum gradually became narrower. On observing this, I stopped the current, and found that a filament of carbon had grown upwards from the lower electrode. On examining it carefully it appeared to have numerous short branches, all of which pointed in the direction of the electrode towards which the filament was growing. The time which it took to form between the electrodes was, I think, under two minutes. PEIVATE BUSINESS. A Ballot was then taken, and the following were elected British Honorary Fellows : — Professor E. Frankland, LL.D., F.R.S. ; William Huggins, D.C.L., LL.D., F.R.S. ; and Professor Burdon Sanderson, LL.D., F.R.S. The following were elected Ordinary Fellows: — David Alan Stevenson, Esq., B.Sc., C.E. j Sheriff Thoms; R. W. Mylne, Esq., C.E., F.R.S.; and William Evans, Esq., F.S.A. of Edinburgh, Session 1883—84. 757 Monday, 21st Jidy 1884. The Eight Hon. LOED MONCEEIFF, President, in the Chair. The President read to the Society a letter from M. Pasteur, Chairman of the Committee constituted for the purpose of erecting a Statue at Alais to the memory of Jean Baptiste Dumas. He intimated that the Fellows of the Society who wished to subscribe might send their subscriptions to the Librarian. 1. Observations on Coral Eeefs and Calcareous Formations of some of the Islands in the Solomon Group. By H. B. Guppey, M.D., H.M.S. ‘‘ Lark,” with Notes by John Murray, Esq. Communicated by John Murray, Esq. 2. Further Note on the Compressibility of Water. By Professor Tait. I had hoped to be able, during the winter, to extend my observa- tions to temperatures near the freezing point, but the lowest temperature reached by the large compression apparatus was 6°'3 C.; while the highest is (at present) about 15° C. From so small a range nothing can be expected as to the temperature effect on the compressibility of water, further than an approximation to its values through that range. The following table gives the mean values of the average com- pression per ton weight per square inch : — Pressure in Tons. 1. 2. 2i. 3. 4 6°*3 C. 0-00704 692 684 672 7°*6 682 670 660 ir*3 684 670 654 13°*1 666 648 637 15°*2 673 654 ... 633 These are all fairly represented by the expression 0*00743 - 0*000038 1 - 0*00015 p. 758 Proceedings of the Royal Soeiety where t is the temperature centigrade, and p the pressure in tons weight per square inch. This, of course, cannot he the true formula, hut it is sufficient for ordinary purposes within the limits of temperature and pressure above stated. It represents the value of With a new set of compression apparatus, very much larger and more sensitive than those employed in the above research, I have just obtained the following mean values for the single temperature 15° -5 C. Pressure in Tons. 1. 1|-. 2. 3. Fresh water, . 0-00678 663 657 638 Sea water, 0-00627 618 609 593 These are the values of ^ ; and they give, for the true com- pv^ pressibility at any pressure, and temperature 15° *5 C., the formulae. Freshwater, . . 0*00698(1 - 0*05 p) Seawater, . . . 0*00645(1 -0*05^) The ratio is 0*925, i.e., the compressibility of sea water at the above temperature is only 92*5 per cent, of that of fresh water. \_Added 28th October 1884.] With the notation employed {ante,^. 229), ^^^ = 0*000038/152 p being in atmospheres ; while we have e = {t - 4)/72,000. Hence U 0*000038. - Thus, for hp = \52 atmospheres, i.e., 1 ton weight per square inch, we have U= -2°*74 C. This agrees, in a remarkable and altogether unexpected manner, with the result 2° *7 C. obtained by direct measurement {ante, p. 228). of Eclinhurgh, Session 1883—84. 759 3. Critical Note on the latest Theory in Vertebrate Morphology. By Mr J. T. Cunningham, B.A. In the attempt to trace the vertebrate organisation by comparative anatomy and embryology back to a simpler state, the origin of the limbs has been made the subject of various hypotheses. Many years ago Gegenbaur brought forward a method of regarding the morphology of the limbs, by which each could be derived from a gill arch supporting a series of gill rays, from such a system as forms the skeleton of a gill in a typical Selachian of the present day. This comparison was instituted without any particular stress being laid on the relation of the ancestral vertebrate to invertebrate forms. He supposed that the central ray of the series in the branchia gradually grew more prominent, and as it increased in length the rays near it lost their attachment to the arch, and became articulated to the sides of the central ray : in this way he obtained an imaginary limb skeleton which he called the Archipterygium. This theory is usually supported by reference to the structure of the limb skeleton of Ceratodus. The shoulder girdle of this animal is an arch of cartilage more or less ossified, with the upper end of which the free limb articulates. This limb is composed of an axial rod of cartilage broken up into a series of short segments, and on each side of this cartilaginous axis a series of cartilaginous rays is situated : each ray articulating with one of the segments of the axial rod. In another Dipnoan, Protopteriis, there is a still more striking indication of the relation between limb and branchia. In this animal the shoulder girdle, as Wiedersheim pointed out, has a deeper position than it has in other fishes, a position in relation to the surface of the body similar to that of the branchial skele- ton. In the second place, the shoulder girdle of this animal bears throughout hfe functionally active external giUs j and thirdly, not only the shoulder muscles, but the whole limb as well, are innervated in great part by branches of the vagus nerve. On this hypothesis of the morphology of the limbs, the original position of the limb would have been such, that the plane in which it was expanded was vertical to the longitudinal axis of the body, as it is in Teleosteans and Ganoids. But in Selachians, although in adult life the plane of the limb in most cases approaches this 760 Proceedings of the Poyal Society position, in the embryo the limb grows out in a plane parallel to the axis of the body ; and as there is every indication that to the Selachians we must usually look for the most primitive condition of vertebrate organs, this is a strong argument against Gegenhaur’s hypothesis. Based on a study of the development of the limbs in Selachians, is the view of the morphology of the limbs advocated by Thacker, Mivart, and Balfour, and especially supported by the researches of the latter. According to this view, which like the branchial hypothesis of Gegenbaur, makes no attempt to bring the supposed original condition into relation with the organisation of any invertebrate form, the two pairs of limbs in fishes are the speci- ally modified remnants of a longitudinal fold, which originally ran along each side of the body, and was similar in structure to the median folds from which the unpaired fins are derived. The em- bryological facts which support this view are briefly thus. In Selachians the first rudiments of the paired fins appear as slight longitudinal ridge-like thickenings of the epiblast similar to the rudiments of the unpaired fins. There are two such ridges on each side — one anterior behind the last branchial arch, one posterior on the level of the cloaca. In most Elasmobranch embryos, especially in Torpedo, they are connected by a line of columnar epiblast cells, which very soon disappears. The presence of this connecting ridge is suggestive of the original continuity of the two fins, on each side. As the fin grows out mesoblast extends into it, and in the mesoblast appears embryonic cartilage, which breaks up into a longitudinal series of rays, and these are continuous at their base with a longitudinal bar termed by Balfour the basipterygium. From the anterior end of this longitudinal cartilage there pass off an upward and a downward process, which form the rudiment of the limb girdle. The longitudinal bar may be due to secondary development, the series of cartilaginous rays being the primitive part of the fin which is thus reduced to the same structure as an unpaired fin. The pelvic fin in a Selachian never departs much from the primitive ar- rangement, the only alteration being that the basipterygium segments between the anterior and succeeding ray, and the posterior end of it segments off as the terminal ray. In the pectoral fin the changes are more extensive : the basipterygium is rotated outwards from the body until it forms the posterior border of the limb, and constitutes 761 of Edinburgh, Session 1883-84. that part of the adult fin called metapterygium by Gegenbaur, and then becomes segmented off from the pectoral girdle articulating with its hinder edge. The propterygium and mesopterygium are merely the anterior part of the original basipterygium which divides into two pieces, articulating directly with the pectoral girdle. Thus the metapterygium is the homologue of the basal cartilage of the pelvic fin. It is obvious that the facts of the development dis- covered by Balfour are absolutely incompatible with Gegenbaur’s view of the origin of the limb from a branchial arch and its rays. According to Gegenbaur’s view, the limb of Ceratodus is the most primitive form, and the metapterygium in the Elasmobranch corresponds to the central axis in Ceratodus, the posterior rays having disappeared. The development of the fins in the dog fish shows that the metapterygium is the basal part of the fin grown outwards, and could never have borne posterior rays. In the earliest sketch of the genealogy of vertebrates put forward by Dr Dohrn in 1875,* he also maintained that the vertebrate paired limbs originated from gills, not gills constructed on the plan of those of a fish of the present day, but branched tree-like giUs resembling those of living annelids, such, for example, as those of Arenicola piscatorum. He supposed that special muscles first became separated from the dermo-muscular tube, in order to move the gills for the sake of more efficient respiration that then the gills began to be used as locomotive organs ; and finally, when respiration was confined to the anterior giU slits, two pair of these gills were preserved, and com- pletely changed into locomotive organs on account of the suitability of their position for keeping the equilibrium of the cylindrical body in the water. The assumption in this view, that a limb was originally a process of a single somite of the body, could not well be main- tained in face of the facts of the structure and development of the fins of fishes. In Elasmobranchs it is obvious that a lateral fin be- longs to several somites of the body, not to a single one. Balfour found that the muscles of a limb in an embryo Elasmobranch were derived from buds of several muscle plates, that is from several somites. In a recent paper f on the orgin of the paired and unpaired * Ursprung der WirbeltMere, Leipzig, 1875. + “Studien zur Urgeschichte des Wirbelthierkorpers VI.” Mittheil. aus der Zoologisdien Station zu Neapel, Band V. Heft 1. 762 Proceedings of the Boy at Society fins of Selachians, Dr Dohrn abandons his former view, and gives a detailed account of the origin of the musculature of both median and paired fins. He confirms Balfour’s statement of the origin of the musculature of the paired fins from buds of the muscle plates, and extends the same to the unpaired fins, He also shows that muscular buds, similar to those which form the muscles of the pectoral fin and pelvic fin, are given off in those myotomes which belong to the part of the trunk between these, but afterwards atrophy. This fact confirms Balfour’s view, that the pectoral and pelvic fins were originally continuous. He then shows that muscle buds similar to those which form the muscles of the pelvic fins are given off behind the anus, forming a continuous series with those belonging to the pelvic fin ; and that from these the muscles of the anal fin are derived. From this, he argues that the anal fin has been formed phylogenetically from the ventral coalescence of two lateral folds continuous with those whose remnants form the pectoral and pelvic fins. The reason why coalescence has taken place posteriorly, and not in the region anterior to the anus, is that the gut has disappeared from the posterior end of the body, and not from the anterior pre-anal part. The gut is shown by the existence of the embryonic post-anal gut to have originally extended to the posterior extremity of the body where the original anus was, while after the formation of the present anus, a secondary structure, the posterior part of the gut disappeared, and then by the reduction in size of the ventral part of the tail, the two lateral folds were brought together and formed the median ventral fin. He further shows that the musculature of the dorsal median fin arises from muscle buds given off on each side from the dorsal ends of the myotomes, and con- cludes from this, since similar ventral buds form two lateral fins, that the dorsal fin was also orignally derived from the coalescence of two lateral fins. The effective cause for the coalescence here was, in his opinion, the folding over of the original flat plate of the central nervous system to form a canal. Going one step further back, he supposes each of these four lateral folds, composed as they are, of buds from successive segments, to have been originally a series of separate processes ; and then he points out that we have an animal similar to an annelid, each segment bearing a pair of notopodia, and a pair of ventral neuropodia. of Eclinhurgh, Session 1883-84. 763 To trace the supposed transformatiou in the reverse order, it is thus. The original annelid-like ancestor first of all changed its position in locomotion, so that its nervous system became dorsal instead of ventral. Then, by the folding over of its median nervous plate to form a tube, the two series of neuropodia were brought together, coalesced, and formed the dorsal fin of the fish. The animal having obtained a new anus some distance from the end of the body, the posterior part of the intestine disappeared, being no longer funtional; and by the consequent reduction of this part of the body, the posterior part of the two series of notopodia coalesced in the median line and formed the anal fin. Anteriorly the successive notopodia united in two separate regions to form the pectoral and pelvic fins, and in the intermediate region disappeared. In the course of my observations on the development of floating Teleostean ova, carried on in the month of June last, I was im- pressed with the incompatability of Dohrn’s ingenious theory, with the existence of a pre-anal ventral median fin in the larvae of one species. The larvae in question were hatched in the Scottish Marine Station at Granton, from transparent floating eggs obtained by means of a fine tow-net in considerable numbers, about 50 miles east of the Isle of May. I do not know at present to what fish the ova belong, but as the ova and embryos are well characterised, they may be identified at some future time with eggs taken from some ripe adult fish. The yolk in both the developing ovum and the hatched larva is extremely pellucid, and divided into separate por- tions with polygonal outlines : there are no oil-globules in the yolk, the notochord is composed of a single column of vacuolated cells in the formed embryo, and in the larva the anus is situated at some distance from the yolk-sac and close to the posterior extremity of 764 Proceedings of the Boyal Society the body. The newly- hatched larva is 3 mm. in length. A larva with these characteristics is described by Von Hensen in the fourth Eeport of the Commission zur Untersuchung der Deutschen Meere in Kiel, part ii. ; the species is there also left undetermined. The relation of the ventral median fin to the anus is not discussed by Von Hensen. This relation is as follows, and is shown in the woodcut. The median fin extends continuously along the median dorsal line round the end of the tail to the anus, and passes continuously from thence to the yolk-sac, having about the same breadth throughout. There is no break in the fin at the anus, as the latter opens on the edge of the fin, the terminal portion of the intestine projecting downwards from the trunk. There is at least one other Teleostean larva in which the prim- ordial median fin has exactly the same relations to the anus and yolk-sac as in the larva just described. This second case is that of the herring. The existence of a pre-anal portion of the median ventral fin in the herring larva was pointed out by Dr C. Kupfier* in 1878, but he includes it in his general description, laying no particular stress on it.f Balfour, in his Corny. Embryology, although he refers to Kupffer’s work, has overlooked this fact in the structure of the herring larva, making the general statement that in the young Teleostean the ventral fold of the median fin ends anteriority at the anus. It is uncertain whether there are other Teleostean larvae in which the same state of matters obtains, and I do not know at present what relation the development of the pelvic fins bears to the ventral median fold in the two cases mentioned. On the two occasions, when I had the undetermined larvae above described in the laboratory, I was unable to keep any alive for more than six days after hatching. At the end of that time the pre-anal ventral fin was still unchanged, and no trace of pelvic fins could be seen, * Laichen u. EntwicTclung des Ostsee Herings, Berlin, 1878. t Having carefully studied the development of the herring in the month of August, 1 can fully confirm Kupffer’s description of the newly-hatched larva. The proportion of the length of the body through which the pre-anal ventral fin extends is considerable, the whole length of the larva being 5 *2 mm. , while the length of the pre-anal fin is 2 ’5 mm. The larva of the herring is closely similar to the first larva described above ; it is quite transparent ; the yolk consists of separate spherules, and the notochord has but one column of cells. {Note added Sept. 19, 1884.) Vol XII. PI, VIII No. 11. ce smoothed and holes on surface 25 ft. breadth. 8 ft. ' E HILL (BUTE) Section 430 Ft. WEST. W. Sc A.K Joinstoii, Edinburgh i London No. 5. No. 4. SOUTH * b;-'" ^ o No. 5. # 4^^ - .. ^-. Il ■W. ScA.K JoMstDTi, Edm'burgli S London. ISLAND OF COLL. No. 43. Fig. 2. c c? is a section of the part of the hill on which the boulder rests ; a 6 is a cliff about 30 feet, nearly vertical ; 6 c is a shelf on which the boulder rests ; c t/ is a steep ledge of rock against wliich the boulder abuts at its east end. It there rests partly on rock, partly on small boulders. Fig. 2. An enlarged vieto of the Boulder to shotv position and blockage W- Jcfimston, Edni'liurfli 6 Ltmdjon. V _ V'.' ft, : of Edinburgh, Session 1883-84. 765 although the pectoral fins were present as horizontal folds with a - semicircular outer border. It is obvious that unless the pre-anal ventral fin in the cases mentioned can he explained as a secondary arrangement of certain Teleosteans (a supposition which is not rendered more probable by the fact that the herring is a physostornous form with pelvic fins in their original position), its presence forms an obstacle to the universal application of D ohm’s theory ; and a re-examination of this most interesting subject is necessary in view of the facts I have pointed out. From Dohrn’s point of view the coexistence of functional intestine and median ventral fin in the same part of the body is impossible. 4. Tenth and Final Eeport of the Boulder Committee ; with Appendix, containing an Abstract of the informa- tion in the Mne Annual Eeports of the Committee; and a Summary of the principal points apparently established by the information so received. (Plates VIII. to X.) The Committee are of opinion that it is now time to submit a final Eeport to the Council. Xine Annual Eeports have already been presented, extending altogether to about 400 pages, as printed in the Proceedings of the Society. The appointment of the Com- mittee took place in April 1871, and the first Eeport was presented in April 1872, by which time a considerable number of answers were received to circulars sent by the Committee, first to the parochial clergy, and next to the parochial schoolmasters, asking for information. The Committee do not expect that, by continuing inquiries on the lines available to them, much additional information of importance would be obtained. At all events, it is now desirable to arrange the information which has been obtained, in such a way as to make it more readily accessible — as, for example, to show, in what dis- tricts the most interesting Boulders are situated, and also to indi- cate the conclusions which the positions of the Boulders, or any markings on them, suggest. 766 Proceedings of the Royal Society Before, however, explaining the means which the Committee have agreed to adopt for classifying the information obtained, the Committee think it right to record, in a few sentences, the circumstances which led to the appointment of the Committee. The subject of the transportation across the country of masses of rock by some natural agency, has from a very early period been discussed in the Eoyal Society of Edinburgh. In the year 1812, Sir J ames Hall, the Society’s President, was the first to break ground, by reading a valuable Memoir, afterwards published in the Society’s Transactions. The subject was from time to time again brought before the Society by different Fellows, — whose names merely may be mentioned, — viz.. Principal James Forbes, Professor Fleming, Professor Mcol, Mr James Smith of Jordanhill, Mr Charles Maclaren, Mr Bobert Chambers, Eev. Thomas Brown, and Mr Milne Home. The facts brought forward in this way, of course, were only such as happened to have been noticed in particular districts by individual observers. But as it was known that the distribution of Boulders was universal over Scotland, not only on the Mainland, but on the Islands of the Hebrides, Orkneys, and Shetland, it was felt, in order to pave the way for a complete discussion, that inquiries of a more comprehensive character were desirable. In the year 1870, Mr Milne Home received a communication from Professor Favre of Geneva, stating that an inquiry of this character had, with the co-operation of the Swiss Geological Society, been commenced in Switzerland; that the Geological Society of France had resolved to follow the example ; and he expressed a hope that Mr Milne Home, who he heard had taken some interest in the Boulder question, would endeavour to institute a similar inquiry for Scotland. Mr Milne Home submitted this correspondence to the late Sir Eobert Christison, and he having expressed approval of Professor Favre’s suggestions, Mr Milne Home read a paper in the Society, embracing his correspondence with the Swiss Professor, and sug- gesting the appointment of a Committee, with power to make the requisite inquiries. Such a committee was shortly thereafter (April 1871), on the motion of Sir Eobert Christison, appointed by the Society’s Council. Altogether about 1500 circulars were issued by the Committee; answers to a considerable number of which were, in the course of the of Edinburgh, Session 1883-84. 767 following year, received. About one half of these answers supplied information, which gave materials for the two first Keports. Most of these answers were useful also, by indicating the localities of remarkable Boulders, and thus enabling members of the Com- mittee to visit them. In recording the information from time to time obtained, the Committee could do no more in preparing the Annual Eeports than mention the particular county where the Boulder was reported to be situated. The consequence is, if any one wishes to discover what or where are the Boulders, described as occurring in any particular county, he must hunt through the whole nine Annual Reports to obtain this knowledge. In order to remove this inconvenience, the Committee have framed a compendium or abstract of the whole information in these Reports, so as to represent for each county, in alphabetical order, what is said in them regarding Boulders. This abstract will be found in Appendix I. In addition to a geographical arrangement of the information contained in the Annual Reports, it occurred to some members of the Committee, that it would be useful to have a Summary of the most material facts found in the Reports, and of the inferences which these facts suggest, in so far as they seem to throw light on the question, by what agency Boulders could have been trans- ported. Such a Summary has been undertaken by the Convener, and it forms Appendix No. II. This Summary consists almost entirely of the facts set forth in the Annual Reports and in Appendix I. ; but the inferences from these facts involve opinions in which all persons may not agree. Therefore the Committee do not commit themselves either to the adoption or to the rejection of these opinions, though they quite allow that they are valuable as indicating points worthy of consideration. The Committee, whilst aware that their business was to investi- gate the subject of Scotch Boulders, have not deemed it any departure from the objects of their appointment to advert to well authenticated cases of Boulders situated in English counties, which have been on good grounds traced to parent rocks in the south of Scotland {Abstract^ pp. 796, 797, 838, and 852). The bearing of this discovery on the direction of Boulder 768 Proceedings of the Royal Society transport, both, in England and in Scotland, is very obvious, and will no doubt be noticed in the forthcoming General and Einal Eeport of the British Association Boulder Committee. It may here be right to remark, that the appointment of the English Boulder Committee, which took place at the Meeting of the British Association at Edinburgh in August 1871, was at the instance of Professor Archibald Geikie, who, in advocating the appointment, remarked on the importance of extending to England and Ireland the inquiry, which had already commenced in Scotland. The Convener learns from the Rev. Mr Crosskey, Chairman of the English Boulder Committee, that his Committee intend soon to frame an Abstract of their nine Annual Reports. These Einal Reports, embracing the most interesting discoveries on this subject in England and Scotland respectively, may, it is hoped, throw new light on a subject of much geological interest. David Milne Home, Convener. Edinburgh, ‘lith June 1884. of Edinburgh, Session 1883-84. Y69 APPENDIX I. Abstract of Information in the Nine Annual Reports of the Committee, Aberdeenshire. Aberdeen, Toivn of. — In excavating for foundation of house in Union Street, a boulder of syenitic granite, with hornblende crystals, found 6x5x4 feet, weighing about tons. The under surface of boulder covered with ruts, all parallel with longer axis, some o them 3 feet long. Longer axis pointed E. and W. No rock like that of boulder nearer than Belhelvie, 10 miles to north, or Huntly, 40 miles to X.W., or Ballater, about 40 miles W.S.W. Dr Cruick- shank having, in July 1870, got notice of the boulder, made it known to late Professor Xicol, who caused it to be split, and the striated part set up in court of Marischall College {First Report, p. 21, and letter to Convener from Dr Cruickshank). A syenite boulder 5 x,3 x feet, with, striae parallel to longer axis, built into a wall in King Street Road. In Aberdeen newspaper of November 1881, account given of granite boulder, weighing about 8 tons, at the east end of Urqiihart Road, found in excavating a bed of sand. Mounds and ridges of shingle and gravel, all water rolled, abound north of . Aberdeen, near shore. Large boulders of trap, granite, and gneiss rest on top and surfaces of these ridges. Foreran. — In a field on Drums Farm, a huge granite boulder, called The Grey Stone,^^ measuring 54 feet in circumference, with a height of 7 feet above ground. Another block, also apparently a transported mass, measures 78 feet in circumference, and projects 6 feet out of ground. A little to the north of Drums, on one of these gravel ridges, lies a boulder, 8- x 5 feet. A layer of red clay about 9 inches thick, overlies the gravel. Boulder rests on gravel, but clay over the gravel encircles its base {Seventh Report, p. 39). Ballater. — Morven Hill, 2963 feet above sea, is situated a few miles north of Ballater, It stands many miles apart from any hill 3 D VOL, XII. 770 Proceedings of the Royal Society of like elevation. Boulders of granite, quartzose gneiss, and laminated quartz lie on western brow of mountain and up to summit. No granite rocks occur in situ in Morven. Bocks there consist of greenish hornblende and white felspar (^Seventh Rejport^ p. 40). Belhelvie—^lQmiio, boulder about 8 feet in diameter, called “ Kepjple Stonef near public school. Bocks in situ^ near boulder, are granite [First Report , p, 21). Several greenstone boulders (supposed to be Druidical) — called “ Altar Stone f v/eighing 18 tons; “ Bell Stanef weighing about 20 tons; Wallace's Putting Stone f 24 feet in girth; and other two, called Piper's Stone" and Maiden Stone," Boddam.—^Qsre the Bullers of Buchan stands the Hare or Qleft Stone, a granite boulder 9x8 feet, which marks boundary between parishes of Cruden and Peterhead. Another granite boulder, in a ravine, 14x8x5 feet; another 18 X 12 X 5J feet ; another 13x9x5 feet. Along the south side of Peterhead Bay, and as far as Buchan Ness, the shore strewed with blocks of granite, gneiss, trap, and sandstone ; many of them com- posed of rocks not found nearer than 20 or 30 miles [First Report, p. 23, and Second Report, p, 20). In Boddam Dean, a granite boulder called The Hanging Stone," 37 feet in girth and 27 feet over it. Half a mile east, another of 20 tons. Huge granite boulder, called the “ Grey Stone of Ardendr aught," was broken up in the year 1779 to build walls of a new parish church. It was the stone on which All Hallow fires" used to be lighted {First Report, p. 2), Braemar,- — There is a hill close to village named “ Cairn~a- reaching an elevation of 2700 feet. Near the top of the hill, viz., about 70 yards to the north, lies a block of coarse granite 12 feet long, with many other boulders of the same kind. The rocks of the upper part of the hill consist not of granite, but of quartzose gneiss. Opinion expressed by Mr Jamieson of Ellon, that the large block, and many of the others near it, came from mountains to the north, the granite of which is identical with that of the boulders. In letter to Convener, Mr Jamieson mentions that, near shooting lodge on this hill, there is a cluster of four or five immense granite boulders touching one another [First Report, p, 22, and Seventh Report, p, 41). Ben Uarn More forms the culminating peak of the great ridge of Edinburgh, Session 1883-84. 771 that divides the shires of Aberdeen and Perth, reaching to a height of 3587 feet. Mr Jamieson found blocks of a peculiar porphyry on the northern slope of the hill, near the top ; but no such rock exists there in situ. The rock of the hill is quartz (Ibid.). Chapel Garioch. — Boulder 19 x 15|- x 11 J feet, weighing about 250 tons. Longer axis E. and W. The boulder differs in composition from rocks adjoining. It rests on drift. Legend, that thrown by Devil, from Bennachie Hill, which is situated to H.W. {First Report, p. 22). Cidsalmond. — Boulder of blue gneiss, feet high x 5|- feet in girth, known to archaeologists as the Newton Stone, having on it Ogham and other very antique inscriptions [First Report, p. 24). Kemnay. — Seven large boulders of gneiss, whilst rocks adjoining are granite. The largest weighs about 380 tons. Most of them lie on hill-sides facing W. and W. The gneiss hills of Bennachie and Cairnwilliam from which these boulders are supposed to have come, are situated towards W.H.W. and H.W., distant 6 or 8 miles. The valley of Don is between these hills and the boulders. On Quarry Hill, situated not far from these boulders to north, rock stria tions show movement from west [First Report, p. 24, and Second Report, p. 148). To the S.E, of the above boulders, another bluish-grey granite boulder called Soutads Stone,^^ weighing about 270 tons. Height above sea about 500 feet. Lies in muddy sediment, on a hill-side facing IST.W. A hill, running H, and S. for 500 yards, lies to H.W., about a quarter of a mile distant, and with ridge about 100 feet above boulder. If boulder came from H.W., it must have been carried across top of this hill (which is very improbable), or else have come round one end, and have been carried by an eddy into its present position [Second Report, p. 148). Striations on rocks here show movement from W. New Deer. — Many boulders from 1 cwt. to several tons in weight lie in a sort of line for more than a mile south from farm of Green of Savoch, as far as to the hill of Coldwells and Toddlehills in * For speculations regarding the inscriptions, see Trans. Soc. of Scottish Antiquaries, for years 1862 and 1882. Mentioned in last paper, that another gneiss boulder of much same size stands near, with figure of a serpent on it, barred with the Z -shaped sceptre symbol. Added that Culsalmond parish abounds with relics of paganism. 772 Proceedings of the Poyal Society Ellon parish. In this parish formerly, a rocking stone called “ The Muchle Stane of AuchmcdiddieS A (so called) Druidical block formerly on Culsb Hill (Pratt’s Account of Buchan, 1858). On Whitestone, Ellon, andDudwich Hills, chalk flints found abundantly [First Reyort^ p. 25). Towie. — Block of unhewn granite, reaching a height of 7 feet above the ground, on north side of river Don, near bridge. Supposed to be Druidical i^First Report, p. 25). Cruden. — Granite boulder measuring 37 feet in girth and 27 feet over it, supposed to be Druidical. Another weighs 20 tons. Another huge granite boulder, on which said, that All Hallow Fires ” used to be lighted [First Report, p. 22). Ellon. — Several boulders, one 22 x x 8J feet, and another still larger, which have come from W. or W.H.W. [First Report, p. 24). Glass. — Several large boulders differing from adjoining rocks, more than 1000 feet above sea. 1, Hotes by Mr T. F. Jamieson, Ellon (from Quarterly Journal of London Geological Society, 7th Feb. 1866) : — (1) On coast, south of Fraserburgh, there are several localities where the rocks are smoothed and striated in such a way as to show a movement over them from 40° FT. to 60° W. (2) In the neighbourhood of Peterhead (at Invernettie Brick- work), many boulders of red and grey sandstone, and also of a tough greenish coloured stone, all which resemble rocks that occur in Caithness, but not in the adjoining parts of Aberdeenshire [First Report, p. 29). (3) At King-Edivard, ‘Hhere are deep masses of unstratified pebbly mud of a dark grey colour, very hard and firm, containing stones (some of which are ice- worn and striated), and fragments of shells, which are likewise occasionally scratched. It is like the Caithness drift in every respect.” — “ Besides this coarse stony mud, there are some beds of fine stratified sand, which often contain remains of shells in considerable abundance, most of them broken, but many of them entire.” — “ There is another bed of fine dark grey silt, free from stones, containing arctic shells entire, and apparently in situ, with the epidermis on.” The Tellina calcaria occurs here of large size, with both valves connected by the ligament and shut. of Edinburgh, Session 1883-84. 773 Argyleshire. Kintyre. — (1) At Southend, and also along east coast, south of Camphelton, the Convener saw and examined a number of boulders of a whitish-grey colour, which the schoolmaster considered to he granites, adding, that he knew of no rocks of that nature in Kintyre. The Convener found pebbles of same rock in gravel pits at Camphelton, and was there informed that rock of same nature occurs to the north of Camphelton, Professor Kicol of Aberdeen, when he visited Kintyre, saw these boulders, and thought they had been transported from Arran, where there is rock of the same kind ; in which case, they must have travelled 25 miles across the deep hollow of Kilbrennan Sound in a direction from K.E. {Quarterly Journal of London Geological Society, voL viii. p. 422). About a mile to east of Camphelton, smoothed rocks occur, dipping or sloping K.KW. — as if smoothing agent had come from that quarter {Sixth Report, p. 5). (2) Near Kilhenzie^ a few miles west of Camphelton, a hill reach- ing to a height of from 500 to 600 feet, is covered with drift, and (on its western slopes) with gneiss and mica slate boulders, several weighing above 150 tons. Old Eed Sandstone rock on west eoastj covered with drift ; and on the drift, boulders of granite and gneiss. Diagram given in Sixth Report, representing these on a bank sloping down N.N.W. towards sea, at angle of 25°. A boulder of gneiss found lying on mica schist strata, blocked at south endj its longer axis lying N. by E. and S. by W. Boulder said to have come from north {Lithograph No. 1, Plate VIII.). In a fissure of the mica slate strata on the sea- shore of west coast near Tangy Burn (the fissure running N Wa and S.E.), a boulder of hard gneiss, weighing about 1 5 tons, has fallen into the fissure. It presses on S^W. wall of fissure, showing that the boulder had pro- bably come from some N. or N.E. point. Fissure about 6 feet wide. A chip of one of the granite boulders found on west coast, having been submitted to Professor Heddle, he said that it was a peculiar variety, well known in the Mourne Mountains in the N.E. of Ireland, on account of there being frequently in it crystals of topaz. In the chip from Kintyre, sent to him by Convener, the Professor found two topaz crystals. 774 Proceedings of the Royal Society Loch Long. — On ridge (about 350 feet above sea), between this Locb and Garelocb, there are several boulders of mica slate. Largest 11x6x6 feet. The rocks in situ are clay slate. Longer axis in most is N. by E., parallel with Loch Long valley. Two of boulders blocked at south ends. In the Gareloch, on east beach, a little below Shandon, a gneiss boulder 18 x 15 x 12 feet (240 tons), with sharp end pointing E.W. At that end, surface is smooth — at south end, surface is rough. In Third Boulder Report (p. 5), reference made to an account of the grey granite boulders seen by the late Charles Maclaren, amount- ing in number to several hundreds, one weighing 30 tons. Mr Maclaren inferred that these had all come from N.N.W. The opinion of Dr Robert Chambers and Sir Roderick I. Murchison also referred to. On east side of the loch, opposite to Ardentinny, gneiss boulder called “ Jenny Meullensf weighing about 380 tons, lying jammed in a gorge formed by rocky banks of a rivulet {Lithograph Ho. 2, Plate YIIL). Seemed from position to have come from north {Third Boulder Report, p. 1). Another gneiss boulder 12x8x8 feet, with longer axis H.W. by H. Strite on rocks adjoining run H. 2° or 3° W. The smoothed surfaces of rocks dip towards north. On Loch Goil, above Carrick Castle, gneiss boulder called Clach Udalain^’ {i.e>f^ Stone unstahle^^), at height of 1526 feet above sea, lying on clay slate (about 300 tons) {Lithograph Ho. 3, Plate VIII.) {Tim'd Report, p. 2). Loch Goit and Loch Long, junction of. — “ Giant Pidting Stone,” resting on smoothed rock 450 feet above sea. Rocks smoothed only on north aspects {Lithograph Ho. 4, Plate VIII.), Knap Farm, — Several boulders lying on similarly smoothed rocks {Lithograph Ho. 5, Plate YIIL). Glen Finnart. — Gneiss boulder about 7 feet high, 824 feet above sea, called “ Pulag,” — butted against a rock at its south end. Reasons given why this boulder and others of smaller size appear to have come from north. Firth of Clyde. — At Dunoon, Kirn, Innellan, Toward Lighthouse, and Loch Striven, there are numerous boulders, many of large size on and near the shore, some of them with local names and legends. They differ from adjoining rocks. of Edinburgh, Session 1883—84. 775 On east side of Firth, near Gourock, immense numbers of blocks, on or near the shore, belonging to rocks situated to the N.W. in the districts about Loch Goil, Loch Eck, Loch Fjme, and Inveraray. — Among the rocks around Glasgowf 1881, by Dugald Bell, p. 152.) Hear Loch Glashan (400 feet above sea) smoothed and striated rocks, dipping down H.H.E, covered with boulders, apparently brought from H.E, where an opening among hills, towards Loch Awe {Sixth Report, p. 9) {Lithogra'ph Ho. 6, Plate VIII.). East Loch Tarbert, — -About 2 miles H.W. of the town, a conical hill, whose top is 710 feet above sea, well clustered with boulders, as shown on annexed woodcut. Very summit of hill has one reniark- BoUklers on Hill, East Tarbert, Kilityre, able boulder on it, 8 feet high and 5 feet each v/ay in width. The boulders are all gneiss, whilst rock of hill is day^^slaie. This hill separated from adjoining hills, which form a sort of amphitheatre round it, at a distance of about a mile. The boulder has the fanciful gaelic name of Gopel Cloiche, mean- ing Stone Mare. Between the above-mentioned hill and the village of Tarbert, on south side of road, there is a lower hill, also conical, having two large boulders on its H.W, slope. Convener did not reach them to examine them. On hills adjoining East Tarbert village on the south, at from 280 to 300 feet above sea, there are marks of some violent agent having 776 Proceeclmgs of the Royal Society swej^t through, the valley (now a sea loch) from westward {Eighth Report, pp. 4, 5). On one of hills on north side of sea loch, and sloping down towards loch, a boulder found at height of 400 feet above sea. Boulder 7 x 5 x 3J. Boulder apparently brought from S. or S.W. {Ninth Report, p. 3). Crinan Summit level between Loch Fyne and Crinan Bay, about 150 feet above sea. At summit level, a ridge of rocks which present smoothed surfaces on north, but rough surfaces on south side of ridge. On both sides of ridge there are boulders, but ten times more on north than on south side. Boulders are a syenitic gneiss, the rocks in situ a shivery clay slate; dipping steeply towards south. Three or four boulders are butted or squeezed up against ridge on north side, apparently obstructed by ridge in their further progress southwards {Seventh Report, p. 4). Ardchattan, — Granite boulder 14x12x6 feet. One rut on its top running whole length. Height above sea 57 feet. Hearest rock of same nature is on Ben Breac, 3 miles eastward. Near boulder, a ridge of sand and gravel running 1|^ miles {Reporter, Captain White, R.E.).* Loch Fyne. — Near Loch Gair, a boulder 23x17x12 feet of coarse gneiss (286 tons), lying on a knoll of gravel in an amphitheatre surrounded by hills. Its longer axis N.N.E. and S.S.W. Inveraray. — Boulder of porphyry, pointed out to Convener by Duke of Argyll, at height of 1000 feet above sea. Boulder of coarse Conglonlerate in same district, from 700 to 800 feet above sea, which probably came from westward, where rocks of Conglomerate are situated {Fourth Report, p. 10). On summit of range of hills separating Loch Fyne and Loch Awe, about 1800 feet above sea, the rocks present a well-rounded and * Whilst these sheets are being printed, the Convener has had the pleasure of receiving a communication from W. Andersoti Smith of Ledaig (Argyleshire), enclosing for perusal and inspection a Memoir by him entitled Benderloch Boulders, along with fifteen sheets of Illustrations.^’ Beriderloch is the name of the district in Argyleshire situated between Lochs Etive and Creran, and in which the highest point is Ben Breac, 2338 feet. Mr Anderson Smith, in his letter accompanying the Memoir, mentioned that as it is intended to be read during the present session of the Glasgow Geological Society, he wishes it returned after the Convener has perused it, unless he wishes to bring it before of Edinhurgh, Session 1883—84. 777 smooth surface. Direction of abrading forces there is from N.N.E. Eemarked that, “ in this case, glacier action impossible ; ” and that apparently the peak had been a rocky islet, on which floating ice- bergs drifted. “On some of the lower ridges, towards Loch Fyne, there are remarkable examples of large blocks of granite perched upon the very summits, in positions which it is impossible to suppose them to have attained, by any other means than by transportation upon ice ” (Duke of Argyll, Proceedings of Royed Society of Edinhurgh^ vol. hi. p. 457). Loch Awe. — (1) About a mile south of Port Sonnachan, a perched boulder of compact gneiss, 13x12x6 feet, stands on a narrow ridge of soft mica schist, in a peculiarly precarious position. Its longer axis and S. Its height above sea 1026 feet. Sides of hill to the ridge, so steep, that Convener could with great difficulty climb up to the ridge. There being no higher hills near, supposed that boulder could have come only by floating ice, and from north, where there is the greatest opening {Lithograph No. 7, Plate VIII. {Sixth Report, p. 8). (2) On hills to eastward, about 900 feet above sea, the slopes facing north are well covered by boulders. The largest, 18x10x10 feet (130 tons), has its longer axis lying N, and S. {Sixth Report, p. 10). Brander^ Pass of. — On its east side two terraces, at 68 and his colleagues of the Boulder Committee, and that the Convener is free to refer to the paper in any way. The Convener thinks very highly of Mr Anderson Smith’s paper, and especi- ally of the illustrations. But he does not feel justified in detaining it, as the meetings of the Glasgow Geological Society for the present session will prob- ably soon terminate. The great value of Mr Anderson Smith’s illustrations may be judged of even from the mere titles of a few of them. (1) Granite Boulder (12 to 15 tons), a few feet from the top on northern face of a hill over Loch Creran; greatest diameter 10 feet N.W, and S.E. ; smallest end N-W. (2) Boulder on Table land, below the above (10 tons); N.W. and S.E, ; smallest end N.W. (3) Black Granite Boulder (10 tons) ; greatest diameter 8 feet, lying N.W. and S.E. ; smallest end N.W. (4) Grey Granite Boulder, over Barcaldine Gardens, 400 feet above sea, 19 X 12 X 7 feet ; longest axis N.W, and S.E. (5) Grey Granite Boulder, 300 feet above sea ; 13 x 7 x 5 feet ; longest diameter N. and S. (6) Ardchattan Boulder (mentioned in this Committee’s Report) is in one of the illustrations represented as partly buried in moss, and weighing about 50 tons. 778 Proceedings of the Royal Society 120 feet resj)ectively, above Loch Awe, with several boulders on each [Fourth Report, p. 9). (3) Eemarks of a general nature (p. 11) applicable to boulders at Dalmally and Tyndruni. (4) Boulder 24 x 11 x 7 feet (136 tons), resting on a gravel knol on south bank of Loch Awe, at Kaim (west of Port Sonnachan). Boulder in a meadow surrounded by steep hills on all sides but one, viz., the West (Sixth Report, p. 11). Between Port Sonnachan and Kaim, rocks smoothed and striated, seen on road side. On the island of Innisdraiodhnich (Druid’s Isle), in Loch Awe, a large boulder was reported to Convener by Mr Muir, the proprietor, but Convener was unable to visit the island (see notice in vol. vii. p. 226, -of Transactions of Society of Scotch Antiquaries). Ardrishaig — on Loch Gilp, a branch of Loch Fyne. On hills above town, boulders and striated rocks, suggesting transport from north ; and in one case, transport through a lateral valley from N.W. [Sixth Report, p. 12). On Auchendarroch lands, two large boulders seen, with N. and S. axis, lying on a hill slope facing S.Ei, at a height of 300 feet above the sea. Ascending to a higher levels where hill slope faces K.N.E., several boulders found, of sizes not so great as the above. All these appeared to have come from northern points. Aeh-na-briach (Field of Spots), near Loch Gilphead, visited to see sculptured cup or ring markings on smoothed rocks. Bock surfaces evidently smoothed by natural agency. They are in different parts of field. All slope down at angle of 10° or 12° toward.s S.W.' One small boulder seen on west side of rocks, as if intercepted by rock in its progress eastwards. Difl&cult to say how or from what direction smoothings effected. May have been by heavy mantle of ice, sliding over rocks from hills to N.E. The concentric ruts are numerous, and of various diameters and depths, some even 2 feet across. The straight rut issuing from centre and across circular ruts, generally, though not always, follows downwards slope of rock [Ninth Report, p. 10). Loch Kille&pori. — A little to west of Ormsary House, on the shore, three very large boulders of gneiss, two weighing respectively of Edinhm^gli, Session 1883—84. 779 106 and 300 tons. Two have longer axis pointing N.W.j the other with sharpest end pointing W.S.W. About a quarter of a mile east of Ormsary House, a boulder, from which part at west end broken off. Before being broken, size was 52 X 36 X 20 feet, containing about 2770 tons lying on drift at the foot of old sea-bank, whose base is about 40 feet above seadevel. In this part of coast an immense number of other boulders of different weights up to 400 tons, some touching or lying on others. They are mostly on slopes facing westward {Lithograph I7o. 8, Plate VIII.) (Sixth Report^ p. 14, and Ninth Report^ p. 4). Valley of Auchloss, about 2 miles to east, shows smoothed rocks. The direction of valley is E. and W*; the direction of striae W. by N. In Baronlongart Valley, running and W. between Ormsary and Achloss, rocks ground down and smoothed, evidently from westward. A few boulders in valley. (5) Glach Briach Hill (Stone Spotted Hill), about 400 feet above sea, well covered by boulders^ many very larger Some so placed as to show they had probably come from N. W, Bounded on H. W. and rough on S.E. ends. Apparently all of same description of rock as “ Big Boulder ” before mentioned, a compact fine-grained gneiss. Kocks of hill, a soft schist, and on edge (Diagrams in Ninth Report, p. 4). Fragments broken off S.E. ends of several large boulders, by some natural agency. Two large boulders, 17 x 8 x 8 feet and 18x10x10, touching one another in such a way as to show that the last which came probably came from N.W. Loch Sweyn — an arm of sea 10 miles west of Lochgilphead. (1) At Keill, on north side of Loch, at mouth, several granite and gneiss boulders lie on the shore, and on slopes facing Jura Island, Kocks in situ, are dark coloured Silurian. (2) In Carig Bay, near Lochgilphead, in north Knapdale parish, a boulder is on a hill slope facing H.W. and Jura Island. (3) At Loch Mhurrich, a boulder 36 x 15 x 13 feet (520 tons), resting on a knoll of drift, in a meadow, surrounded by low hills j * This boulder, first made known to Convener by Mr Campbell of Islay, who stated that it is the largest boulder he had seen or heard of in Scotland. 780 Proceedings of the Boycd Soeiety which are also well coated with boulders. Its longer axis, W.S.W. Its west end, 5 feet thick vertically; its east end, 12 feet thick vertically, must have come from westward, by an opening in the hills in that direction {Sixth Report, p. 16, and Ninth Report, p. 7). (4) hJ’umerous small lateral valleys opening on Loch Sweyn, the sides of which coated with boulders, these sides sloping down chiefly towards and facing W.NiW. (5) Kilmory Bay. — Eocks smoothed and striated, with large boulders lying close at hand — their longer axis generally W.S.W. {Seventh Report, p. 10, and Ninth Report, p. 9). The smoothed rock surfaces here dip down towards S. by E., South, S.S.E., and S.E. Where the rock slopes down S.E., the surface is not striated, only smoothed. The rock has been most severely striated on its surface sloping down S. and S. by E. Some of the striae more deeply cut at one end than at the other, viz., at their west ends, where some as much as 3 inches wide. The striating agent had therefore moved from W. by S., or from due West. Portions of the smoothed surface were broken into small cup- shaped hollows, containing hard pebbles firmly compacted, — probably samples of the tools which effected the striations (see Ninth Report, p. 9, and Lithograph ISTo, 11, Plate VIII.), The hill to the east consists of a ridge running about E. and W., and rising to a height of about 600 feet. Its north flank slopes steeply down towards Loch Sweynj and is covered by boulders in immense numbers, and some of great size. The hill slope faces down N.N.W., but almost all the boulders lie with their longer axis pointing W.H.W. About half a mile farther east, on a much steeper part of this hill slope, there is a cluster of huge boulders, the uppermost lying on the rest in such a way as to show it must have come from the west- ward (see Ninth Report, p. 10, and Lithograph ISTo. 10, Plate VIII.). Taynish. — (1) A large assemblage of boulders lying on rock of shore near Taynish House (property of Captain Campbell of Inver- neil). Largest 18x11x8 feet, lies on broken edges of vertical strata. Longer axis lies W, by S. ; and its narrowest end points west. There is another boulder 19x15x5 feet ; its longer axis H.E. and S.W. Greatest number of boulders lie on rocky slope facing north- westerly. of Edinburgh, Session 1883-84. 781 Several other large boulders near Taynisb House reported, but not seen. (2) On each side of road to Ardrisbaig, many boulders observed ; — occupying cbiefly nortb-westerly bill slopes. (3) Hear Crinan Canal at Ballanach, about J mile from canal, at 300 feet above sea, boulder, 16x9x9, on north side of valley. It lies on bared rocks. Its longer axis coincides with axis of valley, viz., S.W. by S. {Ninth Report, p. 8). Humbers of large boulders lie on bills to eastward, cbiefly on slopes facing H.W. — (Diagram given in Ninth Report.) (4) Dana, Island of — On the shore of this island, forming the Dana Boulder, north bank of Loch Sweyn^ and nearly opposite Castle Sweyn, there is on the shore a boulder weighing from 70 to 80 tons (see prefixed woodcut). Hs sharpest end is towards west, and longest axis parallel with the axis of the loch {Seventh Report, p. 12). On the south bank of loch here, there is a projecting mass of rock on which Castle Sweyn has been built. On the west side of this rocky mass, a number of boulders lie, as if intercepted by the rock in their progress from the west. The narrowest part of the Loch is here ; so that on this account there is the more probability of blockage having, occurred at this point. Oban and Neighbourhood. — (1) Grey granite boulder 12x8x6 feet at Dunolly. Nearest granite rocks are on Loch Etive, to east- ward, but doubted whether of same variety. The boulder is at foot of a cliff of Conglomerate rock. (2) A mass of Conglomerate rock above the town, well rounded. On the side facing H.W. the hard pebbles are all ground down ; on east side the pebbles of the rock are rough. 782 Proceedings of the Pioyal Society (3) Qhan.^Ki soutli end of town, there are cliffs of old conglome- rate roch, from which blocks have been carried southwards and are strewn on a meadow to a distance of from 100 to 200 yards from the cliffs {Semnhh Pejyovt^ p. 4). A plan given to show where these boulders situated, many being on hill slopes facing N. and INAV. These boulders are mostly all grey granite. On the hills, near Professor Blackie’s cottage, there are several large grey granite boulders on slopes facing N. and N.W. On small island in Oban Bay, several grey granite boulders, so situated, as to show transport from north [Seventh Reyort^ p. 7). On the farm of Dunbeg, near Connal Perry, a boulder of grey granite lying on rocks of clay-slate, in a position showing transport from iN’AY, [Seventh Report, p. 8). At Dunstaffnage, about 5 miles N.E. of Oban, the rocks smoothed in such a way as to. suggest movement over them of an agent from eastwo^rd, viz., down Boch Etive, Along the shore, up towards Loch Awe, there a^re rocks sinrilarly smoothed, as shown on the annexed woodcuts. WEST. EAST. Eocks smoothed from Eastward in Loch Etive. (4) At Lailt,” a dark porphyry boulder called Clach-a-CurraiV^ [i.e., perched houlder), from its precarious position. Differs from all the rocks in district. Eemains of a granite boulder also here. (5) Glenlonan. — Several boulders, at heights of from 1600 to 1700 feet, of various kinds of rooks. Boulders are on both sides of summit level, but the greater number are on slopes facing the north, and the smoothed rocks also chiefly face the north. (6) Loch Etive. — At Airde Point, many boulders on slopes look- of Edinburgh, Session 1883-84, 783 ing up towards Loch Awe and Ben Cruachan, as if brought by glacier ; but they might also have come from north by floating ice, Kocks on south shore of loch, above and below Connell Ferry, showing smoothings, strongly indicative of glacier from head of loch. Angular grey granite boulder, 11 x 9x 7 feet, above Bonawe Ferry at Innerlievern, (7) Kerrera, Island (/, ---Numerous grey granite boulders on beach at north end of island ; so placed, as to show transport from the north. Granite boulders with red tinge, found on Ballimore farm at from 350 to 440 feet above sea; but no granite rocks on island. Nearest place where such granite known is at Morven, about 12 miles across the sea to the north. The Mull granite said to be different. On the farm of Bod-na-BoJc, about 20 boulders seen by Convener, all granite except one, (8) Easdale. — ^Many grey granite boulders lying on blue clay slate rooks. Supposed to have coine from Mull Island, it being nearest place for such granite ; and no obstruction in that direction. One clay stone boulder of a purple colour was found -said that rock of this character exists to the south, (9) Ben Cruachan ascended to height of 2725 feet. Until contour of 1335 reached, few boulders seen. Above that, very numerous on N.W. shoulder of hill. Towards N.W. less obstruction to trans- port, than from any other quarter. Towards W,N.W and N.W. no hills, but those in Mull and A,rdnamuinhan, distant 30 to 40 miles. Boulders are of red and grey granite. The sizes of four or five of largest given, The rocks of Cruachan, where these boulders lay, are chiefly a red granite. Longer axis of boulders and rock s trim, generally point N.W, At heights of 334 feet and less, rocks appeared to have been smoothed from W.S.W., as if by glacier from Loch Awe. Above that height, the direction of the strim is N.W. by N,., N.N.Mh, and W.N.W,, the last being most persistent in the highest parts of the hill. Borne of these Cruachan boulders lie on beds of gravel, up to a height of 2000 feet (Fifth Report, p. 48), Lismore, Island o/,-— Boulders of granite, red and grey, lie on the Limestone rooks. Old sea terrace well marked on island. Appin^—Ow the shore of Linnhe Loch, two granite boulders, one 784 Proceedings of the Royal Society 20 X 18 X 11 feet (292 tons), the other 15 x 11 x 10 feet (122 tons), differing from adjoining rocks, which are clay slate {First Report, p. 26). Loch Creran. — At Fasnacloich, boulders of black granite, two of 380 and 280 tons respectively. The boulders have their sharpest ends pointing towards mouth of Loch Creran, viz., to S.W. The rocks in situ are different. Chips from these boulders having been submitted by the Convener to Professor Judd (Kensington Department), he identified them as similar in composition to rooks seen by him in Skye, Mull, and Ard- namurchan. It appeared to him that the Appin boulders, before mentioned, were the same in composition as the Fasnacloich boulders. Professor Judd stated, that these Loch Creran and Appin boulders are not granites, but ‘Crocks of a basic composition, — a gabbro with some black mica” {Fourth Report, p. 11). At mouth of loch, rocks smoothed (when facing W.N.W.) up to about 70 feet above sea. About a. mile higher up loch, smoothed rocks face W.S.W. at height of 80 feet above sea. Near sea level, smoothing seemed due to, some force moving down valley. Pocks at a higher level seemed to. have been smoothed by force moving from. K.Wo^ In Glen Creran most of boulders lie on drift At one place boulders form a cluster on a rocky knoll. Statement by Mr Hall, an intelligent residenter, that a trainee of boulders is traceable from Glen Creran through Carroban Pass, situated on S,E. part, of Glen Creran {Fifth Report)^ Ayrshire. Granite boulder II x 7 J x 5 feet. Longer axis N. and S. There are four more boulder.s, weighing respectively 4, 8, and 1 2 tons, and form n line running K. and S. Legend that King Coil dined on large boulder {First Report, p. 28). Dailly. — rGranite boulder about 36 tons on Killochan estate, called “ Baron’s Stone,” about 100 feet above sea. Lies on Silurian rocks ; various other granite boulders south of Piver Girvan, on hill slopes. One on Maxwelton Farm, contains 240 cubic feet. Another on top of Barony Hill above Lannistane, 1047 feet above sea {First Report, p. 28). of Eclinhurgli, Session 1883—84. _ 785 Doune Loch. — Two miles south of, granite boulder called “ The Kirhstanef 25 x 20 x 12 feet (444 tons), so called because used as a pulpit for preaching from {First Report, p. 29). Girvan. — Thousands of granite boulders and some whinstone boulders, for miles along the shore near Turnberry Point. Kocks in situ are sandstone. Nearest granite rocks are in Arran. Along coast 4 miles south, in a ravine, two. boulders of altered greywacke ; one weighing 180 tons, the other 100 tons {First Report., p. 29). Kilwinning. — On Misk Farm a pit was sunk for coal through boulder clay. Boulder of dolerite and a flint nodule found, at depth of 23 feet from surface. Flint was inches in diameter and 21- inches thick. Dolerite was; water-worn and roughly scratched. A flint nodule found on Inohlonaig, an island in Loch Lomond, in boulder clay, with arctic shells (Letter to Convener from Rev. David Robertson, Glasgow, dated 10th November 1876)."