.-'t- PROCEEDINGS OF THE ROYAL SOCIETY EDINBURGH. YOL. XVIII. EDINBURGH: PRINTED BY NEILL AND COMPANY. MDCCCXCII. CONTENTS. Election of Office-Bearers at the General Statutory Meeting, Monday, Nov. 24, 1890, ....... Chairman’s Opening Address, ..... On the Occurrence of Sulphur in Marine Muds and Nodules, and its hearing on their Mode of Formation. By J. Y. Buchanan, F.R.S., ........ On a Simple Pocket Dust-Counter. By John Aitken, F.R.S. (With a Plate), ....... On the Action of Metallic (and other) Salts on Carbonate of Lime. By Robert Irvine, F.C.S., and W. S. Anderson, . Manganese Deposits in Marine Muds. By Robert Irvine, F.C.S., and John Gibson, Ph.D., .... On a Difference between the Diurnal Barometric Curves at Green- wich and at Kew. By Alexander Buchan, LL.D., Barographic Record in the Vicinity of a Tornado. By John Anderson. Communicated by Dr Buchan. (With a Plate), Note on Potassium Persulphate. By Hugh Marshall, D.Sc., On the Soaring of Birds : being a Communication from Mr R. E. Froude in continuation of the Extract from a Letter by the late Mr William Froude to Sir William Thomson, published in these “ Proceedings,” Match 19, 1888, . On some hitherto unproved Theorems in Determinants. By Thomas Muir, LL.D., ...... rjpn yn Equation of the Glissette of the Two-term Oval — +r^=l, and Cognate Curves. By the Hon. Lord McLaren, . The Influence of High Winds on the Barometer at the Ben Nevis Observatory. By Alexander Buchan, LL.D., Electrolytic Synthesis of Dibasic Acids. Alkyl Derivatives of Succinic Acid. By Professor Crum Brown and Dr James Walker, ........ PAGE 1 2 IV 39 52 54 59 62 63 65 73 83 88 95 iv Contents. Proposed Extension of the Powers of Quaternion Differentiation. By Alexander M‘Aulay, Ormond College, Melbourne. Com- municated by Professor Tait, ..... On the Interaction of Longitudinal and Circular Magnetisations in Iron and Nickel Wires. (Second Note.) By Professor Cargill G. Knott, ...... On the Composition of some Deep-Sea Deposits from the Medi- terranean. By J. Y. Buchanan, F.B.S., .... On the Temperature of the Salt and Fresh Water Lochs of the West of Scotland, at Different Depths and Seasons, during the Years 1887 and 1888. By John Murray, LL.D., Ph.D., On Silica and the Siliceous Remains of Organisms in Modern Seas. By John Murray, LL.D., Ph.D., &c., and Robert Irvine, F.C.S., A New Method for the Estimating the Specific Gravity of the Blood. By John Berry Hay craft, M.D., D.Sc., . On the Estimation of Uric Acid in the Urine. A Reply to Criticisms upon the Silver Method. By John Berry Hay craft, M.D., D.Sc., . On a Method of Observing and Counting the Number of Water Particles in a Fog. By John Aitken, F.R.S., On an Optical Proof of the Existence of Suspended Matter in Flames. By Sir G. G. Stokes, Bart., F.R.S. (In a letter to Professor Tait), ....... Note on the Isothermals of Ethyl Oxide. By Professor Tait, Additional Observations on the Development and Life-Histories of the Marine Food-Fishes, and the Distribution of their Ova. By Professor W. C. M‘Intosh, F.R.S., .... A Case of Defective Endochondral Ossification in a Human Foetus (so-called Cretinoid). By Johnson Symington, M.D., and Henry Alexis Thomson, M.D. (With Three Plates), On the Blood of the Invertebrata. By Dr A. B. Griffiths, F.R.S.E., F.C.S., &c., A New Ship for the Study of the Sea. By His Serene Highness the Prince of Monaco, ...... The Electric Resistance of Cobalt at High Temperatures. By Professor Cargill G. Knott, D.Sc., F.R.S.E. (With a Diagram), The Thermoelectric Positions of Cobalt and Bismuth. By Pro- fessor Cargill G. Knott, D.Sc., F.R.S.E., .... PAGE 98 124 131 139 229 251 255 259 263 265 268 271 288 295 303 310 Contents. v Oil the Effect of Longitudinal Magnetisation on the Interior Volume of Iron and Nickel Tubes. By Professor Cargill G. Knott, D.Sc., F.B.S.E., ...... On some Relations between Magnetism and Twist. Parts II., III. By Professor Cargill G. Knott, D.Sc., F.R.S.E., . On the Gravimetric Composition of Water. A Preliminary Com- munication. By Professor W. Dittmar, F.R.S., . Investigation of the Action of Nicol’s Polarising Eye-Piece. By Edward Sang, LL.D. (With a Plate), . Note on Dr Sang’s Paper. By Professor Tait, On the Extension of Brouncker’s Method to the Comparison of several Magnitudes. By Edward Sang, LL.D., . Meetings of the Royal Society — Session 1890-91, . Donations to the Library, ...... Obituaky Notices, ...... i- Tndex, ....... PAGE 315 318 320 323 337 341 349 357 -xxiii xxv PROCEEDINGS OF THE BOYAL SOCIETY OF EDINBURGH, vol. xviii. 1890-91. The 108th Session. GENERAL STATUTORY MEETING. Monday , 24 th November 1890. The following Council were elected: — • President. Sir DOUGLAS MACLAGAN, M.D., F.R.C.P.E. Vice-Presidents. The Hon. Lord Maclaren, LL.D. ] Professor Chrystal, LL.D. F.R.A.S. I Thomas Muir, Esq., LL.D. Rev. Professor Flint, D.D. I Sir Arthur Mitchell, K.C.B., LL.D. A. Forbes Irvine, Esq. of Drum, LL.D. General Secretary— Professor Tait. Secretaries to Ordinary Meetings. Professor Sir W. Turner, LL.D., D.C.L., 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., LL.D. Professor Isaac B. Balfour, F.R.S. Professor Ewing, F.R.S. Professor Jack, LL.D. Professor James Geikie, LL.D. F.R.S. Professor W. H. Perkin, D.Sc., F.R.S. A. Beatson Bell, Esq., Advocate. Hon. Lord Kingsburgh, C.B., LL.D., F.R.S. John Murray, Esq., LL.D. Alexander Bruce, M.A., M.D. Dr R. H. Traquair, F.R.S. Dr Byrom Bramwell, F.R.C.P.E. Professor Copeland, Astronomer- Royal for Scotland. Ordinary Members of Council. The Rt. 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.G., K.T., LL.D., D.C.L. The Right Hon. LORD MONCREIFF of Tulliebole, LL.D. Sir WILLIAM THOMSON, LL.D., D.C.L., P.R.S., Foreign Associate of the Institute of France. VOL. XVIII. 31/12/90 A 2 Proceedings of Eoyal Society of Edinburgh. Professor Sir DOUGLAS MACLAGAN, President, in the Chair. Chairman’s Opening Address. (Read December 1, 1890.) My duty this evening is to give the usual Introductory Address at the opening of a new Session, this which commences this evening being the Society’s 108th. Before doing so, however, I must try to disburden myself of a weight which has hung heavy upon me for the last few days, and consists in the difficulty, which I find to he insuperable, how to select adequate terms in which to express my sense of the honour which you have conferred upon me, in placing me in the position of your President. In my wildest dreams it never occurred to me that such an event was possible, till a short while ago when certain members of the Council hinted to me that such a step was in contemplation ; and I can assure you that it was not without con- siderable hesitation that I acceded to the request that I should allow myself to be put in nomination. You will, I trust, believe me, when I say that this hesitation in no way arose from any want of appreciation on my part of the greatness of the honour to he conferred on me. It was exactly the contrary. What I felt, and do feel, is not for myself, hut for the Royal Society. I knew that my life has been little else than that of a practitioner and teacher of medicine. However constantly I have watched with interest the progress of Science in its various departments, my studies and any little work which I have done have been chiefly with the object of keeping myself au courant du jour for the purpose of teaching; and as regards her real work I have been to Science, in Horatian phrase, cultor yarcus et infrequens. I feared, therefore, that the Royal Society might suffer in its prestige by its appearing to the outer world as if it had no man of scientific repute to fill its Chair. I know, of course, that this is not the case, that there are men among you who by their published works have made for themselves a reputa- tion that would have truly justified their elevation to the President- ship. It did not escape the notice of the Council, and it must have occurred to all of you, that the man who stood out as the 1890-91.] Chairmans Opening Address. 3 worthiest successor to Sir William Thomson was our indefatigable General Secretary. But Professor Tait, with that appetite for work which does not know the meaning of satiety, thought that he could be of more use to the Society in his present office than in the more dignified position of your President, and thus he sacrificed that distinction, which might be a legitimate object of ambition to any man, for the general good of us all. The Bellows of the Society will not fail to appreciate this act of self-sacrifice on his part ; and will not for a moment fancy that I have less sense of the honour I now enjoy, because Professor Tait had not seen fit to accept of it. Our learned Vice-President, Lord McLaren, who in July last occupied this Chair at the closing meeting of the preceding Session, adverted to the loss the Society had sustained since the commence- ment of the Session, by the removal by death of ten of its Ordinary, and one of its Honorary, Bellows ; and he mentioned in the case of several of them a few of the incidents in their respective careers by which they had made themselves honourably known. Since that address was delivered eight more of our Ordinary Bellows have died, and I wish to be allowed now briefly to say a few words regarding each of them. Dr James Stark, who joined the Eoyal Society in 1850, was born in Edinburgh in 1811. He was the son of Mr John Stark, Printer, also a Bellow, and a zealous cultivator of Natural History. James Stark studied for the medical profession at the University of Edinburgh, and took the degree of M.D. in 1833. His Thesis on that occasion was on the way in which the colours of substances affected the absorption by them of odours to which they were exposed. His experiments led him to the conclusion that odours were most readily absorbed by dark surfaces ; and he conjectured that perhaps contagious emanations followed a similar law, which led him to the somewhat wide induction that the established dress of the physician, the “ customary suits of solemn black,” were the worst adapted for his profession. Dr James Stark is most to be remembered as a pioneer in Scot- land in the cultivation of that important and fundamental branch of Sanitary Science, Vital Statistics. In 1854, shortly after the office of the Registrar-General for Scotland was established, he 4 Proceedings of Royal Society of Edinburgh. [sess. was appointed to be Superintendent of Statistics ; and, in fact, be organised that valuable department of the public service. He wrote much upon the subject of Vital Statistics. In 1846 he gave an interesting report on the mortality of Edin- burgh and Leith; and in 1847 published an inquiry into the sanitary state of Edinburgh, and the rate of its mortality since 1780 ; and in 1851 he published his Vital Statistics of Scotland. He was also a contributor to the Transactions of the Royal Society. Ho doubt his writings are now very much superseded by the subse- quent works of such authors as Earre, Simon, Newsholme, and many others, but it behooves us not to forget one who led the way in our country, when Sanitary Science had not attained its present develop- ment and its strong interest for the public mind. Ecclesiastically he was a warm and thorough adherent of the late Rev. Dr Robert Lee, and was an elder in Old Greyfriars Church. From long-continued and depressing bad health Dr Stark retired from official duty in 1873. He thereafter lived quite in retirement, and died at Nairn on 2nd July 1890. The Rev. James Grant, D.D., died at Edinburgh on 28th July last, in the ninety-first year of his age. Dr Grant was long a notable personality in Edinburgh. He was a son of the manse, having been born in January 1800 at Portmoakin Kinross-shire, of which parish his father was minister. The elder Dr Grant was afterwards one of the clergy of St Andrew’s Church, Edinburgh, and was Moderator of the General Assembly in 1809. James Grant received his earlier education in the school of his native parish. He was afterwards a pupil of the High School of Edinburgh, subsequently went to the University, and having passed through the Arts curriculum entered the Divinity Hall, and in due time was licensed. He was, in those days of patronage, appointed in 1824 to the first charge of South Leith, he being then only twenty-four years of age. In this charge he remained till 1843, when he was appointed to the parish of St Mary’s in Edinburgh, and there he remained till he resigned in 1871. He was perhaps hardly what could be called a popular preacher in the usual acceptation of that expression, but his services were always listened to with much acceptance, because his sermons, like every- thing which he wrote or spoke, were characterised by great elegance of diction and clearness of utterance. Ho man in Edinburgh could 1890-91.] Chairman's Opening Address. 5 excel, and few equal, Dr Grant in the often troublesome task of proposing or replying to a toast, and consequently he was often called on to perform such duties. A notable instance of this lives in the memory of the present writer. It was on the occasion of a dinner to Professor Syme, when, in the unexpected absence of some- one who had undertaken the duty, Dr Grant was abruptly called on to propose the toast of the Royal Infirmary, which he did in such appropriate and elegant terms that his was decidedly voted to he the speech of the evening. Besides being an earnest parish minister, and a zealous promoter of education and of all measures for improving the condition of the poor, Dr Grant took a prominent part, and had great influence, in the Councils of the Church of Scotland. Though always ready to co-operate in matters of philanthropy with the brethren of other denominations, his strong ecclesiastical conservatism led him to become a powerful opponent of those of whose Church politics he did not approve. In the stormy predisruption times, which culmin- ated in the great secession of 1843, Dr Grant was generally to be found in the front of the battle. He sympathised with the Presby- tery of Strathbogie, who set at defiance the injunctions of the General Assembly, and was along with others put under discipline ; but the chief result of this was his receiving an address from the Town Council of Leith, which was signed by many, it is said by thousands, of members of the Church of Scotland, approving of his action. That he retained the esteem of the Church was evidenced in 1854 when he received, as his father had in 1809, the highest ecclesiastical distinction which could be conferred on him, in his elevation to the Moderatorship of the General Assembly. Dr Grant received the degree of D.D. from the Presbytery of Glasgow, and in the year of his Moderatorship Oxford bestowed on him the distinction of D.C.L. Dr Grant became a Fellow of the Royal Society in 1851. He is to be reckoned as having belonged to the class of literary Fellows, but he was for long a regular attender at the meetings when scien- tific subjects were under discussion; and when from his advanced age it became unsuitable for him to go out in the evening, he even during his last year made his appearance at the Extraordinary Meetings which took place in the afternoon. 6 Proceedings of Royal Society of Edinburgh. [sess. Dr Grant held numerous appointments of a clerical nature. He was a member of the Ecclesiastical Commission of Edinburgh, and was its Chairman up to about six months before his death. He was in 1841 appointed Chaplain to the Highland Society, and retained that office to the last. He was an Honorary Member of the Harveian Society of Edinburgh, and was its Chaplain for fifty- five years, having been appointed in 1844. In 1888, at the 106th Festival, the Society revived the title of Pontifex Maximus , which had been in abeyance since the time of Dr Grant’s predecessor the Rev. Dr Moodie, and conferred it on its venerable Chaplain, who had but rarely missed a meeting during his long incumbency. Dr Grant was a genial man, though with a dry manner, and was much respected and esteemed by all who knew him. By the death of Dr James Matthews Duncan, British Medicine, especially in the departments of Obstetrics and Gynaecology, lost one of its foremost men, and a blank has been left in the ranks of the profession which will not easily be filled up. Dr Matthews Duncan was born in Aberdeen in 1826, and in that city he received his early as well as his academic education. He graduated there as M.A. in 1843, and in 1846 he took the degree of M.D. He subsequently studied Medicine in Edinburgh, bestowing special attention on the subject of Midwifery ; and thereafter he went to Paris in pursuit of further knowledge in his own special department. He was for some time a private assistant to Sir James Young Simpson, but unhappily a quarrel arose between these two distinguished men, which led to their alienation. Duncan there- after settled in practice in Edinburgh, becoming a Fellow of the Royal College of Physicians in 1851, and two years afterwards he commenced to deliver lectures on Midwifery and the Diseases of Women and Children, which, although at first kept in the shade by the renown and name of Simpson, soon began to show enough of brilliancy to attract an earnest though not large class of students. His reputation among his professional brethren, and subsequently with the public, led to his acquiring a large and important practice ; and on the illness and subsequent death of Simpson, he unques- tionably stood at the head of the Obstetric Physicians of Edin- burgh. This naturally led, when Simpson died, to the general belief that he would succeed him in his chair ; but the fact of 1890-91.] Chairman's Opening Address. 7 his having quarrelled with Simpson had a heavy, and in many respects unjust, effect on his prospects, and he was not appointed. His failure, however, had no discouraging effect upon him, and he went on bravely and with ever-increasing success with his practice and his teaching. In 1877 he was offered and accepted the appointment of Teacher of Midwifery in, and Obstetric Physician to, St Bartholomew’s Hospital, and he accordingly removed to London, to the widespread, we may say universal, regret of his brethren not only in Edinburgh but throughout Scotland. The reputation which led to his call to London was founded, and that justly, on the number, practical value, and, above all, the scientific character of his writings. Numerous honours were bestowed upon him. He became a Fellow of the Royal College of Physicians of London ; a Fellow of the Royal Societies of London and Edinburgh; LL.D. of Edinburgh and Cambridge; and an Honorary M.D. of the University of Dublin. In London lie soon acquired a very large practice, having gained the confidence and esteem of the profession and the public in the English, as he had done in the Scottish, metropolis. Duncan’s writings were numerous and important, and all partook of that scientific character which was apparent in all that he did, both as an author and practitioner. Many of them were purely practical, and chiefly concern those who are engaged in the same line of practice. Beyond this large circle he is best known by his Treatises on Fecundity, Fertility, and Sterility, which have an interest not only to the practitioner but to the statistician and political economist. What was the source of Matthews Duncan’s marked professional success ? It was the genuineness of his character, personal and professional. Assuredly it was from no blandishments in his hearing or demeanour, for though a perfect gentleman in the truest sense of the word, he was, as the Countess of Rousillon says in “All’s well that ends well,” “an unseason’d courtier.” There was a certain dryness and abruptness in his manner which at first repelled some people, hut a short knowledge of him, whether as patient or casual acquaintance, showed that under this somewhat dry shell there was a soft kernel of kindness and true courtesy which made him trusted, relied on, and beloved. It was all founded 8 Proceedings of Royal Society of Edinburgh. [sess. on his genuine sterling worth, so that he fully merited the encomium of the aforesaid Countess : — “His skill was almost as great as his honesty, and had it stretched so far, would have made Nature immortal, and death should have play for lack of work.” Duncan had a naturally robust constitution, hut it was observed by his friends for some months before his death that his health was seriously impaired, and a general feeling was entertained that his unwearied devotion to work was at the root of this. He abandoned teaching and professional duty, and went for a short and thorough rest to Belgium, and subsequently to Baden-Baden, where he had a severe attack of angina pectoris, from which how- ever he rallied, and had made arrangements for his return home when he died suddenly on 1st September last. He left behind him his amiable lady, and a family of five sons and four daughters. James Matthews Duncan will long be remembered by his pro- fessional brethren, and those who benefited by his skill, as a true- hearted friend and adviser, an unobtrusively pious Christian, and a genuine sample of that honest man who is the noblest work of God. David Milne Home of Milne-Graden was born in 1805. His father was Admiral Sir David Milne, his brother being Admiral of the Fleet Sir Alexander Milne. He assumed the surname of Home on his marriage in 1832 with Miss Home of Paxton, in Berwickshire. He devoted himself to the study of Law, entered the Faculty of Advocates in 1826, and at the time of his death was the second oldest member of that learned body. In 1844 he was Senior Advocate-Depute, but did not continue to practise at the bar after he succeeded to the family estates. He betook himself to country life, but did not confine himself to the management and enjoyment of his property, but devoted himself to Science, for which he had manifested a strong inclination from his boyhood. He became a Fellow of the Royal Society of Edinburgh in 1828, and was for a long time a Vice-President and active member of the Council. He was Vice-President of the Royal Scottish Geographical Society, the Meteorological Society of Scotland, and the Geological Society of Scotland, of which he was elected President in 1874. This office he held at the period of his death. In 1870 the University of Edinburgh, in consideration of his scientific attainments, conferred on him the degree of LL.D. 1890-91.] Chairman's Opening Address. 9 His favourite departments of Science were Meteorology and more especially Geology, for although his first published paper was an essay on Comets, it is by his geological writings that he is best known. Our Transactions bear abundant evidence of his activity and industry as a geologist. In the 14th volume is to be found a series of papers “On the Mid-Lothian and East Lothian Coalfields,” which attracted much attention at the time; and in that same volume there are two other papers, one on the “ Depletion or Drying- up of the Rivers Teviot, JSTith, and Clyde,” the other on “Two Storms which Swept over the British Islands,” both of which events occurred in November 1838. In the 15th volume of our Transactions appeared an account of the “ Geology of Roxburghshire ; ” and in the 16th volume a paper “ On the Parallel Roads of Lochaber,” which is doubly interesting as being of a controversial nature, his antagonist being so redoubtable a scientific warrior as Charles Darwin, who, however, with the courtesy of a true knight, subsequently acknowledged him- self to have been worsted in the encounter. To the 25th volume of the Transactions , published in 1869, Milne Home contributed a paper “On the Origin of the Boulder Clay.” This subject had always a special interest for him, and a goodly boulder anywhere excited in him an enthusiasm which neither advanced age nor failing health could check. He was appointed by the Society Convener of the Boulder Committee which was estab- lished in 1871 ; and under his supervision the Committee published ten valuable Reports, which are contained in the Society’s Proceed- ings. These are only part of Mr Milne Home’s contributions to Science. He was the author of many other papers both within and without the domain of Geology, and of two books, one on the “Estuary of the Firth of Forth and Adjoining Districts viewed Geologically,” and the other on “Ancient Water-lines.” Mr Milne Home had within the last two years a severe and pro- tracted illness, which carried him off on the 19th September 1890. He leaves us an admirable example of what may be done for Science by a country gentleman possessed of means and leisure, but animated by the laudable ambition to extend the knowledge of his fellow- men. The Hon. Lord Lee (Robert Lee) was born in 1830, and was a son of the Rev. John Lee, D.D., Principal of the University of 10 Proceedings of Royal Society of Edinburgh. [sess. Edinburgh. He devoted himself to the study of Law, and be&ame a Member of the Faculty of Advocates in 1853. He had a fair, but not what is regarded as a large, practice at the Ear ; but he was noted for his earnest devotion to his duties both as Barrister and subsequently as a Judge. He was made an Advocate-Depute in 1867, and held that office till he was appointed Sheriff of Stirling and Dumbarton in 1875, from which he was transferred to the more important Sheriffship of Perthshire. He was for many years Procurator of the Church of Scotland, and performed the duties of that legal office with much earnestness and general acceptance. He was raised to the Bench in 1880. He formed his opinions slowly, deliberately, and conscientiously, and was very tenacious of them when once formed, his firmness in this respect being by some cynical people called obstinacy. His leading characteristics were his earnestness of purpose, and his unwearied patience. He became a Fellow of the Royal Society in 1872, but did not take any special part in its proceedings. In private life he was much esteemed, and had a considerable fund of genuine humour. Robert Lee was for a long time in delicate health, suffering for many years from bronchial asthma. He had been enjoying in Ireland a holiday, which he had intended extending to St Andrews, but a sharp inflammatory attack came on, and proved fatal on 11th October 1890. He left a widow, daughter of the late Dr Borthwick of Edinburgh, and a family of three sons and three daughters. Mr David Grieve was educated at the University of Edinburgh, and became a solicitor-at-law. He subsequently entered H.M. Customs, and was collector at Banff, Great Grimsby, and Dover. He took much interest in .Natural Science, particularly in Geology and Anthropology. He made a large collection of fossils. He was several times President of the Royal Physical Society, and was elected a Fellow of this Society in 1872. He died in June of last year. As Medical Science sustained a great loss in Matthews Duncan, so did Classical Literature in the person of Professor William Young Sellar. There was a considerable parallelism between the two men in their earnest devotion to work, in their clearness of judgment, and, above all, in their contempt for everything that was not in accordance with the highest ethical standards. Professor Sellar was the son of the late Mr Patrick Sellar, and was 1890-91.] Chairman’s Opening Address. 11 born at Morvich, in Sutherlandshire, in 1825. From his earliest years he was a classical scholar. His earlier education was got at the Edinburgh Academy under Archdeacon Williams. He went to Glasgow University at the early age of fourteen, carrying with him from the Academy so much of classical lore as to lead him to go at once into the Senior University Classes, whence he came forth with highest honours in Greek and Latin, and much distinction in the other classes. He was elected to a scholarship at Balliol College, Oxford, in 1843. In 1847 he obtained first-class honours in Literce humaniores , and in 1850 was made a Fellow of Oriel. He had for contemporaries a brilliant assemblage of men more or less connected with Scotland, two of them, Shairp and Grant, subsequently becoming Principals of Scottish Universities. After acting as Assistant to the Professor of Humanity in Glasgow, and to the Professor of Greek in St Andrews, he was in 1859 elected to the Greek Chair in the latter University, and from this he was transferred to the Latin Chair in Edinburgh in 1863. Honours flowed in upon him. He received the degree of LL.D. both from St Andrews and Dublin, and was admitted to the membership of the Athenaeum Club, without ballot, “ as being of distinguished eminence in literature.” Though his first published writing was an article on Thucydides, which appeared in the Oxford Essays, the works by which he is best known, and for which he is everywhere appreciated, were in con- nection with Latin literature. His volumes on the “ Roman Poets of the Republic,” and the “ Roman Poets of the Augustan Age,” hold a foremost place in modern classical literature, have passed through several editions, and are valued by all scholars, British and Con- tinental. His teaching as a professor, though his minute scholarship was profound, was characterised by great breadth ; and he imparted to his students a large share of that with which he was himself imbued, the insight which the study of the Roman poets gives into the political, social, and moral characteristics of the Romans. He had been working for some time at a new volume of the Roman poets, which would embrace studies of Horace, Ovid, Propertius, Tibullus, and Martial, and which a few weeks more of work would have completed. But unhappily this was not to be, for an unexpected attack of hepatic disease proved fatal to him at his country residence in Kirkcudbrightshire on 12th October. It is to 12 Proceedings of Royal Society of Edinburgh. be hoped that a volume so far advanced may see the light, as it will assuredly give to the world another brilliant picture of Roman life, though wanting the finishing touches of the master. By the death of Sellar classical literature has sustained a severe loss, the University of Edinburgh has a Chair vacant, which he had ably filled for twenty-seven years, and his colleagues and all who knew him have to mourn their bereavement of a genial friend and accomplished gentleman. Mr Alexander Yule Fraser was born near Perth. He was edu- cated at the University of Aberdeen, where he distinguished himself specially in the departments of Mathematics and Physics, though he did not neglect the other subjects of the Arts course. After graduating with first-class honours in Mathematics and Physics, he was appointed second mathematical master in George Watson’s College, Edinburgh. When George Heriot’s Hospital was opened as a day-school, Mr Fraser was entrusted with the charge of the Mathematical and Physical Departments ; and it is not too much to say that not a little of the success of this school is due to the energy with which he threw himself into the work of his department. He spared no pains in providing for the due equipment of the Physical Laboratory, and in preparing courses of Practical Geometry and 'Experimental Physics suitable for boys. Just a little over a year ago, Mr Eraser was appointed Headmaster of Allan Glen’s Institution, Glasgow, one of the most important technical schools in the country • and it was hoped that he would now have an opportunity of displaying to the full his special qualifications for a post of this nature. But he had been at work little more than two months when he was attacked with pleurisy and threatened consumption, and felt compelled to tender his resignation. The governors of the school, however, were so much impressed with the value of his work that they declined to accept his resignation, and granted him instead nine months’ leave of absence, in the hope that a change of climate, and a complete rest for this period, would restore him to health. In search of health Mr Fraser visited South Africa, where he resided for several months. About three months ago he returned to this country, and resumed his duties at the beginning of the present Session. He soon found, however, that his health was again giving way, and he had to resign his position 1890-91.] Chairman's Opening Address. 13 finally. He had made up his mind to return to South Africa with the purpose of residing there permanently, when he caught a chill, which led to acute inflammation ; and to this he succumbed on the 9th of November last, at the early age of thirty- three. One of the objects that absorbed a very large amount of Mr Fraser’s attention during the last eight years of his life was the Edinburgh Mathematical Society. This Society may be said to owe its existence mainly to him. The idea of starting such a Society- originated with him ; and as its Secretary during the first four or five years of its existence, he had all the trouble connected with the arrangements necessary to put such an institution upon a firm basis. This Society is now in its 9th Session, has about 150 members, and publishes a volume of Proceedings annually. Mr Fraser has made contributions to nearly every volume of the Proceedings. A subject that interested him from the time of his student days was the history of the controversy on the foundations of the Differential Calculus. Till within three weeks of his death he 'had hoped to he able to give an address to the Mathematical Society on this subject at the meeting held on the 14th of November. It is still hoped that it may he possible to put the notes he left on this subject into a form that will prove useful. Mr Fraser also contributed several articles to the edition of Chambers's Encyclopaedia which is now being issued. The mathematicians that interested him most were De Morgan and Clifford. Of Clifford’s hook On the Common Sense of the Exact Sciences , he wrote a review which appeared in the pages of the Academy. In poetry Mr Fraser had a great fondness for the works of Matthew Arnold. Mr Fraser was remarkable, among other things, for the activity of his intellect, an intellect that could never he idle ; and for the energy with which he devoted himself to any work he undertook. His friends always found a talk with him to have a stimulating effect, and many will find in the future want of this stimulus a loss which it will not he easy to make good. I had intended to have said a few words to the Society, chiefly by way of contrast, regarding the various distinguished men who have occupied this Chair since its foundation in 1783, but I have already too much tried your patience, and have exceeded the time which I had assigned to myself for the delivery of this address. 14 Proceedings of Royal Society of Edinburgh. [sess. I wish to allude to only two of the previous Presidents of the Society. I need not say that when I mention the name of Sir Walter Scott, I am not presumptuous enough to make any remarks about him at any time or anywhere, but especially here, and on Scottish ground. I merely desire to state to you an interesting circumstance which is perhaps new to most of you, and which does not appear in that interesting Journal which has been so ably edited and pub- lished by Mr David Douglas of this city. It is that the Council has recently made a valuable addition to the Society’s collection of manuscripts by securing a holograph letter of Sir Walter’s, in which ho tenders his resignation of the Presidency of the Society. It appears that in the latter part of the year 1830, Sir Walter, with the view of residing constantly at Abbotsford, contemplated renouncing all associations which would detain him in Edinburgh. In a letter to his friend, Mr James Skene, dated Abbotsford, 18th September 1830, he says : — “ It is time to think what is to be done about the Eoyal Society, as the time of my retirement draws nigh, Qnd I am determined at whatever loss not to drag out the last sands of my life in that sand cart of a place the Parliament House. This is, however, a subject for future consideration, as I have not breathed a syllable about resigning the Chair to anyone, but it must soon follow as matter of course.” On the 18th of the following month he wrote the letter to which I have referred as having now come into the possession of the Society. It is as follows : — “ I have the honour to acquaint you for the information of the Eoyal Society, its Council, and Members, that being conscious of the entire want of that scientific knowledge which would be the most fit qualification for supporting f the honour of their body, I have hitherto endeavoured to show my sense of the distinguished honour of President to which their pleasure has raised me by regular atten- dance upon the meetings of the Society and duties of the office. As I am now retired from Edinburgh to live almost entirely at this place, which must necessarily prevent my discharging the efficient duty of President of the Society, and prevent almost entirely my 1890-91.] Chairman’s Opening Address. 15 present attendance, I think it due to the Royal Society to resign the high honour which they have conferred on me with heartfelt thanks and best wishes for the prosperity of the Institution, “ I remain with sincere regard, “ Sir, “ Your most obedient Servant, “Walter Scott.” “Abbotsford, 18 th October 1830.” “ John Robison, Esq., Secretary to the “ Royal Society of Edinburgh.” This letter was submitted to the Council at a meeting held on the 8th of November 1830. The following is the minute regarding it : — “ Read a letter from Sir Walter Scott intimating his intention of residing in the country, and proposing on that account that he should cease to hold the office of President of the Society. “ The Council having considered his letter were unanimously of opinion, that although they could not under the circumstances hope to have the benefit of Sir Walter Scott’s frequent presence amongst them, yet that it was very desirable for the interests and reputation of the Society that he should still continue at their head. The meeting therefore instructed the Secretary to write on their behalf to Sir Walter Scott, and to request that he would again permit them to propose his name as on former occasions of election.” In consequence of his resignation not being accepted, Sir Walter continued to be President till his death. The other President whom I desire to name is the distinguished gentleman who has been my immediate predecessor. Of Sir William Thomson, who held the post of President for the full term of five years (1873-1878), and who has now, at his own request, been per- mitted to retire before the completion of a second term of office, it is perhaps sufficient to say that he leaves our Chair only in order that he may be enabled to assume the corresponding post in the Royal Society, London. His position is practically unique, for, while second to none in the rajaks of pure Science, he is absolutely without a concurrent in 16 Proceedings of Royal Society of Edinburgh. [sess. the technical applications of some of its most recondite principles, The grandest works of the engineer are usually based on very simple scientific elements, and his skill is shown mainly in new and bold combinations of familiar properties. Thomson has done much splendid work in this direction also — witness his galvanometers and electrometers, his siphon-recorder, and his harmonic analyser. But it will never be forgotten that it was he who so applied the profound analysis of Fourier as to render rapid signalling possible through a submarine cable — thus making ocean telegraphy a mer- cantile success — so that we owe to him one of the grandest safe- guards of our empire, our practically instantaneous communication with our most distant and isolated colonies. You have already at your election meeting expressed and recorded your thanks to Sir William Thomson for his conduct as our President. You will, I am sure, with unanimity and cordiality, express your wishes for his comfort and success in the sphere of distinction and duty to which he has been called. Three Prizes were awarded during the past Session. The Gunning Victoria Jubilee Prize for 1887-90 was presented to Professor Tait for his work in connection with the “ Challenger Expedition,” and his other researches in Physical Science. His contributions to Physical Science are too numerous for me to enumerate ; but in reference to his “ Challenger ” work I may call attention to the ingenuity with which he has determined the physical properties of sea water, such as compressibility, thermal expansivity, and its temperature of maximum density for any given pressure. He has also included in his investigation the compres- sibilities of glass. The Keith Prize for 1887-89 was presented to Professor Letts for his researches into the “ Organic Compounds of Phosphorus.” The work was difficult, and the results are of great importance. The special interest of the investigations depends on the remarkable similarities, and equally remarkable dissimilarities, shown by the corresponding compounds of phosphorus, nitrogen, and sulphur. These researches have been published in our Transactions. The Neill Prize for 1886-89 was presented to Mr Kobert Kidston for his “ Eesearches in Fossil Botany.” He has devoted himself to the 1890-91.] Chairman’s Opening Address. 17 study of Palseophytology, and has sought to determine the affinities of palaeozoic genera and species with those of existing forms. With this view he has described the fructification of a number of carboni- ferous ferns and lycopods. He has compared the plant remains of several British coalfields with each other, and with those of the coalfields of other countries. The most important results of his investigations have appeared in our Transactions. On the Occurrence of Sulphur in Marine Muds and Nodules, and its bearing on their Mode of Forma- tion. By J. Y. Buchanan, Esq., F.R.S. (Read December 1, 1890.) In the first section of the cruise of the “ Challenger,” that from Tenerife to Sombrero, the existence was established of deep-sea muds, perfectly free from carbonate of lime, consisting mainly of silicates mixed with ochreous material, principally hydrated oxides of iron and manganese, and of local concentrations of these materials in the form of nodules and of coatings or incrustations on dead calcareous matter. The qualitative composition of these concentra- tions was carefully determined, and it was particularly noted that whether in the form of nodules or of incrustations they were aggre- gations of the general materials of the bottom, and not concretions or coatings of pure hydrous oxides. On the section between Bermuda and the Azores some very suggestive specimens were got from the bottom on 27th June 1873, when the ship dredged in 1675 fathoms in lat. 38° 18' N., long. 34° 48' W. A number of light-coloured concretions were brought up which were much perforated by worm-holes, the walls of which were all stained blackish brown. The substance of the concretions consisted of carbonate of lime and silicates, and the black lining of the holes was peroxide of manganese. The various specimens obtained on this occasion showed the deposition of oxide of man- ganese in various stages, from those which showed only specks or stains to those containing a considerable percentage.* The most remarkable fact, however, was the close association of the oxide of manganese, especially at its first appearance, with the work of * They are described in my report, Proc. Roy. Soc., 1876, vol. xxiv. p. 606. VOL. XVIII. 31/12/90 B 18 Proceedings of Royal Society of Edinburgh. [sess. annelids, and this produced a strong conviction that the occurrence of peroxide of manganese at the bottom of the sea depended in some way or other on the organic life existing there. After this comparatively little manganese was met with, until, on approaching the south coast of Australia, a large haul was obtained from a depth of 2600 fathoms in lat. 42° 42' S., long. 134° 10' E. and throughout the whole of the Pacific, when the trawl was put over in water sufficiently deep and sufficiently far from land, it rarely failed to collect abundance of manganese nodules, of all shapes and sizes, and surrounding all kinds of nuclei. Concretions also were obtained from time to time, recalling those of the North Atlantic above referred to. Thus, on the plateau of the Kermadec Islands, large lumps of a tufaceous sandstone were brought up, which were much perforated by serpular borings, and these were lined with peroxide of manganese. At the first station after leaving Japan, and on the landward side of the deep gully which runs parallel with the islands, a large haul was obtained, chiefly of pumice, tuff, and volcanic mud concretions. These were much perforated by worms, and the holes were lined with black oxide of manganese. One concretion, a portion of which is on the table, was broken open in the plane of one of the worm-holes, and the worm was found dead in it.* On another portion a dead worm was found adhering, and on removing it a black stain was found below it consisting of peroxide of manganese. The connection of the peroxide of manganese with the life of these animals was very marked in this case, and continued to occupy my attention from time to time, though without arriving at any satisfactory solution, during the cruise. It must not be forgotten that an invariable feature of the nodules was that they gave off abundance of alkaline and empyreumatic-smelling water on being heated, which served further to connect them with the organic world. After the return of the “ Challenger ” I did a good deal of dredging in the summers of several years (1877-1882) in the seas on the west coast of Scotland, and on the 21st September 1878 I brought up from the deepest parts of Loch Fyne (104 fathoms) a quantity of sandy mud, with large quantities of dead pecten shells, and along with tfliem true manganese nodules, with all the outward * The body of this worm was tested and found free from manganese. 1890-91.] Mr J. Y. Buchanan on Sulphur in Marine Muds. 19 characteristics of those from the greatest depths of the open ocean; and this similarity was maintained on chemical examination. The dredging anchor must on this occasion have heen dropped in the very richest part of the deposit ; for the mud, which had undergone no concentrating process, was found, on being submitted to mechani- cal analysis, to consist of rather over 30 per cent, of nodules.* This was a very remarkable discovery ; for although peroxide of manganese was not wanting in the shallower dredgings of the “ Challenger,” it existed only as coatings and similar deposits and not as nodules, which were believed to he dependent for their formation on the conditions obtaining in very deep water. After this particular attention was paid to the occurrence of manganese in all dredgings, and it was found to be abundant all round our coasts as a coating on shells, and more especially as the binding and colouring matter of worm tubes ; but no nodules were anywhere found except in the deep part of Loch Tyne. Some years afterwards Mr Murray found them in great abundance on the Skelmorlie Bank in the Firth of Clyde in 10 fathoms. In the same summer of 1878 I made a number of observations in the channel off the north-east part of the Island of Arran, where the water reaches a depth of 90 fathoms. A galvanised iron bucket was used as dredge, with a weight attached behind, and one before it ; so that its action was rather to skim the surface than to dig into the lower layers of the bottom. It brought up a quantity of a very fine red mud, in which manganese grains could he detected, not apparently differing from those found in oceanic red clays. In the process of levigation, when the mud was stirred up with water and the light flocculent portion poured off, the heavier portion which had settled to the bottom of the vessel had the appearance of having heen cast into elongated pellets. When these were stirred up again with water they were partially broken up into flocculent matter, which was poured off, leaving again pellets as before; and this could he continued until the whole of the mud had heen washed away as flocculi, produced by the breaking up of these pellets. In the case of the particular mud under description, hardly anything in the shape of sand or coarser material remained behind. The ground- fauna, chiefly ophiurids, seemed to he abundant ; and the pellets * Nature , 1878, vol. xviii. p. 628. 20 Proceedings of Royal Society of Edinburgh. [sess. above described were tbe casts excreted by these creatures, which subsist on what nutriment they can pick up by triturating and passing the sand or mud through their bodies. In some of these animals the triturating apparatus takes formidable proportions, as in sea-urchins ; and it is probable that the sand found at low water owes its state of comminution largely to these animals and to worms, such as the ordinary lob-worm used for bait. When examining deep-sea clays in the “ Challenger ” I had observed the pellet formation, without, however, being able to refer it to any probable cause. Now, however, it became probable that the same causes are at work in deep as in shallow seas, and that the matter forming the bottom of the sea is being continually passed and repassed through the bodies of the numerous tribes of animals which demonstrably subsist on the mud and its contents. In the following season, 1879, I made an extended cruise through the greater part of the waters of the west coast of Scotland, visiting most of the deeper spots, and paying particular attention to the occurrence of coprolitic mouldings of the mud. Thus, on 16th June 1879, dredging in the deep part of the Sound of Eaasay in 155 fathoms,* “a little mud came up. It was a fine gray clay, which effervesced with acids and smelled of H2S. On washing a quantity of it there remained the coprolitic masses and very little fine sand. There appeared to be a good deal of carbonate in a very fine state of division. There were very few shell particles visible, and the effervescence of what looked like flocculent clay was not incon- siderable.” At the time I explained this flocculent carbonate as having been produced out of the silicates of the mud by the ground animals forming sulphide of calcium, which was transformed into carbonate by the carbonic acid of the water. On the following day another haul was got in the same locality and with similar results ; it is noted that — “ Sticking to the outside of the bag were many legs of ophiurids, which will account for the coprolites.” When attention had once been paid to it, the coprolitic moulding of the mud, when of a suitable consistency, was found to be practically universal round our shores, f * From deck-book of Steam Yacht “ Mallard,” 1879. t Later, in the year 1886, when in charge of the expedition to survey the Gulf of Guinea in the steamship “ Buccaneer,” I found the same thing practically 1890-91.] Mr J. Y. Buchanan on Sulphur in Marine Muds. 21 Shore muds, that is, the terrigenous deposits which are found all along the shores of continents, and even at great depths — generally present the characteristic appearance of a reddish surface layer, overlying a bluish substratum. This characteristic is observed in deposits even far out at sea, and, where it is not masked by large amounts of calcareous matter, is evidently due to the oxidation of the bluish ferrous salts, on their coming in contact with the sea water, which always contains dissolved oxygen.t A very remarkable example of a blue clay — for it was too tenacious to be called a mud — was obtained in the Sound of Jura, and it was particularly noticeable for the amount of sulphides which it contained, and instructive by their complete disappearance on drying. It is worthy of more particular mention. On 6th July 1879 the anchor dredge was put over in the Sound of Jura, where a depth of 120 fathoms was marked on the chart. It did not hold, and the yacht drifted, dragging it over the ground in a northerly direction before the wind and tide. Suddenly it hooked the ground, and brought the vessel up with a great strain on the cable. In heaving up it was with difficulty that the anchor was broken out of the ground ; and when it was brought to the surface the hag was full of a fine, unctuous, very tenacious blue clay, with some of the reddish-brown surface mud covering it. There were a few pieces of broken shell and rock, also smooth and rounded pebbles, which seemed to occur principally in the part separating the surface mud from the blue clay, but there was very little of this kind of matter. The whole bagful, weighing more than universal all along the African coast, and developed in a most remarkable manner on the coast flat within a considerable radius of the mouth of the river Congo. Here it was necessary to introduce a new designation for muds, and in this district the most frequent entries in the deck-book as to the nature of the bottom are “cop. m.,” meaning coprolitic mud. These so-called coprolites were almost jet black and of the size of mice droppings, and they were covered with the same substance in flocculent form, or were free from it, according to the scour of the tide in the locality. It was best developed in comparatively shallow water, and more especially in a depth of 50 fathoms, when the large ash bucket, to the use of which as a dredge I found it convenient to revert, came up full of these coprolites, without any flocculent matter whatever. All along the coast the mud of the locality was moulded in a similar way, though it was not so striking. When the course of the cruise took us across the open ocean to Ascension, and thence northwards, we were able to trace the transition of the more earthy shore coprolites into the more mineralised and glauconitic pelagic ones. 22 Proceedings of Royal Society of Edinburgh. [sess. 1 cwt., consisted almost entirely of homogeneous blue clay of a tenacity similar to the clay dug for brickmaking, and quite different from ordinary “ blue muds.” The clay was rather foul-smelling, and gave off abundance of sulphuretted hydrogen when treated with hydrochloric acid. It was so tenacious that it was impossible to break it up in water for the purpose of levigation, which is always very easily accomplished with ordinary muds. A considerable por- tion of it was dried and taken for analysis. It was found that, as soon as dry, not a trace of sulphide was to be found ; hut the mass of the clay was permeated with fine particles of oxide of iron, each of which represented a previous particle of sulphide. A specimen of this clay is on the table. The contrast between the fresh moist clay, which was thoroughly impregnated with sulphides, and the dried clay, without a trace of them, was very striking.