^ Mayhole. — Granite boulder, flat and oblong, on slop© of hill above River Doon, on Auchindrane, at height of 230 feet above sea, known as Wallace’s Stone, from tradition that a rude cross now carved on it represents his sword [Notes of cases from Dailly, Girvan, and Mayhole, sent by Professor Geikie] {First Repo-rt,. p. 29). Ardrossan. — Near Hunterston on the shore,, boulder of grey com- pact granite 11 x 6 x 5J feet and 20J feet in girth, opposite to great Cumbra© Island and about 12 miles from Arran {Second Report, p. 149). On the shore about 2 mRes to^ N.W. of Ardrossan^ the ^^Boyd- stone'' boulder of porphyry, about 19 x 19 feet (about 320 tons), on property belonging to Mr Alexander. Rocks here are Old Red Sandstone, Boulder partly buried in mud of the shore, but about 9 feet in height visible. Two other boulders on Mr Alexander's property, one of them even larger than the foregoing, — -of gneiss {Second Report, p. 149, Third Report, p. 3). Stinchar YaMey.. — Boulder of claystone a cubic yard in size lies near hamlet of Pouaidland. Seemed identical in mineralogical * In voL vi, part 2, of Glasgow Geological Society’s Transactions, pp. 186- 190, notices will be found of flint nodules found on various other pa,rts of the Ayrshire coast. VOL. XII. 3 E 786 Proceedings of the Royal Society character with rock of Glassal Hill situated to H.E., and also with rock on shore to west at Bennane Head (Sixth Report, p. 33). Culmonelh — Half a mile to north, at height of about 200 feet above sea, a dolerite boulder 27 x23xl2 feet (552 tons), its longer axis and S. It lies on till A small boulder, apparently a frag- ment of large boulder, lies to the south (Sixth Report, p, 33). Another boulder of dolerite, which had been 21x21x10 feet (326 tons), with longer axis and S.; — -now rent into fragments. Query. — Did boulder break by falling from a height? Rendalfoot. — A little to north, an Old Red Sandstone Con- glomerate boulder 8x6x6 feet It is undistinguishable from the Conglomerate rock of Wemyss Bay, situated about 30 miles to the north (Sixth Report, p. 33). Beith. — On Cuifs Hill, consisting pf porphyry, there are on its north sicle many small granite blocks which must have come from the west or H.W, (1) Mr Robert Craig of Beith, in several papers read before the Geological Society of Glasgow (Trans., vol. iv. parts 1 and 2), divides the boulders in the north of Aryshire into two classes. One class con- sists of rocks foreign to the district, viz., Old Red Sandstone, granite, quartz, gneiss, inica of chlorite, schists, and clay slate. These he thinks were transported from mountains in the N.W., distant from 50 to 70 miles, by drift ice and marine agency. The other class he derives from rocks situated to the K.E, and at no great distance, transported by land ice. (2) Messrs Crosskey and Robertson also sent to the Glasgow Geological Society (Trans., vol. iv. part 1) an account of boulders of great ske, and in large numbers, found in excavating new docks at Greenock, The great majority of the larger boulders are sandstones of the neighbourhood the remainder are of quartz, mica schist, &c., from the Argyleshire mountains to the H.W. (3) Mr Robertson, in the Glasgow Geological Society’s Transac- tions, 19th Jan. 1877, gives an account of large boulders, covered with Balani and Serpulw, in a bed of sandy mud 18 feet deep, con- taining also nodules of flint, The conclusions he drew from the boulder being covered with marine zoophytes was, that after being so covered, they had been lifted up by shore ice and transported to their present position. of Edinburgh, Session 1883—84. 787 Banffshiei). Banff. — Between Banff and Peterliead, beds of glacial clay, similar to that of Caithness, aiid probably drifted from thence {First Report, p. 29). Near Peterhead, many boulders of granite and trapj one of these of a greenish colour, not known in situ in AherdeeD shire, hut occurs in Caithness (Jamieson, Lond. Geol. Soc. Jour., xxii. p, 272)^ Boyndie. — Hypersthene boulders found along shore for some miles. Supposed to have come from rocks to S.E. {First Report, p. 29). Fordyce. — A line of boulders through several parishes in a S. and N. direction. They are a blue whiustone. In Ordiquhill parish, so close as to touch. Height above sea 500 feet {First Report, p. 29). Beewiceshirbj Berwiclc. — On Castle Terrace, boulder clay excavated for water pipes. Many boulders found in clay bed, of granite, gneiss, lime- stone, blue whinstone, greywacke, &c., all rounded. The granites showed two varieties, grey and red. Nearest granite hill is Cock- burn Law, about 30 miles to N.W.j — -nearest blue whinstone in rock, is about 25 miles to west {Second Report, p. 149). Berwick. — About half a mile to north of the town, four boulders pointed out to Convener by Captain Norman, RN., on side of a road leading to Halidon Hill, The boulders are each ftom half a ton to a ton in weight. Two are of fine grained granite, — one grey in colour, the other with a shade of pink. The other two boulders are a dark porphyry; — the nearest locality for which is Lambertoh Hill, situated about 2 miles to N. and N.N.W. {Seventh Report, p. 13). Burnmouth. — Near railway station, in a gravel bed over greywacke rocks, a well rounded block of pinkish granite found by Convener. He sent a chip to Mr Macdonald, granite worker, Aberdeen, He answered that it was a rare variety of granite, He knew of its existence in situ, only at Kincardine O’Neil (Deeside) and about Ballatar and Braemar, in the form of boulders, and as a rock in the Island of Uist (Hebrides) {Second Report, p,- 149), Coldstream. — A block of white chert limestone, about 4 feet square, very irregular in shape, found in a gravel bed at the Hirsel (the Earl of Home’s). 788 Proceedings of the Royal Society The only place where rocks in situ of this nature found, is on the opposite, ^.e., the south side of the Tweed, at Carham and Nottylees, distant from Hirsel 3 or 4 miles, and bearing W. by S. {Second Report, p. 150). Duns. — On farm of Cockburn, 2 miles of Duns, a boulder of mica schist, from 2 to 3 feet in length and breadth, lying at base of a steep hill facing the south, hlo mica schist rocks in Berwickshire, or nearer than the Grampians {Second Report, p. 150). Foidden. — Several small boulders of coarse syenite, lying onOldEed Sandstone, composed of red felspar, black hornblende, and small flakes of mica; largest boulder is 5 x 3 J x 2 feet. Sharpest end points N.W. Nearest hill where similar rocks occur is Cockburn Law, 8 miles to N.W. {Second Report, p. 150). Greenlaw. — At Marchmont (residence of Sir Hugh Hume Campbell) about 930 feet above sea, a blue whinstone boulder 9 J x 5 x feet, with faint striae on top, parallel with longer axis. Rocks in situ. Old Red Sandstone. Nearest whinstone rocks are in Gordon parish, 5 miles to west {Second Rep)ort, p. 150). Gavinton. — Boulder clay 10 to 12 feet deep, covered by beds of gravel and sand, in some places 12 feet thick. In the clay, the boulders composed of rocks recognised as occurring in situ in localities W. by N., as at Kyles Hill and Dirrington, — these hiUs being from 3 to 6 miles distant {Fourth Report, p. 20). Ayton Parish — Several small boulders of grey granite, 270 feet above sea, on Whitfield farm. Nearest granite hill, Cockburn Law, 10 miles W.N.W. Near Ayton Castle, pieces of coal found in deep bed of sand, about 200 feet above sea. Coal strata occur in Mid-Lothian on north side of Lammermuir Hills, 40 miles to N.W. {Sixth Report, p. 17). Coldingham Parish. — On Cocklaw Karm, well rounded masses of hematite ore found, turned up by plough, at height of 500 feet above sea. Nearest place where hematite known is in East Lothian, about 30 miles to N.W. On the same farm, blocks of white sandstone found, which is not known to be in situ nearer than East Lothian {Sixth Report, p. 17). On the rocks near Coldingham Loch, and at St Abb’s Head, the striae on the lochs show a movement from N. by W. (Ed. R. S. Tr., vol. xxvii. p. 36). of Edinhiorgh, Session 1883-84. 789 Cliirnside Parish. — On Oldcastle Farm, numerous boulders of grey granite, from one to two tons in weight and 300 feet above sea. Nearest granite hill is Cockburn Law and Stenchel, about 8 miles to N.W. {Sixth Report, p. 17). Edrom Parish. — At Blackadder, a boulder of blue whinstone on knoll of gravel, about 250 feet above sea. Nearest rock of same kind is at Hardens, 5 miles to N.W., which is 500 feet above sea. Hutton Parish. — In Paxton brickwork, blue whinstone boulder found X X 3 feet, weighing about 10 tons, with strise on one of its sides parallel with longer axis. Its longer axis N.W. by N., about 230 feet above sea. In that direction only there is whin- stone rock in situ, viz., Borthwick Hill, situated 12 miles to N.N. W., about 600 feet above sea» At same brickwork, in a bed of boulder clay, small boulders of red conglomerate, grey wacke, and chert found ; also the brick-coloured porphyries of Kyles Hill and Dirring- ton, situated from 14 to 16 miles to westward. The whinstone boulder taken by Convener into Paxton Policy for preservation. Blocks of same blue whinstone occur on adjoining lands of Broadmeadows and Sunwick. Blocks of a very peculiar crystalline greywacke, with cavities, and of a black colour, occur in Pistol Plantations (Edrom parish). The only locality in Berwickshire for this rock is in the channel of the Eiver Whitadder, east of Cockburn Law, at a distance of 12 miles N.W. Blocks of the same rock are found on the farms whicli lie between Pistol Plantations and Cockburn Law (Sixth Report, p. 18). Stitch el Parish, — Pebbles of Old Eed Sandstone lying on blue whinstone rocks at Stitchel Craggs, at 600 feet above sea. Nearest place where Eed Sandstone strata known is some miles to west (Sixth Report, p. 18). On west sides of those craggs, smoothed surfaces of whinstone dipping towards or facing W.N.W. (Sixth Report, p. 18). At Baillie Knowe in same parish, 300 feet above sea, a whinstone hill, with similar smoothed surfaces, fronting W.N.W. On Smailholm Craggs (3 miles west of Stitchell) at 570 feet above sea, rocks facing W.N.W. show striae by an agent moving from W.S.W. Earlston —Blocks of felspar porphyry, from Cowden- 790 Proceedings of the Royal Society knows Hill, strewed over muirs to east^ resting on Old Red Sandstone strata {Sixth Report^ p. 18)» Hume Parish, — Rocks on craggs there at 7 40 feet above sea, smoothed and striated in E. and W. directions {Sixth Report^ p* 19). (For other cases in Berwickshire, see paper by Mr Stevenson, in Berw. Nat. Club. Trans.., voh viii p. 20.) Mordington. — A block of very coarse-grained syetiite found near top of Halidon Hill, on a slope facing west, at a height of about 400 feet above sea. The only hill in Berwickshire where syenite rock occurs is the Stenchel, on east side of Gockburn Law, about 10 miles to W.X.W. The Convener submitted a specimen of the block to the late Mr Stevenson of Duns, who was a good geologist^ and well acquainted with Berwickshire rocks. He was of opinion that the block closely resembled a syenite which he had seen in Mull {Ninth Report, p. 11). Kaims. — In different parts of this county there are numerous examples of Kaims. One on Greenlaw Muir is continuous for nearly 2 miles. They are numerous also in the lower districts, and are there more or less parallel to one another, and to the general axis of the Tweed valley. The average direction near Kelso is K.E. by K. ; — in the east part of the county the average direction is E; 10° S. (Ed. R. S. Tr., vol. xxvii. p. 29)^ Buteshire. Big Cumbrde Island.— 'M.saiY boulders of mica schist lying on Old Red Sandstone rocks of island. Largest boulder seen 12x6x3 feet, with longer axis N.KE. lying in valley running N.N.E. at north end of island. Mica schist boulders occur also at S.W. end of island {Second Report, p. 151, and Sixth Report, p. 24). Little Cumhrae Island. — On highest part of island, about 400 feet above sea, rocks in situ (clay stone trap) sloping down towards K.W., have been smoothed by some heavy agent passing over them, from N. by W. Several boulders of Old Red Conglomerate found. The largest is about 5 feet square and rests on rock, with so small a basis that it can be rocked, known by the name of ^Hell Stane.'^ Rev. Mr Lytteil suggested to Convener that name may have been originally “ Beltane, on account of fires lighted on it in Pagan times. Close of Edinburgh, Session 1883—84. 791 to this block there is another Conglomerate boulder of smaller size, with an ancient cup-shape hollow on its surface, apparently artificial, 4 inches in diameter and J inch deep. Height above sea 190 feet (Sixth Report, p. 25). No Old Red or Conglomerate ranks in island. Nearest are at To- ward Point and Rothesay, from 12 to 20 miles across the sea to N.W. Split Boulder f first mentioned by Smith of Jordanhill, visited. Lies at sea-level, on rocks much smoothed and striated, forming east side of a trough, axis of which runs N.E. by N. Some of the striae are continuous for 30 yards. Striating agent must have moved from due north (Sixth Report, p. 25). Ailsa Craig, a mass of white p.orphyry, reaches to a height of 1114 feet. At a height of 600 feet, on north side, there is a bed of clay mixed with sand of a red colour, derived probably from the debris of the Old Red Sandstone rocks of Arran, Big Cumbrae, Rothesay, and Toward ; — ^all situated to the N. and N.W. Pebbles of granite and quartz said to have been seen on the Craig (Sixth Boidder Report, p. 23), Arran, Island of. — (1) In Brodick Bay (East Coast), no boulders ; but along coast, to north and also to south, numerous and large boulders. Corriegill. — Boulder of grey granite, has longer axis and sharp end to N.W. Same kind of granite in Goatfell mountain, distant 4 miles bearing N.N.W. Another boulder, 12x9x8 feet, half a mile to north, has its longer axis N, and S. (2) Near Carrie, two large boulders of granite sit near each other on plateau or terrace, about 93 feet above sea. Largest may weigh about 620 tons. Longer axis and sharpest end point N. by W. Rock on which it lies is Carboniferous sandstone. These two boulders must have been carWec?,— there being no adjoining hill rom which they could fall. Goatfell bears from them W. by S., and is distant about 3 miles. By a glacier they could not have been carried, as they are not in a valley, or near any valley from which a glacier could have issued (Sixth Report, p. 21), (3) To the north of Corrie, about 2 miles, the road passes a large boulder on the sea-shore called the “ Catstane,^' whose weight is esti- mated at 362 tons. 792 Troceedings of the Royal Society Near this boulder there is a granite boulder, with a weight of about 212 tons, Its longer axis lies N. and S., the narrowest end being to the north, (4) There is another granite boulder on the old sea-beach, at a height of 12 feet above high water. It rests on Conglomerate strata, which dip towards the south. It is blocked at south end, by a knob of Conglomerate rock, which seems to have obstructed it in its progress from the north (see Diagram in Sixth Report^ pi. xix. fig. 5 j also Lithog^'apli No. 9, Plate VIII.), Many blocks of this Conglomerate Sandstone have been carried along the shore southwards ; — none found to the north. (5) On the hills west of Corrie there are rocks with striae on smoothed surfaces at a height of 158 feet above sea. The direction of the striae is N.W. and S E. On these hills, up to 587 feet above the sea, there are many boulders, — mostly of grey granite, and a few of Conglomerate. Between those hills and Goatfell there is a deep valley, well strewed with granite blocks, Most of them are rounded. On west side of valley, hill climbed to a height of about 1270 feet. One boulder attracted attention, being 23 feet long 9 feet wide and 12 feet high (184 tons). This, and many others, lay with longer axis N. and S, Its position showed that it had not fallen from any hill, and must have been cavried to its present site. (6) In crossing to. Loch Ranza, Convener saw to the south of the high road numerous ’‘’‘-gtevehed^^ blocks on the tops and ridges of the hills at heights of from 1503 to 2000 feet above the sea. He regretted not being able to examine them. They were most numerous on hill slopes facing N,W. The absence of boulders in Brodick Bay, whilst they abound along the shore to the north and south, invites special explanation. If a glacier descended from Qoatfell, boulders should have been numerous in the bay and valley leading up from it to Goatfell. If the boulders came on floating ice from the N, or N.N.E. they would be dropped along the east shore, and on the hill slopes facing the north. But they would be deflected from Brodick Bay, by a high ridge of rocks which comes down from Goatfell to the north of Brodick Bay {Sixth Report^ p. 22), (7) Beds of fine clay in south end of Arran (first described by uf Edmhiirgh, Session 1883—84. 793 Eev. Mr Watson) contain Arctic shells, sometimes in a broken or crushed state. This fossiliferous stratum is covered by a great thick- ness, of what Mr Watson calls hmlder clay, but which Messrs Bryce and Croskey call upper drift beds. The upper stuff also contains broken shells {Jamieson in paper published in Proceedings of London Geological Society of February 1866, p. 276). Bute Island. — East coast, north of Bothesay, examined, and a list of boulders found there given. They consist chiefly of schists lying on Old Pted Sandstone and clay slate rocks, — and must have come from the hills to the north {^Seventh Report, p. 14). Along west coast, north of Ettrick Bay, there are numerous boulders, also of schists, which show by their positions that they also came from north. Several of these boulders are standing on end leaning against rocks on their east sides (^Seventh Report, p. 16) {Lithograph No. 12, Plate YIII.). Barone Hill, situated about 3 miles S. W. of Rothesay, at a height above the sea of about 500 feet, has at its west end a rocky gorge with remarkable striae on sides, which indicate passage through gorge of a powerful current of some kind, hurrying through it from a northerly point, stones and rubbish. A diagram given of some of the striae, showing that they have been incised more deeply at north ends than elsewhere, in consequence probably of the pebbles becoming blunted by friction by being squeezed against the rock. This spot is referred to in a paper “ On Glacial Drift in Scotland,” by Professor Geikie, who gives it as his opinion that “ the abrasion (of these Barone Hill rocks) has been done by an agent, which came up the steep northern face of that eminence, went right over its summit, and pursued its course down into the next valley beyond. The striations (the Professor adds) run from N. 15° W. to N. 20° E.” {Seventh Report, p. 20) {Lithograph No. 13, Plate VIII.). Caithness. Dunnet. — Conglomerate boulder of small size, appaj.’ently from Maiden Pap Hill, 30 miles to south. Several large boulders in parishes of Olrich and Cannesby {First Report, p. 29). Thurso. — Near Castletown, large granite boulder. Between Wey- 3 F VOL. XII. 794 Proceedings of the Roycd Society darle and Stonegiin, several large Conglomerate boulders. Kev. Mr Joass, of Golspie, states that nearest granite and Conglomerate rocks in the county are situated in N.W. districts (^First Report, p. 30). Keiss Parish. — Conglomerate boulder 9x7x5 feet called “ Grey Stone.’' Longest axis W. by N. Differs from any rock in locality. It marked, where it stood, boundary between two parishes and two estates. It has lately been blasted into four fragments, of which three still remain {Eighth Report, p. 8). Mr Jamieson of Ellon, having examined Keiss Harbour, states that a bed of ‘‘drift,” 40 feet thick is there, the lower half of which consists of unstratified sandy mud, containing broken shells and stones, some of which are scratched. The scratches and grooves point K 35° to 40° W. Scrabster Harbour. — Mr Jamieson reports that here the boulder clay is more than 100 feet thick. It is charged with small stones more or less rubbed and scratched. He found in it fragments of shells. Wick. — Three boulders, each weighing from 20 to 30 tons. One is a Conglomerate, supposed to have come from hills 20 miles to south. But Rev. Mr Joass states that Conglomerate rock occurs to west- ward at less distance. Wick Bay. — Mr Jamieson found here a similar bed of boulder clay, containing fragments of shells and numerous large water-worn boulders of sandstone, quartzose, mica slate, and granite, on which glacial scorings are well marked. One granite boulder was 12 feet in length (First Report, p. 30, and Proceedings of London Geological Society, 7th February 1866, p. 265). In the same paper, Mr Jamieson states that in Caithness generally, the shells, as a rule, in the clay beds and drift, are broken. But exceptions occur. He himself found one entire valve of Astarte Borealis ; and he saw several entire specimens in local collections. He adds, that one of the objects he “ had particularly in view was to note the direction of the glacial markings on the rocks, and to ascertain whether they could be accounted for by a move- ment of ice proceeding from the interior of the country towards the coast. I therefore lost no opportunity of noting the bearings of of Edinburgh, Session 1883-84. 795 scratches whenever I saw them.” Mr Jamieson then gives the bearings at twenty localities in Caithness, from which he concludes that the movement had been from N.W. to S.E.; and he adds, that ‘‘ a movement of ice from IST. W. to S.E. across Caithness is totally at variance with the notion of the scratches having been caused by glacier action proceeding from the interior of the country towards the present coast.” In a footnote, Mr Jamieson adds, that “ the presence of marine organisms (in the Caithness drift), and the direction of the glacial striae, which indicate a movement from the N.W., where there is now nothing but open sea for an immense distance, together with the absence of moraines, are all suggestive of marine conditions having prevailed during the deposition of the Caithness drifts In year 1828, the late Sir Eoderick Murchison published a paper in Proceedings of London Geological Society, in which he men- tions that “ the highest hills in the Brora district afford, upon their sides and summits, distinct traces of a strong diluvial current, which has swept them free of covering matter, and deposited in the plain of Clyne, Milltown, a mass composed of the debris of the denuded hills. A large portion of the turf having been recently removed, the surface of the rock was seen to be scored with parallel lines. The direction of the markings is uniformly from H.N.W. to S.S.E.” Dumbartonshire, Luss. — On west bank of Loch Lomond, about 150 feet above sea, in channel of a brook entering Fruin Water, a mica schist boulder 28 X 18 X 7 feet (246 tons). Longer axis E. and W., with sharp end to west. Kocks adjoining— Old Red Sandstone. Nearest mica schist hills about 5 miles to N. and W. If boulder came from that direc- tion, it must have been carried across hills from 1000 to 2000 feet high. If it came from north, down Loch Lomond valley, it must, after coming so far, have changed its course and moved at right angles to westward to gain its present site (^Second Report, p. 153, Fourth Report, p. 20). On a moor, about half a mile to N.E. of the above boulder, there are several smaller boulders of mica schist, all with longer axis in similar direction, viz., east and west. On west side of Loch Lomond, at Arden, a low valley running 3 G VOL. XII. 796 Proceedings of the Royal Society up from loch, shows many small boulders, — their longer axis and sharpest ends pointing IST. W. {Fourth Report^ P-21, Sixth Report^ p. 6). On east hank of Loch Lomond, nearly opposite to Arden, at about 337 feet above sea, a grey granite boulder 5x4x4 feet, much rounded — lying on Old Bed Sandstone strata. Longer axis E. and W. ; — it had probably crossed loch, from west {Sixth Report, p. 7). In Cameron House Policy, gneiss boulder 6J x 5 x 5 feet, with longer axis N.W. and S.E, About 3 miles to S.W. of the south end of Loch Lomond there is a hill called “ Caer-manf reaching to height of 720 feet above sea. Rocks on top are a coarse porphyry. The rocks on western aspects are well rounded ; — on eastern aspect, the rocks are rough. There are huge fragments on east side of top, none on west side {Fourth Report, p. 21). Dumfriesshire. Kirkconnel. — Granite boulder, 7 feet in diameter, 20 to 30 tons, 700 feet above sea. Differs from adjoining rocks. Ho granite rock nearer than Spango Water {First Report, p. 30). Tynron. — Three whinstone boulders, each weighing from 20 to 30 tons, also several Conglomerate boulders ; — all have apparently come from H.W. {First Report, p. 30). Wamphray. — Large whinstone boulder {First Report, p. 36). Moffat. — Several large perched boulders near Loch Skene, at height of 1900 feet above sea — {Mr Ralph Richardson inferred that they were “ transported by a local, glacier ”) — {Seventh Report, p. 28). (See notes regarding these boulders, by Convener, in the Transac- tions of the Edinburgh Geological Society for May 1881.) Langholm. — In Wauchope valley, and also in bed of that river, granite boulder 16 x 11 x feet, weighing from 50 to 70 tons, lying on Sandstone rocks. Many others scattered about {W. Strachan Schoolmaster, Langholm). Cairnsmore of Fleet, a hill 2331 feet high, situated in Kirkcud brightshire; — composed of coarse grey granite. — “Boulders of Cairnsmore granite are scattered over the hills to the S.E. One is on the west face of the Nether Hill, at the height of 1100 feet, and 8 miles distant from its source ” {Survey of Dumfriesshire by Scotch Government Surveyors in Memoir, No. 9, p. 39). of Edinburgh, Session 1883-84. 797 {Extract from the Fourth Report of the Boulder Committee of British Association) : — Professor Harkness mentions a boulder of Silurian Conglomerate at the village of Bothal, North Cumberland, 20 X 9 X 5 feet. It is striated on its western side. It is between 400 and 500 feet above sea-level, and, in his opinion, was trans- ported from Dumfriesshire, having therefore travelled about 40 miles from N.N.W. Elgin. Dallas. — Many small granite boulders here, which are supposed to have come from Eoss- shire {First Report, p. 31). Duffus. — Conglomerate boulder 21 x 14 x 4 feet, longer axis N.W., on Eoseisle estate {First Report, p. 31). Llanbryde, St Andrews. — Gneiss boulder in bed of Old Spynie Loch, 15x9x7 feet, longer axis N.N.E. Neio Spynie. — Eour Conglomerate boulders lying on Old Eed Sandstone rock {First Report, p. 31). Rothes. — Six horneblende boulders lying on gneiss rocks. Dyhe. — NearDarnaway Castle, in the approach to, several granite and gneiss boulders from 2 to 3 tons. A kaim \ mile long, running N. and S. {Second Report, p. 152). Elgin. — Boulder called “ Carlin^ s Stone f on BogtonEarm, a coarse Conglomerate 230 feet above sea, with pebbles of flesh-coloured quartzite. About half a mile to N.W. another Conglomerate boulder, called “ Young Carlin's Stone." Hundreds of smaller boulders of granite, gneiss, &c., embedded in clay or sand, which seems to have been pushed or rolled, being all well rounded. Carden Hill has been ground down and striated. Direction of striae varies between W. by N. and N.W. Numerous boulders on ridge of hill, and on both sides of it. At several places on ridge, rocks broken up, and fragments pushed over southern slope. At one spot on Carden Hill, the N.W. striae crossed by others from N.E. Quarrywood Hill, composed of Sandstone rocks, has four or five large Conglomerate boulders on its N.W. slope. 798 Proceedings of the Royal Society Forres. — Conglomerate boulder on Upper Caliper Farm, about 44 tons, lies on bill-side facing Cromarty, which bears U.W. by FT. 10 miles across Moray Firth. Another Conglomerate boulder on same farm, much buried in drift. These boulders contain reddish quartzite pebbles. Forres to Nairn. — Extensive beds of sand and gravel, mostly stratified. Pebbles and boulders in these beds well-rounded; angular boulders chiefly on surface {Second Report, p. 155). Lossiemouth. — On old sea margin, Conglomerate boulders of same character as those in other parishes. In boulder clay over Limestone rocks, boulders of oolite found, which must have come from Koss or Sutherland. Portions of an oolite boulder seen by Convener, near DufFus Schoolhouse, 125 feet above sea. Conglomerate boulder, called “ Witch-stonef similar to all the others. Longer axis U.W., and sharpest end towards that quarter. Lies on bed of sand. On Clarkely Hill, hard sandstone rock forming a surface sloping down to W. striated from H.W. Several boulders of granite and gneiss on hill {Second Report, p. 155). Mr William Jolly, Inspector of Schools, Inverness, sent to the Committee valuable notes regarding the distribution and parentage of Morayshire boulders, which are given in Fifth and, Sixth Reports. He says — “ There would seem to be two varieties of Conglomerate boulders distributed through the ‘ Laigh of Moray. ^ ” One variety is a Conglomerate, containing ‘‘a dark purplish or liver-coloured quartzite, in pieces of considerable size.” Great rocks of it occur on both banks of Loch Hess, and especially in the hill situated on the north bank called Mealfourvonie, reaching to a height of 3060 feet. This rock breaks into cubical-shaped mosses, and probably has produced the remarkable boulders in the counties of Hairn, Moray, and Banff, known as “ GuUoden or Cumberland Stone f •' Tom Reoch,’’^ Clach-an-Oidhe^^ or “Stone of the Virgin,” 20 x 15 x 9 feet, close to Geddes Public School. Grey Stone in Caw- dor woods, — “ Clach-na-Calliach,” or “ Stone of the Witch,” — “ Glach-nan-Gillean or Bog’’s-stonef and various others. The other variety of Conglomerate rock, found in boulders in the of Edinburgh, Session 1883-84. 799 same counties, “ consists of more angular components, and is entirely without the liver-coloured quartzite or porphyry j” Mr Jolly says that examples of it may be seen embedded in boulder clay at Links- field, near Elgin, and on the crest of the hill of Eoseisle. Mr Jolly adds that the boulders of this last-named variety of Conglomerate seem to have been transported at an earlier period than those of the liver-coloured variety, being generally embedded in boulder clay or drift, whilst the boulders of the liver-coloured variety lie more on the surface of the country. It is some cor- roboration of this view, that there are two sets of striae on the rocks, viz., from 6° S. of West, and 15° N. of West. The Con- glomerate boulders from the Loch Ness Hills may have come in the first-named direction ; — the other set of boulders, across the Moray Firth, from Ross-shire {Sixth Report, p. 48). Eifeshire. Balmerino. — Mica schist 12x9x8 feet (now destroyed) {First Report, p. 32). Crail. — Granite boulder 10x8x6 feet, “Blue Stone of Bal- comie,” close to sea, at East Neuk. Also trap boulder 12x8x8 feet {First Report, p. 32). Dunfermline. — Whinstone boulder 7 x 15 x 6 feet “The Witch Stone.” Leslie. — Kaim of drift 100 to 300 feet wide, 220 feet high, now cut through by a rivulet {First Report, p. 32). Newburgh, — Boulder of sienitic gneiss weighing 15 tons. Legend is, that it was thrown by a giant from Perthshire, viz., from North or N.W. West Lomond. — Boulders of Red Sandstone and porphyry lying on Carboniferous Limestone rocks {First Report, p. 32). Isle of May. — Small sienitic boulders on west side of island, seen by Convener. Rocks on west side, smoothed by an agency from W. J N. No boulders or smoothings on east side of island {Fourth Report, p. 22). Bogward Den. — Three miles west of St Andrews, a Conglomerate boulder. The nearest rock of same kind is Drum Garro Craig, situated some miles to N.W. {Fourth Report, p. 22). 800 Proceedings of the Royal Society Kincraig. — On beach, a granite boulder with girth of 2B feet and height of 4 feet lying on trap tuff. Portions of this trap tuff found in blocks 2 miles to eastward. Elie. — Whinstone boulder 8 x 4 x 2|- feet, with striae on its surface bearing N.W. Its longer axis H.W. {Fourth Report^ p. 23). East Lomond Hill, at height of 1075 feet above sea, a large number of dolerite boulders on west slope, and much rounded {Eighth Report, p. 28). Auchluishy Hill, one of the Ochils, at 1025 feet above sea, a small red granite boulder lying on a slope facing W.hT.W. On ascending Benty Knowe, directly opposite to Auchluisky Hill to the west, another red granite boulder found. The rocks of the Ochils here are trap, “ a rotting clinkstone.” Bendeuch, at a height of 2200 feet has on it two boulders, one of greywacke, — a peculiar kind, marked by nodules of white quartz, which is known by Professor Heddle to occur on the north spur of Ben Lomond, at a height of from 2230 to 2240 feet above sea. The same rock also occurs about 8 miles to the east of Ben Lomond. The other boulder is of gneiss, laminated and convoluted, like rocks occurring in the district of Loch Earn and Glen Ealloch {Eighth Report, p. 29). Oddis. — In Alva, Silver, and Tillicoultry Glens, there used to be many boulders of granite and mica schist ; but they have been all broken up for building purposes {Eighth Report, p. 5). Forfar. Airlie. — Bemarkable kaim running east from Airlie Castle 2 miles long {First Report, p. 32). Barry. — Granite, sienitic, and gneiss boulders on shore, and on raised beaches 11 and 45 feet above shore {First Report, p. 32). Benholm. — Huge granite boulder, now destroyed. It stood on apex of a trap knoll. In trap of this knoll are agate pebbles em- bedded, flattened on west side. Small hills scalloped by some agent which has passed across from west {First Report, p. 32). Carmyllie. — Granite or gneiss boulder lying on a height. Differs from rocks in situ, — supposed to have come from hills 30 miles to north {First Report, p. 33). of Edinburgh^ Session 1883-84. 801 Cortacliy. — Wliinstone(?) boulder, 13x10x8. Longer axis E. and AY., supposed to have come from trap situated to N.W. Mica schist boulder within Earl of Airlie’s park. Parent rock supposed to be 2 or 3 miles to hT.W. {First Report^ p. 33). Far7iell. — Boulder weighing about 12 tons. Supposed to have come 30 miles from N.W. Inverarity. — Two grey granite boulders from 2 to 5 tons. Kirkden. — Kaims of gravel and sand 440 paces long, running E. and W. Kirriemuir. — Granite boulders, both red and grey. Supposed to have come from Aberdeenshire. Several kaims of granite pebbles and sand on Airlie estate, running KW. and S.E. {First Report, p. 33). Liff. — Several boulders of mica schist, called “ Gows of Gowrie.^^ A Druidical circle composed of boulders {Fwst Report, p. 34). Menmuir. — Two large granite boulders, each about 35 tons, besides others of smaller size. Montrose. — On Garnock and other hills, striae on rocks point W. by N. obliquely across hill. On Sunny side Hill, blocks of red shale derived from rocks in situ some miles to N.W. {First Boulder Report, p. 34). RescoMe.—FLmSb slate boulder 13x7 x 7, near top of Pitscandly Hill, lying on drift. Eocks in situ are Old Eed Sandstone. Late Sir Charles Lyall was of opinion it came from Creigh Hill, about 17 miles W.H.W. Yalley of Strathmore lies between boulder and parent rock. There are also several hills higher than boulder be- tween it and parent rock {First Boidder Repo^d, p. 34). St Vigeans. — Gneiss boulder now destroyed. Supposed to have come from mountains situated to H.AY. If so, it must have crossed several ridges of hills and valleys. Kaim in the parish full of gneiss and granite boulders. * Haddingtonshire. Prestonpans. — A large basaltic boulder on the beach, known to the fishermen by the popular name of Johnny Moat,^^ in memory of a corpulent member of their class, who had formerly lived in the village. There being no basaltic rocks towards the east, the boulder must have come from the west {First Report, p. 18), 802 Proceedings of the Royal Society Linton. — (1) On Dry! aw Farm, a limestone boulder x 3J x 3 feet, met with in cutting a deep trench through boulder clay. The longer axis N.N.W. The FT.W. end more pointed than east end, also well rounded and polished by friction. Boulder tolerably flat on upper side, but no striae visible. On each of the two sides, meeting at N. W. end, boulder not only smoothed but striated — chiefly along side facing N.N'.W. The nearest rocks of same composition as boulder, are in Garlton Hill, about 6 miles distant, and bearing W. by H. (by compass). If agent which smoothed and striated the sides of the boulder came, as is probable, from the westward, it seems, when it reached the boulder at A C (its west end), to have divided into two streams, — Drylaw Boulder. one, A B, flowing along north side E.N.E., the^other, C D, along the south side S.S.E. The clay in which the boulder was buried, contained blocks and pebbles, some of them, soft (such as shale, coal, &c., from the west), and others, hard (rock or greenstone, granite, &c.), quite capable of smoothing and striating the boulder, if driven and squeezed against it by some agent of sufhcient weight and magnitude. (2) In the village of Linton, several portions of porphyritic rock recently exposed, which are smoothed and striated. On one portion of rock, the surface of which is horizontal, the direction of striae is W.H.W. and E.S.E. 803 of Edinburgh, Session 1883-84. On another portion, the surface of which slopes down towards north at an angle of about 35°, the direction of the strise is due E. and W. Each set of striae might he produced by the same agent. If its normal direction was W.N.W., it would, on striking the rock which slopes down north, he deflected into an E. and W. direction. (3) A still more remarkable case of the same kind occurs in a cutting of the North British Railway, about half a mile to the west of Linton station. The rock is on the south side of the line. The smoothed surface is about 18 feet high and 25 feet in Striated Rock' in Railway Cutting near Linton Station. length. The surface there slopes down northwards at an angle of from N. 11° W. to N. 20° W. The striae run across the rocky surface in a direction E. 15° N. — the deflection from the normal direction of the striating agent being greater here than at Linton village, on account of the larger area of the opposing surface. It may be added that, whilst in the lower part of the rocky sur- face, the striae are horizontal, near the top of the rock they rise up towards the east at an angle of 4° or 5°. If the striating agent consisted of a mass of drift, the pebbles and blocks in the lower part would move horizontally, and produce horizontal striae. But 804 Proceedings of the Royal Soeiety in the upper part of the mass, blocks and pebbles would not have the same weight above them to keep them down, and, in consequence of severe lateral pressure, they would have a tendency to rise. North Berioick Law. — (1) An account was given by Mr David Stevenson, C.E., regarding striations on the rock of this hill. In his paper read to Edinburgh Eoyal Society, 1st February 1875 (vol. viii. p. 481), he states that the west side of the Law consists of exposed rock, the east side being covered by gravel, clay, and stones. On a steeply inclined part of the hill, there is a surface of the rock, consisting of felspar porphyry, on which he found smoothings forming a sheet of about 200 feet in length, with occasional deep striae or scorings on it. He says — “ The grooving of the surface is very distinctly marked, and must have been done by the passage of some dense but yielding body, which could be moulded to the different irregularities, both vertical and horizontal, on the surface of the hill. The striae must have been made by the passage of sharp-pointed bodies, harder than the felspar porphyry of the Law.” “ As viewed from a little distance, the scorings appear to be nearly parallel and horizontal ; but on examining such as can be reached, I found, on using the clinometer, that this is by no means the case. On one patch of rock I found two striae within 1 8 inches of each other, the upper of which had a dip of 4°, and the lower a dip of 20°, and both markings were dipping towards the icest, being the directions from whence the movement came, as indicated by the ‘ tail ’ on the eastern side of the Law. This rise in the direction of motion may have been caused by local pressure, due to the obstruction offered to the passage of the mass by the Law.” Mr Stevenson adds, that “ the rock surface discovered by him had been entirely concealed by debris, till it was removed, to allow of the rock being quarried. A similar mass of debris extends along the whole northern and southern faces of the hill, and, if removed, I have no doubt similar markings would be found along both sides.” (2) The Convener of the Committee, thinking that North Berwick Law deserved a farther examination, proceeded to it, and gave the results of his examination in a paper read before the Eoyal Society of Edinburgh on 7th July 1879 (vol. x. p. 261). of Edinhurgh, Session 1883-84. 805 He found that the rock surface described by Mr Stevenson is situated on the H.W. side of the Law, and that the smoothed part slopes down towards the and H.W., at an angle of from 65° to 70°. Parts of the smoothed surface face H.W., other parts face due north, and some H. by E.; but wherever the rock faced a more easterly direction, there was no smoothing. The only parts of the smoothed rock surface striated were those fronting H.W. by N., or a few degrees on either side of that point. Their direction is W. by S., or W.S.W.j and most of them are apparently horizontal. Some of the ruts and striae, especially at their west ends, are deeply incised in the rock, showing the extreme and continuous pressure which predominated there. The particular direction in which the striating agent moved, may be inferred, by considering, that if it came in a direction 'parallel SOUTH North Berwick Law. with the rock surface, it might grind or smooth, but would hardly produce ruts or striae; nor would it have this effect, if it came against the rock surface at right angles. A line parallel with the rock surface, would be S.W., and a line at right angles would be about H.N.W. The intermediate point would be W.N.W. ; — from which direction therefore, (the Convener inferred) the striating agent moved on and against North Lerwick Law. 806 Proceedings of the Royal Society In the Convener’s paper a diagram was given, as shown by the foregoing woodcut, of a well-marked portion of the rock, where it slopes down towards N. 10° W. The striations are very distinct, running horizontally, towards E. 22° But where the rock surface slopes down 23° E., which it does towards the east, there are no striae, and the rock is only smoothed. (3) On the farm of Kingston, 2 miles south of North Berwick, the Convener found a small boulder of red granite. (4) A very large boulder of basalt stands on the beach, near Tantallan Castle, which could have come only from the westward. Hebrides. 1. Islay. — (1) Near Port Askaig, on Lossit Farm, four or five boulders of large size. One of these 13x8x8 feet, a composite rock, extremely hard, containing crystals of quartz, augite, and hornblende ; boulder resting on bed of bright yellow clay; rocks of district a slaty schist. Height above sea 300 feet. (2) On Arnahoo Farm, 3 miles N. of -Port Askaig and 228 feet above sea, porphyry boulder stands on summit of hill in a precarious position (pi. iii. fig. 8, in Fourth Report, p. 17) {Lithograph No. 14, Plate VIII. ). This boulder must have come from a direction N. by E., as explained in Eeport. Mull is in that direction. Boulder is of hard porphyry, quite different from rock of hill. (3) On Persihus Farm, about 3 miles S.W of Port Askaig, four or five boulders, well rounded ; all, a hard porphyritic rock, differing from any Islay rock. Their height above sea 228 feet. Towards N. by E. an opening among hills, through which these boulders might have been carried on floating ice. (4) On a hill, 2 miles north of Persihus, a boulder 18x12x1 feet, differing from adjoining rocks. Height above sea 410 feet. An igneous rock. (5) On south of turnpike road, between Bridgend and Port Helen, a large boulder lying at north base of a hill, which probably intercepted it iu its progress towards the south. (5) On west coast, in Kilchrenan parish below old parish church, several boulders, which apparently came from N.W of Edinburgh, Session 1883-84. 807 2. Colonsay. — Notes sent to Committee by Mr Murray of 167 West George Street, Glasgow, and Mr Donald McNeill, farmer in Colonsay, long resident in the island. The following points are taken from these notes : — (1) By Mr Murray. — Shores on west side of island thickly strewn with boulders, many resembling yellow Mull granite. A large boulder on west shore, called FingaVs Pvtting StoneS At Kiloran, on N.W. part of island, there are many boulders. On several ridges sloping down towards west boulders occur, some above a ton in weight (^Seventh Report, p. 21). On west coast there are some granite blocks of a yellowish-red colour, different from any rocks seen in Colonsay. In Oronsay Island there are blocks of syenite, which probably may have come from Kiloran Bay in Colonsay, distant 9 miles N.N.W., also grey granite which may have come from Colonsay. There are fragments of red granite with large crystals; — but no rocks of that variety, known in Oronsay or Colonsay. On east side of Oronsay, boulder of coarse-grained granite, pinky in colour, which is supposed to have come from east coast of Colonsay, There are boulders of quartzite, and nodules of chocolate red sand- stone— but which cannot be referred to any rocks on either Colonsay or Oronsay {Ninth Report, p. 17). 3. Midi. — On road to Torloisk from Tobermory, Professor Duns found numerous granite boulders — for most part the reddish variety — others are grey. The largest boulder seen was gneiss. A small quartzite boulder was also seen. All of them are rounded and smooth. Four boulders lie en trainee, the line being N. and S. In approaching west coast of North Mull, boulders decrease in number. The contrast is most striking, as the boulders are very numerous towards east coast. “ Has ice, moving from the N. W., begun to drop its entangled boulders near the west coast, and the rate of deposit increased as it passed over the tract between Runa- Gal and Mishnisli and the S.E. of Glen Frisa? Be this as it may, there is no doubt as to the numerical increase of the boulders in this direction. They are all much rounded. ” Ascended Spy on More, 2435 feet above sea-level. Found a good many boulders scattered over the hill — all, so far as could be ascertained, granites — no granite rock occurring in situ in this part 808 Proceedings of the Royal Society of Mull. “ One of the boulders lies on the very top of Spyon More. Another is met with half-way down the hill. The rocks at the summit, are well glaciated ; and a great heap of moraine-like debris rests on it” (Ninth Report, p. 27). 4. Iona. — On east coast of island a granite boulder 24 x 18 x 6 feet, weighing about 190 tons. Longer axis N.W. There are many boulders on E.S.E. side of island, opposite to Ross of Mull, which have led some persons to suggest that these may have been transported across the narrow arm of the sea which divides Mull from Iona. But the Duke of Argyll is quoted as thinking that the Iona granite boulders are a different variety (First Report, p. 27). In Ross of Mull two varieties of granite (red and grey) extensively quarried (Second Report, p. 157). About half a mile north of the large boulder above specified, there is another large red granite boulder about 12 feet square. East end rests on clay slate rocks of Iona. There is a groove (which was seen by Convener) on under surface of boulder, running N.E., indicating that it had been pushed in or from that direction (Second Report, p. 157). To IST.E. of Cathedral, along the shore, hundreds of granite boulders (chiefly the red variety) ; — several exceeding 20 tons. The rocks of Iona are chiefly clay slate. Convener saw no other, and he was told there are no granite rocks. At the south end of the island, many granite boulders (mostly red, but some also of grey variety) lying on high ground from 200 to 300 feet above sea. One of these seen by Convener, standing upon end, leaning against a rock on its S.W. side, as if it had come from a hl.E. direction (Lithograph No. 15, Plate VIII.). Most of the bouldg^i’s in south end of Iona lie with longer axis N.E. and E.KE. Convener heard of a large boulder on west side of island in two fragments, which to his informant had suggested the idea of the boulder having been broken by falling from a height (Second Report, p. 155). The highest hill on island is called “ Dun J.” On the hr.hf.W. side of this hill there is a plateau at height of 230 feet above sea. On the plateau, where it joins the hill, there is a large red granite boulder, weighing about 400 tons, cubical in shape, and very 809 of Edinhurgh, Session 1883-84. angular, 22x16x16 feet, its base resting on the plateau, and its top leaning against side of hill {Lithograph No. 16, Plate IX.). On ascending to summit of hill (which reaches to height of 400 feet above sea) Convener found several boulders of red granite. Mr Allan McDonald (schoolmaster) doubts the theory that the red granite boulders on “Dun I ” Hill came from the Ross of Mull ; — firsts because the rocks at Ross of Mull do not reach to so high a level as 400 feet ; second, because, as regards the 400 ton boulder, “ Dun I ” Hill is situated between it and the Ross of Mull, so that transportation from Ross is hardly conceivable. Ross of Mull bears from boulder S.S.E. The smooth faces of the rocks in Iona, front N. by E., the rough faces front south {Second Report, p. 156). In a subsequent year (1878) the Convener again visited Iona, and went to look at the large boulder on “ Dun I.” He then observed that the boulder was composed of coarse-grained red granite — more coarse than the boulders on east side of island previously referred to. The prevailing rocks of Iona are a fine-grained gneiss, approach- ing in many places to clay slate. The boulder on “Dun I” Hill seemed to indicate that it had been brought by some agent from a north-westerly point, which agent had stranded on the hill, and stuck there, till boulder dropped from it. Captain Stewart of Coll was with Convener when latter examined the boulder. On examining the portions broken off, as also another small boulder lying below, exactly similar in composition, Captain Stewart at once exclaimed — “ This is Coll granite.” In reference to this suggestion, it is to some extent confirmed by the fact, that the island of Coll bears about N.N.W. from Iona, and is distant about 20 miles. But the Convener, having visited Coll a few days afterwards, did not fall in with any granite rocks there. They were all gneiss, with only occasional veins of granite. But he did find granite boulders in Coll, somewhat similar in composition to the large boulder on “ Dun I ” {Fifth Report, p. 4). A well rounded boulder of Conglomerate was found by Convener on east coast of Iona. Heard that similar blocks occur on west shore in St Columba’s Bay. There are no Conglomerate rocks in Iona. The nearest spot is said to be Inch Kenneth Island (on west of Mull), where, according to Macculloch, it forms cliffs about 100 feet high 810 Proceedings of the Royal Society {Western Islands^ vol. i. p. 515). Inch Kenneth is about 10 miles K.E. from Iona {Second Report^ p. 155). 5. Staffa was visited by Convener. He found on it, at his first visit, several small boulders of red granite. There are no rocks of granite' on the island. It consists entirely of blue trap {Second Report, p. 1 57). In a small hay on east side of island, the Convener (on his second visit) found several small boulders of red granite, gneiss, quartzite, and limestone, none of which occur in Staffa as rochs. About 20 yards from this bay. Convener found an old sea-beach 36 feet above high water mark, from the gradual breaking up of which the foregoing boulders are probably derived. Quotation given from Dr Macculloch to show how perplexed he was to account for the occurrence on Staffa of “ transported stones,” which, he assumes, must have been carried by natural agency from some of the neighbouring islands {Fifth Report, p. 11). 6. Tiree. — (1) Haynish Hill, in S.W., end of island, reaches to 600 feet above sea. It consists of gneiss, in some parts passing into granite. The hill on its west side coincides with sea-cliffs, and has on it a number of rocky knolls. Almost every knoll has on its K.W. side {i.e., facing the Atlantic) boulders more or less rounded. The following are particulars of some : — Boulder 11x8x5 feet resting on side of knoll facing W.N.W. Boulder 9x4x5 feet resting on side of knoll facing W. by K. at height of 360 feet above sea, which is a quarter of a mile distant, with access from the sea between S. and K.K.W. points. This boulder is a coarse granite, — the knoll is gneiss. Boulder 8x7x5 feet resting on side of knoll facing K.W. by N. at height of 365 feet above sea. Sea half a mile distant, and access from it open at any point between S.W. and due north. Two clusters of large boulders met with, the uppermost on the cluster so posed as to show it must have come from westward. The sea is within half a mile to westward. On this Haynish Hill boulders more numerous on sides or slopes facing W. and N.W. than on any other. On slopes facing E. and S.E. there are also boulders, but fewer in number. (2) Passing due north, along Big Cornish Road, Convener found on east side of road several rocky knolls, tops of which are from 80 to of Edinburgh, Session 1883-84. 811 110 feet above sea. Most of these knolls present hare rock on west sides, and have boulders on those sides. On one of the knolls a boulder 10 x 6 x 6 feet, very near its top — a light coloured gneiss. Hock of knoll also gneiss, but dark coloured. Another rocky knoll, about a mile to N.E. of last, has on it a number of large boulders called “ The Giant's Pebbles f in reference to a legend that they were thrown by giants from Barra, an island N.W. of Tiree, and distant about 40 miles. There are here from twenty to thirty boulders of all sizes, almost all on the knoll, and none on the adjoining fiat land. Suggestion offered, that knoll had intercepted the raft which carried the boulders. (3) Ben Gott Hill forms a rocky ridge running N. and S. about 120 to 130 feet above sea. A very large number of boulders chiefly on its N.W. flanks. Some are on S.E. flanks, possibly pushed over ridge. On flat ground S.E. of ridge, boulders are few in number. (4) Great beds of sand and shingle in different parts of island, showing that sea had prevailed over it at a comparatively recent period, to a height exceeding 40 feet above present sea-level. 7. Coll. — Visited Bein Hoch; hill on west side of island, reaching to 290 feet above sea. There are two boulders at top : — one near the summit which slopes down towards l^.W., the other on a flat which forms summit of hill [Lithogra/ph No. 17, Plate IX.). Near foot of hill, on its N.W. side, there is a rocky plateau abutting against it, at a height of 80 feet above sea. On this low hill there is a large boulder 16 x 20 x 13 feet (308 tons). All these boulders are a coarse granite, passing sometimes into dark coloured gneiss. Eock of hill is gneiss. The sea (viz., Atlantic) is towards west and north, distant about half a mile. There can hardly be no doubt, that these boulders were brought here across the sea. (2) At Grassi]pol an immense accumulation of houlders in a meadow, which has a range of vertical rocks on its S.E. side {Litho- graph No. 18, Plate IX.). These boulders seem to have been inter- cepted in their farther progress by the rocks on S.E.. Sea is about three-quarters of a mile distant to N.W. One of the boulders is 30 feet high. On west side of this meadow, a rocky knoll covered by boulders, 3 H VOL. XII. 812 Proceedings of the Royal Society about 18 or 20 in number — tbe uppermost resting on the others in such a way as to show it had come from N.W. {Lithograph No. 19, Plate IX.). Near this knoll, a vein of quartz, smoothed on its edges in such a way as to show smoothing from N.W. (3) On east side of island, near Arinagour, the boulders few in number and small. Towards the N.W. part of island, when Arniboat schoolhouse is passed, boulders increase in number and size. (4) At S.W. end of island, there are many large granite boulders near Coll House. Convener measured one and found it 35 x 15 x 8 feet (312 tons). It was on its S.E. end, leaning on or pressing against a gneiss rock. The granite boulder is of a coarse variety, the fragments composing it being of large size. This was probably the boulder which Captain Stewart was thinking of, when he com- pared the large Iona boulder to Coll granite. (5) Macculloch, in his account of the Geology of Coll, refers to a “ block of augite ” which he found at a great distance from the shore, and which he thought must “ be a transported hlochj' as he had seen no rock of that kind in the island. He says that it probably came from Eum Island, where that rock abounds. Eum is situated N. by E. from Coll, and distant about 20 miles. Convener omitted to inquire for this augite block. 8. Eigg. — Mr MTherson, proprietor of the island, drew out for the Committee some valuable notes. One large boulder rests on the Scopr ridge, — a remarkable ridge of pitchstone porphyry which runs for about 2 miles across the island in an east and west direction. It reaches, at its east end, to a height of 1300 feet above the sea — at its west end, to a height of 900 to 990 feet. It rises from a plateau which is about 400 feet above sea. Both north and south sides of the Scoor are precipitous, almost vertical, showing a cliff on the north side of 270 feet, on the south side of 400 feet. The boulder on this ridge is near its western extremity, and on a part of the ridge which is lower than any other part, viz., 890 feet above sea. It is close to top of ridge, and on the slope facing the north. This boulder is said to be of granite or gneiss — a rock not existing in the island. of Edinhurglij Session 1883-84. 813 Many other boulders of the same kind are strewed over the island. On N.E. part of island there is a granite boulder of a larger size than any other, and is of a darker colour. It is on the side of a hill sloping down towards S.W., at about 300 feet above sea. Hill itself is about 900 feet above sea. Mr M‘Pherson says that he has seen on the shores of Loch Alsh, to the east of Skye, rocks resembling this boulder. Chips of these Eigg boulders were procured. They were sub- mitted to Professor Geikie. Among the chips he detected one which appeared to him to have come from the Torridon group of Old Red Sandstone, viz., the coast of the mainland to the north- east of Skye. Professor Geikie, in his account of the Geology of Eigg, adverts to the finding of “ pieces of Red Sandstone of Cambrian derivation,” which (he says) make it clear that the higher grounds from which they were borne could not have lain to the S. or E. but to the N. W. or H.” {Lond. Geol. Soe. Proc.^ vol. xxvii. p. 309) {Ninth Report, p. 22). 9. Canna. — Convener told by an experienced contractor for build- ing that he had found on the islet of Sanda (forming the south side of Canna harbour) blocks of a red sandstone, which he made use of for the lintels and corners of a new schoolhouse. The largest was 6x4x2 feet. These sandstones differ from the rock of the island, which is a blue slaty schist, ill- adapted for building. He knew that these sandstone rocks abound in Rum Island, as he had quarried them there. Macculloch noticed these red sandstone blocks on Canna, which he says differ from Canna rocks ; and he states that similar sandstone rocks occur in Rum and Skye (Western Highlands, vol. i. p. 467). 10. Barra. — A very large boulder of coarse gneiss approaching to granite exists here near the base of Ben Erival, on its side sloping down to north. The hill reaches to about 600 feet above sea-level. Height of boulder 28 or 26 feet, its extreme length 37 to 38 feet, and its width about 18 feet; assuming 2 tons for one cubic yard, its approximate weight would be 890 tons (Fifth Report, p. 12) (Lithograph No. 20, Plate IX.). Convener prevailed on tenant of the hill to dig under the boulder to discover the nature of the materials forming its site. An account 814 Proceedings of the Royal Society is given on p. 67 of tlie Eeport, from which it appears that the materials were gravel and earth, with sea shells. The boulder was evidently not lying on rock. The supposition of the Convener was, that when brought to its present site it fell on what was then sea-bottom. The site of the boulder is now 230 feet above sea. A plan is given in the Eeport, to assist consideration of the question, from what direction the boulder probably came to its present site ; — the result of the Convener’s consideration being that it must have come either from the N.W. or the IST.E., there being open sea only in these two directions. About 100 yards to the west of the Big Boidder^’ there is a rocky isolated knoll, about 255 feet above the sea, clustered with boulders. These are lying partly on rock, partly on shelly gravel, and chiefly on the N.W. side of the knoll. On a study of the positions of the boulders on this knoll, it appeared to Convener that the uppermost boulders to get into their positions must have come from N.W. point. About 200 yards N.E. of Big Boulder there is a boulder lying on a smoothed rock surface, which dips due north on an angle of 20"". This boulder is 5 x 4 x 2 feet. It could not have obtained and retained its position unless by having been brought from the north. About 300 yards to S.E. of “ Big Boidder ” there is a boulder 8x6x3 feet, at height of 228 feet above sea. The boulder at its east end presses closely on rock which has prevented it moving further in an easterly direction [Lithograph No. 21, Plate IX.). On N.W. of Ben Erival, where its sides slope down steeply to the sea, there are numerous boulders, many of which press against the rocks of the hill in such a manner as to show that they must have come there from some point between west and north. They are at various heights from 400 to 500 feet above sea, which is here the Atlantic. Ben More is a hill on Eoligarry Earm. Its west end forms a steepish sea-cliff rising to a height of 330 feet above sea. Half- way up this sea-cliff there is a boulder, 20 x 10x5 feet, resting on the rocky surface, which here dips W.S.W. But the rock, judging by the marks on it, has been smoothed by something passing over it of Edinburgh, Session 1883-84. 