* The fact then had been demonstrated that the mud is being con- tinually passed and repassed through the bodies of animals in- habiting the bottom of the sea. In doing so the mineral matter of which it consists comes in contact with the organic secretions of the animals, mixed with sea water, and is ground up along with them in the milling organs of the animals. The Eeducing Action of organic matter on sulphates has long been known, and its importance as an agent in geological metamorphosis was thoroughly recognised by Bischof.f The effect of Trituration in promoting the chemical decomposition of silicates by water was demonstrated by Daubree,}; more par- ticularly in the case of Felspar. I found the observations to hold good also for Augite. Clear crystals of this mineral from the Tristan da Cunha group, when pulverised with water in an agate mortar, rendered the water alkaline to turmeric paper. It is evident therefore that at the bottom of the sea a number of conditions occur together, which are favourable to the production of chemical change. The ground animals, in the search of food, pass the mud through their bodies, grinding it up, and bringing it * A condensed account of my views of the part played by the sulphates of the sea water in the production of the ochreous deposits on the bottom of the ocean, and of the carbonate of lime of the shells of the Mollusca, is published in the Reports of the British Association (York), 1881, p. 584. t Bischof, Lehrluch der Chemischen und Physikalischen GeoJogie (1868), i. 31, 358. X Daubree, Geologic Experimentale , i. 268. 1890-91.] Mr J. Y. Buchanan on Sulphur in Marine Muds. 23 thoroughly into contact at the moment of comminution with the sea water and the digestive secretions of the animal. The action of these secretions on the sulphates in the sea water is to produce sulphides, and the actions of the sulphides on the ochreous matter of the bottom is to produce sulphides of iron and manganese. Even if the bottom were covered with felspathic or augitic sand, the sulphides, acting on these silicates in the moment of partial decomposition, would convert the ochreous oxides by degrees into sulphides. That the volcanic material, lava, dust, scoriae, pumice, which forms the bulk of tbe unaltered material of tbe bottom of the ocean, is so dealt with by the animals, is evident from the specimen from the Pacific on the table, which is not a singular specimen, but ratber a typical one. Having extracted what nutriment they can from the mud, the animals reject it, containing a certain proportion of sulphides of iron and manganese. These sulphides, it is well known, are exceed- ingly5 unstable in presence of water and oxygen, and if they come to lie on the surface of the mud, where they are exposed to the action of the sea water, which always contains dissolved oxygen, they must be quickly transformed into oxides. In the oxidation of ferrous sulphide by this process .there is always separation of free sulphur, which, however, is to a great extent further oxidised; but it is probable that some would persist. If then the process just described represents at all what takes place in nature, we should expect to find in the ochreous deposits (the hydrous oxides of iron and manganese) some relics of their connection with the organic world. These are not wanting. All the deep-sea muds and manganese concretions, of every diversity of form, gave without exception, when freshly collected and heated in a tube over the lamp, a large quantity of ammoniacal water. It was important to see if sulphur could be detected. And here it is well to bear in mind that in the case of a “blue mud,” which may contain unaltered sulphide, the sulphur found in the dried sample will come at least in part from that sulphide, and will be due to the oxidation by the atmosphere in the process of drying. In the case of an oceanic “ red clay ” or manganese nodule, where no blue matter is present, any sulphur which is found may be properly ascribed to oxidation on the bottom of the sea. 24 Proceedings of Royal Society of Edinburgh. -Acting on these considerations, in the winter of 1880-81, a number of muds and nodules were examined with a view to the detection, and if possible the estimation, of free sulphur. Estimation of Sulphur in Muds. A certain quantity of the clay, dried at about 80°, was put into a bottle with a known weight of chloroform. The stopper was tied down, and it was then put into a water-bath for about an hour at about the temperature of boiling chloroform (61° C.). It was then allowed to cool, filtered into a weighed fractionating flask, and washed twice with a little more chloroform. The chloroform was then distilled off, and the residue heated slightly and weighed. The residue was treated with hot nitric and hydrochloric acids, diluted, and filtered if necessary, barium chloride solution added, allowed to stand, filtered, and the precipitate of barium sulphate weighed. In the first few samples the barium sulphate was not weighed, but the quantity of sulphur judged by the amount of barium sul- phate precipitated. At first bisulphide of carbon was used, but it was departed from, because, although perfectly pure, and leaving no trace of sulphur on evaporation, it was thought that it would be well to use a solvent not containing any sulphur. A portion of the blue clay from the Sound of Jura, which -when fresh contains much sulphide, was in the dried state tested writh both solvents, with the following results. Treatment with Bisulphide of Carbon. — A quantity of the clay was pounded and dried at about 80°. 50*00 grammes were put into a bottle with 236*0 grammes of bisulphide of carbon, and allowed to stand all night. A weighed portion of the carbon bisulphide was then taken out and put into a weighed flask, and the carbon bisulphide distilled off, and the residue weighed. 0*28 per cent, of sulphur was found in this way. The sulphur dissolved completely in a small quantity of bisul- phide. Next day another portion of carbon bisulphide was taken out and put into a weighed flask, distilled, and the residue weighed. This gave 0*33 per cent, of sulphur. The bisulphide was tested to see whether it contained any free sulphur ; it turned out to be very nearly pure. Table giving the Results of the Treatment of various Samples of Sea-Bottom with Chloroform for the Extraction of Sulphur. 1890-91.] Mr J. Y. Buchanan on Sulphur in Marine Muds. 25 i o «3 02 Ph 'H (’samurai*)) ^OS^a JopiSPAY w i e •anpisajj jo -juao .xaa o o II •(sauiui'B.io) anpisay « jo jxiSiaAY • (samurai*)) pappt? tuiojoi omo jo W^PAY rO ■(samurai*)) aidurag e jo jqSia^Y o & CO ; c o» . c: o - ooi-i*-hcoooiocoooootHoo oooooooooooooooo -HCOC5 ;ohco pop © © © IQ vO lO lO lO »o >o csoHQCiK^r OHOJrlQOrlCK . • © © p © © © oooooooooooooooo T^COIOCC COC^ CO tH C50iococo»oco(NO(^r> (^OOOOOOOOpO ooooooooooo O (M >0 CO NiOCiiOOD^HQ^^CdH^OCOCO O ^HCOC5>p»pMONO(f) wcowrioiwiii'o QO(NCOH(MCOIO>OOH'^ CO (M ( i CJ O N H OO »p i • YO CO GO O l> < OODOONN^^lOip^H OCX)^OTH^T^OOt^CiOO »Cll>l>QDC0HC0l>O5l'-b» >o>oonohcd»o^co>ocooo9^ci C5COOiOC5HiOTt<^COOCOCiiO>OCi CO 5 ^ S +3 T& o CD CO S g-g §2? H 02 S >53 S I u d S o ■sSSs . CO ^ >y o «m d EL ✓-n 2d > °6£ds§s o O & . i A, H WCO^iOOhCOQOH (MCO^'OONXCJOHfMiOr^OCON 26 Proceedings of Royal Society of Edinburgh. [sess. Treatment with Chloroform. — Another 50-00 grammes of clay were treated with 183 ’6 grammes of chloroform. The mixture was heated for an hour oil the water-bath at about the temperature of boiling chloroform (61° C.). A portion of the chloroform was then taken out, evaporated, and the residue weighed. This gave 039 per cent, of sulphur. There was very little oil present in the residue, which was nearly pure sulphur. In the first ten samples the BaS04 was not weighed, hut the residue was always oxidised and the presence of sulphur proved by the formation of sulphuric acid. When sulphur was found constantly and in appreciable quantity, I then decided to weigh it, the opera- tion being, from an analytical point of view, an advantageous one, as the sulphate of barium weighed weighs seven times more than the sulphur to he estimated. By far the largest amount of sulphur is contained in the clay from the Sound of Jura, which, in its fresh state, contained large quantities of sulphides, which were completely oxidised on drying. TheO'197 grammes of residue may be taken to be pure sulphur, which makes about 0‘4 per cent. By far the greater part, if not the whole, of this sulphur was formed by oxida- tion during drying. Had it been possible to collect and examine separate^ the reddish-brown surface layer, we should, no doubt, have found very much less sulphur, but it would have been mainly due to oxidation by the oxygen of the bottom water. The “ oil,” which is extracted from all the muds along with the sulphur, and which varies a good deal in quantity, is due to the animal debris intimately mixed with the mud and with the materials of the nodules, which are made up, for the most part, of the materials of the bottom. Nos. 2 and 3. — The manganese nodules of the 12th July 1875, from the North Pacific, in lat. 37° 52' N., long 160° 17' W., came from a depth of 2740 fathoms, where they appear to have been exceptionally abundant. Those of the 16th September 1875 came from a locality where they were equally abundant. The water was a little shallower, being 2350 fathoms, in lat. 13° 28' S., long. 149° 30' W. In both the samples of these nodules examined, the weight of the residue is considerable, hut as there was a little oil in both cases it is not possible to give the percentage of sulphur. 1890-91.] Mr J. Y. Buchanan on Sulphur in Marine Mucls. 27 No. 4. — The mud from the Sound of Raasay, off the west coast of Ross-shire, was dredged from 150 fathoms, and consisted of very fine soft grey mud, which on washing left a large residue of coprolitic pellets. No. 5 is a similar mud from Loch Duich, also in Ross-shire ; it harboured many annelids. No. 6 is from the station in Loch Fyne, where, for the first time, manganese nodules were obtained in comparatively shallow water. It is a sandy clay with many dead shells. No. 7 is the red clay from 90 fathoms in the Firth of Clyde, off the north-east part of the Island of Arran, which has already been referred to. It is a very fine red ochreous mud, much resembling the oceanic clays. On washing, it is found to he almost com- pletely moulded into coprolitic pellets, and supports an abundant ground fauna. Like oceanic clays, on careful washing, grains of peroxide of manganese can he isolated, and it contains over 1 per cent, of phosphoric acid. No. 8 is red clay from lat. 18° 56' N., long. 59° 35' W., depth 2975 fathoms, in the western basin of the North Atlantic. No. 9 is a coating of peroxide of manganese from an oceanic concretion, but the locality has been, omitted to be noted. No. 10 is mud from 115 fathoms in the channel between the Island of Searba and the Garvelloch Islands, about twenty miles S.W. of Oban. Peroxide of manganese is very abundant here as a coating on dead shells. No. 11 is from the upper basin of Loch Fyne, in 60 fathoms. The mud here contains a remarkably large amount of sulphur. The upper basin of a sea loch is, as regards many of its conditions, and notably as regards the nature of the mud at its bottom, in a state intermediate between that of the open sea and that of a fresh-water lake. The mineral constituents are usually in a lower state of oxidation than outside; and this is accompanied by, and partly due to, the relatively large amount of vegetable debris from the land. All these circumstances may retard the disappearance of the sulphur. Nos. 12 and 13 are globigerina oozes from the Pacific and the Atlantic respectively, their particular locality not noted. No. 14 is from the same locality as No. 10. 28 Proceedings of Royal Society of Edinburgh. [sess. No. 15 is from a position north-east of the Island of Rum, in 147 fathoms, soft grey mud. No. 16 is a blue mud, from 2050 fathoms in the Celebes Sea. No. 17 is a glauconitic mud from the east coast of Australia, in 410 fathoms, lat. 34° 13' S., long. 151° 38' E. No. 18 is a diatomaceous mud from the Antarctic Ocean, in 1950 fathoms, lat. 53° 55' S., long. 148° 35' E. No. 19 is a red clay dredged on the 13th March 1874, in 2600 fathoms, lat. 42° 42' S., long. 134° 10' E. Along with the mud a large quantity of manganese nodules was brought up. No. 20 is a radiolarian ooze from the North Pacific, lat. 12° 40' N., long. 152° 1' W., depth 2900 fathoms. Nos. 21 and 22 are again samples of globigerina ooze from the Atlantic and the Pacific respectively. These samples differ from Nos. 12 and 13 inasmuch as the Pacific sample now contains more sulphur than the Atlantic one. No. 23 is the insoluble residue left after treating a nodule from the same locality as No. 2 with hydrochloric acid and ferrous chloride. The difference is very remarkable. In No. 2 the sulphur was not determined — that is, the barium sulphate produced by its oxidation was not weighed ; but it was one of these samples which showed that the amount present was so appreciable that it was worth while determining it as accurately as possible, so that it is certain that it must have contained at least an average amount. In the case of the natural nodule (No. 2) the weight of chloroform residue per 100 grammes substance was 29 milligrammes; in the case of the extracted nodule No. 23 it is 2 milligrammes, and the weight of sulphate of barium is put down as 1 decimilli- gramme. In fact, the sulphur in the nodule had disappeared under the treatment. No. 24 is from Loch Eyne, in 87 fathoms, opposite Otter House, and a little further up the loch than the station No. 6, but both of them in the outer loch, as opposed to No. 11, which is in the upper and semi-enclosed basin. The contrast between No. 24 and No. 11 is remarkable. In the upper basin the amount of the chloroform residue per 100 grms. substance was 74 milligrms., and 10 milligrms. of it was sulphur. In the outer loch there were only 17 milligrms. of residue and 1 milligrm. sulphur. 1890-91.] Mr J. Y. Buchanan on Sulphur in Marine Muds. 29 No. 25 is a very remarkable white clay from the bottom of Loch Ness, and therefore a fresh-water formation. It occurs in a small area opposite Urquhart Castle, and in various depths, often covered by a thin layer of peaty substance ; but in some places, in depths of about 30 fathoms, the sounding-tube brings up the white clay alone. It was observed also in Loch Oich. It is chemically quite distinct from the marine clays, being much more acid. The amount of matter extracted by chloroform is enormous, being 374 milligrms. per 100 grms., most of which is oil or wax, but con- taining 4 milligrms. of oxidisable sulphur. It is not impossible that in this case the sulphur may exist as an organic compound ; and the amount of oily matter in the clay is interesting in the indication which it gives of the possible mode of formation of our oil-bearing shales. No. 26 is from the anchorage of Isle Oronsay in the Sound of Sleat. No. 27 is from a depth of 87 fathoms off Garroch Head, in the Firth of Clyde. Both in this case and in that of No. 26 the amounts of residue and of sulphur are insignificant. Sulphur was thus detected in all these samples and determined in the greater number of them. Putting aside shallow water coast muds, the largest amounts of sulphur are found in the Celebes Sea (No. 16), in the Diatomaceous ooze of the Antarctic (No. 18), and in the Badiolarian ooze of the Pacific (No. 20). -So far, therefore, as it goes, we have the evidence of the sulphur in favour of former organic agency. It is worthy of remark that the property of giving off alkaline water on heating has in the course of years disappeared, and in its place the nodules on being heated give off acid vapours, which, it is true, contain some ammonia, but along with an excess of nitric acid, which is without doubt due to the gradual oxidation of the nitrogenous matter. It is possible that the finely divided sulphur may diminish and finally disappear in the same way. But in 1881, there was still enough to be easily determined. Let us consider the chemical reactions more closely. When a mud containing ferrous sulphide is treated with dilute hydrochloric acid, the sulphide dissolves with evolution of sulphur- etted hydrogen, so long as there is no substance present which has a decomposing action on the sulphuretted hydrogen. If there be 30 Proceedings of Royal Society of Edinburgh. ferric salt either mixed with the mud or in the solution, then it is reduced to ferrous salt, with the destruction of the equivalent amount of H2S and separation of sulphur. If the ferric salt be in excess, no sulphuretted hydrogen makes its appearance at all. The reaction is very simple — because the 2HC1 appears on both sides of the equation, and is in fact unnecessary. A trace of free acid is no doubt necessary, and it is turned over and over again in the reaction of indefinite quantities of FeS on Fe2Cl6, after the manner of a catalytic action. The same reaction takes place if we use ferric sulphate in place of ferric chloride. It is evident, therefore, that if we have a sample of mud contain- ing sulphide, and we mix it thoroughly with a solution of Fe2Cl6 or Fe2(S04)3, we shall have in the ferric salt reduced a measure of the decomposable sulphide present. The ferrous salt can be readily determined by permanganate of potash or otherwise. It will be seen from the above equation that one molecule FeS decomposes one molecule Fe2Cl6 with the formation of three molecules FeCl2, so that the FeS in the mud is one-third of the ferrous salt found. In order to make some preliminary experiments, a mixture of 100 grms. alum and 30 grms. ferrous sulphate were dissolved in about f litre of water and precipitated with ammonia and sulphide of ammonium. The precipitate was thoroughly washed by repeated decantations, the flask being always filled up to the neck, and corked and allowed to settle. When it was completely washed the surplus water was poured off, and the precipitate, suspended in about \ litre of water, was preserved in a well-stoppered reagent bottle. The precipitate consists of alumina and sulphide of iron, and may therefore be taken as an imitation of a simple form of mud. I made some experiments to see with what amount of agreement in the results one could titrate a number of different samples of the same mud. Three flasks were placed side by side, and into each 50 c.c. sus- pended FeS mud were measured. The mixture of FeS + A1203 was and by addition FeS + 2HC1 =FeCl2 +H2S H2S + Fe2Cl6 = 2FeCl2 + 2HC1 + S FeS + Fe2Cl6 = 3FeCl2 + S 1890-91.] Mr J. Y. Buchanan on Sulphur in Marine Muds. 31 thoroughly shaken up, then run into a narrow graduated cylinder, holding 50 c.c., which was emptied into the flask and then washed once into it with distilled water. To each of the flasks was then added 10 c.c. of the reddish-brown hut still acid, ferric sulphate solution, and the contents shaken. In a few seconds the black colour of the sediment had disappeared entirely, being replaced by a yellowish-red precipitate, which disappeared for the most part on the addition of dilute sulphuric acid. Water was then added to bring up the volume to 250 c.c., and the titration was effected with permanganate of potash solution ^1 litre containing grms.^ The three portions of 50 c.c. required each 1 1 *6, 1 1 *6, and 11 -7 c.c. permanganate respectively. We see then that a suspended pre- cipitate can be measured off about as accurately as a dissolved salt. It is evident, then, that if we have a mud containing FeS and other ferrous compounds decomposable by HC1, we can determine first the FeS by adding Fe2Cl6 and titrating a portion with perman- ganate; then the other ferrous compounds, by adding HCland titrating another portion with permanganate, due account being kept of the weights and volumes used. In order to try the method in practice, three soundings were made ; — on 30th September 1881 in the Sound of Raasay, off Croulin Island, 120 fathoms ; and on the 1st October 1881 in Loch Duich, in 49 and 51 fathoms. The first of these re- presents more or less the conditions in the open sea of coast waters ; the last two represent the conditions in a semi-enclosed loch basin. The Sound of Raasay mud was a light grey mud, with no offensive qualities. Both samples from Loch Duich were very foul smelling. All three samples were tightly stoppered up in their wet condition, and examined on 20th and 21st October 1881 in my laboratory in Edinburgh. I unfortunately had no suitable* ferric solution afloat with me so as to treat them immediately. In the three weeks that both muds from Loch Duich were kept in bottles, the surface layer got completely oxidised, and on opening the bottles the smell was gone ; but, on breaking through the surface layer, the unaltered black mud was exposed with all its original qualities, including its peculiar odour. The following was the method used in the case of the Loch Duich 32 Proceedings of Royal Society of Edinburgh. mud from 49 fathoms. Two portions of the damp unaltered mud were weighed out; one portion, 6 ‘724 grms., was dried at 100° C., and the other, 7*881 grms., was treated with deep red Fe2Cl6 in a 100 c.c. flask, which was then filled up to the mark with water. 50 c.c. of this solution, containing 3*94 grms. damp mud, were acidified with sul- 'KMn04 r, \ — grms. per litre), phuric acid and titrated with permanganate ^ 50 using T9 c.c. To the remaining 50 c.c. with sediment (the volume of which may here be neglected) were added 4 c.c. of strong hydrochloric acid (12 -5 HC1 grms. per litre), filled up to the mark, and allowed to settle. 50 c.c. of this solution, containing 1 ’97 grms. damp mud, were further acidified with sulphuric acid and titrated with the same permanganate, of which 1 *7 c.c. were used. A litre of the above permanganate oxidises 5*6 grms. iron from the ferrous to the ferric state. In the first operation, 50 c.c. solution used T9 c.c. permanganate, therefore the^whole amount of mud, 7*881 grms., when treated with ferric chloride, would require 3*8 c.c. = 0*0213 grm. iron. After treatment with hydrochloric acid a quantity of solution equivalent to 1*97 grms. wet mud required T7 c.c. permanganate, so that 7*881 grms. mud would require 6*8 c.c. when treated with both HC1 and Fe2Cl6, which represents 0*0381 grm. iron. Therefore, total iron found by Permanganate in HC1 + Fe2Cl6 solution, . . 0*0381 grm. Deduct Iron found in Fe2Cl6 solution, . . 0*0213 „ 0*0168 Leaves Iron present as Ferrous Salt extracted by Hydrochloric Acid, ..... Of the 0*213 grm. iron found in the first solution we have seen that only one-third is to he reckoned as .belonging to the mud, and to he taken as forming FeS, so that in 7*881 grms. wet mud we have 0*0071 grm. iron present as sulphide, equal to 0*0112 grm. FeS, and 0*0168 grm. iron present as ferrous oxide extracted by hydrochloric acid, equal to 0*0216 grm. FeO. The 6*724 grms. wet mud weighed when dried at 100° C., during which it was oxidised as well as dried, 2*011 grms., equal to a loss of 70*1 per cent. Therefore the dry mud is 29*9 per cent, of the damp mud taken. The 7*881 grms. damp mud therefore represent 1890-91.] Mr J. Y. Buchanan on Sulphur in Marine Muds. 33 2 *35 6 4 grins, dry mud, and therefore we find that the mud taken as dry contains 047 per cent. FeS and 092 per cent. FeO in some other easily decomposable combination. The other samples were treated in the same way, and in the Loch Duich mud, from 51 fathoms, 0'94 per cent. FeS + 065 per cent. FeO were found. It is remarkable that the amount of F2S should be so small in such offensive muds. In the outside mud from 120 fathoms in the Sound of Raasay only 0*05 per cent. FeS and OT per cent. FeO were found. In connection with this mud, which contained some shell debris, the method was found to be less applicable than to muds free from calcareous matter. The reason is obvious ; because, on adding a neutral ferric solution to a mud containing carbonate of lime, precipitation of the ferric oxide by the lime immediately commences. This would not really interfere with the reaction, because the FeS would reduce the precipitated Fe203 all the same, and the ferrous salt can still be determined by permanganate ; but in truly calcareous bottoms this action is troublesome, and the method will require special study in this direction. In the semi- enclosed basins of the sea lochs, which, as has already been observed, form a transition between the open sea and fresh-water lakes, the bottom resembles more nearly that of the fresh-water lakes, in the absence of mollusca, and in the abundance of organic matter of vegetable origin, than that of the open sea with its abundant and varied ground fauna. It differs from those of fresh-water lakes in being bathed by sea-water largely impregnated with sulphates. Con- sequently it is in the inner basins of sea lochs that the conditions for a constant production of sulphides are present, while the same conditions are hostile to the presence of calcareous organisms. Hence it is in these basins that the greatest quantities of sulphides are found, and it is in their muds that the above method is most applicable. The sulphuretted muds, however, are so alterable by atmos- pheric influences that it is essential that they should be treated immediately on collection. For this purpose weighed wide- mouthed bottles with good stoppers should be provided. When a specimen of mud is brought up from the bottom, a sample of it is immediately taken with a spatula and put into one vol. xviii. 31/12/90 c 34 Proceedings of Royal Society of Edinburgh. [sess. of these bottles containing a known quantity of ferric chloride solution, at least sufficient to completely cover the sample of mud. Another sample, as nearly similar to the first as possible, is taken and stoppered in another bottle for drying. In this way a large amount of valuable information might be gained; but it will be evident from the nature of the case that the actual figures obtained in any one particular case are affected by a considerable possible error. In the month of June 1881 I carried out a number of laboratory experiments bearing on this subject, using the sulphides of different metals of the iron group. These bodies were all prepared in the same way, namely, by precipitating the sulphates with sulphide of ammonium, and washing by decantation in stoppered bottles, always filled up quite full. A quantity of hydrated ferric oxide was also prepared by precipitating ferric chloride with ammonia and washing. All of these precipitates, when thoroughly washed, were preserved suspended in distilled water in well-stoppered reagent bottles. Ferrous Sulphide and Ferric Oxide. — When quite neutral these substances do not react on one another, at least at once. But if the water has the slightest acid reaction reduction of the sesquioxide and production of sulphur take place rapidly. A mixture of Fe203 and FeS in water and quite neutral was corked up and allowed to stand for five days, when the sediment was found to be separated into two sharply-defined layers — the upper red, consisting of the oxide, and the lower black, of the sulphide. When brought together, therefore, in presence of nothing but distilled water, there is no appreciable resultant action. Manganous Sulphide can be preserved perfectly under distilled water in well-stoppered bottles filled to the neck. A considerable quantity was prepared in the summer of 1881, and, when thoroughly washed, it was put away in three separate bottles. The contents of only one bottle were used for experimental purposes, and the upper part of it got coloured immediately black with oxide of manganese, from the oxidation of the flakes of sulphide which adhered to the surface of the upper part of the bottle, left dry when some of the water and precipitate had been poured out. This took place at the time, and was to be expected. The two other bottles, which were 1890-91.] Mr J. Y. Buchanan on Sulphur in Marine Muds. 35 filled up with the manganous sulphide at the time of preparation, have never been opened since, though they have all the time been exposed to the light, and are exactly in the condition in which they were when bottled nine and a half years ago. There is no trace of oxidation. Manganous Sulphide and Hydrous Ferric Oxide. — Both substances are used, suspended in distilled water. If the ferric oxide he cautiously added to the sulphide of manganese, and both suspended in w^ater, the red patches are seen to disappear, and the general colour of the suspended matter becomes rather lighter in colour than the MnS, and there is no formation of FeS. If further additions of Fe203 he made, red flakes deposit themselves. They do not appear to he unaltered Fe203, hut are exactly like the “red cherty par- ticles ” of manganese bottoms. On still further additions of Fe203, the colour changes quickly, though not instantaneously, to black, with, however, a large admixture of white particles, the two being easily seen to he perfectly distinct. There is also a quantity of pre- cipitated sulphur which remains floating in the liquid long after the heavy matter has subsided. Prosecuting this line of experiment, I made three mixtures in suitable flasks. Ho. 1 contained MnS and Fe203, the MnS being in excess. There was formation of red cherty particles, hut nothing black. No. 2. The same substances, but containing the Fe203 in excess ; the mixture quickly turned black. No. 3. The same as No. 2, only it was made up with warm water, and it turned black almost at once. These experiments were repeated, and with the same results. The above flasks, Nos. 1, 2, and 3, were corked up and allowed to stand over night. No. 1 contained numerous black particles, as well as red cherty ones, and an excess of MnS as well as sulphur. Nos. 2 and 3 were much as they had been the night before, except that the white particles had almost entirely disappeared, as also all red particles. The reactions are considerably accelerated by heat. On examining the contents of each of these flasks, no peroxide of manganese was found, hut large quantities of sulphide of iron. The likeness in the red flakes to the cherty particles of the bottom muds in the manganese districts of the South Pacific, and of the 36 Proceedings of Royal Society of Edinburgh [sess. kernels of some manganese nodules was very striking. It is not improbable that the first action of the MnS on the Fe203 may be accompanied by the formation of mixed oxides of iron and man- ganese ; but there is much to be done in this direction in the strictly quantitative investigation of the interaction of the insoluble, but not inert, compounds of this as well as of other groups of metals. Ferric Sulphate and Manganous Sulphide. — Experiments were now made, using the iron as a ferric salt in solution, and for this purpose ferric sulphate was used. It was made as nearly neutral as possible by addition of ammonia. The MnS was, as before, sus- pended in distilled water. On adding ferric sulphate to excess of MnS, the formation of FeS is immediate. On adding a large excess of Fe2(S04)3 the FeS is decomposed, there is formation of basic salt, and on dissolving it with H2S04 the solution contains large quantities of ferrous sulphate. On experimenting with solution of ferrous sulphate it was found that excess of MnS precipitates the iron completely as FeS, acting exactly like an alkaline sulphide. The rationale, therefore, of the above reaction is very simple. Thus Fe2(S04)3 + MnS = 2FeS04 + MnS04 + S and 2FeS04 + 2MnS = 2FeS + 2MnSO, adding (1) and (2) we have Fe2(S04)3 + 3MnS = 2FeS + 3MnS04 + S and 2Fe2(S04)3 + 2FeS =6FeS04 + 2S . . . and (3) + (4) = 3Fe2(S04)3 + 3MnS = 6FeS04 + 3MnS04 + 3S A3 (1) (2) (3) (4) (5) or jks= Fe2(S04)3 + MnS = 2FeS04 + MnS04 + S . (6) \6) which is identical with (1), and by adding more MnS we get the conditions of equation (2), and so on, repeating the cycle. Hence, if we add MnS to excess of Fe2(S04)3, we should get reduction of the ferric salt without formation of FeS. On adding excess of MnS, we get formation of FeS, and then on adding excess of Fe2(SO)4 we get back to the same state of things as at first. The reaction of equation (1) can be obtained by very cautiously adding small quantities of suspended MnS to a very large excess of 1890-91.] Mr J. Y. Buchanan on Sulphur in Marine Muds. 37 Fe2 (S04)3. Still there is always local formation of FeS which dis- appears on mixing, so that the reaction is really that of the whole cycle. The action, therefore, of MnS on soluble iron salts is in the first instance to reduce whatever is in the ferric state to the ferrous, and then at once to precipitate the ferrous salt as sulphide, a man- ganous salt taking the place of the ferrous salt in the solution. When added in great excess to solutions of nickel sulphate, man- ganous sulphide precipitates it as NiS. When added to solution of sulphate of zinc, it either does not precipitate it at all or only very slightly at ordinary temperatures. Sulphide of zinc was not found to precipitate manganese sulphate solution. As the result, then, of the observations and experiments which have been recited I was led to believe that the principal agent in the comminution of the mineral matter found at the bottom of both deep and shallow seas and oceans is the ground fauna of the sea, which depends for its subsistence on the organic matter which it can extract from the mud. In order to fit them for collecting their nutriment in this way the animals have been fitted with different forms of masticating or milling apparatus, so as to thoroughly deal with the matter which they pass through their bodies. It has been shown that most silicates are decomposed to a certain extent when ground or pulverised under water ; so that the mere mastication of the sand or mud in presence of pure water would have a decomposing action on the silicates which it contains. This action is much assisted, in the case of marine animals, by the fact that the water which they pass through their bodies along witb the sand is charged with sulphates. These are easily reduced to sulphides by the action of the organic matter of the secretions of the animals. The resulting sulphide at once suffers double decomposition with any oxide of iron or man- ganese which is present as such in the mud, or may be being set at liberty from silicates under the decomposing influence of trituration under water. The sulphides of manganese and iron so formed are in course of nature extruded by the animals, and if exposed to the sea water on the surface of the mud are quickly oxidised, the manganese taking priority. The mud below the surface layer, in localities where ground life is abundant, remains blue, being protected by the oxidation of what is above it. 38 Proceedings of Royal Society of Edinburgh. [sess. At the bottom of the ocean the mineral matter is thus exposed to a reducing process due to the life of the animals which inhabit it, and to an oxidising process due to the oxygen dissolved in the water. Other things being equal, the redness or blueness of a mud or clay depends on the relative activity of these processes. They also exercise a controlling or modifying influence on one another. For, although marine animals are much less sensitive to variation in the amount of oxygen in their atmosphere than terrestrial animals, it is certain that there must be a limit to the deficiency of oxygen which each animal can support ; and when this limit is approached, its reducing activity is diminished, or, it may be, extinguished. The water in the course of circulation is being con- tinually renewed, and, meeting with a diminished amount of freshly reduced matter, it is able to push the oxidation of the mud to a greater depth. It is easily conceivable that in many of the deep parts of the ocean the amount of ground life may be so limited that the water has no difficulty in oxidising at once its ejecta ; and these conditions would be favourable to the formation of a red clay or chocolate mud according to the preponderance of iron or manganese. While dealing with this subject it is proper to refer to Darwin’s book on Vegetable Mould and Earthworms , which was published in 1881. His masterly investigations in the kindred department of the part played by earthworms in the formation of the terrestrial soil strengthened me much in my belief in the soundness of the views above developed as to the formation of marine muds. Indeed, to a certain extent he extends his views himself to the case of marine muds. At page 256, after noticing that it is due to the milling action of the gizzards of worms that the supply of exceedingly finely divided mineral matter, which is removed from the surfaces of every field by every shower of rain, is constantly renewed, he adds in a note : “ This conclusion reminds me of the vast amount of extremely fine chalky mud which is formed within the lagoons of many atolls, where the sea is tranquil and waves cannot triturate the blocks of coral. The mud must, so I believe, be attributed to the innumerable annelids and others animals which burrow into the dead coral, and to the fishes, Holothurians, &c., which browse on the living corals.” Darwin further gives an 1890-91.] Mr J. Y. Buchanan on Sulphur in Marine Muds. 39 approximate numerical result or estimate of the work of earth- worms which is interesting. At page 258 he says : “ Nor should we forget, in considering the power which worms exert in tritur- ating particles of rock, that there is good evidence that on each acre of land which is sufficiently damp and not too sandy, gravelly, or rocky for worms to inhabit, a weight of more than 10 tons of earth annually passes through their bodies and is brought to tho surface.” On a Simple Pocket Dust-Counter. By John Aitken, Esq. (With a Plate.) (Read December 1, 1890.) It is now a year and a half since I communicated to this Society a description of a portable form of apparatus for enabling us to count the number of particles of dust in the atmosphere. The working of that instrument in my hands has been most satisfactory, and though it has occasionally given trouble, yet it has not given more than might have been expected. Though that apparatus has worked quite pleasantly with me, and enabled a beginning to be made of an investigation into the amount, and the effects, of dust in our atmosphere, yet very few have as yet followed up this line of inquiry. This has probably been owing to there being something in the complicated nature of the apparatus which has deterred others from joining in the work. I therefore determined to see if a simpler, and at the same time a reliable, form of the apparatus could not he devised. After the experience gained in making thousands of observations with the portable apparatus, I have acquired an acquaintance with its weak points, and a knowledge of what it would be necessary for an instrument of this kind to do under the different conditions in which it would he required to work, and I may now sum up the indictment against the portable apparatus under the following heads : — It is too complicated ; it has too many weak points ; it is too heavy; it has an unnecessarily wide range for meteorological work ; and it is too expensive. If an instrument could he con- 40 Proceedings of Royal Society of Edinburgh. [sess. structed free from the first four charges, it is probable the fifth would vanish. First, as regards weight, the experience gained with the portable apparatus has shown that the size may be very much reduced if the instrument is to be used only for testing air of country districts — i.e ., air free from immediate local pollution. Experience has shown that in country air the number of particles is rarely over a few thousands per cubic centimetre. It is therefore not necessary to use the small measures of the portable apparatus under these condi- tions, as we can with the air-pump alone test air up to an impurity of 25,000 per cubic centimetre. It is ouly for air of greater im- purity than this that the stopcock measures are required. These small measures may therefore be omitted. Again, when testing country air, the proportion of pure air to impure air required to make a test does not vary greatly — from 4 to 1 to 19 to 1. The receiver of the instrument does not therefore require to be so large as when the air to be tested requires to be mixed with some hundred times its volume of pure air. This admits of the receiver, and therefore of the whole apparatus, being greatly reduced in size. The capacity of the receiver in the pocket instrument has therefore been reduced to one-fifth of that of the portable apparatus. This at once effects a great reduction in the weight, and the stopcock measures not being required reduces the expense as well as the weight. Turning now to the weak and troublesome parts, these are principally : — (1) The air-pump valves are liable to get out of order, and occasionally give rise to trouble. (2) The india-rubber tube for closing the opening through which the stirrer-rod passes occasionally fails, and gives trouble by leaking. Further, these india-rubber tubes with closed ends require to be specially prepared for the instrument, and it is difficult to get suitable tube for the purpose. And (3) the silver counting stages are delicate and troublesome to keep. So far as my experience goes this is not the case, as after a little practice no trouble has been experienced, and the first silver stage put into my instrument is still in use and in good condition. My experience, however, is not that of others, and it seemed in the highest degree desirable that some improve- ment be made in this direction by the introduction of a counting stage that could be more easily kept in working order. 1890-91.] Mr J. Aitken on a Simple Pocket-Dust-Counter. 41 Returning now to the first weak point, viz., the air-pump valves, reference to the Plate given with this paper will show how this difficulty has been overcome. The figures on the plate show the new pocket instrument drawn full size. In the figures, R is the receiver, and P the pump. It will be observed that the receiver R communicates with the pump P by means of the stopcock K, and it will be noticed that all difficulty with the valves is got over by simply removing them altogether, and making the stopcock K act the double part of air-pump valves, and valve for admitting the air to be tested. The passage through the plug of the stopcock K is not straight, but is bored at right angles as shown. It will also be noticed that there are three ports in the body of the stopcock — one communicating with the pump P, one with the receiver R, and one with the outer air. It will be observed that the lower part of the air-pump is similar in design to that of the portable apparatus. The continuation of the pump-barrel G forms a guide for the piston-rod of the pump, and has a scale graduated on it to enable the observer to introduce into the receiver different proportions of impure air for testing. At fig. 4 is shown a separate drawing of the guide-tube, and on it is shown the scale marked with the figiires Au, rh> t- This scale is so divided that when the guide-collar is drawn down to those respective marks it enables us to introduce into the receiver measured quantities of impure air, such that when mixed with the pure air in the receiver and expanded there will be these propor- tions of impure air in the receiver. So that on making a test and counting the number of drops per cubic centimetre in the mixed and expanded airs in the receiver, the number so obtained must be multiplied by the proportion of impure air used. Suppose, for instance, that we drew down the pump to the mark on the scale, and on testing the mixture of this amount of air with the pure air in the receiver, and observed, in say, ten tests, an average of two drops per square millimetre, then as there is one centimetre of air above the counting stage, two drops per square millimetre will be 200 per cubic centimetre in the air of the receiver, but this figure must in this case be multiplied by 20 to get the number of particles in the outer air, which in this case would be 4000. The guide G is fitted to the cylinder cover of the air-pump by 42 Proceedings of Royal Society of Edinburgh. SESS. means of a screw to enable it to be taken to pieces for the con- venience of packing. The piston of the air-pump is packed with the usual cupped leather. To this I have added a small spring ring, as shown in drawing, at the lower part of the piston. This ring, so far as experience yet goes, has been found to be an advantage, and has kept the piston always tight with varying degrees of dryness of the leather. The second weak point in the portable apparatus, to which reference has been made, is the india-rubber tube making the air- tight joint between the rod of the stirrer and the receiver. Here, again, as will be seen from the drawing of the pocket instrument, the difficulty has been got over by simply removing it, and closing the end of the tube with a metal cap. This is possible in the pocket instrument, because we can move the stirrer without touching it. It is only necessary to invert the instrument, when the stirrer drops to the other end, and on again bringing the instrument to its original position, the stirrer again drops to the bottom. These movements are made two or three times to make the mixing thorough. Some little attention is necessary in the construction of the stirrer. It will not do to put a diaphragm into the receiver and allow it to fall anyhow. The effect of that would be to manu- facture a great quantity of nuclei, and copious showers would invariably follow its use. These showers are caused by nuclei formed by the wet surface of the stirrer splashing on the wet surface of the receiver. It will be seen from the drawing that the stirrer is caused to move truly by means of a small rod fixed in it, and projecting downwards. The lower end of this rod enters a tube which projects through the bottom of the receiver, the lower end of this tube being closed. Both ends of the guide-rod are pointed to reduce this splashing surface to a minimum. When the instrument is inverted, the falling stirrer keeps parallel to the top and bottom of the receiver, but touches neither, save at the points, and nuclei are rarely formed. As in the other instru- ments, both sides of the stirrer and the bottom of the instrument are covered with blotting-paper, cemented on with india-rubber solution. The blotting-paper is kept moist to saturate the air, and supply water for the rain drops, when the entering air is dry. On referring to the drawing it will be seen that there is no 1890-91.] Mr J. Aitken on a Simple Pocket Dust-Counter. 43 filtering apparatus attached to the pocket instrument. With the removal of the air-pump valves its use would he inconvenient, and it is not a necessary part of the apparatus. For viewing the counting stage the magnifying lens M is used. A common single lens of about two-centimetre focus does very well for the purpose. It is lighter and less expensive than a compound one. The lens is mounted in a tube which slides into another tube, this larger tube is attached to a disc of brass of the same diameter as the top of the receiver. This disc has a flange all round it of such a size that, when cut so as to give it a spring, it grasps the top of the receiver firmly, but in such a way that it can be easily lifted off. This is necessary, as the inside of the glass cover of the receiver often gets dewed, and the easiest way of removing the condensed moisture is to lift off the cover carrying the lens, and hold the finger on the glass to heat and evaporate the moisture from the inside surface. Before proceeding to describe the improvements in the counting stage, it will he as well to describe the manner of using the new instrument. The first thing to he done is to see that the inside of the receiver is wet. If it is, then examine the inside surface of the glass cover of the receiver, and see" if it is free from condensed moisture, which would interfere with a clear view of the stage. If it is not clear, take off the metal cover and hold a finger on the centre of the glass plate till it begins to clear, and then replace the cover. Too much heating should be avoided, as it gives rise to trouble with the counting stage. Now examine the surface of the counting stage, and see if it is free from specks. If it is not satisfactory, take it out and clean it with a piece of clean cloth. Care is advisable in doing this to see that the cloth is perfectly clean, as otherwise the stage will look dirty and streaky in the humid atmosphere in the receiver. If the stage is simply dewed, then touch the underside of it with a finger to heat it slightly. If the finger is not quite clean, put a thickness of cloth or other protection over it. If these two glass surfaces are in good order, the instrument is ready for making a test. If it has been necessary to take the counting stage out of the receiver to clean it, then this will have admitted much impure air, aud as there is no filter to enable us to fill the receiver with pure 44 Proceedings of Royal Society of Edinburgh. [sess. air, we must now purify it in another way. To do this the stop- cock A is closed, and the stopcock K is turned so as to put the pump into communication with the receiver, that is, in the position shown in fig. 1. A stroke of the pump is now made. This causes condensation to take place on the dust particles when some of them drop out of the air. The piston is again put to its top position, and another stroke made, when more particles settle, or are deposited on the sides by the rush of air. After this expanding and condensing process has been done a few times all the particles of dust will have become nuclei, and be deposited on the bottom of the receiver. The air will now be pure, no drops falling when expan- sion is made. This process of purifying the air in the receiver is quite as quick as the filtering one. Indeed, when the filtering process is used, it is always quicker to end by showers of the last particles. The air in the receiver being now purified so that no drops are seen falling when expansion is made, the next thing to be done is to introduce into the receiver the necessary quantity of the air to be tested. However, before doing this, it is advisable to turn the stopcock K a quarter turn to the left, so as to bring the receiver into communication with the outer air. The object of doing this is to bring the pressure inside the receiver to that of the open air. When making the repeated expansions to purify the air in the receiver, some air may have leaked in past the piston, and it is to get rid of this air that the stopcock is opened and the receiver put into communication with the outer air before taking in the measured quantity. If this was not done the amount measured in would be too small by the amount of the leakage. There will be no leakage if everything is in good working order ; still it is a good precaution always before taking in the air to be tested to turn the stopcock and allow any plus pressure to escape. The air in the receiver being at the same pressure as the outer air, the measured quantity of the air to be tested is then taken into the receiver in the following manner : — The piston being at the top of its stroke, where it ought always to be at the end and beginning of every test, and the stopcock in the position shown in the draw- ing, the piston is then drawn down the amount that is thought will be suitable under the conditions. Say it is drawn down to the mark on the scale, by this movement there is taken out of 1890-91.] Mr J. Aitken on a Simple Pocket Bud-Counter. 