815 from N.W., and the boulder is hloched at its S.E. end by a rocky portion of the bill (as shown by Lithograph l^’o. 22, Plate IX.). At Castle Bay (at south end of Barra) the bills are covered with boulders, but more on their X.W. slopes than on any other. Mr Campbell {Paper on “ Glacial Phenomena of Hebrides'^) states that he took rubbings of strise at Castle Bay, which showed that striating agent had moved from X. by W. (magnetic). He mentions that on the small island of Berner a, about 12 miles south of Barra, he got striae at a height of 720 feet above sea, cross- ing the strike of the rocks from N.N.W. On hill called Scurrival, whose west side rises abruptly from sea to height of 240 feet, the hard gneiss rocks show proofs of a grinding action on them from X. W, The strata are horizontal, and form blocks with their longer axis lying about X. and S. The west sides of these blocks facing sea present frequent smoothings, especially at their north ends, whilst the south ends remain rough, showing action on the blocks from X.W. On this hill the boulders are numerous, and many of them are blocked at their S.E. ends. They are from 200 to 300 yards from the sea, and about 100 or 150 feet above sea-level The situations and positions of these boulders combine to show that they must have come here from a north-westerly direction. On the summit of the hill, which consists of well rounded and smoothed surfaces of gneiss, numerous boulders lie scattered, most of them on that part of the top which faces W.X.W. 11. South JJist. — Xear south end, there is Carshavaule Hill, on west side of which is Loch Dunkellie. On east bank of loch, a gneiss rock well striated, — the striae running X.W. by X. At a little distance to S.E., on south of Carshavaule Hill, a valley through which current might have passed, after striating the rock. Loch Boisdale. — On east coast. Kennet Hill, situated on north side of loch, presents numerous examples on its west flanks of smoothed surfaces and of large boulders, many of them abut- ting on rocks at their east ends (see Diagrams in Fifth Report, p. 17). One of these boulders is 19x13x8 feet, 146 tons {Lithograph Xo. 23, Plate IX.). At junction of roads from Barra and Loch Boisdale, where Boman Catholic and Free Churches are situated, there is a cluster of 81G Proceedings of the Royal Society boulders. One 16x6x5 feet, leaning on the others, must have come from N.W. to attain its position. On hill to east of Ashernish^ and on Mingary Hill^ there are many large boulders, chiefly on west flanks, as also striated rocks, well deserving of study {Lithograph N’o. 24, Plate IX.). About 3 miles to north of Askernish there is a block of granite perched on the pointed summit of a rocky hill. The boulder is 14x12x8 feet (about 100 tons) {Lithograph Xo. 25, Plate IX.). There is no way in which it could have attained its position except by floating ice. At Jocdar, IJ miles south of ferry between Uist and Benbecula, there are smoothed rocks “ literally covered by parallel striae, ruts, and grooves,” the direction of which is X. W. by W. The smoothed surface of the rocks here slopes down to westward, at an angle of about 10° or 12°. Some of the ruts are 4 or 5 feet long. One at its X.W. end measures 8 inches across and 2 inches in depth j another 12 inches across and IJ inch deep. Towards the S.E. they lessen in width and depth. There can be no doubt that the striating agent here came from X. W. The height of this place is about 25 feet above the sea — the Atlantic — and of a mile distant. There is a similar good example of striated rocks about half a mile to the west of the above mentioned {Lithograph Xo. 26, Plate X.). On road between Grogary (mansion-house of Lady Gordon Cathcart) and Loch Skiport (on east coast) there are many striking examples of striated rocks and boulders. Loch Eport is a remarkably narrow area of the sea on the east coast, which runs more than half-way across Xorth Uist. From deck of steamboat Convener saw, on both sides of Loch, many boulders, resting chiefly on rocky knolls, and many rocks with faces smoothed on west sides. North Uist. — Loch Maddy^ a sea-loch on east coast. An hour's walk for about a mile from the shore, showed Convener that rocks here have their smoothest sides facing X.W. {Fifth Report^ p. 22). Professor Heddle, in a subsequent year, visited Loch Maddy^ and reported that rocks there generally showed smoothings by some agent passing over them from the westward. He refers also to two islets of trap rock called Maddy More and Maddy Beg, which are (as he says) “ porpoise-nosed to the west, and of EdinUtryh, Session 1883-84. 817 cliffs to the eastf as indicating probably the direction of the agent which flowed over them. Professor Heddle on this occasion, at Loch Maddy, met a gentleman, a member of the Glasgow Geological Society, who had just returned from Newton on the coast of North Uist. He described to the Professor a boulder he had seen there, 13x5x4 feet, and another 9x5x5 feet. The former lay with its longer axis N.N.W. He stated also that the rocks on the west shore were generally glaciated, and from points between N.W. and S.W. {Sixth Report, p. 34). On Ganneum, a rocky islet north of Loch Maddy, there are two boulders of Laurentian gneiss, weighing, the one about 15, the other about 50, tons. Prom the corresponding slopes of the two ends which face each other, it has been inferred that they were originally one boulder, though now about 1 00 feet apart from one another, and with a projecting rocky knoll between them. The reporter, Alex. Carmichael, suggested that the boulder may have fallen from a height on this rock, and been broken into two frag- ments {First Report, p. 35). Harris. — (1) At Rodil (south end of Harris), rocks on Stron- davelhill smooth on west faces, rough on east faces. (2) At Borve, on west coast, a remarkable assemblage of boulders on hill about SOO^feet high, sloping down to W. by N., close to shore of the Atlantic {Lithograph No. 27, Plate IX.). The boulders lie on and against benches of gneiss rocks, these rocks also beiug smoothed and ground down from westward. These boulders lie in such a way as to show they have come from westward {Fifth Report, p. 23). (3) Similar appearances in Loch Castle Bay and Valley. (4) About 1 J mile south of Tarbert, several large boulders, which probably reached their positions by coming through depressions existing in the range of hills to N.W. (5) On hills north of Tarbert, up to height of 800 feet above sea- level, Convener saw many evidences of a N.W. current loaded with ice, which has brought boulders and smoothed the rocks {Fifth Report, p. 26, plate viii. fig. 28). Professor Heddle separately visited Tarbert, and specifies certain hornblendic boulders, which he traced to a rock identical in character a few hundred yards to westward {Sixth Report, p. 35). 818 Proceedings of the Royal Society (6) At Fincastle, on sliore west of Locli Tarbert, Convener found boulder so situated as to indicate transport from ]S[.W. (7) Scalpa Island. — Three granite boulders found by Professor Heddle [Lithograph i^o. 28, Plate IX.), one of them hutted up^^ against a knoll of gneiss rock (see plate xviii. fig. 6, in Sixth Report, and p. 35). On faces of hill on Harris shore, opposite Scalpa, a great bed of granite, from which Scalpa boulders probably came. (8) Shiant Islands. — On western shores Professor Heddle found several blocks of rocks foreign to the islands, and occurring in situ in the Long Island to the west. Some Conglomerate boulders he considered had come from Stornoway, 30 miles to north, the nearest place for Conglomerate rocks [Sixth Report, p. 36). Boulders of trap on eastern shores of the islands supposed to have been pushed from rocks on west side of the islands [Transactions of Norfolk and Norwich Ncduralistd Society, vol. iii., 27th Jan. 1880). 12. Leivis. — Professor Heddle examined the district between Tarbert in Harris and Stornoway on foot, a distance of 28 miles. He was struck with the general flatness of the district, especially in its northern part, considering that the rocks there come generally to the surface, and are on edge. They suggested the idea of some great abrad- ing agent which had passed over the district [Eighth Report, p. 29). (1) Hear Ardrourlie, on Loch Seaforth, a trainee of boulders, forming a line E. by X. and W. by S., apparently traceable to gap in chain of hills to S.W. Clusters of boulders seen there, so piled on one another as to show that the topmost had come from westward. (2) At and near Soval, 12 miles south of Stornoway, rocks forming cliffs, smooth on sides facing west, rough on sides facing east. On one of these cliffs facing the west there is a boulder on edge of rocky cliff, which there forms a surface sloping down towards W.X.W. at an angle of from 20° to 30°. Longer axis of boulder W.X.W. Seemed to Convener clearly to have come from west- ward [Sketch in Fifth Report, plate" viii. fig. 29). (3) Lochs Ourn and Shiel, on east coast. Boulders seen by Con- vener on hills adjoining, positions of which all indicated transport from west. (4) Uig, on ivest coast. Bocks near road at two spots, smoothed oj EdinJmrgli, Session 1883-84. 819 and striated from Euts deeper at west ends than at east ends {Fifth Report, p. 28). (5) Miavig, an arm of sea branching up from Loch Eoag on west coast. On top of a hill called Dramainan Voltas, 270 feet above sea, there is an immense assemblage of boulders, chiefly on north and west slopes {Lithograph JSTo. 29, Plate X.) {Fifth Report, p. 29). (6) Garry-na-hine to Carlowrie. Eocks along and near road, show smooth faces towards west. At low levels they vary in their aspects, as W.; — W. by S.; — and even W.S.W. But at higher levels, viz., above 300 feet, the smoothed faces are pretty uniformly towards W.N.W. {Fifth Report, p. 30). The explanation of this seemed to be that the rocks at high levels were exposed to a normal current from X.W., whilst rocks at low levels were exposed to diverging and eddying currents. Convener examined particularly striated rocks described by Dr James Geikie {Lond. Geol. Journal for 1873, p. 537), who expressed an opinion that the striae had been formed by a glacier which moved across the slope of the rocks from the S.E. The Convener, after twice examining these rocks, was of opinion that the striae had been formed by some agent passing from the X.W., inasmuch as indi- vidual striae were most deeply cut at their X.W. ends (see sketches in Fifth Report, p. 30, and plate viii. fig. 32). Boulders seen leaning against rocks on their east sides, as if thereby stopped in their progress eastwards. (7) Beinn-a-Bhune, a hill about 400 feet above sea, mentioned by Dr Geikie. Eocks seen by Convener smoothed, and boulders so situated as to show probable movement from W.X.W. (8) Barvas Hills, 800 to 900 feet high, 5 miles north of Storno- way, examined by Convener, who found on them smoothed rock, and boulders indicating movement from X. and X.W. (9) In district between Barvas Hills and sea-coast to north there are long lines of escars, composed chiefly of coarse gravel, with boulders lying occasionally on their ridges ; these boulders in many places piled on one another, and in such a way as to show transport from X.W. Several of these escars run for miles continuously, and reach to the north coast, following a direction generally X.W., with occa- sional deflections. 820 Proceedings of the Royal Society When viewed from top of Barvas Hills they form a striking feature, as the bright green of the grass covering them con- trasts with the dark brown or black colour of the widespread muirs which they traverse. These escars reach to a height of from 30 to 50 feet above the adjoining flat ground. At one place (about 2 miles north of Barvas Hills) an escar expands and divides into a series of knolls, on which many boulders now rest. The highest knolls have on them the greatest number of boulders. At two places the boulders form groups, piled on one another. They had formed (as was mentioned by a shepherd) hiding places in times of trouble. Most of the boulders on these escars show transport from IS.W., but some indicate a transport from WhS.W. ; one from N.N.E. In this part of the island there are numerous lakelets, whose longer axis is generally parallel with the lines of escar, — a fact all the more remarkable, as the outcrops of the gneiss rocks generally form lines in the direction of N.E. and S.W. and dipping S.E. Dr Geikie was much struck with this fact, and expressed an opinion that the formation of the escars and of these lakelets must be due to one and the same agency, viz., a glacier or ice-sheet, which came across the “ Minch ” from Eoss-shire. (10) Along coast from Barvas^ eastward, boulders of granite, differing from any rocks near them, and alleged by a local mason seen by Convener to be same as rocks 7 or 8 miles to westward. A great monolith here, 18 feet 9 inches high and with a girth of 16 feet, called “ Clachan Treudach^^ or “ Gathering StoneJ^ (11) Dalheag Hills, about 9 miles west of Barvas. Smoothed rocks and boulders indicating movement from westward. (12) At Tolsta (12 miles IST.E. of Stornoway) a boulder 18x5x4 feet, and 358 feet above sea, called the “Eocking Stone.” Eocked when Convener lifted it, or when he rested his weight on it, at either end of its longer axis. Its central part rests on bare smooth gneiss rock. Its longer axis points hf.N.W. It is well surrounded by high hills but towards N. W. there is an opening in the range of hills through which boulder might have come [Fifth Report, p. 31). (13) Eye Peninsula to east of Stornoway, where rocks are Old Eed Sandstone. Boulders of gneiss occur there, which almost certainly must have come from Barvas Hills, situated about 7 miles to IST.W. 821 of Edinburgh, Session 1883-84. (14) On Eye Peninsula a brickwork of boulder clay, in which, at a height of about 200 feet above sea, fragments of marine shells seen by Convener. Dr Geikie mentions those, and states that similar shells were found by him in a deposit stretching across the north part of the Lewis, from shore to shore {Fifth Report, p. 36). (15) With reference to the above-mentioned group of islands, sometimes called the Long Island, remarks of a general character may not be inappropriate. Mr J. F. Campbell (formerly of Islay), author of Frost and Fire, wrote as follows to the Convener : — “ In the Long Island, from Barra Head to the Butt of Lewis, the whole country is glaciated, with boulders everywhere perched on the hills. Wherever the surface is newly exposed, the striations and smoothings are so perfect that the marks can be copied as ^Brasses’ are copied.” In a letter from the same gentleman to Mr Alex. Carmichael of the Inland Eeveiiue, a native of the Hebrides, the former re- marks ; — “ Glacial striae occur upon fixed rocks in Tiree, Mingley, Barra, South and Horth Uist, and correspond with a direction from N.W. or thereabouts. The hills are ice- worn to the very tops. Transported blocks are scattered over all these islands.” 13. Skye. — The Convener regrets that the Committee received no report from this island ; nor had he an opportunity of visiting it himself, except at one spot, viz.. Loch Scavaig, on the west coast, where the steamboat stops for an hour to allow passengers to see Goriusk. The Convener then saw and examined a large boulder {Lithograph Ho. 30, Plate X.). Its position, on a rock between the sea and the adjoining lake, is described on page 66, Sixth Report. The rock on which it stands slopes steeply towards W. by X., and it is in so precarious a position that it must have been very gently let down by the agent, whatever it was, which transported it. Professor Heddle reported that in the year 1879 he walked along H.E. part of Skye from Aird Point to Portree, and partially among the hills, but saw no boulders. He visited Stainchol Island, situated off the east coast, and found Cambrian Conglomerate blocks, similar to what he had seen on the Shiant Islands, and similar also to the rocks existing in the Lewis, 822 Proceedings of the Royal Society near Stornoway. On Stainchol shore the Professor found dolerite boulder containing Lahradorite. He states that the parent rock is situated^about fifty yards to H.H.W. {Sixth Report, p. 38). Judging from what is casually said by Dr Macculloch and Principal James Forbes, regarding boulders in Skye, they must be numerous and interesting. Thus Forbes refers to boulders '‘'•poised upon others, or fantastically balanced on the tops of elliptical domes of roclcs; ” and Macculloch says that the summits (on which some of the boulders stand) are not only hare, hut often very narrow, while their declivities are steep, and sometimes perpendicular. Macculloch confesses his inability to explain these phenomena. Inverness-shiee. Loch Nevis, on west coast. Several large boulders of coarse- grained granite seen near Inverie House, lying on slate rocks. On road towards Gussern, several boulders of interest pointed out to Convener by late Mr James Baird, the proprietor. At height of 360 feet above sea, and near sea-shore, rocks smoothed and striated from IST.W. by W. Two large boulders lie on side of a hill, which slopes down to the W.H.W. One of these, of elongated shape, has its longer axis N.W. and S.E. A large boulder, consisting of two fragments, pointed out by Mr Baird, in consequence of his believing that the boulder had been broken by falling from a height, and striking on the hare rock, where these fragments now lie. The two fragments are four or five feet apart. Whilst the opposing surfaces correspond in shape, they are so weathered, as to show that the fracture was not of recent date. At summit level between Inverie and Gussern, there is a horizontal terrace, facing the sea, and at from 400 to 500 feet above sea, with a number of boulders on it. At Invergussern, lower part of valley blocked by a huge gravel ridge, now cut through by river, quite in the position of a terminal moraine. But, being composed of nearly horizontal beds of gravel and sand, from 40 to 50 feet deep, more probable that it is a sea deposit, and that it for some time confined a lake; for on the sides of valley horizontal water-lines occur {Second Report, p. 164). of Edinburgh^ Session 1883-84. 823 2. Loch Corry, near Morvern, has its rocky shores well glaciated, A large knoll of red granite, at month of loch, has had its W.K.W. sides rounded, and partly striated up to 150 feet. The S.E. side of knoll rough and craggy {Eighth Report, p. 29). On north shore there is an angular block 27 x27 x11 feet, apparently moved 28 yards from a rocky cliff situated to N.W., of which it had been part. The hills on the Glen Sanda property, reach- ing to a height of 1800 feet and more, are glaciated to their very tops. 3. On Loch Shiel, several similar cases of large blocks (from 1 to 10 tons weight) apparently forced from rocky cliffs and carried east- wards. White granite vein or dyke met with near top of hill, 2718 feet above sea, from outcrop of which, blocks detached, and carried east- ward nearly one-third of a mile. 4. In Glen Oban, remarkable examples of rounded rock-surfaces, some more than 100 feet high ; also of perched boiddersf on isolated rocky knolls, each from 300 to 400 feet high, and inacces- sible, as shown in woodcut annexed. 5. Mid Lochaber. — Memoir by Rev. Professor Duns, on Surface- Geology of, and particularly on the boulders found to Is", and W. of Ben ISlevis. The Professor says — “ Granite boulders are lying on the mica schist rocks, where the side of the mountain slopes down so steeply as to make it a puzzle to understand how they can remain in position.” 824 Proceedings of the Royal Soeiety The author expresses belief that the phenomena may find explan- ation in the recognition of two movements, — one outward from Ben Nevis as a centre, the other a force travelling from the W.N.W. or KN.W. (Eighth Report, p. 21). Notes on boulders, situated to the west of Fort-William, by Mr Colin Livingston, teacher of public school, Bort- William. The author enumerates boulders and striated rocks on west side of Ben Nevis, and expresses a confident opinion that two glaciers existed, the one descending Glen Nevis, the other Glen Spean and Glen More. He refers to immense mounds and ridges of detrital matter, (having animperfect stratification) towards Inverlochy and Torlundy, — such as might have been produced, if it fell from some height (Eighth Report, pp. 23, 27). 6. Since the time when Mr Livingstone’s Notes (given in the Eighth Eeport) were framed, he has made a further inspection of the hills to the W. and S.W. of Ben Nevis, and has communicated to Convener the following additional facts : — Stoh Ban, reaching a height of 3274 feet above sea, is situated west of Glen Nevis. It is composed of quartzite, which accounts for its Gaelic name of White Pin. Boulders of this rock are found to the eastward, on various parts of the west slopes of Ben Nevis. Another hill of interest is Mulloch-Nan-Coirean,^^ 3077 feet, having a rounded top of red granite. On its top there is a slab of mica slate. How it came there, Mr Livingstone says is a mystery. He admits that mica slate rock exists in large quantities towards Sghor Challum, a hill 1823 feet, situated to the west. But he sees the difficulty of conceiving that any glacier could have brought it. On the same hill there are boulders of micaceous gneiss and quartz. The quartz boulders, he says, may have come from Stoh Ban ; the birthplace of the gneiss boulders is (he says) uncertain. 7. Notes on Ben Nevis and Craig Dhu, by Professor Heddle of St Andrews, were sent to Committee. He expresses an opinion that a glacier swept down Glen Nevis, even overtopping a hill of 3077 feet. He also suggested the probable existence of another vast glacier cradled in the gorges between Aonach Beg and Aonach Mor. 8. Ben Nevis. — Convener ascended to top, by a path leading up the N.W. side of hill. Enormous boulders of grey granite lie on N.W. slopes. A few on each side of path were measured, and gave of Edinhurgli, Session 1883-84. 825 the following results: — 16 x 10 x 10 feet (118 tons) (partially sunk in gravel); 15x7x5 feet (lying on bare rock) ; 13x7x4 feet; one nearly cubical, the sides being each about 4 feet square. The first three have longer axis JST.W. They are from 900 to 1200 feet above sea. But there are some, up to 2000 feet above sea. Mr Doig, builder, Fort-William, who accompanied Convener, mentioned that there had been one boulder at the foot of mountain, on its hl.W. side, so large as to afford materials for building the entire front wall of the Town Hospital of Fort- William. Mr Doig stated that he considered that the boulders on west flank of the mountain were generally different from Ben He vis rocks {Fifth Report, p. 65). 9. On Treshlik Hill, 1566 above sea, on north side of Linnhe Loch (opposite to Fort-William), Convener, under guidance of Mr Livingstone, inspected a coarse-grained granite block, 8 feet high, 52 feet below summit, on west slope of hill. This hill forms a ridge about half a mile long, running W.S.W. Kocks in situ are clay slate. Boulder must have been transported from some westerly point, and put down very gently, as slope exceedingly steep where boulder rests {Lithograph Ho. 31, Plate X.) {Second Report, p. 161). Bocks on north and west sides of hill near top are well smoothed ; rocks on S. E. side of hill are rough. The smoothed rocks are chiefly on a space along north side of hill, from 30 to 60 feet below summit. Many coarse-grained granite blocks, and water-worn pebbles, lie along north face of hill near the top. 10. Boleskien, Ahertarff, and Dores. — Well rounded granite boulders of red and grey varieties occur over district of Strath- errick. One above ground measured 20 x 10 x 7 feet, and there seemed to be as much below. Its longer axis H. and S. Another at Fall of Foyers measured (above ground) 12x6x6 feet. Several are poised on tops of isolated hills. Highest hills in this district about 2900 feet above sea. Boulders are chiefly above the level of 2350 feet. Below this level they are generally of a smaller size. Beported by Captain White, B.E. {Second Report, p. 137). 11. Lochaher. — In this district one of the most interesting hills is Glen Dim 2200 feet, between Glen Boy and Glen Spean. Pro- fessor Heddle, having visited it, expressed an opinion that the large 826 Proceedings of the Royal Society boulders on and near the top had come from a S.S.E. direction {Eighth Report, p. 37). As other geologists have visited this hill, and recorded views which contain further information, it is right to refer to them. Thus Mr Jamieson of Ellon mentions having seen several large boulders of syenitic granite on or near the top of Qraig Dhu, a gneiss hill, at a height of 2100 feet above sea. He says— “ What is remarkable is, that the largest and most angular are more numerous high up on the very brow of the hill than further down. Thus” (he says), “ one 12x9x6 feet lay only 130 feet below the summit j another was a magnificent block, 15x10x6 feet” {L. G. S. J., vol. xvii. p. 175). The late Professor Mcol of Aberdeen, well known as a geolo- gist, refers to the Craig Dim boulders in these terms : — “ I found huge blocks of black granite and smaller masses of red porphyry within a few yards of the summit of Craig Dhu, a conical mountain of mica slate. One block must weigh 40 tons. They are evidently ice-borne, probably floated from the H.W.” {Lond. GeoL Soc. Proc., August 1869, p. 283). The Convener visited Craig Dhu, and noted the following points : — (1) The boulders on the hill, in so far as not of a round shape, have their longer axis E. and W. A little above 1391 feet level, found boulder on bare rock, which here forms a flat surface, glaciated like the rest from W. by The boulder must have come after glaciation of rocks. Looking towards west, saw a line in that direction clearing all the hills, showing an opening for a move- ment from west towards and upon Craig Dhu. Masses of white quartz rock were found glaciated from west. A boulder near top of the hill, with longer axis W. by S. {Edin. Roy. Soc. Trans., vol. xxvii. p. 641). Mr Jamieson refers to a granite boulder on the top of Boliun- tine, a hill 2000 feet high, not far from Craig Dhu {Eighth Report, p. 639.) Mr Jamieson, in describing smoothings and scorings of the rocks at Loch Treig, up to 1280 feet, states that he found perchedj houlders'' and rounded surfaces of rock much higher, and even up to the top (about 3155 feet above the sea). The gneiss, though it runs in nearly vertical stratifications, is neverthe- of Edinburgh, Session 1883-84. 827 less so free from any loose fragments on its surface, and the ends of the strata are often so rounded in outline as “ to raise a suspicion that some denuding agent bad flowed over it, at a period geologi- cally recent” {Lond. Geol. Soc. Proc., vol. xviii. p. 172). The following cases of boulders were reported by the Convener : — On the summit of the hills, at the head of Glen Roy (1320 feet above the sea), there are enormous granite boulders. “ Some rest on bare rock, but traces of clay and gravel in their vicinity suggest that they may originally have been embedded in drift, which has been since mostly washed away from under and about them ” {Edin. Roy. Soc. Trans., vol. xxvii. p. 639). The late Charles Darwin, who visited Lochaber, and wrote an instructive memoir on the “ Parallel Eoads ” question, refers to the Ben Erin hills, — their height reaching to 1600 feet above the sea. He says that “ on the mountains between Glen Eoy and Glen Glouy, on a hillock hT.IST.'W’. of the summit of Ben Erin, I found several masses of granite, one of which was 4 x 3 x 2 feet, resting on the surface of the gneiss. This hillock seemed to be entirely com- posed of the latter rock, and it was separated from all other hills by a valley. On the flanks of Ben Erin, at about the same level, there were several boulders of granite.” — “With respect to these Ben Erin boulders, they are completely cut off from every granite district by valleys, the highest point of which is 920 feet below a boidder, the altitude of which I measured ; that is, it would be impossible to walk from granite in situ, to these boulders, without ascending at least that number of feet” (Darwin, “On the Parallel Eoads of Glen Eoy,” Phil. Trans, of Roy. Soc.^of London, for 1839, page 69). Sir John Eamsden of Ardverikie (on Loch Laggan) informed Convener that on the top of two contiguous hills, forming part of his estate, east of Loch Laggan (one of these hills exceeding 3000 feet in height), there are large granite boulders. Sir John Eamsden guided the Convener to the Wester Beinin Hill (situated on the west side of Loch Laggan) to see several grey granite boulders. The rocks of the hill are red granite. One of the boulders is on a shelf about 1516 feet above the sea, on the side of a hill sloping down to W.S.W. Facts bearing on the direction of boulder transport in Loch- aber have been noticed by several geologists. Thus, Mr Jamieson mentions that on the hilly ridge between Glen Spean and Glen 3 I VOL. XII. 828 Proceedings of the Royal Society Gluoy the direction of the striae at a height of 800 or 900 feet above the sea is from W. 20° N. to W. 40° N. ; and as the western sides of the rocks were most worn, the action had come from that side” {Lond, Geol. Soc. Journ.^ 21st January 1863, p. 246). In Glen Eoy (at about 1200 feet above the sea) he found, much to his surprise, that “ ice had come from the S. W. up the glen^ and had gone out in a wide stream, towards the wide valley of the Spey,” viz., eastward. 11. Black Mount district, near Rannoch. — Boulders of a peculiar white granite, found by Professor Heddle, forming a trainee. He investigated from what hills they came, and traced them to Alban- nach Hill, reaching to a height of 3425 feet above the sea, and situated about 10 miles H.W. from Loch Tulla. Keference is made by the Professor to an enormous boulder weighing about 1900 tons, in a narrow part of a valley at Loch Dochart, where traces were seen of some very “powerful agent” which had passed through the valley eastward. 12. In the Fourth Boulder Report (p. 14) an account is given of the Fassnacloich boulders, a species of black granite. Specimens were sent to Mr Judd of London, on account of his personal know- ledge of rocks in the West Highlands. His opinion was that the rock of the boulder was identical with rocks in Mull and Ardna- murchan, from which district, therefore, he supposed the boulders may probably have been transported. On the shore of the Linnhe Loch, at Appin, there are two huge well-rounded boulders of the same kind of granite. Their position favours Mr Judd’s suggestion, that all these boulders had been transported from the westward. The granite boulders on the top of Craig Dim, already men- tioned in Lochaber, are of a dark colour. Is it possible that the mountains of Mull and Ardnamurchan could have supplied all these boulders when the sea stood 2000 feet or more above its present level ? {Fourth Report, p. 45). 12J. Ardgour district, on north side of Linnhe Loch. — Professor Heddle of St Andrews, in Seventh Report, p. 36, states that on Stoh Ghoire a Chearchaill he found a trainee of boulders lying along the ridge for nearly a mile, at heights varying from 2400 to 1800 feet above the sea. The direction of the trainee was H.H.W. Most of these boulders consisted of syenite, with red felspar crystals of Edinburgh, Session 1883-84. 829 and green hornblende. Thinking that these boulders might also be found on the south side of the Linnhe Loch, he crossed, and on two hills there, viz., Bein Blian, at a height of 1500 feet, and on Beinn na Gucaig, at a height of 2017 feet, he found boulders of the same syenite as he had found on the north side of the loch. In the Eighth Report (p. 33) Professor Heddle mentions his dis- covery of more boulders of the same peculiar syenite, as seen by him on hills nearer Ben Nevis and on Ben Nevis itself, at an altitude of 2200 feet. This discovery led him to change his opinion as to the direction of the transport of these boulders. 13. Loch Creran. — The boulders there were examined by Professor Heddle. He was much puzzled to explain from what district they came. There were strise on the rocks of the hills adjoining, at heights exceeding 2000 feet above the sea. He was inclined to think that the boulders had crossed the Linnhe Loch from Loch Sunart and Glen Tarbert. On some of the hills of this district boulders were discovered at heights exceeding 2000 feet, which Professor Heddle was satis- fied must have crossed valleys to reach their positions, and by means of floating ice {Sixth Report, p. 43). 14. Glencoe District. — On the western slopes of a hill, in the higher part of Glencoe, near Loch Tulla, boulders of a peculiar white granite were found by Professor Heddle. They were different from the adjoining rocks. He already knew that the rocks in the hills to the eastward were also different; so, in expectation of finding the parent rocks, a search towards the west was commenced. On reaching the Aonach-Eagach range of hills the same kind of boulders were seen, fewer in number, but larger in size. They were lying chiefly on the eastern side of the narrow ridge leading up to the summit of the nameless peak marked 2938 feet on the Ordnance map. On the next rounded haunch (2880 feet) they were not seen, but they reappeared on the ridge as it ascended to the eastern peak of Meal Dearg (3090 feet), and almost up to the summit of the western peak (3118 feet). “ Their position,” adds Professor Heddle, was most peculiar. They lay on a ridge not many times wider than their own hulh, and only on the eastern slopes of that ridge ; while on the lower hills, where they were first seen, the same boulder lay on the west slopes” {Sixth Report, p. 44). “It is a fact of con- siderable importance, bearing on any theory of transport, that these 830 Proceedings of the Royal Society boulders on Aonach-Eagach occupy positions much higher in level than any of the hills in a very ivide extent of country, so tliat it is difficult, if not impossible, to adopt for them the explanation of any local glacier ” {Sixth Report, p. 46). In the following year. Professor Heddle returned to the Rannoch district, to search for any farther traces of this stream of white granite boulders. To the S.E. of Loch Rannoch he found two hills, Gea Qharn and Greag Mhor (2595 and 2250 feet), forming a sort of ridge running nearly N. and S., and so situated as to cross what might have been the line of stream. Two boulders found, each weighing about 7 tons, very similar in colour and composition to Loch Tulla boulders. He next proceeded to Schehallion, situated about 3 miles farther east, and found on its western slope, about 140 feet below the summit, i.e., 3407 feet above the sea, a boulder of the Loch Tulla group, about three-quarters of a ton in weight. Reference is made to other geologists who had previously found boulders on Schehallion, near its top — one being Robert Chambers, who concluded from the striations on the rocks of Schehallion, that the stream which brought the boulders had flowed from W. 30° H. {Seventh Boulder Report, p. 34). Convener passed through Glencoe Valley thrice, the last time on foot, beginning near the upper end. He was impressed with the belief from what he saw, that ice had passed down the glen, smoothing the rocks along bottom, and so far up each of the sides, — and carrying blocks of these rocks for some distance down the valley. On the other hand, it appeared to him that blocks of rocks foreign to the valley had come up the valley at a subsequent period, — brought therefore, by the action of floating ice. One of these, a huge mass of Conglomerate, was resting on a terrace of gravel ; and above the gravel there were, on the hillsides adjoining, “extensive beds of sand” reaching to heights exceeding 2000 feet above the sea. Besides this Conglomerate boulder, there were granite boulders in such positions as to show that they also had come up the glen. The Con- vener concluded that the glen had first been occupied by a glacier; and that at a later period the land sank to more than 2000 feet below its present level, which would allow floating ice to pass over the Glencoe Hills, and to deposit on them some of the boulders they might be carrying {Fifth Report, pp. 52, 53) {Lithograph No. 33, Plate X.). 15. Kilmallie. — One boulder, 12 x 10 feet, fully 2000 feet above of Edinburgh, Session 1883-84. 831 sea, on summit of a hill. Another, larger, between Loch Shiel and Loch Askaig [First Eeport, p. 38). 16. Fort Augustus. — About 2 miles to S.W. of the town, on Corryarrick road, a boulder of grey gneiss, on a steep bank of gravel at base of a buff-coloured felspathic rock. As the hill-slope faces [N'.W., boulder seemed to have come from that quarter. It happens to be exactly at same height above Loch ISTess (207 feet) as boulder seen to the east of Urquhart [Fifth Report, p. 64). 17. Strathglass and Glen Urguhart (north of Loch Ness).* — (1) On hill above Affric Hotel, on east side of river Cannich, at height of about 720 feet above sea, rock planed and striated, the striae running N. by W. coinciding with direction of valley. At height of 970 feet above sea, a granite boulder lying on up- turned edges of gneiss rock — its position indicating that it had come from W. by N. [Fifth Report, p. 63). At summit of hill, about 1170 feet above sea, numerous boulders found, chiefly on slopes facing N.W. (2) On public road to Urquhart, a few miles from Affric Hotel, rocks on south side of road ground down and striated, in a line about E. and W., i.e., parallel with axis of main valley. At top of hill, about 660 feet above sea, several boulders found, resting on a bed of sandy clay, and on a slope of hill facing W. by S. The west sides of boulders chiefly rounded, as if worn by friction of bodies passing over them from west. All the rocks exposed show smoothings on sides facing west, as far up as hill reaches, viz., 927 feet above sea. (3) Whole of Glen Urquhart indicates, by quantity of gravel and sand on both sides, that it has formerly been choked by drift, which cut through and scoured out by the river. (4) On north bank of Loch Ness, half a mile east of Urquhart, many conglomerate boulders lie on hill sloping towards Loch Ness, from 200 feet up to 800 feet above Loch Ness. Eocks of hill here are gneiss ; Mealfourvonie hill, situated some miles to west, consists of Conglomerate rock. * Convener made this excursion accompanied by Mr Jolly (Inverness), to ascend Maum Saul, a mountain reaching a height of 3880 above sea, in order to investigate the truth of a report by Ordnance surveyors, that on the west side of this mountain, at a height of 3800 feet, horizontal beds of sand and gravel had been seen by them. After the foot of the mountain was reached, bad weather prevented the ascent. 832 Proceedings of the Royal Society At height of 450 feet above loch, deep beds of a fine sandy clay occur. One of the boulders is at a height of 340 feet above loch, which corresponds with a horizontal terrace on south side of loch. 18. Glen Morriston and Glendoe, on north side of Loch Ness, — (1) In Eighth Rejport (p. 15) Professor Heddle describes several boulders on the hills at the head of Glen Morriston, near Clunie Inn, at great heights, and some on very steep slopes, apparently transported from westward. (2) The Convener (^Fourth Report^ p. 23) describes a visit to Glendoe, at head of Glen Morriston, where he found several boulders of large size, at heights of from 919 feet to 1205 feet above the sea. These boulders rest on gravel and sand, and in height correspond occasionally with horizontal terraces occurring on opposite side of the valley where they occur. In a higher part of valley, viz., about 1190 feet above sea, deep beds of sand and gravel found. Terrace seen by Ordnance surveyors at height of 1280 feet, at top of glen. The Convener was told of a still larger boulder, about 1 6 feet high, at Clachnaharry, on south side of Loch Clunie, 2 or 3 miles west of Glendoe. 19. (1) In Stratherrick, a large patch of grey granite rocks occurs. They are extensively quarried, and therefore are easily recognisable. Blocks have been carried eastward, even to near Elgin. They occur also on the tops of the Conglomerate hills between Loch Kecklis and Loch Hess, at heights of from 1400 to 1500 feet {Jolly ^ in Fifth Report, p. 72). (2) Along north bank of Loch Hess, near east end, a patch of red granite occurs, blocks of which have been recognised in the Tomna- hurich gravel hill near Inverness, and even on towards Hairn and Forres {Fifth Report, p. 69). Along south bank of Loch Hess, near east end, a peculiar liver- coloured Conglomerate rock occurs, blocks from which seem identical with a number of large boulders east of Inverness {Fifth Report, p. 71, and Sixth Report, p. 47). The late George Anderson of Inverness states that in some of the drift deposits near Inverness there are pebbles and boulders “ that appear to have come from very distant parts of the country. Such,” he says, “are the white stone of Ben Hevis and of Strathconon of Edinburgh, Session 1883-84. 833 (Ross-shire), and the quartz rock of Royers” {Wernerian Trans., vol. iv. p. 205). Mr Jamieson of Ellon adverts to this same drift accumulation, known as Tornain Hill, in the following terms : — “ There are masses of coarse water- worn gravel rudely piled together, 200 feet thick. The stones are all water-rolled, and show no glacial striae. The pebbles are of various kinds of metamorphic and crystalline schists, red sandstones, conglomerates, granites, and porphyries. These materials look as if derived fromdhe rocks along the valley to the south-west” {Proceedings of the London Geological Society, January 11, 1865). (3) In town of Inverness, a boulder of greenstone or black granite, called Clacli-na-Gudaine''^ — Stone of the tub,’’ now standing in High Street, with pillar on it supporting town armorial bearings. Stone had formerly stood at top of clilf above River Hess, and from time immemorial afforded a convenient rest for the tubs or pitchers in which the women brought up water for household use. When a supply of water was brought into the town by pipes, the magistrates proposed to break up the boulder, but the townspeople objected at first even to its removal. A compromise was come to by the boulder being shifted to the side of the street, opposite to the Court-House, and by the erection on it of the Town Arms {First Report, p. 18). (4) At Clachnaharry , a boulder weighing about 100 tons, called “The Watchman’s Stone,” resting on a projecting part of the coast (opposite to Inverness), from which a good view can be had of Moray and Beauly Firths. Above Clachnaharry there are smoothed rocks, with grooves run- ning E. and W., a direction parallel with Beauly valley. (5) Culloden Muir. — Here stands “ The Duke of Cumberland’s Stone,” a Conglomerate boulder with six sides, height about 6 feet, and girth not quite 60 feet. Its longer axis W.H.W. On top of boul- der traces of striae running W. by H. Boulder lies on an extensive plateau about 450 feet above the sea. At nearly the same level a horizontal terrace is visible, looking south, on the hills to the south of the River Nairn, about two miles distant {Second Report, p. 158). There are no Conglomerate rocks, except on Loch Ness, which bear W.N.W. ; — or at Kilmorack (on River Beauly), which bear N.W., each place about 20 miles distant. Craig, Parish of. — About half a mile S.W. of village, a mica schist boulder, 17x8x9 feet. It lies on hills sloping down N.W. 834 Proceedings of the Boyal Society There is also a Conglomerate boulder known by name of “ Tom RiacJiT Its west side 18 feet, north side 21 feet, east side 24 feet, south side 21 feet, and height 20 feet — 652 tons. Boulder rests on gneiss rock. Lower surface seems smooth, as if it had been pushed over hard materials. Boulder has by some means apparently come down the valley of the Nairn, viz., from westward {Second Report^ p. 158). On plateau, 4 miles south of Inverness, at about 774 feet above sea, another Conglomerate boulder, with thin stratum of Old Red Sandstone on its top. Its girth about 51 feet, height 9 feet. Longer axis N. and S. A kaim of gravel and sand, about 900 feet above sea, situated north of boulder, running E. and W., or parallel with Nairn valley, on north side of which it occurs {Second Report ^ p. 158). (6) Dallanossie Parish, — Boulder (apparently coarse granite) 30 X 18 X 9 feet (360 tons), on Dallry Farm, Moy estate. Boulder split into two parts, which gives its name, viz., “ Glach Schuiltf or “ Cloven Stone” Height above sea 2090 feet {Captain White of Ordnance Survey). (7) Duntelchah Hill, west of Inverness, about 900 feet above sea, composed of coarse Conglomerate. On N.W. side rocks are ground down and smoothed; on S.E. side rocks rough and steep. Granite boulder, 7x4 feet, lies on N.W. slope of hill, about 30 feet below top. Longer axis N.W., with sharp end towards that quarter. No granite rocks in this district except to west, about 10 miles distant. (8) Flichity Valley (about 8 or 9 miles S.W. of Inverness), through which River Nairn flows. An isolated hill on south side of valley, about 1620 feet above sea, well covered with boulders, which are precariously situated on account of steepness of hill-side {Lithograph No. 32, Plate X.). They are chiefly on west slopes. On this hill there are horizontal terraces, with boulders on them. At east end of Flichity valley a great embankment, which, before being cut through by River Nairn, must have been the means of forming a lake filling the valley. The cut across this embank- ment, through which river flows, is about 200 feet deep. There are also in the upper part of Nairn valley many large gneiss boulders, supposed by Mr Jolly to have come from the west, several of which are split ; one at height of 2260 feet above sea-level. At Farr, in Nairn valley, to the east of the embankment, and near junction with another valley which runs N.W. up to Duntelchak, there of Edinburgh, Session 1883-84. 835 is a remarkable assemblage of gneiss or mica slate houldeis {Lithograph No. 34, Plate X.). They were first pointed out to the Convener by Mr Jolly. Some rest on glaciated rock surfaces, sloping down to westward, and which therefore suggest transport of the boulders from westward. Eeasons given for suggesting first a glacier, which passed down eastward, and subsequently a submergence of the land under the ocean (Second Report, p. 159). (9) About 6 miles S.W. of Inverness, an extensive plain, about 645 feet above sea-level, covered with drift, on which several Con- glomerate boulders occur. They probably came from Duntelchaig and other hills to westward. One is 24x21x8 feet — 310 tons. Longer axis W.N.W. On “ Graig-a-Claclianf at a height of about 1100 feet above sea, a large Conglomerate boulder called “ Watch Stone^' — made known to Convener by Mr J oily. It lies on gneiss rock, and on very edge of a precipice of 100 feet vertically below it, on its N.E. side. In order to reach a site in this position it could have come in no other way than in a direction between W. by N. and W.N.W., and almost certainly on floating ice. On the same hill there are other boulders of smaller size, whose position in like manner suggests transport from westward. (10) Some miles farther south there is a lake bearing name of Loch Clachanf probably on account of the number of boulders on its banks and the hills adjoining. Most of these are of grey granite. By reference to Professor Geikie’s Geological Map of Scotland, it will be seen that the nearest position for granite rocks in this district is Loch Paraline, about 15 miles westward. One of these boulders is 21 x 20 x 14 feet (218 tons) at 983 feet above sea. Another about same size, and at about 1259 feet above sea has its sharp end towards west. The east end is broad, and butted up against a gneiss rock, which would obstruct its passage eastward. On this gneiss rock there are E. and W. striae, which might have been made by the boulder pushing and pressing hard pebbles over the rock. (The facts given in (9) and (10) are taken from Convener’s Treatise on Ancient Water Lines, pp. 86, 87.) (11) Craig Phaedrich Hill, consisting of Conglomerate rock. On its N.W. slopes the rocks are bared, rounded, and smoothed, with boulders of gneiss lying on the N.W. slopes. Hardly any boulders or striated rocks are on south slopes of the hill. 836 Proceedings of the Boyal Society On several parts of the hill, especially on its south slopes, the rocks are broken up into large cubical fragments, resembling, in shape and composition, the boulders mentioned in (5) above {Second Report^ p. 163). (12) In the Ninth Report (pp. 10-12) there is an interesting list of boulders in the neighbourhood of Inverness by Mr Wallace, High School, Inverness. (13) Kingussie. — On Clunie M‘Pherson’s lands, two boulders of a coarse-grained granite. One is 1 1 x 9 x 6 feet, the other is about double the size of the former, with felspar crystals of a green colour, and mica plates about 1 inch square.* Longer axis of both, about E, and W. Both lie on a hill-slope, facing down west. Height above sea 1035 and 1080 feet. Eocks of district are clay slate. The nearest hill is Craig Dim, situated 4 miles to north on opposite side of Spey, the rock of which is also clay slate. Another boulder on Belville estate, 2 miles from Hewtonmoor Eailway Station, from 950 to 1000 feet above sea. Greatest length 14 feet, breadth at top 8 feet, height 9 feet. Longer axis S.S.W. At Laggan Free Church, a well-rounded granite boulder, 9x6x6 feet, with longer axis E. and W., corresponding with directions of numerous strise on a well-smoothed rock on which boulder lies. Nearest hills of granite are some miles to the west. KlNCARDINESHmE. 1. Banehory-Devenieh, near Glassel Eailway Station. Boulder called ‘‘ Bishop’s Stone”; circumference 44 feet, height above ground 8 feet, estimated weight 70 tons. Bluish granite, differing from adjoining granite rocks. An ancient stone circle of boulders about 200 yards distant. About 2 miles to north, rocks on Hill of Farre glaciated with strise, running E. and W., — parallel with axis of Dee valley. Fettereairn. — No boulders now in parish, of any size. Long banks of sand and gravel, running parallel with one another. 2. Maryeidter. — Boulder 5J x 6 x 6 feet. Longer axis N. and S. Eock of boulder supposed to be same as rocks to eastward {First Rep>ort^ p. 40). * The only other boulder with felspar and mica crystals, similar to those met with by Convener, is that mentioned as occurring on Treshlik Hill, p. 63. of Edinburgh, Session 837 Kirkcudbright. 1. Galloway. — Great accumulation of boulders at head of valley, at Loch Karroch. Among these are boulders of the peculiar graphic granite of Loch Eroch to the north, so that these must have been carried southwards across various ridges and valleys to places where now found. Craiglee, remarkable for numbers of perched blocks, some of immense size; their numbers on a long ridge of hill resemble a broken-toothed saw. Travelled blocks occur, even on summit of Merrick, highest hill in Galloway (2764 feet). A number of poised blocks, and ‘‘rock- ing stones ” {First Rejport p. 40). 2. Kells. — On Craigenbay Farm, a grey whinstone boulder 17 feet long and 10 feet high, 800 feet above sea. Longer axis K. and S. 3. Kirhbean. — On sea-shore at Arbigland, grey granite boulder 16 X X 7|- feet (about 80 tons), resting on sandstone rocks. Criffel Hill is about 3 miles to K.K.W. Eock there, same as boulder. In all the glens between Criffel and sea-shore numerous granite boulders, generally arranged in lines parallel with glens. 4. Penninghame. — Granite boulders chiefly; supposed to have come from Minnigaff Hills situated to K.E. Some large boulders on watersheds between Lochs Dee and Troul. 5. Twynholm. — Granite boulder supposed to have come from Gallo- way Hills, 6 or 7 miles to westward. Several Druidical circles here. 6. Borgue. — Boulder of red syenitic granite; oblong in shape. Longest axis K.W. Bests on low hill of decomposed trap. South-east end vertical and rough. Girth at 3 feet above base 23 feet. Ho granite rocks nearer than about 10 miles, viz., a range of hills between Dalbeattie (east of boulder) and Creetown (west of boulder). Sketch of boulder given {First Report, p. 40). 7. Generally. — Large rounded fragments of granite and syenite abundantly scattered over Stewartry, and so arranged as to indicate that they have been dispersed by some force proceeding from H.W. {Sixth Report, p. 27 ; Highland Societfs Trans., vol. viii. p. 716, Hay Cunningham). Professor Harkness, in the year 1870, made known to the Lon- don Geological Society his discovery of Criffel granite boulders in Cumberland. In his paper (published in the Quarterly Journal for Hovember 1870, p. 522) he states that “this Criffel granite occurs 838 Proceedings of the Eoyal Society not only in the form of blocks on the surface^ hut also in the hoidder claysP The Criffel granite blocks are also commou in the houlder days of the vale of Eden, He adds that there are also “ Eshars in the valley, which yield blocks of Criffel granite.” In the Mnth Eeport of the English Boulder Committee, an ac- count is given of the boulders found while excavating for the new docks at Maryport, on the south side of the Solway ; among them were granite blocks, varying in size from pebbles to blocks of a ton. It is remarked in the Eeport that “ the nearest granite occurs in “ Kirkcudbrightshire Hills, 15 or 20 miles distant, nearly due north.” In the Eifth Eeport of the English Boulder Committee (Br. Pr. for 1877, p. 82) there is notice of a Criffel granite boulder found near Liverpool in excavating for new docks. It is added “ that Mr J. Geikie and Mr Horne pronounced specimens which were sent to them to he from the outskirts of the Criffel granite area.” There is ground for believing that Criffel granite boulders occur even so far south as Lancashire. Mr Mellard Eeade of Liverpool, C.E. and F.L.G.S., wrote in the course of 1882 to the Convener, that having for some years, while investigating the drift deposits near Liverpool, collected specimens from boulders, some of which were evidently derived from rocks different from any belonging to that part of England, he wished to submit these to any person known to the Convener to he well acquainted with the rocks of the S.W. of Scotland. The Convener having suggested Mr Dudgeon of Cargen, Dumfriesshire, Mr Eeade transmitted the specimens to him, the result of which is explained in the following extract of a letter from Mr Eeade to the Convener-— “Mr Dudgeon recognises with certainty Criffel granite, having assured himself of its identification by having seen in some of the specimens submitted to him the minerals sphene and alla- nite, which he is not aware occur in any other granitic district nearer than Aberdeenshire and Sutherland. He also thinks some of the granites come from veins in the Silurian rocks about 7 miles from Dumfries.” ^ * Mr M. Reade has since (Feb. 1884) read in the London Geological Society a paper narrating a visit he made to Kirkcudbrightshire, for the purpose of comparing chips from the Lancashire boulders with the supposed parent rocks. In this paper he mentions his identification not only of granite boulders with the rocks of Criffel and Cairnsmore of Fleet, but also of Liver- pool Silurian boulders with Kirkcudbrightshire rocks. When his paper was of Edinhurgh, Session 1883-84. 839 Lanarkshire. Glasgoio. — (1) linear Fossil, sandstone rocks under boulder clay, striated, partly from N.W. partly from N.E., oldest apparently being from bT.W., judging by length and depth of striae. Boulders in the clay, recognised by Mr John Young of Glasgow University Museum, some from Kilpatrick Hills to K.W., and others from Campsie Hills to K.E. (2) At Brickwork, near Garscube Eoad, sandstone rocks, also striated from K.W., and more deeply than at Fossil. At this place, numerous boulders of old red conglomerate, grey granite, schists, &c., supposed to be from Bonaw and Kilpatrick Hills to K.W. {Second Report, p. 165). Linlithgowshire. 1. Bonnington Distinct . — (1) On Fumpherston estate, the ^^Ballen- geicli Boulder, in girth 10 or 12 feet; but now broken up into eight fragments. It is a coarse dolerite, of which no rocks nearer than Bathgate Hills, about 2 miles to K.W. Had been about 60 tons in weight. The boulder was lying on boulder clay. Hot far from this boulder there is another of quartzite, about a quarter of a ton in weight, and containing crystals of green mica, most probably transported from Highlands. (2) On Tornain Hill, Bonnington Farm, occupied by Mr James Melvin, another dolerite boulder, known as the “ Witch's Stone," about same size as that at Fumpherston, and about same height above sea, viz., 431 feet. It lies on a slope which faces W.K.AY. On digging below the boulder, Mr Melvin found it resting on decom- posed trap. Nearest rock of same kind is on Bathgate Hills, situated 5 miles W.N.W. There is a valley between Tornain Hill and Bathgate Hills, across which boulder had probably been transported. If a line be drawn from this boulder to Bathgate Hills, it passes close to “ Ballengeich " boulder. This boulder also has been broken into six fragments. Some archaeological interest attaches to boulder, as on one of its frag- ments there are “ cup markings.” (3) Formerly, on S.E. side of Tornain, another dolerite boulder, read he exhibited chips from these boulders and the parent rocks for com- parison. In this paper there is a becoming acknowledgment that Mr Mackintosh had been the first to refer the Lancashire granite boulders to Criffel (A G. S. Trans, vol. xl. p. 270). 840 Proceedings of the Royal Society 21x5x4 feet, lying with longer axis E. and W., and at height of about 300 feet above sea. If it also came from Bathgate Hills it probably had to come by floating ice, round Tornain Hill, by valley between Tornain Hill and the Crow Hills. (4) In channel of Eiver Almond, below Kirkliston, a boulder of Old Eed Sandstone conglomerate, 5 J x 4J x 4 feet ; nearest rock for which, is at Callander, about 40 miles to N.W., with several valleys and ranges of hills between. (5) At Eatho Eailway Station, rocks smoothed and striated on west sides, the direction of the striae being W.K.W. {Seventh Report^ pp. 23, 24). 2. Kirkliston. — The remarkable stone known to archaeologists as the “ Catstonef bearing a very ancient Latin inscription, which the late Sir James Y. Simpson deciphered, is described by him as ‘‘a massive unhewn block of secondary greenstone, many large boulders of which lie in the bed of the neighbouring river.” The block is 7 feet 3 inches in length and 12 feet in circumference {Proc. of Society of Scotch Antiquaries^ vol. iv. p. 122). Midlothian or Edinburghshire. 1. Pentland Hills. — The late Charles Maclaren was the first who described e boulders on these hills. The one of most interest is of mica slate, weighing 8 or 10 tons. The nearest spot from which it could have come is at or near Loch Vennacher or Loch Earn, about 80 miles to the K.W. With reference to the transport of this boulder, Mr Maclaren says: — “To reach the spot where it lies, it must have passed over extensive tracts of country from 500 to 600 feet lower than this spot. Even were all Scotland converted into a mer de glace, like Greenland, no moving mass in the shape of a glacier could carry this boulder (and there are many such) from its native seat in Perthshire or Argyleshire to Habbie’s Howe. An iceberg from the Korth or West Highlands, and floating in a sea 1500 or 2000 feet above the present level of the Atlantic, is an agent capable of effecting the transportation of the stone, and offers, I think, the only conceivable solution of the problem” {Edin. New Phil. Journal, 1846, p. 138). Eeferring to this boulder, and to another, also of mica slate, on the Pentlands, weighing about three quarters of a ton, the late Professor of Edinburgh, Session 1883-84. 841 Nicol remarked : — “ When it is considered that these masses must have been carried upwards of 40 miles in a direct line, floating ice seems the only agent to which their transportation can be ascribed ” {Lond. Geol. Soc. Journal, vol. v. p. 23). He adds : — ‘‘ Some of these Pentland Hill boulders are of kinds of rock which I have never seen in Scotland. On one hill, 1500 to 1600 feet high, I found these travelled stones particularly abundant, and apparently increasing in number from below upwards. In some places they appeared to form broad bands, running nearly in straight lines from H.H.W. to S.S.E., — and without any reference to the present declivity of the ground, — except becoming more numerous towards the summit of the ridge ” {Sixth Report, p. 26). A number of rock surfaces occur on the Pentlands with striee. Mr James Croll, of the Scotch Geological Survey, describes one of these on the very summit of Allermuir Hill, at a height of 1617 feet above the sea. On examining the striae he says he had no ‘‘ diffi- culty in determining that the ice which effected them came from the west. On the summit of the hills we found patches of boulder clay in hollow basins of the rock. Of one hundred pebbles collected from the clay, every one, with the exception of three or four com- posed of hard quartz, presented a flattened and ice-worn surface, and forty-four were distinctly stratified. A number of these stones must have come from the Highlands to the H.W.” {Fifth Report, P.82). In like manner. Professor Geikie, in his interesting Memoir on the Geology of the Neighbourhood of Edinburgh, observes that “ boulder clay lies along the H. W. flanks of the Pentlands, rising to a level of at least 1300 feet. When the clay has been removed, we usually find the rocks below polished, grooved, and scratched, in a direction nearly E. and W. or E.S.E. and W.S.W. The parallelism of the striations throughout the present district shows that the floating ice must have moved in a pretty uniform direction ; and that it was from the west, is rendered clear, by the striation of the western faces of the hills, by the great depth of drift on their eastern sides, and by the fact that the transported boulders, when traceable to their parent rock, have been carried from W. to E. The drift in this district indicates a period of slow submergence, which went on until probably every hill had sunk far below the sea-level, and when ice-borne blocks from the snow-covered islets of Isla or the 842 Proceedings of the Boyal Society Grampians, were dropped on the submarine slopes of the Pent- lands” {Memoir 'No. 33, p. 127) {Fifth Report^ p. 18). 2. Edinburgh and Suburbs. — The late Charles Maclaren, in his Geology of Fife and the Lothians, published in 1838, refers to boulders which he found on or near Arthur’s Seat, the Castle Hill, and Calton Hill. On Arthur’s Seat, about twenty or thirty boulders are specified up to 30 tons, most of which he identified with rocks situated to the west of the boulders. Others (of sandstone) he found at much higher levels than any sandstone rocks now on the adjoining hills (p. 64, 2nd edition). To the east of the Castle Hill, numerous boulders are mentioned as having been found to the eastward, which are with good reason referred to the Castle rock ; but other boulders are mentioned (p. 91) as having been found on the west side of the Castle rock, which must be referred to some more distant locality. It is right for Convener to notice a Conglomerate boulder standing on a stone pillar in the public gardens at the foot of the Castle rock. It was brought there as an ornament to the gardens by Mr Henderson, nurseryman, who had been entrusted by the magistrates with the ar- rangement of the gardens. He had found it in his own Nursery Gar- dens, Leith W alk. It is probably a true erratic, hailing from Callander. On the Calton Hill, boulders are mentioned by Mr Maclaren as found there, “ of the very peculiar syenitic greenstone of Cor- storphine Hill” (p. 72). In the year 1847,* a new road (at the expense of Government), was made round Arthur’s Seat, which required an excavation to be made on the S.W. side of the hill, between the main body of the hill and an outlying knoll known on account of its basaltic columns as “ Sampson’s ribs,” at height of 390 feet above the sea. The hollow between the hill and the knoll was excavated to a depth of 20 or 30 feet, in order to lessen the steepness of the road. Thereby a trough or gully, with rocky sides sloping steeply towards the axis of the gully, was disclosed. The axis of the trough was about N.W. and S.E. ; its length about 120 yards; its width at the narrowest part where the road was made, about 10 yards. As the rocky sides of the gully sloped down towards the * The particulars here given will be found in a paper by the Convener published in the New Edinburgh Philosophical Journal for January 1847. ' j of Edinhurgh, Session 1883-84. 843 axis, these sides would probably meet below j but the excavation for the road did not reach that point. The gully had been filled with till, and contained numerous boulders, — almost all of which were found to be different from any of the rocks on Arthur’s Seat, viz., felspar, greenstone, porphyry, limestone (both lacustrine and marine), quartz, greywacke, with fragments of shale and coal. Many of these blocks were found in contact with both sides of the gully. The largest blocks were near the north end. The large blocks were well rounded ; the small blocks less so. One large boulder on the west side of the gully appeared to have been pressed against the rock there, and had stuck in that position, being rounded and also partially striated on its N.E. side, — an indication of the friction it had undergone, by materials forced through the gully from a IST.W. direction. The gully was not throughout of equal breadth ; at its narrowest point, the sides (when the boulder clay and drift were cleared away) were found at one place to be about 15 feet nearer one another than elsewhere. The rocks on the east side had been ground down, smoothed, and striated, some of the striae being continuous for nearly 6 feet, and J of an inch deep. Generally, the striae were horizontal; but at and near the narrowest part of the gully the striae were seen to rise up at an angle of 4° or 5°; — caused probably by the obstruction to the drift when being forced through the gully. One peculiarity in the striations deserves notice, as showing the direction from which the striating agent moved. The striae were most numerous and deepest on the east side, suggesting that the striating agent had moved in a direction from a more westerly point than bT.W. The rock surfaces facing the S. and S.W. were neither striated nor smoothed. There is another spot, on the south side of Arthur’s Seat, worthy of notice, on account of the boulders there, and the position occupied by them. It is on the west side of Windy Gowl. When the new road was being made there, a thick bed of clay and sand, in stratified layers, was exposed to view. In this bed, many blocks from the overhanging rocks of the hill were found embedded. The bed of sand and clay had been formed round these boulders^ showing 3 K VOL. XII. 844 Proceedings of the Uoyal Society that after they fell sedimentary matter brought by water had been deposited. The largest of the blocks was round and smooth on its west side, rough and angular on its east side. Besides the blocks of stone, which were of the same nature as the rocks of Arthur’s Seat, there were in this bed of sand and clay blocks foreign to Arthur’s Seat (brought from the west probably), viz., red compact felspar, red syenitic porphyry, marine limestone, and clay iron- stone. At Easter Duddingstone the excavations for the ^Torth British Bailway exposed a number of large boulders embedded in the stiff blue till. Two of the boulders were of Old Bed Sandstone Con- glomerate— one an old porphyry, one a black basalt — rocks not existing in the immediate neighbourhood, but belonging to localities in the far west. Most of them were on their upper surfaces flat, smooth, and striated, the striae running in directions varying between hT.W. and At the sea-shore, between Joppa and Magdalen Bridge, the Con- vener examined many large boulders sticking in the blue till, most of them flattened on their upper surfaces with striae pointing Several presented smoothings and furrows on their west sides, none on their east sides. One of the boulders presented two sets of striae — one running hJ.X.W., the other running W. by S., the former partly obliterated by the latter, which therefore must have been the more recent. 3. Dalmahoy. — Two boulders, one 13 x 10 x 6 feet, and the other 10x8x5 feet, lie at the side of the Water of Leith. The longer axis of both is E. and W. Both were covered with striae also running E. and W. {Sixth Report, p. 27). 4. Craiglochhart. — Excavations were made in boulder clay for a hydropathic establishment. A number of boulders were seen by Convener in their original undisturbed positions. There were several of sandstone. The contractor for the building, having his attention drawn to these by the Convener, was asked if he knew any locality where there was sandstone rock of the same variety ? He said that the sandstone rock quarried extensively at Hailes and at Bedhall was exactly the same. On being asked to indicate the situation of these quarries, he pointed in a direction H.W. (by compass), distant about a mile. of Edinhurgh, Session 1883-84. 845 5. Tynecastle, in west suburbs of Edinburgh. — A basaltic boulder examined by Convener and Mr Stevenson, C.E., x 4 x 2 feet, buried in a knoll of muddy sand, discovered on removal of the knoll. The sand contained numerous pebbles of all kinds, hard and soft, such as quartz, shale, coal. Height above sea 200 feet. Sides of boulder well rounded. Smallest end of boulder pointed westward. Both upper and under sides of boulder striated. Striae more deeply cut on under than on upper surface. The striae on under surface showed they had begun to be formed at east end of boulder, probably by the boulder having been pushed towards east, over hard rocks. The striae on upper surface showed that the tools which formed them had acted on the boulder first at west end. 6. Grant on. — The sandstone rocks at the Old Quarry near the sea were covered by boulder clay, which had embedded in it many blocks derived from Linlithgow and Stirling shires. The striae on their upper surfaces all run E. and W., viz., a direction parallel with the general axis of the Eirth of Eorth {Edin. Neiv Phil. Journal for January 1847). At Granton Harbour^ on the west side of, at the shore, there are two large whinstone boulders, with striae on their upper surfaces, the direction of which is W. 3° S. (magnetic). 7. Leith Docks. — In new Albert Docks excavations were made in the boulder clay, in course of which a number of large boulders were found. They consisted mostly of blue whinstone, also some of quartz, limestone, greywacke, sandstone, and black ironstone concretions derived from beds of coal and shale. On most of the boulders there were smoothed surfaces and striae, bearing nearly the same direction, viz., points between W. and Among these there were two metcdlic boulders, which, having a strange appearance, were brought to the Convener by the Inspector of Works ; and to Professor Crum Brown (of Edinburgh University), the Convener submitted them for examination. One, nearly spheri- cal, measuring 7J inches in circumference, and weighing 26 oz., had been found about 4J feet down in the clay bed, among the general mass of boulders. The other, more exactly spherical, measured in girth 30 inches one way and 31 inches transversely, and weighed 54 lbs. It was found 10 feet below the top of the boulder clay bed. 846 Proceedings of the Royal Society Professor Crum Brown having analysed both balls, reported the largest to have a specific gravity of 3*36, and to be composed of silica 52*3 per cent, and of pyrites 47 '7 per cent. The smallest had a specific gravity of 4 “6 3, and was found to consist of the pure ore of white iron pyrites or marcasite, unmixed with any other sub- stance. Mr Murray, of the “Challenger” Expedition, having kindly under- taken to examine the larger ball, reported that a microscopic ex- amination revealed that it consisted “ of crystalline particles of quartz and marcasite. The marcasite fills the interstices between the grains of quartz ; and among the quartz there are pieces of mica.” Mr Charles Peach at the same time informed the Convener that in several districts to the west (viz., Falkirk, Slamannan, and Kilsyth) there are beds of shale and coal, containing ironstone nodules, known among the miners as “ brassy balls f some of which contain marcasite. He added that “ the direction of the strice and carry of the boulders in this (the Kilsyth) district is E. or E. 5° K. Either of these sources (he remarked) could supply '‘Palls'’' at Leith, as they are right in the direction of the “ ice-flow ” {Fourth Report, p. 29). In consequence of the foregoing information, the Convener went to Campsie (about 8 miles K.E. from Glasgow), and in the work- ings of coal and shale there he obtained several ironstone balls, which, on being submitted to Professor Crum Brown, he reported contained almost exactly the same constituents as the specimens found at Leith. He added, that “deducting the coaly matter, the iron and sulphur were in the proportion in which they are generally found in marcasite, viz., iron 45*6, and sulphur 54*8. As to chemical compositions, therefore, the small metallic boulder may be considered as exactly agreeing with the nodules found in the Campsie coal strata.” With regard to the larger ball, not so purely metallic, Mr Hutchi- son of Carlowrie having accidentally seen in the Convener’s house, Edinburgh, the specimen excavated from the Leith boulder clay, informed the Convener that balls of the same appearance, and much larger, were found in sandstone rocks quarried at Dalmeny and Humbie. The Convener thereupon visited these quarries, and of Edinburgliy Session 1883-84. 847 saw several specimens of sncli balls, apparently concretions in the rock. Having brought one or two specimens to Edinburgh, he submitted them to Professor Crum Brown, who reported that they “ consist externally of a thin shell of sandstone, and internally of a mixture of quartz and marcasite, closely resembling the substance of the large ball from Leith. The mean specific gravity of the ball was 3-49.” These facts regarding the two metallic boulders found in the Leith boulder clay, therefore afford strong presumptive evidence that they had been transported across Scotland, along with other bouldres, whose parent rocks occur also in the west. As to the mode of transport, Mr Peach, in his letter to the Con- vener (printed on p. 29 of Fourth Boulder Report), whilst allowing that the balls might have come from Kilsyth or Slamannan, in con- formity with the general “ direction of the striae and carry of the boulders in this district,” viz., E., or E. 5° N., suggested ^Hce-jloio^^ as the medium of transport, but without explaining whether he meant sea ice or land ice. With reference to this question, it is right to keep in view that the Campsie district, from which the metallic boulders are assumed to have come, is only 150 feet above the present sea-level ; and that, as this district is about 30 miles distant from Leith, the gradient would not be sufficient for the movement of a glacier, even if there had been mountains at or near Campsie sufficiently high to have generated a glacier."^ 8. Alnwick Hill, near Liherton. — Excavations having been made in the boulder clay here, for the formation of large water reservoirs, innumerable boulders were excavated. They were chiefly whin- stones, felspar, porphyries, limestones, and Old Eed Sandstone — all most probably from the K.W. Some of these boulders showed strise both on the under and the upper sides, the direction of wliich was approximately K.W. {Fourth Report, p. 29). Inchkeith. — The Convener visited the island, under the guidance of Colonel Muggridge, RE., and found that the rocks consist chiefly of basalt and porphyry, intruding among coal strata. In various * A small map of district, given afterwards in reference to Stirlingshire boulders, may here he referred to. 848 Proceedings of the Royal Society places, tlie rocks were covered by beds of boulder-clay, gravel, and occasionally sand. The Inspector of Works informed the Convener, that at the east end of the island, when removing a bed of shingle (about 60 feet above the sea), he had picked up out of the shingle two pebbles of red granite^ about the size of a hen’s egg. Thinking it curious to find granite there, he had laid them aside, but could not now find them. The Convener, having been informed that there was a shingly beach at the H.W. end of the island, descended to it, and found large pebbles of granite (both red and grey), gneiss, quartz, and hard Silurian rocks. On the highest part of the island (west of the Lighthouse) at 182 feet above the sea, the rocks on portions of the hill facing the hl.W. have been planed down to even surfaces by some agency from the W. No striae were distinguishable {Sixth Report, p. 26). Morayshire. Dyhe. — Near west end of approach to Darnaway Castle several boulders of granite and gneiss, from 2 to 3 tons each. Forres. — Conglomerate boulder, 9 J x 8 x 8 feet, weighing about 44 tons. It is situated on hill side fronting Cromarty, which bears N.W. by N., from whence boulders are supposed to have come across the Moray Tirth. Convener heard of another boulder of same description in a higher part of the hill, to the eastward. Elgin. — Boulder called “ Carlings Stone,'' on Bogton Farm, about 230 feet above sea ; a coarse Conglomerate. About half a mile to N. W. a smaller Conglomerate boulder, called Young Carlin's Stone" {First Report, p. 31, and Second Report, p. 152). There are no Conglomerate rocks in the low-lying districts, where these boulders are situated. Wherever they have come from, they must have been carried. Conglomerate rocks exist in the hills to the south, distant 5 or 6 miles. Convener was informed by Mr Martin, teacher, Elgin (well acquainted with the rocks of the district), that the Conglomerate for- mations in the hills are, in mineralogical composition, distinguishable of Edinhurgli, Session 1883-84. 849 from the Conglomerate hoiilders in the counties of Moray, Nairn, and Banff. Two other sources were considered by him more pro- bable— Cromarty to the N.W., and the hills near the east end of the Caledonian Canal. Throughout the county there are hundreds of rounded boulders of granite, gneiss, and mica slate, whose shape suggests that they have been pushed or rolled over the surface. These are chiefly em- bedded in gravel, clay, and sand. Pluscardine Hill has had lodged on its north slope a number of boulders which have apparently come from N.W. There is a gneiss boulder, 13x8x6 feet, about 46 tons, called Chapel Stone f situated to west of Pluscardine Chapel ; also a Syenite boulder, 12x8x3 feet, about 1 3 tons. The rocks in situ here are Old Red Sandstone. Carden Hill forms a rocky sandstone range running about E. and W. Between it and Pluscardine Hill, there is a shallow valley, through which boulders may have been rafted to their present sites in an easterly direction. The two Carlin Stones might have come that way. The rocks along ridge of Carden Hill, have been ground down by some agent which has passed over it from N.W. Many boulders of granite and gneiss lie on the ridge, most of which have longer axis N. W. by W. Some lie along ridge, on its northern edge, apparently stopped there in their farther progress ; others lie on south side of ridge, as if pushed over it, and placed beyond reach of transporting agent. Blocks of the Carden Hill sandstone rock are also there, as if broken off the ridge by the agent which passed over from north. The ridge of Carden Hill extends for about a mile, and is at a height of 400 feet above sea. Many smoothed and striated surfaces are visible, the direction of the striae having been observed at different places as follows : — W. by N. ; W.N.W. ; N.W. by W., and N.W. The most frequent direction was N.W. At one spot, striae observed N. by E., and crossing the N.W. striae ; the forming appearing, therefore, to have been first formed {Second Report, p. 154). Quarrywood Hill, about 200 feet above the sea, composed of sandstone rocks. On N.W. slope there are four or five large Con- glomerate boulders, about 140 feet above sea-level. 850 Proceedings of the Royal Society Burgh-head. — Eev. Dr Gordon of Birnie conducted Convener to Clarkeley Hill, on which several granite and gneiss boulders were found lying on slope of hill. One has its longer axis N.W. and S.E. Several others showed strice in same direction. On Eoseile estate here, Hare'^ or “ Witch Stonef a Conglome- rate boulder 21 x 14 x 4 feet, with longer axis H.W. Inmrugie Lime Quarries. — Limestone rocks striated in an E. and W. direction. In boulder clay here, boulders of oolite found, which must have come from Eoss or Sutherland shires. Duff us Puhlic School. — Convener had shown to him portion of an oolite boulder found here, 125 feet above sea. “ Witch Stone f a large Conglomerate boulder, at 250 feet above sea, on hill-side sloping down to N'.W. It is exactly similar to ‘‘ Carlings Stonef in respect of nodules of granite, gneiss, or purple- coloured quartz contained in it. Its longer axis is H.W. and S.E. It lies on a thick bed of sand. Lossiemouth. — About IJ mile west of Covesea lighthouse, a large boulder of silicated sandstone, on a hill sloping to N.W., with striae on boulder running H.W. and S.E. On old sea margin, 20 feet above present sea-level, a Conglomerate boulder, same in composition as Carlin Stone. New Spynie. — Four Conglomerate boulders, lying on Old Eed Sandstone rocks. Lla7ihryde, St Andrews. — Gneiss boulder called “ Grey Stone f 15x9x7 feet, about 70 tons, lying in bed of old Spynie Loch. Rothes. — Convener informed by Mr Martin, teacher, of six hornblende boulders, lying on gneiss rocks {First Report , p. 31). Between Forres and Hairn there are extensive beds of sand and gravel, mostly in stratified beds, and containing boulders almost always rounded. The angular boulders are generally on the surface, not so embedded. Hairnshire. Grog. — “ Tom Riachf boulder of Conglomerate. — See Inverness county, under head of “Inverness and Croy” {First Report^ p. 43) {Lithograph No. 35, Plate X.). Cawdor. — On hill of Urchany, composed of granite, at levels above sea, of from 300 to 700 feet, four immense Conglomerate boulders 851 of Edinlmrgli, Session 1883-84. with popular names, described in First Report, p. 42 [Lithograph No. 34, Plate X.). There are granite rocks in hills to south, on which blocks of Old Eed Sandstone lie, and in such quantities that the}’’ are gathered for the building of walls. These blocks probably came from the north, where there are rocks of the same kind [First Report, p. 42, and Second Report, p. 166) [Lithograph No. 36, Plate X.). On “ Piper's Hill," where rocks are Old Red Sandstone, a Con- glomerate boulder, weighing about 10 tons, lies on the N.W. side of a gravel kaim. These Conglomerate boulders are all mineralogically similar, being composed of quartz, limestone, syenite, felspar, and other hard angular pebbles. Most of them are partly buried in sandy drift. The district on which they lie slopes down towards N.W., and is about 200 feet above sea, from which distant about a mile. The longer axis of these boulders is chiefly N.W., and on that' side they present smooth surfaces, whilst east side is rough and angular (see Diagram 8 in Second Report, and p. 166, and also First Report, p. 42). Captain White of Ordnance Survey informed Convener that, having tried to find out where these boulders came from, he was of opinion that they had come from Ross-shire. He reported also having met with granite boulders (both red and grey varieties) — the largest 1 2 x 8 J x 8 feet, and with longest axis N.W. A kaim of gravel and sand, with steep sides, runs on an average E. and W. through parish, but occasionally deviates slightly from this direction. Its average height above adjoining district is 30 feet [Second Report, p. 166). Ar detach. — In Bog of Fortnightly, about 5 miles distant from the sea, and about 270 feet above it, a Conglomerate boulder with live sides, having girth of 51 feet, and 9 feet above ground. The block is scarcely rounded at its edges and corners, and therefore has probably been carried, not pushed, rolled, or thrown down, but planted gently on its site. It is smoothest on N.W. side, roughest on S.E. It is surrounded by hills on every side except towards N.W. [First Report, p. 42). Kinsteary (about 2 miles S.E. of Nairn). — A peculiar flesh- coloured fine-grained granite rock is worked, blocks of which are stated by Mr Jolly of Inverness to have been transported eastwards 852 Proceedings of the Royal Society beyond Forres, — gradually lessening in size and numbers, reaching to Elgin, Lossiemouth, and even farther e.ast. Pieces also occur on the shores of Loch Spynie [Fifth Report, pp. 74, 75). Mr Wallace of Inverness mentions having found a specimen of this Kinsteary granite beside Buckie harbour, about 20 miles east of Lossiemouth [Sixth Report, p. 49), and he has seen many smaller specimens in the fields. Neither rock nor boulders of this peculiar granite have been found uiest of ETairn. Northumberland. In Chillingham Park (Earl Tankerville’s seat), between Wooler and Alnwick, there is a large boulder of red porphyry, besides several small boulders of granite. The rocks there in situ are Carboniferous sandstones and limestones. The nearest localities for porphyry and granite are the Cheviot Hills, about 8 miles to "W.N.W., which reach a height of 1800 feet above sea. Many ridges and valleys lie in the intervening district [Fourth Report, p. 34, and Edin. Roy. Soc. Trans., vol. xvii. p. 35). Orkney. Eday. — Conglomerate boulder, about 8 tons, situated near top of hill, about 250 feet above sea, called Giant's Stone." Legend as to it having been thrown from island of Stronsay, where there are said to be Conglomerate rocks, of which none in Eday. Longer axis points S.W. and N.E. Patrick Neill, in his Orkney, Visit to, at p. 38, refers to “ the great Stone of E dap," as “a huge flag rising about 16 feet upright in the midst of a moor.” Frith and Stennis. — Peebles of white sandstone lie on the hills. Kocks of island are all red sandstone. Sanday. — Gneiss boulder about 14 tons. Rocks of island are Old Red Sandstone. At Stromness, 30 miles to S.W., gneiss rocks occur in situ. A legend that the boulder was thrown by a giant from Shetland [First Report, pp. 10, 44). The late Dr Patrick Neill states that, if this boulder came from Stromness, it would have to cross several arms of the sea in a distance of 34 miles, from W.S.W. [First Report, p. 44, and Second Report, p. 167). of Edinhitrgh, Session 1883-84. 853 Stromness. — Two granite boulders lie on Old Ked Sandstone, near Manse. Range of granite bills 6 miles long, situated to eastward {Second Report, p. 169). Walls (in south end of group). — Lydian stone boulder, weight about 28 tons. Large numbers of granite boulders scattered over hills. The valleys show (in opinion of reporter, James Russell, teacher) both glacier and iceberg agency {First Report, p. 44). In a paper on the “ Glaciation of the Orkneys,” by Messrs Peach and Horne of the Government Scotch Geological Survey {London Geological Society's Journal for November 1880), it is said that boulders do not occur very plentifully.” The only island in which boulders are mentioned as seen by them, is Westra, where “ blocks of granite and quartzite are on the slopes of Cleat Hill ; and rounded boulders of red sandstone from Eda occur in the southern district, as well as along the western shores.” Messrs Peach and Horne state ‘‘ that the only part of the. Orkneys which has granite or other crys- talline rocks is at Stromness, where they form a strip about 4 miles long by 1 in breadth.” If the Westra boulders came from Strom- ness, they must have been transported about 40 miles in a N. or N.N.E. direction, across what now is occupied by several groups of islands and deep sea sounds. If, on the other theory, the boulders of sandstone on the southern and western shores of Westra came from Eda (as suggested in the above passage), they must have been transported about 10 to 12 miles in a N.W. direction, across what is now a sea sound, in some places 25 fathoms deep. Messrs Horne and Peach, in the memoir now referred to, re- ferring to the beds of red boulder clay in the islands of Eda, Sanday, Stromsa, and Sliapinsliay, mention that in these clay beds there are boulders smoothed and striated, most of them foreign to the islands," and in many cases, accompanied by “ numerous frag- ments of marine shells ; " — “ these fragments being smoothed and striated like the stones in the boulder clay,” — characteristics, which (they say) there can be no doubt are due to the very same cause in both cases ” (pp. 656, 657). North Ronaldshay. — Boulders foreign to the island mentioned {Eighth Report, p. 7). In Ninth Bo^dder Report (p. 20) there is a further account of 854 Proceedings of the Royal Society blocks of stone, foreign to the rocks of the island, viz. , Conglomerates, granite, syenite, chalk, oolite, limestone, and sandstone. In Eonaldshay boulder clay, containing these blocks, there are fragments of Oyprina Islandica, Astarte^ Dentalium^ and other marine shells. The Conglomerate boulders are supposed to have been carried from the adjacent island of Sanday ; the blocks of granite and syenite from Stromness and Pomona, distant about 45 miles to S.W. Messrs Horne and Peach {Journ. of Lond. Geol. Soc. for Hov. 1880) mention that in Stronsa Island (not far from Eonaldshay) there is a bed of clay, 20 to 30 feet thick, containing granite, gneiss, oolite, and chalk flints, &c., all foreign to the island, besides frag- ments of marine shells. Mainland. — Mr Miller of Ben Scarth reports a valley bissecting the island, which he thinks was formerly an arm of the sea. The lochs of S tennis and Stanay now occupy it. Ho large boulders ; but on north exposures of hills there are small stones strewed over the surface, quite different from rocks in situ. The former are chiefly white freestone ; the rocks Old Eed Sandstones or flagstones {Second Report, p. 167), Messrs Peach and Horne express an opinion that all the boulders in the Orkneys, as well as in the Shetlands, were carried or pushed across the islands by a Scandinavian ice sheet from the S.E. Objections to that theory were suggested by the Convener, in articles which appeared in the Geological Magazine for 1881, and in an address by him to the Edinburgh Geological Society in May 1881. In addition to the foregoing notes respecting Orkney boulders, it is proper to notice the researches of Messrs Peach and Horne. In a paper, published in the Journal of the London Geological Society for Hovember 1880, it is mentioned, as the result of their survey, “ that the islands have been glaciated in one determinate direction, independently of their physical features. When we con- sider that the glaciated surfaces along the cliff tops, as well as the roches moutonnees on the hill-slopes, prove that the islands must have been overflowed hy ice, we cannot resist the conclusion that the ice 855 of Edinhurgli, Session 1883-84. movement during the primary glaciation originated beyond the limits of Orkney ” (p. 654). “ From the manner in which the rock striations maintain their N.W. bend, irrespective of the physical features of the country^ it is evident that the agent which produced them must have acted independently of the islands^' (p. 660). Peeblesshire. Kirkurd. — Three boulders of gneiss or trap, differing from rocks of district {First Report^ p. 44). Newlands. — Remarkable kaims {First Report, p. 44). Peebles. — At east end of town boulder of white quartz, S x 2^ feet, used to stand in field, to which it gave name of “ White Stone Knowe,” — alluded to as a boundary stone in year 1436. Mr Richardson, of Edinburgh Geological Society, who was the first to take public notice of the boulder, states that “ the nearest beds of quartz are about 80 miles to the N.W.” Height above sea 550 feet {Fourth Report, p. 31). The late Professor Hicol refers “ to boulders of gneiss, granite, and mica slate in Peeblesshire, which belong to rocks unknown in the hills of that county;” — and adds, “they seem to require for their transport more powerful agents than mere currents of running water ” {Sixth Report, p. 28). Perthshire. Aberfeldy. — (1) On north of Tullypowrie village considerable numbers of schist boulders — rocks in situ being clay state. Boulders well rounded, as if rolled. One of them called “ Clack Chin'uinf or “ Stone of Doom ” {First Report, p. 45). (2) Two miles H. of Tullypowrie, two very large boulders of mica slate at about 1500 feet above sea, shown to Convener by Mr M‘Haughton, merchant. They rest apparently on drift. Cubical in form. One found* to be 71 feet in girth, and 17 feet high, weighing about 600 tons. Surrounded by hills on north and west, which overtop boulders by about 700 feet. But H. W. from boulders there is a depression in hills. 856 Proceedings of the Royal Society summit level of wliicli only about 200 feet above boulders. Through this gap boulders may have come ; but boulders are so cubical and sharp in angles that they must have been very gently lodged in present position. If they had fallen from any height they would have been fractured. These boulders have popular name of Claehan M‘‘hadf or “ Stones of the Fox ” {First Report, p. 45). (3) Above Pitnacree House, schist boulder resembling hypers- thene, 15xlljx4, differing from all rocks near it, called “ Clach Odharf or Dun StoneP Auchtergaven. — Granite boulder, 10 x 8 x 3 feet, weighing about 8 tons, about 200 feet above sea, called “ DeiVs StaneP Longer axis N.E. Numerous cup markings on it. Supposed to have come from hills 30 miles to north. Aherfoyle. — Arndrum Hill is a ridge of the Conglomerate rocks which cross Scotland from Dumbarton by Callander in an E.N.E. direction. On this ridge near Aberfoyle (230 feet above sea) there are six boulders of greywacke, forming a line bearing N. and S. — each about 3 cubic yards in size, and from 2 to 20 feet apart from each other. To the west of this line of boulders, four other similar boulders lie along the ridge, stretching to nearly top of hill, viz., to 454 feet above sea {Ninth Report, p. 16). Blairgowrie. — Seven boulders of granite and mica schist, about 200 feet above sea. No rocks of same kind nearer than Braemar range of hills, about 30 miles to N.W. Callander. — Gneiss boulder on top of Bochastle Hill, called ^^Sam- soFs Putting Stone,” resting on Conglomerate rocks. Longer axis N.E. In a very unstable position, being close to edge of a precipice, facing W.S.W., and about 330 feet above valley. About 50 feet below the above boulder there is another gneiss boulder, lying on a very steep slope of the same hill, facing westward, — from which quarter it must also have probably come {FBst Report, p. 46, and Second Report, p. 169) {Lithograph No. 37, Plate X.). Chinie. — Several boulders on tops of knolls. They probably have come from Grampians, which lie to N.W. {Second Report, p. 170). Crieff. — Two large Conglomerates, one called “ Witched Stone,” and two of granite, one called “ Cradle Stone,” lying on the ‘‘ Knock ” Hill {First Report, p. 467). of Edinburgh, Session 1883-84. 857 Doune (near Kilbride). — A large Conglomerate boulder, weighing about 900 tons (First Report, p. 46). The nearest Conglomerate rocks in situ are W.K. W. from boulder, and distant about 7 miles. The boulder in shape is angular. It lies on gravel. The boulder must have been carried to its site (Estuary of the Foidh, p. 41). Dunblane. — Gneiss boulder on Cromlix estate, about 4 miles south of Grampians, 17 x 10 x 5 feet. Longer axis S.W. and K. E. In Redgorton parish, four boulders (at west end of gravel ridge) reported to be Silurians; distant from Grampians 12 miles (lliird Report, p. 5). Dunkeld. — On Craigiebarns Hill, to K.E. of town, mica schist boulders, lying chiefly on knolls and other exposed surfaces which face K.W. at a height of about 1000 feet above Eiver Tay. On this hill, rocks smoothed and striated, by some agency which evidently passed over them from N.K.W. The directions of the striae at lower levels correspond more with axis of valley, which is about K.E. The highest striations seem to indicate an agent which passed obliquely across the valley (Second Report, pp. 170, 171). Fortingall. — Gneiss boulder, 24 x 16 x 13 feet, called Clach an Salainer Height above sea, 2500 feet. Longer axis K.W. Com- posed of six or seven large fragments, weighing about 300 tons. Rests on coarse gritty sand. Rocks in situ clay slate. About 500 feet below boulder, thick beds of clay, sand, and gravel, denoting aqueous agency (First Report, p. 46, and Second Report, p. 172). Fowlis. — Several granite boulders near Abercairney, lying on Old Red Sandstone. Have come most probably from K.W., in which direction, at a distance of about 20 miles, there are granite rocks. Supposed to have been used as places of worship and sepulture in ancient times (First Report, p. 47, and Second Report, p. 171). Killiecrankie.- — ^A large angular limestone boulder, half a mile north of Tenandry Manse ; — believed to have come from Beii-y- Gloe, or some other mountain adjoining to the north. On Fascally estate, immense beds of stratified gravel and sand (filling the valley, and cut through by mountain torrents), traced by Convener up to height of 1570 feet above sea. He was told by Rev. Mr Grant of Tenandry of there being similar beds at 858 Froceedings of the Boyal Society a still higher level on Ben-y-Gloe. Boulders of granite, gneiss, quartz, porphyry seen by Convener in the Bascally drift-beds {Second Report, p. 172). Killin. — On hill to west, about 1350 feet above Loch Tay, thick beds of gravel and sand; and therefore about 1650 feet above sea {Second Report, p. 173). On Morenish, east of Killin, and about 1100 feet above Loch Tay, several large boulders {Fourth Report, p. 31), of which sketch given. These, as shown by positions, have all come from westward. Kilspindie. — Seven granite boulders, from 5 to 6 tons weight. Five form a line, having a K.W. direction, all differing from the adjoining rocks {First Report, p. 47). Kirhmichael. — RocMng Stone, 7 x 5 x 2J feet, and several tall boulders near it, called Qlachan Sleuchdaidhf or Stones of Worship ” {First Report, p. 47). Logie Almond, — A whinstone boulder called Ker Stonef about 48 tons in weight, on north bank of River Almond, near a bog ; “ Carr ” being Gaelic for “ Bog.” There is another boulder, a Conglomerate, resting on Old Red Sandstone, called “ Cid na Cloich,” or “ Stone Rook.” A stream forms a nook or angle with the drum or ridge, on which boulder stands. Another Conglomerate boulder on Risk Farm {First Report, p. 47). Glen Dochart. — The axis of valley is about E. and W. On its slopes facing the north, and near bottom, there are many large boulders of granite, which may have come from Ben Cruachan. They occur also on the ridges, on south side of valley ; — some so placed as to show transport from westward. At height of 1250 feet above sea, a vertical rock, well smoothed, with horizontal groovings on its west and north sides, indicative of some agent which has pressed severely on it in passing from west- ward {Fourth Report, p. 32) {Lithograph Ko. 38, Plate X.). Schehallion Mountain (top of, 3560 feet above sea). — Gravel beds indicative of aqueous action, seen by Convener, up to about 3000 feet, to which height small blocks of a fine-grained grey granite seen. Side of hill with smoothest rock surfaces looks X.W. by W. Xo striae seen {Second Report, p. 173). Mr Jamieson of Ellon states {Quart. Journ. Lond. Geol. Soc. for of Edinlurghy Session 1883-84. 859 1865, p. 165) that Schehallion is marked on top, as well as on its flanks, by traces of ice passing over it from the north. He further states, that along the north slopes of the great ridge of mica slate, stretching from Schehallion in an E._ and W. direction for 10 miles, he saw many houlders of granite and porphyry^ at heights exceeding 2000 feet, above the sea ; — the one at the highest elevation, being a granite boulder, at an elevation of 2370 feet. On the ridge where these houlders lie there are no granite or porphyry rocks ; but such rocks do occur to the northward (as in Glen Tilt)^ where, therefore, probably is the source from, which the houlders came {Seventh Report^ p. 40). On the Perthshire Hills, between. Blair Athole and Dunkeld, Mr Jamieson found ice-worn surfaces of rock on the tops of hills, at elevations of 2200 feet, as if caused by ice pressing over them from the N.W. ; — and transported houlders at even greater heights. On the highest watersheds of the Oehils^ at altitudes of about 2000 feet, Mr Jamieson found pieces of mica schist full of garnets, which seemed to him to have come from the Grampian Hills to the N.W., showing that the transporting agent had overflowed the Ochil range {Seventh Report , p. 42). Pitlochry. — On road to Straloch, a. mica slate boulder, about 8 tons weight, called Gledstonef about 1800 feet above sea, lying on gravel drift ; adjoining rocks are clay slate. Legend that this boulder gave nanae to Gladstone family, an infant having been found at boulder by shepherd, who took it to his wife to he nursed. Near parish church of Straloch, “ Clach Mhor^' {Great Stone), a boulder of coarse granite, about 24 x 20 feet, and weighing about 800 tons. Many other houlders of mica slate and quartzite beside it. Supposed to have come from the north, through a valley there. Adjacent rocks, clay slate {First Report, p. 47). Luih. — Large houlders lying in a line along ridge and top of Beinn nan Clach. One, much rounded, on the solid rock of the very summit, 2309 feet above sea. Summit rock also much rounded. The outcrop of the strata on hill-side have been broken off by some means {Ninth Report, p. 13, and Lithograph No. 39, Plate X.). .Penfrewshire. Kilharchan. — A porphyry boulder, 27x17x12 feet, weighing 3 L VOL. XII. 860 Proceedings of the Boyal Society about 300 tons, called “ Clach a Druidh ” {Stone of Druid). Eocks of same kind as boulder in hills to W, and 1ST. about 2 miles distant {First Report, p. 48), Paisley. — Mr Jamieson of Ellon describes boulders in clay beds of brickworks. Many of these boulders’ show glacial striae. It is common to find Balani sticking on under surface of these boulders. Suggested in explanation, that after Balani had grown on boulders, the boulders were floated away by ice, and dropped on mud where now found. Mr Jamieson adds that “I some- times found, on heaving up a boulder, a number of young crushed mussel shells beneath it, as if squashed by the fall of the stone.” The clay round also occasionally exhibits black stains, as if from the decay of sea- weed that had been attached to the stone ” {Bond. Geol, Soc. Proc,, xx. p. 276 {Seventh Report, p. 43). Boss AND Ceomarty. Glenelg (West Coast).-— On right bank of Elg, a grey granite boulder 21x18x10 feet, (280 tqns) — its sharp end points JNT.N.W. {Fourth Report, pp. 3, 4). Glen Rossdale, — About 8 miles from Glenelg, several boulders, which, on account of positions, seem to have come from the X.W. Ordnance surveyors reported several horizontal terraces among the hills of this glen, up to 800 feet above sea-level {Fourth Report, p. 49). Lochalsh (West Coast). — Gneiss and quartz boulders. Longer axis of first, E. and W. ; — -of second, N. W. and S.E. {First Report, p. 49). Granite boulders of large size at Ardross, Hewmore, and Achnacloich {Second Report, p. 175). Shieldag (LooXiCdiiroia). — Boulderl8 x 10 x 10. Longer axis E. and W, ; also another. Both in precarious positions {First Report, p. 50). Applecross (viz., on West Coast), — Three large boulders, one near shore at Eossel, called Clach Oiuf weighing about 60 tons; other two about 30 tons each, called respectively Clach Mhoir^^ and Clach Bhan ” used as landmarks from the sea. Kaims at Ardbain and Ardrishach, each extending more than 2 miles along coast {First Report, p. 48). The late Professor Mcol notes that on the tops of the Applecross Hills there are boulders of large size. He says that the direction of the rock stri^ there is S. 20° W. (true). Gairloch (West Coast). — -hrumerous boulders were found by 861 of Edinliirgh, Session 1883-84. Convener along coast to north of the Gairloch Hotel, and at all heights up to the very summits of the hills, reaching to nearly 1 000 feet above sea. The late Professor McoPs description of these boulders is not inappropriate, when he says that these “ hills about Loch Maree and Gairloch are strewed with innumerable fragments of red sandstone, perched, like sentinels, in the most exposed and perilous positions, on the very edge of some lofty cliff, or on the polished summit of domes of gneiss.” These red sandstone boulders belong mostly to what has been termed the Cambrian formation, reddish-brown sandstone rocks, which exist along the coast towards the north, and partially also in the east coast of the Lewis. The rocks of the Gairloch Hills are generally gneiss. Lithograph JSTo, 40 (Plate X.) represents a granite boulder on the edge of a high sea-clifiE facing the west, 747 feet above the sea, projecting 2|- feet beyond the edge of the cliff ; having apparently been lodged there by some agent which, striking upon the cliff, caused the boulder to slide off upon the cliff. Lithograph Xo. 41 (Plate X.) represents one of the hills on the coast, to the north of the Gairloch Hotel, 585 feet above the sea, with two boulders on the west side of its summit. The Convener, on ascending the hill to examine the boulders, found that the large boulder was 7 feet long by 3.J feet high, and that it projected 2 feet beyond the edge of the cliff. As the rock on which it rests slopes down towards X.W. at an angle of 15°, the Convener thought there would not be much difficulty, by means of a crowbar, in projecting it over the cliff altogether. Lithograph Xo. 42 (Plate X.) shows the foregoing boulder, with the rock it rests on, on a larger scale. This boulder is a blue whinstone, the small boulder a red sandstone, and the rock of the hill clay slate. Lithograph Xo. 43 (Plate X.) shows a rocky knoll, near the base of the same hill, on which a number of true erratics are clustered. The uppermost of these (6x5x3 feet) rests on the others, in such a position as to show that it had come from the X. W. On the hills between Gairloch and Loch Pionn, the position of the smoothed rocks, and also of boulders, seemed to indicate a movement rather from W.S.W. than from the usual direction of X.W. The deflection, the Convener thought, could be accounted for by a range of hills there, against which the transporting agent may have struck {Fifth Report^ p. 56), 862 Proceedings of the Boy at Society Loch Maree. — Rocks on road between Gairlocb and Loch Maree showed striae, in usual direction of W.N.W. and E.S.E. Boulders are visible on all the hills. Near Loch Maree Hotel, at height of about 1000 feet above sea, a plateau found by Couvener, well covered by boulders lying on drift. On another hill near the hotel, about 900 feet above the sea, a well-rounded boulder was found, very near the top, on its west side, lodged in a shelf, where it pressed at its east end against the rock of the hill, as shown on Lithograph No. 44, Plate X. Achnasheen {Dingwall and Strome Ferry Bailway). — A boulder 15 feet in girth of grey granite, on a gra,vel terrace, 610 feet above sea. Locality interesting, on account of the immense beds of gravel and sand which have been formed here — no doubt by the agency of the sea ; and probably flattened by lacustrine waters, of which Loch Rosque is a remnant. Several hills to the south ascended by Professor Heddle; — one of them, Sgurr-na-Lapaig feet), requiring ‘‘the hardest climb ” he had ever experienced. For about 1500 feet above “ Loch Mullardoch the slope was at an angle of 47°. At height of 1530 feet there rests on this slope a boulder 12x8x7 feet, of hard quartzy gneiss, which he says must have been brought there,” as it differs from the rock of the hill {Ninth Report, p. 16). Ben Wyvis (3426 feet), near Pingwall, — Its N.W. shoulder pre- sents whole acres of rock swept bare of soil, with rounded and polished boulders of a peculiar veined granite, identified with rocks to the westward, in the tract called Dirriemore. These boulders are found half way up Ben Wyvis. Similar boulders occur, strewed over the country both north (Alness and Ault Grand), and south (Strathgarve) of Ben Wyvis. In Strathgarve some of the boulders are as large as cottages {Fh'st Report, p. 48). Dirriemore. — Mr Jolly of Inverness states that the peculiar granite of this district has been carried “ eastward f none of it ^hvestward.” It has been carried across the Cromarty Eirth, and scattered in large masses even over the Black Isle. It is plentiful over the “ Laigh of Moray ” and along the sea-shore, between Burghead and Lossiemouth {Sixth Report, p. 47). Mr Wallace of Inverness also reports having seen Dirriemore of Edinburgh) Session 1883-84 863 granite in numerous boulders in tlie excavations for tbe new harbour at Buckie in Banffshire {Sixth Report, p. 49). Edderton (west of Tain), — Three large boulders of grey granite pointed out to Convener at about 1000 feet above sea, on side of hills sloping down tov/ards IST.N.W, Books on which they rest are Old Bed. A horizontal terrace is site of one. The idea that they came from Cairn na Gunneig^^ {Hill of Pitcher), situated 12 miles to N.W. (as suggested by Bev. Mr Joass of Golspie), is disputed, as rocks there are stated to be a red granite. Another idea is that they came from hills near Bogart, 10 or 12 miles to N. or kf. by E., as rocks there said to be grey granite {First Report, p. 49, and Second Report, p. 175), Fannich Mountains (situated west of Ben Wyvis), — Mr J. F. Campbell (Islay) wrote to Convener that on these hills, 2700 feet above sea, there is a boulder of grey gneiss with garnets. Its local name is Clack Mhor na BiachdoilF It is 30 x 10 x 3 feet, and there is a train of large boulders to be seen in a valley not far off. Bocks smoothed and striated. Direction of striae, parallel with valleys {First Report, p, 49). Fodderty. — Boulder angular in shape, 14x8x5 feet. Looked on as Druidical. There is another with an inscription, which is supposed to commemorate a battle between two clans. Tain. — Granite boulder, weighing about 60 tons, lying on Old Bed Sandstone, about 2 miles N, of Tain at road side, ‘‘ Sir Walter Scott ’’ boulder of red granite, supposed to have come from “ Cairn na Cunneig ” mountains, situated to N,W. {First Report, p. 50). Tarhet Ness. — “ Balnahruach ” boulder, a coarse reddish granite, 33 feet in girth and 9 feet high. Longer axis E, and W. This boulder, and another near it, not so large, supposed to have come from “ Cairn na Cunneig ” hill, which visible from boulder bearing W.N. W. and distant about 30 miles, A line from boulder to this hill would cross arm of the sea, 10 or 12 miles wide, between coast at Tain and Tarbet Eess {First Report, p. 80, and Second Report, p, 175). Dingwall. — Mr Morrison, teacher in the Academy, and Secretary of the Boss-shire Field Club, sent notes, of which the following is an abstract : — On the south slope of Tulloch Hill there are three boulders of a pinkish granite, of the following dimensions : — 11 x 7 x 7 feet, major 864 Proceedings of the Royal Society axis ^^.N. W., at about 550 feet above sea ; — 8 x 5 x 5 feet, major axis N.JST.W., at about 400 feet above sea ; — a flat block of mica schist 11x7 X 2 feet, at 620 feet above sea, major axis E. and W. On this last-mentioned boulder there are ruts and striae running N.W., and about thirty-six artificial cup-markings. On Drynie Farm, S.W. of last mentioned boulder, at 610 feet above sea, a mica schist boulder 12x8x4 feet, major axis KKW. On its surface six stria tions, running N. and S., with one cup-mark at south end. On Tulloch Hill, another pinkish-coloured granite boulder 900 feet above sea, 8x6x4 feet, with major axis N.W. The prevailing rock on Tulloch Hill is bluish-grey indurated sandstone slate. Where strata crop out on opposite side of valley their edges have been rubbed and smoothed on their north faces by some natural agency moving in a direction from H.W. On north slope of Tulloch Hill a moor stretches up to height of about 1100 feet, on which many small boulders of same kind as above, — and to be found also all the way down to Cromarty Firth. Mr Morrison set out on an excursion to west, with the idea of discovering the direction from which these Tulloch boulders had come. At Ach-na-Clerach he found “ a gigantic mass of the same kind of granite as the boulders, 25x23x12 feet, — the rock on which it was resting being different from that of the boulders. At the confluence of the rivers Glascarnoch and Strathvaick he found rock of the same variety as the Tulloch boulders, but at a lower level than Tulloch Hill. He inferred that the boulders had been carried eastwards over the south shoulder of Little Wyvis, and that “ they probably came from Carn-Cuineag through the open- ing occupied by Loch Glass.” Mr Morrison, accompanied by some geological friends, proceeded next to Cairn Cuuneag^ 2744 feet above sea. It is the highest hill in Easter Koss. Its two peaks, or Pitcher lugs^ are pinnacles of granite. Its slopes are covered by enormous masses of granite semi-cubical in shape. An opinion was formed that most of the boulders in Easter Koss had been derived from this mountain, and its lesser neighbours Carn-Maine, and Cam an Lochan. The saddle between the two peaks appears like a shingly beach ; — rounded stones of about 10 pounds weight are packed here and 865 of Edinburgh, Session 1883-84 there in crevices, with longer axes of the stones lying generally in one and the same direction. HoXBURGHSHlRE. Gastleton. — Many blocks of granite (red ^nd grey varieties) lie on greywacke and Carboniferous rocks, — -which apparently came from Dumfries and Kirkcudbright shires, 30 to 40 miles distant^ crossing Esk and other rivers {Siodh Report, p, 28). Rounded boulders of grey granite occur on the fields and moors near Castleton Manse, where Convener saw several from 3 to 4 feet in diameter. On east bank of River Esk, about 2 miles below Lang- holm, Convener saw granite boulders — both red and grey varieties — ■ some of them very large. A number occur also in the Gill burn, which flows into the Liddell above its junction with the Esk. These granite blocks lie on the greywacke strata, as well as on the coal measures. The nearest known hill of granite is CrifFel, which consists almost entirely of grey granite, situated about 20 miles W.S.W. from these boulder^. The next nearest place where granite rocks occur is in Ayrshire, at Loch Doune, bearing about W. by K. from the boulders. In a small stream north of Tofts House, and about three quarters of a mile east of Edgerstone, there were seen by Convener several angular blocks of greywacke, resting on a purplish porphyry rock. The nearest point where there are greywacke rocks in situ is about half a mile to west, between which, however, and these blocks, there is a porphyry hill several hundred feet high. There is no greywacke to the south or east (“Geological Account of Roxburghshire,” Trans. Edin. Roy. Soc., vol. xv. p. 412). In this parish there is a remarkable kaim, composed partly of gravel, partly of sand, in horizontal beds. It runs for about half a mile ; is about 200 feet wide at base, and from 50 to 60 feet high. In the gravel there are blocks and pebbles of granite (both red and grey), as well as fragments of shale and coal, — derived, no doubt, from rocks to the westward. The kaim forms nearly a straight line, the direction of which is K.E. by E. {Trans. Edin. Roy. Soc., vol. XV. p. 463). Another long ridge of sand occurs near Eckford, on the River Cayle, running E.K.E, 866 Proceedings of the Royal Society Jedburgh. — Porphyry boulder, supposed to have come from Dunion Hill, which is 2 miles to the west. Pormerly a Granite boulder on this hill (seen by Convener), which must have come from Galloway or Dumfriesshire (First Report, p. 50). Neshit. — Hear the village (about 8 miles S.W. of Kelso) a green- stone boulder, identical in composition with rocks on Penielheugh Hill, on which stands Waterloo Pillar. Boulder is on a knoll, a little to H.W. of top of knoll. Penielheugh is S.W. from boulder, and about a mile distant. Transporting agent moved, therefore, here in a HE, direction. Hill is 774 feet above sea, and boulder 224 feet above sea. Eocks where boulder lies are Old Eed Sandstone. Ruber slaw. — On this hill a large boulder of greywacke found by Convener, lying on Old Eed Sandstone rocks. Hearest greywacke rocks in situ are about 3 miles to westward. If boulder came from these greywacke rocks it must have crossed low ground 800 feet below level of boulder (Edin. Roy. Soc. Trans., vol. xv. p. 454). Selkirkshire. Galashiels. — On the top of Meigie Hill, 1430 feet above the sea, there is a Silurian boulder 6 x 4J x 3J feet, with its longer axis H.W. and its sharpest end pointing in that direction. The boulder is on the east side of the apex of the hill, and 12 feet below it. It is lying on drift. Meigie Hill is composed of Silurian rockSi It stands by itself ; there being no hills of equal altitude within some miles of it. Other boulders of a smaller size occur on the hill. They seemed to the Convener to be all erratics (Sixth Report, p. 30). Shetland. Br assay Island. — A number of coarse white sandstone boulders on east side of island, at heights of from 40 to 360 feet above the sea, differing from rocks in situ^ which consist of Conglomerate and Old Eed Sandstone flags. Largest boulder 10 x 7 x 4 feet. Its longer axis H.W. There are said to be distinct groovings on it, some of them 3 inches deep ; — their direction E. and W. Agent which striated rocks must in that case have crossed a valley at right angles (Dr Gordon of Birnie, Eeporter) (First Report, p. 43, and Second Report, p. 176). of Edinburgh, Session 1883-84. 867 Foula Island, — Situated about 20 miles from nearest other island, and with a sound between, of 50 fathoms in depth {Second Report, p. 177). On this island, which has on it a hill reaching to a height of 1370 feet, several boulders were reported to the Committee. The Eev. James Kussell, in 1873 (who was then resident in Walls), visited the island, and refers to several boulders — situated in the south half of the island, — the north half he had not examined. From the middle of the island, to south end, he reported drift as high up as 700 feet, containing much granite and gneiss, which he supposed to have come from Mainland. In the middle of the island there are two boulders of irregular shape, each weighing about 2 tons, — their composition he does not mention. Mr Eussell stated that at the south end of the island there are three boulders of gneiss and two boulders of granite, each weighing from 3 to 5 cwt., and which he supposed came from the Culswick and Delting Hills on Mainland, towards the N.E. Messrs Peach and Horne, on the other hand, suggest that these boulders may belong to rocks in situ on Foula itself, inasmuch as the eastern part of the island (they say) consists of gneissose rocks, with a mass of granite in the N.E. corner {Geol. Mag. for August 1881, p. 372). Messrs Peach and Horne, however, mention that they discovered in the boulder clay of Foula a block of epidotic syenite from Dun- rossness ; — a locality which bears S.E. from Foula, separated by sea at least 50 miles in breadth^ and having a depth of 70 fathoms. Houssay Island. — Oti a clitf 200 feet above sea there are loose blocks resting on rounded and polished rocky knolls ; the knolls having been evidently polished before receiving the boulders {First Report, p. 43). Rapa Stour Island was visited by the late Dr Hibbert in the year 1822 {Edin. Journ. Science for 1831, vol iv. p. 86). He found in it several peculiar schists, foreign to the island, apparently derived from rocks at Hilswick Ness, situated to the N.E., and distant about 12 miles across St Magnus Bay, which has a depth of 40 fathoms. This island Was visited also by Professor Geikie, who states that he found on it many “ transported blocks of gneiss, schist, and other rocks foreign to the locality ” {Nature, vol. xvi. p. 415). 868 Proceedings of the Boyal Society Besides the boulders pointed out by Dr Hibbert, Messrs Peach and Horne say that on Papa /SYowr they saw others of “ Old Bed rocks, derived from the area occupied by the rocks between Sand- ness and Bixiter Voe;” — places on Mainland, situated to the S.E. of Papa Stour, and separated from it by an arm of the sea. Hilswick NesSf the south end of an isthmus, on the north side of St Magnus Bay. Dr Hibbert refers to a transported boUldet on the summit of this promontory ; — describing it as “ a surprising block of granite ; — ■ removed from a rock, the nearest site of which is about 2 miles north” {Edin, Journ. Science^ vol. iv. p. 89). Messrs Peach and Horne, who had not mentioned this boulder in their paper, adverting to Dr Hibbert’s notice of it^ say that “ this boulder might have been derived from some of the masses of the same material, lying at a slightly greater distance to the E. and H.E. of Hilswick” [Geol. Mag\ for August 1881, p. 372)* If that view be taken, the transport must have been across an arm of the sea running H. and S. on the east side of Hilswick Hess. Roeness Hill, on Horth Mavine, 1476 feet high; — Dr Hibbert says, this hill being “ composed of red granite^ I was struck with the immense number of boulders of a primary greenstone', which appear to have been removed from a site 2 or 3 miles oil’, and to have been brought in a southerly or south-westerly direction up a gradual ascent of 3 or 4 miles {Edin. Joiirn, Science, vol. ivi p* 89). Messrs Peach and Horne admit the facts as here stated. They say they “ entirely support our conclusions, viz.j of the boulder having been carried up hill by the Scandanavian ice-sheet, in a S.W. direction” {Geol. Mag. for August 1881, p. 371). Additional Localities. — The Kev, Dr Gordon of Birnie visited Shetland in the year 1872, and sent to the Committee the following notes (1) Boulders. — Hear Horth Mavitie (the extreme north of Main- land) there are large boulders between Hilswick and Ollaberry. He sent to the Committee pencil sketches of three boulders, situated in the same Horth Mavine district, between St Magnus Bay and Yell Sound. They are syenitic. One near Eela water is 16x12x6 feet. Another called Crupnd (bent) is 11x8x8 feet. The third called Bonhus, situated between the other two, is8xl0xll feet. 869 of Edinburgh, Session 1883-84. (2) Strice on rocks seen by Dr Gordon, at two places, about 20 miles asunder ; one a mile north of the fishing huts of Stennis on N.W. shore of St Magnus Bay, on coarse Conglomerate rock. The other place was at Islebury, where there is a valley running N. and S. The striae showed that striating agent had crossed valley in E. and W. direction {Second Report, p. 177). Lunnasting — Stones of Stoffas. — Specimens from these blocks were shown to late Professor Nicol of Aberdeen, who after examination considered them to be gneiss^ the same as the rock of the island- They are from 20 to 22 feet high, and 90 feet in girth. Height above sea 100 to 120 feet. The Professor, from the account given to him of them, thought the stones had probably been carried f- — there being no land near them at a higher level {Second Report, p. 193). The following notes were sent to Convener, by some person, evidently well acquainted with the locality, but whose name has unfortunately not been preserved : — Four boulders, looking “ like pale granite,” on the estate of Lunna. Nos. 1, 2, and 3 stand near each other in north part of parish, not far from sea, and at a height above sea-level of from 150 to 200 feet. No. 1 is in height 22 feet; length, 36 feet; breadth, 25 feet, angular in shape ; direction of longest axis N.Mh No. 2 is in height 19 feet; length, 34 feet; breadth, 14 feet; angular direction of longest axis N.E. No. 3 is in height 11 feet 4 in. ; length, 8 feet 7 in. ; breadth, 8 feet 2 in. ; direction of longest axis NtW. Nos. 1 and 2 separated from each other by a distance of 10 or 12 feet; the intervening space being filled with large masses which have apparently fallen from No. 2. , Nos. 1 and 2, known as “ The stones of Stoffas T This word said to be a corruption of ‘‘ Stay fast ”; the legend being, that two giants were passing through Lunnaness, when some superior power arrested their farther progress by pronouncing the words, “ Stoffas / ” No. 4 stands by itself, surrounded by deep moss, within a few yards of the highest point of a hill, about 4 miles to the south of the other three stones. Note by Convener.- — The stones of Stofias are referred to by late Dr Hibbert, in his volume on Shetland. He describes them as “ enormous detached masses, which do not seem to have undergone 870 Proceedings of the Eoyal Society any distant removal, since they repose on rocks of a precisely similar kind ” (p. 179). Professor Heddle of St Andrews informs Convener that he examined these stones, and thought they had been detached and wrenched off from other rocks, and moved in a direction towards E.S.E. (^Eighth Report, p. 7). Fair Isle Parish.— ^qy. Mr Laurence, catechist, reported that there are no boulders above 10 tons, but that there are several small boulders of Conglomerate quite differing from any rocks in island {Eighth Report, p. 7). He adds that there was one large block of sandstone which was blown up in 1880. It differed from any rocks in island, and was similar to the Eday sandstone. The island of Eday is about 13 miles to S.S.W. of Fair Isle {Eighth Report, p. 8). North Unst. — All over Unst the rocks show abrasion, and, in many places, deposits of drift, enclosing stones of various sizes. Mr Peach, senior, at the request of the late Sir Roderick Murchison, examined this most northern isle of the Shetlands, and gave in a Report to the British Association in the year 1864. He stated that he “ascended the Muckle Heog Hill, reaching to a height of 500 feet; and found the W.lsT.W. end vertical, and polished to the depth of at least 150 feet.” Professor Geikie in an article in Nature, of 17th September 1877, refers to the foregoing report by Mr Peach, and says “ that from his own observations he can speak confidently as to the correctness of Mr Peach’s deter- minations.” Sumburgh Head. — Conglomerate botilder lying on sandstone rocks {Second Report, p. 44). In addition to the information in the foregoing notes, regarding boulders, it is right to refer to the information given by Messrs Peach and Horne (in their paper on the Shetlands) regarding the extent to which all the hills, even the highestj show traces of glacia- tion {Jour, of Lond. Geol. Soc. for November 1879). They say — that “ from Sumburgh Head northwards to Unst we found everywhere the clearest evidence that Shetland must have been at one time smothered in ice ” (p. 706), “ It is apparent, on a moment’s consideration, that the direction of of Edinburgh, Session 1883-84. 871 the striae would have been widely different, had the island radiated its own ice, and had the glaciation been purely local ” (p. 791). “ Tor these various reasons, we are justified in inferring that the glaciation of these outlying islets is due to the action of an ice-sheet originating far beyond the sphere of Shetland,” (p. 792). “ The highest ground in the centre of the Mainland is likewise ground down and striated. The ridge which extends from Weesdale Hill (842 feet) to Scallafield (916 feet) reveals the fine lines as well the flutings of the ice-chisel ” (p. 793). Stirlingshire. 1. Alloa. — Basaltic boulder, 13x12x11 feet, called ^Mlair Sto7ie,” about 7 0 feet above sea. Longer axis N. and S. Assuming boulder to have come through valley ox kyle, between Abbot’s Craig and Damyat, it must have travelled in a direction from N.W. by W. {First Report, p. 50). 2. Kilsyth and Strathblane. — Mr Jack, of Scotch Government Geological Survey, reported two boulders, — one of mica slate, weigh- ing about 6 tons, 1260 feet above sea, its parent rock supposed by him to be to the N., and distant 15 miles. The other boulder is Conglomerate, 8x4x3 feet, its longer axis being W. 20° N., its parent rock supposed by him to. be also to N.W. {First Report, p. 51). 