45 the receiver a measured quantity of air. The stopcock K is now turned one quarter turn to the left, so as to bring the inside of the receiver into communication with the outer air. When this is done the measured quantity of air rushes into the receiver. The quantity of air we have taken out of the receiver to make room for the air to be tested is, however, still in the pump, and must now be got quit of. To do this it is only necessary to return the piston to the top of its stroke before turning the stopcock back again to bring the receiver into connection with the pump. When the stopcock K is turned to the position to admit the outer air to the receiver, it will be seen from the drawing that the pump is then also in com- munication with the outer air by means of a small passage drilled longitudinally through the plug of the stopcock. By this arrange- ment only one movement of the stopcock is necessary for admitting the air to the receiver, and opening the discharge valve of the pump, and when the stopcock is again turned to bring the receiver into connection with the pump, the discharge valve is closed. From this it will be seen, that though we have dispensed with the air- pump valves in this new arrangement, we have not increased the number of stopcocks required, nor the number of movements necessary for making a test. The necessary quantity of air being admitted to the receiver, and the pump emptied, and the stopcock turned to its original position, so that the receiver is in communication with the pump, the instrument is then inverted so as to cause the stirrer to drop inside the receiver, and again brought to its vertical position when the stirrer again drops. This is done two or three times to mix the impure air with the pure air in the receiver. When this is done, the instrument is held, with the top of the receiver horizontal, and in a convenient position for the observer viewing the counting stage through the magnifying glass. Expansion is then made, and the number of rain drops counted in the usual way. If in this trial more than five drops fall per square milli- metre, then too much impure air has been taken in, and a smaller proportion of impure air must be used to get a correct test. From the number of drops observed it is easy to determine whether Jq or Jg. will be the best proportion to use for testing under the existing conditions. On the other hand, if, in this preliminary 46 Proceedings of Royal Society of Edinburgh. [sess. trial, less than one drop per square millimetre fell, then the quantity of impure air ought to be increased to, say, impure air. Sometimes, however, the air is so pure that i is too little, and it is desirable to have no pure air in the receiver, and to fill it entirely with the air to be tested. When this is the case, the stopcock K is turned so as to put the receiver into communication with the outer air, and the air is drawn out of the receiver through the stop- cock A. This may be done either by means of the mouth, or by any simple piece of apparatus. The current must be kept flowing through the receiver till all the pure air has been drawn out. After this the stopcock A is closed, the receiver put into communication with the pump, the stirrer worked, expansion made, and the drops counted in the usual way. When working in this way the number obtained per cubic centimetre in the air of the receiver has to be multiplied by 1*4 to allow for the reduction in number produced by the expansion. When working in pure air it is often necessary, instead of confining the attention to one square millimetre, to observe the number of drops that fall on a square of four squares, or on a square of nine squares, that is, of nine square millimetres. Having described the manner of working the new apparatus, we shall now proceed to describe what has been done to improve the counting stage, and make it more simple and easily kept in working order. Naturally glass seemed the most suitable substance for making those stages on account of the perfection of its surface, as well as for the ease with which it can be kept clean. I had pre- viously tried glass, but with no good results ; but though I had hitherto failed, the many advantages to be derived from the use of glass induced me to make a fresh attempt. The difficulty with glass is that the drops when they fall on it are nearly invisible. It does not matter whether we use glass mirrors or blackened glass — in all cases it is difficult to see the drops. On examining into the cause of this difference between glass and silver surfaces, water spray was allowed to fall on these surfaces, and the drops were then examined by means of a magnifying lens as they rested on the different surfaces. It was seen that on the silver, the drops scarcely touched the surface, but formed little flattened balls, and their brilliancy is due to the light reflected from the internal concave surface furthest from the light ; whereas the drops on glass adhere 1890-91.] Mr J. Aitken on a Simple Pocket Dust-Counter. 47 to and spread themselves over it, more or less, but there is no internal reflection, and only a slight external one on the convex side next the light. The problem then came to be — Could it not be possible to prevent the drops adhering to and spreading themselves on the glass ? In some trials I got encouragement to suppose this might be possible by coating the surface of the glass with some substance that would repel the water. The manner of testing this was to coat a clean plate of glass with the substance under trial, allow a shower of spray to fall on it, and examine the drops with a lens. In this manner many substances were tried, but the best results were got with paraffin-wax and refined beeswax. These substances were put on the glass, and then rubbed off till their presence could scarcely be detected. Glass so treated was found to act exactly like silver ; the spray rested on the surface in little round balls, and showed the internal reflection well. These substances were then tried in the dust-counter, on small silvered glass counting stages, and it was found that they did perfectly under certain conditions, but it was difficult always to secure these conditions with the very small pieces of glass. The treatment was tried in practice for a< time, but it was found to be troublesome, as it did not always produce the desired result. The plan was therefore abandoned as it was not thought good enough, nor sufficiently simple, and certain in its action, to be put into the hands of most observers. Experiments were therefore begun in another direction, and trials made of the effect of illuminating the stage from beneath. If we place a mirror underneath the glass stage so as to reflect the light of the sky through the stage, no satisfactory result is obtained owing to the general glare of light. However, I have fortunately succeeded in lighting the stage from beneath in such a way that not only are the drops visible, but they are seen with a distinctness far superior to anything yet obtained, even with silver in its best condition and best lighting. Not only so, but a very low degree of illumination is sufficient to show the drops clearly. One great advantage of this is, that observations can be made in early morning and late evening, when the light is far too feeble for working with silver. 48 Proceedings of Royal Society of Edinburgh . [sess. This method of illumination is shown in the drawing of the instrument (see figs. 1 and 3). The counting stage is made of glass, and is illuminated from beneath, the light being reflected upwards by what we might call a spot-mirror, which is simply an ordinary mirror with a black circular space in the centre. This enables the drops to be illuminated by means of a slightly oblique light, while an image of the black spot covers the field of the lens. The result is the drops are seen shining brilliantly on a nearly black field, and are counted with great ease. After satisfying myself of the value of this method of working, a difficulty presented itself. I had an ordinary micrometer made of a size suitable for the counting stage. This micrometer was made by a professional maker of these instruments ; but on fitting it into the dust- counter, the method of illumination was found to be so powerful and trying, that it brought out all manner of imperfections and blemishes on the micrometer which were not seen with a magnify- ing glass and ordinary illumination. The cross lines on the micrometer looked rough, with a crystalline glistening appearance, and there were so many specks on its surface that working with it was very difficult, as few squares were free from spots, which were apt to be counted as drops. The makers of the micrometer were therefore written to about these imperfections ; their reply was that “ they had done their best, carefully selecting the glass, &c., and that they thought it would be difficult to get a better instrument.” If better could not be got, I felt that the value of the new arrangement would be greatly decreased. I therefore determined to attempt the manufacture of micrometers myself, to see what could be done. A piece of patent plate-glass was procured, this was cut into suitable sizes and very carefully examined with a strong lens, while it was illuminated by means of a spot-mirror. After finding a fairly good piece in the glass, any specks which were on its surface were tested with a pointed piece of soft wood, and if they were not found to be removable, the part was rejected and the search continued. In this way a few pieces were obtained large enough for the purpose, and perfectly free from specks. These perfect pieces were marked off on the glass, cut out, and fine cross lines at one millimetre apart were engraved on their surfaces ; after which they were turned into little circular discs of the required diameter. 1890-91.] Mr J. Aitken on a Simple Pocket Dust-Counter. 49 Two methods of engraving these lines have been tried, and both of them give much better lines for the purpose than is obtained by the usual method of engraving micrometers. One method is to cover the glass with beeswax, and draw the lines with a fine needle point, and then etch with hydrofluoric acid. The lines obtained by the use of ordinary hydrofluoric acid are not very suitable, as they require to be of some breadth before they are visible with the spot-mirror illumination, and they then show as bright glistening lines. The mixture known as “white acid,” how- ever, gives a fine line with just that degree of white visibility which makes them appear clear without glancing and distracting the attention. In this manner the micrometer which is at present in use was prepared, and it has been found in every way satisfactory. The vapour of hydrofluoric acid also gives good results. In etching these lines, trial must be made with the acid and a piece of the same glass to find the correct time the micrometer requires to be kept in the acid to etch to the required depth, the trial pieces being tested under the spot-mirror illumination. The difficulty of draw- ing these lines with a diamond is, that when they are made strong enough to be easily seen, they have always bright spots on them. It will be observed from the drawing that these micrometers or counting stages are made of thick glass. The object of this is to prevent any speck, or anything adhering to the under side of the glass, interfering with the clearness of the field. The thickness of the glass puts them so much out of focus that they do little harm. There is then, therefore, no real barrier to the use of these micro- meters, only the glass must be selected when under the illumination of a spot-mirror. It may be remarked here that the spot-mirror may be found useful for other purposes. It gives us a powerful means of detecting flaws in lenses, &c. The surface of a new lens when examined by means of it looks so full of imperfections that it seems scarcely possible it can give a perfect image, while the imperfec- tions must give rise to the dispersion of a good deal of light. The other method of engraving the lines on the glass, which has been tried and found to give good results, is to cover the glass with very fine emery powder, wetted with turpentine, and scratch the lines with a needle point ; or better, to tip the needle with a little diamond bort. The fineness of these lines can be made VOL. XVII. 21/2/91 D 50 Proceedings of Royal Society of Edinburgh. [sess. all that is desired, and there is little trouble from the needle blunting under the operation. In ruling these lines, it is, of course, necessary to keep the pressure on the needle constant, and to make the same number of strokes across the glass for each line, in order that the lines may be equally thick. The pocket instrument has been occasionally in use during the whole of this summer, first with a silver stage and then with a glass one, and has been working quite satisfactorily, and giving results agreeing with those of the larger instrument. The instru- ment appears to be now so simple, it can be easily worked by any one. So far as can be seen at present, the weakest point in the instrument now, and the only one likely to cause trouble, is the piston packing. If the piston is not tight, correct work cannot be done. Fortunately, the conditions of testing make it impossible, with ordinary care, to make a test with a badly-fitting piston ; because it would be impossible with it to thoroughly purify the air in the receiver. When air leaks in past the piston, nuclei are admitted, and these prevent the showers in the receiver ceasing completely. If the piston leaks a little, at each stroke of the pump, though no air has been admitted by the stopcock, a few drops will be seen falling, and call the attention of the observer to the imperfection. To reduce the trouble from this cause as much as possible, I have introduced the spring ring already referred to, under the leather cup packing, and so far this has worked well ; the piston has given no trouble since its introduction. One objection to the cup leather packing is, that if it gets out of order the repair of it might not be within the powers of the observer. To obviate this objection, the arrangement shown in fig. 5 has been designed, tried, and found satisfactory. It consists simply of the substitution of a plunger- pump for a piston one. The advantage of the plunger is, that any one can easily pack the stuffing-box, and some kind of material for doing it can always be obtained. In appearance, the plunger-pump is not so compact as the piston one, on account of the diameter of the stuffing-box requiring the guide-tube to be made of much greater diameter. Yet this is little disadvantage so far as compact- ness for packing is concerned, as the pump-barrel can be slipped inside the guide-tube, when unscrewed for packing in its case. 1890-91.] Mr J. Aitken on a Simple Pocket Dust-Counter. 51 It may be asked — Does this simple instrument displace the more complicated earlier forms of the apparatus ? Have the earlier forms been unnecessarily complicated 1 The answer to this is — That the pocket instrument is designed for special work, and only for that work ; while the earlier forms are still necessary, and can do work in conditions in which the pocket instrument would be use- less. The large instrument fitted up in the Ben Nevis Observatory, with its arrangement of circulating pipes, aspirator, and artificial illumination, is still the best form for a first-class observatory, where observations have to be made in all ;weathers, and during night as well as day. The Portable instrument is still necessary when we wish to test locally poluted air, such as that near human inhabita- tions, that is for sanitary work ; while the use of the Pocket instrument is confined to meteorological work in the open air, and its advantages are simplicity and lightness. It may be remarked here that the Pocket instrument may be used to give a rough indication of the impurity of polluted air. The manner of using it for this purpose is as follows : — First, turn the stopcock K a quarter turn to the left, and draw down the piston. This takes the impure air into the cylinder. The whole of this air is then discharged by pushing the piston to the top of its stroke. By these movements nearly, but not quite, all the impure air is expelled from the cylinder. The small passage between the stopcock and the piston is still full of impure air. Immediately on pushing the piston to the top of its stroke, the stopcock is returned to its original position; the piston is then drawn down, and at once returned to its top position. By these movements we have taken some of the pure air out of the receiver and mixed it with the small amount of impure air in the pump passage, and the return stroke has sent the mixture into the receiver, where after being stirred, a shower is produced, and the drops counted. This cannot give a very accurate result, as some of the particles must be lost when the air is drawn in from the receiver to mix with the impure air in the pump passage. This loss, however, does not seem to be great, owing probably to the higher temperature of the pump-barrel, from contact with the hands, preventing con- densation. Owing to the possibility of some air being left between the top of the piston and the cylinder, it would be difficult to 52 Proceedings of Royal Society of Edinburgh. [sess. gauge by measurement the capacity of the space not emptied, when the piston of the pump is returned, to enable us to make the necessary calculations to find the number of particles. Perhaps the best way of gauging would be to test air which gave, say, five drops per square millimetre, when using ~ of impure air, and working in the usual way. Then test this same air and see how many it gave when using the contents of the small space above the piston. Perhaps it might give one drop per four square millimetres. If a series of tests give these figures as the average number, we would know that the capacity of the space was of the ~ measure, or the ToVo that of the receiver. So that whatever number we observed in the air of the receiver when working in this manner would require to be multiplied by 1000 to get the number in the air tested. The instrument is so constructed, that when the different parts are unscrewed they fit into a case 4§ inches by 2J inches by 1J inches deep, or little larger than a well-filled cigar-case. The weight of the instrument, without the case, is a little under 8 oz. On the Action of Metallic (and other) Salts on Carbonate of Lime. By Robert Irvine, F.C.S., and W. S. Anderson. (Read January 9, 1891.) It is well known that pseudomorphic changes take place with many minerals. These changes may be either by alteration or displacement. In the case of carbonate of lime they are generally of the former order. Among other work conducted at the Marine Station, Granton, during the past year, a number of experiments were instituted with the view of showing how far carbonate of lime was influenced in this direction by metallic and other salts. Corals, preferably the more porous and soft varieties, were selected for this purpose, and these were exposed to the action of solutions of the following salts : — Chloride of manganese, sulphate of iron, chloride of zinc, chloride of chromium, nitrate of nickel, nitrate of cobalt, nitrate of copper, nitrate of lead, chloride of mercury, chloride of tin, nitrate of silver, phosphate of ammonia. In many cases me action was very slow, especially in the case of Vol. XVIII Proc. Roy. Soc. Edin. MR. JOHN AITKEN ON POCKET DUST-COONTER. 1890-91.] Mr Irvine and Mr Anderson on Action of Salts. 53 the salts of nickel and cobalt. On the other hand, with salts of copper and manganese, the action was sufficiently rapid so as to make a material difference, within a few weeks, in the composition of the coral exposed to their action. In most cases there is a direct interchange between the lime (of the carbonate of lime) and the oxide of the metal which takes its place. Thus we have : — 1. With a copper salt, in seven months, 26*4 per cent, of carbonate of copper taking the place of an equivalent amount of car- bonate of lime. 2. "With chloride of manganese, in twelve months, 58*4 per cent. of carbonate of manganese. 3. With salts of iron practically the whole coral is altered — first, into carbonate, and ultimately, on exposure to air, into sesquioxide of iron. 4. With salts of zinc, 26 ‘8 per cent, of carbonate of zinc had formed in six months. 5. With phosphate of ammonia the transference was between the carbonic acid of the coral and the ammonia of the salt. The lime having combined with the phosphoric acid to an extent equal to 60 per cent, of phosphate of lime. Without doubt, phosphate of lime deposits, especially those found on old coral islands, have had their origin in this manner, the phosphoric acid being derived from the excreta of wild fowl, deposited upon dead coral or carbonate of lime, the amount of pseudomorphic change being in accordance with the quantity of guano deposited. Of course, transference between carbonate of lime and alkaline phosphates can only take place in the presence of water, so that we have no such, pseudomorphs where the climate is rainless ; there the guano remains as deposited, whilst these deposits in rainy zones always assume the form of insoluble phos- phate of lime. Carbonate of lime, with silver and mercury salts, seems to throw down oxides, not carbonates. But the compounds with nickel and cobalt we have, as yet, been unable to determine. With a true pseudomorph, the structural form of the carbonate of lime, be it in the shape of coral , shells , or calcite , remains 54 Proceedings of Royal Society of Edinburgh. [sess. unchanged ; when, however, an oxide is produced, as in the case with tin and mercury salts, it forms merely a superficial coating. From the results of numerous experiments, which it is unneces- sary to record here, we have good grounds for assuming that carbonate of lime, either in a massive or comminuted condition, or in solution, carries out the most important function of withdrawing metallic and other bodies from sea-water, which may he said to hold (often in minute amount) almost every elementary substance in solution, and fixing these in a concentrated condition. The geological significance attaching to this property of carbonate of lime is apparent, as, without question, many metallic ores owe their origin to this source. Manganese Deposits in Marine Muds. By Robert Irvine, F.C.S., and John Gibson, Ph.D. (Read January 9, 1891.) Two theories have been put forward in order to explain the formation of manganese deposits in marine muds, and more particularly with regard to manganese nodules : one by Murray, in a paper read before this Society in 1876, the other by Buchanan in 1888. Murray assumes the gradual oxidation of carbonate of manganese resulting ultimately in the formation of hydrated peroxide of manganese. Buchanan first propounded his theory in 1880, and subsequently, in a paper read before this Society in December 1890, argues as follows : — “ The principal agent in the comminution of the mineral matter found at the bottom of both deep and shallow seas and oceans is the ground fauna of the sea, which depends for its subsistence on the organic matter which it can extract from the mud. “ In order to fit them for collecting their nutriment in this way, the animals have been fitted with different forms of masticating or milling apparatus, so as to thoroughly deal with the matter which they pass through their bodies. It has been shown that most silicates are decomposed to a certain extent when ground or pul- verised under water ; so that the mere mastication of the sand or mud in presence of pure water would have a decomposing action on 1890-91.] Mr Irvine and Dr Gibson on Manganese Deposits. 55 the silicates which it contains. This action is much assisted, in the case of marine animals, by the fact that the water which they pass through their bodies along with the sand is charged with sulphates. These are easily reduced to sulphides by the action of the organic matter of the secretions of the animals. The resulting sulphide at once suffers double decomposition with any oxide of iron or manganese which is present as such in the mud, or may be being set at liberty from silicates under the decomposing influence of trituration under water. The sulphides of manganese and iron so formed are, in course of nature, extruded by the animals, and if exposed to the sea-water on the surface of the mud are quickly oxidised, the manganese taking priority. The mud below the surface layer, where ground life is abundant, remains blue, being protected by the oxidation of what is above it. “ At the bottom of the ocean the mineral matter is thus exposed to a reducing process due to the life of the animals which inhabit it, and to an oxidising process due to the oxygen dissolved in the water. Other things being equal, the redness or blueness of a mud or clay depends on the relative activity of these processes. They also require a controlling or modifying influence on one another. For, although marine animals are much less sensitive to variations in the amount of oxygen in their atmosphere than terrestrial animals, it is certain that there must be a limit to the deficiency of oxygen which each animal can support; and when this limit is approached, its reducing activity is diminished, or it may be extinguished. The water in the course of circulation is being continually renewed, and, meeting with a diminished amount of freshly-reduced matter, it is able to push the oxidation of the mud to a greater depth. It is easily conceivable that in many of the deep parts of the ocean the amount of ground life may be so limited that the water has no difficulty in oxidising at once its ejecta; and these conditions would be favourable to the formation of a red clay or chocolate mud, according to the preponderance of iron or manganese.” In a word, that the animals passing sand or mud through their bodies with sea-water tend to reduce the sulphates present in the sea-water, and the alkaline sulphides so formed cause the formation 56 Proceedings of Iioyal Society of Edinburgh. of sulphides of iron and manganese, which, on subsequent exposure to sea-water containing oxygen, are quickly oxidised — the manganese taking priority. It is obvious that any conclusion as to the relative correctness of these two theories cannot be arrived at solely by chemical con- siderations, but must depend largely upon such questions as the relative abundance and distribution of animal life upon the sea- floor ; and, further, upon the physical structure of the deposits. In this paper we propose to confine ourselves chiefly to the chemical aspect of the subject, and more particularly to certain reactions of manganese, which we believe to have a very direct bearing upon it. A. — Behaviour of Hydrated Protoxide of Manganese. If freshly-precipitated hydrated protoxide of manganese be added to sea-water, it is pretty freely dissolved, and if the sea-water be in large excess, the manganese remains in solutions for a very con- siderable time. If, however, more hydrated protoxide of manganese be added than is sufficient to form carbonate of manganese with the carbonic acid in the sea-water, the excess of manganese is pre- cipitated, after a comparatively short period, as hydrated oxide of manganese (more or less completely peroxidised), provided the water is sufficiently aerated. B. — Behaviour of Carbonate of Manganese. Carbonate of manganese, when freshly precipitated and amor- phous, dissolves in sea-water in notable quantity, but is very sparingly soluble in the crystalline form. Purther, when carbonate of manganese is dissolved in sea-water, it remains in solution. Such solutions do not give rise to any rapid production of peroxide of manganese. This is in accordance with what has been hitherto ascertained concerning the behaviour of carbonate of manganese, which, as has been shown by Bischoff and others, is very slowly oxidised under ordinary circumstances. A. Gorgeu ( Comptes Rendus, cviii. 1006-1009) states “that native manganese car- bonate or diallogite is very stable, and remains unaltered after contact with aerated water for three years. Precipitated manganese 1890-91.] Mr Irvine and Dr Gibson on Manganese Deposits. 57 carbonate, which has become crystalline, remains in contact with aerated water, at an ordinary temperature, without any peroxide. If the precipitated carbonate remains in contact with aerated water for ten years about one-third is decomposed, and the product has the composition MnO,Mn02. Two specimens, containing respec- tively eighty and seventy per cent, of manganese carbonate, were exposed to air in the dry state for eight years. In the first case thirty-three per cent., and in the second fourteen per cent., of manganese carbonate remained — the rest being converted into “ the oxide MnO,Mn02.” Other observers have found that under certain conditions, and notably in presence of carbonate of lime, peroxida- tion takes place, although very slowly. This is in accordance with our own experience. Some eighteen months ago, in connection with Irvine and Anderson’s investigation on the action of metallic salts on carbonate of lime,* some pieces of coral and chalk were placed in a weak solution of chloride of manganese in sea-water. Interchange has taken place, and fully fifty per cent, of the calcium has been replaced by the manganese. The outer portion of the coral is blackened, owing to the peroxidation of the carbonate, and the bottle in which the coral was placed has become covered with a film of peroxide of manganese. There is also a distinct precipitation of peroxide in the liquid. C. — Behaviour of Sulphide of Manganese. Precipitated sulphide of manganese in a moist condition is well known to be very unstable in presence of oxygen or air, and rapidly becomes brown owing to peroxidation. It also behaves like an alkaline sulphide towards certain metallic salts, and even gives up its sulphur to ferric hydrate, as was found by Buchanan (see his paper read before this Society, December 1890). In the presence, however, of carbonic acid sulphide of manganese is quickly and completely decomposed — sulphuretted hydrogen being given off and carbonate of manganese formed. This decomposition of sulphide of manganese takes place even when the carbonic acid is loosely combined, as in solution of bicarbonate of lime or manganese. Further, in the presence of carbonate of lime and oxygenated sea- * Proc. Boy. Soc. Edin. , vol. xvi., p. 319. || 'A tfj 58 Proceedings of Royal Society of Edinburgh. [sess. water, sulphide of manganese is not peroxidised, carbonate of manganese and sulphate of lime being formed. This is shown by the following experiment : — Equivalent proportions of sulphide of manganese and precipitated carbonate of lime were added to sea- water, and a current of air was passed through the mixture for twelve hours. The mixture did not become brown, and when examined it was found that the whole of the manganese had been converted into carbonate, and the lime into sulphate. A similar quantity of sulphide of manganese to that used in the above experiment was mixed with distilled water and exposed to the action of a current of air for a like period. It became brown, and instead of giving off sulphuretted hydrogen on addition of hydro- chloric acid, chlorine was evolved, so that the decomposition of the sulphide by oxidation was in this case evidently complete. We find, further, that when sulphide of manganese is added to sea-water, in quantity not more than sufficient to form carbonate of manganese with all the carbonic acid present in the sea-water, the sulphide is completely decomposed, sulphuretted hydrogen liberated, and the manganese dissolved. These facts appeared to us to be incompatible with the theory of the formation of manganese deposits propounded by Buchanan, which hitherto had appeared to us to offer a very plausible and probable explanation of many of the points connected with these curious formations. In this change of view we were confirmed by the following experiment : — A mixture of ferrous and manganous carbonates was added to sea-water along with a quantity of decomposing mussel flesh, and the whole mass allowed to decompose, air being excluded. After four or five days the contents of the vessel became black, and sulphuretted hydrogen was freely evolved. Air was then blown for twelve hours through a portion of the mixture, which was then filtered and carefully washed. The residue left in the filter was then examined for manganese, which was found to be entirely absent. Another portion of the decomposing mixture was examined for sulphide of iron. The whole of the iron which had been added as carbonate was found in the form of sulphide. 1890-91.] Mr Irvine and Dr Gibson on Manganese Deposits. 59 From the behaviour of manganese as above described, we have come to the conclusion that the formation of sulphide of manganese cannot be a result of the animal life, or the decomposition of animal matter at the sea-bottom, as supposed by Buchanan ; inasmuch as sea-water containing excess of carbonic acid must be always present. Buchanan does not give any evidence whatever to show that sulphide of manganese is formed, but appears to rely upon the supposed analogy in the behaviour of iron and manganese. Under conditions such as those referred to by him, sulphide of iron is necessarily formed. Unlike sulphide of manganese, sulphide of iron is readily formed in the presence of sea-water, whether mixed with carbonate of lime or not, and solutions of carbonic acid or bicarbonates do not decompose it or prevent its formation. Thus in all cases where, through the life processes of animals, sulphide of iron is formed as a result of the reduction of sulphates, the excess of carbonic acid necessarily formed at the same time must prevent the formation of sulphide of manganese. This holds equally in the case of the decomposition of the dead bodies of animals at the sea-bottom. On a Difference between the Diurnal Barometric Curves at Greenwich and at Kew, By Alexander Buchan, LL.D. (Read June 16, 1890.) In the “Challenger” Report on atmospherical circulation, the diurnal barometric curves at Gries and Klagenfurt in the Tyrol, and at Cordova in the Argentine Republic, are specially examined. The most noticeable feature of these daily barometric oscillations is their very large amounts, those at Gries, for example, though in lat. 46° 30' N., being quite tropical in amount ; and the singular circumstance is that in no season does the morning minimum fall so low as the daily mean. Gries, Klagenfurt, and Cordova are each situated in a deep valley. In such situations, during night, the whole surface of the region is cooled by radiation below the air above it, and the air in immediate contact with the ground becoming 60 Proceedings of Royal Society of Edinburgh. [sess. also] cooled, a system of descending air-currents sets in over the whole face of the country bounding the deep valley. The direction and velocity of these descending currents are modified by the irregularities of the ground, and, like currents of water, they con- verge in the bottom of the valleys, which they fill to a considerable height with the cold air they bring down from the sides of the mountains. This cold and relatively dense air rises above the barometers which happen to be down in the valley, with the result that a higher mean pressure is maintained during the night. In summer, when the daily range of temperature reaches the maximum, the pressure during the coldest time of the night is maintained 0*040 inch higher at Gries than it is in open situations in that part of Europe. On the other hand, during the day these deep valleys become highly heated by the sun, and a strong ascending current of air is thereby formed, under which pressure falls unusually low. Thus, while at Vienna the afternoon minimum falls 0026 inch below the daily mean, at Gries the amount of the fall is 0*058 inch, and at Cordova 0*061 inch. The general result is, that in these deep valleys atmospheric pres- sure stands much higher during the night and falls much lower during the day than is elsewhere the case. The amounts increase in proportion to the daily range of temperature ; or, strictly speaking, to the amounts the temperature falls below the daily mean during the night, and rises above it during the day. The object of this paper is to show that the same rule holds in comparatively shallow valleys such as that of the Thames. Mr Francis C. Bayard has calculated, for the five years 1876-80, the diurnal range of barometric pressure for nine stations in the British Islands, including the two Observatories at Greenwich and Kew. The paper has recently been published by the Meteoro- logical Council, in which the Tables give the diurnal range to the ten-thousandths of an inch. The diurnal range for these two places, which are only seven miles apart, being for the same five years, are therefore strictly comparable, and the fourth decimal renders possible a more exact comparison of the results. The following are the departures from the daily means at Green- wich and Kew for June, from 9 a.m. to Koon, in ten-thousandths of an inch : — 1890-91.] Dr A. Buchan on Diurnal Barometric Curves. 61 Greenwich. Kew. Difference. 7 A.M. + 59 + 79 20 8 „ + 85 + 99 14 9 „ + 87 + 87 0 10 „ + 91 + 67 -24 11 „ + 67 + 45 - 22 Noon. + 17 - 7 -24 This comparison has been made for the whole year, and the differ- ences are entered in their places in the accompanying Table, where the minus sign indicates that, at the hour specified, Kew was that amount relatively lower with respect to its daily mean than Green- wich was with respect to its daily mean, and the plus sign that it was relatively higher. A longer period of comparison between these two barometers than five years will doubtless give still smoother curves than the Table indicates. Meantime, it is very evident that the ordinary diurnal barometric curve at Kew has superimposed on it a strongly marked curve, due to the relatively low position of the Observatory in the valley of the Thames. Table showing Comparison of Kew and Greenwich Barometers in Ten-thousandths of an Inch. Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec. Year. 1 A.M. - 2 0 +11 + 6 + 5 +28 + 17 + 8 + 9 - 2 - 5 - 2 + 6 2 „ 0 - 1 + 8 + 6 +13 +26 +24 + 18 +14 + 3 - 7 + 8 +10 3 ,, + 2 - 3 + 5 + 3 +11 +28 + 25 +20 + 19 - 7 -12 0 + 8 4 „ + 2 -12 + 9 + 5 + 9 +24 + 21 +30 + 13 + 15 - 7 -11 + 8 5 „ - 5 -13 - 3 - 1 +17 +26 +23 +15 + 8 + 7 - 6 -14 + 5 6 „ - 7 -13 - 3 + 7 +22 +30 +29 +28 +21 +14 - 1 - 3 + 11 7 ,, - 9 - 1 - 5 0 +22 +20 +24 + 15 +11 - 1 - 3 - 5 + 5 8 „ -10 +11 - 8 - 1 +16 +14 +18 + 15 + 9 + 3 +10 1 + 8 9 », -15 +11 + 3 - 3 + 6 0 + 5 + 1 + 7 + 7 + 6 13 + 1 10 „ - 1 + 7 +11 -11 -10 -24 - 8 - 5 - 5 - 9 + 8 + 4 - 4 11 „ + 1 +13 + 7 - 8 -13 -22 -16 -10 +13 + 1 + 9 + 8 - 1 Noon. + 12 + 3 - 9 -18 -23 -24 -16 - 7 + 3 - 3 - 4 - 8 - 6 1 P.M. + 6 + 5 - 9 -10 -17 -16 -18 -16 - 1 - 3 - 5 + 2 - 7 2 „ -18 -15 -27 -36 -45 -38 -36 -27 -17 - 9 -10 -16 -25 3 „ -17 - 7 -13 -12 -33 -26 -20 -22 — 23 -11 -15 -12 -18 4 „ —15 - 9 -15 -21 — 36 -36 -34 -33 -29 - 5 - 8 - 4 -20 5 „ -17 - 7 - 9 -19 -24 -28 -23 -35 -17 -11 -10 -12 -19 6 „ +10 + 1 -17 - 5 -18 -24 -28 -25 -17 - 7 - 2 - 1 -12 7 „ + 5 + 3 - 3 +16 - 2 -16 -24 -11 -17 - 3 + 9 + 5 - 4 8 „ +17 +11 + 5 + 23 + 14 + 8 - 1 - 2 - 1 + 8 +19 + 9 + 8 9 „ +17 +11 +11 +23 + 15 + 6 + 3 - 3 - 4 + 5 +10 +22 + 9 10 „ + 18 + 8 + 11 + 27 +25 +10 + 9 + 8 +11 + 5 +15 + 17 +12 11 „ +12 + 3 +13 + 5 +21 +10 +13 +10 - 1 - 1 + 8 +10 + 8 Midnight. + 2 + 7 + 12 + 8 +15 +16 +14 + 8 + 2 +13 +11 +16 + 9 62 Proceedings of Royal Society of Edinburgh. [sess. Barographic Record in the Vicinity of a Tornado. By- John Anderson. Communicated by Dr Buchan. (With a Plate.) (Read June 2, 1890.) The fluctuation shown by the barographic record occurred imme- diately after 6 p.m., at the time of the passage of the tornado of Thursday, March 27, 1890, near Owensboro, Davies County, Kentucky. The distance of the barograph from the nearest point of the tornado can be approximated by the evidences of damage the tornado left, and did not exceed a mile and a quarter or a mile and a half. At this distance to the south-east of Owensboro there is a ridge 150 or 200 feet high, and a large brick house on top was unroofed and partially demolished. This is the first evidence of destruction in the vicinity of Owensboro, but previous to this the noise of the approaching tornado was plainly audible to persons on the streets of the town. Until reaching the ridge above mentioned, the tornado appears to have passed in the air, accompanied by a roaring sound, without doing any damage in its passage. From a point about twelve miles to the south-west a tornado passed over the latter city two hours later. The rate of progress of the cyclonic area of low pressure, as shown by the signal service map, was forty miles an hour. On the same day a parallel tornado passed about thirty miles to the south of Owensboro, near south Carrolton. There was none to the northwards. The sudden dip in the barometric curve at 6 p.m. of March 27th is shown on the accompanying Plate. Though the centre of the tornado was from a mile and a quarter to a mile and a half distant, yet the barometer fell suddenly about the tenth of an inch, and immediately thereafter rose as suddenly to a point nearly two- hundredths of an inch higher than the point from which it fell. This observation, which is new to science, gives the explanation of the wrecking of buildings by tornados as by an explosive force within the buildings. The sudden lowering of the pressure outside, which must greatly exceed the tenth of an inch near the centre of the tornado, is amply sufficient to account for the fearful energy developed in these tempests. Proc. Roy. Soc. E din. Vol.XVlII Diagram Shewing the Barometric Curve at Owensboro’, Kentucky, during March 27th, 28th, and 29th, 1890. The X indicates the hour of OCCURRENCE OF THE SUDDEN DlP OF THE BAROMETER WHEN THE CENTRE OF the Tornado passed near the Station. X 1890-91.] Dr H. Marshall on Potassium Persulphate. 63 Note on Potassium Persulphate. By Hugh Marshall, D.Sc. (Read February 16, 1891.) Persulphuric anhydride and the corresponding acid have been known for some time. Berth elot obtained the former by subjecting a mixture of sulphurous anhydride and oxygen to the effluve electrique (as in the preparation of ozone), and a mixture of the latter with sulphuric acid, by adding the anhydride to water. He also pre- pared a similar mixture by the electrolysis of sulphuric acid solu- tion in a cell where the electrodes were separated by a porous pot. Both substances he found to he very easily decomposed, spon- taneously evolving oxygen. Up till now, however, the correspond- ing salts have not been prepared. In fact, Mendeleef, while commenting on Berthelot’s results, expresses the opinion that per- sulphuric anhydride is not a true acid-forming oxide, hut a peroxide similar to those of the metals barium, lead, &c., and that Berthelot’s persulphuric acid is analogous to peroxide of hydrogen. Becently, however, I have obtained the potassium salt, and have since succeeded in preparing it in quantity. While oxidising a solution of cobaltous sulphate in presence of potassium sulphate and sulphuric acid, by electrolysing it in a divided cell, as in Berthelot’s experiment, I obtained a quantity of white feathery crystals. These were filtered off, washed with cold water, and dried on porous plate over sulphuric acid. The sub- stance was found to possess powerful oxidising properties. When heated it fused and soon decomposed, evolving acid fumes and leaving a white residue which proved to be potassium sulphate. A solution of the substance gave only a faint precipitate with barium chloride solution, but on boiling a dense precipitate of barium sulphate separated gradually while chlorine was simultaneously evolved. These properties .seemed to point to the salt being a per- sulphate, and analysis confirmed this opinion. A known quantity was ignited and the resulting sulphate of potassium weighed. The residue amounted to 64*2 per cent, of the original. For potassium persulphate theory requires 64'4. The 64 Proceedings of Royal Society of Edinburgh. [sess. oxidising power was estimated by titration with ferrous sulphate and potassium permanganate. The extra oxygen thus found was 5*92 per cent, (equal to 35*5 of S04). Theory requires 5’93 (35*6 of SO*). I have since prepared a considerable quantity of the salt by electrolysing a solution of potassium hydrogen sulphate in a divided cell. After some hours the persulphate crystallises out from the liquid surrounding the anode. Potassium persulphate dissolves fairly readily in water at the ordinary temperature, easily in hot water. If the solution be boiled, especially if it is acid, decomposition with evolution of oxygen occurs. By solution in warm water, and cooling, the salt can be recrystallised in prisms resembling those of potassium per- manganate, with which the persulphate is evidently isomorphous. Dr James Walker has kindly determined the electric conductivity of the solution, and his results show that the formula is KS04, the solution behaving in a manner comparable to one of potassium perchlorate (which is also isomorphous with the permanganate). The solution of the pure salt is neutral to litmus, and appears to be stable at ordinary temperatures. It gives no precipitate with solution of barium salt. With silver nitrate it gives no immediate precipitate, but what appears to be silver peroxide separates out on standing. When mixed with potassium iodide solution, iodine is liberated only gradually, but more quickly on heating. The solu- tion is not decomposed by peroxide of hydrogen. It is attacked by ferrous sulphate in the cold, ferric and potassium sulphates being produced. If some of the solid substance be added to a small quantity of strong ferrous sulphate solution, as the salt dissolves the green colour changes to brown, and the liquid becomes warm. When the solid is gently warmed with strong nitric or sulphuric acid, oxygen highly charged with ozone is evolved. Hydrochloric acid gives chlorine. The properties of the salt have been as yet but superficially examined, and no attempt has been made to prepare other persul- phates. I am, however, engaged in a fuller investigation of the subject, and also in examining the behaviour of salts of other acids when electrolysed in a divided cell. 1890-91.] Mr R. E. Froude on the Soaring of Birds. 65 On the Soaring: of Birds : being a Communication from Mr R. E. Froude in continuation of the Extract from a Letter by the late Mr William Froude to Sir William Thomson, published in these 11 Proceedings,” March 19, 1888. (Read January 5, 1891.) The object of the present communication is to give the purport of the remainder of the letter referred to in the title, as well as that of other letters bearing on the same subject written by the late Mr Froude shortly afterwards, which were not at hand at the time the extract referred to was printed. In the extract already printed, Mr Froude expressed the view that the continued “ soaring ” (or “ sailing flight,” as it has also been called) of birds only took place where there was an ascending current of air of sufficient speed. And he noticed as an apparent exception, which he had observed one day on the passage to the Cape on board H.M.S. “ Boadicea,” that in a very light wind some albatrosses were seen soaring (manifestly without wing stroke) “ almost ad libitum ,” where there could not possibly be any ascend- ing current due to deflection of wind by the ship. He suggested as a possible explanation, and one which to all appearance fairly accorded with the birds’ visible movements, that they were availing themselves of the ascending stratum of air which must have extended above the advancing slope of each wave of the well- marked ground-swell which was running. From the dimensions of this, the maximum upward speed of such air current was estimated at about 3 feet per second. Thus far the extract already printed. In the original letter there followed a mathematical investigation to determine whether this up- ward air current of 3 feet per second could suffice for the supposed effect. This I now paraphrase and somewhat abbreviate as follows : — Suppose a bird soaring with constant speed and direction in still, or uniformly moving, air ; and let a = the angle (taken downwards from horizontal, in a fore and aft vertical plane) of the wing surface ; and, a + tr = that (similarly taken) of the direction of motion through the air. Hence, r= 1 '5. These values for P and F are approximately the values fairly well established for water, multiplied by the specific gravity of air ; F not increased on the score of the greater viscosity of air, but P doubled on the score of advantage that might con- * These figures give ^=’91. Memoranda of Mr Froude’s include weights A and measurements afterwards obtained, which show much higher values. Recent measurements of my own of an . albatross preserved in spirits at the W Museum of Zoology, Cambridge, give = 2*3. A 1890-91.] Mr H. E. Froude on the Soaring of Birds. 