3. Campsie. — Mr John Young of the Hunterian Museum, Glasgow, accompanied Convener to an inspection of the district near Campsie, and pointed out the following objects of interest : — (1) On Craigend Moor, about 450 feet above sea, sandstone rock presented great sheets of smoothed surface, evidently ground down by severe or long-continued friction, with occasional striae running S.E. by S. In some places there were quartz pebbles in the sandstone rock, which were ground down, showing marks of rubbing chiefly on the N.W. sides. At four other places there were striations on rocks, pointing re- spectively S.E. by S. and S.E. J S., S.E. by S., S.S.E. Looking from this moor towards the IST.W., hills are seen about a 1000 feet high, at one place with an opening between them of about IJ miles in width, through which, if there was a current, it might pass over Craigend Moor. 872 Proceedings of the Royal Society Several boulders were pointed out. Two were of a species of trap common in the Kilpatrick Hills, situated some miles to W.K.W. Another boulder was a grey granite, which, judging from the size of its felspar crystals, Mr Young supposed might have come from Ben Awe, a mountain situated to N.W., and distant about 30 miles. There were also several Conglomerate boulders, derived probably from the belt of that rock, which, running from Dumbarton, crosses Loch Lomond in a K.E. direction towards Aberfoyle. The Convener at another time, when on Campsie Hills, found rocks at 800 feet above the sea, striated in a direction E. and W. On the Kilsyth Hills, a few miles further east, the rock striae point the same way. On Croy Hill, a knoll of trap rock, being the summit level between the Eirths of Clyde and Eorth, about 160 feet above the sea, there is an immense accumulation of boulders. Some of the boulders are of old Conglomerate, which must have come from the westward and stuck on the knoll {Fourth Report, p. 42). The relative positions of these localities may be more readily understood, by referring to the annexed map. - — ^ Direetion of roqk striae ; B, Craigend Moor ; K, Croy Hill ; Boulders shown by black dots, * , * 4. St Ninians. — Boulder weighing about 200 tons, at height of 1250 feet above sea, reported by Mr Jack, but no particulars given {First Report, p. 51). 5. Sheriffmuir , 3 miles from Bridge of Allan, a large boulder called “ Wallace’s Putting Stone ” {Fourth Reyort, p. 34), of Edinburgh, Session 1883-84. 873 6. Stirling and Doune districts. — Conglomerate boulders occur at the following localities {Sixth Report, p. 31) : — (1) At Kilbride, boulder of about 900 tons (mentioned under Perthshire). (2) On Landrick Estate, boulder of about 360 tons. (3) At Keltie Bridge, boulder weighing about 60 tons. (4) On Gartincaber, boulder weighing about 16 tons. (5) On North side of River Teith, boulder weighing about 13 tons. (6) In the Burn of Campsie, two boulders each weighing about 13 and 24 tons. (7) In the district traversed by the hill road between Doune and Callander, multitudes of smaller size. (8) At Cornton Brickwork (between Stirling and Bridge of Allan), small boulder found in bed of clay. (9) On the rocks adjoining Stirling Castle on the north, small Conglomerate boulders, besides others of gneiss and greywacke. (10) At Loch Coulter and' Gillies Hill (places 3 miles south of Stirling), several Conglomerate boulders, besides others of mica slate and felspar porphyry. (11) On Plean Estate (4 miles S.E. of Stirling), boulders of Con- glomerate, gneiss, granite, greywacke, and whinstone. (12) At Glenbervie, near Torwood (5- miles S.S.E. of Stirling), a Conglomerate boulder, 6 feet square, found by Convener. (13) On Dunmore Estate (9 miles S.E. of Stirling), a Conglomerate boulder of about 10 tons, found by Convener. A more particular account of the foregoing boulders may be found in “ The Estuary of the Forth," p. 41, where it will be seen, that all those which are elongated in shape, generally have their longer axis in a direction N.W. and S.E. There can be no doubt that all these boulders had been carried from hills situated to the H.W., near Callander and Aberfoyle, as there are rocks there of the kind composing the boulders, and in no nearer district. On the north side of Stirling Castle the trap rocks are traversed by narrow gorges, running about E. and W., the sides of which in many places present smoothings and striae, especially on the south sides, indicating transport from a point a little to the north of west. * Edmonston & Douglas, Publishers (1871). 874 Proceedings of the Royal Society The strise are generally horizontal, hut occasionally are inclined slightly upwards towards the east. A few small boulders, well rounded, occur in several of the gorges. Among them,, granites a,nd conglomerates were observed. Craigforth Hill, about 2 miles west of Stirling, has smoothings on its rocks near the top (198 feet above sea), and a few striae running in a N. W. and S.E. direction. The Convener found on it also small boulders, apparently from, rocks situated at or near Aberfoyle, which bears W. J N. from Craigforth. On or near the Racecourse at Stirling (situated S.W. from the Castle), about ISO. to IGO feet above the sea, there are several granite boulders lying on smootked sandstone rocks. The largest is 7x3x4 feet. It is on a rocky knoll, the smoothest part of which slopes down towards K.bT.W. As the boulder, from its composition, most probably came from the hills situated to the N.W., it must have lodged on what would be. the lee side of the knoll. 7. Aberfoyle. — Arndrum HiU, reaching to height of 454 feet above sea, forms part of the ridge of Conglomerate rock, which traverses country in a N.E. and S.W. direction by Callander and Loch Lomond. On this ridge Professor. Heddle, at a height of 230 feet, found a line of six boulders of angular gneiss, stretching N. and S. They are from 2 to 20 feet apart, aiid are from three-quarters to 3 cubic yards in size. To the west of this line, four other similar boulders lay along the summit of the ridge, and thus at right angles to the first line {Ninth Report, p. IG). SUTHERLAND3HIEE. Assynt. — Two. large boulders, one at IJnapool, the other at Stonechrubie, called Qlaph.. na Patainf {Stone of the Button) {First Report, p. 51), Golspie. — An Old Eed Sandstone borilder, 16 x 10 x 4 feet, about 248 feet above sea, lying on oolitic rocks, — subangular, — with longer axis N.I7.W. Three smaller boulders of Old Eed Sandstone lie about 100 yards to S.E. The Old Eed Sandstone formation is situated to N. and W., about 3 miles from those boulders {First Report, p. 51). Eev. Mr Joass, of Golspie, refers to a large boulder of gneiss, weighing about 120 tons, called “ Clach Mhie Mhios" Clach being of Edinhurgh, Session 1883-84. 875 Gaelic for Stone f Mhief of a son^ Mhiosf of a month; this name having been given by legend, that stone was thrown from a hill 2 miles distant by a child of Fingal, when only one month old {First Report, p. 10). West and North Goastsi — The late Eobert Chambers visited the west coast of Sutherland, travelling round by Cape Wrath, and along the north coast as far as Tongue Bay, with the following results : — 1. At a height of 1700 and 1800 feet, he found strise on the rocks of Cuineag and Ganish (quartz hills in Assynt, about 30 miles north of Gairloch), running from about 60° W. with certain exceptions. One of these exceptions was at the base of Gidneag, where the streaks are from the direct north, apparently by reason of a turn or deflection which the agent had there received at and hy reason of the base of an adjoining hill. Another exception was at the hollow dividing the mass of the hill from its loftiest top, where another system of streaking had come in from the direct west. 2. On a summit south froni Ben More^ fully 1500 feet high and 4 or 5 miles to the south of Cuineag, there are streakings on the quartz, observing the normal direction of this general movement, viz., from N. 60° W. 3. On the gneissic platform between Gout More and Sulvean Dr Chambers found polished surfaces striated from N.W. and from W. To the west and north of the latter mountain are markings in all respects similar. These are situations, observes Chambers, where no local glaciers could exist. 4. Streakings precisely the same as those on Cuineag and Canish exist at an elevation of at least 2000 feet on the similar quartz mountain called Ben Eay, south of Loch Maree, and 40 miles from Assynt ; — this striation being from NW, or thereabouts, anS totally irrespective of the form of the hill. 5. Passing northward to Rhiconish, we find near that place striae coming in from the coast, viz., from the hf.W., and passing across a high moor, with no regard whatever to the inequalities of the ground.” 6. A little farther north, at Laxford, a fine surface is marked with striations from the 17. W., being across the valley in ivhich is 3 M VOL. XII. 876 Proceedmgs of the Boyal Society occurs. At an opening in the bold gneissic coast, which looks out upon the Pentland Firth, there is strong marking in a direction from N.iNr.'Vy. The high desolate tract between Loch Eribol and Tongue Bay, where there is nothing tlicd could restrain or guide the move- ment of the ice, exhibits striations from N. 28° W. Strise in nearly the same direction, viz., N. 25° W., occur 4 miles to the east of Tongue. On perfectly free ground, at Armadale, the markings point almost directly from the north. When we pass on to Caithness we find traces of striation, still from points hetAveen N. and N.W., which is directly transverse to a line pointing to the neighbouring hills” {Fifth Pegort, p. 62). The late Professor Mcol observes that, on the whole N.W. coast, from Cape Wrath southwards, numerous ‘perched’ boulders occur on summits and sides of hills, in most exposed situations. They are especially numerous around Loch Maree” {First Report, p. 51). In another paper {Brit. Assoc. Reports for 1855, p. 89) the Pro- fessor states that “on the west coast of Sutherland, near Loch Laxford, enormous blocks are perched on the top of rounded bosses, or on the very verge of precipices. As the slightest impulse seems sufficient to dislodge these boulders, the manner in which they were placed in their present positions is very problematical.” It is matter of regret that no reports came to the Committee re- garding the boulders on the N.W. and H. coasts of Sutherlandshire, though frequent applications for them were made. For want of reports it has been thought right to refer to the foregoing observa- tions by Dr Chambers and Professor ISTicol. Clyne. — Pemarkable kaims, apparently moraines, lateral and terminal, in Brora valley. At Clynlish quarry the sandstone rocks striated in a direction from W. by N. to N.W. {First Report, p. 51). Wigtownshire. G lasserto7i.— boulder, 9x6x6 feet, weighing about 24 tons. Longer axis N.E. and S.W. Two other boulders in a line with it. These supposed to have come from mountains to IST.E., crossing an arm of the sea. Several kaims in the parish, full of granite pebbles {First Report, p. 38). of Edinhurgh, Session 1883-84. 877 Glentuce. — The Rev. Mr Wilson reports the finding of water- worn nodules oi flints in beds of stratified drifts, at different places along the coast for about 6 miles. Various localities named, where flints were found by Mr Wilson in drift beds up to 200 feet above sea. He suggests that some of the drift materials probably came from Arran, and the flints from Armagh in Ireland {Ninth Report, p, 26). Faroe Islands. Though these islands form no part of Scottish territory, they are not so far from the Hebrides, Orkney, and Shetlands, as not to warrant some notice of their glacial phenomena. Moreover, having been visited by several Scotch geologists, who reported on them to the Edinburgh Royal Society, it may he allowable to add a few notes bearing on the boulders and rock striations of these islands I. Erratics. 1. The first traveller who noticed the glacial phenomena of the Faroes was the Rev. G. Landt, a Danish clergyman, whose book was translated into English in 1810. In page 8 of his treatise he says ‘ —• “ There are sometimes to be seen in the valleys, single stones, 6, 8, or 10 feet in diameter, in places where it is impossible they could have fallen dovm from the hills, SuOh stones are found also here and there, at a consideraMe height on the hills, where there is no other eminence in the neighbourhood, from which they might have rolled down.” He adds, a little farther on, that these stones are generally round ” in shape. 2. Dr James Geikie, in his elaborate and valuable Memoir on the Faroe Islands, lately published in the Edinburgh Royal Society Transactions, vol. xxx. p. 260, says, under the head of E'nuimg, that “ large angular blocks of basalt rock are of common occurrence. Hear Thorshavn, many are of large size, measuring occasionally upwards of 20 feet across. They occupy positions which preclude the possibility of their having fallen or rolled down the hills ] and as they are now and again associated with moraine debris, I do not doubt they have been deposited during the melting of the ice-sheet ” (p. 250). . ... While perched blocks are quite absent from the 878 Proceedings of the Boyal Society hill-tops, which give no evidence of glaciation, they are often scat- tered abundantly over the surface of high ground which has been glacially abraded. This is well seen upon the ridge between Grdth and Skeelfiork, where isolated erratics are sprinkled about upon the moutonnee surface ” (p. 250). In the same paper, Dr Geikie else- where repeats that “ the large erratics scattered over hill-tops and hill-sides were doubtless deposited by the mer de glace during its final dissolution” (p. 262), II. Rock Stride. In the year 1812 Faroe was visited by Sir George Mackenzie and Mr Allan, both Fellows of the Edinburgh Royal Society, and both of them well-versed in geological inquiries. Both of them read to the Society accounts of their visit. Sir George, in his paper, expressed much satisfaction in having induced Mr Allan to be his companion, on account of “ his great experience in geological examinations” {Edin. Roy. Soc. Trans.^ vol. vik p. 215). Mr Allan, in his paper, refers more than once to a “ headland near the village of Eide, which (he says) presents a perpendicular front to the ocean.” So much interested was he in this “headland,” that he attempted to measure its height, and found it to be 1134 feet (page 242). In a subsequent passage, he again alludes to this “headland” as a thing “of interest,” on account of the “ remarkable , instance (it presented) of the abrasion of its surface, where the rock appears to have been worn down by the friction of heavy bodies ” (p. 244). Then remarking that generally in Earoe, where the rocks do “not consist of impracticable cliffs, they present a solid, smooth surface, always highly inclined,” he goes on to say, “ it would be curious to investigate whether this smoothness on the sides of the mountains could be traced to any external cause, such as that which has been observed by Sir James Hall on Corstorphine Hill and other parts of the country, indicating the passage of heavy bodies along the sur- face, Hear Eide I observed a very remarkable example of this description. There the rock was scooped and scratched in a very wonderful degree, not only on the horizontal surface, but also on a vertical one, of 30 to 40 feet high, which had been opposed to the of Edinhurgh, Session 1883-84. 879 current, and presented the same scooping and polished appearance with the rest of the rock, both above and below.” In the year 1855 the late Eobert Chambers, also a Fellow of the Eoyal Society, who had previously paid much attention to glacial phenomena, visited the Faroes, and wrote an interesting account of what he saw. He explains, that being aware of Mr Allan’s dis- covery at Fide, he went there on purpose to study the markings on the rocks. The following is his description ir— “ There are some small fields under cultivation. Every here and there the rocks are presented on the surface, where they are invariably seen rounded or flattened, with peculiar deep channelings, precisely like those rocks which are now generally believed to have been abraded by ice. My attention being arrested by these features, I looked narrowly for the striae or scratches which ice generally leaves on surfaces over which it has passed. They presented themselves in abundance, in. several places, most strikingly of all, within sea-mark on the shore of the quiet bay, heing all directed from the north, which is also, the direction of the canaugc- or channel- ings, and further of the passage or isthmus in which the village (of Eide) lies.” In his Memoir on th& Faroe Islands, Dr James Gcikie (p. 246) referring to the same locality of Eide, says, that “ perhaps the best preserved roches moutonnees we anywhere observed were in Osteroe and Sandoe., It was with considerable interest that we^ visited the northern portion of the former island, for we felt that the evidence to be gathered there would, go a long way to settle the question which we had come to solve. Ho difficulty was experienced in finding the- locality described so long ago by Allan, and subse- quently visited by Chambers, but the striae, instead of being ‘ directed from the north,^ had clearly been graved by ice coming from quite the opposite point of the compass. The Kodlen peninsula we found glaciated all over, the roches moidonn'ees on both sides of the isthmus being beautifully perfect, and showing Stogs and Lee- seiten in the most admirable manner. In many places the striae are well seen, and long ruts and channelings, or grooves and trenches, well smoothed and ice-worn, traverse the rock surface. We traced the glaciated contour up to a height of 1302 feet, which was the summit level of the pass leading from Eide to Funding ; but the 880 Proceedings of the Boyal Soeiety slopes facing the sound between Osteroe and Stromoe seemed to be glaciated to a somewhat greater height. The direction of glaciation upon those slopes, so far as we could observe them, seemed to be in a direction corresponding with the trend of the sound, namely, from S.S.E. to KN.W.” As any facts bearing on the smoothed and striated rocks at Eide and the Kodlen peninsula deserve attention, the following addi- tional paragraphs in Professor Geikie’s Memoir are quoted : — On page 254 he states that the soundiugs on the chart prove, that the long fiord which separates Stromoe from Osteroe occupies the bed of two submerged valleys, with a low separating col, over which there is shallow water, This col occurs in the narrow part of the sound between Kordskaale and Ore ; and the soundings show that from this point the water deepens, both towards N. W. and S.E. The fiord is shallower at its mouth near Eide, where there are and 9 fathoms of water, than it is at and above Haldervig, where we get depths of 18 to 30 fathoms.” On page 261 Professor Geikie states that “the long sound that separates Osteroe from Stromoe brimmed with ice, which flowed in two directions. J^orth of Nordskaale the movement was northerly ; while south of the shallow part of that sound the ice held on a southerly course.” A point, apparently of some importance, is brought out in Dr Geikie’s Memoir, viz., that m_any of the hills show smoothing of rocks, only up to a certain height. Thus it is stated that “ the lower part of the mountains that over- look Kolfaredel are smoothed and abraded in a S.E, direction, and we estimated the height reached by the glacial outline to be some 1500 or 1600 feet, Above that level all is rough and rugged, and destitute of the slightest trace of glacial abrasion ” (p. 245). Then, on an adjoining mountain, where there is a pass at 1243 feet above the sea, there are “ roches moutonneesf but we saw no stri^. The glaciated outline was continued up the mountain slopes above us, for not less than 400 feet” (p. 245). In another locality, “ the col, we found to be 1693 feet above the sea, and the glaciation came close up to this level. But abraded rocks with the characteristic glaciated contour certainly reached 1600 feet” (p. 246), of Edinhurgli, Session 1883-84. 881 At p. 246 it is mentioned that “the upper parts of the hills between Fundingsfiord and Andafiord were above the limits of gla- ciation.” . . . “ Suderoe has supported a considerable mass of ice ; for we traced the glaciated outline up to a height of 1040 feet. Above that level all is rough, angular, and serrated ” (p. 248). The explanation suggested by Dr Geikie of these interesting facts is, that “ when the islands were enveloped in their ice-sheet, the action of frost would he confined to such ridges and hill tops as pro- jected above the mer de glace, while severe glacial abrasion would go on below ” (p. 260). Dr Geikie, in his Memoir, more than once takes notice of the “ scarcity of moraine mounds, which, he says, “ it is difficult to account for satisfactorily ; ” — but he offers under that head several suggestions, “ the principal ” being,' “ probably the continuous and comparatively rapid dissolution of the ice, after the snow-line had retreated several hundred feet above the sea-level ” (p. 263). LIST OF LITHOGRAPHS. Argyleshire. Plate VIII. Ho. 1. On west coast of Kintyre, a gneiss boulder, lying on Old Red Sandstone strata; blocked at south end, indicating probable transport from north. {Abstract, p. 773.) Plate VIII. Ho. 2. View of a gneiss boulder jammed between rocky banks of a small stream. {Abstract, p. 774.) Plate VIIL Ho. 3. Gneiss boulder, called Clacli TJdelain'^ or “ Unstable Bloch, in consequence of its precarious position. {Abstract, p. 774.) Plate VIII. Ho. 4. “ Giant Pidting &tonef on rock smoothed from the north. Site of boulder on rock 18x12 inches. {Abstraxt, p. 774.) Plate VIII. Ho. 5. Two boulders on similarly smoothed rock called “The Pig’s Back,” on Knap Farm. {Abstract, p. 774.) Plate VIIL Ho. 6. Loch Glaslian. — A boulder on Knock Farm, resting on smoothed rock, which dips H.H.E. at 30°. Longer axis of boulder and sharpest end point H. by E. {Abstract, p. 775.) Plate VIIL Ho. 7. Three lithographs (1), (2), (3) of a boulder 882 Proceedings of the Boyal Society perched on top of a ridge, among hills to the south of Loch Awe. {Abstract, p. 777.) Plate VIII. No. 8. Great assemblage of boulders on south shore of Loch Killesport. B is boulder of 2770 tons weight. A is line of 40 feet old sea-cliff. {Abstract^ p. 779.) Plate VIII. No. 11. Bock smoothed and striated at Kilmory. {Abstract^ p. 780.) Plate VIII. No. 10. Cluster of boulders on steep hilkside, Killes- port. {Abstract, p. 780.) Bute. Plate VIII. No. 9. Arran.— east shore of, a granite boulder (B) lying on Old Red Sandstone, and blocked at its south end. The shape of boulder shown by fig. A. {Abstract, p, 792.) Plate VIII. No. 12. In Ettrich Bay, west coast of Bute, boulder of gneiss standing upon its thick end, against edges of slate strata, which block it on its south side. {Abstract, p. 793.) Plate VIII. No. 13. Barone Hill. — Showing smoothing and stria- tion of rocks on both sides of a gorge, through which striating agent had passed from north. {Abstract, p. 793.) Hebrides. Plate VIII. No, 14. Lslay Island.- — Porphyry boulder on N.E. side of summit of a steep hill. {Abstract, p. 806.) Plate VIII. No. 15. Iona. — Granite boulder, standing on one end against clay-slate rocks. {Abstract, p, 808.) Plate IX. No. 16. Granite boulder of about 400 tons, on plateau 230 feet above sea, leaning on west side of Dun I Hill. {Abstract, p. 809.) Plate IX. No. 17. Coll Island, Bein Hock hill, showung N.W. front, with two boulders on summit, A B, and one on a plateau at its base, C. {Abstract, p. 811.) Plate IX. No. 18. Coll Island, Grassipol meadow, having a ver- tical wall of rocks on S.B. side, showing a great accumulation of boulders. {Abstract, p. 811.) Plate IX, No. 1 9. Coll Island. — A rocky knoll covered by boulders, showing that uppermost boulder had come from N.W. {Abstract, p. 812.) Plate IX. No. 20, Barra. — Boulder of 890 tons, 230 feet above of Eclinlurgli, Session 1883-84. 883 sea, on a terrace of drift, on north slope of Ben Erival. {Abstract^ p. 813.) Plate IX. No. 21. Barm. — Boulder 228 feet above sea, on north slope of Ben Erival, hutted at its east end against rock. {Ahstrad, p. 814.) Plate IX. No. 22. Boulder on west slope of Ben More hill, on shore of Atlantic, at height of 165 feet above sea, butted by rock at its east end. {Abstract^ p. 815.) Plate IX. No. 23. Loch Boisdale. — Two boulders, A and B; A butted at its east end on rock of Kennet Hill, and B resting with its east side on A. {Abstract, p. 815.) Plate IX. No. 24. South Wist, Mingary Hill, showing terrace on its N.W. side, with boulders of various sizes. {Abstract, p. 816.) Plate IX. No. 25. Wist. — Askernish. — Granite boulder perched on point of a rocky knoll (two views) (1) and (2). {Abstract, p. 816.) Plate X. No, 26, South Wist, Jocdar; rocks extensively smoothed and striated from N.W. {Abstract, p. 816.) Plate IX. No. 27. Harris, at Borve, on shore of Atlantic ; two boulders on hill-side sloping down towards sea, the uppermost having apparently come from, west. {Abstract, p. 817.) Plate IX. No. 28. West Loch. TarberL — Scalpa Island. Granite boulder butted by rock at its east end. {Abstract, p. 818.) Plate X. No. 29. The Lewis. — Hill top at Miavig, covered by boulders chiefly on west side. {Abstract, p. 812.) Plate X. No. 30. Shye. — Boulder on rocky ridge, between Loch Scavaig and sea, on west coast. {Abstract, p. 821.) Inverness-shire. Plate X. No. 31. Fort-William. — Boulder on steep western side of Treshlik Hill. Two, views given ; upper one shows part of hill on which boulder lies ; lower one shows steepness of slope. {Abstract, p. 825.) Plate X. No. 32. Flichity Valley.— Yiq-w of an isolated hill, about 1620 feet above sea, with many boulders on west side. Two views given ; that on left hand, to show shape of hill and position of the boulders j the other to show steepness of hill slope. {Abstract, p. 834.) Plate X. No. 33. Glencoe. — Boulders of gneiss, lying at foot of cliff, which faces east; supposed by Convener to have come up valley, till obstructed in farther progress by cliff. {Abstract, p. 830.) 884 Proceedings of the Royal Soeiety Plate X. Xo, 34. Farr Parish. — Boulders on rocks smoothed, and sloping down to westward. {Abstract., p. 835.) Xairnshire, Plate X. Xo,. 35. Cray. — ‘‘Tom Rioch” — large angular Con- glomerate boulder — to show shape, notwithstanding long distance carried, {Abstract, p. 850.) Plate X. Xo, 36.. Cawdor. — Sketch of four other large angular Conglomerate boulders given for same reason. {Abstract, p. 851.) Perthshire, Plate X, Xo. 37. Callander. — -Bochastle Hill. Two gneiss boulders, lying on Conglomerate rock, which forms west part of hill. The largest (14x9x9 feet) is on very summit of hill. Its shape shown by fig. a in diagram ; that of smaller one by fig. b. {Abstract, p. 856.) Plate X. Xo. 38. Dochart Valley. — Rock on south side of, smoothed and rutted horizontally from west. {Abstract, p. 858.) Plate X. Xo, 39. Boulders on ridge of hills, 2300 feet above sea, and horizontal strata broken up. {Abstract, p. 859,) Ross-shire. Plate X. Xo. 40. Gairloch. — Granite boulder 747 feet above sea, on edge of a high clilf, facing west ; resting on schistose gneiss. It jDrojects feet beyond edge of oliff. {Abstract, p. 861.) Plate X. Xo. 41. Gairloch. — Hill X.E, from Gairloch Hotel, 585 feet above sea, on summit of which there are two boulders. {Abstract, p. 861.) Plate X. Xo. 42. Shows the largest of these boulders, projecting 2 feet beyond edge of precipice, and sloping down towards X.W. at an angle of 15°, The smaller boulder lies on a rocky surface sloping down W,X,W. {Abstract, p. 861,) Plate X, Xo, 43. Rocky knoll, near base of above hill, with a cluster of boulders on it, showing that uppermost boulder had come from west. {Abstract, p. 861.) Plate X. Xo. 44. Loch Maree. — On hill to west of hotel, a boulder near top on west slope, butted against rock at its east end. {Abstract, p. 862.) of Eclinlurgli, Session 1883-84. 885 APPENDIX II. Summary op Facts contained in the Nine Annual Eeports op THE Committee, and op Inperences apparently deducible PROM THESE FaCTS, BEARING ON THE QUESTION, BY WHAT Agency Boulders were transported to their present Sites. I. Distrihidion of Boulders in Scotland. It might be possible to extract from the Eeports, approximately, the numhers of boulders in each county, so far as made known to the Committee. But these numbers would give a very incorrect idea of either the prevalence or the paucity, originally, of the boulders in different parts of Scotland, — firsts because counties vary extremely in size ; second., because from some counties the informa- tion sent was more copious than from others ; third, because in some counties, where agricultural impiwements have been extensive, boulders in thousands have long ago disappeared by wholesale ex- tirpation. In the absence of precise statistics, it may be stated generally, that there is no Scotch county where boulders do not exist, and that on all the islands, including the Hebrides, Orkney, Shetlands, and the Faroes, boulders are found. If, however, an opinion on this point is of any value, the Convener may say, that having visited two-thirds of the Scotch counties, to inspect and search for boulders, he considers that they are in much larger numbers on the West Coast, and the hills adjoining the West Coast, than on any other district of the same extent. 886 Proceedings of the Royal Society II. ^ize or Weights of Boulders. It will be seen from tbe Abstract, and still more from the Annual Keports, that the dimensions of the boulders, when of con- siderable size, are in most cases there given. But in this Summary, it may be sufficient to refer to cases of boulders made known to the Committee exceeding 10,0 tons in weight. The element of large size or weight has some bearing on the ques- tion, What could be the agency by which boulders were transported ? especially if it appears that many were transported great distances, and across valleys and hill ranges, as to fulfil these conditions the transporting agent would require to be of peculiar power and magnitude. Examples on Bpulders exceeding 100 Tons in Weight. 1. On Mainlcmd. Aberdeenshire — Chapel Garioch, boulder 250 tons (Abstract, p. 771). Kemnay, two boulders, 270 and 380 tons (Abstract, p. 77-1). ArgylesMre — Kilhenzie, boulder 150 tons, Loch Goil, Loch Long, Loch Fy no, Gareloch, Loch Awe, 300 380 286 240 130 13,6 (Abstract, 773, 774, 776). ' (Abstract, p. 777). (Abstract, p. 778). Loch Killesport, two boulders, 106 and 300 tons (^Abstract, p. 778). Loch Killesport, boulder 2770 tons (Abstract, p. 779). „ „ 520 „ (Abstract, p. 779). Clach Briach „ 138 ,, (Abstract, p. 779). Taynish, two boulders, 108 and 116 tons (Abstract, p. 780). Appin, two boulders, 1 24 and 292tons (Abstract, p. 784). Loch Creran, two boulders, 280 and 380 tons (Abstract, p. 784). of Edinburgh, Session 1883-84. 887 Ayrshire — Loch Doune, boulder, 444 tons (Abstract, p. 785). Girvan, two boulders, 100 and 180 tons (Abstract p. 785). Ardrossan, boulder, 320 tons (Abstract, p. 785). Culmonell, two boulders, 326 and 552 tons (Abstract, p. 786). Dumbartonshire — Loch Lomond, boulder, 246 tons (Abstract,^. 795). Inverness-shire — Dochart, boulder if), 1950 tons (Abstract, p. 828). Ben Nevis, „ 118 (Abstract, p. 825). Clachnaharry, boulder, 100 „ (Abstract, p. 833). S.W. of Inverness, boulder, 310 tons (Abstract, p. 834), Loch Clachan, boulder, 218 tons (Abstract, p. 835). Morayshire — Craig, boulder, 652 tons (Abstract, p. 834). Dallanossie, boulder, 360 tons (Abstract, p. 834). Perthshire — Aberfeldy, boulder, 600 tons (Abstract, p. 855). Doune, „ 900 „ (Abstract, p. 857). Fortingall, „ 300 ,, (Abstract, p. 857). Pitlochry, „ 600 „ (^Abstract, p. 859). Renfrewshire — Kilbarchan, boulder (?), 300 tons (Abstract, p. 859). Ross-shire (West Coast) — Glenelg, boulder, 280 tons (Abstract, p. 860). Stirlingshire — St Mnians, boulder, 200 tons (Abstract, p. 872). Landrick, „ 360 „ (Abstract, p. 873). Sutherlandshire — Golspie, „ 120 „ (Abstract, p. 874). 2. On Islands. In Arran — boulders respectively of 212, 362, 184, and 620 tons (Abstract, pp. 791, 792). Coll Island — boulder of 308 tons (Abstract, p. 811). Iona — two boulders, 400 and 190 tons (Abstract, pp. 808, 809). Barra — boulder of 890 tons (Abstract, p. 813). South Uist, Boisdale, boulder, 146 tons (Abstract, p. 815). Shetlands — (Lunnasting), two masses of rock (supposed to have been carried some distance), respectively 1466 and 670 tons (Abstract, p. 869). If cases of boulders (say) above 50 tons, had been enumerated, the number would have been at least twenty times greater. 888 Proceedings of the Royal Society III, Shapes of Boidders. Two classes may be specified — (1) angular and rough, (2) rounded and smooth, on. the surface. In all the Scotch counties, both of these classes exist]— with this distinction, that the second class are generally embedded in drift, whilst the first are mostly, at all events, now, on the surface of the district {Abstract, pp. 849, 850). If, as may be assumed, the erratic blocks referred to in the Com- mittee’s Eeports were originally fragments from rocks in situ, then it is ]3i’obable that the most rounded are those which have undergone most wear and tear ” by transportation. Boulders of both classes, have often a long and a short axis smooth boulders more frequently so, than others. The latter are also frequently Pear-shaped,^' indicating that one end has probably undergone more friction than the opposite end. See, as an example, Dana, boulder,” on p. 781 of Abstract, In such cases it has also been observed that when one end is smooth and sharp-pointed, the opposite end is generally square or rough. IV. Partieidar Alarhings on Boulders. On some Boulders there are occasionally grooves, ruts, strise, and scratches upon their surface when smooth. The incisions generally form lines approximately parallel with the longer axis of the boulder. They may occur on one or more of the sides, i,e,, along the upper, lateral, and under surfaces. Examples of marks on the under surface will be seen by referring to the Abstract, p. 769 {Aberd.een)\ p, 808 {lonai) ; p. 845 {Tynecastle) and p. 847 {Alnioick Hill), It has been thought, that from a close examination of ruts and striae, whether on boulders or on rocks, the direction of the striating agent can be inferred by observing at which end the striae have been most deeply cut. In multitudes of cases it has been observed, that the striae are more deeply cut at one end, whilst towards the other end they gradually thin away and disappear. In explanation of this fact, it is suggested that hard pebbles or stones, acting as incising tools, would, in advancing along 889 of Edinhurgh, Session 1883-84. the surface of the boulder or the rock, become blunted under severe pressure, and be at length crushed to pieces. In the Tynecastle boulder, strise were seen on both the upper and the under surface. Those on the upper surface showed incision from a ivesterly point j those on the under surface, showed incision from an easterly point, judging by the test before referred to. If the boulder had been pushed over sharp rocks from the westward, the ruts on the lower surface would, according to that test, show that they had begun to be formed at the east end. After the boulder had become fixed in position, a drift of hard shingle pass- ing over the top from the west would produce striae beginning at the west end. It is evident that striae could be formed less easily on the vertical or lateral sides of a boulder than on the upper or under sides, as the incising pebbles might not, in the first casej so easily continue to move in a horizontal direction. One boulder is mentioned where striae were seen on both sides of the boulder — these sides meet- ing at, and radiating from, a point at one end, as shown in the woodcut on p. 802 of Abstract. The case is interesting on account of its bearing on the agency which produced the striae, as it must have been such as to be capable of being separated into two currents when it reached the boulder, in which case a current would flow along each side, pushing and pressing drift on the surface of the boulder as it passed. It is proper also to notice, as bearing on the same question, that boulders sometimes show two sets of striae, the one set crossing the other obliquely, indicating a change in the direction of the striating agent, or else in the position of the boulder. The case, for example, on page 844 of Abstract^ shows one set of striae running N.H.W., and the other W. by S. (Easter Duddingstone). As the study of striations may throw light on the nature of the transporting agent, it is right to take notice of striations on solid rocks \ for if there are on them two sets of striations crossing one another, the cause must be ascribed either to a change of direction in the movement of the striating agent, or to the advent of another striating agent from a different quarter. Examples of two sets of strioe on a rock surface will be seen in Abstract, p. 839 {Glasgoio) and p. 849 {Garden Hill), 890 Proceedings of the Royal Society That the striations on rocks were produced by an agent, the same as, or similar to, that which caused striation on boulders, is evident from the multitudes of cases where there are striated boulders and striated rocks close to or near one another, the direction and appearance of the striae on both being generally the same. Great numbers of rock striations occur in the Hebrides, most of which are described in the Fifth Report. Thus (at p. 816) an account is given of smoothed rocks at Jocdar, on which there are twelve or fourteen deep ruts, some of them 4 or 5 feet in length. One measures 8 inches across and 2 inches in depth, and there are others of similar width and depth,— the ruts being in all cases deeper and wider at their west than at their east ends. In the Lewis^ at TJig and Carlowrie {Ahstmd^ p. 819), similar cases occur; also Kilmory [Abstract, p. 780), Buteshire [Abstract, p. 791). These rock striations are found not only on surfaces more or less horizontal, but also on surfaces which slope, and even on surfaces which are vertical. As examples take the two following cases — 1. In Bute, there is a rocky defile, about 30 yards wide^ at Barone Hill [Abstract, p. 793), through which boulders and drift materials have evidently passed. One side of this defile presents extensive smoothings, on which there are ruts, some of them 1 2 feet in length, and more deeply cut into the rock^ at the end where the striating agent entered the gorge, viz., the N.Wd The direction of movement is farther shown by the fact, that from that end the ruts slope ujpwards at angles of from 20° to 30°, the result, no doubt, of the force with which the materials were pushed or driven through the gorge [Seventh Report, p. 19). 2. Another example occurs on the West side of Arthur's Seat, Edinburgh, as explained in Abstract, p. 843. Boulders and other drift materials had passed through this gorge, which is only about 10 yards wide. A boulder sticking on one of the sides was striated on its exposed side. One of the rocky sides also presented numerous striations, — some of them 6 feet in length, and J of an inch deep. At the narrowest part of the defile, where there would be the greatest difficulty in forcing a passage, the striae are rising up at an angle of 4° or 5° from the end where the materials had entered the defile. of Edinburgh, Session 1883-84. 891 V. Partimlar Positions of Boulders. Explained under the following heads : — 1. In beds of clay, gravel, and sand. 2. On the surface of the country. a. Lying on flattest side. h. Standing on end. c. Butted against rocks or resting on other boulders. d. Besting on steep slopes of hills. e. Besting on ridges and tops of very high hills. 1. Embedded in Clay, Gravel, or Sand. In Aberdeenshire a boulder of 8 tons found in a bed of sand {Abstract, p. 769). In Ayrshire, large boulders found in a bed of sandy mud at a depth of 18 feet, the boulders being covered with Balani and Serpidce {Abstract, p. 786 (3)). In Renfrewshire, near Paisley, boulders in clay beds, found with Balani, which had grown on them {Abstract, p. 860). On an island in Loch Lomond, a bed of boulder clay occurs con- taining Arctic shells. In Arran, beds of boulder clay occur, with blocks and broken shells {Abstract, p. 793.) In Aberdeenshire, thick masses of unstratified pebbly mud occur, with stones and Arctic shells, most of them broken, but some entire {Abstract, p. 772). In the Lewis, at several places, boulder clay occurs, with boulders and fragments of sea-shells {Abstract, p. 821). In Caithness, at Keiss, Wick Bay, and Scrabster, there are beds of boulder clay and drift, containing shells and stones, some of which are scratched; one boulder in the Wick clay bed is 12 feet in length {Abstract, p. 794). In the Orkneys, the islands of Eda, Sanday, Stromsa, Shapiushay, and Bonaldshay present clay beds containing boulders foreign to the islands, and marine shells, most of them broken or striated, as well as the boulders {Abstract, p. 853). 3 N VOL. XII. 892 Proceedings of the Boyal Society The cases of boulders, with Balani and Serpuloe found on them, have been explained by supposing that after these fish had grown on them the boulders were lifted by floating ice and dropped elsewhere {Abstract, pp. 786 and 860), 2. Boulders on Surface of the Country. {a) Boidders lying on flattest side occur so frequently that it is not necessary to quote cases. {h) A less frequent case is ivhen boidders occur standing on end. This observed occasionally, when boulders embedded in clay or sandy mud (see Estuary of Forth, p. 99, and Ed. Roy. Soc. Trans., vol. xxvii. p. 630, and Ramsaifs Physical Geology, p. 155). Also observed on open surface of the country; when the boulder leans against a rock, as at Iona, in the case of the large boulder at Dun I ; — and of a small boulder near south end of island {Abstract, p. 808). (c) Butted against rochs, or resting on or against other boidders. See such cases mentioned {Abstract pp. 773, 780, 793, 808, 810, 812, 818, 836, 861, 862). {d) On steep sides of hills. In Abstract, p. 825, there is notice of an isolated hill (Treshlik Hill), on an exceedingly steep side of which a large boulder rests {Lithograiph Ho. 31, Plate X.). JjaAbstract,p. 834, there is notice of another isolated hill in Plichity valley, on which there are several boulders precariously situated, because of the steepness of the hill-side {Lithograph Ho. 32, Plate X.). In Abstract, p: 824, a remark by Professor Duns is referred to, with regard to some granite boulders lying on a part of Ben Hevis, where the mountain slopes down so steeply, “as to make it a puzzle to understand how they can remain in position.” In Abstract, p. 856, see similar cases, on Bochastle Hill and Clunie. In Abstract, p. 862, notice will be found of a large boulder resting on a slope at an angle of so much as 47°. (e) On tops of hills. In Aberdeenshire {Ballater), boulders of granite and gneiss are on the summit of a hill, at height of 2963 feet; there being no rocks of that nature in situ on the hill {Abstract, p. 770). In Aberdeenshire {Braemar) there are boulders on tops of hills of Edinburgh, Session 1883-84. 893 reaching 2700 feet and 3587 feet above the sea (Abstract, pp. 770 and 771). In Inverness-shire, at the heights of 2000, 3000, and 3155 feet, Lochaher (Abstract, pp. 824, 826, and 827); — of 3425, Alhannach (Abstract, pp. 828, 829) ; 3407, Schehallion (Abstract p. 830). In island of Mull, a boulder on the top of Spyon More, at a height of 2435 feet above sea (Abstract, p. 808). In Kirkcudbrightshire, at a height of 2764 on summit of Merrick (Abstract, p. 837). In Glencoe district, boulders found on summits and peaks of Aonach and Eagacli, and Meal Dearg, at height of 3110 feet above sea. Professor Heddle remarks that “ these boulders lay on a ridge not many times wider than their own bulk,” and ‘‘ occupy positions much higher in level than any of the hills in a very wide extent of country, so that it is difficult, if not impossible, to adopt for them the explanation of any local glacier” (Abstract, p. 830). The following are cases where boulders are on tops of hills of less height above the sea than in the cases just mentioned ; but, being higher than any other hills in the district, they present a feature similar to that just noticed by Professor Heddle. As examples of these, re- ference is made to boulders on East Loch Tarbert (Abstract, p. 775) ; Inverary and Loch Awe (Abstract, p. 777) ; Islay Island (Arnahoo) (Abstract,^. Forfarshire (Abstract,^. ^01) ] Lochaber (Abstract, p. 825) ; Kirkcudbright (Abstract, p. 837); Midlothian (Abstract, p. 840) ; and in Sutherlandshire (Abstract, p. 875). Similar cases of boulders perched on very precarious positions probably occur in Skye, judging by what is said of them by Macculloch and Forbes (Abstract, p. 822). VI. Gases ivhere Parent Rocks of Boulders have almost certainly been ascertained. 1. In Berwickshire, granite, sienite, porphyry, and whinstone boulders are clearly traceable to hills situated several miles to the westward (Abstract, pp. 787, 788, 789, 790). 2. In Roxburghshire there are similar cases (Abstract, p. 865), in some instances the parent rocks being at least 20 miles to the westward. 3. In Peeblesshire, a quartz boulder, with much probability referred to beds of quartz about 80 miles to the westward (Abstract, p. 855). 894 Proceedings of the Royal Society 4. In Haddmgtonshire, Isle of May^ and Inchheith there are granite boulders which must have been carried at least 100 miles from westward {Abstract, pp. 801 and 802). 5. In Midlothian there are numerous cases of granite and other boulders, which must have been carried 50 to 80 miles from west- ward {Abstract, pp. 840, 844, and 847). 6. In Linlithgoivshire cases are mentioned of whinstone and Conglomerate boulders carried from westward {Abstract, 839, 840). 7. In Aberdeenshire, granite blocks from hills situated many miles distant to N. and KW. {Abstract, p. 769 and 770). 8. In Forfarshire, mica schist boulder from rocks 17 miles to W.KW. {Abstract, p. 801). 9. Inverness-shire, granite boulders at and near Loch Tulla traced to hill 10 miles to westward, also near Inverness {Abstract, pp. 828, 832, and 833). 10. In Argyleshire (Kerrera, Easdale, and Lismore), granite boulders, referred to sources situated to the north, across the sea {Abstract, p. 783). 11. In the Lewis, granite boulders from Barvas Hills, situated to H.W. {Abstract, 820). 12. In Perthshire, a Conglomerate boulder, weighing 900 tons, carried about 7 miles from westward {Abstract, p. 857). 13. In Stirlingshire, numerous cases of Conglomerate boulders in different localities, carried from 10 to 20 miles from westward (Abstract, p. 873). 14. In Glencoe, boulders which must have come down valley, viz., from S.E. {Abstract, p. 830). 15. In Morayshire, Nairn, Elgin, and Boss-shire, boulders of Con- glomerate, and various kinds of granite, which have travelled 10 to 30 miles from westward {Abstract, pp. 798, 848, 851, and 852). 16. In Buteshire {Gumbraes), boulders of Conglomerate from H.W. {Abstract, p. 791). 17. In Kirkcudbrightshire, Criffel granite boulders carried S.E. even to Cumberland and Lancashire {Abstract, pp. 796, 797, and 838). VII. Special Facts indicating direction in which Transporting Agent moved. 1. Longer axis of boulders and sharp ends of boulders generally point north-westward. of Ediribiorgh, Session 1883-84. 895 The cases showing this, which are mentioned in the Keports and Abstract, are so numerous that they need not be particularised. Testimony to the north-westerly direction from which boulders in Scotland have been carried, is given by the following geological authorities — Professor Geikie {Abstract^ p. 841) ; Sir Eoderick Mur- chison {Abstract^ p. 795) ; Charles Maclaren {Abstract, p. 840) ; Eobert Chambers {Abstract, p. 876); J. F. Campbell {Abstract, p. 815); J. F. Jamieson {Abstract, p. 795) ; Professor Harkness {Abstract, p. 797); W. Jolly {Abstract, p, 799); Mr Anderson Smith {Abstract, p. 776); John Young (Glasgow University) {Abstract, p. 839); James Croll {Abstract, p. 841); T. Hay Cunningham {Abstract, p. 838). In the Lewis there are kaims or escars on a very large scale, — continuous for several miles, whose north-westerly direction, and numbers of boulders lying upon them, suggest the idea that they may be due to the same agency which has transported the boulders {Abstract, p. 820). 2. But whilst a movement from north-westward is very general in Scotland, it is right to notice exceptional cases. In Loch Long and Loch Fyne there has been a movement from N. or H. by E. {Abstract, p. 774, 775). In Islay {Abstract, p. 806). Buteshire {Abstract, p. 791). In Morayshire and Elgin Mr Jolly points out two streams, one from 6° S. of west, — the other from 15° H. of west {Abstract, p. 799). In Perthshire {Dunkelcl) the direction of the strise on the rocks at a high level is from JST.N.W., — whilst at a lower level, in the same valley, it is from N.E. {Abstract, p. 857). In the Lewis a similar case occurs; — the direction of the movement at a high level being from W.N. W. ; and at a low level, in the same district, from W., or even W.S.W. {Abstract, p. 819). In Assynt, whilst the normal direction is N. 60° W., the direction changes to due north, caused (as Chambers supposes) by the interference of a hill {Abstract, p. 875). So also near Gairloch, whilst the normal movement is from W.H.W., as shown by boulders and stri93, there is a locality among the hills, where the movement is shown to have been from W.S.W. {Abstract, p. 861). Cases have already been noticed, where there are two sets of strise crossing one another. Thus in Morayshire {Abstract, p. 849) the H.W. striae are crossed by others of a later date coming from H. by E. 896 Proceedings of the Royal Society Near Glasgoiu there are rock surfaces presenting two sets of strise, one implying a movement from the N.W. and N.E. respectively i^Ahstract^ p. 838). These different directions in the lines of striae may, in some cases, indicate two separate agencies, moving independently of one another at different periods. But it is also possible that the same agent might he deflected from its normal direction by local conditions. An example of such a deflection is given by Sir James Hall, in his well-known paper on “Eevolutions on the Earth’s Surface” read by him in the year 1812, and printed in the 7th vol. of the Ed. Roy. Soc. Trans. He names a locality (p. 196), where “the rock presents furrows and scratches similar to those on Corstorphine Hill,” — but where “ the action of the stream has undergone a visible modifica- tion, by the prominent form of some parts of the rock, in conse- quence of which the dressings have in some places been turned to the amount of 5° or 6° out of the general direction, which, how- ever, they resume gradually in the course of a few yards.” In Haddingtonshire, whilst the normal direction is generally from W.N.W. on horizontal rock surfaces, the movement slightly changes where the striating agent struck upon, and had to pass over, a rock which sloped. For example, at Linton, on a rock surface sloping down due north, at an angle of 35°, the direction on that surface is E. and W. {Abstract, p. 803). At the railway cutting, not far from Linton, the rock surface slopes down due north, at an angle of 10° to 20° ; and the opposing rock surface being here of considerable extent, the direction of the striae is E. 15° N. {Abstract, p. 803). On North Berwick Laio the smoothed rock surface dips down N. 10° W., and the direction of the striae is E. 22° N. {Abstract, p. 805). 3. Another set of facts, hearing on the direction in which the transporting agent has moved, is the position of individual boulders. A very large proportion of boulders have been lodged on the west slopes of hills. Many are hutted up against rocks, or lying on other boulders, in a way which shows that they came from the westward. 4. Another fact has been observed, which shows that there has been a general movement over this part of Europe from a westerly point. Thus in describing the beds of boulder clay in the neighbourhood of Edinlurgh^ Session 1883-84. 897 of Edinburgh, the Rev. Dr Fleming cites different localities where it clearly appears that the materials composing the boulder clay, had been by some extraneous agency pushed towards the east; and pushed so violently, that the strata of rock covered by the boulder clay had their edges broken off^ and carried towards the east [Litho- logy of Edinburgh^ pp. 52 to 60). In like manner. Professor Geikie says that “ the mass of the boulder clay (in the basin of the Firth of Forth for instance) con- sists of the comminuted debris of the Carboniferous and other rocks which form the framework of the district. We can also gather that this loose fragmentary matter has moved from west to east. In the upper part of the basin of the Firth of Forth the coal fields are covered with red boulder clay, abounding in fragments of the rocks that lie towards the N.W., and deriving its prevalent tint from the waste of the Old Red Sandstones, and stretches up to the foot of the Highland mountains” (Glacial drift, p. 805). 5. If tlie foregoing data are sufficient to establish the general fact that the transporting and striating agent has moved in most parts of Scotland from the north-westward, the question arises, What was that agent ? In regard to boulders in Forfarshire and Aberdeenshire, it might be inferred that they were brought by glaciers from the Grampians and other mountainous districts there. But some of these boulders are at such heights as to suggest doubts whether any glacier could have been generated at such a level as to bring these boulders. Moreover, several of the Forfarshire boulders, if they came from the mountains to the west, must have crossed valleys and ridges of hills, which would have seriously obstructed the flow of a glacier (Abstract, p. 801). In some districts, however, there is undoubtedly evidence to establish glacier action ; — as in Glencoe (Abstract, p. 830). Professor Heddle and Mr Livingstone satisfied themselves of the existence of one or more glaciers on the west flanks of Ben Nevis, though Mr Livingstone sees difficulties which he cannot explain (Abstract, p. 824). Professor Duns seems also to recognise the probability of a Ben Nevis glacier (Abstract, p. 824). In Nairn Valley there are also appearances which suggest the agency of a local glacier (Abstract, p. 835). Loch Skene is another (Abstract, p. 796). 898 Proceedings of the Poyal Soeiety In Glen Etive and Loch Etive there are indubitable traces of glacial action at a low level, moving from Loch Awe {Abstract, p. 782). But in Inverness-shire there are boulders, reported on by Pro- fessor Heddle, which, as they must have crossed deep valleys, floating ice must be preferred for agency of transport in these cases {Ab- stract, p. 829). See also Ruber slaw {Abstract, p. 866) ; Shetland {Abstract^ p. 869). Forfarshire {Abstract, p. 801). Sutherland {Abstract, p. 875). That at the Boulder period floating ice of some kind existed can scarcely be doubted. The confident testimony of Dr Chambers, Professor Nicol, and Mr Jamieson, that the positions of the boulders and the direction of the rock striations on the north-west coast are inexplicable, except on the supposition that the transporting and striating agent came there from the sea, scarcely leaves room for doubt {Abstract, p. 795). The transport of boulders from the westward is especially interest- ing in those localities on the north and north-west of Scotland, where towards the west there is nothing but open sea. Thus, on the islands of Tiree and Coll, and at Borve on the west coast of Harris, the boulders are in such positions, that to reach these positions they must have come across the sea. In the Shetlands and Orkneys there are on almost every island boulders which, differing in mineral constituents from the rocks of the island, must have been transported across some portion of sea; and accordingly Messrs Peach and Horne, w^ho have lately explored the geology and the glacial phenomena of the islands, give a decided opinion that on these islands land glaciers were not the transport- ing agent. They say that in the Orkneys “ the islands must have been overflowed by ice ; ” — ice which “ originated beyond the limits of Orkney ” {Abstract, p. 855). So also of Shetland, they say that ‘At must have been at one time smothered in ice^^—“ originating far beyond the sphere of Shetland ” {Abstract, p. 871). With regard to the direction of the movement of the transporting agent in Shetland and the Orkneys, there is not the same uniformity as on the mainland of Scotland. In the island of North Hnst, the northernmost island of Shetland, the direction is of Edinburgh, Session 1883-84. 899 from W-N-W. [Abstract, p. 870). On the island of Papa Stour there are blocks which apparently came across St Magnus Bay from a IST.E. direction [Abstract, p. 867). Butin other cases the boulders on the islands must have been floated from many different directions. It is also proper to notice the fact, that in some of the islands of the Hebrides, and even on portions of the west coast of the Main- land, the positions of the boulders indicate a movement, not from W.N.W. (the normal direction for Scotland generally), but from H. or H. by E., as in Islay [Abstract, p. 806), in Iona [Abstract, p. 808). Loch Fyne [Abstract,^. 777); Kintyre [Abstract,^. 773). Buteshire [Abstract, p 791). But these exceptions do not greatly detract from the value of the generally concurring evidence, everywhere else, of a direction from W.KW. It is also an important circumstance that the part of Scotland where the boulders are largest, heaviest, and most numerous, is along the west coast (see p. 886). If floating ice brought boulders across the Atlantic, the first place where boulders would be dis- charged would be where the sea bottom rose high enough to inter- rupt the progress of the ice. The ice carrying the largest and heaviest boulders would most probably strike the sea bottom soonest ; whilst the ice carrying smaller cargoes would flow on, till these reached the submarine rocks which now form the present inland mountains. As bearing on the question, whether land ice or sea ice was the transporting agent, another circumstance brought out in the Reports must be kept in view. Some boulders on the tops and ridges of mountains are at heights far above what could be reached by a glacier having its birthplace in any adjoining district. Such are the boulders at heights exceeding 3000 feet ; and even when at lower heights, it would be necessary, for upholding the glacier theory, to have mountains pointed out where glaciers could have been formed, and with a valley through which the glacier could have flowed in the direction of the boulder. But even if this difficulty of levels could be overcome, there is still another in explaining how a glacier could set down on the very tops of hills, or on excessively steep slopes of hills, boulders which are frequently seen in these critical positions. Floating ice stranding on mountain tops or slopes, might, by 900 Proceedings of the Royal Society gradually melting, allow boulders to obtain these singular lodg- ments. Of course, if the theory of floating ice be adopted, the position of boulders at heights of 3000 feet implies a sea which must have stood at that height, or more, above the present sea-level in Britain. In that supposition there is no improbability. Moreover, beds of sand, mud, and gravel (proofs of marine conditions) actually exist in several parts of Perthshire, up to a level of 1500 feet, 1600 feet, 2000 feet and more {Abstract, pp. 857, 858) ; on Ben Cruachan, up to 2000 feet {Abstract, p. 783) j in Glencoe, up to 2000 feet {Ab- stract, p. 830) ; and on Schehallion, at a height of 3000 feet {Abstract, p. 858). The Ordnance surveyors reported drift beds at a height of even 3800 feet {Abstract, p. 831, footnote). Terraces on gravel andsand at 1200 feet {Abstract, p. 832). In Scotland, sea-shells — and generally of an Arctic type — have been found in clay or gravel beds up to a height of about 520 feet above sea-level. In several parts of the west of England these shells occur in similar deposits up to a height of about 1200 feet, and in Ireland (near Dublin) up to a height of 1400 feet above sea-level. At the time when the sea stood at either of these heights in England and Ireland, it could not with any probability have been lower in Scotland. Allusion has been made to deflections in the direction of the transporting agent, when it struck upon rocks, which slope towards certain points, and at different angles. These deflections can be understood and accounted for on the supposition of an oceanic current with floating ice. Eor by flowing over a rock, which obstructed its normal progress, the current might be deflected from its usual course. These deflections it would not be easy to explain on the theory of solid land ice moving over the country. Another circumstance favouring the theory of an oceanic current, with floating ice, to account for the movement of boulders, and the striation of both boulders and rocks, is the presence of marine shells, of Arctic types, in beds of drift containing boulders. In most of the cases referred to some of the shells have been crushed, whilst others are entire and unhurt. What more probable ex- planation can be given of these facts, than that masses of ice float- ing on a sea current would, on touching the sea bottom, discharge of Ediriburgh, Session 1883-84. 