69 ceivably be derived from the curvature of the wing surface;* also r is taken as 1*5, instead of over 2’0 as it prima facie should be, on the score of eddies conceivably annulling in part the friction on the upper surfaces of the wings. These values put into equation (8) give no less than 4 *7 feet 'per second as the value for V^cq + oq). Thus, apparently — (1) The formula as interpreted by these constants requires no less than 4 '7 ft. per second rate of descent. (2) The suggested explanation of the soaring admits of no more than 3 ft. per second. (3) The fact that birds can sustain flight in still air admits of very much less still , unless we can suppose that in birds the relative power capacity is many times greater than it is in horses and men. It is not my purpose here to attempt to clear up this paradox. Mr Froude appears to have considered the formula unimpeachable in structure, at least as a fair approximation (and so I think it evidently is), but the constants probably in error. At any rate, he seems to have treated the argument from the power capacity of animals as sufficient prima facie evidence that the updraught of the advancing wave slopes would suffice for soaring ; because in subsequent letters he describes further observations made^with the object of identifying the occasions of soaring in a calm with position of the bird over the advancing wave slopes. But first he had an opportunity of observ- ing soaring in a strong wind, under circumstances which appeared to defy the idea that advantage was being taken of local ascending currents. This must be described in his own words, in a letter to myself dated 14th February 1879 : — “ But since I have been here we have had a lot of S.E. gales ; and though the sea surface has been like that at Torquay pierhead in a S.S.W. gale, and thus without any big waves, we have seen a lot of whale birds , as they are called, playing the skim trick in the most marvellous and fascinating way. “The albatrosses did occasionally flap, but these birds went high and went low, went fast and went slow, with the wind or against * As a justification for this, Mr Froude suggests the circumstance that in the cup anemometer the circumferential speed of the cups is accounted to be § the speed of the wind ; hence the relative speed of the wind facing the con- cave surfaces is only one-half that facing the convex surfaces, yet the wind presumably exerts the same force on both. 70 Proceedings of Royal Society of Edinburgh. [sess. the wind, now hove to close to the water, and near enough to the ship for the most definite scrutiny, and then going ahead and up- wards if they pleased, not flapping a wing once for hours, I may swear ! — all in such a way as to be dumbfoundering, unless it be possible to suppose an ascending current apparently uniformly dis- tributed over a level ocean, and reaching to at least 50 or 60 feet above it, and with a rate of ascent sufficient to explain the birds’ behaviour. This supposition is prima facie an inadmissible one, for the air, if it was all ascending , would leave a vacuum over the water. “ At first I thought that the retarding action of the water friction (which was plainly enormous, for it was tearing the water surface to tatters) might explain the action by the circumstance that the retardation would crumple up the lower air strata endways, and by thickening them, would in effect produce an ascending motion in them. “ But in spite of the more vigorous frictional action close to the water surface, the ascent of the particles due to the crumpling up would be nil at the surface ; yet the birds seemed to find the ascent as active there as anywhere. Still I think there is something in this view. “ Two days later, however, when the gale was a good bit more furious, I had a better proof of what was happening, though the ‘ how it happened ’ is still a puzzle. “ You know how in a heavy gale the sea surface seems to drift like dust ? Well, in this case, the air was for a long time so full of sea spray up to a level of 50 or 60 feet, that it looked as if a heavy April shower was passing, though there was a clear blue sky overhead, and sunshine. “ Now, whatever could carry spray to that height would answer the birds’ purpose. To-day the birds are again about, but the wind is only a double reef cutter breeze, if so much ; and to-day, though they do a good deal of skimming, they have also to do a great deal of flapping at intervals.” As an explanation of the ascent of the particles of spray, Mr Broude goes on to suggest that the frictional eddies in the air must receive their most effective renewal of energy from the friction on their under sides nearest the water surface, and that consequently their 1890-91.] Mr R. E. Froude on the Soaring of Birds. 71 speed must be greater on the ascending side than on the descending side. The particles of spray passing across and through the vortices must be subjected alternately to the upward and downward forces due to the ascending and descending speeds. True, the ascending streams, being thinner in proportion as their speed is greater, will presumably act on the particles for a proportionately smaller share of the total time; but the resistance being as speed squared, the aggregate upward momentum imparted to the particles will never- theless exceed the aggregate downward momentum. This suggestion is interesting, as a plausible explanation of the phenomenon of the rising spray ; at the same time I hardly think the suggested operation can favour the soaring of birds except by a second order quantity. For, in proportion as the bird’s speed is high (as I think it must be), relatively to the speed of the eddies, the effect of the local contrarities of the eddy speeds becomes to the bird one simply of small differences in angle of impact on the wings ; and, since the pressure on an obliquely moving plane varies simply as the angle (for small angles), the consequent differences in upward pressure would be proportional to the times for which those pres- sures act, so that the aggregate upward momentum and mean upward force would be the same as in still air. I imagine that the soaring witnessed by Mr Froude on the occa- sion which he describes, is to be ascribed to an operation which, so far as I know, was first suggested by Lord Rayleigh in a com- munication to Nature of 5th April 1883, viz., a utilisation by the birds of the difference of wind-speed at different levels. But this explanation evidently did not occur to Mr Froude at the time, and I need make no further reference to it here. Mr Froude’s next letter bearing on the subject was dated Saldanha Bay, 24th February 1879, and in it he says : — “ The voyage up from Simons Bay was delightful ; for it was a glassy calm ; and as there was also a tolerably pronounced swell, especially the latter part of the way, I was able (and Tower helped me) to watch the albatross’s flight in a calm, with the following results : — When flying high they had to flap their wings continuously, except when descending. When near the surface they c skimmed ’ occasionally, and, as far as we could distinguish, they did this only when traversing a region over an ascending wave slope. 72 Proceedings of Royal Society of Edinburgh. [sess. Very often this was conspicuous. Now and then I noticed one or more of the birds skimming for a half-moment at a time in a position which must have been so, viz., when they were hidden, or all but hidden, from us by a wave crest, the back or the descending side of which was towards the ship. As the waves were long and not high, it was only by keeping exactly in this position that a bird could remain invisible, or visible only partially and for a second or two at a time, as the wave varied in form a little, or as he rose and fell a little. “ It also frequently happened that two, three, or four of the birds were flying in close company, generally in single file. When they were thus flying close to the water, they occasionally ‘skimmed,’ and then after a few seconds began again to flap. And it was noticeable that they all made the change simultaneously , implying that they had simultaneously arrived at a suitable region.” At the end of a letter on other subjects, dated 10th March 1879, he says — “ I have made quite sure that the skimming birds follow the ascending wave-slopes as I had surmised.” These remarks of Mr Froude seem to make it clear that the up- draught of the advancing slopes of a ground swell in a calm may sometimes be a cause of soaring. It certainly seems to be the only cause which can account for soaring in a calm or very light wind ; on the other hand, it is a cause which can operate only when there is a large swell, and when the wind is either very light or not in the direction of the swell. Perhaps the most interesting feature of the letters consists in the analysis of the theoretical conditions of flight, and the paradox which thence results. For this paradox has an important bearing on the computation of air resistances in general, and any information which may serve to throw light upon it has a correspondingly wide significance. 1890-91.] Dr T. Muir on some unproved Theorems. 73 On some hitherto unproved Theorems in Determinants^ By Thomas Muir, LL.D. (Read January 19, 1891.) Most of the theorems in question occur at the outset of a paper * by Professor Cayley, entitled, “ Chapters on the Analytical Geometry of n Dimensions”; they constitute, in fact, Chapter I. The first theorem I should prefer, for the present, to enunciate as follows : — If m determinants of the nth order all have the same n - 1 columns in common , and all vanish , then every determinant of the nth order whose n columns are chosen from the m + n - 1 different columns must vanish likewise. Taking the case where m = 3 and n — 4, and where therefore we have [oq&2C3^4] = |^i^2p3^5l = !^1^2C3^6i = ^ » we are required to show that the twelve other determinants of the 4th order formed from the array a 2 ct^ dg hi h2 b3 &4 h5 b6 C1 C2 C3 C4 C5 C6 d x d2 d3 dy x dfy d'Q also vanish. To this end we note first that any two of the given three are connected with one of the twelve by a linear relation, in virtue of which the latter vanishes when the two former simultane- ously vanish. If we write the first two in the shorter form |1234|, |1235|, the relation in question is |1234| jl257| - |1235||1247| + |1237| |1245| = 0 , (A) 7 being the suffix-number of any new arbitrary column. Inter- changing 2 and 3 we have also |1324j |1357| - |1325| jl347| + |1327| |1345| = 0 , (A') and interchanging 1 and 2 in this we have |2314| |2357| - |2315||2347| + |2317| |2345| = 0 . (A") * Cambridge Mathematical Journal, \o\. iv. pp. 119-127; or, Collected Math. Papers, vol. i. pp. 55-62. 7 4 Proceedings of Royal Society of Edinburgh. [sess. It is thus seen that the vanishing of |1234] and |1235| entails the vanishing of |1245|, |1345|, [2345|. Similarly from the vanishing of |1234| and 1 1 236 1 we infer the vanishing of |1246, |1346|, |2346| ; and from the vanishing of jl235| and |1236| we infer the vanishing of |1256|, |1356|, |2356|. In the next place all the three original determinants are con- nected with one of the twelve by a linear relation, and from this like consequences ensue. The relation is |1234| |1567| - |1235| |1467| + |1236||1457| - |1237| |1456| = 0, (B) from which by interchange as before we have also |2134||2567i - |2135||2467| + |2136||2457| - |2137| |2456| = 0 , (B') |3214| |3567| - |3215||3467| + |3216||3457| - |3217| |3456| = 0 . (B") It is thus seen that the vanishing of |1234|, |1235|, |1236| entails the vanishing of |1456|, |2456|, |3456|, which are the last three deter- minants of the twelve. The identities (A) and (B) have long been known ; the one is an extensional of |34||57| - |35| |47| + |37||45| = 0, and the other an extensional of |234||567| - |235| |467| + |236| |457| - |237||456| = 0. These are the first two cases of a general theorem discovered and brought into notice by Sylvester, hut included in a wider generalisa- tion of earlier date. Had the determinants with which we started been of a higher order than the 4th, we might have required to use the next case, viz., the extensional of |2345]|6789| - |2346||5789| + |2347j |5689| - |2348||5679| + |2349| |5678 | = 0. Cayley’s mode of enunciation is : — The 15 { C6,4) equations al a2 CO e a5 a6 h h h h h C1 C2 C3 C4 C5 *1 d2 d% ^5 d§ are not independent, hut are reducible to 3 ; and if these he (1) = 0 , (2) = 0 , (3) = 0, 1890-91.] Dr T. Muir on some unproved Theorems. 75 then any one of the twelve other determinants is expressible in the form 0i(1) + 02(2) + <93(3). The above demonstration has the advantage of showing what 0V 6 0?j are in every case. There is, however, quite a different mode of viewing and investi- gating the theorem. The identities (A), (A'), (A"), (B), (B'), (B") may each be looked on as furnishing the result of an elimination. For example, having used (A) to prove that if |1234| = 0 and |1235| = 0 then |1245| = 0, we may manifestly view the work thus accomplished as the elimination of the suffix 3 from the given equations. The question consequently arises, May the demonstra- tion not be presented in the form of an ordinary process of elimina- tion? Writing the first given equation in the form a1|&2c3^4| - a2|51c3c?4| + a3|&1c2c?4| - a4|&1c2c?3| = 0 , and the second in a similar manner, ai\heA\ - a2\bicsdb\ + as\bic2db\ - a5\blC2d5\ = 0> and from these eliminating a3 we have a\{ ~\blG2d^\b)2C^d^ 4* \b\G2d^\\b2C^d^[\ - a2{ - \blC3d4\ + WC2d±\WCA\} + a^{\biG2d^[ l^lC2^sl} ~ ^{\blC2dMblC2ds\) =°> from which, on striking out the common factor | there results - a$icA\ + ai\hic2db\ “ a5|&iC2^4| = 0, i.e. |cq&2e4dy = 0. Turning now to (B), and observing that the result there ob- tained is the elimination of the suffixes 2, 3 from the equations |1234| = 0, |1235| = 0, |1236| = 0, we write the said equations in the form ail^2C3^4:l — %|^ic2^4l “ ^4|^lc2^3l = 0 j \ ai\b2C3d5\ ~ a2^1C3^5l + a3^1C2^5l ~ a5^1C2^3l = ^ 5 «il ~ az\bicA\ + a*\blC2d6\ ~ aQ\blG2ds\ ~ 0 » ' 76 Proceedings of Royal Society of Edinburgh. [sess. and thence eliminate a2, av The result is ttll^2C3^4l — ^41^1^2^31 J&jCgC^J l^lc2^4l ^ll ^2^3^51 1 rt5l^lC2^3l i^lC3^5l l^lC2^5l ^ll^2C3^6l ” ^gI^1C2^3I h°A\ h^dQ\ M * * a i.e. i.e. 0. \\0zd,\ \\c,d,\ |^2C3^5l l^lC3^5l |^lC2^5l ah |^2C3^6l l^lC3^6l l^lC2^6l % =0, . 1 d± Cj b1 ax hci\ -\hA\ • d± c4 &4 a4 H^i^sl lc:AI * ^5 C5 ^5 a5 l^2C3l 1^2^31 lC2^3l d6 c6 b6 a6 = 0 so that on dividing by \\c2df? we have {af^df- 0 , as was to be proved. Let us pass now from the determinants of the 4th order arising out of the rectangular array with which we commenced to the determinants of the same order arising out of the square array h h d} d:> d2 di h h d-0 C1 c2 °3 °4 °6 /i /a fs ft A A and let us inquire how many of these minors are independent. We know that the total number of them is (C6,4)2, i.e., 225, and that they constitute the elements of the 4th compound of \a1b2csd4e5fQ\ . We see further that the first row of this compound determinant con- sists of the fifteen determinants dealt with above, and that therefore only three of the fifteen are independent. Similarly it follows that the vanishing of the first three of the second row entails the vanishing of all the rest of the row, and that the vanishing of the first three in the 1890-91.] Dr T Muir on some unproved Theorems. 77 third row entails like consequences. But the first three elements of the first three rows constitute likewise the first three elements of the first three columns ; and the elements of a column are related to each other exactly as the elements of a row are; consequently the vanishing of these nine elements entails the vanishing of all the other elements of the first three columns. Finally, viewing these last elements as constituting the first three elements of the 4 th and remaining rows, we see that all the 225 minors will vanish if the nine minors common to the first three rows and first three columns vanish. Had the original determinant been of the nth order and the minors formed from it been of the mth, the compound determinant would have been of the order Cn> m> and all the elements of its first row could have been shown to vanish if 0 = |1,2,3, . . . , m- 1, m| = |l,2,3, . . . m- 1, m+ 1| = . . . , =|1,2,3, . . . m- 1, n\, that is to say, if n — m + 1 of them vanished. The general theorem we have thus proved is — All the minors of the mth order formed from a determinant of the nth order will vanish if (n-m + 1)2 of them vanish. If the original determinant be axisymmetric, the compound deter- minant is also axisymmetric, and therefore the said (n-m + 1)2 minors are not in this case all different. In fact, instead of there being n-m + 1 different minors to be counted in each row, there is 1 less in the second row, 2 in the third, and so on, the total thus being only (n - m + 1) + (n - m) + (n - m - 1) + • • • + 1 . i.e. -m+l)(n-m + 2) . This result was enunciated without proof by Sylvester in the Philosophical Magazine for September 1850. It appears from the foregoing to be an easy deduction from Cayley’s theorem published seven years before. Cayley’s next theorem is bound up with a certain notation intro- duced by him, and forms indeed the fundamental justification for the use of the said notation. To indicate that all the 15 determi- nants of the 4th order formed from the array 78 Proceedings of Royal Society of Edinburgh. [sess. ax a2 a3 a4 b\ ^2 ^3 ^4 C1 C2 C3 G1 dx c^2 <^3 d ^ d^f d^y vanish, Cayley wrote al a2 at <% a6 h h h «1 C2 C3 «4 C5 C6 d. d2 d3 d 4 < d6 and the theorem referred to is that if this group of equations holds it follows that the similar group got by the quasi-multiplication of both sides by the determinant |A.1/a2v3p4ct5t6! holds also ; in other words, that so far as multiplication by |A.1ju,2v3p4o-5r6| is concerned, we may view the rectangular array as if it denoted a single entity. Taking the first of the fifteen determinants of the new group, viz. : Ajdq + X2a2 + . . . + Ai^i + A2&2 + . . . 4- V6 AiCi + A2c2 + . . . + A6c6 AjC^i + A2c?2 + . . . + Xfl g Piai + . . . + n6a6 Pfl + * • • + P&^6 P \G\ + • • • + Pqcq P\d\ + . . . + fi6d6 viai + . . . +v6% v1b1 + .. .+v6bQ v1c1 + ...+v6Cq V\dx + . . . + Vq d§ Piai + • • • + PQaQ Pl\ + • • • P1C1 + . . .+pqCq P\dx + • . • + Pftdft , we see that it is equal to the sum of products usually represented by ai a2 a 3 a 4 a5 a6 A2 A3 K A6 h h be Pi P2 H Pi Pb pQ ci C2 CS C4 C5 «6 Vl V2 V3 vi Vb dx d2 d3 d 6 that is to say, it is equal to 2|ai&2c3dy-|Ai//,2i/3p4| , and consequently must vanish, because the first factor of every one of these products vanishes. The same is readily seen to be true of any other one of the fifteen determinants; in fact, the equivalents of the fifteen are 79 1890-91.] Dr T. Muir on some unproved Theorems. 2|(2i&2C3^4l‘|^'iAt'21/3P4l E|«i&2cA|-|A.1/x2v3 being a function of the eighth degree equated to a function of the sixth. The elimination of the glissette of the ellipse may be performed in the same way, only in this case we have in (a), (b), and (c), instead of a and p, quantities containing x2 and y2. Hence for the ellipse (1) is of the 3rd degree, (2) is of the 4th degree, the two equations immediately derived from these are of the 5th and 6th degrees, and the final equation is of the 10th degree. Dr Muir has shown, in a paper just read, that the final equation is divisible by a quadratic factor, and is thus of the same degree as its limiting form, the glissette of the parabola. Since the glissette of any curve may be found from the equation of the pedal (supposing the latter can be found), the glissette may be considered as belonging to a system of derivative curves which includes the pedal, the inverse, the reciprocal-polar, and (as shown by the writer in a previous paper) the caustic for parallel rays ( Proc . Roy. Soc.Edin ., 1 890, p. 280). In this system of derivative curves, the curves of each species are defined by a relation between the primitive 1890-91.] Lord M‘Laren on Glisseite of Two-term Oval. 87 curve and the coordinates of its tangents, normals, and radii, and the required equation is found by elimination between two equations, one of which is of the 1st degree. Other curves of the same system exist, and their equations may be found, e.g., the locus of the intersection of normals, where a curve moves in contact with rec- tangular guides. Here the coordinates, x and y , are the differences, Pi-7ff2 and i?2_2sri i Pi> Pz being the perpendiculars drawn from the pole of the curve to the tangent guides, and zsq , being the perpendiculars drawn from the pole to the normals. Proceedings of Royal Society of Edinburgh . [sess. 88 The Influence of High Winds on the Barometer at the Ben Nevis Observatory. By Alexander Buchan, LL.D, (Read March 2, 1891.) The question of the effect of wind on the readings of the baro- meter was first examined by Sir Henry James in a paper read to the Society on March 15, 1852.* The observations were made during the succession of gales from the south-west which occurred in January and February of that year, at his house in Granton, with an aneroid barometer, laid horizontally in succession on the table of his room in the cottage, on the seat of the open summer- house, and on the surface of the ground close to the summer-house, all at the same level. The anemometer employed was of a very simple construction, being on the same principle as the instrument used for weighing letters, the weight or pressure being indicated by the compression of a spiral spring in a tube. A table of results is added, giving the depression of the barometer in decimals of an inch for the velocity of the wind from 14 to 40 miles per hour. At 14 miles the barometric depression was 0010 inch, and increased gradually to a depression of 0 045 inch at 40 miles per hour. Un- fortunately, the number of observations on which the depression for each wind-velocity has been deduced are not given, and the obser- vations in the cottage and those at the open summer-house are com- bined into one result. It may be safely assumed that the results arrived at indicate too large barometric depressions for the different wind-velocities as barometers are usually observed, namely, in houses. The depression on the lee side of any obstruction in the wind such as a summer-house is greater than it is in the room of a dwelling-house. Further, a barometer laid on the ground during strong winds will, if the wind brush briskly over the key- hole of the instrument, indicate a less pressure than that of the air. Since, however, in such a position, the wind will only at a few points have access to the connecting opening between the aneroid and the free atmosphere, it may be assumed that the instrument * Transactions , vol. xx. p. 377. 1890-91.] Dr Buchan on the Influence of High Winds. 89 will, in the great majority of cases, show a higher reading than that of the free atmosphere. Bor these reasons, these barometric depressions are too large. Since 1852 meteorologists have taken no action on the results of Sir Henry James’s inquiry in discussions on barometric readings and wind-velocities ; and practically no advance has been made in this branch of meteorology. Various arrangements have been proposed, but none of them can be regarded as satisfactory, to arrive at the knowledge of the actual pressure of the free atmosphere during high winds. The difficulty consists in finding a perfectly unscreened position for the barometer, and securing at the same time that the wind, brushing past the small openings connecting the mercury of the cistern with the air outside, will not partially lower the pressure on the mercury in the cistern, and so render the instrument no longer indicative of the true pressure of the free atmosphere. The same remark applies to aneroids. In carrying out, during the past five months, the instructions of the directors of the Ben Nevis Observatory to discuss the observa- tions made at the High and Low Level Observatories, it quickly became apparent that the influence of high winds on the barometer was the first inquiry calling for serious attention. The depression of the barometer during high winds was plainly so serious as to render the examination of many questions all but a hopeless task, until some approximation was made to the values of these depres- sions for different wind velocities. Now, since the horizontal distance of the High and Low Level Observatories is only about four miles, it follows that the two may virtually be treated as one as regards the geographical distribution of pressure. But the Observatory at the top of the mountain is peculiarly exposed to high winds, which are occasionally so violent that the observers must be roped together on going outside to make the observations ; and it not unfrequently occurs that very strong winds prevail, while over the surrounding low country calms and light winds only prevail. On the other hand, the Low Level Observatory at Fort- William is in a sheltered position, and high winds are of comparatively rare occurrence. Thus, then, these two Observatories present the conditions which are essential to this inquiry, viz., one of the barometers is in a building exposed to 90 Proceedings of Royal Society of Edinburgh. winds of all velocities up to at least 150 miles an hour, whereas the other is in a building where either calms or light winds only at the time prevail — so that this barometer may be regarded as recording the pressure of the free atmosphere. It was therefore resolved to institute a comparison between the sea-level pressures of these two barometers, employing only those cases when winds at the Fort- William Observatory were light. The scale used on Ben Nevis for the observations of the force of the wind is a modification of Beaufort’s scale, 0 to 12. Much attention has been given to ascertain the wind’s rate in miles per hour, corresponding to each of the figures of Beaufort’s scale. For this purpose, a modification of Robinson’s anemometer was de- signed by Professor Chrystal for the Observatory ; and during the times the instrument is not frozen up in a thick covering of ice, the comparisons have been made. These have been discussed by Mr Omond in a paper read to the Society. The comparison is given at the top of Table I. The reductions of the barometric readings on the top of Ben Nevis to sea-level have been made by Table VIII. prepared for the purpose, as given in the volume of the Transactions recently pub- lished,* and the readings at Fort-William in the usual way. The differences of the two reduced readings were then entered in columns headed 0, 1, 2, 3, &c., and according to the wind force at the Ben Nevis Observatory at the time. Table I. gives the mean differences for each wind force for each wind ; and the figures in the second half of the Table show the number of observations from which each mean difference has been calculated. The comparison for the six months was made from the hourly observations at both Observatories, from August 1890 to January 1891. But since this period gave too few observations for the higher wind velocities for good averages, the observations from January 1885 to July 1890 were utilised for the five hours of the day at which corresponding observations were made at Fort-William. Only the wind forces from 5 to 11 have been thus utilised, and the results have been incorporated with those for the six months, and entered at the foot of Table I. In all 4596 of the Ben Nevis observations have been reduced to sea-level for these comparisons. * Trans. Roy. Soc. Edin vol. xxxiv. pp. 60-61. Table I. — Showing (1) the Equivalent in miles per hour for the figures of Beaufort Scale; (2) the Depression of the Barometer, in inches, with increased Wind Velocity; and (3) the Number of Observations from which the Mean Results have been computed. 1890-91.] Dr Buchan on the Influence of High Winds. 91 * These last Means and Sums are inclusive of all cases of Wind Force from 5 to 11 recorded in the years January 1885 to July 1890. 92 Proceedings of Royal Society of Edinburgh. [sess. The following summarises the results, showing the barometer with each wind velocity : — the depression of Miles per hour. Baro. Depression, inch. Miles per hour. Baro. Depression, inch. 0 -0*001 50 -0 035 5 -0*004 63 -0*050 12 -0*005 83 -0*070 21 -0*010 96 -0*104 31 -0*014 108 -0*122 39 -0*026 120 -0*150 Thus in calm weather, the two reduced barometers are practically the same, but with every increase of wind the depression of the barometer steadily augments. It is not till a velocity of more than 20 miles an hour is attained that the depression amounts to one hundredth of an inch. At 63 miles an hour, it is 0*050 inch ; at 96 miles, 0T04 inch; and at 120 miles, 0*150 inch. The amount of the depression of the barometer is thus practically proportional to the velocity of the wind, from zero to a velocity of 120 miles per hour. This depression of the barometer is no doubt occasioned by the wind drawing out the air from the room where the barometer is hung, as it rushes past the observatory, thus producing a partial vacuum and consequently a lower pressure. If a window or door is opened on the side of the room exposed to the wind, the readings of the barometer are thereby raised ; whereas on the lee side of buildings, in rooms connected therewith, and in rooms with chimneys, the barometric readings are lowered. Now, as the barometer of the Ben Nevis Observatory is hung in a room, with the usual chimney, door, and windows, these results may be regarded as applicable to the readings of barometers generally, since they are in almost every case suspended in situations similar to that of the Ben Nevis barometer. In a paper on the Mean Atmospheric Pressure of the British Islands, published by the Scottish Meterological Society ten years ago,* monthly and annual isobars are given for every two-hun- dredths of an inch of pressure. These isobars show a lower pressure over those parts of the country where the prevailing winds are stronger than elsewhere. It may now be regarded as probable that the curved courses taken by the isobars do not indicate any * Journal Scot. Meteorol. Soc., new series, vol. vi. p. 4-40. 1890-91.] Dr Buchan on the Influence of High Winds. 93 real lowering of atmospheric pressure in these districts, but are only an increased depression of the barometer brought about by the stronger winds which prevail in those parts of the country. In forecasting weather it will be necessary to keep this effect of high winds on the barometer constantly in mind, with the view of arriving at a better approximation to the real geographical distribu- tion of pressure at the time the forecasts are being framed. In working out the question of the barometric gradient from actual observations, particularly the relations of the higher gradients to the wind velocities, the results hitherto arrived at cannot be said to he satisfactory. The reason is that, while the wind velocities were known with tolerable accuracy, the pressure of the free atmosphere could not be dealt with, because the observations did not record it ; what the observatories recorded was only the barometric readings, not reduced proportionally to the force of the wind at each observa- tory. For such discussions to be satisfactory, the amount of the depression of the barometer, owing to the force of the wind prevailing at the time, should be approximated to and allowed for. Table II., showing the mean diurnal variation of the differences between the two reduced barometers for the six months has been prepared in this way : The differences for each hour of the day were corrected by adding, in each case, the corrections indicated in Table I., according to the wind force at the time, from which the monthly means were calculated. The six months’ means show that from 7 p.m. to 9 a.m., the reduced High Level Barometer reads the higher, and from 10 a.m. to 6 p.m. that it reads the lower. In these reductions the mean temperature of the stratum of atmo- sphere from the bottom to the top of the mountain has been assumed to be the same as the mean at the two observatories. If it be sup- posed that the diurnal variations for the six months in Table II. are simply an expression of the degree to which the mean temperature of the two observatories falls short of, or exceeds, the mean of the whole intervening stratum, it follows that during the warmer hours of the day the temperature of the whole intervening stratum is about 0o,8 lower, and during the colder hours of the night 0°*8 higher than the mean of the two observatories. The variations of differences are of course much larger and more uniform in their distribution during the hours of the day. It will 94 Proceedings of Royal Society of Edinburgh [sess. be observed that the means for August and September differ con- siderably from each other. The results point to two marked peculiarities in the differences of the reduced barometers in wet, cyclonic weather, as shown by the August curve ; and in dry, anti- cyclonic weather, as in the September curve. During the times of abnormally high temperature and great dryness, which are so characteristic of anti-cyclonic weather, the reduced barometer at the top reads higher than at Fort- William; and, on the other hand, during advancing cyclones, when the atmosphere is highly charged with vapour, the reduced barometer at the top reads lower. Table II. — Showing the Mean Diurnal Variation of the Differences between the Reduced Barometers of the two Observatories for the Six Months ending January 1891. The minus sign indi- cates that the mean of the reduced High Level Barometer was the lower of the two ; no sign that it was the higher. Aug. Sept. Oct. Nov. Dec. Jan. 6 Months inch. inch. inch. inch. inch. inch. inch. 1 A.M. •010 •016 •002 •ooo •002 -•005 •004 2 „ •007 •017 •ooo -•002 •005 -•005 •004 3 „ •007 •018 •001 •ooo •004 - -006 •004 4 „ •007 •016 -•001 •003 •001 -•007 •003 5 ,, •006 •012 •002 •001 •ooo -•001 •003 6 „ •002 •012 •002 -•002 -•001 •ooo •002 7 „ •001 •012 •003 •002 •001 •001 •003 8 „ -•006 •007 -•001 •002 -•001 •003 •001 9 „ -•008 •003 -•002 •001 •003 •004 •ooo 10 „ -•011 •001 -•005 -•002 •002 -•002 - -003 11 „ -•010 •001 -•006 - -004 - -002 - -001 - 004 Noon. - -012 •003 -•007 -•005 -•006 -•001 -•005 1 P.M. -•009 •007 -•007 -•009 -•006 -•001 -•004 2 „ -•009 •001 -•007 -•007 -•006 - *006 - -006 3 „ -•009 •001 -•007 -•006 -•005 -•004 -•005 4 „ -•007 ■002 - -009 -•007 -•004 -•002 -•004 5 „ -•005 •007 -•002 -•007 -•003 •006 -•001 .6 „ -•004 •007 -•003 -•009 -•001 •004 -•001 7 „ •002 •015 •002 -•005 •ooo •004 •003 8 „ •003 •015 -•002 -•006 •002 -•004 •001 9 „ •007 •021 •002 - -004 •004 - -002 •005 10 „ •007 •017 •003 -•003 •001 -•004 •004 11 „ •009 •020 •002 •003 •003 -•003 •006 Midnight ■008 •018 •000 •001 -•001 - -005 •004 1890-91.] Prof. Brown and Dr Walker on Dibasic Acids . 95 Electrolytic Synthesis of Dibasic Acids. Alkyl Deriva- tives of Succinic Acid. By Professor Crum Brown and Dr James Walker. (Read April 6, 1891.) {Abstract.) In onr previous communications to the Society (see Trans. xxxvi. 211) we described the behaviour of the ethyl potassium salts of normal dibasic acids on electrolysis. These we found always to yield the diethyl esters of normal acids of the same series. We have now extended our investigation to acids with side chains, and in this paper give an account of the electrolysis of ethylpotassium methylmalonate and ethylpotassium ethyl- malonate. The esters formed according to the general equation, 2EtO(CO). R".(C0)0- = EtO(CO).R".R".(CO).OEt + 2C02, are evidently always symmetrical, so that from methylmalonic acid we should expect to obtain symmetrical dimethylsuccinic acid : — 2EtO(CO). CH(CH3).(C0)0- = EtO(CO).CH(CH3).CH(CH3).(CO)OEt + 2C02. This dimethylsuccinic acid contains two similarly si luated asym- metric carbon atoms, and is thus, like tartaric acid, capable of existence in four isomeric forms — two optically active, and two optically inactive, one of these latter (corresponding to racemic acid) being a compound or mixture in equal proportions of the two opposite optically active acids. As the optically active forms are produced in equal proportions by any purely chemical process from inactive materials, we were justified in expecting to obtain by electrolysis a mixture of the esters of the two inactive symmetrical dimethylsuccinic acids. The synthesis was conducted in precisely the same manner as in our previous experiments. 150 grams of ethylpotassium methyl- malonate yielded about 60 grams of an ethereal product, which, on distillation, gave a fraction of 30 grams, boiling between 194° C. and 206° C. This portion was saponified with boiling alcoholic potash, and the potassium salt thus formed converted into the 96 Proceedings of Royal Society of Edinburgh. [sess. acid, which was then extracted with ether. The crude acid was freed from a small quantity of an oily substance by drying on porous tile, and then subjected to systematic fractional crystal- lisation from water. We succeeded in separating and purifying two acids — one, the less soluble, having the melting-point 193° C., the other melting at 120°-121° C. The acids on analysis proved to have the same composition, both corresponding to the formula caH10o4. I. T166 gr. more soluble acid gave *2100 gr. C02 and -0737 gr. H20 II. T350 gr. less soluble acid gave -2432 gr. C02 and -0855 gr. H20 I Fotmd- ^ Calculated for C6H10O4 C 49-12 49-13 49-31 H 7-02 7-04 6-87 The acid melting at 193° would thus seem to be identical with the para-s-dimethylsuccinic acid of Bischoff (melting-point 194°); and that melting at 120°-121° with his anti-s-dimethylsuccinic acid (melting-point 120°). For further confirmation we measured the electrolytic conductivity of solutions of the acids, and found the following dissociation-constants : — Para-acid, K=‘0208 (K=-0205, Bethmann). Anti-acid, K= -0138 (K= *0122, Bischoff and Walden). In a similar manner we performed the electrolysis of ethyl potassium ethylmalonate, and from 150 grams of the salt obtained 63 grams of an ethereal liquid. The portion of this boiling above 200°, was saponified, the potassium salt acidified, and the crude acid extracted with ether and purified as in the preceding case. Besides water as a means of fractional crystallisation, we found benzene a useful solvent for effecting the separation of the isomeric acids. As before, we obtained in the pure state two acids, one melting at 192° €. with decomposition, the other at 130° C. Analysis gave the following numbers : — I. -1252 gr. acid, melting-point 192° C., gave *2530 gr. C02 and '0915 gr. H20 1890-91.] Prof. Brown and Dr Walker on Dibasic Acids. 97 II. *1224 gr. acid, melting-point 130° C., gave *2465 gr. C02 and '0894 gr. H20 Calculated for C8H1404 55*17 j 8-11 The acids have thus the composition of diethylsuccinic acid, and from their mode of formation are symmetrical. Two sym- metrical diethylsuccinic acids were prepared by Bischoff and Hjelt, which are evidently identical with ours, viz., para-s-diethylsuccinic acids, melting-point 192°, with decomposition, and anti-s-diethyl- succinic acid, melting-point 129°. We found the following values of the dissociation-constants of the two acids : — Para-acid, K = *0237 (K='0245, Bischoff and Walden). Anti-acid, K = -0347 (K = -0343 u m ). Found. I. II. C 55-11 54-93 H 8T2 8-12 VOL. XVIII. 29/4/91 G 98 Proceedings of Royal Society of Edinburgh. [sess. Proposed Extension of the Powers of Quaternion Differ- entiation. By Alexander M‘Aulay, Ormond College, Melbourne. Communicated by Professor Tait. (Read December 15, 1890.) It will, I think, be acknowledged that Quaternions, while pro- viding for the physicist a machinery much more natural and graceful than the Cartesian, for all conceptions strictly geometrical, do not at present afford equal facilities for the consideration of questions involving differentiation. It is true that there is one well-known symbol of differentiation of great utility, which enables Quaternions to deal in a suitable manner with many such questions ; but there are left whole classes of differentiations in which the symbol is of no avail. This has led me to the consideration of other symbols of differen- tiation, and to a slight generalisation of the powers of the symbol already mentioned. I had thought it necessary only to define the extensions here referred to, and proceed to apply them. But Pro- fessor Tait, while kindly procuring me this opportunity of bringing forward my views, has given me fair warning that the repugnance of physicists to some of my notation may prove an insuperable obstacle to their paying any attention to investigations conducted in that notation. This personal reference will explain why, in the present short paper, an apology for, and explanation of, the methods are entered into, much more detailed than could otherwise be con- sidered advisable or even justifiable. In what follows, after an explanation of the proposed changes of, and additions to, quaternion differential notation, a brief account in the abstract is given of the reasons for and against what can be called innovation; and the rest of the paper is devoted to some examples of the application to the theories of elasticity and electro- statics. I may here remark that, in a short paper like the present, it is impossible to do full justice to the views enunciated, because for this purpose it would be necessary to go over a large part of the ground covered by mathematical physics : but if the slight variations from previous custom indicated below do not meet with 1890-91.] Mr A. M'Aulay on Quaternion Differentiation. 99 that studied discountenance from all authorities in the matter, which I have been assured they must, I could give in a future paper some few applications of the methods which would probably prove in- teresting to physicists, and which cannot be treated readily, if at all, by methods other than those in question. As is well known, Hamilton’s symbol V may be defined by the equation ,d .d 7 d v = lJx+JTy + kdz where i,j, k, x , y , z have the usual meanings. Hamilton himself did not examine the utility of V . This explains, most likely, why he did not state more exactly how to consider to what symbols the differentiations implied should refer. In the simplest applications of V these differentiations will refer to that symbol, and only to it, which immediately follows the operator. Very little practice in the application of V to physical questions serves to show that, if we are to be bound by this rule, at least seven-eighths of the potential utility of V must be sacrificed. Professor Tait has recognised this in the 3rd edition of his Quaternions , where he freely separates the V from the symbol or symbols it affects ; and, according to a well- known custom, indicates the connection between the operator and the symbols affected by attaching the same suffix to both. This I had already done in a paper to be referred to immediately. We seem then to be led by a natural process to the following state- ment : — The operator V and its operand or operands may have any relative positions in a term which are convenient , the connection between them being indicated in the usual way by suffixes. For the propriety of this view, I now wish to contend, although at the time of writing the 3rd ed. of Quaternions Professor Tait was not prepared to endorse it in full. Notwithstanding that it is immaterial how great, in a term, be the separation of a V from the symbol affected, so long as the V is on the left of the symbol, he* emphatically — observe his italics — lays down the law, that the V must not be removed to the right of the symbol, even the immediate * With regard to the use of v Professor Tait ( Quaternions , 3rd ed., § 149) says: — “The precautions necessary in such matters are twofold — ( a ) The operator must never be placed after the operand ; ( b ) its commutative or non - commutative character must be carefully kept in view. ” 100 Proceedings of Royal Society of Edinburgh. [sess. right. Is it not akin to inconsistency to say in effect — “ It is justifiable to violate, for convenience, the custom of writing an operator to the immediate left of the symbol affected, and to indi- cate the connection by some other method, but the justification only covers a limited violation of the custom. It matters not that the new method of indication will equally well serve whatever be the relative positions in a term of the operator and the symbol affected — we will strictly adhere to one part of the restriction hitherto imposed upon this relativity of position, though freeing ourselves from the other.” It may be — has been — urged that to place a V to the right of the symbol affected is as criminally ridiculous as to write X— for dx • It may be equally well urged that the removal of V to the left dx from its primitive position is on a par with writing — XY for dx xdY Xdx It must be conceded that both of these violations of custom are objectionable, and cannot be justified, unless some convenience accrues greater than the counterbalancing inconvenience of having to show by some method, other than that of juxtaposition, the con- nection between the operator and the symbol affected. Whether such convenience does exist must be left undecided till we come to the applications. What I want to point out here is, that it is extremely inconvenient, and there is absolutely no ground whatever for not utilising this new’ method of indication in all cases where it is applicable. To take an instance. In considering Maxwell’s electrostatic theory below, we are led to consider the very simple stress, whose corresponding linear vector function is given by the equation o) = V2)o>(5 , where £) and (& are the electric displacement and electro-motive force respectively.* The force per unit volume due to this is di d_& dk dV^jiS dV^m dx dy dz dx dy dz * Maxwell’s Elect, and Mag., 2nd ed., § 68. 1890-91.] Mr A. M'Aulay on Quaternion Differentiation. 101 Now, what possible objection can there be to writing this last equation in the form (1). On the left of this equation the V , as indicated by the suffixes, refers to the symbol immediately preceding it. On the right it refers to both the symbol immediately preceding and also to that immediately following. Certainly the expression on the right can be written V5)V@ + Vp = -SVA.V * To explain my notation I will quote from a paper f on this sub- ject, written in 1884 : — “ If be any linear quaternion function , <£ itself being a function of the position of a point . _dcf>i + dj ^ defile dx dy dz It is necessary, as will be seen below, that this A should be dis- tinguished from V . Whenever numerical suffixes occur in this paper it will be to * Tait’s Quaternions, 3rd ed., § 508. The following words of Professor Tait seem to me to form a powerful argument in favour of my natural notation : — “ The highest art is the absence of artifice. .... The difficulties of Physics are sufficiently great in themselves to tax the highest resources of the human intellect ; to mix them up with avoidable mathematical difficulties is unreason little short of crime In Quaternions, a subject uniquely adapted to Euclidian space, this entire freedom from artifice and its inevitable compli- cations is the chief feature What is required for Physics is, that we should be enabled at every step to feel instinctively what we are doing. Till we have banished artifice we are not entitled to hope for full success in such an undertaking” (Tait, “On the Importance of Quaternions in Physics,” Phil. Mag., 5th series, vol. xxix. pp. 84-97). t Mess, of Math. , vol. xiv. p. 26. I have substituted in the present paper A for the v' of the original paper. 102 Proceedings of Royal Society of Edinburgh. [sess. show to what quantities the operator V refers, both the V and the quantities having, for this purpose, the same suffix. Thus below, •Tv^v^y.yS^i+vi^s^h... 1 2 1 2 dx dx dz dy dz One advantage of this notation is, that the V/s, V2’s, &c., as well as the oq’s, be any linear quaternion function of a quaternion, then with Professor Tait’s ( Quaternions , 3rd ed., § 482) notation for integration — * According to Professor Tait this must be written in some such form as the following :—YVi(S72 + ' * • where r is any quaternion. He suggests no notation for . . . where 0 is a general linear quaternion function. His symbols < and > do not obey the laws of vectors, the first only because it is not allowed the freedom of a vector. £ The proof is given in the paper already quoted from. 1890-91.] Mr A. M'Aulay on Quaternion Differentiation. 103 f(dP)=/f(VUv& )ds (2), JJW vds ==///<]> Ad* ...... (3). The last equation shows at once, as pointed out in the paper already- referred to, that the stress (when has the particular form of a vector function of a vector) causes a force per unit volume A . Before considering the properties and applications of V in this extended form, I will now introduce all the innovations that I propose. A large class of differentiations can he included under a symbol somewhat analogous to V . Suppose we have a linear vector func- tion, «f>, of a vector depending on the nine scalars, a, b , c, a\ b\ c, a", b'\ c", by means of the equations — k = a"i + b'j + c"k Then a, 6, c, &c., can be called the coordinates of . Again, P, Q, B, L, M, N may be called the coordinates of the self-conjugate linear vector function, zf, of a vector, if tffi = P i + N; + Mk zsj = Ne + Q j + L k rsk = M i 4- Lj + B& . Now, just as, if u, v, w are the coordinates of an independent vector o-, o-V may be defined as a symbolic vector, whose coordinates are ~t -- > ; so if a, A c. a\ b\ c\ a\ \ c'9 be the coordinates of du dv aw an independent linear vector function, <£, of a vector, may be * defined as a symbolic linear vector function, whose coordinates are — d d d d d d d d d da 5 db 5 dc 9 da' 9 db' 5 dc' 9 da ' 5 db" 5 dc" ’ If 7tf be an independent self-conjugate linear vector function of a * I use the inverted D to suggest the analogy to Hamilton’s inverted A. It is advisable to write o-V, &c., instead of v or ft) = Q(fi>fi)- Similarly, if Q(a,/?,y,8) be a function of four vectors, a,/?,y,S, linear in each, we may put Q( ^ vPv ^ 2^2) = Q(^1?^15^2^2) ’ and so to any number of pairs of £’s. Of course if there be only one pair the suffix may be dropped entirely. I now state a number of theorems in pure mathematics which will be useful, for brevity leaving them unproved. If be any linear vector function of a vector, and ' be its con- jugate, -£Sw<££ ........ (4), ( - $')(!) = VV£<££.to ...... (5). If Q(a ,/3) be any quaternion function of two vectors, a and (3 , which is linear in each, Q(M£)-Q(«,i) ...... (6). To apply this in practice, it is convenient to remember it in words : — In any term in which £ and <££ occur, ice may , without altering the value of that term , substitute for them <£'£ and £ respectively . (It is 1890-91.] Mr A. M'Aulay on Quaternion Differentiation. 105 not necessary to say that the term is linear in each of the symbols £ and <££, for from the definition of £ it must be so.) If /3) | Q(^^) = 2Q(a,/3) / ' • ' ’ ' If m have the usual* meaning with reference to the linear vector function 6m = S£1£2£3S<^£1^>£2^>£3 ..... (9). (10) From these we deduce that if — — S(0 V .(X <£ 1(i) 3 Y V j V gSwo-jO^ SViV2V3SW3 >■ . (11). 3 Y O'jO’gScO V ! V 2 S V 1 V 2 V 3So-1o-2o-3 If and if/, two linear vector functions of a vector, be connected by the equation S<££xf = » where ^ is a perfectly arbitrary linear vector function of a vector,! it follows that or, again, if y he self-conjugate but otherwise perfectly arbitrary and the above equation hold, it follows that — V' where 2cf) — (f) + cf)’ and similarly for if/, i.e., , if/ are the pure parts of and i/r. * Tait’s Quaternions, 3rd ed., §§ 158 et seq. t This frequently -recurring and cumbrous phrase is very annoying. Might I suggest the term Hamiltonian. Thus, in the present case, we should say — “If and i p be two Hamiltonians connected by the equation S 4>(xC=S'l/CxC where x is a perfectly arbitrary Hamiltonian,” &c. 106 Proceedings of Royal Society of Edinburgh. [sess. If Q be any function of an independent variable vector cr, we already know (Tait’s Quaternions , 3rd ed., § 480) that dQ= -SdovV.Q (12). A similar theorem in a bolds. If Q be any function of an inde- pendent variable linear vector function of a vector (whether general or self-conjugate) dQ= - Qi^dcfj^a^ (13). From this it is not hard to show that a is an invariant. That is, it is a symbol, independent in meaning of the three mutually per- pendicular unit vectors, i,j , &, used in defining it. I now proceed to a few examples of the use, in the subject of Elasticity , of the symbols introduced. Assuming uniformity of temperature throughout, let us investigate the general equations connected with the state of an elastic body. The two usual assumptions will not be made (1) that the strain is small, and (2) that there is no molecular couple. Let d, where is a linear vector function not necessarily self-conjugate. is a function of p', or of p only, and does not in any way depend on p^ or YV1^>p1 as it might be indifferently written.) Let now Viv',ds' stand for the unit normal and element of surface at a point of the boundary of the portion of the body considered, in its strained state. Let also df stand for the strained volume of the element d$. Then noting that by Tait’s Quaternions , 3rd ed., § 384, the rotation of the ele- ment due to the additional displacement is YV'Sp72, we see that the last equation gives fff Swds = - ff&8p \Jv'ds + ffids + fffSeffSp'ds, where e is put for Y£<££/2, and .*. (equation (5) above). <£ = ?+Ve( ) (15), where stands for the pure part of c£. Transforming now the surf. int. into a vol. int. by equation (3) above, we have f/S8p'Uv'ds' = fffSSpffk'dd =./Z7Xsfy>i<£vi + S Sp'faVJds. Combining this with the other volume integrals, and noting that - S3pi<^vi + SeviVi = - SSp^v/, we get fff8ivd, and a rotational part, Ye ( ). For the first part 6, and for the last 3, independent scalars must be assigned, and it is only the first 6 that have anything to do with the pot. en. Expressed in physical language : — A stress can only be split up in one way , into two stresses, of which the first is an ordinary stress, producing no couple per unit volume, and the second is a couple-stress. The latter is quite independent of the pot. en. Here, by a “ couple-stress,” is meant a stress which produces on any interface, whatever be the direction of its normal, a tangential force. Shortly stated, the above may be put : — The part of the stress to which the couple per unit of volume is due, is independent of the pot. en. This is strictly analogous to the well-known corresponding strain theorem that the rotation of an element is independent of the pot. en.* We may anticipate here by saying that this part of the stress is therefore also independent of the strain, though of course other means enable us to determine it. In fact, in order that an element should not have infinite angular acceleration, it is easy to see that on the whole it must be subject to zero couple per unit volume. In other words, if be the given external couple per unit volume of the unstrained body m + 2me = 0 (17) is the equation which gives the part of <£ we have called e. Here m stands for d=-Sa>V.p' (25). The physical meaning of x may be thus explained. Let <*> be the vector coordinate before strain of any point P, very near to another point 0, relatively to the latter ; then yo> is the coordinate of the strained position of P relative to the strained position of 0. In symbols dp = XdP (26). From this equation we may at once deduce the expression for V' in terms of V and conversely. For S dPV = Stfp'V' = SxdpV' = Stfpx'V' . • . since dp is perfectly arbitrary V =x V' or V' = x'_1V ..... (27) We have thus from equation (24) 8w= - mSSp^x "1^7! (28). 110 Proceedings of Royal Society of Edinburgh. [sess. Now 8X(o= -SP'1Sa>V1 (29). Hence we see from equation (7) that in any expression, linear both in V 1 and Sp\, such as the last expression for Sw, we may substi- tute instead of these two £, Sx£ respectively. Hence 8w-lf»S8xWx,-1{ (30). This expresses Sw in terms of the variation of strain. It is con- venient to modify the last equation by means of equation (6). Applying the rule given in connection with that equation, and changing £,x-1£ into X-1£j£ respectively, we get Sw = — raSSxx-1^^ (31). Suppose, now * that the strain x is made up of a pure strain if/, followed by a rotation of q( )q_1, so that Xw = qif/wq-1 (32). Then it is easy to prove that 8Xo> = 2WSgr(Z~1*X<0 Substituting in the last expression for Sw, we get Siv/m = - 2S NSqq^X^t ~ • The first term on the right is zero, * . * V£<££= 0. That 8q should disappear from the expression for Sw is, of course, what we should expect. It is, however, well to show that this follows as a mathe- matical consequence of our fundamental assumptions. We now have Siv= - mSSifrx’^q'^q = - mSSif/if/^iq^^q-^Cq [by substituting for x-1 in terms of if/ and q] = - mS8ifnf/-1Zq-1(q£q-1)q [by substituting £, q^q-1 for q ~1£q,£ respectively] = - mSSi^i/'-1^^ * See Tait’s Quaternions, 3rd ed., § 381, where it is shown how to deter- mine both r]/ and q in terms of x • 1890-91.] Mr A. M‘Aulay on Quaternion Differentiation. Ill where tsr is a self-conjugate linear vector function of a vector defined by the equation tfw = q~l(c[ioq~x)q (33). Substituting for respectively in the last expression for Sir, we finally get 8w = - mSSif/iiTffif/^Z (34). Thus the only infinitesimal appearing in Sw is Si f/. It follows that w can only be a function of the pure strain if/. This is not an obvious truth, as I have before remarked. Assuming it now, we have by equation (13) Sw = - SSi/^aw;£ . Comparing this with the last equation, and noticing that Sif/ is a perfectly arbitrary self-conjugate linear vector function of a vector, we see (p. 103 above) that 2v|,aw = m(2ffi/f_1 + i/'~V) (35), V J(srt/'"1 + is the pure part of 73*1 if/'1. The last equation can be easily shown to lead to mzsoj - ^dwxl/o) + Y Oif/u) . . . \ where r . . . (36). e = (xf/ + sm)-1^aw^ .) This, with equation (33) above, completes the present problem of expressing the stress <£ explicitly in terms of the strain q and if/. 7v can be easily shown to be that stress which cf> becomes when the body is rotated by the operator g_1( )q, without altering the force exerted across any interface of the body. We thus see why it is ts and not which bears the simplest relation to if/. (jy + Yew, where e is perfectly arbitrary so far as the strain is concerned, is the force exerted on the strained area w. This last would more properly be denoted by w'. Calling it w', and denot- ing by w the same vector area before strain, we have *■ (o' = (37). * By Tait’s Quaternions , 3rd ed., §§ 157, 158, we have Y xtJLXv==mX “W fxv. If fx , v be taken as the conterminous edges of a small parallelogram in the unstrained state Y/xv will be its vector area ; x ^ Xv will be the edges of the strained parallelogram, and Vxv-X1' its vector area. 112 Proceedings of Royal Society of Edinburgh. [sess. Hence the force <£ co' becomes mcf>f~1(D = 7ncf)f~1(D + mVef _1o>. Thus we see that the force on an elementary area, which before strain is a), is a linear vector function of w, but even in the case when there is no molecular couple, this function is not in general (large strain) self-conjugate. If there be no rotation, this force = m Tffip ~ ho + mV e\J/ ~ 1 w = ^dwto + Y 6 m + . If now the rotation take place this force merely rotates with the body, and we get for the force rw on the area, due to the^ strain iH )t\ TO) = q(^dW(o + Y6(t) + mY€xl/~1(D)q~1. . . . (38). It is not hard to see from the above that the couple per unit volume of the unstrained body is 2mqeq~1. The force per unit volume of the unstrained body can be shown by means of equation (3) to be r A. From these we can write down equations of motion in which i}/ occurs. To obtain equations of motion in which only p and its derivatives occur explicitly we must adopt a different method. Consider w a given function, not of i]r as above, but of «//2 or fx (Tait’s Quaternions, 3rd ed., § 381). Let ^O) = l/^20D = = V j^So) V 2SpiP2 .... (39). In assuming that w is given as an explicit function of the coordinates of \I>, we are following Thomson and Tait, for these coordinates will be found to be the A,B,C ,a,b,c of Appendix C of their Nat. Phil. To see the enormous advantage of employing quaternions in such questions as the present, it is only necessary to compare the pro- cesses and results of the present investigation with theirs. The results below are considerably more general than theirs, and yet how much less cumbrous. By the methods already so often applied, it is easy to prove both the following identities : — S8x^x'_1^ = sx'sx^x"%''^ = sSx'xCx' W’f- 1890-91.] Mr A. M‘Aulay on Quaternion Differentiation . 113 Thus we see from equation (30) that - is(x'sx + sx'x)£x~!<£x = -hsmx'tx'-'t- Eut we also have by equation (13) above 8«;= -SS^a«o£. Hence from p. 104 above we see that %aw = mx-'4>x-\ or (40)- (It is easy from here to go back and prove all our previous results over again. Perhaps this, in fact, would be the shortest method, but it would not be the most natural. To do so it is only necessary to notice that since SSi/^d£ = SS4>£^a£, it can be proved that ^<3 = ^Gi]/ + ij/^a where the differentiations on the right are not to act upon if/.) Substitute from equation (27) for V ' in the equations (17) and (20) of equilibrium. Thus 8 - " V , + V , = 0 . Noticing that since by equation (11) 2m\~1 w= - Yp'jp'gSoo V i V 2 > we have my" 1 A = 0 , this last equation can be written g -|V^x'‘]A+m^x'"1A = 0, Substituting now for an(^ o) — o). Also = 0, and .-. 6 of equations (36) = 0. Thus equation (36) gives » = (45). It is worth while giving one of these for comparison. I may remark that many of the results arrived at above, although quite simple enough in their quaternion form to be manageable, and therefore useful, become so extra- ordinarily complicated when translated into Cartesian notation as to be utterly unmanageable and useless. The equation referred to is d {■£(=*>)■ dw da dw da \ dx *~db Hz + dc dy J d dy f dw da dw l dy + da da dw i dz dc ' ijD1)} -\ dz 1 f dw da dw l dQ~dz + da da dw dy + db 1 (£+*)} 1890-91.] Mr A. M‘Aulay on Quaternion Differentiation. 115 Since we are dealing with small strains, it is convenient to alter the notation slightly. Instead of our previous y and ifr we shall now write 1 + y anc^ 1 + ^ respectively, so that both y and if/ are small, and if/ is the pure part of y. And, further, w'e shall write p = p + 7], so that rj is the small displacement. Thus yoD = — Sa> V .7] (16) ifru) = — ^(^Sw V 1 + V .... (17). Since the strain ifr is small, the stress z*r, i.e., Qw is linear in if/, and .’. w is quadratic. Now, for any such quadratic expression as can be easily proved w= -|Si fs£ffUo£ (18), . \ from equation (45) we have M? = - JSi/r£ar£ (19). Also w, being quadratic in if/, is, if regarded as a function of zsr, quadratic in it. Hence -|S (50), and .'.by the last equation and p. 104 above, ^=„aw (51). Instead of regarding w as a function of if/ or of nr, it is perhaps simpler, from the mathematical point of view, to start with assum- ing it a given function of the first space derivatives of rj. Let, in fact, w = w(v1,rj1,v2,rj2) (52) where w(a,/3,y,8) is a scalar function of the vectors a, ft , y, S, which is (1) linear in each of its constituents ; (2) symmetrical in a and (3, and also in y and 8 ; (3) such that the pair a, ft may be interchanged with the pair y, 8 without altering the value of the function. (If this last is not true in the first form of w chosen, it may be made so by writing \iv(a,ft,y,8) + ^w(y,8,a,/3) instead of w(a,/3,y,8), as this does not affect equation (52).) Such a function can be proved to involve twenty-one independent scalar constants, which is the number also required to determine an arbitrary homogeneous quadratic function of the six coordinates of ifr. 116 Proceedings of Roigal Society of Edinburgh. [sess. We may from this form of w at once go back to that in terms of i j/ by means of equation (8) above. Thus, W — (53), or, again, by equation (7), w = ^2>x4) (54). Hence by substituting - £S for ij/£v we get -is - s MitAtvUv'I'Qh and .*. by p. 104 77*o = 2£w(£, *0,^,1/^). ..... (55), or, again, by equation (8), 27*0 = 2£w>(£,*o, V (56). The equation (23) of equilibrium thus becomes in this case 3 + 2£w(£,A, V = 0 (57) Thus in the case of isotropic bodies in which c is the compressi- bility and n the rigidity, we have {Mess, of Math., vol. xiv. pp. 30, 31) = 2nij/o) ~(f ~ (58), .... (59). 27co (60). 6n 9c Thus from these equations and equation (49) W= S’W Again, from the first of these equations and equation (8) we have ( C 71 \ V)= -nSV1>pTll + {^ -j)S2Vr], or 2 w = rcS V 1%S V iVl + reS V 1 V 2SW2 + (c - -|»)s2 Vv . (61 ), and from equation (56) 27*o = — wSoo V . rj - n V lS*o771 — {m — ?^)*oS V rj . . (62), 1890-91.] Mr A. M'Aulay on Quaternion Differentiation . 117 where m stands for c + ~ . This last may be derived in a great O many other ways still more simple. The equation of equilibrium thus becomes g = rcV277 + mVSV77 (63). As a final application in the theory of elasticity let us consider St Tenant’s torsion problem from a quaternion point of view. Let r, , z be ordinary columnar coordinates whose axis is parallel to the generating lines of the cylinder. Let A, fi, v be unit vectors in the directions of dr , dcfj, dz respectively, so that _ . d ad d V = A.— H — + v— • dr r d dz It is required to determine v a scalar function of r and <£, so that rj given by the equation rj = r(zrfji + vv) . (64)) where r is a given small scalar constant, may satisfy (1) equation (63) of equilibrium, and (2) the equation 0 = = - wSw V . r] — n V iSco^ — (m — w)o>S V rj at every point of the curved surface ; co in this case standing for the normal at the point. Q having the same general meaning as on p. 104 above, we have Q( v 1^1) = TMQ( V) ~ Q(^A)] + + Q( V v,v)} (65). In the case when Q is symmetrical in its constituents this takes the simple form Q( ^7D'7i) = 'r{^Q(^) + Q( Vv,v)} .... (66). From the first of these we have V rj = r{ (2 zv — rX) 4- V w } = r{ V (t? — ^r2) + Vw} so that SV?7 = 0 and V2r] = vV2v. Thus equation (63) becomes V2v = 0 (67). From equations (62) and (66) above, we see that in the present case the stress is given by 7X(d = - nr{r(fji$(i)v + vStoju,) + (vSto Vv + V^Scov)} . (68), 118 Proceedings of Royal 'Society of Edinburgh. [sess. and therefore consists of two shears ; the first of magnitude mr , with faces perpendicular to n and v, and the second of magnitude nrT V v, with faces perpendicular to v and V v. Assuming w to be the normal at a point of the curved surface, and therefore perpen- dicular to v, we have 0 = rSw/x + So) V v = -iSvo>V(r2) + ScoVv. Thus dv _d /r2\ dn dl\ 2 / (69), where djdn denotes differentiation along the normal outwards, and djdl differentiation in the positive direction round the boundary. The surface traction on the plane end = 23V = + V V ). Hence the total moment round the axis = nrff (r2 - rSfx V v)d,A ' Kr+//-v/A)> where dA is an element of area of the cross-section, and I is the moment of inertia of the cross-section round the axis. Thus the torsional rigidity is, as usual, n(l+ff^dA^. We leave the problem here to the theories of complex variables and Fourier’s theorem. It is in the general theories of electrostatics and electro- magnetism that I have found the methods now being defended the most powerful. I have been led to believe that there is in all the accepted theories which are based on general dynamical reason- ing an error of a somewhat serious character. I have also been led to a considerable modification and extension of Poynting’s theories. There are two reasons against giving these here. I have been told that this preliminary apology, as it may be termed, for my methods should be as short and simple as possible. Moreover, the greater part of my notes on this subject are at present inaccessible. I therefore limit myself in this branch to a single example. Maxwell has not investigated what are the general mechanical results of his electrostatic theory for crystallised dielectrics. 1890-91.] Mr A. M‘Aulay on Quaternion Differentiation. 119 According to him, the properties of the medium depend on six independent constants for each point, called the coefficients of spec, ind. cap. These coefficients will themselves he functions of the state of the medium, and therefore in particular of its strain. Assume with Maxwell that ®=-v», = (70), where K is not a mere scalar, hut a self-conjugate linear vector function of a vector. K is itself a function of the position of a point and also of the strain at the point. Here v is for obvious reasons put for Maxwell’s V. Assume further, that if W be the pot. en. of the field ; D,o- he the volume and surface density of electricity ; and the rest of the notation be identical with Maxwell’s, = / ■■■■(' >’ and * . \ W = ffvads + fffvDds + ifffSQ&s . . . (72), D=-SV3) o- = [S2)UV]a + [S2)Uv]6 . . (73), the last occurring only at a surface of discontinuity in !£), UV point- ing away from the region of the corresponding 2), and the two regions hounded by the surface being denoted by the suffixes a and b. In future, such expressions as [ ]a + [ ]6 will, for brevity, be written [ ]a+6 All our integrals are supposed to extend throughout all space * though, as K = 0 for conductors, these may be excluded. The boundaries of space are the surface at infinity and all surfaces of discontinuity in 3) or To find the mechanical results flowing from the above assumptions, let p be the present (whether strained or not) vector coordinate of any point, and let the medium be (additionally) strained by a small displacement Srj, vanishing at infinity. Let SW be the increment in W Then if 8W can be expressed in the form 8W = -///Shield? ..... (74), * In taking this for the form of W, and operating upon it as follows, we are following Helmholtz for the particular case when K is a mere scalar. See Wiss. Abh., equation (2 d), p. 805. For the various assumptions above see Maxwell’s Electricity and Magnetism, part i. 120 Proceedings of Royal Society of Edinburgh. [sess. we shall have the following expressions for % and the forces per unit volufhe and surface respectively due to the electric system. S = M &=-[>Uv],,+s. .... (75). And, further, if he self-conjugate, both these forces will he explained by a stress <£, as can he seen by the above work on stress. For proof we have by equation (3) above 8 W = -fff^yi^ V xdq = —ffS8rjcf>XJvds + fff^y7lV whence SV = V1S8^1V (76), which might have been derived from the equation (27) V' = \~1 V. Assuming that the strain due to 8r) does not alter the charge of any portion of matter, 0 = S(Dc?s) = 8(crds) (77). To find 8W, notice that 8d@S VSV + i-S@SK @)rfs . Also JJJ'8vS)ds + fffhv.crds = - ff/8v S V 2)c?s + ffhvSUv'&ds [equations (73)] = ff/S($)'V§vd) = Ka> + V€Ko> , 8Kr(o = YcKa)-KY6a). S@8Kr® - S®eK® - S(£KY€(£ = 87rSe£>(£ , whence giving € its value, JY V Srj, ~ Sg8Krg = JS V SjjVSe . 07 T If we put w for the pot. en. per unit volume we have w= -iS2>e= -ls@Kg .... (78). 07 r K is a function of the independent variables e and i f/, where if/ is the pure strain given by if/ W = — Vj+ V jScjO^j). 122 Proceedings of Royal Society of Edinburgh. [sess. Thus w may be regarded as a function of the independent variables (£, €, i {/, and we shall have p S(S8K,e = S 8+LawZ, = 8SVl aw V ! 07T r by equations (13) and (8) above. Thus sw = -fffSSrjfi V jSS)® - (SS V + JY VftX^-^awV Jdfe or W=fjfSSVl(§VXV1® + i//awV1)d<: . . . (79). Hence we see that g = - |V£)A®- dwA (80) % = [kVX)Vi& + *awVv-L» .... (81), and that these forces per unit volume and surface respectively can be supposed due to a stress given by (^a)=-|YM-^(0 (82). From this we see that the stresses in the electric field can only be determined when for the particular strain existing at any point forty-two scalar functions of that strain are known, viz., the six coefficients of specific inductive capacity and their thirty-six dif- ferential coefficients with respect to the six coefficients of pure strain. The two parts of the stress cf> (1) that which is independent of the variation of specific inductive capacity with strain, and (2) that which depends on this variation are conveniently considered separately. The first is more general than Maxwell’s, because we have not, as he does in this connection, assumed that X is parallel to (S'. It consists of a tension in the direction bisecting the positive directions (or negative directions) of both X and (5*, of magnitude JT£)T(§, an equal pressure in the direction bisecting the positive direction of either and the negative direction of the other, and a pressure at right angles to both, of magnitude — JS^)(S or w. This stress, of course, reduces to Maxwell’s when X is parallel to (£• The other part of the stress — flw = can be only 1890-91.] Mr A. M‘Aulay on Quaternion Differentiation. 123 usefully considered when certain simplifying assumptions are made. In Professor J. J. Thomson’s consideration of this subject ( Applica- tions of Dynamics to Physics and Chemistry, §§. 35 and 39), he not only assumes K to be a mere scalar both before and after strain, but he also does not consider the most general case of strain which involves 6 instead of 3 independent coefficients. If this last restric- tion had not been made, our 42 constants would have reduced to 7, and in his case they reduce to 4. In either of these cases the stress . . @2 is simple enough, viz., — aK ,* 07 TV * For other particular cases of the stress under consideration, see Helmholtz, Wiss. Abh., i. 798 ; Korteweg, Wied. Ann., ix. 48; Lorberg, Wied. Ann., xxi. 300 ; KirchofF, Wied. Ann., xxiv. 52, xxv. 601. 124 Proceedings of Royal Society of Edinburgh. [sess. On the Interaction of Longitudinal and Circular Magnet- isations in Iron and Nickel Wires. (Second Note.) By Professor Cargill G. Knott. (Read February 16, 1891.) In a preliminary note communicated last July,* I drew attention to what seemed a novel property of iron wire under the combined influence of circular and longitudinal magnetisations. Similar ex- periments were subsequently tried with nickel, and similar results obtained. It appeared, however, that in some respects nickel behaved oppositely to iron. The first series of observations brought out the fact that a current along the nickel wire seemed to assist the ac- quiring, under a longitudinal magnetising force, of a polarity oppositely directed to the direction of the current. Unfortunately the necessity of stopping work during the hot summer months postponed the discovery that much if not all of the supposed curious effect in iron and nickel was due to the existence of a twist in the wire. It should he mentioned that the wires were set up with great care, being first annealed, then brazed to terminal pieces, then annealed a second time under horizontal tension sufficient to keep them straight in a direction perpendicular to the magnetic meridian. To one of the terminals two copper wires, laid parallel to and on each side of the nickel or iron wire, were soldered ; and the set of three wires was placed in position in suitably arranged grooves cut along the plane surface of a semi-cylinder of wood. The other half of the cylinder was then superposed so as to keep the wires firmly in position ; and the whole arrangement was lifted from the place where the final annealing had been accomplished and inserted into its position in the heart of the magnetising coil. Exactly when the wire got twisted it is impossible to say. It must have been a small twist ; but that it did acquire a permanent twist is sufficiently proved by later experiments in the months of October and November 1890. In these later experiments a slightly different arrangement was adopted. The wire to be treated, after careful annealing, was * See also Phil. Mag. for September 1890. 1890-91.] Prof. Knott on Interaction of Magnetisations. 125 slipped through a glass tube a little longer than the internal metal wall of the tube on which the well-insulated magnetising coil was coiled. This metal wall was used as the return channel for the cur- rent, so that all possibility of an appreciable direct electro-magnetic effect of the circuit upon the magnetometer was quite excluded. The end of the iron or nickle wire nearer to the magnetometer was gripped vice-wise by a cleft metal plug of conical shape, which, when pushed into the end of the magnetising coil, established good pressure contacts between the end of the wire and the metal wall. The other end of the wire projected backwards out of the magnetis- ing coil sufficiently to enable it to be clamped to a twisting gear. From this end, and from the neighbouring end of the tube wall, wires well insulated and well twisted together were led to the commutator connected with the battery. It was only after a series of experiments, in which the effect mentioned in my earlier note was observed to take place sometimes in one way and sometimes in the other, that I came to the conclusion that there must be an original permanent twist in the wire. Thick wires showed comparatively small effects, steel wire showed the effect only when it was drawn thin, and so on. Nickel wires be- haved in an especially confusing manner, even after the greatest care was taken to insert them untwisted into the magnetising coil. The twisting gear mentioned above was added to the apparatus so as to make a direct experiment upon the effect of a small voluntarily applied twist. That large twists might reasonably be expected to produce peculiar disturbances in the magnetic distribution under the combined influence of longitudinal and circular magnetisations will be at once admitted when it is remembered to what an extent twist- ing affects the result of either taken alone. I was not prepared, however, for the pronounced influence exerted by even a small twist previously existing in the wire upon subsequently applied longi- tudinal and circular magnetisations. To prevent the possibility of such twists being inadvertently applied, the wire was, in the later experiments, annealed with a weight hanging free at the one end. This left the wire permanently magnetised under the influence of the earth’s vertical field ; but in the stronger cyclic field to which it became subjected the wire soon lost all trace of this original polarity. After being annealed the 126 Proceedings of Boy at Society of Edinburgh. wire was gently lowered without rotation by means of a screw until the weight came to rest on a shelf. The wire was then sharply cut a little above its lower end, the glass tube slipped over it, and a second severance made near its upper end. The glass tube with contained wire was next inserted into the magnetising coil, and the ends carefully clamped after the manner already indicated. In the following table the results of one experiment with the iron are given. The word “ current ” means the current along the wire ; the word “field” means the longitudinal magnetising force to which the wire was subjected. A current is positive when it flows in the direction of the lines of force, of what is conventionally taken as the positive field — that is, in the experiments under consideration, towards the east. Under the column headed “ range ” is given the range of scale readings corresponding to the cyclic variation of field under the circumstances indicated. The column headed “ polarity ” contains the mean of the extreme scale readings. For Iron Wire of Diameter 0*94 mm. Current. Field. Range. Polarity. 0 ± 324 -6 + 2*2 3 J < 175 -7-5 -2-2 5 5 180 -7 0 J 5 317 -4-5 0 321 -2-5 + 1*47 > 5 208 -5 -1*47 206 -4 0 325 -7-5 + 0-83 275 -5-5 -0-83 5 > 277 -6-5 + 0-5 287 -6*5 -0-5 ” 282 -7 Here, the only apparent effect of passing a current along the wire is to decrease the range of intensity due to a given cyclic variation of field. The susceptibility is markedly diminished, and the more so as the current is taken stronger. There is not the least evidence of an accumulated polarity changing sign with the current, as de- scribed in my first note. In the next series of experiments the wire (current and field being both zero) was twisted right-handedly through an angle of 10° in a 1890-91.] Prof. Knott on Interaction of Magnetisations. 127 length of 48 centimetres, or 12 J minutes per centimetre length. The results' obtained were as follows for this and other twists, all indicated in the first column : — Twist. Current. Field. Range. Polarity. + 12'-5 0 ± 343 + 1-5 + 2-1 195 + 12*5 -2T 3 3 187 -18-5 + 25' 0 3 3 350 -5 + 21 195 + 17-5 -21 33 193 -24-5 + 37 *'5 0 > ) 338 -6 + 21 3 3 168 + 39 -21 3 3 167 -43-5 + 12' -5 0 3 3 355 + 0*5 + 21 202 -4 -21 3 5 202 -1 0 + 21 207 -1-5 -21 33 211 -3-5 -37-5 0 3 3 357 + 1-5 + 21 3 3 205 -10-5 -21 3 3 206 + 5 In Part II. of my paper on certain relations between magnetism and twist on twisted iron and nickel wires,* I have worked out in detail the changes of longitudinal polarity produced by twisting a wire when a current is passing along it, or by reversing the current along it when the wire is twisted. In the latter case, if the wire is twisted right-handedly (so that any line in it originally parallel to the axis becomes a right-handed screw), the longitudinal intensity is co-directional with the current in iron, anti-directional in nickel —a fact first established by Wiedemann. In the light of this fact, the experiments just described become intelligible. The sign of the polarity acquired is to a large extent determined by the twist in the wire. In the fourth series, in which the wire was untwisted * Not yet published. See, however, a short paper on “ Magnetic Priming and Lagging in Twisted Iron and Nickel Wires,” Journal of the College of Science, Imperial University, Japan, vol. iii. (1889) — Abstract in Wiede- mann’s Beiblatter, vol. xiii. 128 Proceedings of Royal Society of Edinburgh. back to its first stage of positive twist, there is a hint at a change in the law of the acquired polarity. It is obvious, however, that this is simply the result of torsional after-effect. The wire, in fact, has become elastically untwisted, although it has not become so as regards the relative positions of its end-sections. On continuing the untwisting past the original zero, we find that it is some time before a pronounced effect is produced. Even for the twist — 37'*5 the difference in the average polarities for the two directions of current attains to nothing like the first difference for the twist of + 37'*5. This comparative vanishing away of the polarity differ- ence effect as the wire is partially untwisted is quite analogous to what is observed when, with no sustained longitudinal magnetising force, the current along a wire is reversed at different stages of untwisting. There is one particular, however, in which the results of the present experiments differ from what might be expected if the accumulation of polarity was simply due to the magnetic effect of the current along the twisted wire. First, it should be noted that the twist in a wire subjected only to the magnetising influence of a longitudinal field varied cyclically has no determinate effect in causing a change in the average polarity. Whatever be the polarity produced by a current passing along the twisted wire, we might naturally expect a cyclic field superposed thereon to give rise to a symmetrical variation of magnetic intensity about this acquired polarity as a mean. Con- sequently the difference of the average polarities for positive and negative currents should be equal to the range of polarity when the current is reversed in the twisted wire. As a fact, however, it is much greater. For instance, in the case given above for twist + 25' the range of polarity produced by reversing the current, the field being zero, was only 25 ; whereas the difference of polarities as given in the table is 42. Similarly, for twist + 37'*5, the range was 49, as compared with the difference 82 5; for the (second) twist 12'"5 the range was zero ; and for twist - 37'*5 the range was 6, as compared with the difference 15*5. The same peculiarity is shown to a more pronounced extent in nickel wire, of which I give here only one experiment. In spite of the greatest care in setting up the nickel wire, a change of average 1890-91.] Prof. Knott on Interaction of Magnetisations. 129 polarity was in this case obtained at the first putting on of the current. The necessary fingering of the wire when clamping its ends seemed to give a slight twist, sufficient, however, to produce the effect spoken of. We may suppose the existence of the effect to prove that a twist did originally exist in the wire. I shall call for convenience this unknown initial twist x'. The results are these : — For Nickel Wire of Diameter 09 mm. Twist. Current. Field. Range. Polarity. x' 0 ± 273 + 20*5 + 2*43 3 3 240 + 113 -2*43 3 3 238 - 46*5 £c' + 12'*5 0 3 3 287 + 29*5 + 2*43 237 - 66*5 -2*43 3 3 239 + 102*5 In the first series (for twist x'), the range of polarity due to the reversal of the current was only 10, whereas the difference of the average polarities associated with positive and negative currents is as much as 159*5. It will he noticed that in passing from twist x' to twist x' + 10', the sign of the difference of polarities changes from positive to negative ; while the amounts of the differences are nearly the same. This would indicate that x ' had a value of approxi- mately - 5' ; so that a?' +10 becomes +5'. I am by no means satisfied, however, that (in nickel wire at any rate) there does not exist a measurable difference of polarities due to the current only. The great difficulty is to be sure that no twist exists in the wire ; for it is quite evident that a very small twist is sufficient to produce a very large average polarity, when the wire is subjected to a steady circularly magnetising force in conjunction with a cyclically vary- ing longitudinal field. If the effect is due only to the twist in the wire, we have here an extremely sensitive process for demonstrating the existence of a twist, especially in nickel wire. The whole subject calls for more detailed discussion ; and I am impelled to communicate these earlier results chiefly with the desire of correcting any false impressions that my preliminary note of last July might very easily give rise to. The facts there described are vol. xviii. 30/4/91 i 130 Proceedings of Royal Society of Edinburgh. [sess. accurate ; but we see now that the more curious of them are com- paratively easily explained as being due to an initial twist in the wire of a few minutes per unit length. This is true not only of the average polarity acquired, but also of the asymmetrical form of the curve with reference to the line of zero field. For, as may be seen by a study of Ewing’s curves {e.g., Phil. Trans., plate lx. fig. 17, 1885), such an asymmetry exists in a cyclic curve taken about a mean value of field other than zero. Now here we have a finite mean value of longitudinal intensity supported by the current along the wire. if, in the curves shown in the preliminary note, we shift the upper narrow graph to the right and the lower one to the left so that their mean points have abscissae equal to the longitudinal fields corresponding to their ordinates regarded as intensities, we shall see at once a sufficient reason for their asymmetrical form. All that can be safely said regarding the effect of a current along an iron or nickel wire, upon the susceptibility of the same to a longitudinal field, is that the susceptibility is markedly diminished, and that the residual magnetism* falls off more quickly than the total reduced magnetism. In other words, a current along a wire diminishes the hysteresis (to use Ewing’s word) relatively to a cyclically varying longitudinal field. The former conclusion agrees with the result obtained by Schultze (Wied. Ann., xxiv., 1885) in his experiments on the reciprocal action of mutually perpen- dicular magnetisms. He experimented with iron and steel tubes, and the circular magnetisation was induced by currents altogether outside the iron. He does not seem to have discussed the properties of cyclic magnetic graphs, or even the ratio of the residual to the total induced longitudinal magnetism, with or without the circular magnetism. It is therefore impossible at present to say whether the diminished hysteresis here noted is due to the magnetic effect of the current in the wire, or, as is perhaps more probable, to the direct vibratory action of the current upon the molecules, thereby accelerating the breaking up of unstable molecular groupings. * The experiments proving this are reserved, as not being quite completed. 1890-91.] Mr J. Y. Buchanan on Deep-Sea Deposits. 131 On the Composition of some Deep-Sea Deposits from the Mediterranean. By J. Y. Buchanan, Esq., F.R.S. (Read January 9, 1891.) The muds, the analyses of which are reported in this paper, were collected in September 1879, during the laying of a cable between Marseilles and Algiers by the India Rubber, Cutta-Percha, and Tele- graph Works Company, Limited, of Silvertown, the ship employed being the s.s. “ Dacia.” The numbers of the samples are those which were affixed to them on hoard ship. Nos. 31 to 43 are all from localities lying near the African Coast ; Nos. 45 and 46 are from positions between the African Coast and the Balearic Bank. Nos. 64 and 65 are from the Balearic Bank, and Nos. 86 to 89 are from the Gulf of Lyons. The positions and depths are collected in Table I. Table I. — Giving the Position of the Ship where each Sample of Mud was Collected , and the Depth of Water there. No. of Sample. Position. Nature of Bottom. Depth (fathoms). Latitude N. Longitude E. 31 o / 36 57| o / 3 21 Soft mud. 1080 32 37 3 3 17 5 ? Clayey mud. 1238 35 37 5 3 26 1258 36 37 9! 3 23 Mud. 1343 39 37 12 3 31 ? 5 Soft mud. 1454 41 37 21 3 38 1502 43 37 39 3 53 9 9 1536 45 37 56 4 6 1494 46 38 11 4 6 5 ? 1469 64 39 26 4 36 782 65 39 35 4 40 5 ? 646 86 42 47 5 ID Grey ooze. 780 87 42 53 5 18! Clayey mud. 542 88 43 3 5 12 Mud and ooze. 530 89 43 1! 5 15 Mud. 265 The samples, as received, were in the condition in which they had been collected, having been transferred from the sounding-tube to the bottle without any form of preparation or drying. Some were therefore much wetter than others, and the diversity in their 132 Proceedings of Royal Society of Edinburgh. [sess. condition in this respect is well shown in the percentage column of Table II. The actual state of the mud when put up in the sample bottle on board depends on so many fortuitous circumstances that no physical importance must be attached to the figures in this Table. In order to bring all the muds, as far as possible, into a similar condition, they were heated in the water-bath until they ceased to lose weight. It was necessary, therefore, to determine their weights, and they have accordingly been tabulated, and will give roughly an idea of the difference between a wet mud and a dry one. Table II. Preparation of Substance for Analysis. — About half of the sample was placed in a tared porcelain basin and dried in the water-bath till it was in a fit form for handling. It was then weighed, and the loss of weight called water. Table II. — Preparation of Samples for Analysis , by Drying on the Water-Batli. No. of Sample. Weight of Mud taken (grammes). Weight of Mud dry (grammes). Loss (grammes). Per cent, of Loss. a b c=a-b a. 1 © | ° 1 ^ * * 1 31 28-4 19*3 9-1 32-04 32 23-8 18-15 5-65 23-71 35 22'9 15-3 7-6 33-18 j 36 23-0 16*4 6-6 28-69 39 14-7 11-7 3-0 20-40 41 26-3 16-9 9-4 35-73 43 29-5 20-0 9-5 32-20 45 25-1 20-2 4-9 19-52 46 19*9 16-1 3-8 19-09 64 24'6 19-7 4-9 19-91 65 38*5 27-3 11-2 29-09 86 25-4 19-2 6-2 24-41 87 25-4 20-7 4-7 18-50 88 29*5 19-8 9-7 33-25 89 22-0 16-9 5-1 23-18 The dried portion was broken up in an agate mortar, and pre- served in a well-stoppered bottle. Sufficient quantities of each sample were thus prepared in a uniform manner, and the bottles in which they were preserved were carefully weighed and kept under a bell-jar. In this way any alteration in the substance is at once detected. If this precaution be not taken it is necessary, in dealing with substances which are more or less hygroscopic, to weigh out at 133 1890-91.] Mr J. Y. Buchanan on Deep-Sect Deposits. once all the portions of any one sample which will be required for the various determinations which are to he made, in order to be certain that a uniform material is used for each. This is attended with much inconvenience, which is obviated by preserving the sample in such a way that it will he unlikely to alter, and by keep- ing strict account of its weight, so as at once to detect any alter- ation which may occur. Table III. — Determination of Loss on Ignition, , and of the Water ancl Carbonic Acid expelled thereby. No. of Sample. Weight oJ Before Heating (grammes) l Sample. After Heating (grammes) Loss (grammes) Per cent, of Loss. Weight of Water absorbed by CaCl2 (grammes) Per cent, of h2o. Weight of C02 absorbed by Soda- lime (grammes) Per cent, of C02. | i =if 4 -h — d \ b c=a-b c 1 d=m- e /=1< g h = 100-2 a i 31 0-8180 0-7905 0-0275 3-36 0-0327 3-99 0-0086 , 1-05 1-68 32 0-7114 0-6873 0-0241 3-38 1 0-0200 2-81 0*0125 1-75 1-18 35 0-8978 0-8670 0-0308 3-38 1 0-0200 2-22 0-0240 1 2-67 1-51 36 0-7337 0-7068 0-0269 3-66 0-0242 3-29 0-0120 1-63 1-26 39 0-6940 0-6702 0-0238 3-42 0-0205 2-75 0-0007 o-io - 0-57 41 1-0103 0-9724 0-0379 3-75 0-0322 3-18 o-oooo o-oo -0-57 43 0-7640 0-7363 | 0-0277 3-62 0-0252 3-29 0-0041 0-53 0-20 45 0-4669 0-4539 0-0130 2-90 0-0168 3-59 0-0083 1-77 2-46 46 0-5529 0-5317 0-0212 3-83 i 0-0156 3-00 0-0088 1-59 0-76 64 0-5160 0-4598 0-0562 10-89 0-0451 8-74 0-0084 1-62 - 0-53 65 0-6972 0-6551 ! 0-0421 6-03 0-0364 5-22 0-0090 1-29 0-48 86 0-7951 0-7500 1 0-0451 5-67 0-0301 5-68 0-0182 2-29 2-30 87 0-7999 0-7442 0-0557 6-96 0-0236 2-95 0-0300 3-75 -0-26 88 0-6339 0-6071 0-0268 4-22 0-0207 3-26 0-0137 2-16 1-20 89 0-6010 0-5663 0-0347 1 5-77 1 0-0220 3-66 1 0-0065 1-08 -1-03 Table III. Determincdion of the Moisture , Carbonic Acid , dncl Total Loss. — A quantity of the substance was weighed into a porcelain boat, placed in a combustion tube, and heated strongly in a current of air freed from moisture and carbonic acid by passing it through a tube filled with soda-lime and another filled with calcium chloride. The water was collected in a calcium chloride tube, and the carbonic acid in a soda-lime tube, and weighed. The boat was again weighed after the heating, and the difference in weight is called total loss. In every case the mud was of a reddish colour after heating. It will be observed that in all cases the loss of weight of the substance is different from the gain 134 Proceedings of Royal Society of Edinburgh. [sess. of weight of the tubes ; as a rule, it is decidedly less. In so complex a substance as a deep-sea mud it is impossible to account for this in detail ; but organic matter, which is never absent from such muds, would, by its oxidation, increase the weight of the tubes at the expense of the air, while the oxidation of the fixed com- ponents, such as ferrous oxide, would have a like effect on the ignited mud. The figures, therefore, in the Table give a complex result, from which it is impossible to isolate the separate items. It is evident, from the general agreement of the figures, that the drying process (Table II.) has brought the various samples into a very fairly comparable condition. Table IY. Determination of the Carbonic Acid. — A weighed quantity of the substance was placed in a flask and sulphuric acid added. The carbonic acid was collected in soda-lime tubes, being first dried by passing it through a U tube filled with pumice, moistened with concentrated sulphuric acid, and a tube filled with calcium chloride. Tarle IV. — Determination of Amount of Carbonic Acid. No. of Sample. Weight of Sample taken (grammes). Weight of C02 absorbed by 1st Soda-lime Tube (grammes). Weight of C02 absorbed by 2nd Soda-lime Tube (grammes). Total Weight of C02 (grammes). Per cent, of co2. Per cent. of CaC03. a b c d=b+c e=ioo| / 31 1*7395 0*1396 0*1396 8*037 18*3 32 1*1346 0*0987 0*0987 8*10 18*4 35 1 *5251 0*1268 0*001 0*1269 8*38 19*1 36 1*5970 0*1385 0*0006 0*1391 8*71 20*0 39 1*0160 0*1083 0*0017 0*1100 10*83 24*5 41 1*3468 0*1238 0*1238 9*19 21*0 43 1*5683 0*1600 0*1600 10*10 23*6 45 1*3200 0*1853 0*0002 0*1855 14*05 32*4 46 1*2864 0*2165 0*0009 0*2166 16*82 38*2 64 1*1379 0*2378 0*2378 20*90 47*1 65 1*8921 0*3129 0*3129 16*08 36*6 86 1*2456 0*1767 0*1767 14*19 32*5 87 1*4305 0*1909 0*1909 13*34 30*8 88 1*5087 0*2131 0*2131 14*12 32*5 89 1*4595 0*2024 0*2024 13*87 31*8 The flask was boiled to expel the gas, and a current of air, free from carbonic acid, was drawn through the apparatus to sweep out all the carbonic acid. 1890-91.] Mr J. Y. Buchanan on Deep-Sea Deposits. 135 Near the African coast the amount of C02 varies between 8 and 10 per cent. It increases with distance from the land, being no doubt less masked by land debris. The maximum 20-97 of C02 (47 T 7 CaC03) is found on the Balearic Bank. The depth here was only 782 fathoms, and the land drainage is insignificant. Table Y. Treatment with Hydrochloric Acid. — (A.) A weighed quantity of the substance was placed in a porcelain basin and 100 c.c. of 20 per cent, hydrochloric acid added. The basin was placed on a water-bath and evaporated to dryness. It was then placed on an air-bath and heated so as to convert any soluble silica into the insoluble form. Then it was treated with hydrochloric acid and filtered. The precipitate was weighed, and called the “ residue.” (B) The “ residue ” was fused with potassium sodium carbonate, and the silica determined in the usual way. Table Y. — Determination of the Residue Insoluble in 20 per cent. HC1, and of the Total Silica. No. of Sample. Weight of Sample taken (grammes). Weight of Insoluble Residue (grammes). Per cent, of Insoluble Residue. Per cent. Soluble in Acid. Weight of Si02 in Insoluble Residue (grammes). Per cent, of Si02 in Sample. Per cent, of Si02 in Insoluble Residue. a b c=100— a 100 -c d » ! 11 ! s j /=1005 31 1-4796 0-8836 59*72 40-28 0-6456 43-64 73-06 32 1-8465 1-0952 59-31 40-69 0-8071 43-71 73-69 35 1-1713 04136 35*31 64-69 0*3213 27-43 78-08 36 0-8916 0-5896 66-13 33-87 0-3772 42-31 63-98 39 1-1890 0-6561 55-18 44-82 0-5276 44-37 80*41 41 1-7195 0-9598 55-81 44-19 0-7337 33-89 76-44 43 1-9403 1 -0937 56*37 43-63 0-7219 32-41 66-00 45 1-3528 0-5774 42-68 57-32 0-4433 32-77 76-77 46 1-5053 0-5895 39-16 60-84 0-4715 31-32 79-98 64 1-3351 0-3755 28-13 71-87 0-2966 22-21 78-98 65 1-4602 0-4244 29-06 70-94 0-2160 14-79 50-89 86 1-7149 0-8339 48-63 51-37 0-5851 34-12 70-16 87 1-4539 0-6300 43-23 56-77 0-5349 36-79 85-10 88 1-5478 0-7622 49-25 50-75 0-5820 37-60 76-36 89 1-6682 0-8015 48-04 51-96 0-6300 37-68 78-60 Table Va. Estimation of Iron and Alumina. — The hydrochloric acid solution (the filtrate from the insoluble residue) was peroxidised with potassium chlorate, and ammonia was added till the precipitate locally formed was very slow in dissolving. Acetate of ammonium 136 Proceedings of Royal Society of Edinburgh. [sess. was then added, and the mixture boiled and filtered, and the pre- cipitate washed. The precipitate was dissolved in hydrochloric acid,- and ferric hydrate precipitated with pure caustic potash in a platinum basin. It was then diluted and filtered, ignited and weighed. To the filtrate ammonium chloride was added, and the solution boiled till ammonia ceased to come off. The precipitate was filtered, ignited to A1203, and weighed. In the Fe203 the variations are not great. The minimum, 3 ’45 per cent., is on the Balearic Bank, and the maximum, 6 ’64, in the deep water near the African shore. In this neighbourhood all the muds have large amounts of Fe203 and small amounts of A1203, except No. 35, where the amount of Fe203 is small and that of A1203 very large — in fact, the maximum (12 ’3 per cent.). It is remarkable that at No. 41 we find the maximum of Fe203 (6 ’64 per cent.), and the minimum of A1203 (1*3 per cent.). The deep water between Africa and the Balearic Islands covers muds comparatively rich both in A1203 and Fe203 ; on the Balearic Bank the amounts are small, and in the Gulf of Lyons moderate. Table Ya. — Determination of Fe203 and A1203 in Hydrochloric Acid Solution of Table V. No. of Sample. Weight of Sample taken (grammes). Weight of Fe203 (grammes), Per cent, of Fe203. Weight of A1203 (grammes). Per cent, of A1203. a b c=100 - a d C* | . ii ! i ■ ... 31 1-4796 0-0826 5-58 0-0203 1-37 32 1-8465 0-0991 5-37 0-0415 2-45 35 1*1713 0-0452 3-86 0-1441 12-30 36 1 -5547 0-0956 6-17 0-0538 3-46 39 1-1890 0-0788 6-54 0-0460 3-87 41 1-7195 0-1060 6-64 0-0224 1-30 43 1-9403 0-1235 6-22 0-1864 9-60 45 1-3528 0-0720 4-23 0-1389 10-27 46 1-5053 0-0732 4-86 0-1645 10-93 64 1-1908 0-0505 4-24 0 0302 2-54 65 1-3671 0-0472 3-45 0-0292 2-04 86 1-7149 0-1073 6-26 0-0920 4-26 87 1-4539 0-0783 5-39 0-1212 8-34 88 1-7470 0-0763 4-37 0-0680 3-89 89 1-6682 0-0726 4-42 0-0765 4-58 Table YI. Estimation of FeO and Fe203. — A weighed quantity of the substance was placed in a 200 c.c. flask and the flask filled Table VI. — Determination of the State of Oxidation of the Iron extracted, by Hydrochloric Acid. 1890-91.] Mr J. Y. Buchanan on Deep-Sea Deposits. 137 O o rH II NMCOKiniOClN^tNQHHCOOKM N010H^®ON®01^000IN®N S© g J ^ 0 EH 00NON(NTHTH(NW«0^i0®aN(N >O»O(TOCDQ0«0l10«0'^-^'^C0cblb-SH-^ Per cent, of total Fe extracted (expressed as Fe203). e>l e o o II fflCOW>Q!NOO'^?0«0'^K?OCOHffiiffi ^©NlOOOpffiOOSOOipiOW'^IO |’o ®r® Q C4H Ph o -SlS o o HNO)H00W!N«K0a 00 00(NON00 HCTH^O^MffiWOOOlNOOtOOlK OOOOt-HOOOOOOOOOOO 'o i >3 ^ o ® ® ■g 3 §>o -9 § | ^ hh S o ,52 02 ^ Si II 0-00041 0-00125 0-00074 0-00205 0-00356 0-00172 0-00135 0-00363 0-00172 0-00248 0-00366 0-00406 0-00399 0*00144 0-00119 0-00365 Equivalent Weight of Fe203 (grammes). Si 0-01081 0-01245 0-01034 0 01245 0-00996 0-00987 0-00855 0-01043 0-00822 0-00808 0-00781 0-00861 0-01239 0-01344 0-01079 0-01205 Volume of SnCl2(c.c.) (mean of two esti- mations). 's 0 1000(3 3 0UQ(3CDiOLOONN IM©(3©HHTO(3NN(»005(310(» C.»pC<) S4J 2 41-5 41 '5 fc’-gjlgS § al- ii''8 41*7 41-5 41-7 41-5 41:5f 41:5 41*4+ 41;4 41 ‘4f Observation made 4 fathom deeper than indicated, t Observation made 1 fathom deeper than % Observation made J fathom less deep than indicated indicated. SCOTTISH MARINE STATION. 145 1887. LOCH MORAR. Date . Position J Hour . Wind . Weather & ( Sea . . | Depth Temp, of Air April 29 S. of Islands, N. of Rudha Garbh, near centre of W. basin 8.45 E., 2 Sunshine, roughish 33 April 29 f mile E. of Islands, centre of Loch 9.10 E., 3 Sunshine, cloud, rough 82 April 29 Between Inbhir Beag and Lettermore 9.45 E., 3 Sunshine, cloud, rough 118 April 29 £ mile W. of line between Brinacory Island and Allenhara e”*2 Sunshine, roughish 111 April 29 About lg miles E. of last position 10.55 E., 3 Sunshine, rough 147 April 29 Little W. of line between Swordland & Mouth of River Moble 11.30 E., 3 Sunshine, rough 165 April 29 1 mile East of Tarbet, centre of Loch 12.30 E., 3 Cloudy, rough 157 Fathoms 0 43-1 42-9 431 43-4 1 43:4 43 ’8 431 43-5 2 3 4 5 6 7 8 42-9 9 10 42*6 12 14 16 18 20 42-3 22 24 26 28 30 42-3 32 42'2f 34 36 38 40 42 44 46 48 50 52 54 56 42 :0f 58 60 62 421 64 66 68 70 421 72 74 76 78 421 80 82 42:0 84 86 88 90 98 104 42*0 110 42-0 112 118 42 ’0 125 147 42 *0 42 0 157 165 42 *0 42*0 VOL. XVIII. t Observation made 1 fathom deeper than indicated. 14/5/91 K 146 SCOTTISH MARINE STATION. 1887. LOCH MORAR. LOCH SHIEL. LOCH SUNART. SOUND OF MULL. Date . ( Position . - j Hour . . ^ Wind . Weather &J Sea . . 1 Depth Temp, of Air April 29 Within mile of E. end of Loch, Oban, and Kinloch morar 14.50 E.,2 Cloudy, ripply 57 April 29 On section bet. Tarbet Point and Cruch Dhubh an Ruidhe Fhefine 16.30 E., 1 Sunshine, smooth 170 Off Ben Rosipol 31 May 1 1 mile East of Mor Island 10.50 E., 0-5 Cloudy, smooth 42 46-2 May 1 N.E. Charna Island wV," 3 Showery, overcast, smooth, roughish 64 May 1 Off Auliston Point, East of Big Stirk 13.45 W., 2 Overcast, roughish 65 May 1 Between Fishnish Bay and Savory River 15.30 W., 2 Overcast, fine, smooth 58 46-4 Fathoms 0 43-9 43-5 43-9 46-2 46-6 45-8 45-9 1 43*3 45-8 45-8 2 43-7 44-0 3 43-7 43*1 4 5 43-5 43-1 43*3 461 45 ‘9 457 45*5 6 7 43-3 8 9 10 43-0 43-0 43-0 45:6 457 45;8 45 ’5 12 14 42*6f 16 45:3+ 18 20 42-3 43-0 43-0 45*5f 22 457+ 24 46 :0 26 28 30 42 ’2 42 :8 43:0+ 4 5 *3+ 32 34 36 QQ 42-0f 45:5+ oo 40 45:2+ 42 457+ 44 461 46 421+ 48 50 52 54 56 421+ 45*6+ 58 60 62 457+ 64 46 :2 66 | 68 70 421 72 74 76 78 80 82 84 86 88 90 92 94 96 98 112 170 42 "0 t Observation made 1 fathom deeper than indicated. SCOTTISH MARINE STATION. 