901 their cargoes of rocks and rubbish, and at the same time plough through the sea bottom, pushing forward boulders, and crushing shell fish? (Seep. 891.) It is a fact confirmatory of this view, that beds of boulder clay never show stratification, and that, moreover, in respect of colour and materials, they closely resemble hardened or compressed mud, apparently composed of the debris of rocks which had undergone disruption and friction by some extraneous agent. Boulder clay is found everywhere in Scotland, — so that there must have been one general agent instrumental in forming the deposit ; and it is difficult to conceive a more probable agent than sea currents, with floating ice, grinding and grating over submarine rocks. Another circumstance (shown in the Committee’s Eeports) indicates oceanic agency, viz., the uniformity all over Scotland of the direction of the striae on rocks and boulders, and of the direction of the longer axis of boulders. In almost every part of Scotland there has manifestly been some agent of immense power, which has been for a long period passing over from the W.N.W. What other agent would produce these concurrent effects over a con- siderable portion of the earth’s surface than a great oceanic current ? No such effects are likely to have been produced by an ice- sheet however gigantic, or still less by local glaciers. The deflections from that normal direction, which are mentioned in the Reports as occurring in some localities, are not only not incon- sistent with the theory of an oceanic current, but are just what might be expected, inasmuch as when currents flow over a bed which contains obstructions, eddies and deflections are produced, so that these partial deviations from the normal direction strengthen rather than weaken the theory of a great sea current. There are also two districts crossing Scotland where the movement has been, by some special cause, deflected from the normal N.W. direction. In the low-level district between the Firths of Clyde and Forth, where the highest point is about 150 feet above the sea, the direction is about due E. and W. {Abstract, pp. 847 and 872). So also in the valley crossing the south of Scotland, the east part of which is occupied by the River Tweed and its tributaries, and the west part by the Rivers Liddell and Esk, the direction as shown by boulders, and by striations on rocks, is from W.S.W. in the western 902 Proceedings of the Royal Society districts {Abstract, p. 865), and N. 10° W. {Abstract, p. 790) in the eastern districts. These deflections from the normal direction, both on the west coast and in the two districts across Scotland just referred to, can be explained on the theory of a N.W. oceanic current. The current, on reaching what are now the high mountains of Argyleshire, might be deflected there into a more southern direction; and when the current reached the two valleys referred to, it might be drawn through them by the absence in them of any obstruction. That some oceanic current has passed through the southern valley seems evident from the numbers and direction of the kaims in Koxburghshire and Berwickshire {Abstract, pp. 865 and 790). The Convener (in a paper in the Edin. Roy. Soc. Trans., vol. xxvii. p. 44) ascribed the formation of these kaims to oceanic action through a submarine channel, formed by a range of hills on each side ; and in support of his view he referred to the following passage in Professor Geikie’s work on the Great Ice Age (p. 248), where he observes, that “when we note that strings of gravel ridges and mounds may sometimes be followed up one valley, across the dividing col, into a totally different drainage system, we cannot but conclude that ordinary river action is out of the question as an explanation of the phenomena. In the present state of our know- ledge we appear to have no alternative but in such cases to admit the marine origin of such haims.^’ These Berwickshire and Koxburghshire kaims present features similar to the kaims of the Lewis {Abstract, p. 819), except that the agent which formed them moved in a different direction, owing to the difference of the conditions which influenced the current in the respective localities. 6. A question may be asked, that if there existed both local glaciers and floating ice, as agencies for the transport of boulders and the striation of rocks, which of these agencies was first in operation ? The data are too scanty to allow of this question being answered with any confidence. In the Abstract, p. 831, where reference is made to Glencoe, and in Abstract, p. 835, where reference is made to Farr, it will be seen that an opinion is offered that glaciers existed first, and that submerg- ence of the country took place afterioards. 903 of Edinhurgh, Session 1883-84. 7. It remains to notice what light is thrown on the subject by the Faroe Islands. As Professor Geikie is satisfied that glaciers, or an ice sheet of some kind, existed, capable of glaciating the rocks and moving boulders, that view, entertained by an observer of so much experience and intelligence, will be at once accepted. But the farther question arises. Whether there is evidence of there having existed also, at some other period, the agency of floating ice ? Professor Geikie does not admit that there is such evidence; and it has to be confessed that only one place on the islands has as yet been pointed out where such evidence is alleged to exist. Mr Allan having drawn attention to the peninsula of Eide, as presenting rock smoothings and striations similar to those pointed out by Sir James Hall on Corstorphine Hill, Dr Eobert Chambers, when he visited the Earoes forty years afterwards, went to Eide, on purpose (as he says) to study the appearances which Mr Allan had only generally described. He states that he ‘‘ looked narrowly for the striae or scratches ; ” and saw that “ they presented themselves in abundance in several places ; ” and he says that he was satisfied that they were “ all directed from the north.” Professor Geikie, in his Memoir, adverting to these same rocks, states, they are “perhaps the best preserved roc7^e5 moutonnees he anywhere observed;” — but as to the direction in which the smooth- ing and striating agent had moved, which Dr Chambers alleged to be “ from the north,” Professor Geikie states that the striae “ had clearly been graved by ice, coming from guile the opposite point of the compass ” (p. 246). The Professor follows up this statement by explaining (p. 261) that “the long sound that separates Osteroe from Strombe (must have) brimmed with ice, which fiowed in two directions ; north of Hordskaale the movement was northerly, while south of the shallow part of that sound the ice held on a southerly course.” It is unfortunate that thus Professor Geikie and Dr Chambers, both of them competent and experienced observers, should have given opposite testimonies in this matter. The question at issue being, as Professor Geikie states, one of 904 Proceedings of the Royal Society ‘‘considerable interest,” it may be allowable to inquire whether any circumstances exist calculated to throw light upon it. The glaciation and striae on the rocks at Eide were by Dr Chambers ascribed to agency which came “ from the north,” viz., sea-ice. By Professor Geikie these were ascribed to the agency of land-ice, filling what is now the sound of Nordskaale, of which land-ice, one portion flowed north towards Eide, and the other por- tion held on a southerly course, each thus flowing in opposite directions from what had once been a col, or head of two separate valleys. (1) There is one circumstance which seems to favour the view taken by Chambers, viz., that Mr Allan, when he examined the rocks, evidently considered that the agent which produced the markings, was the sea. He adopted for an explanation of these. Sir James Hall’s opinion, suggested by the similar phenomena on Corstorphine Hill, viz., diluvial agency. The smoothed and striated rocks on the sea-coast at Eide forming a “ headland,” as Mr Allan called it, would no doubt seem to him well suited to illustrate such an agency. He accordingly takes notice of these rocks as “ scooped and scratched in a very wonderful degree, not only on the horizontal surface, but also on a vertical one, of 30 to 40 feet high, ivhicli had been o'pjposed to the current, and presented the same scooping and polished appearance with the rest of the rocks, both above and below If this be a correct view of Mr Allan’s opinion, he is so far a witness corroborative of Chambers. (2) Another circumstance bearing on the question, is the apparent difficulty of any glacier being formed which could reach the rocks at Eide, glaciated as they are, up to a height of 1302 feet (Abstract, p. 879). The distance of Eide from the col (from which Professor Geikie supposes the glacier to have flowed in -its northward course) is between 8 and 9 miles. At the col (as the map shows) the valley is exceedingly narrow, and the hills on each side apparently are not so high or so shaped as to afford good gathering ground for a large accumulation of ice. The hills there do not seem to be above 2000 feet high. Supposing ice to have filled the valley there even up to that height, and to flow towards the north, would it ever reach Eide ? 905 of Edinhiirgh, Session 1883-84. There are two difhculties in the way. First, the map shows that between the Col and Fide the valley widens immensely, so that the glacier would almost certainly stop and break up at that place where there is both breadth and depth. Second, there is no gradient along the bottom of the valley from the Col to Fide to draw down a glacier, because, as Professor Geikie explains, the depth of water in the sound at Fide is much less than at places between Fide and the Col {Abstract, p. 880). In these circumstances, there seems more probability that at this place the striations and smoothings were made by sea-ice than by a glacier. (3) The mouth of the fiord is open towards the north, and when the Faroes were 1600 or 2000 feet submerged, there would be ample opportunity for floating ice to pass through the sound. This view is to a certain extent supported by the curious circumstance, that in many parts of the Faroes the hills are glaciated everywhere below a pretty uniform level of 1600 feet, whilst above that level most of them are rough. In that northern latitude, if land-ice prevailed generally, so as to produce an ice-sheet or local glaciers, one does not see why the hills should not have been covered and glaciated to their tops. Moreover, if it is established that to the W. and H.W. of the mainland of Scotland floating ice was brought by some north-west oceanic current, the fact that the Faroes are 2° farther north in latitude would bring them the more readily within reach of such a current. 8. The conclusion to which the facts set forth in this summary lead is, that if boulders were brought to this country by a great north-westerly oceanic current, some of these boulders now on our hills may, in mineralogical composition, be found to differ from British rocks ; and in that view, it is only right to notice, that two geologists, having considerable personal knowledge of British rocks, state that boulders have been seen by them in this country, differing in mineral composition from any rocks in Great Britain with which they were acquainted. One of these authorities is the late Pro- fessor Mcol of Aberdeen University {Abstract, p. 841). The other is Mr James Plant of lioicester, to whom the English Boulder 906 Proceedings of the Boyal Soeiety Committee, in their Second Re^port (for 1874, p. 197), refer in these terms : — Mr James Plant reports both “ isolated boulders and groups of boulders, and be records one remarkable fact of especial importance, viz., that a group of boulders bad been exposed in an excavation made in Leicester, 25 feet deep, composed of rocks, which Mr Plant failed to recognise as British.’’ If this testimony be verified, the fact would be in pari cases with the case of the three plants * found in the Hebrides and the west coast of Ireland, but unknown in any other part of Europe, whose native habitat is Boreal America, and whose transportation to our shores the late Professor Edward Forbes did not hesitate to ascribe to floating ice {Memoirs of the Geological Survey of Great Britain, vol. i.). Finally, it may be asked, if the theory of an oceanic current with floating ice be adopted to account for most of the boulders in Scot- land, especially those on the west and north-west coasts, — from what country could the boulders have come, and what could have produced this current ? The Committee, though not acknowledging the impossibility of suggesting an answer to this question, think that were they to venture on doing so, they would be trespassing beyond the objects of their appointment. Their proper province has been simply to collect facts bearing on boulders in Scotland, embracing their distribution, their positions, and the agencies probably concerned in their transport. To explain the source or origin of these agencies, or, in other words, to unravel the conditions of the earth’s previous history, so as to account for these agencies, is a problem the solution of which must be left to others. The names of these plants are Eriocaulon se;ptangulare, Neottia gemmipare, and Sisyrinchium anceps. of Edinburgh, Session 1883-84 90,7 5. Remarks by Mr Milne Home on presenting Tenth Report of Boulder Committee, 21st July 1884. In presenting this the Tenth and Final Report of the Society’s Boulder Committee, I hope to be allowed to offer some explanations bearing on the work which the Committee has been able to accom- plish. The chief object for which the Committee was appointed, being to obtain from Scotland, generally, as much information as possible regarding boulders, the Committee could think of no better plan of commencing work, than by addressing circulars, first to the clergy- man, and next to the schoolmaster in every rural parish (including the Hebrides, Orkney, and Shetland), asking whether any boulders of large size existed in these parishes'? — and if so, inviting informa- tion regarding such boulders, on points which it was expected might without much difficulty be imderstood and answered by .the parties addressed. The Committee were gratified by the readiness with which these appeals were responded to ; and I now, in name of the Committee, or rather, may I venture to say, in name of the Royal Society, beg to express our thanks for the courtesy shown to us by those who sent answers. Independently of information about boulders contained in the answers to our Circulars, the Committee discovered from many of these answers, the names and addresses of persons in different parts of the country, who, we were told, took an interest in the objects of the Committee, and who were even so obliging as to allow it to be mentioned to us, that they would be happy to show the boulders in their neighbourhood to any members of the Committee. These offers came not only from clergymen and schoolmasters, but from resident landed proprietors and others, who through the clergy and the schoolmasters in their several parishes happened to hear of the 3 o VOL. XII. 908 Proceedings of the Poyal Society inquiries whieli our Society had set on foot ; and now, by way of acknowledging the services, and in some cases also the hospitality rendered by the persons to whom I refer, I propose to leave in the hands of our Secretary the names and addresses of these persons, not doubting that, if any one desires to obtain further information regarding boulders situated at or near the places where they reside, they would, if applied to, be still willing to aid in the inquiry. At the close of the Committee’s Report, there is in Appendix II. a memorandum, called a Summary of Facts, and of inferences from the facts, hearing on the question. What was the nature of the agency by which boulders were brought to their present sites ? This being the critical question, for the elucidation and discussion of which the Committee was expected to gather data, it would have been desirable had the Committee, as a united body, pro- nounced findings in which the members could all concur. I knew, however, that it was hardly possible to expect this ; and I saw that the best course would he for me, as Convener, to undertake the duty of framing a memorandum, and submitting it to the Committee for insertion in the Report, as an Appendix, on the understanding, however, that no one but myself should be committed to the views contained in it. This course was approved of by the Committee. But I felt my own responsibility in this matter so much, that at our last Committee meeting, I earnestly urged one of my colleagues, who I believed was eminently competent, to draw out a memo- randum of his own views, independently and irrespective of mine. I regret to say, that on the ground of his not thinking himself able for the duty, he too modestly declined it ; though from what I knew, and what the Council knows of this gentleman’s qualifica- tions, I feel sure that any memorandum from him would have added greatly to the value of this Report. I may now state in a few sentences the conclusions to which, as Convener, I have come in this inquiry, after giving mature consideration to the investigations of the Committee. These are — 1. That at some period, geologically recent in the earth’s his- tory, an Arctic climate prevailed in this part of bTorthern Europe, which had the effect of producing local glaciers in Scotland ; of Some of which glaciers there are traces still visible in the most mountainous of our districts, as pointed out in our last Report. of Edinburgh, Session 1883-84, 909 2. That subsequently Scotland was for a considerable time submerged beneath the sea, which over-topped our highest mountains, covering them, and filling most of our valleys with sand, gravel, and mud, beds of which are noticed in our Reports as still visible, up to a height of at least 3000 feet above the present sea-level, — thereby concealing to* a great extent, traces of the pre- vious local land glaciation. 3. That whilst Scotland was so submerged, and probably simultaneously, with the whole of the British Isles, and much of Northern Europe, an oceanic current from some north-westerly quarter prevailed, bringing masses of floating ice, with boulders upon them, which boulders were deposited on our hills (then sub- marine) when the ice stranded on these hills. 4. That the existence of this north-westerly current is, if not certainly proved, at all events made highly probable, by the foUow- ing considerations : — (1) That boulders of all sizes, and differing from the rocks on which they lie, are more numerous on the west coast of Scotland (including the Hebrides), than elsewhere. (2) That when boulders are on hill slopes anywhere in Scot- land, these slopes 7nore frequently face the west than any other point. (3) That when boulders have a longer and a shorter axis, and are narrower at one end than at the other, the longer axis and the narrow end very generally point towards the N.W. (4) That when boulders are found lying against a rock, in such a way as to show that this rock had stopped the farther progress of the boulder, the relative positions of the boulder and of the obstructing rock imply, in a great majority of cases, transport of the boulder from the westward. (5) That many boulders are found on or near the tops of hills, at such heights above sea-level that no local glacier, assuming such to have been generated in neighbouring hills, could have the posi- tions of the boulders. (6) That on open ground, almost everywhere in Scotland, and more especially on the west coast of Scotland, including the Hebrides, the smoothings and the striations of the rocks show a movement over them from some north-westerly point. 910 Proceedings of the Royal Society (7) That several plants are found on the west of Scotland and of Ireland, but nowhere else in Great Britian or ISTorthern Europe, which plants are stated, on botanical authority, to abound in Boreal America^ as their native habitats. With reference to the view thus taken, that boulders in Scotland were carried on ice floated by the sea, it is curious, historically, that we should now come back to the theory suggested in this Society sixty-two years ago by a remarkable man, then President of the Society, Sir James Hall of Dunglass, whose views, however, on this subject have not always been correctly represented by geological authors. It has been alleged that in his well-known paper, dated March 16, 1812, “On the Kevolutions of the Earth’s Surface,” published in our Transactions, vol. vii. pp. 139-211, Sir James sought to explain the transport of boulders by diluvial action alone; i.e., by great sea waves, such as those which ingulfed Lisbon and several cities on the west coast of South America. But this is a mistake, as I should like to show, by quoting one or two sentences from his paper. At page 161, Sir James, alluding to the different theories started by Saussure and others to account for the transport of boulders, mentions one, suggested by a Professor Wrede of Berlin, viz., that the boulders in Horth Germany “ had been transported across the Baltic, by means of the wind on floats of ice, and settling in their present place, had been left there by the retiring waters.” Sir James then expresses his own opinion thus — “ If the pheno- mena on the banks of the lake of Geneva were really occasioned by a torrent of water, its magnitude must have been such as to leave few vestiges of the human race, and we can only expect proofs of it in geological facts. It may, however, be alleged, as I have already hinted, that it woidd be impossible for water of any depth whatever, or moving ivith any velocity, to carry blocks of such magnitude to such situations; and this consideration is of such importance, that I am induced, in attempting to unite the ideas of Saussure with those of Hutton, to retain part of the system pro- posed by Professor Wrede, in so far as to consider those granite blocks as having been made to float by means of masses of ice. The opinion thus adopted and propounded by Sir James Hall was conceived at a time when nothing was known of icebergs and of Edinhurgh, Session 1883-84. 911 icefloes in the Arctic regions carrying boulders and depositing them at a distance from the parent rocks, and is a proof of the same remarkable intuition which was manifested by Sir James in other well-known philosophical speculations. In conclusion, and as I will probably not have another oppor- tunity in this Society of saying so,, may I express a hope that the subject of ^^hoidder transport will continue to excite interest among our members. If important truths bearing on the most recent revolutions on the Earth’s surface are, as I venture to think they are, likely to be established by investigations such as those which have been for some years carried on in Scotland, and which are now carried on also in England by the Committee of the British Association, I trust that any proposal to have a new Committee will be favourably listened to. It should not be forgotten that our Society, so far back as 1812, was the first in Great Britain to bring this subject before the scientific world ; and also that in the year 1871, at the instance of the late Sir Bobert Christison, then our President, we again led the way in originating an extended inquiry. In these circumstances, I cannot doubt that the Society, for the sake alike of past memories, as of future probable dis- coveries, will be disposed to encourage further research in this interesting field of geological knowledge. Names of Persons who were particularly serviceable to THE Boulder Committee. Clergymen.. Rev. Mr Joass, Golspie. „ Dr Gordon, Birnie. „ Mr Craig, Ardentinny, „ Mr Leitteib, Cumbrae. „ Dr Clark, Kilmallie. „ Mr Cameron, Kilmonivaig. „ Mr John G. Campbell, Tyree Island, ,, Mr M‘Ewen, Edderton. „ Mr McDonald, South Uist. . „ Mr Alexander Eraser, Coll Island. Mr George Campbell, Tarbet. 3 p j) VOL. XII. 912 Proceedings of the Royal Society Schoolmasters. Mr Alexander, Lochgilpliead. Mr Colin Livingston, Fort-William. Mr Martin, Elgin. Mr William Morrison, Dingwall Academy. Mr Wallace, Inverness High School. Mr Campbell, Southend, Kintyre. Mr Allan Macdonald, Iona Island. Mr John MacKillop, Lochgair. Landed Proprietors. The Duke of Argyle, Inveraray. Earl of Dnnmore, Rodil, Harris. General Sir John Douglas of Glenfinnart. Sir John Rarasden of Ardverikie, Lochaber. Lady Gordon Cathcart, Hist and Barra. Clunie M‘Pherson of Clunie Castle, Kingussie. Alexander Campbell of Auchindarroch, Lochgilphead. Edward Ellis of Invergarry, Fort- William. J. Campbell of Stonefield, Greenock. J. Campbell of Ormsay, Lochgilphead. Norman MTherson of Eigg, advocate, Edinburgh. J. F. Campbell, formerly of Islay, London. Alexander Smollett of Bonhill, Dumbarton, Captain Stewart of Coll, E N. Other Persons. John Clark, writer, Oban. W. J. Miller, C.E., Glasgow. Mr Murray, writer, 167 George Street, Glasgow. Alexander Carmichael, Inland Revenue officer, Oban. Mr Ballingall, factor, Islay Island. Mr Mackay, factor, Stornoway, Donald McNeill, farmer, Colonsay. William Stevenson, Meadowfield Place, Edinburgh. Dr M‘Gillivray, farmer, Barra, Hebrides. John Young, Hunterian Museum, University, Glasgow. Vol XII, PI. XI. Proc Roy Soc Edin, Vnl.XII Pl.X W Sc A K. Joinston. Jidinlmrgli 5!: Lonaou Proc. Roy. Soc, Edin. Vol.XII. Pl.XKI, ^ A K, Johnston, Edmhurgh. 8c Londo: of Edinhuryli, Session 1883-84. 913 6. Notice of Two Localities for Eemarkable Grravel Banks or Kaims, and Bonlders, in the West of Scotland, in Supplement of the Boulder Committee’s Tenth Eeport. By David Milne Home, LL.D. (Plates XI. to XIII.) I. Lochaber. About eight or ten years ago,, when- in Lochaber,. studying the “ Parallel Uoads ” problem, I became acquainted with a district in the valley of the Eiver Spean, which presented the phenomena of gravel banks or kaims, and boulders, on a larger scale than I had ever before or have since met with. The lowest of the Parallel Roads^ marked No. IV. on the Ordnance Survey Maps, traverses this district; and whilst tracing the direction of the “ Road^ as it crosses the hnes of these banks and boulders, I was greatly puzzled to account for them, and still more for the lines in which they had been deposited. I took notes, and made rough sketches of both at the time, hoping that I might have an opportunity of a more special investigation. A failure of bodily strength supervened,, which deprived me of the opportunity ; but as I deem the district well worthy of the atten- tion of geologists, on account of the light it seems to throw on questions of much interest, I propose to give a short account of the facts observed on the occasions referred to, taken from notes and sketches made at the time. Much assistance can, now be obtained for an examination of the district from the Ordnance Survey Maps. At the instance of several scientific Societies, Her Majesty’s Government gave autho- rity to the late Sir Henry James, then Director-General of the Survey, to have special maps made, to indicate the ^'Parallel Roads ” in the different Lochaber valleys ; and latterly, at the joint request of the Edinburgh Eoyal and Edinburgh Geological 914 Proceedings of the Royal Society Societies, he caused a map (on the 6-inch scale) to he executed of the particular districts in the Spean valley, to which I am about to refer. This district is in that part of the valley where the Eiver Spean, flowing from Loch Laggan, is joined by a smaller stream from Loch Treigp The Outline Map A (Plate XI,) gives a general idea of the position of the gravel banks, v/ith reference to Loch Treig and the adjoining Bivers Spean and Treig, The dark dotted line indicates shelf lY., being the lowest beach of the lake v/hich stood at a height of about 855 feet above the seadevei. The dark shaded line, sur- rounding the valley, shows generally the position of the adjoining hills, at a level above the sea of from 1300 to 1500 feet. I had my attention first drawn to these banks and boulders when walking along the line of shelf lY, near the mouth of Loch Treig. On looking up at the hill slope situated to the south of this loch, I noticed several projecting lines of terraces, at much higher levels than shelf lY., and at first thought that they might repre- sent some of the shelves of the higher lakes, which had been recognised in other Lochaber glens, but not in this one. I thereupon ascended the hill, and, on doing so, obtained a general view of the low grounds, and of the remarkable assemblage there of kaims and boulders. I at opce saw that many of both formed lines, in some cases rectilinBal^ but also and even more frequently curvilineal^ the inner curves facing the north, ie., down Glen Spean, (See A on Sketch Map, Plate XL) The first terrace on the hill slope which I reached was (by aneroid) at a height of 1120 feet above sea-level, The terrace pre- sented a level surface from 40 to 5,0 feet wide, abutting against the hill, and was composed of water-borne gravel. Two great boulders lay on this terrace, about 200 yards apart. From this terrace I climbed to another, at a height of 1165 feet above seadevei ; on it were three large boulders. There was still another terrace, and its height above the sea I found to be 1175 feet. Again a higher terrace was reached, 1480 feet above the sea, somewhat broader than the others, and having a considerable number of boulders on it, of Edinburgh^ Session 1883-84. 915 I did not observe any terraces at a higher level ; but I saw that there were many boulders on the slope of the hill above, some of large size. With the view of proceeding next to the low grounds, where the extended lines of kaims and boulders were seen to be situated, I walked south along the highest of the above terraces, and observed that it gradually ceased to touch or abut with a flat surface on the hill, and that it became separated from the hill by a narrow trough, as if the detritus next the hill had been scoured out by the action of water currents, or of rain descending on it from the slope of the hill The terrace at length became so narrow as to become a bank or ridge, the outer flank of Which was, of course, much higher than the flank next the hill The upper surface of the terrace now ceased to be horizontal, and sloped down towards the S.E. As I proceeded, I observed, on my right hand, some rocks much smoothed; at a height of from 1500 to 1600 feet. A little further south, I came to a projecting rocky corner of the hill, named Craig DliubJi^ indicated on the one-inch Ordnance ]\Iap by the sudden bending of the contour lines towards the S. W. The surfaces of the rocks there were seen to have been greatly smoothed (apparently from the north), whilst immense masses of rock were lying at the foot of the crag] It was only at this corner of the hill that any smoothing of these masses existed. Eocks con- tinued in a S.W. direction without any such features^ The agent which had produced these effects had, at this point, apparently slanted off towards the S.E. Before descending further, I looked with my glass across the valley towards the hills on the east, and descried there several lines of terrace on the south projecting shoulder of Craig Dhu and Connichte, and also on some high ground near the Rough Burn (Sketch Map B, Plate XI,). These I decided on visiting, after in- spection of the low grounds immediately below me^ In my way towards the low grounds A, I walked along a kaim or gravel bank, whose course followed a direction about E.S.E., and sloped downwards, with steep sides from 20 to SO feet high. I observed that there were also many boulders on the low grounds, some of them forming lines or trainees. 916 Proceedings of the Royal Society The district occupied by these kaims was tolerably flat, and about 2J miles wide (in an east and west direction) across the general course of the Eiver Spean. There were several lines of kaims all approximately parallel, and presenting a slight curvature; — the inner curves facing the north, or down the valley of the Spean. At one place there was an interruption in the continuous line of the northernmost bank, as if it had been broken through by some agent from the north; and I took a rough sketch of it on the spot, being fig. 1 on Plate XIII. At A, the kaim BC ceases for about twenty yards; and between this “ break,” and the other bank DE, there is a heap of boulders. The highest and thiekest of the two banks is BAG, and on it the greatest number of boulders are accumulated. On the low ground to the north of these kaims there are many grey granite boulders of various sizes scattered about, mostly angular. There two knobs about twelve or eighteen feet high attracted my attention, in consequence of there being boulders on their tops. One of the knobs was of detritus; the other of rock^ sloping down steeply on all sides, except the east. In each case the diameter of the flat surface at the top was about six or seven yards, and there were five or six boulders on each; — most of the boulders were on the sides facing the X. and X.W. In several places^ and especially at the north base of the most northern kaim, BAG, there were boulders piled over one another. On studying these, I became impressed with the belief that the uppermost boulder, being the last which came^ should show the quarter from which it must have come, to get into its position. Diagrams on Plate XII. represent these cases, showing that the boulders had come from some northerly point.* There was one place where rocks in situ of grey granite were found smoothed ; the smoothed face being towards the north, and a boulder lying on that side. The farther progress of the boulder to the south had been apparently obstructed by the smoothed rocks. This case is shown by fig. 1, Plate XII. * Explanations of the Plates are appended to this notice. of Edinhurgli, Session 1 883-84, 917 On several occasions subsequently, I examined tbe banks and boulders, occupying tbe district on the east side of the Eiver Spean, and situated to the north of the spot on the Ordnance Map called Rough Burn^ (See B on the Sketch Map, Plate XL)* I found several, and especially two remarkable kaims, running in a somewhat different direction from those on the west side of the valley, viz., towards south, and curving like the rest, — with the inner curve facing the west. I walked along the top of the two highest kaiihs. Their sides were steep, and reached in some spots to a height of 30 to 40 feet, with many boulders on them. These kaims occupy portions of the hill, which slopes up towards the north, from about 1100 to 1245 feet above sea-level. Standing on these kaims, I could descry Loch Treig, which by compass bears from them about S.S.W. The level of the loch is represented in the Ordnance Map as 784 feet above sea-level. Some of the boulders, on the level ground in several parts of the valley, form trainees, more or less parallel with the lines of the kaims. The following are the dimensions of some of the bdulders on the east side of the valley : — One measured in girth 19 paces, and in height 5 feeL Another measured 12 x 3x2 feet, with longer axis S.W. ,5 15x10x4 feet, „ „ It is proper to add, that shelf lY., before referred to as the beach line of the lowest lake, is visibly impressed on the gravel banks, on both sides of the valley ; and they are so indicated on the Ordnance Map. These kaims, therefore, belong to a period in history more ancient than the Lochaber lakes. Theory, With regard to the origin of these banks and boulders, there can be little or no doubt that the materials of the banks, consisting chiefly of well-rounded pebbles and blocks, and in some cases of sand, in beds partially stratified, must be due, in some way, to the agency of water, with deep and powerful currents. 918 Proceedings of the Royal Society The detritus had assuredly not fallen from the adjoining hills, by the natural decay of the rocks composing them. The late Dr Macculloch, who was eminent as mineralogist, geologist, and chemist, visited Lochaber, to seek for data to enable him to try and solve the problem of the parallel roads ; aud wrote an elaborate paper on the subject, which was published in the Transactions of the London Geological Society for 1817, vol. iv. He particularly studied the nature of the gravelly materials lying on the surface of the country, and he found that these were of two descriptions. He observed that the debris of the rocks were angular in shape : — The other class he called “ transported alluvium of pehhles^ sand^ and gravel and these, he observed, generally differed in mineralogical composition from the rocks of the hills on which they lay. “ The alluvium (he says) was not thus rounded by the action of the water which prodmced the lines {i.e., the parallel roads). We must suppose that this rounded alluvium had been, by previous causes, accumulated. If this took place from the action of water {aQid to what other cause can ive assign it .?), it must belong to an epoch prior to the deposits of sharp matter in the upper parts ” (page 330). Again he says : — “ The conoidal hillocks, occurring between Glen Fintec and Glen Glastrie, consist of deposits of fine sandy clayy and rolled stones of different sizes, — disposed in a manner irregularly stratifiedy and in a direction more or less horizontcd. The terraces and hillocks, which occupy positions much inferior to these, all the way along the course of the SpeaUy are of the same materials^* (page 339). The hillocks in Glens Fintec and Glastrie, here mentioned as examples of '•transported alluviumfi occupy positions exceeding 1200 feet above the sea, and are (Macculloch says) the same kind of deposits as those along the course of the Spean, referring, no doubt, to the kaims described in this paper. Examples of these detrital deposits occur in all the Lochaber glens. In Glen Roy and its lateral valleys, there are cliffs of boulder clay, exceeding 200 feet in depth. Along the course of the Spean at Murlaggany on the east bank, there are cliffs of sand, par- tially stratified horizontally, above 80 feet deep; and on the west side, of Edinlurgh, Session 1883-84 919 at Alt-na~Bruach^ there are cliffs of mixed sand and gravel, equally deep, all more or less stratified. The River Treig, near its exit from the loch, has cut through banks of gravel, also stratified, exceeding 70 feet in depths It may be added that any one passing through the Caledonian Canal, near Banavie, may see great gashes on the MCy Hills to the north, occurring in enormous beds of white sand, at a height of 2000 feet above sea-level. Mr Jamieson of Ellon examined the whole of this district carefully, and mentions that at the outlet of Loch Treig he found “ striae running horizontally along the face of the rocks up to 2000 feet;” and he adds, “not that I affirm even this to be their upper limit.” He mentions similar features, even as high as 3055 feet above the sea, “ which (he says) raise a suspicion that some denuding agent has flowed oner it at a period geologically recent.” {Lond. Geol. Soc, Journal, 26th Feb. 1862, p. 172.) In these circumstances, it seems impossible to doubt that the sea has flowed over the whole of this district, and in such a way as to bring detritus of sand, mud, gravely and boulders, and deposit them alike on hills and in valleys. The detritus which forms the kaims in the Spean valley, which I have been describing, must therefore almost certainly have been brought and deposited there by oceanic agency. The gravel banks or kaims of the Spean valley are not unexampled in many other parts of Scotland. In Linlithgowshire a gravel bank, with steep sides, runs from Polmont eastward, nearly two miles continuously, with occasional bends, and is now cut across at several points by small rivers. In Haddingtonshire a similar east and west kaim runs for about a quarter of a mile* In Hairnshire there is a similar kaim, traceable for a greater distance. In Ber- wickshire, on Greenlaw Muir, at a height of about 1000 feet above the sea, there is a gravel bank, high and steep, about three miles in length, presenting several considerable bends in its course, and cut across by two small streams. In consulting the Admiralty Maps, which show the forms of submarine sandbanks, I find many examples running for more than a mile continuously, and, in one case, a bank curved into almost a semicircle. Off the mouth of the Thames, where the tidal currents are strong, there are several such cases. 920 Proceedings of the Royal Soeiety When Scotland was submerged, the currents in this region would probably he rapid, looking to the relative positions of the hills and valleys. If the question he thought of any importance, it may he noticed on the Map, Plate XI., that this part of the Spean valley is so sur- rounded hy hills, as to he an area well fitted for the reception and detention of detritus, its diameter being about three miles. Moreover, it is worthy of notice that the valley in which this area occurs is contracted at its north end, so that if a current flowOd at that end, towards the Spean valley, it would enter the valley with considerable velocity, and in virtue of the way in which it is surrounded hy hills, it might acquire a circular motion, producing whirlpools or eddies. It will be found, on consulting the contour lines of the one-inch Ordnance Map, that whilst the space where the kaims and boulders are situated is (between the contour lines of 1250 feet) three miles across, the breadth of the valley to the north, between the same contour lines, is only IJ miles (see Sketch Map, Plate XI.). To the north of this gorge there is open country, and at a low level ; so that if the country was then sub- merged there would be opportunity for a large body of water flow- ing through the gorge towards the south. Xow it is allowable here to observe that there are strong reasons for believing that when Scotland was submerged a powerful current, with floating ice from some north-westerly point, did pre- vail here, as probably elsewhere in Scotland. A few of the facts bearing on this point may be mentioned. (1) The most important of the lateral glens joining Glen Spean is Glen Roy^ which runs for about 1 6 miles towards its head or col in a S.E. direction. I extract the following paragraph from the notes taken by me when I visited this glen in 1846 : — ‘‘ Visited head of Glen Roy. In upper Glen Roy it is interesting to observe how uniformly the smoothed surfaces of rocks are to the icest, and their rough faces to the east.'’^ As this is a point of some importance, I confirm my own observa- tion by a quotation from the Memoir of Mr Jamieson of Ellon, who, with a view to the ‘‘ Parallel Roads ” problem, made an elaborate survey of all the Lochaber glens, Xear the top of Glen Roy, he 0/ Eclinhurgh, Session 1883-84. 921 says {Land. Geol, Society's Proceedings^ voL xviii. p. 296) — “ I was not a little surprised to find that the ice had come from the S.W., up Glen Eoy. ..... The strata had been so blunted and rubbed on their S, W. exposures as to show plainly that the move- ment came from that quarter; and high up on the brow of the adjoining hill I saw several very large blocks and boulders that appeared to have been shifted or moved some distance ..... by glacial action.” Mr Jamieson suggests that this rubbing of the rocks, on their S.W. exposures, was due to “glacial action.” If ice moved up the glen it could not have been glacier, but floating ice. (2) In Glen Gluoy Valley^ adjoining Glen Roy, and opening like it towards the west, similar proofs exist of a movement up the glen, from the westward (see “Memoir on Parallel Roads,” Ed.inburgh Royal Society Transactions, vol. xxvii. p. 638).* (3) Craig Dhu, a hill situated on the east side of the gorge before mentioned, reaches to a height of 2100 feet, and presents several spots near the summit on its N.W. side, where the edges of the strata show smoothing from the north. The boulders on the hill are also chiefly on the north slopes. (4) Ben Chlinaig is a hill on the west side of the gorge, reaching to a height of 2545 feet. Mr Jolly of Inverness informed me that on its eastern slope he found rock striations at a height of 1840 feet, running KW, and S.E. (5) In the gorge itself, near its lowest level, some of the rocks present large smoothings facing the northj and grooves of great length, evidently caused by violent and severe friction of heavy bodies which had moved over the rocks. (6) Then on the N.W. shoulder of Ben Nevis, at the mouth of * As these pages were being printed, I received from my old and esteemed friend, Colin Livingston of Fort- William, a letter (dated 23rd September 1884) narrating an excursion he had a few days previously made to Glen Gluoy, and mentioning that at a height of about 1750 feet above the sea he had found several granite boulders on the side of a hill facing the west, and lying on quartzite rocks, which were smooth on their west sides and rough on their east sides. He adds that three of these boulders formed a line or trainee of abou a 100 to 120 yards. He became satisfied, from these facts, that the boulders had come up the glen from the westward, and not down the glen, as he had previously supposed. The nearest locality for granite rocks, known to him, is ‘ ‘ Meallan-Suidhe, ” situated some miles to the westward. 922 Proceedings of the Poyol Society a glen called Corny N^Eoin^ I found, at two different spots, rocks so striated as to show that the striating agent had moved from N.lSr.W., in the direction of the Spean valley* (7) In the Spean valley itself there are at least a dozen places where the rocks by the marks on them distinctly show severe pressure and friction by some body passing over them in a S.E. direction,* (8) Keference having been made to terraces or banks of detritus on the slopes of the hills to the south of Loch Treig^ tip to a height of about 1400 feet above the sea, it is proper to mention that similar banks of detritus occur on the hills to the north, and at about much the same level. On ChUnaig Hill (before referred to) there are two SUch banks at a height above the sea of 1253 feet and 1373 feet. The hill on the opposite or east side of this valley shows similar banks, and along which I walked at rather a lower leveL It appeared to me that these had very probably been formed when the land was submerged. They ate essentially different from the old lake beaches, in respect of their Want of horizontality. (9) Lastly, I refer to the fact, that almost at the very tops of the highest adjoining hills great boulders are found, and in such positions as to show that they could not hUve come there except by floating ice. Thus, Darwin refers tb the boulders on the top of hills in Lochaber, at the heights of 1700 and 2200 feet above sea-level. On the tops of two hills adjoining Loch Laggan, exceeding 3000 feet above the sea, I was informed by Sir John Kamsden of Ardverikie, the proprietor of these hills^ that there are several large granite boulders. Whilst expressing my own opinion that the kaims and boulders in the valley near the junction of the Eivers Spean and Treig indicate the agency of the sCaj it is proper to advert to the opinion of my geological friend, Mr Jamieson of Ellon, that these are the moraines of a glacier which, generated in Glen Trieg, advanced into and crossed the Spean valley. Mr Jamieson adopted the view originally suggested by Agassiz, that the barriers of all the old Lochaber lakes consisted of ice. It being necessary to find a barrier for the Glen Eoy Lake not only * These places are named in the “ Memoir on Parellel Roads,” by Professor Prestwick and me respectively. of Edinburgh, Session 1883-84. 923 at the foot of the glen, hut at the head of Glen Glaster, Mr Jamieson saw that the only way of obtaining an ice barrier at this last-men- tioned place was to assume the existence of a glacier in Glen Treig, which he supposed would descend into and cross the valley, then rise up on the opposite side of the valley near the Kough Eurn, and next make a nearly right-angled wheel towards Glen Glaster, dis tant from Loch Treig no less than 6 miles ! I am afraid that I must agree with Professor Prestwick (Phil Trans, of Royal Society of London for 1879, p. 668) in the opinion he has expressed, that the “ Glen Treig glacier would be in- competent to the task assigned to it ” by Mr Jamieson. Professor Prestwick observes, that to block Glen Glaster col the “glacier would have to cross Glen Spean, and after that travel 2 miles with a rise of not less than 500 feet.” I agree with the Professor (page 684), that if there was a glacier from Glen Treig, which protruded into the valley, it would, instead of ascending the slopes on the opposite or east side of the valley, have followed the natural levels of the valley, and flowed down to- wards the north-west. Whilst Mr Jamieson’s primary object in suggesting a Glen Treig glacier was to find a barrier for the head of Glen Glaster, he also availed himself of the services of this glacier for explaining the origin of the kaims and boulders, which form the subject of the present paper. One fatal objection to this view, as it appears to me, is, that the materials composing these kaims are. not such as characterise moraines. They are what IVtacculloch properly calls rounded alluviumf formed by the action of water ; whereas the materials of moraines being merely the dtois of rocks, which fall on the surface of the glacier by meteoric agency, are totally different in character. Another objection to this view is, that the lines of kaims in the valley lie to the south of the march which any glacier from Loch Treig would take. To meet this obvious difiiculty, Mr Jamieson says that “ the glacier on issuing from the narrow gorge at the end of Loch Treig dilated immensely so that its right jianh might carry materials to the position occupied by the kaims and boulders. I think that if the glacier underwent such an immense 924 Pwceedings of the Royal Society dilatation, it would fall to pieces, altogetker in the valley, before it could reach the position of the kaims. At the same time, I am far from denying that Mr Jamieson had good grounds for supposing that a small glacier existed in Glen Treig, and that it even probably protruded a little way into the valley. In his map he indicates glacial striae at a point where they may have been caused by a glacier from Loch Treig. I saw these striae, (Notes, vol, i. p. 8), viz., on masses of rock which had been smoothed and partially striated from the westward. Most of the rock was covered and concealed by detritus, which, on being cleared away by me, showed the smoothed surface of the rock. The explanation which occurred to. me at the time was, that after these rocks had been so smoothed and striated the country became sub- merged, and the whole valley was filled with submarine beds of gravel, sand, and boulders. The spot now referred to is near that marked “ ” on the onednch Ordnance Map (Sketch Map, Plate XL). Whilst offering my opinion, that these kaims in Spean valley are submarine detritus, and have been scoured out into long banks by the action of sea currents, I acknowledge that they deserve much more examination than I had the opportunity of giving; and I trust others who are interested in these researches will visit the locality, and publish the results of their inspection.^ Harbis. In the Fifth Eeport (page 23) of the Boulder Committee it is mentioned that “ at Borve^ on the west coast of Harris, about half- way between Eodel and Tarbert, there is a remarkable accumulation of boulders on the side of the hill sloping down to. the sea. The general slope of the hill (which reaches a height of 800 feet) is towards W. by X. (magnetic). The rocks are of gneiss, and present a series of beds, layers, or benches more or less horizontal, forming as it were a gigantic staircase along the hill face, for about half a mile, all more or less covered by boulders. These benches of rock, in many places, show that they have been rounded by severe pres- sure from W. by N. Many of the boulders which lie on them also give evidence of transport from the west.” of Edinburgh, Session 1883-84. 925 Two figures are appended to the Committee’s Fifth Eeport, to illustrate these facts. But I happen to have in my possession a more graphic representa- tion of the locality, which I now exhibit to the Society. It was made, at my request, by a London landscape-painter, who was taking views at Harris, and whose acquaintance I happened to make, by residing in the same inn with him. He and I on one occasion travelled together in the same conveyance, and had to bait our horse at Borve, near which the hill occurs. He saw me vainly en- deavouring to make in my sketch-book a drawing of the hill ; and, at my request, he was so kind as to give a representation of the place in my sketch-book, which I now reproduce (Plate XIII. fig. 2). It shows how numerous the boulders are on the hill-slope, and that they had found lodgment on the lodges of gneiss rocks which pro- trude from the hill. I give also a representation of one of the boulders (Plate XIII. fig. 3), firmly lodged on the projecting strata of the hill ; its east end abutting against the strata in such a way as, to show that it had probably come from the westward. The interest of the locality arises from the circumstance that the hill on which those boulders lie slopes down in a westerly direc- tion to the Atlantic Ocean ; so that if the boulders on the hill came from the westward, as I think they did, they must have been transported from some land bordering on the Atlantic. EXPLAXATIOX OF PLATES. Plate XI. A sketch map reduced from Ordnance Survey, to show part of Glen Spean valley, with lines of kaims and boulders. Plate XII. (1). Map of smoothed granite rock in Glen Spean valley, AB, running in S.W. direction, and having its smoothed side fronting X.W., with a boulder pressing against it. 926 Proceedings of the Royal Society Loch Treig bears W-S-W, from the rock ; whilst lower part of Spean valley bears N.W. by W. from the rock. If boulder came from Loch Treig it would not have been inter- cepted by the rock, but have passed on to left, viz., in a ^.E. direction. If boulder came up Spean valley it might have been, and most probably would be, obstructed in its farther progress by the rock. (2) . Boulder A rests by one of its corners C on boulder B. A line drawn through centre of A and corner C points S.E. by S., implying transport from N.W. by N. If boulder A had come from Loch Treig it could not have stuck on boulder B,. but have fallen off to one side. (3) . Two boulders resting on north side of a gravel bank in Spean valley. If these boulders had come from Loch Treig they pro- bably could not have stuck there. (4) . Two large boulders in Spean valley, situated S.E. of Loch Treig. Boulder A leans against boulder B in such a way as to show that it came from the north, and not from Loch Treig. More- over, a hill on south side of mouth of Loch Treig is so high that it would have prevented these boulders reaching positions they occupy. (5) and (6). Boulders at north side of a gravel bank in Spean valley. Plate XIII. (1) . Is intended to represent a small portion of two kaims with boulders on their sides, facing the north. The most northern shows an interruption at A, as if it had been broken through by some agent from the north. (2) . Eepresents a hill near Borve (in sloping down to the sea-shore, covered with boulders, apparently brought from a sea- ward direction, viz., the west. (3) . Is one of many boulders on Borve Hill, resting on the rocks in such a way as to show transport from a westerly point. >roc. Roy. Soc. Edin Vol. XII. PI. XIV of Edinburgh, Session 1883-84. 927 7. On the Periodic Variation of Temperature in Tidal Basins. By Hugh Eobert Mill, B.Sc., F.C.S. Com- municated by Professor Crum Brown. (Plate XIV.) The periodic variations of the temperature of water have been studied for some months at the Scottish Marine Station at Granton, The only tidal basin which has been considered as yet is the haven formed by the irruption of the sea into Granton Quarry. It has an area of about 7 acres ; the tidal entrance is on the west side, and is so situated that no water can enter until about half tide ; then it comes in as a very rapid stream for about three-quarters of an hour, when the rate falls off, and near high water it is the same as that of the rising tide on the shore. The ebb is gradual until the tide has narrowed the channel by uncovering the sandbanks which lie on each side of the entrance, then it is rapid for about an hour and a half, after which the water runs out extremely slowly, and does not absolutely cease until the tide begins to re-enter ; but for from four to five hours the water-level inside is practically unaltered. The depth of the quarry at low water varies from 5 to 8 fathoms in the parts where observations were made, and at high water the depth is slightly more than 1 fathom greater. The bottom shelves off abruptly from the bar at the entrance. The variation of water temperature naturally divides itself into two periods — aunual and diurnal. The former can only be ascer- tained by daily observations continued for several years, and such observations of both surface and bottom temperature were com- menced in May 1884, and are being continued. The diurnal variations may be investigated by continuous hourly observations for a number of entire days. Such series of hourly, and in some cases half-hourly, observations were made twice in the month of June for periods of thirty-six hours each, and once in the beginning of July for twenty-five hours, and some interesting facts were brought out by this means. It was made evident in some preliminary trials that the Miller- Casella thermometer was not adapted for rapid work in shallow water. It requires to be immersed from ten to fifteen minutes in 3 Q VOL. XII. 928 Proceedings of the Royal Society order to acquire the temperature of its surroundings ; when drawn up from depths under 10 fathoms, the mercury has not had time to recede from the index, and before it can he read evaporation from the wet bulb lowers the temperature and renders the reading inaccurate. Sir Kohert Christison’s cistern thermometer gave good results, hut it is too heavy an instrument to use continuously for many hours. For the first two sets of observations about to be described Kegretti and Zambra’s patent deep-sea thermometer with Magnaghi’s frame was used. The instrument is constructed so that after it has acquired the temperature of the water it may be turned over ; on this being done the mercury which has passed out of the bulb runs into the upper part of the tube which is now lowermost, and can be measured by means of a scale of degrees when the instrument is drawn up. Tt contains only one fluid — mercury ; and experiment has shown that three minutes are sufficient to enable it to acquire the temperature, although in our observations it was customary to allow four or five minutes as a minimum to make sure. The reversing arrangement of Magnaghi resembles a screw-propeller ; it is turned on drawing the instrument up through the water and releases the thermometer, which then turns over, as its pivots are below the centre of gravity and it never hangs quite perpen- dicularly. The objection to the method is that in shallow places the temperature at the bottom cannot be obtained, since the reversing screw will not act in much less than a fathom of water under the most favourable circumstances, and usually it requires considerably more. A modification of the thermometer was accordingly designed by Professor Chrystal and myself, and the necessary alterations were made in a most satisfactory manner by Mr Frazer of Lothian Street. The Scottish thermometer-frame, as the improved form has been named, differs from Magnaghi’s by the removal of the screw and fans from the pin that holds the thermometer in position, and the substi- tution in their place of a lever kept down by a spiral spring. The lever is forked at the outer end to allow the line to which the ther- mometer is attached to pass between. In order to prevent the line from slipping out of the fork, it is clasped by two thin springs of Edinburgh, Session 1883-84, 929 which rise from a projecting horse-shoe-shaped piece beneath the lever. A hollow cylindrical weight shghtly belled out at the lower end is dropped down the line when the thermometer is to be reversed ; it falls on the forked lever, raises the pin, the upper end of the instrument gets an outward impulse from an india-rubber band slipped over the frame (a device of Mr Buchanan’s), and it rotates sharply, and is clamped by a brass spring. When several of these thermometers are used on one line, as is convenient in taking serial temperatures, the weight for the next lower instrument is hung by a wire to the groove in the toj) ; it helps to pull the ther- mometer over when released, then sliding down the line it strikes the lever of the next, reverses it, and despatches its weight. In this way any number of instruments may be used on one line. The ends of the lever forks are covered with india-rubber to diminish the shock, and the whole apparatus is constructed of brass, so that no galvanic action can be set up between any of its parts. The adaptation of the Negretti and Zambra thermometer to reverse by means of a weight slipped down the line is not new. Mr Rung, of the Meteorological Institute of Copenhagen, has invented a very simple method of doing this ; but, although his frame has worked admirably in his hands, it has the disadvantage of being constructed of wood. A simpler arrangement for the same purpose was employed on the United States ship “ Fish Hawk/’ but, from the account given of it, it seems to be inferior to the Scottish frame, in not clamping the instrument when reversed. The new thermometer was made before the description of either of these earlier forms was seen. It has been found to answer admirably, both in very shallow water and in depths up to 80 fathoms. The first set of observations was made hourly during a period of thirty-six hours, from 9 a.m. on June 17th to 9 p.m. on June 18th. The temperature of the air, of the water at the surface (by an ordinary thermometer), and at the bottom, were taken each time from the Ark, the floating laboratory of the Station. The mean temperatures (corrected) were as follows : — For 30 Hours Daylight. For 6 Hours Darkness. For 36 Hours. Air, . Water, surface, . Water, bottom, . 58-7 54*98 54*60 54*1 54*88 55*01 54-97 54*67 57-9 930 Proceedings of the Royal Soeiety The observations included two complete tides, and it was observed that when the water began to enter at 6 p.m. the bottom temperature began to rise from 54° until at 9 p,m. it reached 55°. The surface temperature was meanwhile falling. The night was cloudy, and from 9 p.m. to 6 a.m. the readings of the surface and bottom thermometers were practically the same. At 6 a.m. the tide began to enter, and the bottom temperature fell slowly from 55° to 54° *6. The whole of the next day was dull and cloudy, and the temperatures of air and of water varied little. The tidal effect observed was somewhat puzzling, for the temperature of the water of the Firth was known by previous observations to be several degrees lower than that in the quarry, and not to vary appreciably with the hour. In order to get additional evidence, the 25th and 26th June were selected for another series of observations. The 25th was cloudy and cool, the air temperature being altogether below the average for the two days, the night was pretty clear, and the 26th turned out bright and warm. As I had more assistance than on the former occasion, observations were made every half hour at three stations in different parts of the quarry — one near the mouth where the depth at low water is 5 fathoms, the second was the Ark in 6 fathoms, the third a buoy in the north-west corner in 8 fathoms. The means of the observed temperatures are as follows : — For 30 Hours Daylight. For 6 Hours Darkness. Air, ... 59-5 54 '9 {Entrance, . 56 ’61 Ark, . . 56 T 7 55 ’52 N.W. corner, 56 ‘52 {Entrance, . 55 '51 55*65 Ark, . . 55*74 55*97 N.W. corner, 54*92 55*82 For 36 Hours. 