147 1887 , SOUND OF MULL. FIRTH 01 LORNE. FIRTH OF LORNE. Date . Position . Hour . Wind . Weather & , Sea . Depth Temp, of Aii r May 1 100 fathoms patch bet. Lismore Light and tMorven Coast Calm Overcast, fine, smooth 100 May 1 Midway bet. Loch Don, Mull, and Kerrera 17.45 S.W., 2 Fine, cloudy, roughish 96 May 2 100 fathoms patch bet. Sheep Island and Mull 11.0 S.W., 1 Ovei’cast, smooth, long swell 96 May 2 Mouth of Loch Buy, Mull 12.55 Calm Sunshine, hazy, ' smooth, swell 53 May 2 Loch Buy, off. Island at head of Loch 13.45 S.W., 0*5 Sunshine, smooth with swell 12 May 3 Halfway bet- Light end off Lismore and Dunolly Castle 17.10 N.E., 2 Cloudy, roughish May 3 Oban Bay 18.20 Calm. Fine, smooth 22 Fathoms 0 45-6 45-5 45-8 47-3 47-3 47T 1 45-3 45-6 46-2 46-9 46-6 2 45-3 45 ‘9 3 45*3 46 :0 46;1 4 5 45-5 45-3 45-2 45*8 45 *4 6 45:9 46 *0 7 45-2 8 45*2 9 45-3 45:0 10 45*3 45-3 45 "5 45:8f 45:9f 12 14 45*4f 45;3f 45:2 16 45-4 45*6 18 45Tf 45:2f 20 22 45-4 45;6f 24 45 *3f 26 28 30 45*3 45-4 32 45-4 34 45 Tf 36 38 40 45-3 42 45:6 44 46 48 50 52 457 54 56 58 45 Tf 45:2f 45:2f 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 45* 2f 45'3f 96 98 45;2f 100 102 104 t Observation made 1 fathom deeper than indicated. 1.48 SCOTTISH MARINE STATION. 1887. Date . Position . •<( Hour . Wind . Weather & Sea . . 1 Depth Temp, of Aii f , May 4 Bet. W. ends of Scabra & the Isles of the Sea 9.10 Calm Sunshine, clouds, smooth, long swell 138 May 4 On Tarbert Bank off Loch Tarbert, N. end of Sound of Islay 12.0 S., 0 to 1 Sunshine, smooth, long swell 8 May 4 Sound of Islay, a little South of Port Askaig 13.50 S.W., 2 Cloudy, sunshine, smooth or roughish 31* May 4 E. by S. of Otter Rock, bet. Islay and Cantyre 16.15 E., 3 Sunshine and cloud, rough 67 Fathoms 0 46-2 47-0 46-2 47*5 1 45-8 45*9 2 45-8 46-8 46-0 46 -4 3 45-7 4 5 45-7 46 :0 46*0 6 7 46-5 8 9 45-5 45 -9 10 45*6 12 14 45-5+ 45:5f 18 20 45-5 46*0* 45 -5 22 24 26 45 ;3 28 30 45 *4 46-0* 32 34 36 38 ... 40 45 ‘5 42 44 46 45*2 48 50 45 ‘5 45*2 52 54 ... 56 ... 58 ... 60 45 :6 62 ... 64 ... ... 66 45 '2 68 70 72 ... ... 74 76 ... 78 ... 80 ... 82 ... oco 84 36 45:5+ 88 90 92 94 96 98 100 45 ’6 ... 117 45-5 137 45-6 * Observation made £ fathom deeper than indicated, t Observation made 1 fathom deeper than indicated. SCOTTISH MARINE STATION. 149 1887. FIRTH OF LORNE. LOCH ETIVE. MULL SOUND. LOCH LINNHE. Date . Position . Hour . Wind . Weather & ( Sea . . 1 Depth Temp, of Air August 18 Off Mull 19.20 N.W., 3 Sunshine, rough, swell 22 August 18 Off Mull further out 19.40 49 August 19 Off Sheep Islands 12.15 Calm Sunshine, cloud, smooth 106 August 20 Off Mouth Cloudy 18 August 22 Between Lismore & Morven Shore 14.45 S.W., 4 Rain, mist, rough 107 August 26 Off Eil haile G-hohhain & Rudha na h’earha 11.55 S.W., 2 Cloud, hazy, sunshine, smooth 54 August 26 Corran Ferry 13.0 S.E., 2 Hazy, smooth 17 Fathoms 0 55-3 55-8 55*5 56*0 1 55-5 55-7 2 55*6 3 4 5 55-4 55*7 55*7 6 55 :0 7 55*5 8 9 10 55-6f 55-2 55*4 55*7 55*4 55*2+ 12 55*6 14 55 -4f 55*4f 16 55*3f 55*1 18 20 55*5+ 55*21 55*4 55 :6 55*6 — 22 24 55*3 55 *5f 26 28 55*3 30 55*5 55*7 55*2 32 55*lf 34 55*4f 36 38 55*3 40 55 '*4 42 54*9f 44 46 48 55*3 50 52 55*5 55*7 54 '7f 54 56 58 60 62 64 55*5f 66 55*7 68 70 72 74 76 78 80 82 84 55;6f 86 55*9 88 90 92 94 96 98 100 55:5f 102 104 106 55*4 108 — f Observation made 1 fathom deeper than indicated. VOL. XVIII. 14/5/91. L 150 SCOTTISH MARINE STATION. 1887. LOCH ABER LOCH LEVEN. LOCH HOURN. Date . Position . -j Hour . Wind . Weather & J Sea . . i Depth Temp, of Air August 26 Off Inver Seadle Bay 13.50 S.W., 2 Hazy, cloudy, smooth 80 August 27 Off Fort William 9.30 S.W., 1 Sunshine, smooth 37 August 27 Off Inver Seadle Bay 10.40 S.W., 2 Sunshine, smooth down to 50 August 27 Off Ballach- ulish Slate Quarries 12.10 S.S.W., 2 Cloud and sunshine, smooth 29 August 29 Centre Sound of Sleat, off Isle Oransay 10.0 S.E., 0-5 Sunshine, smooth 49 August 29 Mouth 10.40 W., 1 Cloud, sun- shine, smooth 66 August 29 Mouth 10.55 W., 1 Cloudy, smooth 95 Fathoms 0 56-3 57-8 56-8 57-0 57-3 571 1 561 2 56-0 55 ’5 561 57 * 2 3 551 4 5 55-2 55-0 56-0 55*7 56 : 5 57*0 6 7 8 551 9 10 55-2 55-0 55*7 56-0 56-5 12 14 55 -2+ 54-7+ 55*3 55*8+ 551+ 16 54-8+ 18 55:4 20 551 54-6+ 551 551 22 55:4+ 24 551+ 55*4+ 55:3+ 26 54-6+ 28 55:3 55:6 30 32 55-0 54-9 55 *3 34 55-2+ 36 54-3+ 38 40 55*2 55:2 55*3 54 '0 42 44 53*7+ 46 48 54*0 50 52 54 551 551 52-0+ 53:3+ 56 58 5540+ 60 50*9 62 64 501+ 66 68 55-2+ 70 72 74 4*9*7 76 78 551+ 80 82 84 49*7 86 88 90 92 94 49*4 96 98 100 102 104 106 108 t Observation made 1 fathom deeper than indicated. SCOTTISH MARINE STATION. 151 1887. LOCH HOURN. Date . Position Hour . Wind . Weather Sea . Depth Temp, of Air Fathoms 0 1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 August 29 Off Coil- Island 12.80 N., 3 Showery, sunshine, smooth 31 57-3 56 '3 56-0 55**8f 55 6 54 T August 29 Bet. Cnoc of Kyle and E. Mouslter 13.0 W.S.W., 3 Sunshine, cloud, smooth 15 56-2 56*3 56 T August 29 Head, off Skiary 13.25 W.S.W., 3 Cloudy, sunshine, smooth 11 56-5 55-9 LOCH CAERON. August 30 Narrows off Port Hulin, West of Strome Ferry 11.35 N.W., 4 Rain, squally, roughish 11 August 30 Centre 12.10 W.N.W., 5 Squally, roughish 56 55-9 55*8 55*4 55*5 55*3 55*2+ 54:9 August 30 Head, off Long Island 13.0 W., 5 Squally, rain, roughish 22 56-9 56 ’3 55*9 55 3f 55*4 55 *3 f 54*5 54 *4 f 54*4f OUTER LOCH CARRON August 31 Bet. Ru Duard and Ru Nauag 15.15 W., 0 Sunshine, smooth 66 64-8 58*9 56*9 55*3 54*6 54*5 53*9f 53**7 53*3 53*0 52*9f 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 100 102 104 106 108 54*2+ 52*9f 52*6+ t Observation made 1 fathom deeper than indicated. 152 SCOTTISH MARINE STATION. 1887. LOCH DUICH. LOCH ALSH. INNER SOUND. LOCH MORAR (Fresh Water) . Date . August 31 Sept. 1 Sept. 1 Sept. 1 Sept. 1 Sept. 3 Sept. 3 Position . -j Off Kintail Head (Anchorage) Off Mouth of Loch Long Off Mouth of Kyle Rhea Bet. Croulin, Mor and Longa Island Off Tarbet, nearly half way across Off Tarbet Hour . 18.0 8.30 10.5 10.55 15.0 9-5 Wind . N.,2 N.N.W., 1 S.W., 2 S.S.W., 3 W., 3 W., 3 Weather &f Sea . . | Overcast, smooth Dull, showery, smooth Rain (heavy) , smooth Rain, cloudy, smooth to roughish Sunshine, roughish Cloudy, showers, roughish Depth 60 7 11 39 127 (no bottom) 162 Temp, of Air 60-5 56-0 61-2 Fathoms 0 59-0 57-0 56-9 56-0 56-9 57-8 1 2 56-2 55-2 56:9 3 4 5 55-5 55-9 56-0 56 T 57*9 6 7 54-9 55-0 8 58-0 9 10 12 54*9 55-5 56-0 54 *4 57:6 57 -6f 57-8 14 16 18 54-9+ 51 -Of 52-Of 55:9 52 T 20 54-7 54 ’0 46*8 47*0 22 ... 24 54-3+ 46 "1 26 45-6|| 28 55-8 44-8|| 30 32 54-2 44 ‘0 44-2 34 53*2f 44’4T 36 38 52-7+ 55:7 40 53T 43*6 o> 42 44 46 'o w 48 52:2+ o 50 52-7 427 o 52 CD § 54 5 O 56 -M c3 c3 58 52:0+ 42-6 cm ^ O O 60 . GO 62 rH 64 66 A 15 68 70 517 42-3 <35 _d 72 '03 <5 •rH H3 74 76 o A 78 c3 (=H 80 42-3 •g & 82 o o 84 86 90 51 :0 42-4 A jj 100 42-3 §3 "o 106 507 += o gO 2 110 42*3 A ° M 116 507 120 42-5 O) A 126 50 :6 03 130 42:3 ri ■ &0 £ 141 ... 42-2 151 42-4 O 161 42 T EH t Observation made 1 fathom deeper than indicated. || Observation made 1 fathom less deep than indicated. SCOTTISH MARINE STATION. 153 1887. UPPER LOCH NEVIS. OUTER LOCH NEVIS. UPPER LOCH SUNART. Date . Position Hour . Wind Weather & Sea . Depth Temp, of Air Sept. 3 Head 15.45 W., 1 Sunshine, smooth 11 Sept. 3 Centre 16.0 W.,3 Sunshine & cloud, rough to smooth 56 59-2 Sept. 3 18.45 W.N.W., 2 Clear, sun- shine, smooth 56 Sept. 4 Bet. North of Eigg and River Moror 10.5 N., 2 Overcast, roughish 54 57-0 Sept. 4 Bet. Muke and Ardna- murchan Light 13. E.N.E., 3 Overcast, roughish swell 113 57'2; 57-5 Sept. 4 Off Ardna- murchan Point 15.50 E.N.E., 3 Sunshine, cloud, roughish swell 43 57'8 Sept. 5 Off Ru Strone na Saoibhaidh 9.0 S.E., 2 Cloudy, smooth 51 Fathoms 0 56*9 56-7 57-0 57'2 57 '6 57'6 567 1 2 571 57 *2 3 4 5 56*1 56-2 56'8 571 57 '4 57 '4 57*2 6 7 8 9 10 56-0 55-9 56*6 57;2 57*3 57:3 571 12 14 16 18 56:2f 57 '4f 57 If 20 55-9 55 '9 571 57 1 57 ’-0 22 57:3 24 26 28 30 55-2, 54-8 56 ‘5 57*3 56-8 32 56 -5f ... 57 '2 34 53:8f 53‘8f 36 ... 38 ... 40 51 :9 57 :3 56:7 42 56 :lf 571 44 46 50 'Of 53 :0f 48 50 56*6 52 55*9+ 54 56 58 49*3f 52‘7f 60 57 :3 62 64 ... 66 68 70 72 74 76 78 80 57*2 82 84 86 88 90 92 94 96 98 100 571 102 57:2 104 106 108 112 57 *2 t Observation made 1 fathom deeper than indicated. 154 SCOTTISH MARINE STATION. 1887. LOCH SUNAET. SOUND OF MULL. LOCH EIL. CALE- DONIAN CANAL (Fresh Water). LOCH LOCHY (Fresh Water). Date . r Position 1 V Hour . Wind . Weather & f Sea . .1 Depth Temp, of Air Sept. 5 N. E. Charna Island 11.15 E.S.E., 2 Cloud, sunshine, smooth 59 58'4 Sept. 5 Off Runan Aulistan 12.20 S.S.E., 3 Overcast, roughish 46 Sept. 5 Off Fishnish Bay 15.5 S.E., 2 Cloudy, sunshine, smooth 59 59-8 Sept. 5 Between Lismore and Morven Shore 18.5 S.E., 2 Overcast, rain, rough 110 56T (wet) Sept. 6 2 miles from inner end of Narrows 17.5 E., 4 Rain, roughish 35 53 '0 (wet) Sept. 7 Gareiochy Loch, end nearest Bannavie 10.30 N.E., 1 Sunshine, clouds, smooth 3 Sept. 7 Off Auchna- carry (South end) 12.45 N.E., 2 Fine, sunshine, smooth to roughish 37 53-0 Fathoms 0 57-4 57 T 56-8 56-5 55-5 55-0 56-5 2 55*0 56 *2 3 4 5 57-2 56-7 55:2 56:0 6 7 8 56 -1 9 10 57-0 57*1 56-7 55-2 56T 12 14 57*0+ 56 7+ 55 ’2 56 ’Of 16 18 53 :8 20 57*1 571 56 '8 56 ’5 47 T 22 24 57-1+ 55 ’3 45:7 26 1 45-1 28 30 57:0 56 :8 45’0f 32 34 57 ‘2f 55 2 36 38 40 56 :9 56-9 56 '5 44:0 42 44 57:3f 46 48 57*0 57 :0 50 52 54 56 58 ' 56 :8 57 -0 60 62 64 66 68 56:6f 70 72 74 76 78 80 82 84 86 88 56*7+ 90 92 94 96 98 100 104 108 56:5f t Observation made 1 fathom deeper than indicated. SCOTTISH MARINE STATION. 155 1887. LOCH LOCHY (Fresh Water). LOCH OICH (Fresh Water). LOCH NESS. (Fresh Water), Date . Position . Hour . Wind . Weather & f Sea . . Depth Temp, of Air Sept. 7 Off Glastard 13.50 N.E., 1 Bright sun- shine, smooth 76 54-8 Sept. 7 Laggan end, about a mile from Locks 14.50 Calm Sunshine, cloud, smooth 13 55-7 Sept. 7 South Basin 16.10 E., 1 Sunshine, clouds, smooth 12 Sept. 7 North Basin 16.40 S.W. byS.,2 Sunshine, high clouds, smooth 23 Sept. 8 At Fort Augustus 8.10 W., 3 Overcast, roughish to smooth . 42 53-5 Sept. 8 I Off Aldourie 11.10 W.S.W., 5 Overcast, very rough 15 56'5 Sept. 8 Off Aberia- chan 11.50 W.S.W., 5 Overcast, occasional sunshine, very rough 70 Fathoms 0 55-9 54-6 58-5 567 54-8 53-8 54-0 1 55*9 54-5 58-2 2 55-2 54-7 54-8 53 -7 ... 3 54-5 4 54-6 58-0 53-7 5 55 -6 54*2 56 *0 54 *6 54 *0 6 57 *9 7 54*2 53 ;6 8 54-5 9 57-8 53:6 10 55-4 53-6 57*7+ 55 '4 54*5 53 '9 12 14 16 18 54-8f 53-4 55-2 48:4f 47:3f 53*4 20 47-0 46- 5 f 53 *9 22 477 24 26 46-8+ 28 30 45*2 45:3f 53 T 32 34 44:6f 36 38 40 44-9 44:7f 47 '8 42 44 46 48 44-Of 50 44*0 52 54 43*8f 56 58 43:4f 60 62 64 44 Tf 66 68 43 ’Of 70 72 74 43 -6f 76 78 80 82 84 86 88 90 92 94 96 98 100 102 104 106 108 t Observation made 1 fathom deeper than indicated. 156 SCOTTISH MARINE STATION. 1887. LOCH NESS. (Fresh Water). LOCH LOCIIY. (Fresh Water). Date . Position . | Hour . Wind . Weather & f Sea . . ^ Depth Temp, of Air Sept. 8 Off Castle Urquliart and Temple Pier 13.0 W.S.W., 5 Cloudy, some rain, rough 121 57 T Sept. 8 Off Foyers 15.15 W.S.W., 6 Ovei’cast, very rough 109 Sept. 8 Off north of Portclair Point 16.25 W.S.W., 4 Overcast, rough 101 Sept. 8 About 1 mile from Fort Augustus 17.15 W.S.W., 5 Overcast, rain, rough 80 Sept. 8 Fort Augustus 18.0 W.S.W., 5 Rain, roughish 42 Sept. 9 Laggan, 1 mile from Locks 11.15 W.S.W., 6 Cloud, sun- shine, rain, very rough 12 Sept. 9 Off Auchna- carry (South end) 12.35 W.S.W., 5 Rain, rough 38 Fathoms 0 54-0 54-5 54-0 51-4 47-8 551 54-8 1 53-9 551 2 53-8 477 54-8 3 4 5 54-0 48-0 471 55-2 547 6 55*2 7 8 46*8 54-0 9 10 53-8 541 52-4 467 46 '0 55 '2 52 ‘6 12 551|| 14 16 53 -6f 45*8+ 45:2f 501+ 49 -2f 18 20 50-3 51 '6 44-7 44*4 44;lf 481 22 24 49 -9f 44 'Of 26 46 ’6 28 46-8 45-8|| 30 48-4 43-3 43 ’5 43 7f 45 -Of 32 34 48 -2f 36 44 "2f 38 40 47:9 45*8 43 : 4 43 If 42 44 46 48 50 44-4 42*9 52 54 56 58 42:8+ 60 43*5 43-0 62 64 66 68 431 42:8+ 70 43 ;0 72 74 76 78 42:6f 80 82 431 84 86 88 90 42*6 92 94 96 98 100 42-6 42 *4 102 104 106 108 42*5 110 42-6 120 421 t Observation made 1 fathom deeper than indicated. Observation made 1 fathom less deep than indicated SCOTTISH MARINE STATION. 157 1887. LOCH ABER. LOCH ETIVE. SOUND OF LORNE. LOCH LINNHE. LOCH ABER. LOCH EIL. Date . Position . | Hour . Wind . Weather & j Sea. . ! Depth Temp, of Air Sept. 10 Off Inver- leadle Bay 9.45 W.S.W., 3-5 Overcast, showers, roughish 81 Sept. 11 Off G-lenoe Farm 11.5 W., 0-5 Sunshine cloud, smooth 61 57-0 April 22 Off Sheep Isle 13.5 S.W., 2 Showery, bright, slight swell 114 47-6 April 23 Midway bet. Squr nan Gillean and Ru'Mor 11.40 N.E., 1 Fine, cloudy, smooth 50 47-6 April 23 Midway bet. Cor ran Ferry and Fort William 13.25 S.W., 1 Dull, cloudy, smooth 77 49-0 April 28 10.25 Calm Smooth 22 45-5 April 28 About If miles from Head 11-25 Calm Sunshine, smooth 18 48-0 Fathoms 0 541 55-0 45-3 45-6 46-1 45-8 45*8 1 54-0 2 54-2 55-1 44**9 45 *2 3 54-7 55-3 4 54-9 5 55-0 56-1 44-9 44-9 44 :9 44**7 45*0 6 55-1 7 55-2 56-1 44*9 8 9 10 55-2 55-6 45-0 44-3 44*6 44**8f 12 44**7 14 55*2+ 54-lf ... 16 18 20 22 24 44-3H 44**7 44*7+ 53*5 45*0 44-4 44 -4 44**5t 52:9+ 26 44-5|| 28 30 53-0 44*6|| 44-3 32 34 53 '2+ 1 36 38 40 55 ‘2 53*5 45 *0 44-81 44*3 42 44 53*7f 46 48 50 53*9 44-911 52 54 56 4*4*1 58 60 54*0 45:0 62 64 66 4*4*2 68 70 72 74 76 44*2 78 80 5*5**1 82 84 44 -8 86 88 90 92 44*9 94 96 98 100 102 104 108 112 45 ’0 t Observation made 1 fathom deeper than indicated. || Observations made 1 fathom less deep than indicated. VOL. XVIII. 14/5/91. M 158 SCOTTISH MARINE STATION. 1888. LOCH ETIYE. Date . April 20 April 21 April 23 April 24 April 24 April 24 April 25 ( Bet. Dubh- Bet. Ard- Off small Sound of sgeir Islet Inbhirguis- chattan Position .•< Islands of Jura, off and S.W. Pt. Head achan vJll JaU. xAllCl Rniivf Chapel and | Jura Dubh Island of Kerrera Chapel Jr oint Stonefield V Island Bay Hour . 9.15 13.0 10.15 17.15 17.50 18.30 13.15 Wind . N.E.byN., 6 N.E., 1-3 E.N.E., 4 N.E., 3 or 4 N.E., 3 or 4 N.E., 3 N.E., 1-2 Weather &/ Overcast, Overcast, Overcast, Sunshine, Sunshine, Sunshine, Sunshine, Sea . . \ very rough rough rough roughish roughish roughish smooth Depth 103 106 57 6 19 75 28 Temp, of Air 52-0 51-8 Fathoms 0 44-0 43-8 43-5 49-0 47-6 45*8 45-4 1 49*0 45-0 2 49-2 47 :0 3 43-6 43-4 49-2 44 #9 4 49-2 5 44-0 43-8 43-5 49-3 481 45 *4 6 481 7 • • • 44*2 8 48 ’3 9 10 43-5 43-7 43-5 48 '3 46 *2 12 14 43*4f 47*8 16 481 44’Of 18 47-0 20 43*3 45 *9 22 24 43 -5f 26 44-Of 28 30 43-3 43-4 48 *3 32 34 36 43-5 38 40 43-3 471 42 44 46 43 *4 48 50 431 43-5 52 54 44 "8 56 43 • 5 58 60 43 *1 . i . 62 64 43*6f 44*5 66 68 70 43 'l 72 74 44 *8 76 78 80 82 43 :0 84 43;5f 86 88 90 92 42:9 • •• 94 96 98 100 102 43 T 104 43 '6f 106 108 t Observation made 1 fathom deeper than indicated. SCOTTISH MARINE STATION. 159 1888. LOCH ETIVE. Date . April 25 April 25 April 25 April 25 April 25 April 25 April 26 Position Head i mile If miles Inbhirguis- Ru Aird Off Mouth Off Mouth from Head from Head i achanChapel Point of Awe of Awe Hour . 16.10 16.25 16.50 17.20 18.10 19.10 10.50 Wind . N.E., down Loch, 3 N.E., 3 N.E.,2-3 N.E., 3 N.E., 3 N.E. W.N.W,, up Loch, 2 Weather & Sunshine, roughish Sunshine, Sunshine, Sunshine, Sunshine, Sunshine, roughish Sunshine, Sea . roughish roughish roughish roughish smooth Depth 6 13 18 22 68 9 10 Temp, of Air 50-2 48-0 Fathoms 0 ... 477 471 46 5 43*8 45*8 1 48-3 2 48-3 47*7 471 3 48-6 4 45*0 45*4 5 6 49-1 48-2 47:6 46*2 7 8 9 49-0 47 '9 48-0 48 *2 44*4 45*3 45*3 10 48*4f 12 14 491 48-9 46*4+ 481 16 18 20 22 24 48*9+ 48-0 46*9f 46 '-8 48-8 26 49-0H 28 47*8 30 47*3 32 34 46:2+ 36 ... 38. 40 451 42 44 o 46 44*8+ faD 48 •g 50 O 52 5PJ tn 54 56 44*8f c5 £ 58 60 62 1 64 ,o 66 44*6f 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 100 102 104 106 108 1 ■" t Observation made 1 fathom deeper than indicated. || Observation made 1 fathom less deep than indicated. 160 SCOTTISH MARINE STATION. 1888. LOCH ETIVE. Date . April 26 April 26 April 26 April 26 April 26 April 27 April 27 7 Off second highest Second Position Quarry, Off Ru Aird Head J mile from If miles Off Mouth Quarry upper Loch, Point Head from Head of Awe above the i above the Awe V Awe Hour . 11.20 12.15 15.30 16.5 16.25 10.25 10.45 Wind . W.N.W., up Loch, 2 W.N.W., 2 W., 2 W., 2-3 W., 1 W.N.W., 4-5 W.N.W., 4 — 5 Weather & J Sea . .1 Sunshine and cloud, smooth to roughish Cloud to sunshine, roughish to smooth Cloudy, roughish to smooth Overcast, showers, roughish Showers, gusts of wind, smooth Overcast, rain, gale, rough Overcast, showers, rough Depth 55 70 8 13 17 11 Temp, of Air 48-7 (wet) Fathoms 0 46-2 46*3 48-5 47*0 45-3 46*2 1 46-0 47-9 47-0 2 47-8 47*9 477 461 3 451 47-9 4 471 5 45-6 45-2 47-9 45*2 47-0 6 477 46*1 7 8 48-1 47 *8 451 9 10 12 45-0 47-0 48*8 48*3+ 44 :8 451 451+ 47:0+ 451+ 14 16 18 45 -2f 451+ 48 *8 20 47-3 47-7 451 22 467+ 48-3 24 46 -If 48-5 451+ 26 48-3 28 477 30 45:2 477 45*0 32 34 45 :1 46:4f 44*8+ 36 38 40 45*1 42 rcS 44 46 48 50 45*0 ci 44*8+ 44*9+ Ci rP +5 ■+=> c3 Note. — 56 Surface up Cg -Q | 58 447+ i I Loch from 60 03 !> U this sta- 62 "MrCS -4-3 .s tion every 64 C +3 bo O few min- 66 s s P P "rt 03 utes 68 70 44:6f M CQ CD +3 11 46 '2 47 '2 72 Cf-| 03 ocT 47*4 74 ° - s ^ 47*2 76 78 g § 46*5 47*2 80 s ® 03 rQ 53 50 52 'S'S 54 3 el 44*7+ 56 * * 58 S 60 .-g g 62 64 § * 44:6f 66 68 70 72 o 3 74 , to J* 03 76 78 80 03 38 -4-5 rH 40 42 X £ § ° 45*1 f 44:7 44 46 o Ss 48 . £ 50 45*2f 52 45-0 54 56 58 60 08 rr) ^ ll 45 •2f 62 45-1 64 -2 2 o5 eP 66 pH 68 .03 70 72 74 . y1 • * ?h 45*0 76 r5 78 ^ £ 80 *4“ 3 82 1 84 86 ® | s oo ••rd 88 90 jj Tj a fn 1-1 ::: 92 jS -g 94 96 PQ hC oi - I 03 « 98 O £ d 100 P oS 102 | 104 1 Cl 106 108 fei ... f Observation made 1 fathom deeper than indicated. SCOTTISH MARINE STATION. 163 1888. LOCH ABER. MULL SOUND. LOCH SUNART. SOUND OF MULL. Date . Position . Hour . Wind . Weather & ( Sea . . | Depth Temp, of Air May 1 Near centre of Loch 11.20 Calm, W., 0-5 Overcast, showers, smooth 85 51-0 May 1 Bet. Morven and Lismore 18.5 W.N.W., 4 Overcast, showers, rough 105 May 4 Bet. Charna and Eil na Gillean 9.0 W.N.W., 3 Sunshine, roughish 63 44-0 May 4 Off Ru Arderinish 10.0 W.N.W., 3 Sunshine, roughish 49 46-0 May 4 Off Ru Strone na Saoibhaidh 11.10 W.N.W., 3-4 Sunshine, cloud, showers, roughish 51 46-2 May 4 OffStrontian Head 11.50 W.N.W., 1-2 Sunshine, smooth 10 May 5 Fishnish Bay 9.20 W.N.W , 4-6 or 7 Hail showers, rain, i*ough 58 41-2 Fathoms 0 45-0 44-5' 451 45-1 45*4 43-8 441 1 44-0 2 43-9 45*1 45 T 451 45-0 441 3 44-8 4 44-8 5 43-8 44-9 44 *9 44 *8 441 6 7 8 9 447 10 12 43-9 43-9 44-8 44*4 447 44 :0 14 16 18 43-9f 44:2f 44;4f 44 If 44 If 20 43-7 45-8 44-4 441 44 ‘3 22 24 26 28 441 30 43*7 44-4 44 '3 32 34 36 44:0f 38 441 40 43 : 4 44 #2 42 44*4 44 46 44 If 48 441 50 52 54 43*4 44*4 44-2 56 44:2f 58 60 62 44*4 64 66 43 -4 68 70 43:2+ 72 74 76 78 80 43 If 82 84 86 88 90 92 94 96 98 100 102 104 106 108 ::: t Observation made 1 fathom deeper than indicated. 164 SCOTTISH MARINE STATION. 1888. FIRTH OF LORNE. LOCH ETIYE Date . Position . -j Hour . , Wind . Weather & ( Sea . . 1 Depth Temp, of Air May 9 Between Mull and Kerrera 11.0 N.W., 1 Overcast, roughish 117 46-5 May 10 Between Mull and Sheep Island 13.55 S., 0-5 l Bright, swell 123 51-2 May 11 Between Loch Buy and Island of the Sea 14.50 S., 1 Bright, swell 33 49-5 May 14 Between Ardchattan and Stone- fleld Bay 10.10 N.W., 2 Partially overcast, smooth 26 46-0 May 14 Off Mouth of Awe 11.10 N.W., 2 Clear, smooth 10 51-0 May 14 Second Quarry above the Awe 11.30 N.W., 3 Bright, smooth 64 48 T May 14 Off Ru Aird Point 12.30 N.W., 2 Sunshine and cloud, smooth 73 49*0 Fathoms 0 44-5 46-8 46-7 47*0 47*8 49*9 51*0 1 47-0 50*0 51*0 2 45 T 47*1 47*3 3 46 *5 47*4 4 46 ;4 46*5 5 44-6 46 *7 46*4 46*2 6 46*5 7 44*7 4*6*2 8 47*6 9 4*6*6 10 12 44*3 44-4 44*7 4*7*0 47-6 46 : 9 47*9+ 14 46:3f 47*7+ 16 47*4 47*5f 18 20 44-2 44-3 46**1 4*6*6 22 44*4 24 46**3f 26 28 4*5*7 30 44-3 45 T 46 *0 32 44*3 34 36 38 40 44:2 44-3 44*9 42 45 *3 f 44 46 48 50 44 -2 52 54 56 45 *3 f 45*2 58 60 44*2 44*2 62 4*5**4f 45*2 64 66 68 70 44 T 72 45*2 74 76 78 80 44*2 82 44:3 84 86 88 90 92 94 96 44*2 98 100 102 44*3 104 106 44*2 108 116 44**1 122 4*4*2 t Observation made 1 fathom deeper than indicated. SCOTTISH MARINE STATION. 165 LOCH ETIVE. Date . May 14,1888 .|May 3, 1887 May 3, 1887 May 3, 1887 May 3, 1887 May 3, 1887 May 3, 1887 f Position , -j l 1J miles from Head Mouth, Lochnell Bay Off Ardchattan Church, and Kilmaronaig Point, Midway bet. , Ards Point , and Eil ’ Durains Off Ru Aird 1 mile from head, off Ru Aird Trileadham S.W. of Sgeir-lag Hour . 14.5 10.0 10.40 11.30 12.30 13.35 15.0 Wind . N.W., 1-3 Calm N., 0-5 Calm W., 1 Calm W., 2 Weather &( Sea . . | Squalls, overcast, smooth Sunshine, blue sky, smooth Bright, sunshine, smooth • Bright sunshine, smooth Sunshine & cloud, smooth to roughish. Cloudy, smooth Cloudy, roughish Depth 17 20 18 33 67 18 61 Temp, of Air 51-2 Fathoms 0 50-3 46-5 47-7 48-6 48*4 48-6 1 46-0 467 46-2 47-0 47-1 2 47-5 45-7 3 45 :5 45-3 46;2 4 46*6 5 46-8 45 : 4 45*3 46-2 6 47-0 7 46*1 45-7 8 45 :4 9 45-2 10 47-6 44;3 45 T 12 481 45 ;3 45 :3 14 44*7t 16 18 47-3 45 *2f 45*9+ 45 ;3 45 -3f 45 :0 1 45*2 20 22 ' 45 ;2 24 26 28 45 -2 30 60 46 :1 46 *0 32 2 45 :2 34 o3 CD 47 :5 47*4 42 44 O a 46 03 47*6 48 g 50 86 5* .3 +3 flJ 88 90 c3 H pH 03 CD 8 4 55-7 5 56*6 55:5 55:3 547 6 54 T 55-8 54 -6 7 55-3 ... 8 541 55:2 9 53-9 10 12 55 '3 53 -6f 55*2 541 541 53*6f 53 If 53:2 14 16 531 52*6 54 *5f 527f 52:6f 51 -9 18 20 54 -2 531 511 51 :9 22 24 26 28 30 52:3+ 50 *0 50 :9 32 34 36 38 r* & O 52 If 40 £ ® O -d 42 44 O +> •^■8.9 0) OT 46 52:2f 48 50 52 54 56 58 S S § O cj 'g oS 60 62 i ►ts g 64 a > ^ 66 % g * 68 AS g 70 ^2 O ^ O (D 72 ei «(-i A 74 « 2 & E 94 96 82 497 M 90 92 64 96 98 100 102 104 106 108 t Observation made 1 fathom deeper than indicated. || Observation made 1 fathom less deep than indicated. 188 SCOTTISH MARINE STATION— TEMPERATURE OF CLYDE SEA AREA. 1887. Date . Position Hour . Wind. Weather Sea . Depth Temp, of Air Fathoms 0 1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 100 102 104 106 108 LOCH FYNE. Dec. 16 Gortans 15.35 S.S.W., 1 Rain, smooth 34 47-0 47-3 47-3 47 *0f 47‘3f 47 -9f Dec. 16 Furnace 16.45 W.3 1 Rain, smooth 38 46-0 46 :2 46 :8 47- 8 48 Tf 48 Tf 48 - 2f 48 -4f 48-3f Dec. 17 Cuill 8.30 W., very heavy gale Rain and hail, rough 15 37-8 38 T 42-4 42- 8 43- 0 43 :9 44- 6 46 T 47-4 47-8 47-9 >' a cS o3 a3 2 £ P Dec. 17 Off Inveraray 10.40 N.W., very heavy gale Showers rain, rough 65 43- 6 43 "7 44- 3 45- 1 45- 3 46- 1 46- 3 47 - 2f 48 - Of 48 :1 48-3 48-3 48 :3 48 :3 47-6 46 :9 tf'© Dec. 17 Strachur 12.0 N.W., 6 Hail shower, rough 74 44-5 44 ;6 46 :1 46 2 46 :5 47-0 47- 3+ 48 T 48- 2 48 "3 f 48 -4f 48:4f 47;8f 47:2f 46 Tf c3 53 ” o 2 ARRAN BASIN. Dec. 18 Skate Island 10.30 N.W., 3-6, squalls Snow showers, rough 107 46-7 46 :8 46-7 47 :0 47:3 47-3 47*4+ 47-3 47 *4f 47- 4 47'6f 47 :7 48*0f 47 '9f 48 ;0f 48- 2 48 :3 48 *4 t Observation made 1 fathom deeper than indicated. || Observation made 1 fathom less deep than indicated. SCOTTISH MARINE STATION— TEMPERATURE OF CLYDE SEA AREA. 189 1S87. KYLES OF BUTE. ARRAN BASIN. PLATEAU. ARRAN BASIN. Date . Position . Hour . Wind . Weather &J Sea. .1 Depth Temp, of Air Dec. 19 Bogany 14.45 N.N.W., 2 Bright 27 Dec. 19 Off Garrocli Head 16.0 N.W., 1 Clear, compara- tively smooth 64 Dec. 22 3J miles E.S.E. Davaar Isl. 11.0 W.S.W., 1 Overcast, compara- tively smooth 22 Dec. 23 Off Carradale 11.45 N.N.W., 2 Bright, roughish 65 Dec. 24 Bet. Carra- dale and Machry Bay 11.0 N., 1 Bright, smooth 49 Dec. 26 North of Pluck Point 11.25 0 Overcast, smooth 44 Dec. 27 S.E. of Ross Island 11.45 S.E., 0-5 Bright, swell 37 Fathoms 0 43-9 44-0 44-7 45-0 44-9 451 44-3 1 44-0 44-7 2 44-5 44-0 44 '9 3 44-5 44-5 4 44-6 44 #6 44 ■ 9 5 45-3 44-8 44-6 451 45*0 6 45-6 451 7 8 46-9 46 T 45-8 9 10 47*4 46 '3 45-8 45 ;2 45 :6 45*3 45*4 12 45-9 14 46 -4f 46 :0f 16 47-5 45 -7 45-5 18 20 47 -3f 46-3 45 -7f 461 45 :7 22 24 46 '2f 45 -9f 26 47 T 46:2 28 30 46:2 46 '3 32 46:2f 34 46;3f 36 461 38 46 :3 40 42 46;5f 46:3f 44 46 :3 46 48 46 ;2 50 52 46 If 54 46 ’2 56 58 60 62 46:4f 64 66 68 46 :3 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 100 102 104 106 108 t Observation made 1 fathom deeper than indicated. Obsei ration made 1 fathom less deep than indicated. vol. xviii. 15/5/91. Q 190 SCOTTISH MARINE STATION— TEMPERATURE OF CLYDE SEA AREA. 1887. ARRAN BASIN. CHANNEL. PLATEAU. ARRAN BASIN. Date . Dec. 28 Dec. 30 Dec. 31 Dec. 31 Dec. 31 Jan. 1, 1888 Jan. 1, 1888 Position .-j^ Bet. Carra- dale and Imacher Bet. Torris- dale and Auchin- gallon 5 miles S.S.W. of Paterson’s ! Rock 1 mile E. of Sheep Island ! 1£ miles off Rhuad Point Loch Ranza Loch Ranza Hour . 12.15 12.0 13.0 14.55 16.10 12.0 13.40 Wind . N.E., 1 0 W., 3 W., 4 W., 2 S.S.E., 5 S.S.E., 4 Weather & j Bright, Bright, Overcast Overcast, rough Overcast, rough Snow, overcast Overcast, Sea . . 1 roughish smooth rough roughish Depth 80 55 49 21 22 9 9 Temp, of Air 41-5 40-2 37-7 Fathoms 0 44-4 44 T 47-2 45-9 44*6 45-0 45 T 1 44-6 2 44-5 44 : 9 45:2 3 44 T 4 44-3 45 T 45 T 5 ... 44:4 45 0 45 T 0 44-6 447 7 44 ’9 45’2 8 45-2 9 10 45 '5 45 ’0 47 '3 46-3 44-5f 45-0 45 ;1 12 45-3+ 14 45 -9f 44*6f 16 45-7 18 20 22 24 45-8 45-8 47-3 46 '9 44*6 f 26 28 47*2 30 46-0 32 34 46 '0 36 38 47 -3 40 46*2 42 44 46 ;2 46 48 50 46 T 47*3 52 54 56 46 ’2 58 46:2f 60 bO S 62 '3 64 g 66 pH 68 46-2+ 02 70 £ 72 ■g 74 76 78 80 46*2f § <8 82 +2 +3 84 -H O fS += 86 88 O rQ C3 90 02 92 & 94 ZD c3 96 £ 98 T* 80 .£h CM 82 C5 4J3 84 46 • 6f 86 ^ s !> 88 ° 90 92 4$ o 94 <3 3 96 PH 98 s CD 100 +3 D 102 104 106 46*8t ; 108 ... t Observation made 1 fathom deeper than indicated. SCOTTISH MARINE STATION— TEMPERATURE OF CLYDE SEA AREA. 195 1888. BUTE PLATEAU. KYLES OF BUTE. ARRAN BASIN. PLATEAU. Date . f Position .-i Hour . Wind . Weather & f Sea . 1 Depth Temp, of Air Jan. 8 Off Port Lamont 11.30 S., 1 Rain, mist, smooth 29 Jan. 8 Half way between Rothesay and Lamont Shore 11.50 S., 2 Rain, mist, roughish 22 Jan. 8 Off Bogany Point 12.10 N.W., 4 Rain, mist, rough 27 50-2 Jan. 8 Off Garroch Head 13.30 S.W., 1 Overcast, rough, swell 63 51-0 Jan. 18 Off Stranraer Head 8.5 E., 1 Overcast, smooth 2 34-0 Jan. IS Off Bennan Head 12.20 E., 1 Bright, smooth 11 Jan. 18 Mouth of Loch Ryan 15.35 S., 1 Bright, smooth 9 Fathoms 0 45'8 45-7 45*5 457 40-0 45-0 44-2 1 40-1 2 40'4 3 4 45-5 45-3 44;2 5 45-6 45 ;4 45 :0 6 45-5 7 8 45-8 441 9 10 4*5 *6 f 45 '6 45*8 45 :3 12 14 45-5+ 16 45-6 18 45*9 20 46 -2f 45 '3 22 24 26 45-1 28 30 32 46-3 45*3 34 36 38 40 42 45 : 5 44 46 48 50 52 45 -5 54 56 58 60 62 45 :8 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 100 102 104 106 108 t Observation made 1 fathom deeper than indicated. 196 SCOTTISH MARINE STATION— TEMPERATURE OF CLYDE SEA AREA. 1888. PLATEAU. LOCH RYAN. LOCH STR1VAN. Date . Jan. 19 Jan. 19 Jan. 19 Jan. 19 Jan. 19 Jan. 20 Jan. 27 Position . -j^ Corsewell Light, ,S.E. | S. 5 miles Corsewell Light, S. £ W. 3 miles Mouth of Loch Ryan £ mile above Cairn Ryan Lighthouse Off Stranraer Harbour Head of Loch Ryan Head Hour . 12.30 14.10 15.0 15.45 16.30 16.0 15.35 Wind . . j S., 2 S.S.E., 2 S.S.E., 3 S.E., 2 S.E., 1 S.S.E., 3 N.N.W., heavy gale Weather & ( Overcast, swell (heavy) 37 Overcast, Overcast, Overcast, Overcast, Dense fog, Cloudy, bright, rough Sea . . 1 rough rough roughish smooth ' smooth Depth 14 8 5 3 3 11 Temp, of Air 35-9 Fathoms 0 45-2 44-9 44-6 42-3 39-8 40*0 45-1 1 39-9 39-9 2 42 '3 39-8 39-9 3 40-0 40 T 4 44-4 42:3 5 45-2 45 :4 6 7 44-7 44-4 § 9 10 12 45 T 44:9t 45 :4 14 16 45 T 18 20 22 24 26 45*4 28 30 32 34 36 38 45 :9 3 > 40 o 42 44 ’Tl &D .s 46 48 50 o 3 a 52 CO > 55 • ■ Land ,, o-ooio o-ooio o-ooio o-ooio y Temperature, 80° F. 1000s 1005s -6 1010s 1015s 1020s 1025s 1028s Time 24 hours, ,, 96 „ 0-0623 0-0723 0-0048 0-0028 0-0028 0-0018 0-0020 0-0013 0-0018 0-0013 0-0018 o-ooio 0-0018 o-ooio * Advantage is taken of this fact in the purification of muddy waters for domestic and manufacturing purposes by adding lime and alumina salts, which induce the separation of suspended matter and its subsidence (see Sidell in Humphreys and Abbot’s Report on the Mississippi , Appendix A, Ho. 2, pp. 495 etseq., 1876; Schultze, Pogg. Ann., vol. 129, p. 366, 1866). 1 242 Proceedings of Royal Society of Edinburgh. [sess. 8 Temperature, 40° to 50° F. 1000s 1005s"6 1010s 1015s 1020s 1025s 1028s Time 6 hours, 0-0558 0-0568 0-0388 0-0388 0-0418 0-0333 „ 24 ,, 0-1215 0-0113 0-0073 0-0053 0-0053 0-0053 0-0053 „ 48 „ 0-0048 0-0038 0-0025 0-0028 0-0031 0-0035 ,, 72 ,, 0-0033 0-0018 0-0018 0-0013 0-0018 0-0018 96 „ 0-0658 0-0028 0-0013 0-0013 0-0013 0-0013 0-0013 e Water (1024s) from shore at Granton. After 24 hours at 80° F. contained 0'0083 grin. ,, „ 50° F. ,, 0-0188 „ £ Clay suspended in Salts of Sea Water. Temperature 80° F. CaS04 MgCL> MgS04 NaCl k2so4 Time 48 hours, .~ 0-0013 0-0015 0-0023 0-0116 0 0563 It will be seen that with waters of all salinities above 1010 the great bulk of the heavier clayey matter is thrown down in the course of twenty-four hours, which is in harmony with the results of pre- vious observers. There is, however, a small residuum which is held in suspension, even in waters of a salinity equal to 1028. The amount, it will be observed, varies with the temperature. At a temperature of 40c to 50° F., and a salinity of 1027, 0-0064 grm. per litre of clay remained in suspension at the end of twenty-four hours,* while, under the same condition as to time, at a temperature of 80° F., only 0*0033 grm. remained in suspension.! At the former temperature, 00018 grm. remained suspended at the end of 106 hours,| and at the latter only 0-0003 grm. at the end of 120 hours.§ It appears, then, that all the clay brought to the ocean by rivers is not precipitated on mixing with sea-water, but a very small quantity may be carried far and wide by ocean currents, the amount thus held * = 27,500 tons per cubic mile of water. t = 14,2Q0 tons per cubic mile of water. X = 7740 tons per cubic mile of water. § = 1300 tohs per cubic mile of water. \ \ 1890-91.] Dr Murray and Mr Irvine on Silica in Seas. 243 in suspension by the sea- water depending largely on the temperature, and to a less extent on the salinity, being greater the lower the temperature and salinity. To ascertain the amount of clayey matter in suspension in the open sea far from land, we procured large samples from the surface of the Atlantic, the Indian Ocean, Red Sea, the Mediterranean, the German Ocean, the Baltic Sea, and the Firth of Forth.* These waters were preserved in stoneware jars thoroughly cleaned and filled with the utmost care, so that no siliceous matter might be accidentally intro- duced. About 14 litres of sea -water were passed through a double ashless filter, and, after carefully washing the solid matter left on the filter to get rid of salts, the whole was burned, and the residue treated in a platinum vessel with pure boiling sulphuric acid, — the silicic acid, iron, and alumina were treated in the usual way. The results are exhibited in the following Table — Table III. — Showing Amount of Mechanically- Suspended Silicates {Clay) present in Water of Different Seas. In 14 Litres of Water. Per Cubic Mile of Water. I. Firth of Forth, 1 mile from shore, II. Atlantic Ocean, lat. 51° 20', long. 31° W., III. German Ocean, 30 miles E. of May Island, IY. Mediterranean, centre of eastern basin, . Y. Baltic Sea, salinity 1005 ‘5 YI. Red Sea, off Brothers Island, YII. Indian Ocean, lat. 15° 46' N., long. 58° \ 51' E., / 0-0259 grm. 0-0052 ,, 0-0063 ,, 0-0065 ,, 0-0105 ,, 0-0006 ,, 0-0006 „ 8000 tons. 1604 „ 1946 ,, 2031 ,, 3200 ,, 264 ,, 264 ,, In the first determination (I.), Firth of Forth, the amount of silica in the clay, represented above, is about one-fourth what our minimum results show as present in a soluble condition in sea-water. In Baltic water (V.), salinity 1005, about one-eighth; in Atlantic, German Ocean, and Mediterranean waters (II., III. and IV.), about one-sixteenth, and in the Indian Ocean and Red Sea still less. This seems to establish the fact that there is always a small * We are indebted to Captains Thomas S. Knox and George Read, of the Anchor Line, for collecting the waters from the Mediterranean, Indian, and Atlantic Oceans. 244 Proceedings of Boyal Society of Edinburgh. [sess. quantity of silicate of alumina or clay present in sea-water, even at very great distances from land, and in the saltest and warmest waters. The above waters were taken from the surface ; hut, by a carefully-collected series of waters from different depths, it might be shown that the deeper and colder waters contained a greater proportion of this fine clayey matter than the surface ones, and it is at once apparent that waters taken near shore will contain more than those from far out at sea. Bearing in mind the above facts, it is interesting to recall what was stated above as to distribution of siliceous organisms in the ocean, they being more abundant in shore waters or in waters of a low salinity and in cold waters — as, for instance, Diatoms in brackish waters and in those of the cold Southern and Polar Oceans, and Eadiolaria in polar waters and in the West Pacific and Eastern Indian Oceans, where there is a relatively low salinity, as well as in deep inter- mediate waters where there is a low temperature. This would seem to indicate that in the ocean siliceous organisms are more abundant where there is most clayey matter in suspension in the sea-water. With the view of gaining some information as to the conditions under which silica might be secreted by organisms, we instituted a number of experiments with Diatoms and other silica-secreting plants. A culture solution, representing the mineral food of plants according to Sachs’ formula, was prepared, consisting of — Distilled water, . . 2000 grms. Chloride of sodium, 1 ,, Nitrate of potash, . 2 ,, Sulphate of lime, . 1 ,, Sulphate of magnesia, . 1 grm, Phosphate of lime, . 1 ,, Ferric chloride, . . 1 ,, (A) Into a portion of this solution a minute patch of Diatoms ( Navicula ) was placed (in August 1890) with a small quantity of silicic acid in the form of jelly. In the course of seventeen days they grew most vigorously, the Diatoms increasing in great numbers —possessing the characteristic yellow-green colour of chlorophyll, giving off oxygen abundantly in sunlight, and moving about with the peculiar motion of these organisms. Prom this patch of Diatoms we obtained the material for the following experiments. (B) A small quantity of living Diatoms from (A) was carefully washed so as to remove all traces of silicic acid or soluble silicates, 1890-91.] Dr Murray and Mr Irvine on Silica in Seas. 245 and transferred to a fresh portion of culture solution pure and simple. For a time the plants continued to live, but their increase was trifling, and after twenty-seven days they presented the appear- ance of dead organisms, being deprived of their green colour, ceasing to give off oxygen in sunlight, and were without motion. (C) Another patch of (A) carefully washed was placed in cul- ture solution, into which a quantity of very finely-levigated clay from the fields was introduced. (This clay by careful washing was entirely freed from any soluble matter.) After a short time the whole clayey matter became entirely altered in appearance, forming a sticky matted-like substance, from which in sunlight oxygen was freely given off, and which under the microscope showed an enormous growth of Diatoms, having the characteristic yellow- green colour of the healthy algse. This experiment has been continued for a number of months, and the results obtained, so far as the development of Diatoms is concerned, has been so extraordinary that we have examined with the utmost care any possible source from which they might derive silica (apparently necessary to their life functions), other than from the clay which was added.* The experiment (B) seemed to prove conclusively enough that siliceous plants cannot obtain silica in sufficient quantity from the glass vessels used for that experiment. We were also suspicious that atmospheric dust might have provided a certain amount of siliceous nourishment, but the fact that the Diatoms in experiment(B) had been unable to live seemed to us to prove that neither from the glass vessels nor from atmospheric dust could they obtain, under the * Johann Nave, writing of Diatoms, remarks that these Algse abound wherever water collects, from the sea to the smallest puddle on the way- side, and are generally associated with clay or mud. Gerstenbergh’s plan for the propagation of Diatoms is instructive. He spreads the mud (containing Diatoms) on a plate or shallow dish, and exposes it to the full light of the sun. Stimulated by its rays, the plants begin to multiply rapidly, and on removal those left in the mud may be stimulated into active production by repeating the same process. By degrees the vitality of the little plant exhausts itself, and it is necessary to revive their vegetative powers. This may be accom- plished by creating an artificial spring and winter. You have only to allow the water to evaporate, and the mud to become nearly, but not quite, dry, when, on fresh water being poured over it, vegetation commences anew. In this way gatherings originally poor may be made to yield an abundant supply of Diatomacea. VOL. XVIII. 20/5/91 Y 246 Proceedings of Royal Society of Edinburgh. [sess. careful conditions of our experiments , sufficient silica for vigorous growth. On placing a small portion of the matted sludgy matter under the microscope, it was interesting to notice that all round the outside, and even piercing into the very centre of the mineral matter composing the mud, there were living Diatoms in great abundance, whilst in the clearer field of the microscope free from clay, only a very few were detected floating about. These experi- ments seem to point to the conclusion that these organisms are in the process of growth able to obtain their silica from (otherwise) insoluble compounds of silicate of alumina. (D) A patch of (A) was introduced (August 1890) into culture solution containing silicate of lime. The result here was an abundant growth of Diatoms. (E) A patch of (A) was introduced (August 1890) into culture solution containing pure amorphous silica. A very few seemed to have lived, hut the major portion had died by December 15, 1890. (F) A patch of (A) was introduced (August 1890) into culture solution containing Diatom Ooze, and when examined shortly after- wards there seemed to be no growth, but subsequently (December 15) a considerable mass of living Diatoms was observed. This may be due to the soluble silica present in Diatom Ooze, but of course such a source of silicic acid for surface Diatoms is out of the question. However, Sponges may obtain their silicic acid in part in this manner. Take now the case of land plants growing in a virgin soil, con- sisting of decomposing rocks, sand, clay, and salts of lime, potash, and so on, or in a barren soil, from which, by repeated cropping, all the soluble food salts have been extracted, but to which manure is added to replace the salts represented in the culture solution used in our experiments. In either case we have bulky crops grown, and on examining the ash left on burning the grain or straw we find large quantities of silicic acid which has been absorbed, as is shown by the following Table : — Table IY. The ash of wheat straw contains 73 ‘57 per cent, silicic acid. 33 barley „ „ 32*73 3 3 33 33 oat ,, „ 38-48 33 33 33 hay „ 53-43 33 33 1890-91.] Dr Murray and Mr Irvine on Silica in Seas. 247 Here we find silicic acid always present, and in many cases bulk- ing very largely of the whole amount of the ash left on incinerating the plants. On looking at the analyses of such soils, we find a very large proportion of their constituents to consist of silicic acid, but in the insoluble form of sand, or in chemical combination with alumina as insoluble clay. In the drainage water from good arable land, the amount of silica found amounts only to 1 part in 100,000. There must therefore be processes at work by which a plant can render soluble and make available the silicic acid of the soil, from which its roots obtain this in common with other mineral food. It has frequently been pointed out * that when polished slabs of marble, dolomite, or apatite were buried in pure sand, in which seeds were planted, wherever the roots of the plants reached the slabs corrosion of the surface took place, which is explained by stating that the fine rootlets secrete acids having a solvent and disintegrating action on the lime-bearing rocks. The rootlets have in all probability a similar effect on siliceous rocks. In the case of what we consider eminently siliceous plants, the silicic acid absorbed from the soil and secreted on the outer cell- walls of the stems and in the joints must, it appears to us, have been so obtained. The clay, or even the sand grains, has been no doubt rendered soluble by plant action, for we have seen that no ordinary soil contains soluble silicic acid in the least degree equal to what is required for the healthy life of such plants as produce siliceous coatings. So far as we know, some plants usually containing silicic acid can be grown to vigorous and complete development under conditions in which they are entirely deprived of silicic acid ; and granting that silicic acid does not appear to be necessary for their nutrition, yet we find it present in most plants, just in the same way as carbonate of lime, although not necessary for the nutrition of animals and plants, yet is always present in Foraminifera, Algae, &c., f where we find it always associated as part of the body structure. At one time agriculturists supposed that by adding soluble sili- cates to the soil, the stems of cereals would be so strengthened that * Sachs’ Physiology of Plants, pp. 262, 263. t See Pouch et and Chabry, “L’eau de mer artificielle comme agent terato- genique,” Journ. de I’Anatomie, 1889, pp. 289-307. 248 Proceedings of Royal Society of Edinburgh. [sess. the laying of crops by stormy weather would be prevented. The result proved that no more silicic acid was secreted by plants under these conditions than when no such addition was made. Here we have apparently proof that the source of silicic acid in plants lies beyond any question of soluble silica present in the soil. As to the secretion of silicic acid by marine plants and animals, we think it is unnecessary to formulate any elaborate chemical theory to account for its absorption and secretion. There can be but little doubt that marine plants and animals have the power of decomposing the in- soluble silicate of alumina, or clay, which we have seen occurs in all sea-waters we have examined. The experiments we have been able to perform with Diatoms in the carefully-washed field clay and pure water, appear to indicate what takes place on such an enormous scale in nature, and to point to suspended clay as a true source from wrhich siliceous organisms derive their silica. In the case of the secretion of silicic acid by Sponges, we may have another condition of things, also capable of explanation in a somewhat similar way. These Sponges grow in a muddy soil, and are provided with spicules, fixing them firmly in the deposit where decomposing organic matter is abundant, under the influence of which alkaline sulphides are continually being formed (by the deoxidation of the alkaline sulphates of sea-water). These sulphides may, acting locally, decompose the clay or silicate of alumina, setting free soluble silicic acid to be absorbed and stored up by the Sponges. It is not impossible that Diatoms, floating as they do near the surface of the water, may also receive silica in this manner, the organic matter present in the floating clay indirectly causing solution of silicic acid. The presence of alumina in a quantity of Diatoms obtained in the Antarctic Ocean seems to point not only to the original presence of clay in the water, but its subsequent decomposition by these algae. There is also distinct solution of silicic acid when muds consisting of the remains of calcareous and siliceous organisms are acted upon by sea-water, as shown by the following experiments. A portion of mixed Diatom and Globigerina Oozes was placed in a litre of sea- water and some mussel flesh added, so as to obtain the conditions attending decomposing organic matter on an ocean floor consisting of these mixed muds. After a week’s exposure, during which time 1890-91.] Dr Murray and Mr Irvine on Silica in Seas. 249 the organic matter had become putrid, the water was carefully filtered from the sediment, and the silicic acid determined in the nitrate. The amount found was equal to 0*025 grm. per litre, or, according to the amount of water, 1 part of silica had been dissolved from the Diatom Ooze in 41,000 parts of sea-water. This action of silicic acid in decomposing carbonate of lime was further proved by exposing 2 grms. of the two oozes to boiling water for half an hour, the amount of silicic acid present in a soluble condition after that period amounting to 0*014, or 1 in 80,000 of water. To check this result, and at the same time to determine whether the decomposing action of silicic acid upon carbonate of lime was continuous, a portion of the mixed oozes was heated with successive quantities of sea-water, when it was found that this action was constant. Thus, in a mixture of 89*42 per cent, of calcareous organisms and 10*58 per cent, of siliceous organisms, the amount of silica was reduced, by 25 successive litres of sea-water, from 10*58 to 3*47 per cent., so that 67 per cent, of the silica present was removed.* On looking at the Tables showing the amount of suspended clay in sea- water (see pp. 241 and 242), and comparing the amount with the soluble silica or silicates in sea- water, it is to be observed that the maximum amount of silica found is much larger than that present as suspended clay. In the actual determinations of this body in the seven waters (shown in Table III., p. 243), the amount of clay found in these waters ranges from 264 to 8000 tons per cubic mile of water, thus roughly representing from 132 to 4000 tons of silica per cubic mile; whilst soluble silica, by the analysts’ results we have quoted, appears at a much higher figure. * In this connection Julien states (“On the Geological Action of Humus Acids,” Pros. Amer. Ass., vol. xxviii. p. 359) — “Considerable evidence now exists that a substance corresponding to humus, simply in its yield of acid solvents of lime, oxides of iron, manganese, &c., enters universally into the constitution of the layer of ooze upon the bottom of the ocean. Its exact com- position has never yet been determined ; but it may be suspected that it resembles that of glairine, especially in its high content of silica. As it has resulted from the continuous decomposition of the cellulose membranes of the diatomacese, &c., and of the gelatinous sarcode of the radiolaria, spongise, and foraminifera, which may be there living or deposited by subsidence from the surface, its composition must differ widely from that of the humus of subaerial eremacausis, in its large proportion of water and nitrogen and in its poverty in carbon. It must thus present the most favourable conditions for rapid dissociation.” 250 Proceedings of Royal Society of Edinburgh. SESS. In either case, without doubt the amount found is sufficient to account for the growth and accumulation of siliceous organisms in modem seas; but a moment’s consideration will show that, by adopting the view that siliceous organisms obtain their siliceous matter also from insoluble matter floating in the water, we can understand to some extent their distribution in the ocean, and how they may obtain what to them is a vast local supply (close at hand) without being required to deal with an enormous quantity of liquid containing but minute traces of silica.* To exemplify what we mean, take, for example, an animal requiring, say, 1 lb. of solid food per day, this is quickly assimilated with the assistance of a small quantity of water ; but if we suppose this same amount of solid food dissolved in from 250,000 to 300,000 times its weight of water, we are unable to conceive the possibility of the animal assim- ilating enough of the solid nutriment contained in this mass of liquid to sustain life. In a future paper we hope to give further results of experiments now in progress on the subjects treated of in this paper. In the analyses and determinations referred to in this communica- tion we have been assisted throughout by Mr W. S. Anderson, Chemist at the Scottish Marine Station, Granton, and we desire to thank him for the great attention he has given to all the experiments. * The abstraction of silicic acid from silicate of alumina will, of course, necessitate that an equivalent amount of alumina should be accounted for. Doubtless this passes into solution, for in all the sea-waters examined by us, after a most careful filtration, alumina has been found in solution (see also Dittmar’s Report, Pliys. Chem. Chall. Exp. , part i. ) 1890-91.] Dr Haycraft on Specific Gravity of the Blood. 251 A New Method for the Estimating the Specific Gravity of the Blood. By John Berry Haycraft, M.D., D.Sc. (. Physiological Laboratory , University of Edinburgh.) (Read January 19, 1891.) The method of Boy for determining the specific gravity of the blood is a very excellent one, and is capable of yielding sufficiently accurate results. Over thirty bottles containing mixtures of glycerine and water of different specific gravity, ranging from 1*030 to 1*070, are used for the estimation, and a drop of blood to be tested is placed in a sample of one of these fluids. If the drop sinks it is heavier, if it floats it has a lower specific gravity, and then another drop of the same blood is tested until by a few experi- ments the exact specific gravity is determined. It might be imagined that this method is more difficult to carry out than it really is, and that it requires many attempts on the part of the experimenter, and the loss of much blood, before the specific gravity is finally settled. This is no doubt true in the case of a patient examined for the first time, but afterwards, knowing beforehand what the specific gravity is likely to be, it is easy, with one or two trials, to find out if any change in the specific gravity has occurred. The chief objection to the method is, however, the cumbrous nature of the apparatus required, which would render it useless for the requirements of private practice, although undoubtedly of much value in the Hospital and Laboratory. > The method I venture to introduce has this advantage that the apparatus used is quite portable, requiring no more room than the space occupied by a small pocket case. The method is accurate, requires only a single drop of blood, and, moreover, it is perhaps more quickly done than that of Boy. Two mixtures of benzyl chloride (sp. gr. 1*100) and toluol (sp. gr. 0*8706) are made, one (A) having a specific gravity of 1*070, and the other (B) having a specific gravity of 1*020. With a cubic centimetre pipette graduated to yj^th c.cm., one c.cm. of (A) is 252 Proceedings of Royal Society of Edinburgh. [sess. measured off into a glass tube, and the drop of blood to be tested is allowed to flow into the tube as well. The drop of blood does not mix with the solution, having a different surface tension from it, and floats on its surface as a tiny red globule. The graduated pipette is now filled with solution (B) and this is allowed to run slowly into the mixing tube, shaking after each addition. As (B) flows in, the specific gravity of the mixture is lowered, and after each addition and shake the red globule returns more and more slowly to the surface. At last it neither tends to rise nor sink, and the mixture now has the specific gravity of the blood itself. The specific gravity of the mixture can readily be calculated, or found from the table attached to the apparatus made by Mr Fraser, Lothian Street. Suppose 0*5 cc. of (B) has been added, the total weight of the fluid divided by its volume will give the specific gravity of the mixture. - 1 cc. at sp. gr. 1070 = 1070 *5 cc. at sp. gr. 1020 = 510 1-5) 1580 1053 As the mixtures of benzyl chloride and toluol expand with heat they will yelvj in their specific gravity, so that a correction for temperature must be made if exactitude is required. The solutions (A) and (B) are prepared at the temperature of 15° -6 Centigrade or 60° F. and if the temperature of the room in which the experiment is made is also 60° F. no correction will be needed. If, however, the temperature is higher than 60° F. the specific gravity of the fluids will be lower, and this fall of specific gravity will be at the rate of 1° for every 2° F. Example 1 cc. of (A) at 1070 = 1070 •5 cc. of (B) at 1020 = 510 1*5) 1580 1053 Temperature of room 66° F., therefore 3° * must be subtracted the real specific gravity of the mixture (and therefore of the blood) being 1*050 at that temperature. * The more accurate allowance for temperature is *88° sp. gr. for every 2° F. of temperature above 60°. For all ordinary purposes 1° sp. gr. is sufficiently accurate and more easy to calculate, and hence that figure is given in the text. 1890-91.] Dr Haycraft on Specific Gravity of the Blood. 253 My first attempt to estimate the specific gravity of blood was by quite another method. While watching a globule of blood slowly descend in a cylindrical vessel filled with oil, it occurred to me that by using drops of the same size, their specific gravity could easily be determined, for the higher their specific gravity the quicker would they fall. By the rate of fall, I found that the specific gravity could be determined with the greatest accuracy, but inasmuch as the viscosity of the oil, and therefore the rate of fall varies with the temperature, this must either remain constant or a correction made for it. As the viscosity varies considerably with even small changes of temperature I abandoned the method, as one incapable of clinical application, though it is, I find, highly to be recommended for laboratory purposes, where the temperature factor can be kept strictly under control. Having spent some time on this method I did not like to relinquish the subject, and the plan already described in this paper was worked out. It occurred to me that if I could obtain two fluids, both of which had a different surface tension from blood, one of which procured a higher, the other a lower specific gravity than blood itself, I could mix them until I hit off the exact specific gravity of any particular drop I might wish to examine. This is of course the principle of the method already detailed in this paper, but I was for some time unable to carry it out in practice, more especially as such fluids must be very mobile in order readily to mix with each other, and mobile fluids of high specific gravity are not very numerous. I first tried mixtures of chloroform and paraffin, one mixture having the sp. gr. 1*070, and the other sp. gr. 1*020. This plan did not succeed at all, for the mixture affects the density of the blood itself, a globule of blood, say of slightly lighter specific gravity than a given mixture of chloroform and paraffin, on its first immersion floating on the surface, but after a few seconds acquiring density and sinking in the fluid. I then tried mixtures of chloroform and toluol (chloroform, sp. gr. 1*498 ; toluol, sp. gr. 0*8706), and this time with success, the specific gravity of the blood remaining constant in the mixture. This method succeeds admirably, but the mixtures are apt to lose specific gravity on keeping, for the chloroform is very volatile, boiling at 61° C. I then sought for another mobile fluid having a higher specific gravity and a high 254 Proceedings of Royal Society of Edinburgh. [sess. boiling-point. After one or two trials I used benzyl chloride, C6H5CH2CL, having a specific gravity of 1‘1 00, and a boiling-point 178° C. The only objection to this is its irritating vapour. It is well not to allow any of the fumes to get into the eyes, or somewhat painful smarting will result. 1890-91.] Dr Haycraft on Uric Acid in the Urine. 255 On the Estimation of Uric Acid in the Urine. A Reply to Criticisms upon the Silver Method. By John Berry Haycraft, M.D., D.Sc. (. Physiological Laboratory , University of Edinburgh.) (Read February 16, 1891.) (Abstract.) I published in the Brit. Med . Jour., December 12, 1885, a method invented by me for the easy and yet accurate estimation of uric acid. The method consists in precipitating the uric acid as a silver salt, estimating the silver, and calculating the uric acid from the silver (168 uric acid to 108 silver). As no process was then invented which had itself been tested, except as Salkowski’s, by the side of others acknowledged to be inexact, I did all my work with weighed quantities of uric acid, and tested my process — the only straightforward way of working — by adding known quantities of uric acid to one of two samples of a urine, and finding as a result of my estimations of the uric acid in the two samples practically the same difference as the weight of acid added. Hermann con- firms my work (Zeitsch. f. physiol. Chemie , Bd. xii. s. 496), and Czapek, working with Professor Huppert, proposes a modifica- tion of my method, while Camerer’s results (Zeitsch. f. Biologie , Bd. xxvii. s. 113) run on parallel lines. My results have been adversely criticised by Salkowski, who still maintains that uric acid and silver do not combine in a definite ratio. This observer published in 1872 twelve analyses, which show, according to his belief, that there is no constancy in the proportion between the silver and uric acid, and in 1889 he again affirms the same thing, bringing forward in proof of his assertion some dozen analyses made by his colleague Professor Jolin and himself. I was for some time unwilling to take up the controversy where Professor Salkowski had left it, for, certain of the care with which my own work had been done, I was quite willing to let the matter be settled by other and less prejudiced persons, especially as such seemed willing enough to undertake the task. As, however, my method had been widely used, especially for clinical purposes, and 256 Proceedings of Boyal Society of Edinburgh. [sess. as I had frequently to answer queries concerning its accuracy, I felt it my duty carefully to examine once more the whole question, and if there was any doubt about it, at once to set that doubt at rest. I was I confess agreeably surprised to find that Professor Salkowski had made a slight mistake, which when rectified places his own results and mine in complete accord. In order to make this point quite clear I will venture to reproduce Professor Salkowski’s results, arranging his analyses in order, beginning with the one having the least uric acid. Salkowski' s first Table (1892). N o. 1 Silver obtained. 2 Uric acid reckoned from 1. 3 Uric acid obtained. 4 Difference in mgrms. 5 Ratio between silver and uric acid. 1 •029 •045 •033 -12 4-1 : 3 o •035 •054 •040 -14 4-09 : 3 3 •037 •057 •042 -15 4-2 : 3 4 •045 •070 •056 -14 3-71 : 3 5 •046 •071 •051 -20 4-03 : 3 6 •049 •077 •056 - 21 4-02 : 3 7 •050 •078 •067 -11 3-43 : 3 8 •051 •079 •100 + 21 2-24 : 3 9 •054 •084 *070 -14 3-36 : 3 10 •060 •094 •083 -11 3-63 : 3 11 •064 •100 •088 -12 3-41 : 3 12 •073 *114 •086 -28 3-96 : 3 I think No. 8 is evidently a spoilt analysis, for no similar result is ever again to he found in the tables of Salkowski, Jolin, Hermann, or Czapek, and the last, urine No. 12, must be considered under the head of “urine saturated with uric acid.” Such urines, and Czapek estimated some of these, stand by themselves, and probably require dilution before the analysis is made. Omitting these two cases, and arranging the results as I have done, it is evident that there is, in each case, an excess of the uric acid estimated from the silver over that actually found by Salkowski’s own process of about 14 mgrms. This difference is as constant as one can expect, for Jolin and Salkowski, in performing two check analyses of the uric acid, in one and the same urine, by one and the same process, fail to get them then to coincide by 3 or 4 .mgrms. What Salkowski 1890-91.] Dr Hay craft on Uric Acid in the Urine . 257 proves, therefore, is that by his method about 14 mgrms. less uric acid are found than by the silver calculation. The mistake he fell into in interpreting his results will be obvious on referring to column 5 of his table. He here calculates the ratio between the silver and uric acid found by his method and does not find it constant. The reason is very obvious, for in the weaker urines the loss of 14 mgrms. will be comparatively a heavy loss, making the ratio of the uric acid to the silver low, while in the stronger urines the loss will be less felt. A glance at the table will show this, for the silver in the upper part of the table is say 4T to 3, while in the lower part it sinks to say 3*4 to 3. The loss of a pound is much to a poor man, but will not inconvenience a rich one, because it bears a small ratio to the sum that he possesses. In Jolin and Salkowski’ s recent paper the same error is repeated without discovery, the table of estimation they give showing still more forcibly a “constant difference” as a result of their estima- tions. In the last two pages of his article this is shown very forcibly in the case of two final experiments made by Salkowski, who estimates both the silver and the uric acid (by his method) in one and the same urine : — No. Uric Acid reckoned from the Silver. Uric Acid di- rectly estimated (Salkowski). Difference. Ratio between Silver and Uric Acid. 1 *0756 •0556 191 3-99 : : 3 2 •0938 •0757 18-1 3*66 : 3 He says “Das yEquivalentverhaltniss zwischen Harnsaure und silber berechnet sich. Aus Yersuch 1 == 3 : 3 *99 aus Yersuch ii. 3 : 3 ‘66. Auch diese Bestimmungen bestatigen, also lediglich meine friiheren Angaben. It is obvious that the existence of a constant difference of about 19 mgrms. (more urine was used than in this case, hence the greater deficit) was all he really proves, and this con- stant deficit tells most in the case of the weaker urine. Salkowski would not have misinterpreted his results had he arranged theiii with sufficient care or put in a column of differences which I have taken the liberty of adding. His results are therefore valuable 258 Proceedings of Boyal Society of Edinburgh. [sess. evidence in favour of the silver process, for a constant difference such as he obtains would not be possible were the compound (we will call it urate of silver) of unfixed and varying composition, and therefore his own results prove the proposition he intended to destroy. The constant difference of 14 mgrms. is due, at any rate in part, to the imperfections of his own method, which he had never taken the trouble, to test, merely comparing his results with those obtained by the unexact method of Heintz. This difference has been reduced to within the limits of manipulative error by Hermann and Czapek, when comparing the silver method with the method introduced by Ludwig. Mr Gossage has also criticised my method on the same grounds as Salkowski, but I am afraid that his results must suffer a totally different explanation. He gives five estimations, in which he obtains the uric acid by the silver method and by Salkowski’s method. His results may therefore strictly be compared with the exactly similar ones of Salkowski and Jolin. His average difference is 32 mgrms., which is more than the extreme difference obtained by the other chemists (28 mgrms.). If we accept the results of Salkowski and Jolin as trustworthy we are forced to look upon Mr Gossage’s analyses as untrustworthy, and indeed his least mani- pulative error is greater than the greatest ever quoted by them. (Lor a full discussion of this question see a paper appearing in the next number of the Zeitschrift f. physiol. Chemie). 1890-91.] Mr Aitken on Water Particles in a Fog. 259 On a Method of Observing and Counting the Number of Water Particles in a Fog. By John Aitken, Esq. (Read May 4, 1891.) The phenomena known as haze, fog, mist, and rain are in a general way but the successive development of the same process, and the line which divides the one from the other is very indefinite. Dust in the atmosphere produces a haze, and the thickness of a haze of this kind depends principally on the amount of dust present when the relative humidity of the atmosphere is very low. But as the humidity increases the effect of the vapour increases also ; the dust particles attract the water vapour which becomes deposited on them, thus increasing their size and their hazing effect, till at last when the air is nearly saturated it becomes very thick, and forms what we call a fog ; when in this condition, the thickness of the atmosphere depends principally on the degree of saturation. Between the haze and the fog, however, there is no recognised dis- tinction in kind, it is principally one of degree. After the air is saturated and the conditions are such as to tend to cause super- saturation, then a change takes place in the condensation. A few of the dust particles have water deposited on them, and after a time they grow and become little drops of water, in which the original dust nucleus hears a very small proportion to the total weight. At this stage it is still called a fog, hut after more water is deposited on the small drops they grow and become what is known as mist, and when the mist drops combine and fall they are called rain-drops. The instrument to he described will, it is hoped, in addition to enabling us to count the water drops, also give us a means of finding by observation the boundary line between a dry fog and a wet one, the latter being the name often given to the first stages in the formation of a mist, when the condensation is taking place at the level of the observer. At present two forms of apparatus are being developed for observing these water particles. The first and simplest is an instrument for observing whether there are any water particles in 260 Proceedings of Royal Society of Edinburgh. [sess. the fog or not, that is, for determining whether it is a wet or a dry fog. This instrument can also be used for counting the number of drops which fall on a given area in a given time. It might he thought it would he quite unnecessary to use an instrument for telling us whether there are any water drops in the fog or not ; because if there are any drops in it, they will be falling, and will wet all exposed surfaces, so that a piece of mirror would be all that would be necessary for the purpose. Such, however, is not the case. I have found in many fogs when all exposed surfaces were quite dry, that there were great quantities of water drops in the air and falling on all exposed surfaces. These drops, however, are so extremely small they are invisible under ordinary conditions, and being so small they rapidly evaporate, as all exposed surfaces are generally more or less heated by radiation during the day. The plan I have adopted for observing these drops is the same as that used for observing the artificially made drops in the “ Pocket Dust-Counter,” described in a previous communication.* The new instrument consists of a glass micrometer divided into squares of a known size, a spot-mirror for illuminating the stage, and a strong lens or a microscope for observing the drops on the stages. The space between the micrometer and the lens is open, so that the air passes freely over the stage, and the drops that fall on its surface are easily seen. These drops are very small ; as yet I have not had an opportunity of measuring them. They of course vary greatly in size, and many of them even when spread on the glass are not more than 0*05 mm. In observing these drops the attention requires to be confined to a limited area of the stage, as many of the drops rapidly evaporate, some almost as soon as they touch the glass, whilst the larger ones remain a few seconds. A square of 1 mm. is rather small an area, but one of Jg-, or ^ cm. does very well when working with a magnifying lens. The following are samples of the results obtained when working with this instrument. On the 19 th February 1891, at 10 a.m., the fog was so thick that objects beyond 100 yards were quite invisible. The surfaces of bodies exposed in the open air were dry. On this occasion the number of drops falling per minute varied greatly from time to time. The highest number observed * Proc. Roy. Soc. Edin. , vol. xviii. 1890-91.] Mr Aitken on Water Particles in a Fog. 261 was 30 drops per min. per sq. mm., that is 3000 per sq. cm., or 19,350 per square inch per min. This high number never lasted for long, and in the intervals the number fell as low as 300 per sq. cm., or to one-tenth ; the temperature at the time was 29°. Two days later, that is on the 21st of February, the air was again very foggy, about the same thickness as it was on the 19th at 10 a.m., and all exposed surfaces were dry; the number counted was 13 per sq. mm. per min., that is 1300 per sq. cm. or 8385 per sq. in. per min. This number remained fairly constant on this occasion, and slowly diminished as the fog cleared away. The temperature at the time was 31°. On both of these occasions the temperature had not risen more than |° above the night minimum. The number of dust particles in the air was also counted on these occasions, and on both days the number was very high, varying from 45,000 to 80,000 per c.c. The number of water particles in a fog, as given by these observa- tions, seems to be very large, and it is difficult to imagine how they evaporate so quickly that exposed surfaces are not wetted by them. It must, however, be remembered that they are very small, so small that they are not felt falling on the hands or face of the observer. Indeed, it is probable they never touch the skin. These fog drops are very similar in size to the little drops artificially produced in the “Dust-counter,” and it is found that, if the stage of the “Dust- counter ” is slightly heated, the drops never reach its surface, but are evaporated in the slightly heated layer of air over it. If we knew the size of these drops we might be able to calculate the velocity of their fall, and from that obtain the number per given volume of air. As it would be more satisfactory to obtain this number from direct observation, the second form of the instrument has been designed. It is constructed on the same principle as the other one, but an arrangement is made by means of which the number of particles that fall from a known height are counted. My first attempts in this direction were not satisfactory, owing to using a magnifying lens for observing. This limited the height of air out of which the drops fell to little more than 1 cm. Another instrument has since been constructed in which this difficulty is overcome. In place of a short focussed lens, a low power microscope is used. This enables us to get easily 5 cm. of air over the stage. VOL. XVIII. 1/6/91 z 262 Proceedings of Royal Society of Edinburgh. [sess. In order to find the number of drops in this height of air the following plan has been adopted. Underneath and concentric with the microscope is mounted a tube 5 cm. long and 4 cm. diameter. This tube is provided with a bottom and a cover ; these are both fixed to an axis parallel with the axis of the tube, so that by turning a handle both top and bottom can be slid sideways, and the tube closed or opened at top and bottom simultaneously, when desired. In the cover is a small opening corresponding to the lens of the microscope, and in the centre of the bottom is fixed a micrometer illuminated by a spot-mirror. When the top and bottom are turned aside the tube is open at both ends, and the air can circulate freely through it. On quickly turning the handle both top and bottom are closed, and the micrometer by the same move- ment is brought under the microscope, and all the drops that fall out of the 5 cm. of air over it are counted on a known area. This ' instrument was only completed just when the fogs were about over for a season, and no satisfactory readings have been as yet obtained. It was, however, thought advisable to give this pre- liminary note at present, as the season for fogs has gone for a time, and it will give an opportunity for any one wishing to make obser- vations in this wTay being prepared for the coming season. It may be mentioned that the instrument first described, may be found useful for observing the larger particles of dust in the atmo- sphere. If it is exposed anywhere with the stage horizontal, the dust that settles on the glass can be distinctly seen with the lens. If the spot-mirror is applied to a microscope it gives an illumination very suitable for examining the smaller particles of dust. The very small particles, which are quite invisible under the ordinary form of illumination, shine out brilliantly when illuminated by the spot- mirror. The spot-mirror has also been found useful in the micro- scopic examination of delicate objects other than dust particles. 1890-91.] Sir G. G. Stokes on Suspended Matter in Flames. 263 On an Optical Proof of the Existence of Suspended Matter in Flames. By Sir G. G. Stokes, Bart., E.R.S. {In a letter to Professor Tait.) (Read June 15, 1891.) 8 Belgrave Crescent, Edinburgh, June 13, 1891. Dear Professor Tait, — I write to put on paper an account of the observation I mentioned to you to-night, in case you should think it worth communicating to the Royal Society of Edinburgh. In the course of last summer I was led, in connection with some questions about lighthouses, to pass a beam of sunlight, condensed by a lens, through the flame of a candle. I noticed that where the cone of rays cut the luminous envelope there were two patches of light brighter than the general flame, which were evidently due to sunlight scattered by matter in the envelope which was in a state of suspension. The patches corresponded in area to the intersection of the double cone by the envelope, and their thickness was, I may say, insensibly small. Within the envelope, as well as outside, there was none of this scattering. The patches were made more conspicuous by viewing the whole through a cell with an ammoniacal solution of a salt of copper, or through a blue glass coloured by cohalt. In the former case the light from the flame was more weakened than the scattered light, which was richer in rays of high refrangibility ; in the latter case the patches were distinguished by a difference of colour, the patches being blue, while the flame (with a suitable thickness of blue glass) was purplish. The light of the patches exhibited the polarisation of light scattered by fine particles — that is to say, when viewed in a direction perpendicular to the incident light it was polarised in a plane passing through the beam and the line of sight. When the beam was passed through the blue base of the flame there was no scattered light. A luminous gas flame showed the patches indicating scattered light like the flame of a candle, but less copiously. They were not seen in a Bunsen flame or in the flame of alcohol, but were well seen in the luminous flame of ether. 264 Proceedings of Royal Society of Edinburgh. [sess. When a glass jar was inverted over burning ether, the blue part, which does not show scattered light, extended higher till, just before the dame went out, the luminous part disappeared altogether. A Bunsen flame, fed with chloride of sodium, did not show the phenomenon, though the flame was fairly luminous. The phenomenon shows very prettily the separation of carbon (associated, it may be, with some hydrogen) in the flame, and at the same time the extreme thinness of the layer which this forms. It shows, too, the mode of separation of the carbon, namely, that it is due to the action of heat on the volatile hydrocarbon or vapour of ether, as the case may be. At the base, where there is a plentiful supply of oxygen, the molecules are burned at once. Higher up the heated products of combustion have time to decompose the com- bustible vapour before it gets oxygen enough to burn it. In the ether just going out, for want of fresh air, the previous decomposi- tion does not take place, probably because the heat arising from the combustion is divided between a large quantity of inert gas (nitrogen and products of combustion) and the combustible vapour, so that the portion which goes to the latter is not sufficient to decompose it prior to combustion. In the Bunsen flame fed with chloride of sodium, the absence of scattered light tallies with the testimony of the prism, that the sodium is in the state of vapour, though I would not insist on this proof, as it is possible that the test of scattering sunlight is not sufficiently delicate to show the presence of so small a quantity of matter in a solid or liquid state. — Yours, sincerely, G. G. Stokes. P.S — I fancy the thinness of the stratum of glowing carbon is due to its being attacked on both sides — on the outside by oxygen, on the inside by carbonic acid, which with the glowing carbon would form carbonic oxide. 1890-91.] Prof. Tait on Isothermals of Ethyl Oxide . 265 Note on the Isothermals of Ethyl Oxide. By Prof. Tait. (Read July 6, 1891.) The first three pressure-columns of the following little table were constructed from the elaborate data given by Drs Ramsay and Young in their important paper “ On Evaporation and Dissociation,” Part IV. (Phil. Mag., May 1887). They give, in metres of mercury, the pressures required to confine one gramme of oxide of ethyl to various specified numbers of cubic centimetres, at temperatures near to that of the critical point. V 193°-8 A B C 2 73. 72-9 2-3 38-6 38-55 38-3 2-4 34. 34-3 3443 34-16 2-5 31-2 31-3 31-53 31-55 2-75 28- 28-1 28-24 28-41 3 . . . 27-7 27-42 27-45 3-3 27-2 + 27-19 27-3 3-7 27-2 27-19 27-2 4 ... tsD Y* LO 27-20 27-2 5 27- 271 27-12 27-1 6 26-6 26-7 26-80 26-46 7 25-9 25-9 26-00 25-6 10 22-9 22-9 22-89 22-86 15 18-3 18-4 18-26 18-0 20 15-0 15-0 14-97 14-8 50 7- 7- 7-01 7-02 100 37 3-69 3.75 300 1-27. 1-28 1-32 The values in the second column are taken directly from the paper referred to (Table I.), in which 193°*8 C. is regarded by the Authors as the critical temperature. Those in column A were calculated for temperature 194° C. from the pressures given in the same table for 195° C. and 200° C. (occasionally 210° or 220° C.). Those in column B were calculated, also for 194° C., from Table II. of Drs Ramsay and Young, which contains their “smoothed” values of 266 Proceedings of Royal Society of Edinburgh. [sess. the constants. Finally, column C has been computed from my own formula, in forms (given below) which are adapted to volumes greater and less than the critical volume, respectively. A glance at column B shows that, so far as the “ smoothed” data are concerned, the critical point should be sought slightly above 194° C. For, at that temperature, the pressure has still distinctly a maximum and a minimum value, both corresponding to volumes between 3 and 5. Column A, calculated from the unsmoothed data, does not show this peculiarity. Hence I have assumed, as approximate data for the critical point, t = 194° C., p = 27-2, v = i. The last of these is, I think, probably a little too large; but we have the express statement of Drs Bamsay and Young that the true critical volume is about 4-06. From their Table II. , above referred to, I quote the first two lines below, giving (usually to only 3 significant figures) values of dpjdt at constant volume : — v 2 2-5 3 4 5 10 20 50 100 300 % 1-60 0-92 -622 414 -319 -133 -056 -019 -009 -0029 dt f -616 426 -320 -131 -056 -019 -009 -0029 "alC'i 1-65 0*90 *633 -405 The third and fourth lines are calculated respectively from the expressions 0-85 + JLyt v + 3/ v and 1-05 \ 1 ^ v - 1*5/ v ’ representing the co-efficient of ( t — t) in my general formula 1- ( v - v)* v(v + a)(v + y) + R(1 + e \t-t v + a ) v Approximate values of the other constants are now easily obtained ; and we have, for the critical isothermal, while the volume exceeds the critical value, p = 27-2(1 {v-if v(y + 3)(y- 0-5) In attempting to construct a corresponding formula for volumes 1890-91.] Prof. Tait on Isothermals of Ethyl Oxide . 267 lower than the critical range, I assumed 3-5 as an inferior critical volume, and obtained jp=27-2^1 (v- 3-5)3 \ v2(v - 1-5)/ ’ As will he seen by the numbers in column C above, which are calculated from them, these formulae represent the experimental results very closely : — but I am not quite satisfied with the first of them, because the value (3), which it assigns to a, seems to he too large in comparison with v. But, on the other hand, if we much reduce this value of a, the closeness of representation of dp/dt is much impaired. Again, the value ( — 1*5) which is assigned for a in the second of these formulae is inconsistent with the fact that at 0° C and 1 atm. the volume of one gramme is 1*4 e.c. nearly. But a very small change of a will entirely remove this objection, and will not perceptibly impair the agreement of the formula with experiment. The general formula is applicable to temperatures considerably under that of the critical point, for volumes greater than 4. In fact Drs Ramsay and Young seem to assert that at any constant volume p is a linear function of t. But I think even their own experiments show that, for v< 4, there is diminution of the value of dpjdt as soon as the temperature falls below the critical value : — i.e., as soon as we begin to deal with liquid alone. And certainly such is the result which theory would lead us to expect. [It is curious to note that if, in my general formulae (Trans. R.S.E., xxxvi. p. 265), we assume we have a = y, A-C eC v + y (y + y)2 3 and this leads to p=p ( 1 with the condition (v - v )3 v(y + y)! )+ E(1 + dq) t-t 3v + 2y = R t/p. This formula differs by want of one disposable constant from (C) of the paper referred to, but approximates much more closely to it than does either (A) or (B).] 268 Proceedings of Boyal Society of Edinburgh. [sess. Additional Observations on the Development and Life- Histories of the Marine Food-Fishes, and the Dis- tribution of their Ova. By Prof. W. C. MTntosh. Abstract. (Read July 20, 1891.) Since the previous communication to the Society by the author and Professor Prince, not a few dubious points have been cleared up, and, by the courtesy of the Fishery Board for Scotland, further investigations on the general subject carried out at the St Andrews Marine Laboratory. Under the former head may be mentioned the large unknown pelagic egg, with a spacious pri vitelline space, termed Ovum of Pleuronectid B. This has been proved by Mr E. W. L. Holt to be the egg of the Long Bough Dab, so that the ambiguity which has existed since the Trawling Expeditions of 1884 is now at an end. The larval and early post-larval stages of the species have already been described and figured. A more detailed series of observations have also been made on the development of the Lemon Dab or Lemon “Sole,” as it is somewhat ambiguously termed, showing how readily ova can be transmitted long distances, and the larval and post-larval stages reared subsequently. Formerly, only the ovarian egg of Muller’s Topknot was described and figured ; now the fertilized and free-floating egg and its develop- ment have been studied. Like the egg of the Turbot and Brill, this has an oil-globule. The larva is tinted of a deep gamboge-yellow on head, trunk, and upper part of yolk-sac, while the oil-globule is con- spicuous at the posterior and lower part of the yolk by an environ- ment of the same bright hue. Amongst forms hitherto unknown is an ovum somewhat less than that of the Gurnard, with a large privitelline space and an oil- globule. Its development has only been partially followed, and its relationships are unknown. The ova of the three-bearded rockling have been procured in great numbers along with other two species of the same group, and the changes during development described. The most interesting additions, however, are those connected with the larger and the lesser Sand-eels, the reproduction of which was 1890-91.] Prof. MTntosh on Marine Food- Fishes. 269 involved in considerable confusion. Both forms have now been shown to have small demersal eggs which possess a single large coloured oil-globule when ripe, and, moreover, have the zona radiata covered by a special papillose layer which causes them to adhere to plates of glass and other foreign bodies. In the larger Sand- eel the oil-globule is greenish yellow, in the lesser it is reddish or brownish yellow. In the earlier stages of the eggs in the ovary, the particles of greenish yellow oil are scattered throughout the granular yolk, but they gradually coalesce until the mature ovarian egg has only a single large globule. Towards the period of hatching, these globules undergo a curious change of tint in the embryos, just before yellowish pigment appears in the trunk, and the special papillose coating of the egg disappears, leaving the zona bare. As in the herring, no vitelline circulation is established, and the yolk is considerably diminished before extrusion. The investi- gation of the developing eggs has also cleared up the relationships of certain larvse, such as D and G,* which are shown to be the early stages of the forms under consideration. They occur in great numbers at certain seasons, as in March. It was apparent that they did not spring from pelagic eggs, since these would have been captured by the various nets before the advent of the young forms. It is now evident that two spawning periods or a much prolonged one are characteristic of the Sand-eel, the larvse of which are found from March to July,, or perhaps even later. By the frequent use of various kinds of tow-nets on board the 4 Garland ’ and at St Andrews, at all seasons, an endeavour has been made to ascertain the distribution of the pelagic eggs of the food-fishes round our shores. They have been found at all depths, surface, midwater, and bottom, and sometimes in great numbers, especially where cod, haddock, whiting, and other forms congregate. Their abundance, as formerly indicated, is generally in keeping with that of the adults in the neighbourhood, though many are swept into adjacent areas where few or no adults occur. Moreover, while there is a general resemblance in the collections of the pelagic ova of the British coasts, certain areas have features of their own. Thus, the floating eggs of the pilchard and mackerel are characteristic of the south and south-west ; the eastern waters of Scotland, as off the * Trans. Roy. Soc. Edin. , vol. xxxv. pt. iii. pp. 860, 861, plate viii. fig. 1. 270 Proceedings of Royal Society of Edinburgh. [sess. Forth, teem with those of gadoids and pleuronectids, amongst which the cod, haddock, whiting, and long rough dab are conspicuous ; while the sea off the west of Scotland, as in the Clyde area, presents such pelagic eggs as those of the variegated sole, witch, mullet-like species and numerous ova of the dragonet. The period of the year is also more or less characterised by the occurrence of certain forms. Thus in January, off the east coast of Scotland, the eggs of rockling and plaice appear, followed by those of the haddock, bib, and long rough dab. In March and April the eggs of the cod, ling, dab, sprat, gurnard, lemon-dab, brill, and other forms are common. As the season advances the ova of the weever, whiting, dragonet, witch, sole, and solenette are found ; those of the turbot and topknot appearing towards the end of July. 1890-91.] Drs Symington & Thomson on Defective Ossification. 271 A Case of Defective Endochondral Ossification in a Human Foetus (so-called Cretinoid). By Johnson Symington, M.D., and Henry Alexis Thomson, M.D. (With Three Plates.) (Read June 15, 1891.) We have ventured to bring our examination of this specimen under the notice of the Society, not so much for its pathological interest, as for the light which it throws upon the normal mode of growth of the skeleton. There has been a tendency of late to regard endochondral ossification as quite secondary in importance to that of membranous ossification, hut we believe that the case illustrates in a very striking manner the important part played by ossification in cartilage in the growth of the greater part of the skeleton. The specimen is a female foetus, which we received last February from Dr Gronin of Pontypool. It was horn at the full time, and the labour was natural, except that the liquor amnii was in great excess, and that the forceps were used to assist the progress of the head. The father is a healthy man, aged twenty-six years. The mother, who is a year or two younger, suffers from occasional fits, regarded by her doctor as epileptic. They have two healthy children, aged four and two. About three months before this, their third child, was horn, the mother was violently assaulted by another woman. There is no history of any relative of the parents having suffered from any malformation of the skeleton. The foetus weighed 8 lbs. 2 oz. Its general external appearances are shown in Plate I., which is the reproduction of a photograph taken by ourselves. The most striking feature is the shortness of the upper and lower extremities, which are not only greatly diminished in length, hut are very thick, and marked by deep transverse sulci. The head and trunk, on the other hand, are of nearly normal size. A closer examination of the head shows, however, a few peculiarities. Thus its upper part is somewhat enlarged, and the fontanelles are abnormally open. There is a deep sulcus at the root of the nose, 'which is exaggerated by the forward bulging of the forehead ; the nose itself is short and thick. This appearance has been described as resembling that of a bull-dog. 272 Proceedings of Royal Society of Edinburgh. [sess. The tongue protrudes from the open mouth 2 cm. beyond the upper lip, and lies upon the projecting lower lip. The trunk, as covered with soft parts, seems well formed. There is a distinct post-anal dimple placed 4 cm. above the anus. The skin, hair, and nails are normal. Table of Measurements. Total length from vertex to heel, . 40-0 cm. Length from vertex to perineum, . 36*5 cm. Length from vertex to umbilicus, . 28-5 cm. Length from finger tip to finger tip, with arms abducted at right angles with trunk, 28 cm. Total length of arm measured from base of axilla to finger tip, .... 7-6 cm. Total length of lower limb measured from centre of Poupart’s ligament to heel, 8-7 cm. Biparietal diameter of head, .... 10-8 cm. Occipito-frontal diameter of head, . 12*3 cm. Circumference, ...... 20-5 cm. The foetus was injected as soon as it came into our possession with Muller’s fluid, and then kept in this fluid, which was frequently changed. After the specimen was hardened it was carefully dissected. On reflecting the skin a layer of normal fat was exposed, which was rather thicker than usual. The muscles, blood-vessels, and nerves did not present any unusual variations. The muscles of the extremities had thick short bellies, due to the shortness of the bones. All the viscera were found to present a normal appearance to the naked eye. The thymus and thyroid were removed, and submitted for exami- nation to Dr G. L. Gulland, who very kindly favoured us with the following report : — “ Thymus. — In weight and dimensions decidedly above the normal, but the organ is subject to considerable variations in size. Micro- scopically there was nothing worth recording, except that the lobules were rather larger than usual, and that the concentric cor- puscles were better formed than is usual in a nine months’ foetus. “ Thyroid. — Weight and dimensions rather above the normal. 1890-91.] Drs Symington & Thomson on Defective Ossification. 273 Microscopically the following changes were observed. The acini were irregular in size and shape. The blood-vessels remarkably distended with blood, and here and there so tortuous, as apparently to project into the lumen of the acini. The epithelial cells were of large size, roughly cubical in shape, with a large nucleus and relatively large amount of protoplasm. In some parts the cells were adherent to the walls of the acini, but for the most part were lying loose in their interior, almost filling them with desquamated cells, from some of which, more granular than the rest, the nucleus had dis- appeared. There was no marked leucocyte infiltration. “ The changes above described may be included in the term acute desquamative catarrh.” As the foetus had been dead about eight days when we received it, the brain and spinal cord were not sufficiently well preserved for microscopic examination, but we succeeded in demonstrating some interesting changes in the general configuration of the brain. As these, however, were secondary to certain deformities in the cranium, we will defer their description until after that of the skull bones. The essential and characteristic lesion in this specimen is found in connection with the skeleton ; and before proceeding to describe in detail the alterations in the individual bones, it appears advisable to state first, in general terms, that the alterations present are confined to certain groups of bones, while others are quite normal. The latter are — (1) Those which are formed entirely in membrane, e.g., the flat bones of the vault of the skull. (2) Those which, although formed in cartilage, remain entirely or mainly cartilaginous till an advanced period of foetal life, so that their general growth is quite independent of endo- chondral ossification. As examples of these may be mentioned the sternum, costal cartilages, patella, and the tarsal and carpal bones. The departures from the normal affect those parts of the skeleton which, formed in cartilage, largely depend for their growth during foetal life upon endochondral ossification, the cause of the departure being a premature arrest or absence of this process. The bones belonging to this group are the long bones of the extremities, the ribs, the posterior part of the base of the skull and the innominate bones. 274 Proceedings of Royal Society of Edinburgh. [sess. Skull. — As the growth and ossification of the skull is a very complex process it affords numerous illustrations of the above generalisations. Thus the various membrane bones are normal, the parts cartilaginous at birth are of their usual size and form, while those bones which are ossified from cartilage at an early period of foetal life are considerably modified. Further, we find at the base of the skull a marked synostosis of certain bony centres. After the entire head with the brain in situ had been well hardened in Muller’s fluid, a sagittal mesial section was made with a large knife. Similar preparations were made of the head of a normal nine months’ foetus for purposes of comparison. In the sections thus obtained, the principal alterations in the base of the skull are well seen. (See Plate II. figs. 1 and 2.) The part of the base which extends from the foramen magnum to the anterior edge of the pre-sphenoid is abnormally short, measuring 2'4 cm. only, as compared with. 3'6 cm. in the normal foetus. This shortened portion of the base is represented by a single osseous nucleus, the os tribasilare of Virchow, so called because it corresponds to the three nuclei — basi-occipital, post- sphenoid, and pre-sphenoid, which Virchow found united in the skull of a cretin. This single osseous nucleus consists of cancellous bone, its margins are regular, excepting the anterior which is markedly irregular, presenting a number of tapering processes which project forwards into the cartilage. This nucleus is usually regarded as being formed by the fusion of three originally distinct nuclei by a process of synostosis ; the appearance of the anterior margin, as above described, suggests the probability that, at any- rate, the pre-sphenoid element has been formed by an extension from an osseous centre lying posterior to it, and not from a separate centre. The mesial portion of the base of the skull in front of the sphenoid being normally cartilaginous at birth, is in this specimen of normal length. Thus the distance from the anterior edge of the os tribasilare to the level of the fronto-nasal suture was 3 cm., and in the normal foetus the distance was the same from the anterior edge of the pre-sphenoid nucleus to the fronto-nasal suture. The continuation of the mes-ethmoid cartilage under the nasal 1890-91.] Drs Symington & Thomson on Defective Ossification. 275 bones towards the tip of the nose is also normal. We find, therefore, a distinct shortening of the base of the cranium in front of the foramen magnum, this shortening being limited to the parts normally ossified at birth, by intra-cartilaginous ossification. Occipital bone. — The upper portion of the supra-occipital (inter- parietal bone of comparative anatomists) which is developed in membrane is well formed ; its junction with the lower portion of the supra-occipital is indicated by the usual fissure extending inwards from the margin on either side. All the parts of the occipital bone ossified from cartilage, viz., the lower part of the supra-occipital, the ex-occipitals, and the basi-occipital, are much smaller than normal, and are not separated from one another by cartilage as in the normal foetus ; the lower part of the supra- occipital being ossified to the ex-occipitals, whereas normally they are separated by a layer of cartilage several millimetres in thickness. Again, the cartilage between the ex-occipitals and the basi-occipital is absent, although there is no osseous union of these bones. The changes in the basi-occipital have already been described. The foramen magnum is remarkably diminished in size, measuring only -65 cm. in its antero-posterior diameter, compared with 2-2 cm., which we found to be the average of four normal skulls. This diminution is, of course, the direct result of the premature ossification and arrested development of the four elements of the occipital bone which surround the foramen, and by the growth of which the foramen increases in size. Sphenoid. — As already mentioned, the pre- and post-sphenoidal nuclei, together with the basi-occipital, are represented by a single osseous mass, the os tribasilare. The pituitary fossa is distinctly smaller than usual, its antero-posterior diameter being *6 cm. as compared with 1*0 cm. The orbito-sphenoids, or lesser wings, are smaller. The alse-sphenoids (greater wings), on the other hand, are fully as large as normal ; this suggests that they are not formed entirely in cartilage as commonly described, but partly in membrane, and the radiating appearance of their outer edge supports this view. Ethmoid. — The mes-ethmoid, which is normally cartilaginous at birth, is, as we have already mentioned, of normal size. Its lateral masses, although well ossified, are distinctly smaller than 276 Proceedings of Royal Society of Edinburgh. [sess. normal. The inferior turbinate, a cartilage bone, is also small and well ossified. Temporal bone. — The membranous portions (squamo-zygomatic and tympanic) are normal, but the petro-mastoid, developed in cartilage, is distinctly smaller than normal, and its cranial surface is irregular in form, the prominence of the superior semicircular canal and the floccular fossa being indistinct. The auditory ossicles are well ossified, and are practically normal in size. All the foramina piercing the cartilaginous portion of the base of the skull are distinctly diminished in size. The bones forming the vault of the skull — frontals, parietals, and upper part of supra- occipital are normally ossified, but the calvaria presents certain peculiarities. Thus all the fontanelles, mesial and lateral, are en- larged, and the two halves of the frontal and the two parietals are further apart than normal. The reason of the enlargement of the fontanelles is found in the fact that the base of the skull is so short that an abnormal separation of the bones of the vault was necessary to give space for the growing brain. For the same reason the vertical plates of the frontal are bulged forwards. There is, therefore, a general enlargement of the vault of the skull compen- satory in character. All the facial bones developed in membrane are practically normal. The lower jaw is the only one presenting any peculiarity. The ossification of this bone is complex, it being formed partly in cartilage and partly in membrane. On the whole it is distinctly smaller than normal; thus it measured 3 ’3 cm. along the lower body of the body from the angle to the symphysis, as compared with 4*5 in a normal specimen. The vertical depth of the body was very slightly diminished. The portion of the body in front of the mental foramen was of normal length, but its anterior extremity corresponding to the central incisor was partly cartilaginous and imperfectly united with the rest of the bone. This is the only portion of the lower jaw which is formed by the ossification of Meckel’s cartilage, the greater part of the body of the jaw being ossified in membrane external to Meckel’s cartilage. The small size of the lower jaw was evidently due to the fact that its posterior portion is ossified in cartilage. Before proceeding to the examination of the other parts of the 1890-91.] Drs Symington & Thomson on Defective Ossification. 277 skeleton, a brief reference may be made to the condition of the Brain. This organ was hardened in situ , and the entire head was then divided by a sagittal mesial section. Fig. 2 of Plate II. is a drawing of the right half of part of this section, while fig. 1 on the same plate shows the same structures in a normal nine months’ foetus. A comparison of these two figures will demonstrate the fact that the normal relations of the brain have been considerably altered, these alterations being secondary to those in the skull. The lower part of the medulla is notably diminished in size ; this is probably due to the smallness of the foramen magnum. The medulla and pons normally extend from the foramen magnum to the upper edge of the dorsum sellae, but in this case fully one-half of the pons lies above the level of the dorsum sellse. The long axis of the medulla and pons, which is usually directed from below upwards and somewhat forwards, is here inclined upwards and backwards. These changes wTere obviously due to the decrease in the length of the base of the skull in front of the foramen magnum. The optic thalami are also displaced backwards and upwards, and lie between the splenium of the corpus callosum above and the corpora quadri- gemina below. Normally these two structures are only about *3 cm. apart, while in our case they are separated a distance of 1*3 cm. as measured from the splenium to the upper extremity of the nates. The posterior part of the corpus callosum is pushed upwards so that its antero-posterior arch is less marked than usual. The most strik- ing changes, however, we found in connection with the form and position of the cerebellum, which is flattened from above downwards and backwards, so that its long axis is directed from the foramen magnum upwards and backwards. Associated with this, there is an alteration in the attachment of the tentorium and in the situation of the lateral sinus, while the falx cerebelli is greatly increased in length. The torcular Herophili is 6*3 cm. distant from the posterior edge of the foramen magnum, whereas it is generally about 2*5 cm. The lateral sinus and attachment of the tentorium cerebelli correspond to the lambdoidal suture, so that the cerebellar fossa reaches to the upper limit of the supra-occipital. No distension of the third or fourth ventricles, the aqueduct of Sylvius or the foramen of Monro, is seen in the mesial section ; and after the removal of one-half of the brain and cutting into it, the lateral ventricle wras also found of the VOL. XVIII. 