58*6 56*05 55*55 55*64 55*24 The course of the temperature curves at the Ark on those two days is shown in Plate XIV., where the tidal effect is plainly notice- able. The observations embraced three complete tides. When the water began to enter at noon, there was a steady rise of bottom temperature, and when it entered at 1 a.m. next day there was as distinct a fall; while on its coming in at 1.30 p.m. a very abrupt rise of almost a degree was observed at each of the stations. The curve of surface temperature followed that of air temperature in the main, as on the previous day. of Edinhurgh, Session 1883-84. 931 The improved thermometer having been constructed and tested in the interval, a set of hourly observations was made at the three stations during a period of twenty-five hours, from 9 a.m. on July 3rd to 10 A.M. on July 4th. The temperature was taken at the surface and the bottom as on previous occasions, and also at a point midway between the two. The third was a hat clear day, but the sky clouded in the evening, and rain fell very heavily during the entire night. A severe thunderstorm was experienced from 11 p.m. on the 3rd to 4.30 a.m. on the 4th. The continual dazzling produced by the lightning flashes made it difficult to read the thermometers with accuracy, but there is reason to believe that no serious error was made, and the observations were carried on regularly. On the third the surface temperature was high, and the interme- diate curve remained close to the bottom one, until 5 p.m,, when it rose rapidly. During the night and on the forenoon of the 4th, the temperature varied but little, and the curves for the surface, bottom, and half depth interlace each other curiously. A distinct rise of the bottom temperature, and fall of that at the surface, marks the inflow of the tide at 8 p.m. The means for this set are — Air, Surface Half-depth Bottom 19 Hours Daylight. 6 Hours Darkness. For 25 Hours. 57-6 55-2 57-0 Entrance, 57-95 57-36 57-78 Ark, 57-73 .57-35 57-65 N.W. corner. 58-10 57-41 57-90 Entrance, 57-59 57-48 57-56 Ark, 57-31 57-47 57-35 KW. corner, 57-23 57-43 57-29 Entrance, 57-19 57-49 57-27 Ark, . 57-20 57-30 57-22 N.W. corner. 56-93 56-83 56-92 In order to eliminate the tidal effect as much as possible, a mean was taken of the hourly results of the first and second series ; the tides, being at opposite phases at the same hour, annul each other to a certain extent. The surface temperature curve in the diagram, representing the result of tidal elimination, follows the air curve very closely; the bottom curve also does so, though to a much slighter extent, and the phase is clearly retarded. The accurate curves embodying all the results have been laid on the table. 932 Proceedings of the Royal Society It is obviously unsafe to generalise from such a small number of observations, but the results brought out by the discussion of the figures may be stated as at least probably true : — (1) During daylight the air was always at a higher temperature than the water, but after sunset the water was warmer than the air ; and taking an average for the whole period, the mean temperature of the air was the higher. (2) The surface temperature followed that of the air, and was little affected by tidal changes. (3) The bottom temperature followed that of the air, but the crest of the heat wave was retarded by several hours, and the curve was profoundly modified by the tides. (4) The temperature was .higher at the surface than at the bottom during the day ; but, as a rule, it was higher at the bottom than at the surface by night. (5) When the tide flowed in the early morning it exercised a cooling effect on the bottom thermometers, but when it flowed at other times it produced a warming effect. The variations of temperature when the tidal effect is eliminated may be accounted for by the direct action of sun heat and radia- tion, propagated by conduction and convection beneath the surface. It is possible that when the tide enters the quarry after the sand over which it must flow to reach the entrance has been exposed for several hours to strong sun-heat, the water may be warmed by contact with it, and so exert a heating effect. On the other hand, when the sand has been uncovered by night, chiUed by radiation, it may cool the water passing over it, or at least not raise its temperature. This hypothesis explains all the phenomena which we have observed as yet, and is supported by a considerable number of experiments; but Mr Peddie and I are about to commence a critical research to test its applicability, and also to investigate the varia- tions produced by the currents in the quarry, the direction of the wind, and other causes. I have to thank Mr Peddie, Mr H. ^N”. Dickson, and Mr Lindsay of the University Physical Laboratory, Mr T. Morton Eitchie, B.Sc., Mr H. J. Gifford, and Mr W. A. P. Tait, for their valuable and self-denying assistance in making the serial observations described in this paper. of Edinburgh, Session 1883-84. 933 8. On the Isothermals and Adiabatics of Water near the Maximum Density Point. By Mr W. Peddie. Com- municated by Professor Crum Brown. The state of water, as regards pressure, volume, temperature, entropy, and energy, may be represented by surfaces in 'a number of ways, depending upon which of the properties we choose to have their numerical values measured off along the*axes to which the surface is referred. The surface most suited for the consideration of the forms of the isothermals and adiabatics is that one the co-ordinates of each point of which represent pressure, volume, and temperature. The nature of this surface as constructed for water, and some of its peculiar features, were first studied by Professor James Thomson, and described by him in a communication made to this Society. Designating pressure, volume, and temperature by the letters p, v, t, the isothermals are the projections upon the plane {p, v) of the lines of intersection of planes of constant temperature with the surface. The adiabatics are the projections, upon the same plane of curves laid down upon the surface, such that, as the substance passes from one state to another as represented by points on the curve, it does so without absorption or emission of heat. The actual curve upon the surface may be termed the complete adia- batic. The chief features of the projection of the surface upon the plane (p, t) are three curves, which separate the regions representing the liquid, solid, and gaseous states. These three curves meet in a point, which Professor J. Thomson terms the triple point. If we measure pressure downwards and temperature to the right, the curve separating the liquid and gaseous regions slopes downwards from this point towards the right. The curve separating the solid and gaseous regions slopes upwards towards the left, making a greater angle with the t axis ; while the other curve slopes down- wards towards the left, and is very much steeper. The maximum- density curve slopes downwards to the left, but is not nearly so steep as the liquid solid curve which it meets at a point corresponding to a pressure of nearly three tons weight per square inch. It also meets the liquid-gaseous curve. Inside the triangular region so bounded the substance is liquid, and the quantity ^ has a negative value. ctz 934 Proceedings of the Royal Society For the liquid condition outside this region ^ is positive. Hence, from the third thermodynamical relation, we find that in this triangular region the adiabatics slope downwards towards the left for increased pressure ; while in the other region they slope downwards towards the right. So if we take a portion of the substance in a state corresponding to a point in the region where ^ is negative, and allow it to expand adiabatically, its temperature rises. From calculations based upon the first and third thermo- dynamical relations, it seems that the slope of the adiabatics in this region is not so steep as the slope of the maximum-density curve. Hence we * have adiabatics meeting this curve. But no such adiabatic can pass into the region where ^ has a positive value, since the maximum-density curve slopes upwards toward the right. It must be determined by experiment then, whether the adiabatic coincides with this curve after meeting it, or if it re-enters the original region, its slope having become steeper. In either case we can have two adiabatics intersecting ; that is, at a given tempera- ture, volume, and pressure, we may have water near the maximum- density point, in at least two states differing in the amount of intrinsic energy possessed. If the adiabatics coincide with the maximum-density curve, we may have an infinite number of such states. Flow consider a portion of the substance in a state represented by a point in the region when ^ is positive. On adiabatic ctz expansion the temperature falls until the maximum-density curve is reached. After this, the temperature rises. Hence there is a point of minimum temperature upon the adiabatic. This point must be looked upon as one in which two adiabatics meet. Probably the course of each adiabatic meeting in one point on the curve {i.e., the adiabatics whose previous courses have been in the region of negative and positive values for ^ respectively), is dv different on further expansion. The amount of intrinsic energy possessed, determines which region the course will pass into on adiabatic compression from such a point. This is equivalent to of Edinburgh, Session 1883-84. 935 saying that lines so meeting are different adiahatics, — not branches of the same one. As Mr Riicker (Proc. Roy. Soc., vol. xxii.) has pointed out, it is possible that there may be a point of maximum temperature on the adiabatics within the region where ^ is negative, for the sub- dt° stance is rising in temperature, while doing work by its expansion. This must be determined by experiment. In the surface referred to above, there are three cylindrical regions, the projections of which on the plane (p, t) give the three curves already mentioned as separating the regions which represent the three different states. The triple point line is the line of intersection of these surfaces, Mr Rucker shows that, along the triple point line, and along all other isothermals in these cylindrical regions, the adiabatics coincide for some distance with the isothermals. He gives formulae for determining the distances for which they coin- cide. Consider portions of the substance in the three different conditions, such that the state of the mixture is represented by a point on the triple-point line. If there is enough steam to just melt all the ice, the adiabatic and isothermal will coincide all along the triple-point line in the direction of lessening volume. If not, then the adiabatic will enter the liquid-solid surface. If more than enough, then it will enter the liquid-gaseous surface. On expan- sion, the lines will only coincide until all the water disappears, when the adiabatic will enter the solid-gaseous surface. If with Professor J. Thomson we consider that portion of an isothermal where change of state occurs to be curved in the plane {p, v), so as to have parts corresponding to unstable condi- tions, there must always be more unstable conditions along an isothermal in the region separating the liquid and gaseous states than in the other two similar regions ; or else there are more such unstable conditions in that region near the triple point line than at a distance from it. 3 R VOL. XII. PEOCEEDINGS OF THE KOYAL SOCIETY OF EDINBURGH, VOL. XII. 1883-84. No. 118. Monday, 21st July 1884 — continued. The President gave a short Eeview of the Session, and added some closing Eemarks as follows : — The President said — This session of the Eoyal Society, not the least interesting or remarkable of the series, is now about to close. I have been furnished with a statement; of the papers which have been read, which exhibits a creditable amount of industry as well as of ability among its members. It seems that of these 16 were in Natural Philosophy, 15 in Mathematics, 6 in Geology, 2 in Chemistry, 6 in Mineralogy, 6 on Meteorology, 2 in Spectroscopic Astronomy, 4 in Natural History, 5 on Botany, 5 in Physiology, 1 on Language, 2 on History and Antiquities, 2 on Anthropology, and 5 on Political Economy. We have sustained some severe losses by death in the course of the Session. Two very celebrated men, whom we had the honour to number among the Foreign Honorary Fellows of the Society, died within a few weeks of each other — M. Dumas, the Perpetual Secretary of the French Academy of Sciences, having died on the 4th of April 1884; and M. Adolphe Wurtz, his friend and fellow- labourer, who pronounced a funeral oration on his death, having himself died on the 12th of May. Both these distinguished men were renowned throughout Europe for the invaluable contributions they had made to Chemical Science, and specially to that branch of it known as Organic Chemistry, in regard to which M. Dumas may be said to have initiated a new departure. He was born in 1800 3 s VOL. XII. 938 Proceedings of the Royal Society in Genoa, and had therefore at his death reached the patriarchal age of 84. The value of his services during that long life to the cause to which it w^as devoted it is impossible to over-estimate. Similar honour is due to M. Wurtz, not only for his valuable labours in the same branch of Chemical Science, but from his numberless publica- tions and discoveries within the whole circle of chemical knowledgef “ It was his good fortune,” says M. Eriedel, in a funeral address, “ as rare as well-merited, that in the midst of such a multitude of different investigations, he never saw one of his results questioned. ’ He W’-as at the time of his death the designated successor of Dumas as Perpetual Secretary of the Academy of Sciences, which had long been an object of his ambition. Among ourselves, we have lost some very eminent and familiar names, to which, on the present occasion, I cannot do more than allude. They will he duly commemorated afterwards. At the head of the list stands that of the late Duke of Buccleuch. I have indi- vidually taken another opportunity of expressing my appreciation and respect for the memory of that distinguished man, to whom Scotland lies under a heavy debt of obligation, and who will long be remembered throughout its length and breadth as one of its most illustrious benefactors. Even had he not possessed these distin guished titles to our grateful remembrance, the fact that he was the lineal representative of the first President of the Society would have given him a claim on our interest. The three other names on the list furnished to me were personal friends of my own, two of them school-fellows whom I had known from boyhood. The first is that of Professor John Hutton Balfour, who was a Eellow of the Eoyal Society for fifty years, a Professor of Botany in the University of Edinburgh for thirty-four years, and Secretary of this Society for nineteen years. It is needless for me to speak to you, who knew him so well, of his kindly genial manner, his devotion to scientific pursuits, which began with his boyish days, and never quitted him during his long and useful life ; and the clear discern- ing capacity, which enabled him to attain and retain the confidence of all who came in contact with him. Nor need I attempt to recount the valuable services which he rendered to the progress of that branch of science to which his life was chiefly devoted. The second name is that of Allen Thomson. He too was a school- of Edinburgh, Session 1883-84, 939 fellow, and a man of very varied accomplishment, and of rare mental quality. Perhaps with a harder grain of fibre he might have attained more general fame, for he was singularly unassuming and gentle, not from want of intellectual force, hut from the balance of a refined nature. But he was especially adapted for the prosecution of exact science by the clear lucidity of his thoughts, and the quiet impartiality of his judgment. As a companion, he was charming, as he had rich resources on which to draw, and a delightful vein of cheerful humour in which all who knew him rejoiced. The last name furnished to me is that of one who well deserves to he commemorated here. It is that of the well-known Provost of Leith, Mr Lindsay. I am glad of this opportunity of expressing not only my sense of the benefits which his labours have conferred on the public, hut my own individual feeling of obligation for friendly co-operation in important public affairs. The Police Act which bears his name, and his exertions in which have earned the gratitude of the public, was not indeed the last word on the sanitary legislation for our crowded towns. But it was the most important contribution towards it of our day, and I doubt, but for Mr Lindsay’s help, it might never have been obtained. I had found on previous attempts that the opinions of the different burghs were so little in unison, that it was almost impossible to hope to adjust them within the compass of a Session of Parliament. But in reply to an applica- tion by Mr Lindsay made to myself as Lord Advocate at the time, to attempt to legislate in this important matter, I said that if he could obtain a reasonable acquiescence from the burghs in a general measure, I should be glad to aid in having it passed into law, Mr Lindsay accepted the proposal, and fulfilled his task with an amount of ability, tact, and patience which did him infinite credit, and deservedly earned for him the distinction which they yielded him. The year has been otherwise memorable in more than one respect. We entered our second century; but on that subject I sufficiently enlarged on a recent occasion. It was also distinguished by the brilliant and most successful celebration of the Tercentenary of the University of Edinburgh. We had, during the celebration week, the great and rare satisfaction of having papers read to us by two of the Honorary Fellows of the Society — one by Dr Helmholtz of Berlin, who has gained a European reputation by his discoveries in 940 Proceedings of the Royal Soeiety physics ; and Professor Cremona of Rome, whose work on the Theory of Projection has met with great celebrity, and has been translated into many European languages. The Society had also the pleasure of hearing an address on Cosmic Dust from the Ahhe Renard, who is not a Eellow of the Royal Society, hut is known to ns by his contributions to the records of the “ Challenger ” Expedition. I have now only to express the hope that the Eellows may meet at the commencement of next Session, recruited for fresh exertions. In connection with the Tercentenary celebration, I ought to mention that the Council did me the honour to appoint me as their delegate to represent the Society on that occasion. To my great regret, I was unable from the state of my health to attend the celebration, and our Secretary, Professor Tait, was appointed in my place. In the course of the discharge of the duty thus devolved on him, he presented a Latin Address from the Royal Society to the University, the terms of which were furnished by our Librarian Mr Gordon, and are as follows: — Amplissimo Cancellario, Rectori magnifico, doctissimoque Senatui Universitatis Edinensis. ViRi iLLusTRissiMi — Societas Regia Edinensis commemorationem tercentenariam Universitatis Jacobi Sexti, Scotorum Regis, con- celebrare et ornare vult. Etenim Societas Regia est filia Universitatis vestrse, cui suavissimo commercio et sanctissima necessitudine devincta est. Quam multi philosophi, Universitatis S^natores, pars magna sunt et fuerunt rerum a Societate gestarum. Hoc die solemni memoriam magnorum virorum Academicorum renovare juvat, et tanquam Jacobi Sexti antecessor, Macbethus, obstupuit proleptica visione seriei regum Scotiae futurorum, sic sed retrospectu contemplamur hodie illos sceptriferos scientise principes, Senatores Universitatis, qui ah urnis suis adhuc intellect turn humanum regunt. En Gregorius, inventor telescopii reflexione agentis; — Maclaurtnus qui sublimiores res cosmicas illustravit, tiuxum refluxumque maris, solis vias, lunseque labores ; — Robisonus et Eorbesius, ambo Secretarii Societatis Regiae, alter expositor encyclopsedicus totius corporis philosophiae naturalis, alter nova theoria de molibus conglaciatis clarissimus ; — Monroi, anatomic! celeherrimi, quorum Primus conditor Infirmarii, Secundus Anatomici 941 of Eclinhiirgh, Session 1883-84. Musei vestri conditor ; — Blackius, fundcator diemiae hodiernae ; — CuLLENUs originator pathologise philosophicae, qui rationales methodos inanibus placitis scholasticis snbstituens, omnes medicos sui sseculi longe exsuperavit ; — Jacobus Gregorius qui de arte medic^ scripsit latinitate elegantiori quam qua utebaiitur Eomani medici; — Carolus Bbllius in seternum memorabilis, qui primus loca modosque functionum nervorum demonstravit ; — Goodsirus, anatoniicus nulli sui sseculi secundus, qui existentiam et structuram novorum animalium marinorum et parasiticorum indicavit, auctor et creator cellularis theorise, et ejus applicationis ad pathologiam et morphologiam transcendentalem ; — Christisonus qui primus vim certorum toxicorum et medicamentorum suo periculo expertus est ; quo nec ulla aetas nec civitas nostra unquam peritiorem aut feliciorem in tuenda et restituenda sanitate vidit ; — Listerus conditor antisepticae chirurgise, novae et efficacioris method i medendi; — Brewsterus et Lesla:us, alter patefaciendo leges lucis, alter leges caloris celeberrimus ; — Eobertsonus, illustris fundator et pater Eegiae nostrae Societatis, qui in immortalibus historiis magnas revolutiones sociales et religiosas gentium facundis- sime enarravit et elucidavit; — Stewartus qui eloquentia antiqua philosophiam Scoticam exposuit, et juvenibus nobilibus, postea imperio Britannico pra3futuris, inculcavit principia renuntiationis et virtutis, atque responsibilitates libertati conjunctas ; — Hamiltonius qui logicam Aristoteliam magnis augmentis ditavit, et novum splendorem philosophise Scoticse addidit ; — Chalmersius, orator, qui perfervida et excelsa eloquentia atque administrativa sapienti^ patriam suam ad altiorem statum religiosum, moralem et politicum sublevare enitebatur, semper urgens et incendens sublimem devo- tionem humanamm energiarum ad assequendas meliores et matu- riores formas cujusdam perfectionis in longinquitate splendentis et evanescentis ; philosophus etiam, qui prsesentiam Dei in rerum natura, majestatem conscientise in homine demonstravit; — Wilsonus, vicisaim grandis et solemnis, l^tus et facetus, nunc miserationem sen pathos movens, nunc salibus Horatii vitia et stultitias insectans, nunc tener^ sensibilitate Virgilii magnificentiani naturae depingens, qui veluti prisci philosophi prsecepta sua perpetuo carmine tradere gaudentes, poetico afflatu incensus tanto splendore imaginationis disseruit de affectionibus, voluntate, et conscientia, ut videretur niti> 942 Proceedings of the Royal Society analysi recondita rejecta, aiiditores ad nobiles actiones et excelsas ideas summopere incitare; Aytounus, quo nullus magis Musis patriae suae dilectus, — nihil quod ille cecinit de heroibus Scotise delebit ^tas. Satis habeatur dicere vos, viri illustrissimi, ab antecessoribus vestris minime abesse, optime de litteris, scientia et artibus meritos. Conjungentes itaque gloriam praeteritorum saeculorum ad splendidum progressum praesentis temporis, ampliore scientiarum curriculo, amplioribus aedificiis fruentis, pergatis rerum patefacere causas, ordinem et connexionem, resolventes problemata, et communicantes inventa quae attinent ad hominem, regnaque naturae varia, Terrasque, tractusque maris, coelumque profundum. Verum enimvero nunquam et nusquam gloria medicinse magis floruit quam apud vestram Universitatem. Quot viri a vobis arte medendi instructi mortalibus segris ministrant intra et extra Garamantas et Indos, ubi flumina !N’ovi Mundi per cataractas stupendiores cataractis Nili ad Oceanum Atlanticum properant, et ubi insulae terris continentibus sequales surgunt e Mari Australi. Quae regio vestri non plena laboris ? Denique vestra Universitate semper strenue statuente eradicare et delere idola tribds, speeds, fori et theatri, olim a Cancellario philosophico Jacobi Sexti reprobata, atque semper in magnis artibus et disciplinis colendis to OZlov Kal to aet assequi enitente, fundamenta vestrse philosophiae posita sunt non solum in cognitionibus a priori sed etiam in experientia ; et fundamenta vestrae ethicse doctrinae non solum in utilitate, vel consuetudine, vel hominum pactis et conventionibus, sed magis in quodam sensu sen facultate regali, ut Platonice loquamur, nobis divinitus insita. Comprecamur ut omnia vobis fausta et felicia eveniant, utque ita de scientiis, de litteris, de patria et de genere humane, ut meriti estis, in posterum magis atque magis mereamini. !N^omine et Auctoritate Societatis Eegise Edinensis, XV Cal. Maias, a.d. mdccclxxxiv. MOKCEEIFF, Praeses. P. G. TAIT, a Secretis. of Edinhurgh, Session 1883-84, 943 An Analysis of the Principles of Economics. By Patrick Geddes. Head 17th March, 7th April, 16th June, 7th July 1884). Introduction. § 1. In a paper * read nearly three years ago to this Society, I have attempted (1) To review the existing state of statistics ; (2) To define the nature of the subject, and its relation to history and the sciences ; (3) Broadly to group and co-ordinate the whole body of existing and possible statistics, in relation to the respective statistical sciences ; and (4) In accordance with the preliminary sciences to frame a classification embracing all existing and possible socio- logical statistics. Moreover, (5) This was shown to involve, or rather actually to constitute, an aspect of the pressing problem of the systematisation of the literature of economics, of which (6) The existing schools were briefly criticised ; (7) The relation of the conceptions of scientific economics to practical economics was outlined ; (8) As also their relation to ethics. The present paper proposes to deal with more attractive aspects of economic science, and although inevitably to some extent also critical, is primarily of systematic and constructive aim. § 2. In the domain of all the studies which directly concern man — in biology and psychology, in ethics, politics, and economics alike — it has often been pointed out how theoretic conceptions are subtly, instinctively, almost inextricably interwoven with practical considerations. Economic literature is especially unfortunate in this respect ; in many authors hardly a sentence is without this double effect. To eliminate then, and reserve for separate subse- * “On the Classification of Statistics and its Results,” Proc. Roy. Soc. Edin., 1881 ; also published separately by A. & C. Black, Edinburgh. 944 Proceedings of the Bayed Society qiient criticism, all practical considerations — to distinguish doctrine from practice, to separate principle from precept, and construct science apart from art — is the first aim of the present inquiry. Precisely as biology underlies medicine, and astronomy navigation, so sound practical economics can only be profitably attempted after sound scientific conceptions have been attained. § 3. The attainment of scientific princi]3les being aimed at, the scientific method, and the scientific method alone, must be used. This involves a further, a sterner, and a far more difficult assay of economic literature than the preceding, which aimed exclusively at the removal of irrelevant practical matter. The influence of other extra-scientific conceptions, theological or metaphysical,' optimistic or pessimistic, has also to be guarded against. § 4. Having then successively eliminated as irrelevant to our present purpose the disturbing elements above referred to, what strictly scientific matter remains 1 Much ; yet this is in such a form as to demand a new analysis. For this, as in the preceding paper on statistics, two postulates are required — (1) the classification of tlie sciences, and (2) the main conceptions of each — the comparatively simple conceptions of physics preceding those of biology ; those of biology being followed by those of psychology, and these again by sociology. The elimination of practical and of philosophical considera- tions does not then suffice. Hew difficulties were in the first place shown * to depend not only upon the profound disagreement as to scope and method of the subject, but as to its very nature, some claiming it “ to be a logical science, others a mathematical, others a physical, others a biological, others a psychological, others a social, and others an ethical science ; while some hold it to belong partly to one of these sciences and partly to another.” Yet others, as if the wealth they are concerned with were not material, and the population of which they discuss the laws did not consist of living organisms, practically isolate it altogether from the sciences, even those of matter and life. The economist of literary or legal training assumes that subtle verbal definition expanded under the rules of formal logic will create a rigid, universal system. The mathematician up- holds the “ statistical method,” or the expression of economic laws by algebra and the calculus. But the economist of more practical * Classification of Statistics, p. 26. of Edinhurgli, Session 1883-84. 945 and concrete tendencies interests himself as exclusively in “ material wealth — its production, distribution, and consumj)tion giving hut scanty consideration to the nature and wants of the community for, and by which, this wealth is produced, distributed, and consumed. Most economists, however, are so far biologists as to recognise the physiological laws made prominent by Malthus. Psychologists and moralists, in insisting upon the estimation of pleasures and pains, or the analysis of mind and motive, have had no small influence upon economic theory ; the historian has now entered the fray, and urges weighty claims to predominance ; so too does the anthropologist ; in short, it has been attempted to constitute the economic science by the aid of almost every possible mode and department of scientific inquiry, and no better evidence of failure can be imagined than is afforded by the claims of each of these inco-ordinated systems to exclusive success. § 5. Yet we are bound to assume the applicability of the sciences, and seeing that all have been by turns applied, how is the “ notorious discord and sterility of modern economics ” * to be explained? There are two main reasons for it — first, that the application of the sciences has not been systematic or in any way co-ordinated; secondly, that although applied, their application has been in almost all cases imperfect or faulty. The “ statistical method ” has been already criticised, and the few applications of higher mathematics yet made will not at present be discussed; but passing to physics, it will at once be evident to any reader, however little versed in science, that the discussions or definitions of the nature of material wealth,” of “ intrinsic value,” and the like, which are to be found at the outset of almost every economic treatise, remain at best in precisely the state in which Smith found them, and are wholly uninfluenced by modern physics. In biology too, — while the law of reproduction discussed by Malthus has become in the hands of Darwin the foundation-stone of that theory of evolution by natural selection, which has not only revolutionised modern biology, and with it our views of the origin, nature, and destiny of man, but has shed new and brilliant light upon the special sciences which concern him, anthropology, philology, * Ingram “On the Present Position, &c., of Pol. Econ.,” Brit. Ass. Beport, 1878. 946 Proceedings of the Royal Society psycliology, and ethics, — the economist alone remains behind, and although long ago armed with the purely biological ideas of com- petition and co-operation, delays to modernise his theories by the aid of the new learning, and treats them as if they were inde- pendent of such general conceptions of struggle for existence, of functional differentiation and change, of polymorphism, and the like, of which they are really special cases. § 6. We see, too, that theories of the mental and moral nature of man hold a large place in the constructive attempts of many econo- mists, yet probably no one will -seriously maintain that these exten- sive psychological postulates have much in common with any school of psychology now extant. Nor do the ordinary economic postulates as to the structure of society and the origin of its insti- tutions contain much which Mr Spencer, Mr Tylor, or Sir Henry Maine would recognise as pertaining to modern sociology, but rather exhibit a closer affinity (suggestive of direct descent) with the “ Contrat Social.” § 7. Enough, then, has probably been said to show that even the economic systematists who seek to apply scientific conceptions at all are unfortunately provided for the most part with archaic or incomplete ones, when indeed they are hot wholly erroneous ; and political economy is thus seen to present in a marked degree that lagging behind the general advance of knowledge which not unfre- quently occurs even in the ranks of the preliminary sciences — witness the obsolete chemical notation conserved by mineralogists. § 8. Political economy must therefore be treated as a crude science, standing to sociology much as the psychology of the last century to that now in process of evolution. Criticism of such provisional syntheses must be (1) appreciative of them as embryonic stages of true science, and for their historical services ; but (2) destructive where they claim vitality and impede progress. The former is a branch of history proper, the latter of what we may call intellectual palaeontology. This criticism by means of the pre- liminary sciences is therefore really conservative, since it affords a touchstone for assaying the whole literature of the subject, sentence by sentence, if need be. Even though the reader may feel contented that the particular system to which he happens to have been trained or attached is of Edinhurgh, Session 1883-84. 947 exhaustive and satisfactory, its usefulness will really be to him none the less, since the synthesis which, through this analysis, we shall ultimately reach must coincide with his own, — thus constituting a brilliant independent verification such as is eagerly sought for in science, — and so establishing his position to the exclusion of all others. § 9. At whatever labour, then, the economist must no longer shrink from acquainting himself with the preliminary sciences ; the common objection that he “ finds it laborious,” or that he “ cannot hope to become a specialist,” and the like, notwithstanding. But fortu- nately such alarm is groundless, for no specialist’s knowledge is required. It will be found in the sequel, that just as the most elementary, if clear, knowledge of mathematics, scarcely extending in algebra beyond simple equations, nor in geometry beyond the construction of rectangles and curves, is shown in statistical treatises to give a new precision and clearness to conceptions of economic quantity ; so a similarly rudimentary, if real, knowledge of physics and physiology — of the doctrines of the permanence of matter through transformation, of conservation and dissipation of energy, and of the functions of living organisms — will here serve for a commence- ment. Nor will more be postulated in the present work. The plan of the undertaking will now be readily understood; it is, in short, once more to prepare for the construction of a “ system of economics ” — not, however, by means of new definitions and old dialectic, nor by the deductive application of a few principles taken at random from an early state of some single science — but in harmony with the organic whole of the preliminary sciences ; using, as far as may be, such materials as after due refining economic literature may afford ; thereafter proceeding as far as possible by investiga- tion. It is necessary then, in the first place, to collect and arrange the materials for such a system by successively extricating from the vast mass of too discordant economic literature, and by observing as far as possible in actual society — first, the most important facts and generalisations of physical and chemical nature ; next, those essentially biological and psychological ; finally, those distinctively sociological — uniting this task of constructive criticism and new observation with such application of those respective sciences as may be possible. Thus principles of economics serviceable for the 948 Froceeclings of the Royal Society subsequent construction of systematic economics can be obtained and tested; and to point out the road which may lead to the elucidation of such principles — without any pretence at exhaustive treatment of detail — is the aim of this paper. The existing economic literature, then, will henceforth be regarded as a storehouse of ideas of all kinds and ages, which, in so far as scientific, we have to disentangle and arrange on the plan above outlined into bodies of principles, dealing with each successive aspect of the subject, physical, biolo- gical, psychological, and social, these forming separate chapters, each accompanied by a summary, while the appreciation of the history of economics will be postponed. The inquiry as to the logical method or grammar of economics, and the mathematical principles involved in its treatment, instead of forming the subject of an initial dissertation, will be relegated to a final appendix also of partially historical character. § 10. But the economist, even if not refusing the systematic application of science above proposed, will urge that economics must not only be pure but applied, not only scientific but practical. Assuredly so ; for while eliminating as irrelevant any admixture of practical considerations with the purely scientific portion of the subject, it will yet be attempted, in an appendix to each chapter, though of course only in the most brief and general way, to indicate the possible lines of modification of each set of factors, whether such modification has been effected or attempted in past or present time, proposed by any of the various schools of practical economists, or suggested by scientific knowledge. § 11. The plan proposed is thus easily applicable to the wants of either specialist or generaliser, whether of scientific or practical bias ; for the chapters may thus be successively read for the doc- trine, and their respective appendices thereafter for the derived practice. And when the work is completed, while those especially familiar with the preliminary sciences will doubtless prefer the ascending order from physics onwards, the student whose interests lie rather in the supreme social and practical aspects of the subject, will without much inconvenience take the chapters and appendices in the reverse or descending order. § 12. But even then we have no system of economics. True, nor has any system yet existed, the innumerable so-called systems 949 of Edinburgh, Session 1883-84. being, as we have seen, complex mixtures of ideas of every possible order, which, from the present point of view, are to be regarded as material to be disentangled and rearranged on the plan above out- lined into bodies of principles dealing with each successive aspect of the subject. Those principles once extricated, however, we obtain a key to the mode of construction of these systems, and an explanation of their incompleteness — each school, as was already pointed out, 'having grasped principles chiefly referable to one order only, and having used these to the practical exclusion of principles belonging to other orders. Hence such efforts as to restrict the domain of economics to questions of statistics, value, or exchange ; and the attempt thus to solve all problems is obviously incomplete. Similarly, the restriction of the subject to material wealth, Avithout consideration of the organisms of which the occupations, rate of repro- duction, mode of competition, &c., furnish biologico-economic prin- ciples. So with the investigation of biological principles without heed of the next order of factors — the psychological principles — or the very frequent attempts at completing a system, by the aid indeed of biolo- gical and psychological considerations, but without passing from the study of the individual to that of the higher unit — the society — with which the sociological principles are alone concerned. These are all examples of an attempt on the part of each preliminary science to annex the province of the succeeding one, an error which of necessity vitiates the system thus obtained. To this intrusion of each preliminary science upon the domain of its ascending successor, the term “ materialism^ though generally restricted to the attempt to reduce all sociology and morals to biology and physics, has with great advantage been sometimes extended. § 13. The existing systems of economics are not only vitiated by this error of some form of “ materialism,” but also largely by the converse and if possible more serious error, that of attempting to make any one science do duty for those which underlie it, — which may conveniently be termed ‘‘ transcendentalism^ The attempts at system vitiated through the error of “ materialism,” which we have just been criticising, have largely indeed been due to an even earlier prevalence of “transcendentalism.” The man of moral bias, in at- tempting to construct a perfectly moral theory of economics without full and constant reference to the facts of exchange, of production, 950 Proceedings of the Boyal Society of population, of their wants, and of the existing society, — which furnish the principles underlying any moral theory, — has long since brought the whole subject of morals into disgrace among econo- mists, with the lamentable yet not unnatural result that any one attempting to introduce ethical considerations, even in their proper place, is apt to he scouted as a ‘‘ sentimentalist.” Again, the econo- mist to whom the society is of paramount interest, frequently ignores its individual components, and so on. So strong, indeed, is this tendency to transcendentalism, that the class of principles with which we shall commence our ascending survey — the physical — has been the very last to secure a hearing. In short, each of the succeeding chapters, physical, biological, &c., looked at alone, is a systematised materialism to its successors, and a transcendentalism to those which precede it. Hence the need for an ultimate synthesis, which must aim at reconciling all these different points of view. § 1 4. The synthesis to be attempted, then, must aim not only at balancing the claims of all these principles without that excessive or defective insistance upon one order of them which constitutes materialism or transcendentalism, but at interw^eaving them into a lasting whole. The postponement of the construction of a system (imperfectly foreshadowed, however, in the Classification of Statistics) to the present task — the discussion of principle — is thus necessitated ; hence the plan of the present work. Chaptek I. — Physical Principles. § 15. General Enunciation of the Problem. — Passing over the dis- cussion of the mathematical aspects of economic phenomena to the consideration of their concrete physical aspect, we are not simply concerned with the abstract theory of statistics or of exchange, but have to investigate the concrete economic facts ; and these not only in their quantitative, but also in their qualitative relations. The apparatus and the processes of social activity have to be observed and classified with an equal eye towards minuteness of detail and extent of generalisation; they must, moreover, be expressed in terms of physical science. Por as the physical physiologist has long since definitely undertaken the task of explaining the mechanism of the individual organism in terms of chemistry and physics ; or as the of Edinburgh, Session 1883-84. 951 physical geologist not only observes the form and changes of the earth’s crust, hut explains them by the aid of the same sciences; so precisely must the physical economist deal with those phenomena of the visible universe Avhich are specially allotted to him. From the present point of view we must constantly bear in mind that all these phenomena are alike material — that all the changes which wm observe, whether in the earth’s crust, in organisms, or in the inter- action of organisms with their environment (an inquiry within which indeed the economic operations of mankind are not only recent but comparatively small), are alike expressible in terms of chemistry and mechanics. Social phenomena are to be viewed simply with regard to the matter and energy consumed or liberated, and physical economics is thus the study of certain forms of matter in motion. § 16. Particular Enunciation of the Problem — Leaving to later chapters those considerations of biological, psychological, sociological, and ethical scope, which are present or latent in almost every extant discussion of “material w^ealth,” and endeavouring to dispense alto- gether with metaphysical thought and metaphorical expression, and postulating simply the elementary facts of physical science, and more especially those of the doctrine of energy, we may enter upon our inquiry. What is this “wealth,” what is meant by its “pro- duction,” its “distribution,” its “consumption?” What are “land, labour, and capital ? ” What is this process of “ exchange,” and what is the meaning of “value? ” What are “ producers and con- sumers,” and so on ? § 17. Qualitative Analysis. — It is convenient to begin with the “producers and consumers.” These indeed as organisms might at first sight seem only admissible when biological aspects of the subject are being discussed, but it has just been pointed out that the physiolo- gist has already in great part interpreted their functions in terms of pure physics, and we are thus not merely entitled, but bound to include them in our present survey. They come before us, how- ever, not in all their complex relations, afterwards to be discussed in the biological chapter, but simply as so many forms of mechanisms constructed from the matter of the earth’s crust and worked by the energy of the sun — as so many species of automata called Homo, Formica, &c. Every such automaton is of course constantly wear- 952 Proceedings of the Royal Society ing out, and its energy running down — and this waste which its functions involve must he repaired by obtaining from the environ- ment periodic supplies of new matter and energy. From the destructive forces of the environment it must similarly be pro- tected ; and so on. From the present standpoint then it is not merely analogous to, but identical with a mechanism ; “ producers ” are those automata devoted to the acquisition of matter and energy from the environment; while all are ‘‘consumers,” and in this aspect in wonderfully similar degree. Without ignoring the historic services of the physiocratic school, the application of the conceptions of modern physics to economics may be fairly said to date from Professor Tait’s discussion of the Sources of Energy in Nature, published about twenty years ago (see N07dh British Revieiv^ vol. xl., also Balfour Stewart on Heat, &c.). The subject has been developed to some extent by other physicists, as Siemens, Thomson, &c., but seldom by economists, with the dis- tinguished exception of Professor Stanley Jevons, whose investi- gations on the coal supply, and whose hypothesis of the correlation of sun spots and commercial crises, are both essentially from the present point of view. Starting then from a given territory at given time, and enumerat- ing the utilisable sources of matter and energy in the form given by Tait, and adopted in the Glassification of Statistics (p. 13, table B), we may proceed to systematise the phenomena of production and consumption, and this is most conveniently done in diagrammatic form. Let us arrange these facts — which should of course aim at statistical precision- — in a first column. (Op. cit. and fig. 3.) After these we may further enumerate the sources of matter not used for the sake of its potential energy, but on account of its other properties (physical, chemical, &c.). This matter and energy are as yet mere raw material or potential products, and require develop- ment into ultimate products ; the requisite processes of production having generally three stages — exploitation, manufacture, and move- ment, the last including transport and exchange ; for exchange from our present point of view is simply part of the process of movement of the product from the place of production to that oi consumption. That proportion of potential products (large in com- plex societies) which has to be converted into apparatus used in of Edinburgh, Session 1883-84. 953 the stages of development is conveniently termed mediate products ; and thus we have an exhaustive classification of all products what- ever in its most generalised form. Finally, much premature dissi- pation and disintegration, termed loss, may occur at all stages of development and must he estimated for."^ {Op. cit., pp. 13 and 14.) As has been already shown, such a table includes not only an account of the processes of transport and exchange, but of the facts of the equally relevant though less investigated subjects of exploitation and manufacture, commonly grouped under technology. The standpoint being thus sufficiently explained, and the stages of production defined, it is obvious that our physical standpoint enables and compels us to inquire into their details. Were this an exhaustive treatise on physical economics, it should commence with a minute statistical survey of the sources of energy and of the pro- cesses of exploitation — agriculture, fisheries, mines, &c. It should include not only the classical quotations from Smith on pin-making and Babbage on the economy of manufactures, but a thorough survey of manufactures and of the vast ap- pliances of modern transport by land and sea; it should summarise those investiga- tions upon the phenomena of exchange, upon which so many economists entirely specialise themselves ; it should also esti- mate the loss at all stages preceding con- sumption ; at every stage, too, it should consider the mediate products and the pro- ducer-automata employed; and, finally, it should classify and estimate the ultimate products. So far, our knowledge would be confined to a given place and time; but such statistics should be sought for all other places and times, these statistics piled up into history, and this history genera- lised and compared. Thus, we should investigate such a hypo- thetical graphic statistic as the accompanying ; aim at approximately comparing, that is to say, the relative income of matter and energy * These considerations are more fully developed in the Classification of Statistics, pp. 13, 14. 3 T PRODUCTION DURING AGE OF ENERGY. - OF IRON. — OF BRONZE. — OF STONE. Fig. 1. VOL. XII. 954 Proceedings of the Royal Soeiety from Nature in tlie various ages of production — stone, bronze, iron — with which the archaeologist (who is indeed essentially an historical economist) has done so much to acquaint us, and compare these with the result in our modern age of energy. The historic evolution of processes and products, both in their varying rates and details, and in aggregate, should further be discussed ; for of the (derived) hypothetical historical curve (fig. 2) our fragmentary historical knowledge would enable us to approximately fix a few points. Such a curve could, of course, be precisely ascertained for some elements of recent production; and valuable conceptions, as, for instance, the “ law of diminishing return,” derived from it by mere inspection. Similarly the specialisation of processes known as “ division of labour,” and the converse process of generalisation, or concentration of labour,” are more clearly intelligible. “ Capital ” is decomposed into the apparatus (mediate products), and energy employed in pro- duction. No elaborate discussion is needed to refer “ money” to its place amidst the apparatus of movement, and so on. But where is the novelty and what the utility of such an analysis, the economist may by this time naturally ask. of Edinburgh, Session 1883-84. 955 Such detailed studies are, of course, largely scattered through economic literature, nor does any one dispute their relevance. Such abundant extant investigations as those upon the phenomena of trade and money, or the vast historical labours which are specially due to the German school, furnish abundant partly co-ordinated material. The present aim is, however, to suggest how such positive results must be systematised and interpreted in terms of physics. And it must now be further shown that not only are our studies of economic processes, so far as consistent with fact, capable of physical expression, and (1) that this leads to greater systematisation — to greater precision of treatment in detail j but also (2) that this mode of treatment involves a considerable change in the conventional theoretic point of view; and (3) that it furnishes grounds for a systematisation of practical action. § 18. Quantitative Analysis. — The conception of the processes of production and consumption as one vast mechanical process ; the view of society as a machine, in which all phenomena are interpreted as integration or disintegration of matter, with transformation or dissipation of energy, affords not only a generalisation of the widest, but a systematisation of the most thorough kind ; nor is its applica- bility qualitative only. It is legitimate, nay inevitable, to apply the quantitative conceptions of physics — the modern measurements of matter and energy. Such and such quantity of matter is exploited, say a units ; so much is lost in each process of production (6 -t- c -f ff) ; so much remains as ultimate product (a- (6 + c -F cf)) ; after con- sumption so much of this becomes available for new exploitation as a waste product. Again, so many units of energy a are exploited ; the processes of exploitation, transport, &c., cost so many units, say h ; the remainder {a - h) is the energy available. This idea is ex pressed by the upper portion of the diagram, fig. 3 {q.v.). The amount of energy and matter exploited during unit time is denoted by the first rectangle, and the quantity disintegrated and dissipated in the process by its upper dotted portion; the difference passes to the manufacturer, whose waste and expenditure of matter and energy are similarly denoted ; the remainder, after again suffering deduction for the processes of movement, and the accompanying losses, repre- sents the amount of ultimate product, of which the transitory and permanent portions are similarly estimable. Taking, for example. 956 Proceedings of the Pioyal Society our most important source of energy — coal ; the complex problems of its ratio of exchange, and the causes of its fluctuation, of the >- cc CD i-u CO I— 1— er unit time. — The quantity of ultimate products obtained per unit time being known, the average store of wealth of the community, and even the details of partition are readily observed and denoted. Thus (fig. 4) the rectangle ABCD may denote the average wealth of a community at one time, pretation. And if space Fig. 4. of Edinburgh, Session 1883-84. 959 and ABEF at another, while the wave lines joining CD and EF respectively denote those deviations from the average partition, termed riches and poverty. But, as was pointed out in the pre- ceding paragraph, tliough these phenomena can he observed, their explanation does not come within our present province. § 20. Quantity of Ultimate Products per aggregate time. Synergy. — The summation of the quantities of product in successive times, though seldom considered, must, notwithstanding, be attempted. Taking the year as our unit time, the quantity of production per lustrum, decade, generation, century, even per economic age, must all be inquired into, and the ultimate aspect, the highest generalisation of production, is that of the collective production of mankind — of the Synergy of the Race, with its material products, transitory and permanent. ^21. Quality of Ultimate Products.- — The problem of classifying the ultimate products now arises. These are frequently arranged (1) according to their sources, or (2) according to the processes by which they are obtained, while (3) the only plan which really treats them as ultimate products at all, arranges them according to their relation to the consumers (these being, as already explained, from the present point of view mere automata needing fuel, shelter, covering, &c.). Ultimate products are thus commonly classified by economists, yet an important rectification is necessary. The number of consumer-automata being definite per unit time, the quantity of ultimate products required per unit time f necessOoriet of life ”), fuel, shelter, &c., for their structural and functional main- tenance is also perfectly definite and ascertainable. Without enter- ing upon an elaborate yet practicable investigation of the details of this, it is evident that a criterion is furnished us by the durability of the automata in question. For, if these last the normal time, it is evident that the necessaries for normal maintenance cannot to any serious extent have been deficient. Thus we should expect a priori considerable definiteness of quality and quantity of ultimate products through all variations of space and time ; yet rather the reverse seems observable. For a Eussian, Norseman, and Scot, living in much the same geographical conditions and for much the same time, the quantity of ultimate products consumed per annum is enormously 960 Proceedings of the Royal Society different, being expressed in money values by a recent authority * as what we may take in round numbers as <£7, £14, and £30 respec- tively. How is this to be accounted for ? The ordinary method of meeting the difficulty is to distinguish ultimate products into necessaries, comforts, and luxuries, and to account for differences in consumption, by assuming a greater amount of the latter. To give this scientific precision, we may first distinguish the ultimate products into a definite quantity of necessaries, plus a variable amount of suyer -necessaries ^ and then inquire what is the quantity and what the quality of the latter. The food consumed in these two places cannot vary much in quantity, the necessary fuel (proteids, fats, amyloids, water) must like be present in each case ; how is the enormous difference in quality to be explained ? If one represents necessary alone, the other represents necessary -i- super-necessary : the former replaces structure and maintains the energies ; but the latter is only intel- igible when we anticipate and borrow a conception from physical physiology : it is addressed to the stimulation of the sense organs, gustatory, visual, and tactile, of the consumer — represents so much cesthesis. The variable super-necessary must henceforth therefore be termed the aesthetic element, and ultimate products are accord- ingly analysed into their necessary and their aesthetic elements. Trom the preceding discussion it is obvious that if population and duration of life be constant, all increase in ultimate products per unit time is expressible in terms of aesthesis, and it remains to investigate the relative amount of this. It is commonly assumed by economists of all schools, that in pro- duction the necessary element enormously predominates — in any but the very poorest communities, however, this conclusion has no justi- fication in observed fact. In the above case of Russian, Horseman, and Scot, even if we assume the consumption of the first as purely of necessaries, the element of aesthesis in the consumption of the last must be approximately (local differences in purchasing power being disregarded, especially as smallest for necessaries) measured by the difference in expenditure above mentioned, and must stand to the necessary element as say 3 to 1. So far, therefore, from calmly ignoring aesthetic considerations, a nearer approximation to * Mulhall, Balance Sheet of the World. of Edinhurgh, Session 1883-84. 9G1 the facts of production and consumption might actually have been reached by economic writers had they restricted themselves to these. Thus, even for the physical study of production while the import- ance of the necessary element is fundamental, that of the aesthetic is superior. In any at all civilised community, in short, every ultimate product has visibly superadded its cesthetic subfunction of visual stimulus, and (without trespassing in any way upon the province of aesthetic criticism by considering its quality) the physical economist must estimate the details and cost of production of each of these two elements respectively. And when we add up the aesthetic subfunctions of all “ necessary ” ultimate products, and add to this the vast quantity of purely aesthetic produets, we see how small the fundamental element of production has become in relation to the superior, and reach the paradoxical generalisation that production, though fundamentally for maintenance, is mainly for art. § 22. Consumption. — Passing to the study of the disintegration and dissipation of energy which we term consumption, we find that this takes place at variable rates. What disappears per unit time as food, clothing, &c., is termed transitory, what remains is relatively permanent. As the unit time is extended from, day to year, and from year to generation and century, the transitory element of course increases at the expense of the permanent. And since the ultimate product newly produced -1- the store of permanent products consti- tute the quantity of wealth per given time, this is seen to be equally modifiable by the two independent variables of production and conservation. The old conceptions of domestic economy find here their place and use, and only require generalisation to be exhaustive. The term consumption is only fairly applicable to its transitory element, and should be superseded in its generalised sense by the homelier term of use. § 23. Economy. — Passing to the most highly generalised concep- tion of use by extending space and time till we reach the synergy of the race (§ 20), the importance of the element of conservation becomes of ever- widening importance, for the accumulated wealth — and con- sequently the historic synergy — may be said to vary almost inversely as the transitory, and directly as the permanent elements of pro- duction. 962 Proceedings of the Boyal Society § 24. Physical Aspects of Population.-— might at first seem that all questions of population must he left to the biologist ; yet a cer- tain aspect of the subject must inevitably he taken here. For the processes of production not only machines hut “ producer automata ” (“hands”) were seen to he necessary; and the latter simply differ from the former in consuming ultimate products as fuel, &c. The portion of ultimate products thus consumed (which then return in fact to the category of mediate products, being hence often included under capital) varies per “ hand ” per unit time — and is accordingly known as the “ standard of comfort.” Increase or decrease of pro- duction (processes and standard of comfort being constant) must therefore he accompanied by proportional increase or decrease of producers, and hence the multiplication of population is seen to have a strictly physical aspect. In other words, the investment or withdrawal of capital in production involves a proportional stimulus, or check to population, and similarly with variations in processes or in standard of comfort. Appendix to Chapter I — Practical Physical Economics. § 25. Practical Physical Economics.— On the plan already outlined of investigating the practical aspect of our subject, we should inquire in what directions do all the various observed social changes tend ? what modifications of them are consistent with physical law ? and by the systematisation of these obtain our ideals or utopias : but it needs no detailed investigation to see that all changes of pro- duction and consumption tend either towards increase or diminution of their results per unit time (even maintenance of production tending strictly to the former), every movement of man upon the globe acting in one or other of these directions ; hence alternative ideals of production appear at once, and admit of simple formulation into rules of practice : 1. Maximise production ) „ ^ V ot ultimate products per unit time ; 2. Minimise production j with subsequent similar rival ideals of consumption, (1) Maximise consumption ) ^ , . , , of ultimate products per unit time. (2) Minimise consumption j 963 of Edinburgh, Session 1883-84. § 26. Ideal of Production. — We are called upon here to select between two alternative ideals, and without entering into any dis- cussion of optimism or pessimism, we are compelled as practical economists to ignore the second, which leads of course to the nega- tion of practical economics altogether. We have simply then to discuss the practical means of maximising production per unit time, though noting that every action in the community is ascertainahly of one or other tendency. § 27. Production. — Starting from the estimate of the attainable sources of energy in nature, and from the scrutiny of the processes of technology and movement already outlined, our maxim leads directly to the organisation of production so as to maximise idtimate products. Inii^rovements in exploitation, increase in inanufactiiiing power, diminution of friction in transport, simplification of trade, are the four great heads of this process of which the endless details need not be here developed, especially as on the theory of conserva- tion of energy all are reducible to the same unit of measurement. With respect to organisms this involves (1) a maximisation of their usefulness for production in every possible way besides the corre spending increase in their numbers. § 28. Consumption. — Passing to the maximisation of consumption per unit time, we see at once that this involves making all pro- ducts transitory; minimising similarly implies making all permanent;. Hence maximisation of permanent products has a reactionary diminutive effect on the producing population, just as the opposite — maximisation of transitory products — involves their indefinite in- crease. In other words, the physical economist, desiring to increase not the population, but the wealth of nations, — instead of simply approving the continuous development of the existing industries, and attempt- ing to increase average well-being by stimulatiug the exploitation, manufacture, or exchange, of the transitory products with which these mainly deal, — must advocate the proportional increase of per- manent ultimate products, and organise industrial processes towards that ideal. We have thus reached the new paradox (c/. § 21) that the sphere of practical physical economics is to discuss the ways and means of increasing not so much bread, as Art. 964 Froceedings of the Royal Society Chapter IL— Biological Principles. § 29. Widely current in economic literature are conceptions whicli seem to have more or less biological character — one hears of “ parasit- ism,” of “ competition,” of laws of population,” of the “ social organ- ism,” and even of its “ circulatory,” and ‘‘ nutritive organs,” and so on, besides many others which though not necessarily couched in current biological language, yet readily hear translation. It is here proposed to criticise and, to some extent, systematise this aspect of economics. At starting, we meet the difficulty, that past economic literature necessarily shares the character of past literature' in general, and more or less completely ignores physiological, zoological, and anthro- pological facts altogether. It is necessary to postulate the results of all these sub-sciences most clearly, and the biologist, avoiding misleading “ comparisons between man and nature,” must w'ork forward from the actual living “man and his place in nature,” without particular respect to the authority of any time-honoured theories of “human nature,” or of the “economic man.” In passing from the physical to the biological aspects of economics, our producers and consumers are no longer regarded as automata, and generalised along with machines ; but are looked on as speci- mens of a species of living organism, to he generalised with the rest of organic nature, terminating the greatest line of genealogical ascent, and supremely successful in the struggle for existence and domination, in virtue of peculiarly high evolution of the nervous system. Our biological studies then commence with a knowledge of the statical aspects of Homo ; with an organised census,"^ in which the quantity and quality of the population are carefully recorded : the * The reader may at first suppose that it is here attempted to discuss ques- tions essentially sociological under biology — but this “materialism” (u § 12) will be carefully guarded against. All that concerns only the objective and bodily side of a man is purely biological ; and this may he summed up for a number of men, looked at simply as a herd or mass, without leaving the field of pure biology. Sociology, on the other hand, concerns itself with indivi- dualities of a higher order : — with aggregates of men integrated into wholes for definite functions ; as firm, bank, company, regiment, post office, and only considers the individual components in their relations to these. The census, then, is primarily biological, but also of course has sociological elements of high importance ; — but these await separate and subsequent discussion. of Edinburgh, Session 1883-84. 965 observations of the biologist, and tbe anthropologist, of the registrar, census-taker and actuary, tbe hygienist and tbe educationist, are all organised into a vast body of knowledge — the statistics and gene- ralisations of the new sub-science of “ demography.” * Eut our survey must be not only statical but dynamical, not only structural but functional ; how are we to approach this 1 Protoplasm undergoes incessant waste, and demands incessant repair, and it is this fact which underlies economic activities. However different in details, all the higher animals agree in obtaining the food needful for repairing the waste of their tissues, from their environment by the performance. of muscular contractions co-ordinated by the ner- vous system. And this furnishes us with the widest definition of productive labour while the “sense of effort,” the “pain,” the “curse of labour” so much insisted on, is at most merely an accom- paniment, incidental either to excessive exertion or defective adaptation to the task. § 30. Evolution of Production. — Prom the simple conception of animal production here laid down, we have to trace the evolution of modern industry; nor are the main steps numerous or difficult. The animal demands only ultimate products, and at first only produces food, accepting for shelter simply what the environment chances to afford. With increasing intelligence, shelters are next constructed : a bird’s nest is as truly an ultimate economic product to its builders as a house to man. In the case of some the aesthetic subfunction begins to appear, and some animals, like the Australian bower-bird, even spend no little labour on purely aesthetic production. Stages of exploitation, manufactures, and movement are frequently more or less distinguishable; but all products as yet are ultimate. Mediate products, however, also tend to arise — like the roads and granaries of the ant, the engineering works of the beaver, or the stick and stone of the higher apes — from which to the rough flint implement of the palaeolithic man the transition is easy. Given this implement, however, man becomes “ a tool-using animal,” and the evolution of ultimate products goes on apace. From this point the history of productive processes is being admirably traced by the combined labours of archaeologists and historical economists. It is sufficient here to recall the origin and aspects of the producers. * Vide Classification of Statistics, passim. 966 Proceedings of the Royal Society Beyond tlie primary economic differentiation involved by sex, all economic functions are at first united in eacb individual. As population increases, the advantage of numbers (tbe “ simple co- operation ” of economists) becomes felt ; then slight variations of individual and circumstance lead to the repeated performance of some one function by particular individuals, the efficiency and rapidity of its performance then alike improve, and the advantages of specialisation of function, or “ division of labour,” become obvious, and tend to be continued and perpetuated. This differ- entiation once set up, it continues as long as circumstances render it advantageous or possible, and the complicated co-operation of the ant-hill or the city alike arises. These familiar considerations show that the “ specialisation of functions ” in Formica and the ‘‘ divi- sion of labour ” in Homo are not merely ‘‘ analogies between man and nature ” — interesting only to those who care to trace such com parisons, — but are absolutely identical. § 31. Result of Specialisation of Function upon Organism. — The differentiation of production leads then to the development of occu- pations, which, especially when perpetuated by heredity, are again seen to be of identical nature with those of the polymorphic indivi duals of the ant-hill. And all occupations are not directly con- cerned with production: some individuals specialise into the indirectly productive service of government; others leave productive operations on surrounding nature for the bodily care and service of their fellows ; others, again, become unoccupied ; and thus the three great classes of occujDations (^Classification of Statistics) are not simply analogous, but identical among bees, ants, or men, and are sometimes more differentiated in the former, sometimes in the latter. Just as the operations of heredity upon man and other organisms are not merely analogous but identical, so also are those of function. Division of labour has specialised the polymorphic castes of the ant-hill; so the same specialisation of function acts towards developing similar polymorphic changes among men. Every one is more or less conscious of this : it is never difficult to distinguish a soldier from a joiner, or a ploughman from a weaver; while the physician reaches almost incredible skill in eading the finer results of occupation on bodily structures, normal and pathological alike. of Edinburgh, Session 1883-84. 967 The biological reader may well wonder at the insistance upon what is to him a commonplace ; but, like so many of the scientific commonplaces enlarged upon in the present analysis, it has been ignored by the vast majority of economic writers. It does not come within the study of processes of production on one hand, nor within that of social aggregates on the other ; the occupations of ploughman and weaver or joiner are alike productive — are all equal in the eye of the politician and before the law. To economists, whose preparatory studies included no biology, any insistance upon the wide difference of these occupations to the men performing them must needs seem mere nonsense, and the proposal to found practical action upon the observed results pure “sentiment.” But, without the slightest postulation of morals, it is a biological fact that, as “ function makes the organ,” it also shapes the organism, and modifies it either for evolution or for degeneration ; moreover, other things equal, determines its quantity of health and limits its length of life. Ploughmen and weavers, joiners or soldiers, then, are incipient castes, as surely as Brahmin and Pariah, queen, worker, and drone, are formed ones ] and the disadvantages of the division of labour, so slowly forced into prominence (as, little to the credit of biologists, they have been) through the sufferings of the many and the moral enthusiasm of an unscientific few, demand study and classification among the “Variations of Animals and Plants under Domestication.” § 32. Modification by Environment, — Even when we study the ancestral environment separately as heredity, and the functional environment or occupation separately as function, besides leaving the social environment for a subsequent discussion, there remains a series of influences, those of the ordinary environment, which probably exceed any others in importance. Food, which alone determines whether the young bee is to be worker or queen, has a thoroughly well-marked influence upon men. The importance of the quality of the atmosphere is becoming recognised. So also with light : the gardener blanches his celery, the zoologist stops the development of the tadpole by withdrawing light, the sphygmo- graph shows how the pulse bounds at every gleam of sunshine, and the physiologist and physician are not hesitating to generalise and apply these results to the development of human life in towns. 968 Proceedings of the Roycd Society It has been assumed by most economists that the “ necessities of life ” were simply food, shelter, &c., and that the subtler factors of the environment need not be included. This pre-biological concep- tion need not be argued with, for the economic problem of the maintenance of men is but one special case of the vast problem of the modification of organism by environment, exactly as the descent of man is a special case of the origin of species. § 33. Mode of Modification of Organism hy Environment. — • Although time and space and knowledge do not admit of tracing out these lines of modification in detail, some idea of the two main lines of evolution and degeneration respectively must be obtained. It is convenient to begin with the latter, since the conditions of degeneration in the organic world are approximately known. These conditions of degeneration are of two very distinct kinds — on the one hand, deprivation of food, light, &c., so leading to imperfect nutrition and innervation ; on the other, a life of repose, with abundant supply of food and decreased exposure to the dangers of the environment. It is noteworthy that while the former only depresses, or at most extinguishes, the specific type, the latter, through that disuse of nervous and other structures, &c., which such simplification of life involves, brings about that far more insidious and thorough degeneration seen in the life history of myriads of parasites. It is noteworthy that both these sets of con- ditions of organic change exist abundantly in society, the former being known as poverty, the latter as “ complete material well- being.” The influence of all this upon the degeneration of indivi- duals and upon the decline and fall of nations alike, need not be insisted upon. Passing now to the less known conditions of evolution as opposed to degeneration, it is obvious that (1) adequate conditions of food, light, atmosphere, are necessary; (2) that the organism, and primarily the nervous system, must be adapted to more and more complex conditions of the environment ; ■i.e., that the nervous system must become more and more highly evolved. Hence arises the physiological explanation of the aesthetic sub- function in production, of which we were compelled to notice the enormous importance even under the preceding analysis of physical principles. It is determined by the need of the various senses, and of Edinburgh, Session 1883-84. 969 tbe cry for so-called ‘‘utility” in ultimate products is frequently nothing more than a demand for the lower forms of sesthesis in preference to the higher. § 34. Definition of Production. — No definition of production is possible from the physical point of view alone, since it involves a knowledge of the organism to which production is adapted. Now, however, production is definable in general terms as the adaptation of the environment to human functions; and every productive action thus tends either towards maintenance and evolution or the reverse. I'his simple idea is not yet, however, sufficiently active in our industrial age. The functions of production are undertaken by industrialists, chiefs and proletaires alike, mainly with the notion of obtaining “ wealth ” in its very variable proportions of main- tenance, power over others, personal immunity from function, &c., a conception of the nature and aim of production upon which our surviving industrial anarchy mainly depends. The adaptation of the world to the wants of the species, which we see to be the beginning and end of production, is again definable in biological language as the substitution of human for natural selection. § 35. Polymorphism and Competition. — We have already seen how, in the evolution of production, specialisation of function in a com- munity of organisms was attended by polymorphism — the resultant structural specialisation. This polymorphism has a most important bearing on the economy of the community. In a little differen- tiated community, competition is at its highest pitch ; in a poly- morphic one, it is reduced almost to zero. In a hydractinia or siphonophore colony, in an ant-hill or bee-hive, competition is mini- mised. Struggle for existence between the members has ceased, the only struggle is with other communities. So far, then, is com- petition from being the sole idea derivable by economics from biology, as is so commonly supposed, that in fact competition is ever in inverse ratio to polymorphism ; and in a given community polymorphism puts an end to internal, though not necessarily of course to intersocial, struggle. Internal competition can only be -intense in large communities where there is but little polymorphism. § 36. Production and Reproduction. — We have seen that for the ela- boration of ultimate products machines and automata are necessary. Increase of production, therefore, involves increase of machines and VOL. XII. 3 u 970 Proceedings of the Royal Society of automata — of both in so far as they are not interchange- able. This increase of animal automata (given that supply of tran- sitory ultimate products known as the standard of comfort) is attained by reproduction, and increase of a given class of population is therefore determined by the amount of the transitory ultimate products supplied — and hence by the “ capital invested ” in that industry. Increase of permanent products, on the other hand, does not tend to increase the population. The reproductive ratio of any class of producers per unit time is thus a fixed and definite one, and approximately ascertainable. {Cf. Appendix to Chap. I. § 28.) The multiplication or decrease of any class of the community is, in short, strictly comparable to the hypertrophy or atrophy of the cells of an organ in proportion to its functional activity and nutri- tive supply. {Cf. article “Reproduction’’ — Encydopcedia Britan- Tiica.) Appendix to Chapter II. — Practical Biological Economics. § 37. Practical Biological Economics. — As in the case of physical economics, so here we have two alternative practical ideals : 1. To maximise the maintenance and evolution of the com- munity. 2. Or to minimise the same. All action is referable to either of these categories, and tends neces- sarily in one of those directions. As practical economists, we are shut up to the selection of the first, and we have only to consider how this ideal can best be realised. This involves a criticism of life from a biological standpoint ; a subject analy sable into endless detail, e.g., the criticism of production alone embracing processes so apparently remote as food-analysis and art-criticism. The details of such a discussion cannot be given here, but the lines to be followed may be indicated. The modifications of the organism must be determined and analysed into their various factors, viz., (1) the effects of organism on organism in heredity (education and compe- tition) j (2) the influence of function on the organism towards degeneration on the one hand, and towards evolution on the other ; (3) the modification of the organism by its material environment, such as food, dwelling, air, light, &c. Not only must these factors 971 of Edinburgh, Session 1883-84. in modification be observed and appreciated, but their modifiability- must be discussed and acted upon. Thus, in the case, when any- given environment or function, however apparently “ productive,” is really fraught with disastrous influence to the organism, its modi- fication must be attempted, or, failing that, its abandonment faced. After a thorough analysis of this sort we can attempt the treat- ment of such practical questions as the state of the poor, or the advancement of social progress in general — since practical action, at present dispersed into special efforts, each dealing with some aspect of organism, function, or environment alone (or of some mixture of these), must on pain of failure attempt the synthetic treatment of all.* It only remains to be pointed out that the ideals of human selec- tion which are beginning to be suggested on all hands, as biological conceptions penetrate modern thought, are to be worked out on one economic basis, that of adapting production to organism. Chapter III. — Psychological Principles. This department of the subject, unlike the two preceding, has an extensive literature, of which it is necessary to examine the main positions at the outset. § 38. Pleasure and Pain. — A psychological basis for economics has often been sought in the theory of pleasure and pain — in the con- ception that we should find at once a theory of observed actions and a basis for expedient action in the pleasure or pain observed to attend them. Without disputing the possible high importance of this standpoint, or insisting too much upon the impossibility of verifying the measurements of pleasure and pain which Mr Jevons and Mr Edgeworth especially have used so freely, it must be pointed out that it is far from furnishing an absolute criterion. According to Spencer, “ pain is correlative of actions injurious to the organism, and pleasure of those which are advantageous.” But a * Le., all beneficent or benevolent agencies whatever thus fall into three genera, or rather brigades {e.g., ecclesiastical, charitable, educational, medical, &c. , into the first ; trades-unions, &c. , into the second ; associations concerned with hygiene, housing, art, &c., into the third). This classification, moreover, corresponds to the developmental succession of such agencies ; and this is now approaching an end, while the requisite co-ordination is becoming possible. 972 Proceedings of the Poyal Society qualification is necessary — since pain is correlative of new adaptations, pleasure of old and familiar ones, which lead through economy of material to degeneration — not improbably one of the most pleasurable of organic processes. This theory, then, will need considerable emendation before being serviceable as a basis for economics. § 39. Conception of Value. — One of the latest and most nearly satisfactory analyses of the much-disputed and ambiguous term value ” is that of Jevons,* w'ho resolves it into three distinct factors : — “ (1) Value in use, or total utility ; (2) esteem, or urgency of desire for more, or final degree of utility ; (3) purchasing power, or ‘ ratio of exchange.^ ” Again, according to Walker, a commodity possesses value when it is an object of man’s desire, and can be obtained only by man’s efforts ; ” while Bastiat explains that value does not reside in the commodities themselves, and is no more to be found in a loaf of bread than in a diamond, the water, or the air.” And such definitions and exjdaiiations are repeated indefinitely in other works. But in terms of the present analysis it is evident that the “ value” of anything has a significance varying with the standpoint of each successive science, — that “ ratio of exchange ” expresses an essen- tially mathematical aspect, “ utility or intrinsic value ” its physical or physiological sense, intensity of desire ” its psychological, and ^‘purchasing power” its sociological aspect. The long disputes respecting the nature of value are thus clearly analogous to the famous case of the gold and silver shield. From the psychological standpoint, for instance, the conception of intrinsic value is clearly irrelevant; and to economists of conventional academic training, acquainted with the current logic and metaphysics, but without a suspicion of physical and biological facts, the exclusion of every other point of view necessarily followed. From this point of view, especially when we bear in mind the idealistic philosophy of the schools, the dogma of Bastiat is a commonplace, and the thoughtless copying of it by equally pre-scientific writers is natural ; it has, however, no more interest to the economist than any other platitude of idealism : the facts for him being, as was above pointed out^ — (1) that loaf and diamond are observed to exchange in a certain ratio .(mathematical value) : (2) that they possess a certain number of * Math. Theory of Pol. Econ. of Edinburgh, Session 1883-84. 973 units of potential energy as combustible (physical value) ; (3) that the former is capable of maintaining an average adult for a definite time, while the latter possesses a definite power of sensory stimulus (physiological value) ; (4) that corresponding to the preceding physiological functions are their subjective aspect, known as wants or desires (psychological value) ; (5) that, as property’-, they acquire a sociological “value,” which cannot as yet be entered upon. The idealistic position, though extremely popular, has never been consistently maintained ; the reverse position is often tacitly taken, as apparently in the dogma that “labour is a commodity,” and the like. The attempt then to base the psychology of economics upon the^ aspects of value, and much more to make it the centre of the whole science, turns out futile ; so far from being fundamental, it is in fact almost superfluous, since it is either the subjective expression of an actual objective value (physical, biological, or sociological), or an erroneous hypothetical estimate of one or more of these. §40. Wants and Desires. — Can “wants and desires,” however,, be taken as completely expressing the psychology of action ? Pro- bably not completely, since there is much ground for suspecting that complex associations never formulated in consciousness play an important part ; perhaps, too, that even lower states of cerebral activity have their share in determining action. Let us see, however, how the conception is developed by econo- mists. Their current positions may most fairly be stated by quota- tions from well-known authors. “ Political economy teaches the relation of man to those objects of his desire which he can obtain only by his efforts ” (Walker, Science of Wealth, p. 2). “ The objects or satisfactions obtained by these efforts are collectively called wealth.” Again, “ wealth is whatever satisfies a desire or serves a purpose.” Again, according to J. B. Say, “that society is most civilised which produces most and consumes most;” or, in other words, which has the greatest quantity of artificial wants. From the preceding it follows — (1) that all wants and desires are equally valid in the eyes of the economist, who can make no other criticism of wealth ; (2) that the only recognisable progress lies in differentiation, and in this most economists fully concur. Despite the importance attached to wants and desires, they have 9Y4 Proceedings of the Royal Society rarely obtained any detailed analysis or classification whatever. The most recent and elaborate attempt is probably that of Syme (Industrial Science^ p. 106). He divides them into (I.) Egoistic, or wants and desires for food, drink, rest, &c. ; (II.) Hemeistic, having for their object the gratification of the social emotions, such as affection, esteem, love, hate, &c. ; (HI.) Allostic, having reference to actions, and having for their object justice. In the vast majority of works, however, no such analysis is attempted ; some generalisation of these varied wants and desires is, however, needed ; this is obtained by boldly uniting them under the term self-interest or egoism — this done, it is evident that self- interest is the mainspring of all economic action, and the basis of orthodox economics is complete. A principle capable of endless deductive applications is obtained, and if any unbelief as to the exhaustiveness of the generalisation arises, the wide prevalence of egoism in the individual and in the community is readily appealed to, and the sceptic held up to derision as a sentimentalist. With all respect, however, to these systems, a new analysis leading to somewhat different conclusions must now be briefly attempted. § 41. Statement of Psychological Principles. — In discussing the biological principles of economics, we considered men as organisms (a) having certain functions applicable to the maintenance and evolution of self and others, or to the contrary ; and (f) with certain wants, ^.e., requiring certain adaptations to the environment, again either in the direction of evolution or of degeneration. We find psychological principles parallel to these. Man is characterised by the enormous specialisation of his nervous system, and psychology though in the past mainly restricted to an imaginary account of an independent entity, of mind “ as a thinking being in vacuo f really deals with the subjective side of the functional aspects of the nervous system. Behind the muscular contractions by which all economic action productive or consumptive alike are performed, are cerebral stimuli inspiring these, and these subjectively considered are wants and desires. The fundamental nature of tbe subject is therefore obvious. As Walker expresses it, ‘'‘the central force is the wants of man.” That however the wants determining produc- tion, &c., are not simple appetites for food, shelter, and the like, is evident when we remember how in the majority of products the of Edinburgh, Session 1883-84. 975 sesthetic sub-function preponderates over that which would merely satisfy the nutritive appetite. That desires realise themselves in efforts, and that efforts attain satisfaction, is the psychological or subjective side of the objective fact that wants necessitate labour, and that labour results in wealth. A simple economic action — say an amoeba devouring a grain of starch, or a labourer consuming food, may be expressed in three ways — (1) physical, the potential energy of the body is increased; (2) biological, the organism is nourished ; (3) psychological, a desire is satisfied. In the very simplest forms of life we find two essential forms of vital action — the nutritive and the reproductive. But Leconte has pointed out that, while the satisfaction of nutritive wants is funda- mentally egoistic, the reproductive desire contains the earliest germ of altruism. If this be admitted, as it must be, the exclusion of the altruistic element as a determinant of economic action is at once seen to be a mere artifice, alike impossible and absurd, if our psychology is to have any relation to living beings ; while the deductively con- structed fabric of orthodox economics collapses without criticism, since one half of its foundation (“self-interest”) alone was laid. Starting, then, from this primal manifestation of egoistic and altru- istic desires, we may briefly follow the development of these with the ever-increasing structural and social complexity of the organisms. With limited supply and space, these nutritive wants and desires must result in competition between the individuals. Competition has, of course, its objective and subjective aspects ; the objective antagonism must be represented by a subjective egoism and mutual antipathy. But every aggregate which can at all be termed a society has risen to some measure of complexity — of division of labour or poly- morphism ; and even these economists who insist most upon “ self- interest ” are not wanting in clear explanation of the economic advan- tage of the process. The subjective aspect of the process is not, however, personal egoism and mutual antipathy; since, for the co-ordinated muscular actions which any increase of polymorphism and synergy imply, a corresponding measure of co-ordination of nervous action is indispensable ; and thus, as competition involved antipathy, so objective co-operation involves subjective sympathy. As mutual antipathy implies individual egoism, so sympathy implies 97d Proceedings of the Royal Society a measure of altruism. Higher and higher differentiation of social' ' structure and function involves corresponding subjective adaptation ; as the economic duties of an individual develop in complexity and remoteness to the immediate result, so must their subjective aspect on pain of failure deepen and widen ; and thus the material evolu- tion demands a moral evolution running parallel to it. That the material evolution has for the time outrun the moral adaptation is, in fact, from the present point of view, the essential explanation of much existing economic anarchy. As the society reaches completer polymorphism, altruism in- creases ; progress towards the physical and biological ideal of pro- ductive synergy involves parallel progress to an ideal of sympathy or maximum altruism. This does not, however, at once extend to- different societies ; between these competition and antipathy may exist to any extent; hut as antagonism becomes subordinated to community of interests, here also antipathy becomes replaced by sympathy. The concomitant parallel progress of reproductive action — incident upon the origin of the family and the progressive integration of families into higher and higher aggregates — is too familiar to need recapitulation here. It is evident that even on the most sternly biological grounds, so far from a scientific basis for economic deduc- tion being furnished by “ the iron law of competition,” the highest generalisation of the phenomena (from which deduction, if anywhere- is alone permissible) is the accurate converse of this — the golden rule of sympathy and synergy. And it is a remarkable result that, without introducing into the argument any so-called moral or senti- mental considerations, hut arguing soberly from the two fundamental! functions and wants of living beings — from nutrition and reproduc-- tion alone — the noblest ideals of politics and morals arise before us. Appendix to Chapter HI. — Practical Psychological Economics. § 42. Can our psychological conceptions of (1) pleasure and pain;. (2) value, (3) of wants and desires, furnish a basis of economic action? Actions may be classified as they produce pleasure or pain, or as they tend to satisfy our desires ; hut such an attempt, |iowever reasonable in constructing a theory of personal action. of Edinburgh, Sessmi 1883-84, 97T has never been successfully applied to social action. Nor is it adequate even in the simplest case. Taking the amoeba and labourer of the preceding illustration, both frequently satisfy desire by the consumption of that which is not food in the biological sense, and of what supplies no energy from the physical. Here then a dilemma arises : if with the majority of economists we recognise no physical or biological aspects in the phenomena of economics, all wants and desires are alike expedient, since no criterion of action exists, and laissez faire becomes the only prac- tical maxim. If, however, we recognise physical and biological facts, and the psychological as the subjective aspect of the latter, then the psychological economist must simply commend those wants and desires which are conducive to maintenance and evolu- tion, and these only. ‘‘It is not enough to transfer the point of view from the indivi- dual to the race, and to take the social factor into account ; we must also frankly accept the biological point of view, which ^ regarding mental functions as vital functions, and states of con- sciousness as separable from states of the organism only in our mode of apprehending them, sets aside the traditional conception of mind as an agent apart from the organism.” From this sharply defined statement of the position of the present chapter (cf. Introduction, § 13), we are thus forced to draw the following economic corollaries : — (1) Since, from the physiological side, the nature, amount, and direction of muscular activities are dominated by cerebral action, the cerebral functions are supreme ; (2) as similarly, from the psychological side, all functions are equally — nay, are solely — expressible as cerebral, the functions of creative and directive thought, the activities of education, &c., are as really “productive” as any. Thus our economic utilita- rianism passes from the crudely practical state to that into which it has been recast by its more philosophical exponents; and if psychology, leaving its academic isolation, assumes its modem position, schoolmaster, hodman, and artist, are alike productive. The problem of practical economics now demands that we pro- duce not that mere maximum of food and eaters, which is the first aspect of the physical ideal ; not even that perfection' of * Lewes, of Psychology, chap. i. 978 Proceedings of the Royal Society quality and quantity of physical life which is the first aspect of the biological ; but the maximum evolution of mental and moral nature which underlies the two former. The problem, in fact, inverts itself, becoming not merely how to fill bellies, but how to place brains in the conditions most favourable to their development and activity, and so the problem of practical psychological economics passes into that of education. The supremacy of the eesthetic factor in production, demonstrated under “ Physical Principles,” is thus explained : — The modification of the environment which is the object of production, while primarily addressing the nutritive system and attending to protective needs, must culminate 'in that complex organisation of the environment which, deliberately addressing itself to the stimulus and evolution of the sensory activities, is of such importance for the process of cerebral evolu- tion (a wealth of impressions being the indispensable raw material of the most complex or highly generalised intellectual conceptions), and which we therefore term fine art. Summary of Chapters I. -III. § 43. At this point it is convenient to pause and briefly review the results of these analyses. Passing over the criticism of economic literature, (1) the physical analysis led to the exposition of the mechanical aspect of society ; to the reorganisation of the theory of production and consumption, culminating in the generalisa- tion of the synergy of the race. (2) The biological chapter outlined the higher aspect of the same phenomena, defined pro- duction, &c., and discussed the relation of organism to the environment and function — a definition of production being obtained in terms of maintenance and evolution. (3) A psycho- logical outline in harmony with the present state of science was attempted ; and many subjects not usually treated under econo- mics were seen to form an integral part of the subject. Yet this is by no means sufficient ; a sociological analysis is wanting ; and the whole series of analyses are but materials for a subsequent synthesis. But a pause may reasonably be made before entering on this, and a clear gain has been made if these results are plain {a) that the analysis of so-called systems of political economy is neces- 979 of Edinhurgh, Session 1883-84. sary and possible, and that on the present lines ; (b) that the analysis does yield many results of clear principle and practical application ; and (c) most important of all, that many of the most burning questions between producer and consumer, worker and capitalist, individualist and socialist, utilitarian and sentimentalist, are soluble on the field of pure science without appeal to sociological or political methods at all.* To the present scheme numerous objections are constantly pro- posed, and these, so far as the writer is aware, may be analysed and grouped as follows: — It is said (1) that the present survey is too wide, that it discusses principles which are not relevant within the proper sphere of economics; (2) it seems difficult to make sure of the actual logical sequence of the argument, and (3) to see its applicability to details ; or (4) there arises a suspicion of the insidious postulation at some early stage of the argument of the ethical considerations which appear as results ; or (5), and most commonly, the results seem too good to be true. To which it may be replied, that (1) hardly any matters are intro- duced which will not be found, in chaotic form indeed, in the standard works on economics, and that the usual restrictions of the subject to one particular division of the subject {e.g., to the theory of production and consumption apart from the relation of these to the organisms), are arbitrary, and proceed usually from ignorance or misconception of the subjects excluded ; and moreover that, even if it may still be thought by some to be too wide in its scope, it is yet a continuous train of reasoning connecting the widest generalisation of knowledge (the classified sciences) on the one hand, with the minutest details of technology or consumption on the other ; while most so-called systems have been set afloat either without cargo of fact or compass of science ; (2) that the present channel of publication is the most direct method known to the writer of challenging and obtaining a keen scientific scrutiny; (3) that the indispensable and yet less pressing question of its applica- tion to detail, although excluded because of limits of space, &c., can not only be tested by any one who cares fairly to master the general * Thus the dispute preceding the passing of the Factory Acts did not lie between “economic science” and “sentiment,” but between the ideals of physical and biological economics (q.v.). 980 Proceedings of the Royal Society. principles^ but is at least to a very great extent vouched for by the mode of construction (not only synthetic and deductive, but analytic and inductive throughout, and embodying the generalisation of long preliminary studies of economic detail) (see Classification of Statistics, p. 19). This difficulty can be best got over by reading these essays side by side with such a vast storehouse of facts as the well-known manual of Eoscher ; though the reader may be once more and finally reminded that he must not expect to find in these rough draughts for the ground plans of successive stories of the economic edifice, the completeness and detail, the colour and per- spective of the projected whole. (4) The suspicion of the prema- ture postulation of ethical considerations, if present, is due to the reader’s discovering more or less clearly for himself that ethics is not an isolated science, but a generalisation of the acts or practice corresponding to each of the orders of scientific considera- tions, physical and biological, &c., and that the ideals of maxi- mum production and maximum evolution respectively were as much the ethic of physical and biological considerations as that of sympathy is that of psychological ones. The fifth objection, due to discouragement from previous failures to find a synthesis, need not of course be argued with. But the real difficulty of the paper lies in its inevitable and extreme compression, and its consequently generalised form — the requisite application of the principles to the familiar details of economics, and their exposition in more literary form, being alike only suggested in an occasional sentence. The essential aim will, however, have been attained if it has been adequately demonstrated (1) to scientific specialists — physicists, biologists, or psychologists alike — that each respective aspect of economics lies fairly within their range, and (2) to professed economists, that such a mode of reinvestigation is not only practicable, but expedient. Donations to the Library of the Eoyal Society from 1881 to 1884. I. Transactions and Proceedings of Learned Societies, Academies, &c. Adelaide. — Transactions and Proceedings of the Adelaide Philosophical Society. Vols. IV.-VI. 1880-83. 8vo. American Association. — See United States. Amsterdam. — Verharidelingen der Kon. Akademie van Wetenschappen. Afd. Natuurkunde, Dl. XXII., XXIII., 1883. Afd. Letter- kunde, Dl. XIY.-XV., 1882-83. Verslagen en Mededeel- ingen, Natuurkunde, 2® Eks., Dl. XVI.-XVIII. Letterkunde, 2® Eks., Dl. X.-XII., 1881-83. Processeii Verhaal, 1881-83. Jaarboek, 1882, 1883. Poemata Latina, 1882. Catalogus der Boeker der Akad. Kon. Zoologisch Genootschap Natura Artis Magistra Tijdschrift Jaarg. V. 1, 1884. — Bijdragen, Utlev. X., 1884. VVijskundig Genootschap, St I.-V., 1882-84. Flora Batava: Afbeelding en Beschrijving van Nederlandsche Gewassen. Voortgezet door F. W. Van Eedden. 249-266 Aheveringen, 1882-84. — From the King of Holland. Annaijolis. — Annual Eegister of the United States Naval Academv. 1881. 8vo. Baltimore. — Johns Hoi^kins University. — The American Journal of Mathematics. Professor Newcomb (Editor-in-chief). Vols. V., VI. 1883, 1884. The American Chemical Journal. Edited bv Professor Eemsen. Vols. V., VI. 1883, 1884. The American Journal of Philology, Edited by Professor Gilder- sleeve. Vol, V. 1883-84. Studies from the Biological Laboratory of the Johns Hopkins University. Vol. III. No. 2. 1884. 8vo. University Studies iiiH istorical and Political Science. 3rd Ser. Vol. I. 1885. Sixth and Seventh Annual Eeports. See Maryland. Basel. — Verhandlungen der Naturforschenden Gesellschaft, 7®"^ Theil, 2®« Hft. 1884. 8 VO. Batavia, The Observatory. — Observations made at the Magnetical and Meteorological Observatory at Batavia. Vol. V. Part 1. 1881. Eegenwaarnemingen in Nederlandsch Indie 4® en 5® Jaarg. 1882-83. _ 8 VO. The Batavian Society of Arts and Sciences. — Natuurkundig Tijdschrift voor Nederlandsch Indie uitgeven door de Kon. Natuurkundige Vereeniging. Deel XII. 1882-83. 8vo. Tijdschrift voor Indische Taal-Land-en Volkenkunde. Deel XXVIII. 1883-84. 8vo. Verhandelingen van het Bataviaasch Genootschap van Kunsten en Wetenschappen. Deel XLIV. 1881. 8vo. Notiilen, Deel XX., XXL 1882-83. Belfast. — Proceedings of the Natural History and Philosophical Society for 1881-82, 1882-83, 1883-84. Bergen. — Museum. — Nye Alcyonider, Gorgonider og Pennatulider ved Koren og Danielsen. Folio. 982 Proceedings of the Eoyal Society Berlin. — Abhandlimgen der Koniglichen Akademie der Wissenscliaften. 1882, 1883. — Sitzungsberichte. 1883-84. 8vo. Fortschritte der Pbysik im Jabre 1877. Dargestellt von der physikaliscbeii Gesellschaft zu Berlin. 1*® Abtheil. — Physik, Akustik, Optik. 2*® Abtheil. — Warmelehre, Elektricitatslehre, Physik der Erde. 8vo. Berlin, 1883. — From the Society. Zeitschrift der Dentschen Meteorologischen Gesellschaft. Nos. 5, 6, 7, 8. 1884. Kbnigliche Technische Hochschule Festschrift, znr Einweihimg ihres neuen Gebaudes. 1884. 4to. Bern. — Beitrage zur geologischen Karte der Schweiz, XX® Lief. 23. 1881. 4to. — From the Commission Federate Ge'ologique. Mittheilungen der Naturforschenden Gesellschaft in Bern, 1882- 84. 8vo. Berwichshire. — Berwickshire Naturalists’ Club, Proceedings of. Vol. X. 1-2. 1882-83. 8vo. Birmingham. — Proceedings of the Birmingham Philosophical Society, Vols. III., IV. ft. 1. 1882-84. 8vo. Bologna. — Memorie dell’ Accademia delle Scienze dell’ Istituto di Bologna. Series IV. Tom. III., IV. 1881-82. 4to.— Kendi- conti, 1879-83. Bombay. — Archaeological Survey of Western India. 4to. Journal of the Bombay ftanch of the Koyal Asiatic Society. Vol. XVI. 1883. Magnetical and Meteorological Observations made at the Govern- ment Observatory from 1879 to 1882. Bombay. 4to. Bonn. — Verhandlungen des Naturhistorischen Vereines der Preussischen Rheinlande und Westfalens. 1*®. 1882-1884. 8vo. Bordeaux. — Memoires de la Societe des Sciences Physiques et Naturelles. 2®Serie. Tome V. 1882-83. 4to. Bulletins de la Societe de Geographie Commerciale. 1883-84. 8vo. Compte Rendu du Congres des Societes Francaises de Geographie, 1882. Boston. — Proceedings of the Boston Society of Natural History. Vol. XXL 1881-83. Proceedings of the American Academy of Arts and Sciences. Vol. XVII., 1882. Vol. XVIII., 1883. Vol. XIX., 1884. Brera. — See Milan. British Association for the Advancement of Science. — Reports and Meetings at Southampton and Sandport. 1882, 1883. Brunswick. — Jahresbericht des Vereins flir Naturwissenschaft. 1880-81. 8vo. Brussels. — Bulletin de l’Acad6mie Royale des Sciences, des Lettres, et des Beaux-Arts de Belgique. Tome LII., 1883. Tome LIII., 1884. 8vo. Memoires de 1’ Academie Royale des Sciences, des Lettres, et des Beaux-Arts de Belgique. Tome XLIV. 1882. 4to. Memoires Couronnes et Autres Memoires publics par I’Academie Royale des Sciences, &c., de Belgique. Tomes XXXII.-XXXV, 1881-1883. Memoires Couronnes et Memoires des Savants l^trangers publies par r Academie Royale des Sciences, &c., de Belgique. Tomes XL.-XLV. 1876-1883. 4to. Biographic Nationale. Tome VII. Pt. 1. 1880. Annuaire de I’Academie Royale. 1883, 1884. 8vo. Vade-Mecum de PAstronomie, par M. Houzeau. Bruxelles, 1882. 8vo. of Edinburgh, Session 1883-84. 983 Brussels. — Bibliographie G4n4rale de I’Astronomie, Tome II. Exposition de la Methode de Wroiiski pour la Eesolution des Problemes de Mecaniqiie Celeste. Par Ch. Lagrange. 1® Partie. 1882. 4to. Annales de rObsers^atoire Eoyal. Nouv. Ser. Annales Astrono- miques. Tonies IV., V. 1884. 4to. — Annales Meteorologiques. Tome I. 1881. 4to. Annnaire de I’Observatoire Eoyal. Annees, 1882, 1883. 8vo. Annales de la Societe Scientifiqae de Bruxelles, 6® et 7® Annees, 1881-1884. 8 VO. — From the Society. Bucharest. — Academia Eomana. Extrasu din Analele Memorie si Notite. 1883-1884. Also Documents relating to the History of Eoumania, and Translations of the Latin Classical Authors into Eoumanian — a Eoumanian and Latin Dictionary, &c. Buda-Pesth. — Kbnigl. Ungarische Naturwissenschaftliche Gesellschaft. Bd. I. 1882-83. 8vo. Ungarische Eevue, 1882-83. Gazette de Hongrie. 1882-83. Chrysididae Faunae Hungaricae. Auctore A. Murray. 1882. 4to. Buenos-Ayres. — Descrqition physique de la Eepublique Argentine, par le Dr H. Burmeister. Tome III"'®. Animaux Vertebres I*"® ptie. Mammiferes Vivants et Eteints. 1879. 8vo. Avec Atlas; f® Tome V®. L4pidopteres. 1^® ptie. 1880. Anales de la Oficina Meteorologica Argentina. Tom. III. 1882. Tom. IV. 1883. 4to. Calcutta. — Asiatic Society of Bengal. — Descriptions of New Indian Lepi- dopterous Insects (Atkinson Collection). Ph. Ehopalocera, by W. C. Hewitson ; Heterocera, by F. Moore. 1879. Pt. 2. Heterocera, 1882. 4to. Proceedings of the Asiatic Society of Bengal for 1882-1884. 8vo. Journal of the Asiatic Society for 1882-1884. 8vo. See Indian Government. Catalogue and Handbook of the Archaeological Collections in the Indian Museum. By Professor John Anderson, M.D, Pt. I — Asoka and Indo-Scythian Galleries. 1883. 8vo. California. — Proceedings of the California Academy of Sciences. 1884. State Mining Bureau. Third Annual Eeport, 1883. Cambridge. — Transactions of the Philosophical Society. Vol. XIII. 1883. 4to. — Proceedings, Vol. IV. 1883. 8vo. Cambridge ( U.S.) — Harvard College. — Annual Eeports of the Curator of the Museum of Comparative Zoology at Harvard College. 1881-1884. Bulletin of the Museum of Comparative Zoology at Harvard College. Vols. X., XI. 1882-1884. 8vo. Memoirs of the Museum of Comparative Zoology at Harvard College. Vols. IX., X. Embryological Monograph. 1883- 1884. 4to. Memoirs of the American Academy of Arts and Sciences. Vol. X. Pt. 1. 1868. — Proceedings. Vol. XL 1884. Annals of the Astronomical Observatory at Harvard College. Vol. XIV. 1884. 4to. Thirty-eighth Annual Eeport of the Director of the Astronomical Observatory of Harvard College. By E. C. Pickering. 1884. 8vo. Canada. — Geological Survey of Canada. Eeports of Progress, 1880-1882. 8vo. — From the Government of the Dominion. 984 Proceedings of the Royal Society Cape of Good Hope. — Catalogue of 12,441 Stars for the Epoch 1880, froiu Observations made during 1871-79. By E. J. Stone, F.E.S. 4to. Catania. — Atti dell’ Accademia Gioenia di Scienze Natural!. Ser. 3^“. Tom. XVII. 1883. 4to. Ceylon Government. — The Lepidoptera of Ceylon. Parts 6-10. By F Moore, F.Z.S. 1882—1884. 4to. Chemnitz. — Berichte der Naturwissenschaftlichen Gesellschaft. 1881- 1884. Cherbourg. — Memoires de la Societe Nationale des Sciences Naturelles et Mathematiques. Tome XXIII. 1881. 8vo. Chicago. — Annual Reports of the Board of Directors of the Chicago Astronomical Society and of the Dearborn Observatory. 1882- 1884. 8vo. Christiania. — Den Norske Nordhavs-Expedition. 1876-78. VIII. Zoologi. Mollusca. 1. Buccinidae', ved Herman Friele. 1882. 4to. IX. Chemi. 1. Om Sovandets Faste Bestanddele. 2. Oni Havbundens Afleiringer, af Ludwig Schmelck. 1882. 4to. X. Meteorologi. 1883. XI. Zoologi. Asteroidea. — From the Norwegian Government. Jahrbuch des Norwegischen Meteorologischen Instituts fiir 1877-1881. Den Norske Nordhavs-Expedition. 1882-83. Forhandlinger i Videnskabs-Selskabet. 1880-83. 8vo. Archiv for Mathematik og Naturvidenskab. Bd. VIII. Hft. 1. 1883. Die Anaemie, von S. Lache. 1883. 8vo. Vandstands Observationer : Udgivet af den Norske Gradmaalings- kommission. Hft. 2. 1880-83. 4to. Etudes sur les Mouvements de I’Atmosphere, by C. M. Guldberg et H. Mohn. 1880. 4to. Classification der Flachen nach der Transformationsgruppe ihrer Geodatischen Curven, von Sophus Lie. 1879. 4to. Krystallographisk -Chemiske Undersogelser, af Th. Hiortdahl. 1881. 4to. Vaextlivet i Norge med saerligt Hensyn til Plantegeographien, af Dr F. C. Schtibeler. 1879. 4to. Enumeratio Insectorum Norwegicorum. Edidit J. S. Schneider. Ease. V. Pt. 1. 1880. 8vo. Die Silurischen Etagen 2 und 3, im Christian iagebiet und auf Eker, von W. C. Brogger. 1882. 8vo. Silurfossiler og Pressede Konglomerater i Bergensskifrene, af Hans H. Reusch. 1882. 8vo. Cincinnati. — The Journal of the Cincinnati Society of Natural History. Vols. VI., VII. 1883-84. University of Cincinnati. — Publications of the Observatory. 1879. 8vo. Connecticut. — Transactions of the Connecticut Academy of Arts and Sciences. Vol. VI. 1884. 8vo. Copenhagen. — Memoires de I’Acadeniie Royale de Copenhague. Classe des Sciences. Vol. XII. No. 6. Spolia Atlantica. Vol. I. Nos. ^ 1-10. Vol. II. Nos. 1-6. 1881-84. 4to. Oversigt over det Kongelige Danske Videnskabernes Selkabs For- handlinger. 1883-84. 8vo. Cordoba {Republica Argentina). — Boletin de la Academia Nacional de Ciencias de la Republica Argentina. Tom. IV. 1. 1882. of Edinhuryli, Session 1883-84. 985 Cordoba. — Informe oficial cle la Comision scientifica de la Expedicion al E,io Negro. Entrega II. Botanica. — III. Geologia. 1881-82. Folio. Besultados de la Oficina Meteorologica Argentina. Tomos III., IV. 1882. 4to. Resnltados del Observatorio Nacional Argentine. Vols. IV., VII. VIII. 1884. 4vo. Corniuall. — Transactions of tlie Royal Geological Society of Cornwall. Vol. X. Pts. 4-6. 1882-84, and Catalogue. Dantzig. — Schriften der Naturforsclienden Gesellschaft. Bd. IV. 1876-78. Bd. V. 1883. Bd. VI. 1883. Davenport. — Proceedings of Academy of Natural Sciences. Vol. Ill, 1883. Delft. — Annales de I’Ecole Poly technique. 1® Liv. 1884. 4to. Dorpat. — Inaugural Dissertations. 1882, 1883. Meteorologische Beobachtungen. 1877-1880. 8vo. Dublin. — Royal Irish Academy Proceedings (Science). Series II. Vol. IV. 1882. Proceedings (Polite Literature and Antiquities). Series II. Vol, II. Nos. 4, 5. 1883. Transactions of the Royal Irish Academy (Science). Vol. XXVIII. Science, I.-XVI. 1883-84. 4to. Irish MS. Series. Vol. I. Pt. 1. Polite Literature and Antiquities. No. V. 1881. 4to. The Scientific Proceedings of the Royal Dublin Society. (New Series.) Vol. IV. 1883-84. The Scientific Transactions of the Royal Dublin Society. Vols, II., III. 1882-84. Journal of the Royal Geological Society of Ireland. Vol. XVI, Part 2. 1882. — From the Society. Dunsink (Dublin). — Astronomical Observations and Researclies made at Dunsink. 5th Part. 1884. — From the Observatory. Edinburgh. — Transactions of the Royal Scottish Society of Arts. Vol. X. Pt. 5. 1883. 8vo. Annual Reports of the Council of the Royal Scottish Academy of Painting, Sculpture, and Architecture. 1883-84. Highland and Agricultural Society of Scotland’s Transactions. 4th Series. Vols. XV. 1883. XVI. 1884. Transactions and Proceedings of the Botanical Society. Vols. XIV., XV. Part 1. 1884. 8vo. Transactions of the Edinburgh Geological Society. Vol. IV. Part 2. Session 1882. 8vo. Proceedings of tlie Edinburgh Mathematical^, Society. 2nd Sess, 1883-84. 8 VO. Journal of the Scottish Meteorological Society. With Tables for 1883. 3rd Series, No. 1. 1884. 8vo. Proceedings of the Royal Physical Society. Session 1881-82, 1882-83. 8vo. Historical Sketch of the Laws of the Royal College of Physicians of Edinburgh from its Institution to August 1882. 1882. 4to, Monthly and Quarterly Returns of the Births, Deaths, and Mar- riages registered in Scotland. July 1882 to December 1884. — From the Registrar-Genaral. Edinburgh Uuiversity Calendar for Sessions 1883-84, 1884-85. 8vo. Geological Survey of Scotland. One-Inch Scale — Maps of Kirk- cudbright (No. 5), of Dumfries and Kirkcudbright (No. 6), of VOL. XII. 3 X 986 Proceedings of the Boycd Society Kelso (No. 25), of Glasgow (No. 30), of Benliolm (N. 57a). Six-Inch Scale — Map of County of Linlithgow (No. 8), of Conntv of Perth (Nos. 133, 134, 135, 139, 140, 141, 142, 143). Hori- zontal Section of Scotland — Mnirkirk Coal Fields. Vertical Section of Scotland — Mnirkirk and Douglas Coal Fields. Vertical Section of Scotland — Entherglen and Carluke Coal Fields. Explanation of Sheet 31, embracing parts of Stirling- shire, Lanarkshire, and Linlithgowshire. Memoirs of the Geological Survey of Scotland. Explanation of Sheet 97. Ekatherinehourg. — Bulletin de la Societe Onralienne d’Amatenrs des Sciences Natnrelles. Tome VII. Livr. 3. 1882. (In Enssian and French.) Erlangen University. — Inaiigrfral Dissertations. 1883. Essex Institute ( U.S.). — See Salem. Fra7ikfurt-a-M. — Abhandlnngen herausgegeben von der Senckenberg- ischen Natnrforschenden Gessellschaft. Bd. XIII. 1883-84. 4to. Berichte liber die Senckenbergische Naturforschende Gesellschaft. Bde. fiir 1881-82, 1882-83. 8vo. Geneva. — Mernoires de la Societe de Physique et d’Histoire Naturelle de Geneve. Tome XXVIII. 1882-83. Genoa. — Annali del Mnseo Civico di Storia Natnrale. II Marchese G. Doria, Direttore. Vol. XIX.-XXI. 1883-84. 8vo. Glasgow. — Proceedings of the Philosophical Societv of Glasgow. Vols. XIV., XV. 1882-84. Transactions of the Geological Society of Glasgow. Vol. VII. 1883. 8 VO. University Catalogue of 6415 Stars for the Epoch 1870. 1884. 4to. ^ Giessen. — Berichte des Oberhess. Gesellschaft fiir Natur- und Heilkunde. 1883. 8vo. Gottingen. — Abhandlungen der Kdnigl. Gesellschaft der Wissenschaften. Bde. XXIX., XXX. 1882-83. Nachrichten von der K. Gesellschaft der Wissenschaften und der Georg- Augustus-Universtat, aus den Jahren 1882-83. 8vo. Mittheilungen des Naturwissenschaftlichen Vereines fiir Steier- mark. Jahrg. 1882-83. 8vo. Greenwich. — Spectroscopic and Photographic Eesults. 1882. (Eoyal Observatory, Greenwich). 4to. Astronomical, Magnetical, and Meteorological Observations, 1878, 1881, 1882. 4to. Haarlem. — Archives Neerlandaises des Sciences Exactes et Naturelles, publiees par la Societe Hollandaise de Harlem. Tomes XVIII., XIX. 1883-84. 8vo. — From the Society. Archives du Musee Teyler. Serie II. 1882-83. Teyler’s Tweede Genootschap. Neuwe Peeks I., II., and Atlas. Teyler’s Godgeleerd Genootschap. N. Serie, Elide Deel. 1883. Halifax. — Proceedings of the Yorkshire Geological and Polytechnic Society. Vol. VIII. 1884. 8vo. Proceedings and Transactions of the Nova Scotian Institute of Natural Science. Vol. VI. 1882-83. Halle. — Nova Acta Academiae Caesareae Leopoldino -Carolinae Germanicae Naturae Curiosorum. Tom. XLIV. 1883. Leopoldina, amtliches Organ der K. Leopold-Carolinisch-Deutschen Akademie der Naturforscher. Hft. XVIII. 1882. 4to. Abhandlungen der Natnrforschenden Gesellschaft. Bd. XVI. 1883-84. 4to. of Edinburgh, Session 1883-84. 987 Halle. — Bericlit iiber die Sitzungeii der Naturforsclieiiden Gesellscliaft. 1882-83. 8 VO. Helsingfors. — Acta Societatis Scientiarmn Femiicae. Tom. XII. 1883. Notiser ur Stdlskapets pro Fauna et Flora Feiinica Forhand- _ liiigar. Ny Serie. Hall't. 5. Ofversigt af Finska Vetenskaps-Societens Forliandlingar. Yols. XXIII., XXIV. 1881-82. 8vo. ^ Observations Meteorologiques, publiees par la Societe des Sciences de Finlande. Amies, 1880. 8vo. Bidrag til Kannedom af Finlands Natnr ocli Folk, utgifna af Finska Vetenskaps-Societeten. Hiift. 36. 1881. 8ro. Indian Government, Calcutta. — Records of the Geological Survey of India, Yols. XV.-XYII. 1882-83. Memoirs of the Geological Survey of India. Yols. XIX., XX. 1882-83. Palaeontologica Indica. Series X. Yol. II. Pt. 4. Camelopardalidge. Yol. III. Pt. 2. 1884. Series X. Yol. III. Pts. 1-5. Series XII. Vol. lY. Pt. 1 — Fossil Flora. Series XIII. Yol. I. Pt. 4 — Salt-range Fossils. Brachiopoda. Series XIY. Yol. L Pts. 3 and 4 — Fossil Echinoidea. 1884. 4to. The Indian Antic)[uary ; A Journal of Oriental Research. 1882-84. The Flora of British India. By Sir J. D. Hooker, M.D. Part IX. 1882. Account of the Operations of the Great Trignometrical Survey of India. Yols. VII., VIII., IX. 1882-83. 4to. Japan. — Transactions of the Seismological Societv. Yols. l.-YI. 1880- 83. Memoirs of the Science Department of the University of Tokio. Earthquake Measurement, by J. A. Ewing, F.R.S.E. Tokio, 1883. 4to. Jena. — Denkschriften der Medicinisch-Naturwissenschaftlichen Gesell- schaft ; — Band I. 2^® Abth. System der Acraspeden, mit Atlas, von Ernst Haeckel. Sitzungsberichte der Jenaischen Gesellschaft fiir Medicin und Naturwissenschaft fiir 1882-83. 8vo. Jenaische Zeitschrift fiir Naturwissenschaft, herausgeben von der Medicinish-Naturwissentchaftlichen Gesellschaft zu Jena. Bde. XYIL, XYIII. 1. 1883. 8ro. Kasan. — Isvestia i Ouchenui Sapiski Imperatorskago Kasanskago Uni- versiteta. 1881-83. 8vo. Kew. — Kew Obseiwatory Report for 1882. 8vo. Kiel. — Yierter Bericht der Commission zur Wissenschaftlichen Unter- suchung der deutschen Meere fiir die Jahre 1877, bis 1881. Abtheil 1-3. Fob Schriften, der Universitat zu Kiel. Bde. X. 1881. 4to. Inaugural University Dissertations. 1882, 1883. Lausanne. — Bulletin de la Society Yaudoise des Sciences Naturelles. 2