1/8/91 2 A 278 Proceedings of Royal Society of Edinburgh. [sess. normal size. In the description of several specimens of a similar nature to ours, hydrocephalus has been assumed to exist from the appearance of the vault of the dried skull in which the fontanelles were increased in size. As already pointed out, we believe this con- dition of the vault is due to the marked diminution in the dimen- sions of the base of the skull, causing the brain to be displaced upwards, and in this way leading to the expansion of the vault. The pituitary body was examined microscopically and found normal. Vertebral Column. — The spine does not differ in length from that of a normal foetus (24 cm.) ; it presents an abnormal curve forwards in its thoracic segment and an unusual degree of lordosis in the lumbo-sacral region • both were found to depend on altera- tions in the thorax and pelvis respectively, as will be described. A mesial sagittal section of the spine showed (1) that the ossify- ing nucleus in the centre of each body was only one-half of the normal size, and (2) that the antero-posterior diameter of each body was *3 cm. less than the average, while the vertical diameter as already mentioned is quite normal. This is explained by the fact that the vertebral bodies grow in the antero-posterior diameter during foetal life by progressive ossification, while increase in their vertical diameter is dependent upon cartilaginous growth. There was no deficiency in the number of the osseous nuclei throughout the spine. The amount of central soft substance in the inter- vertebral discs was excessive. The fourth to the seventh dorsal vertebrae inclusive were examined microscopically ; the appearances which they present will be discussed with those found in the other bones. Thorax. — The thorax, after removal of the soft parts, was found remarkably small and flattened, and on either side presented a furrow or depression along the line of junction of the ribs with their cartilages. The diminution in the capacity of the thorax is indicated by the following comparative measurements— Greatest antero-poste'rior diameter, 3 ‘6 cm. in the specimen, 5*3 in the normal foetus. Greatest transverse diameter, 4 ‘4 cm. in the specimen, 8 in the normal foetus. 1890-91.] Drs Symington & Thomson on Defective Ossification. 279 This remarkable contraction of the chest was found to depend entirely upon the arrested development of the ribs ; the latter are less than half the normal length at birth, while the costal cartilages are of the full average size. The longest, or 7th rib, measured along the convexity 3 "2 cm. in the specimen, 7*8 in the normal. The longest, or 7th costal cartilage, measured along the convexity 5*4 cm. in the specimen, 6 in the normal. The ribs are sharply curved, and join their cartilages at an angle. Externally this angular junction is responsible for the furrow mentioned above, while on the internal or pleural aspect it forms a prominent projection, like that of a rosary. Further, as a result of their shortness, the ribs are more horizontal than normal, and the costal extremity of each is slightly cupped. The 7 th rib and its cartilage were examined microscopically ; the appearances observed will be afterwards referred to. The sternum is of full size and is well formed ; it consists entirely of normal hyaline cartilage, without any trace of osseous nuclei. The Pelvis, like the thorax, is remarkably contracted in all its diameters, especially, however, in the conjugate at the brim, which is less than half of the same diameter at birth. Conjugate at the brim in the specimen, 1*3, in the normal 2 '8 cm. Transverse, „ „ „ 2 -8 „ „ 3 -6 „ Interspinous diameter, . . . 5 '6 ,, „ 7 '4 „ The pelvis is, therefore, generally contracted and flat. Further, the diminution in the size of the pelvis is shown by the fact that the tip of the coccyx projects 3T cm. below the level of the lower border of the pubic symphysis, and 2 cm. below the level of the ischial tuberosity. The above alterations are entirely due to the early arrest of the osseous growth of the constituent elements of the ossa innominata, while the sacro-coccygeal portion of the spine is of the usual size and length, being so independently of ossification. The innominate bone, as examined after dehydration and clearing in naphtha, was found to consist almost entirely of cartilage, the normal osseous 280 Proceedings of Eoyal Society of Edinburgh. [sess. nuclei, to the number of three, having remained exceedingly small. In consequence of this arrest of ossification, the entire bone is dwarfed and sharply curved upon itself, causing the flattening and contraction of the pelvis already referred to. The acetabular cavity was of normal size. Dimensions of innominate bone : — Total height from crest to tuber ischii, in the specimen 4*8, in the normal 6*5 cm. Breadth of ilium from anterior to posterior spine, in the specimen 3*3, in the normal 4*4 cm. Bones of the Extremities. — The various long bones, inasmuch as they depend for their growth in length upon a progressive car- tilaginous ossification during foetal as well as during extra-uterine life, have especially suffered from the arrest of this process. Their total length is, in general terms, only one-half of the normal, as can be readily seen from the following comparative measurements : — In In normal In In normal specimen. foetus* specimen. foetus. Humerus, . . . 3*6 8 ’4 cm. Femur, . . 4 10 cm. Radius, . . . 2*7 6*4 „ Tibia, . . 3*8 8 Ulna, . . . . 2*8 7*3 „ Fibula, . , . . 3*3 7*8 „ Metacarpals, . . 1*2 1*8 „ Metatarsals, . . *8 2*3 „ Proximal phalanges, *8 1'2 „ Proximal phalanges, *5 1 «, These measurements do not fully represent the degree of defective endochondral ossification, because the cartilaginous ends of the bones are of normal size, and the shortening is confined to the diaphyses. This is readily explained by the fact that the carti- laginous ends during foetal life increase in size by growth of cartilage, while, in the case of the shafts, the increase is the result of progressive ossification. The diaphysis is seen, from the following measurements, to be only about one-third of the normal length : — • Length of diaphysis of humerus, in specimen 2T, in normal 6 cm. » „ femur, „ 2*2, „ 7 „ ,, ,, fibula, ,, 1 6, ,, 5*8 ,, 1890—91.] Drs Symington & Thomson on Defective Ossification. 281 In circumference the shafts are quite normal. With scarcely an exception the shafts present very pronounced curvatures, which are in each case an exaggeration of the normal curve of the hone. The humerus is abruptly curved forwards in its lower half, the radius and ulna are uniformly curved, with the concavity on the flexor aspect. The femur is bent almost to a right angle at the junction of the shaft with the lower end, the angle being open posteriorly. The tibia is uniformly convex forwards, and the fibula backwards. The metacarpals and metatarsals have practically no shaft; they possess a minute central osseous nucleus, which is almost surrounded by the cartilaginous ends. The curvatures we have described do not appear to result, like those met with in rickets, from softness of the bones. The shafts are firm and rigid. We would suggest that they depend upon arrest of the cartilaginous ossification and consequent arrest of growth in the axial portion of the shaft, while the peripheral membranous ossification continues. Lastly, the secondary centres of ossification or epiphyses at the ends of long bones, which are normally present at birth, e.g., in lower end of femur and upper end of tibia, are entirely absent. The joints of the extremities have suffered in function in conse- quence of the alterations in the bones. They are disproportionate in size, and their movements are seriously restricted by the large size of the cartilaginous ends of the bones over which the ligaments are tightly stretched. Generally speaking, all the joints are fixed in the flexed position. The condition of the short bones of the extremities is similar to that of the short bones of the trunk. Those which are cartilaginous at birth are of normal size, e.g ., carpus. Those which have a central osseous nucleus at birth, e.g., astragalus, os calcis, but which do not depend for their growth on ossification proceeding from the nucleus, are also of normal size. The central nucleus, however, is distinctly smaller. The difference between the long and short bones is well illustrated by a longitudinal section of the foot passing through the great toe, the tarsus being found of normal size, while the metatarsals and phalanges are extremely short. 282 Proceedings of Royal Society of Edinburgh. [sess. Scapula and Clavicle. — Both these hones were slightly below the normal size — Spec. Normal. Clavicle — total length, . . 3*7 4*5 Scapula — height, . . . 4*2 4-4 „ greatest breadth, . . 2*3 2*6 Microscopical appearances observed in the different Bones of the Skeleton. — After hardening in Muller’s fluid, the bones were decalci- fied in “ Perenje ” and embedded in paraffin. Complete sections were then cut with the large microtome, and mounted in approxi- mate series. Before entering into details, we may state at once that we found no evidence whatsoever of any disease known to affect the foetal skeleton, e.g ., syphilis, rickets. The essential lesion showed itself as an absence, arrest, or perversion of the normal process of endo- chondral ossification of the most definite and universal character in every element of the skeleton in which the process normally takes place during intrauterine life. All the peculiarities which we have described in the specimen are referable to the perversion of ossification, and to this alone. In the examination of the long bones we found that complete sections were of great assistance, especially on comparing these with similar preparations of the normal nine months’ foetus. The large cartilaginous ends consisted of normal hyaline cartilage, actively growing, covered by perichondrium, and traversed by nume- rous large blood-vessels (see Plate III.). The short curved shafts consisted almost exclusively of periosteal bone ; the periosteum itself being actively engaged in ossification in the usual way ; the surface layer beneath the membrane is less compact than is usually the case. From the surface layer a regular system of trabeculae stretches right across the entire thickness of the shaft, to meet a similar series on the opposite side. Peripherally these trabeculae are closely approximated, and are for the most part parallel to each other. In the centre the spaces between the trabeculae are larger and more open, and are filled with marrow ; there is, however, an entire absence of anything in the shape of a medullary canal or endosteum. The process of excavation or hollowing out of the central core of the shaft, so evident in normal bones, is nowhere 1890-91.] Drs Symington & Thomson on Defective Ossification. 283 present. The entire thickness is occupied by the periosteal bone, as described. This condition of affairs naturally presents an important obstacle to the development and ramification of the medullary blood-vessels ; their extension or projection towards the ossifying junction at the ends of the diaphysis would be specially interfered with. Probably this interference with the vessels has played an important part in the causation of the arrest in endo- chondral ossification, to be immediately described. The marrow itself is rich in small vessels, chiefly capillaries, while it is deficient in those of larger size. Further, very few giant cells are to be seen, and scarcely any Howships’ foveolse. The periosteal bone is almost continuously invested by osteoblasts. At the ends of the shaft the periosteal diaphysis is peripherally extended so as to form a cup, which embraces the cartilaginous extremity and a small wedge-shaped mass of endochondral bone. The apex and sides of this endochondral wedge occupy the concavity of the cup, while its base corresponds to the junction between it and the terminal cartilage (see Plate III.). Although the endochondral and periosteal bone are thus in imme- diate contact, they are readily differentiated from each other by their structure and connections. The ossifying junction between the endochondral bone and the terminal cartilage is in the form of an irregularly curved line, concave towards the diaphysis. The endo- chondral bone consists of a very irregular honeycomb, made up of branching masses, each of which contains a core of cartilage in the centre ; the bone is non-lamellated, and stains very intensely with carmine or eosine. It appears to have been formed by a direct conversion or metaplasia of the cartilage into bone, after the manner described by Kassowitz,* as occurring in the course of normal ossi- fication in cartilage, and similar to the process observed under pathological conditions in cartilage of new formation. By direct conversion of cartilage into bone, we further mean to convey that there is an entire absence of proliferative changes, or of any activity whatsoever in the cartilage itself, previous to its ossification ; there are no parallel rows of cells, no progressive formation of medullary spaces by the projection of medullary blood-vessels into the carti- * Die Normale Ossification , Wien, 1881. 284 Proceedings of Royal Society of Edinburgh. [sess. lage. There is an absence of vessels at the ossifying junction. The typical organ-pipe arrangement of structures at the ossifying junction is either not recognisable at all, or only here and there, and that faintly. In several of the bones we further noticed that the zone of cartilage immediately adjoining the ossifying junction was sharply defined or cut off from the main mass of cartilage above it by a curved line or layer, in which the cartilage matrix is partially fibrillated, and the cells flattened and crowded together, resembling the tissue arrangement seen in perichondrium. The appearances described sufficiently account for the remarkable external appearances of the long bones. Previous observers wffio have examined specimens similar to that under consideration, describe as characteristic, the occurrence of an intrusion from the periosteum between the diaphysis and epiphysis, which interferes with the development of bone from the latter (Eberth, Urtel, Bode). We believe this appearance to be fallacious ; it is merely the result of the disproportion in size between the shaft and the terminal cartilage, together with the abrupt curvature of the shaft close to their junction. The apparent intrusion is only seen at the concavity of the curve, in sections close to the surface of the bone. In making our serial sections of the entire bone in its long axis from the surface inwards, we observed that no such intrusion was visible when the level was reached at which complete sections were obtained. The other bones were examined on similar lines ; the seventh rib, for example, with its cartilage, presented appearances which might be exactly compared to those seen in one-half of a long bone ; the short diaphysis of the rib consisted entirely of periosteal bone, cup- shaped at the costal end so as to embrace the cartilage, — a similar arrest of endochondral ossification being observed at the ossifying junction. In the bodies of the vertebrae, the os calcis and astragalus, there was a complete arrest of the ossifying process at the junction of the small central nucleus with the surrounding cartilage; the bone already formed being for the most part nietaplastic, while the marrow was deficient in large vessels and in giant cells. It is obvious that the arrest of ossification in these bones is not to be ascribed to a continuous and excessive formation of periosteal bone 1890-91.] Drs Symington & Thomson on Defective Ossification. 285 without its simultaneous removal or absorption in the interior, which we described as the prominent feature in the -dong bones. Nor can we ascribe the arrest to deficient vascularisation of the general cartilaginous mass in which the arrested nucleus is embedded, for the number and size of the vascular canals in the cartilage is quite equal to the normal. We are absolutely unable to account for the arrested growth in the osseous nuclei in the vertebral bodies, in the os calcis and astragalus, &c., and also for the complete absence of ossifying centres in these bones in which these are normally present at birth (e.g., sternum). Eberth and Muller are of opinion that the arrested development of endochondral bone is the result of an interference arising from an enormous overgrowth of the periosteal bone, while Klebs holds the view that the origin lies in an imperfect development of the medullary vessels supplied to cartilage. We cannot accept the former, because it will not hold for the arrest observed in parts of the skeleton, e.g., os calcis, where there is no periosteal growth whatever, far less excessive growth ; while as regards the latter, our examina- tion of the bones does not show any imperfection in the vessels supplied to cartilage in hones devoid of an external periosteal crust (os calcis). The arteries and nerves of the extremities presented no alteration in their microscopical structure. Most of the published descriptions of similar specimens indicate that the authors are of opinion that it is a real disease of the foetus, instead of regarding the condition, as we do, as a simple arrest of a normal process. Hence many observers describe it as a foetal form of sporadic cretinism, others as a form of foetal rickets. From the latter it is readily differentiated. Its resemblances to rickets are only apparent, thus : — 1. The open fontanelles do not indicate hydrocephalus as has been assumed, but are simply due to the enlarge- ment of the vertex compensatory to the contraction of the base. 2. The contracted chest, the external furrow at the costi- chondral junctions, the apparent rosary, are not due to rachitic changes, but to the shortness of the ribs from arrest of ossification ; the short ribs joining the long carti- lages at an angle. 286 Proceedings of Royal Society of Edinburgh. [sess. 3. The contracted and flat pelvis is not due to softness of the bones, but simply and solely to arrested growth of the innominate bones. 4. The large size of the ends of the long bones is only apparent ; their measurements are the same as the ends of normal bones. 5. The curvatures of the long bones are not the result of any softening, but due to arrest of the central cartilaginous growth and progressive periosteal growth from the peri- phery inwards. The curves, moreover, are all exaggera- tions of the normal curves. 6. The histological changes at the ossifying junctions of the long bones are strikingly different from those seen in rickets. 7. The membrane bones which participate in rachitic processes are quite normal. 8. There is not such a thing as a microscopical record of a pro- gressing foetal rickets, hence its occurrence only rests upon conjecture. The question whether it is, or is not, a foetal form of cretinism is less easily disposed of, chiefly because we really know so very little about cretinism. In the published description of what is called sporadic cretinism, the most striking lesion appears to be a pre- mature arrest of endochondral ossification occurring during infancy or childhood, like that we have here described as having taken place during the early months of intra-uterine life. Further, certain abnormalities of the thyroid have been met with in the former ; and in our specimen there are distinctly abnormal changes in the same organ, consisting in proliferation and desquamation of the alveolar epithelium, together with an extraordinary fulness and distension of the blood-vessels. With reference to the causation of the lesion, we do not regard the assault received by the mother during the sixth month of her pregnancy as of any etiological importance, in virtue of the evident fact that the arrest of development occurred at a much earlier period. Proc. Roy. Soc. E Vol.XVIll u RITCHIE & SON, EDINR. Proc. Roy. Soc.. E din. DEFECTIVE ENDOCHONDRAL OSSIFICATION. 1890-91.] Drs Symington & Thomson on Defective Ossification. 287 INDEX REFERENCE TO LITERATURE. Yirchow, Gesammelte Abhandlungen , Frankfort, 1856, p. 976. ,, Entwickelung des Schadelgrundes, Berlin, 1857. Muller, Wiirzburger med. Zeitsdhrift , i., 1860. Urtel, Foetale Rachitis, In. Diss., Halle, 1878. Eberth, Die foetale Rachitis u. ihre Beziehungen zu d. Kretinismus, Leipzig, 1878. Parrot, Bulletins de la SocUte d' Anthropologic de Paris, 1878, p. 296. Bode, Virchow's Archiv., Bd. 93. Ziegler, Pathol. Anat., II. Theil, 1885, p. 1033. Klebs, AllgemeinePathologie, II. Theil, 1887. , , Beobachtungen u. Versuche uber Kretinismus Arch. f. exp. Path. u. Pharm., Leipzig, 1874, ii. ,, Jahrbuch der Kinderheilkunde , 1880. W. Adams, Trans. Path. Soc. Lond., xxiv. p. 263. T. Barlow, ,, ,, xxvii. 1881. ,, ,, ,, xxxii. 1884. Shattock, ,, ,, xxxii. p. 369, 1884. J. W. Ballantyne, Edin. Medical Journal, June 1890, “Intrauterine Rickets.” EXPLANATION OF PLATES. Plate I. Reproduction from a photograph of the foetus as seen from behind. Plate II. Fig. 1. v.m. section of base of skull and adjacent brain of a normal nine months’ foetus — natural size; B.O., basi-occipital ; B.S., basi-sphenoid ; p.s., pre-sphenoid ; s.o., supra-occipital ; c.g., crista galli ; m., medulla oblongata ; p. pons varolli ; c.g., corpora quadrigemina ; c.c., corpus callosum; O.N., optic nerve; c., mesial lobe of cerebellum ; c\, lateral lobe of cerebellum; F.C., falx cerebelli ; T.U., torcular Herophili. Fig. 2. v.m. section of corresponding region of specimen; O.T., os tri- basilare, representing the three nuclei, B.O., B.S., and P.S., seen in fig. 1. Other lettering as in fig. 1. Plate III. Longitudinal section of right fibula x 6. A. A., cartilaginous extremities traversed by vascular canals ; B., periosteal bone constituting the greater part of the diaphysis ; C.C.C.C., peripheral prolongation of periosteal bone em- bracing cartilaginous extremity ; D.D., wedge-shaped masses of endochondral bone. 288 Proceedings of Poyal Society of Edinburgh. [sess. On the Blood of the Invertebrata. By Dr A. B. Griffiths, F.B.S.E., F.C.S., Ac. (Read 1st June 1891.) I. The Gases of the Blood. — As very little is known concerning the composition and nature of the gases in the blood of the Invertebrata , the following notes may he of some value. The author has ascertained the approximate composition of the gases in the blood of certain Invertebrate animals. The apparatus used for this purpose was that of Gautier slightly modified (fig. 1) ; and the method allows the collection of the blood in vacuo (from the time of leaving the vein, &c.) without any alteration in its composition. The glass receiver ACD (left-hand figure), in which the vacuum is made, has a canula E fastened to its lower end. The canula is drawn out into a fine capillary point, which is pushed into the artery, vein, or under the hypodermis, as the case may be. After introducing the canula into the blood system, the tap B is opened and the blood rises into the receiver. The gases are evolved almost immediately, and by means of the pump they are collected over mercury in the tube ab , where their composition is ascertained. After the introduction of the blood into the receiver the tap B is turned off ; the receiver is then attached to the pump. Before opening the tap A, the receiver is placed in a bath of water heated to about 40° C. The heat assists in the liberation of the gases from the blood. Coagulation is prevented by previously introducing a small quantity of sodium chloride into the receiver (i.e., before the introduction of the blood).* The pump and pneumatic trough do not require description, as they are of the usual kind. The volume of the mixed gases collected in ab having been ascertained, the percentage of each gas is estimated by the ordinary methods of gas analysis. The carbonic * The liberation of carbonic anhydride is accelerated by previously intro- ducing into the receiver a small quantity of a hot solution of tartaric acid. 1890-91.] Dr Griffiths on the Blood of the Invertebrate. 289 Fig. 1. Apparatus for Extracting, &c., the Gases of the Blood. 290 Proceedings of Poyal Society of Edinburgh. [sess. anhydride is absorbed by potash, the oxygen by pyrogallic acid, whilst the amount of nitrogen is represented by what remains. (a) Blood of Sepia officinalis. 100 volumes of the blood of the cuttle-fish contained the follow- ing volumes of the three gases — the volumes being reduced to 0° C. and 760 mm. : — I. II. III. IV. Y. YI. Oxygen, 13-26 12-91 13-14 14-62 14-21 14*34 Carbonic anhydride, 30-12 31-21 32-10 30-14 29-12 29-89 Nitrogen, 1-60 2-00 1-51 1-41 1-73 1-23 The nitrogen is simply dissolved in the blood, but the oxygen and carbonic anhydride are partly dissolved, and partly in a state of loose chemical combination with certain constituents of the blood. The oxygen with the haemocyanin ; and possibly the greater part of the carbonic anhydride is united to certain salts contained in the blood. ( b ) Blood of Cancer pagurus. The blood was obtained from very large individuals, by opening the carapace and passing the capillary point of the canula directly into the heart. 100 volumes of the blood yielded the following volumes of oxygen, carbonic anhydride, and nitrogen, after being reduced to 0° C. and 760 mm. : — I. II. III. IY. Oxygen, ...... 14-79 14-88 14-96 14-85 Carbonic anhydride, 28-62 27-21 27-14 28-39 Nitrogen, 1-01 1-20 1-22 1-30 1890-91.] Dr Griffiths on the Blood of the Invertebrata. 291 (c) Blood of Palinurus vulgaris. 100 volumes of the blood of this animal gave the following results I. IT. III. IV. Oxygen, 14-62 14 71 14-29 14-76 Carbonic anhydride, 30-00 29-62 28-92 2979 Nitrogen, ..... 1-82 1-60 1-20 1-34 (d) Blood of Homarus vulgaris. 100 volumes of the blood obtained from several large lobsters yielded the following results : — I. II. III. Oxygen, 14-99 14-81 14-85 Carbonic anhydride, 31-11 28-84 29-26 Nitrogen, 1-76 1-82 1-85 (e) Blood of Octopus vulgaris. 1 00 volumes of the blood yielded the following results : — I. II. III. Oxygen, ....... 13-33 13-28 13-65 Carbonic anhydride, 30-23 31-29 31-22 Nitrogen, . 1-45 1-30 1-29 (/) Blood of Acherontia atropos. 100 volumes of the blood of the larvae of this moth yielded the following results : — 292 Proceedings of Royal Society of Edinburgh. [sess. I. II. Oxygen, 16*21 16-79 Carbonic anhydride, 32-92 34-24 Nitrogen, ....... 1-09 1-98 It may be stated that the oxygen and carbonic anhydride in the blood of the Invertebrata do not behave according to the law of Dalton (the law of partial pressures) in regard to the absorption of a mixture of gases by a simple fluid. A portion of each gas combines chemically with some constituent or constituents of the blood. It was Magnus ( Poggendorjf s Annalen , vol. xl. p. 583) who first demonstrated that the carbonic anhydride and oxygen of the Vertebrate blood did not obey the law of Dalton; and the same is true concerning the gases of the blood of the Invertebrata. II. The Mineral Matter in the Blood. — The percentages of saline matter contained in the blood of various Invertebrates is given in the following table : — I. II. III. Average. j r Helix pomatia, . 1-065 1-072 1-069 1-068 O 2 05 | Helix aspersa, . . . Limnceus stagnalis, . 1-079 1-080 1-062 1-077 •Sill 1-200 1-203 1-210 1-204 (S 1 Limax flavus , . ( Limax maximus, 1-122 1-119 1-100 1-127 1-115 1*114 1-112 1-120 .2 i . 1 ( Buccinum undatum , . 1-699 1-710 1-698 1-702 i Patella vulgata,'- 1-706 1-721 1-719 1-715 si 1 Anodonta cygnea , 1-002 ' ■ 0-998 1-006 1-002 pq K Mytilus edulis, . 1-796 1-799 1-810 1-801 i| j | Sepia oflicinalis, 2-840 2-862 2-851 2-851 o ,5 | Octopus vulgaris , 3-004 3*032 3-020 3-018 The author has also submitted to analysis the ashes of the blood of several Invertebrate animals. The ashes were obtained by incinerating the blood, partially covered, in a platinum dish at a very low temperature. By so doing the alkaline metals are not volatilised as they are when a high temperature is used. The following results represent the averages of three analyses in each case : — 1890-91.] Dr Griffiths on the Blood of the Invertebrata. 293 Cancer pagurus. Carcinus mcenas. Astacus fluviatilis. Palinurus vulgaris. Homarus vulgaris. Copper oxide (CuO), . 0-22 0-19 0-20 0-18 0-18 Iron oxide (Fe203), trace. trace. trace. Lime (CaO), 3-55 3-57 3-58 3-79 3-54 Magnesia (MgO), 1-91 1-89 1-88 1-90 1-89 Potash (K20), 4-97 4-78 4-82 4-92 4-77 Soda (Na20), 43-90 44-91 44-96 43-98 44-99 Phosphoric acid (P205), 4-90 4-86 4-81 4-87 4-84 Sulphuric acid (S03), . 2*90 2-81 2-75 2-86 2-81 Chlorine, . 37-65 36-98 37-00 37-50 36*96 100-00 99-99 100-00 100-00 99*98 Anodonta cygnea. Mytilus edulis. Pinna squamosa. Sepia officinalis. Octopus vulgaris. Copper oxide (CuO), . 0-23 0-22 trace. 0-24 0-21 Manganese oxide ) (Mn02), . . \ trace. 0-19 Iron oxide (Fe203), trace. Lime (CaO), 3V61 3-72 3-70 2 "31 2V40 Magnesia (MgO), 1-82 1-86 1-83 1-51 1-55 Potash (K20), 4-90 4-80 4-86 4-92 4-90 Soda (Na20), 44-18 43-90 44-02 45-40 45-31 Phosphoric acid (P«05), 4-89 4-82 4-79 4-90 4-88 Sulphuric acid (S03), . 2-80 2-76 2-73 2-81 2-83 Lithium,* . trace. Chlorine, . 37-55 37-92 37*88 37-90 37-92 99-98 100-00 100-00 99-99 100-00 There is no doubt, from the above analyses, that copper f plays an important part in the blood of the Invertebrata ; in fact it plays a similar role to iron in the blood of the higher Vertebrata.% In the majority of the Invertebrata the carrier of oxygen to the tissues is hsemocyanin§ contained in the blood; but in many of the Annelida , as well as in nearly all Vertebrates, the transport of oxygen from the surrounding medium (air or water) to the living tissues is made by means of the haemoglobin of the blood. * Detected by the spectroscope. + See Dr Griffiths’ paper in Chemical News , vol. 48, p. 37 ; also Journal Chemical Society, 1884, p. 94. + In Pinna squamosa, the copper Is replaced by manganese. § Fredericq in Archives de Zoologie Expdrimentale, 1878 ; see also his book La Lutte pour V Existence, p. 84. VOL. XVIII. 1/8/91 2 B 9 294 Proceedings of Royal Society of Edinburgh. [sess. This substance (as is well known) forms an oxygenised combina- tion which is very unstable, and which is carried by the blood across the tissues of the animal, and is there dissociated, yielding its oxygen to the elements of those tissues which require it. Professor Ray Lankester discovered that in some of the Annelida the haemoglobin is replaced by a green-colouring matter — chloro- cruorin ; but in the majority of these animals haemoglobin is present, which the author has proved to be similar in composition to that present in the higher animals. Concerning this point, the author obtained the blood of 500 earthworms ( Lumbricus terrestris) which was treated with benzene. The mixture (in solution) was allowed to stand for twenty-four hours at 0° C., when it separated into two distinct layers. The one containing the colouring matter was now separated from the other ; and about one-sixth its volume of pure absolute alcohol was added. After filtration the alcoholic extract was exposed to - 12° C., when red crystals were obtained. These crystals yielded the following results on analysis : — Blood of Lumbricus. Blood of Dog. I. II. III. Carbon, 53*91 53-86 52-85 Hydrogen, . 7-02 7-10 7-32 Nitrogen, . . . 16-17 Sulphur, 6*41 6*37 0-39 Iron, .... 6-39 0-43 Oxygen, . 21-84 The above analyses prove that the colouring matter of the blood of Lumbricus is comparable chemically to that of a Vertebrate animal — like the dog. The spectrum of this colouring matter is identical with that of Vertebrate haemoglobin. Although haemoglobin is present in the blood of certain Inverte- brates, the chief constituent in the blood of the majority of these animals is haemocyanin — a compound analogous to haemoglobin, but containing copper instead of iron.* * Concerning the coagulation of the blood of certain Invertebrates, the reader is referred to the important paper by Drs J. B. Haycraft and E. W. Carlier in the Proc. Roy. Soc. Edin ., vol. xv., p. 423. 1890-91.] Prince of Monaco on Ship for Study of the Sea. 295 A New Ship for the Study of the Sea. By His Serene Highness the Prince of Monaco. (Read July 15, 1891.) I had wished to render my visit to your country, which has always been in such sympathy with natural science, more interesting by the presence of a new scientific instrument — of a ship con- structed entirely for scientific research; but, in spite of the best of wills, I have, after proceeding for several hours on the way to Edinburgh, been obliged to return to the Thames, in order to allow the builders to finish their work, in which they are unfortunately in arrear. But it would have been very painful for me to give up this visit which promised me so much satisfaction, and I have come even without my ship to speak to you about her and to claim in advance your sympathy with its future work. It is to do honour to Oceanography, — of that science whose field has only just begun to open itself to investigation, — that your society, one of the highest in the scientific world, has assembled to-day. And what is Oceanography? This is a question which, at the present time, may reasonably be asked by anyone of ordinary education, but it is one which will soon appear as strange as would be “What is Geography?” Yet Oceanography constitutes this most important department of Physiography, because it includes the study of the immense realm of the waters, with all the secrets which it can disclose to us of the past of our planet and of the conditions of its formation, while at the same time it can enlighten us on many points of its future. In fact this science includes in its programme the questions of the formation of the solid layers which, slowly deposited at the bottom of the ocean during thousands of centuries, are preparing under our eyes future continents; unless our earth be now too old to react as of old, when the material accumu- lated in the depths of its seas raised itself into subaerial mountains with all its fossil inhabitants, the faithful guardians of the secret of the great problem of the origin of life. 296 Proceedings of Royal Society of Edinburgh. [sess. To establish the laws of Oceanography it is necessary to know the temperature, the motion, the chemical constitution, the density, and the zoology of the waters of the ocean at all depths. It is necessary to borrow a little from all the natural sciences. It is thus that Peter the Great appears to have first broken ground in the science, by having soundings made in the Baltic, the White Sea, and the Sea of Azof. Soon afterwards it was your countryman, James Cook, who, amongst the first, engaged in oceanographical research in one of his great voyages on board the “ Resolution.” As is usual in the early stages of all sciences, the means at disposal were of the most primitive kind, and until your magnifi- cent a Challenger” expedition, the observations collected in the course of numerous voyages, indicate much good will, without offering any of the precision or continuity of accurate observation, which are expected of the scientific observations of our time. But the minds of the men who made these early observations gradually acquired a certain sagacity due to the contemplation of nature in the open, which it is difficult to acquire -within the four walls of a laboratory, and without which great discoveries often remain barren. It is thus that the great Darwin returned from his long voyage in the “Beagle ” absorbed in the conceptions from which sprang the theories which threw a light on the scientific world as unexpected as would the rising of the sun in a new part of the horizon. Nowadays the scientific men who forsake their laboratories for the open air are many, but the organisation of a scientific oceanic expedition is not easy. Sometimes the captain of the ship is not enough of a man of science to understand what science demands and to devote himself with the necessary zeal to it, he executes coldly the orders which he has received; sometimes it is the scientific men on board who are not sufficiently acquainted with the sea and life on board ship to be able to utilise their time to the best advantage of their scientific work. Owing to these causes, also, difficulties often arise between the captain and the scientific observers. Further, the keeping up of millions of men, the manu- facture of hundred ton guns, and the launching of ironclads and torpedo vessels, do not leave much room in the budgets of most nations for intellectual work or for the labour of men who would 1890-91.] Prince of Monaco on Ship for Study of the Sea. 297 willingly devote themselves to the best interests of their fellow- men. It was consequent on such reflections that, some seven or eight years ago, I undertook the mission which lay before me, because I was at once a sailor and devoted to science. The only means at my disposal, a sailing schooner of two hundred tons, was unfortu- nately much too restricted for the realisation of the enterprises which I dreamt of. But what can we not achieve when we are on the path of good and our whole heart is in it ? The “ Hirondelle ” was supplied in 1886 with several hemp ropes of different sizes for sounding and dredging and with a deep-sea trawl similar to that of the “Blake,” and with a large iron pot and various sounding leads. With this material, worked by the arms of the crew, I made soundings, temperature observations, and dredgings in the Gulf of Gascony, down to a depth of five hundred metres. But the labour of these operations was considerable, and the crew were sometimes kept at the capstan for four hours at a time. And as the weather of that year was very bad there were series of twenty-five days during which it was impossible to leave off one’s oil skins, for the trawl could be worked even in a heavy sea. In the intervals of work the 900 metres of dredge rope of the trawl, hardened by the water, and coiled all round the deck of the little schooner, rose like an oval wall above the heads of the men, who, always in the best of spirits, never murmured at the ■work, and even showed much intelligent curiosity in the results. In the following years my working gear was much improved by the use of steel wire for sounding and dredging purposes, as also by the use of a special winch, still, unfortunately, worked only by the muscular exertions of my crew, and I was able to rectify many deficiencies in my methods of work ; aided also by that will of success, which is the firmest support of workers, I succeeded in carrying my researches to a depth of 3000 metres round the Azores and off Newfoundland. But then, perfected in their training and stimulated by a certain pride, my crew worked as long as twenty hours at a stretch in dredging in 2800 metres. A pot similar to one which I had lost in moderate depths in 1886, when used with handier material, gave me magnificent results in depths of as much as 2000 metres, but this was always accompanied by very hard 298 Proceedings of Boyal Society of Edinburgh. [sess. work and continual calls on the imagination to surmount unfore- seen difficulties as they arose. During these expeditions, which extended over three years, I made experiments on the direction and velocity of the great surface currents of the Northern Atlantic, by means of 1700 specially loaded floats, which were thrown overboard in three distinct regions be- tween Europe and America. The results of these expeditions are being gradually published, and they show that the work done in the “ Hirondelle ” will leave a definite mark in the history of the science. Zoology gains several hundreds of new species and genera spread over all its branches, as well as fresh knowledge about the geo- graphical and bathymetrical distribution of certain animals ; and this is due principally to the fact that I have applied systemati- cally all the means of research at my disposal to one and the same region. Oceanography will very shortly be enriched by a chart of the surface currents which I am preparing with the data furnished by the 224 floats which have been picked up out of the 1700 thrown over during my experiments. We have here a photograph on a reduced scale of this work which I am just finishing. On this subject I shall confine myself to-day to pointing out that, possessing exact and authentic information on the positions of departure and arrival of a great number of these floats, which have come at first directly, and sometimes in numbers at a time, towards certain points of the coasts of Europe, I have been able during the six years which have passed to follow their successive appearances from the north of Sweden to the Canary Islands, then their return towards America, and even from some already, the repetition of this cycle. And thanks to these data which all afford mutual support, I have been able to construct my chart under conditions of exacti- tude which make of it an experimental document worthy of complete confidence as regards the general direction and the mean velocity of the currents of the North Atlantic. But if I remind you of these things to-day, it is to direct your attention to the fact that many of the privileged of fortune might easily contribute to the civilisation of humanity by elevating its intellectual power, if they would bring themselves into touch with the great efforts of science. The vast 1890-91.] Prince of Monaco on Ship for Study of the Sea. 299 domain of the sea is full of mysteries which the work of man will surely penetrate, and the collection of observations which enable savants to advance along this path would be a noble aim in the life of many people who weary themselves in the abundance of their goods, and wear themselves out in their uselessness. To-day I am able to realise the plans which I have dreamed of so often, when, each year, during months of struggle with the sea, I could perceive treasures for science without the power of securing them. And I should have rejoiced to bring before yon, the initiators of the great efforts made in this line, the god-parents of the Challenger, to bring before you my ship, the “Princesse Alice,” the work of my waking thoughts and of my devotion to science. The Messrs Green of Blackwall, who have built her, may be proud of their work, and their skill has powerfully aided me in the realisation of my ideas. The yacht “ Princesse Alice ” has a displacement of 650 tons, and I have only fitted her with auxiliary steam power in order to reserve as much space as possible for the arrangements necessary for engaging in serious scientific work, combined with the wants of social family life. Nevertheless, the engine-room is sufficiently large to accommodate various apparatus, which are thus under the management of one engineer ; they are — a dynamo, an ammonia freezing-machine, and a water-still. The dynamo supplies 100 lamps of 16-candle power for interior lighting, three 100-candle power lamps for lighting the deck when work is being carried on during the night, and a search light of 10,000 candles for illuminating the sea when work is being carried on in boats, and for picking up buoys. The freezing-machine has several uses. By means of the liquefaction of ammonia gas, it produces a very low temperature, which is directly communicated to a liquid which does not freeze at this temperature, a brine which is then conveyed in tubes to the refrigerating chamber. This receptacle can contain several moulds of different forms and sizes to receive the objects which, for anatomical, histological, or zoological purposes, it may be wished to freeze, in order to protect them from the damage inseparable from the chemical processes at present in use. Once frozen, these objects will be placed in a cold chamber, kept at a temperature near that of 300 Proceedings of Royal Society of Edinburgh. [sess. congelation by tbe refrigerating liquid which circulates in a coil of pipes close to the roof of the chamber. The refrigerating chamber is placed in the central laboratory ; the cold chamber is immediately below in the hold, where it occupies a space of about five cubic metres. A branch pipe takes the refrigerating liquid to the laboratory tables, to be used in delicate biological experiments. On the other hand, the cold chamber is large enough to accommodate a part of the ship’s provisions. The water-still is a “ Yaryan ” apparatus, very simple and powerful for its size, which furnishes 2J tons of fresh water per twenty-four hours for use in the boilers and the laboratories. Several steam-engines are to be found at different points in the ship ; a winch for working the dredge ropes and lighter lines for temperature and other observations is fixed to the deck in front of the foremast, and can lift 6 tons to a height of 1 metre in a second. A sounding-machine, which I have constructed on new ideas is fixed in front of the mizzen-mast ; it acts automatically, and can indicate any depth to be found in the sea. A large reel with two drums works in' the hold. It carries on one side 6000 metres of cable in one length, to which a reserve of 4000 metres of stronger cable is ready to be joined for very great depths. On the other side there are 5000 metres of cable, divided into lengths of 500 metres. The first will be used for dredging, the second for sending down pots, and generally for operations which require the apparatus used to remain at the bottom of the sea for a time, while the cable is buoyed. Finally, there is another small double reel, which is very light, and carries pieces of cable varying from 100 to 500 metres in length, which are used for small operations, for which it would be useless or inconvenient to use longer pieces. To summarise, the actual equipment of the ship allows of sounding everywhere, dredging in 8000 metres, and laying out pots or other apparatus on the bottom at depths up to 6000 metres without the least difficulty. The stoke-hold is arranged in a way suitable to the equipment of the ship. It contains two boilers, a small and a large one. The first is used to drive the auxiliary machines (winch, dynamo, &c.), and when applied to the main engines can drive the ship three 1890-91.] Prince of Monaco on Ship for Study of the Sea. 301 knots per hour; the second, along with the first, gives a speed of nine knots. Thus the ship can be economically steamed slowly while work is being carried on, and she can also be worked under sail when the wind permits. The products of the scientific work are distributed amongst three laboratories, as follows : — The materials as collected are received in a laboratory situated on deck abaft the mainmast, and communicating by a lift with the central laboratory immediately below, and the lift descends as far as the cold chamber in the hold. After a first picking over, for the elimination of useless matter, the zoological material is sent to the central laboratory, and the oceanographical material to a third labora- tory in the after part of the ship, which is devoted to chemistry and physics. These laboratories are lighted by large scuttle lights , and the arrangement of the tables allows of four or five persons working at each of them without interfering with one another. Like the rest of the ship, they are heated by steam on a special system. As to the general service of the ship,- it is arranged according to what modern progress has recognised as most useful and most practical. I do not think that one ought to carry too far an analysis or other delicate observations during the voyage. The movement and the noise, however subdued they may be, are a cause of constant disturbance ; on the other hand, one would have to have exceptional power over one’s mind, to be able to arrest it in the exciting moments of a general investigation, whilst other experiments, of an engrossing character, were being carried on without interruption, on the largest scale and with full power of the ship. To follow out under these conditions any profound idea does not seem to me to be an easy matter, and I think that it ought to be one’s chief object, during the work at sea, to make the best arrange- ments for collecting a great number of facts at the most favourable moments, and for noting all the details which strike the eye and the mind. It is thus that a painter makes a study from nature, which afterwards becomes a masterpiece, when the impressions he has received have matured in the silence of the studio. And now I regret that I must terminate this communication to the Royal Society very differently from what was originally my intention, viz., without being able to invite you to visit the 302 Proceedings of Royal Society of Edinburgh. [sess. new ship which I should have been proud to show to men such as Sir William Thomson, John Murray, Buchanan, Buchan, and to the intelligent cultivators of science who fill this room. I could then have justified the flattering reception which you are giving me ; but in the hope of repeating at a later date, and under perfectly satisfactory conditions, this visit to the scientific representatives of Edinburgh, who will form the best judges of my future work, I thank you cordially for your very kind attention. 1890-91.] Prof. C. G. Knott on Electric Resistance of Cobalt. 308 The Electric Resistance of Cobalt at High Tempera- tures. By Professor Cargill G. Knott, D.Sc., F.R.S.E. (With a Diagram.) (Read July 6, 1891.) The manner in which the electric resistance of cobalt varies with high temperatures does not seem to have been studied with any great care. The peculiar behaviour of iron and nickel as regards their change of resistance with temperature is now well known.* With a view to discover if cobalt presented any similar peculiarity, I set Mr Omori, one of the physical students in the Imperial Uni- versity, Japan, to investigate the question. The chief results are embodied in the present short paper. The piece of cobalt used was cut from a sheet of rolled cobalt which had been given me by Professor Tait. Dr E. Divers, E.R.S., very kindly determined its composition by analysis of a small quantity (about 20 grains) supplied to him. The result of the analysis is as follows : — Carbon found, . . . . 0*77 per cent. Silicon, . . . . . 0T5 „ Iron, ..... 0*73 „ with a minute quantity of manganese and perhaps y1^ per cent, of a metal undetermined. The carbon might be as much as 1 per cent. Dr Divers regarded the cobalt as of remarkable purity for a furnace product. The experiments now to be described were carried out in January and February of 1890. The method was essentially the same as that used in my earlier investigations on nickel. Four stout copper rods, 60 cm. long, 0'7 square cm. cross-section, were fixed in a vertical position some little distance apart. Their lower extremities were joined in pairs by two coiled wires, one of which was a * See my paper “On the Electric Resistance of Nickel at High Tempera- tures,” Trans. Roy. Soc. Edin., vol. xxxiii., 1886. 304 Proceedings of Royal Society of Edinburgh. [sess. specimen of platinum wire and the other the cobalt strip that was the special object of investigation. The upper extremities of the rods were joined by stout copper strips to a commutator connected to a Wheatstone Bridge resistance-box of ordinary con- struction. In one series of experiments the lower ends of the rods with their connecting wires were dipped in a vessel of oil which could be heated up to a temperature of 240° C. A thermometer, centrally placed so that its bulb lay at the mean level of the platinum and cobalt coils, was used for measuring the temperature. The oil was heated very gradually and was kept briskly stirred until a few seconds before a reading was to be taken. One of the wires was meanwhile thrown into the Wheatstone Bridge, and the resistance adjusted slightly in advance. The temperature was then allowed to rise very slowly until reversal of the commutator in the galvano- meter branch gave no deflection. When the equilibrium was thus attained the thermometer reading was noted. In this experiment chief attention was given to the cobalt ; a few measurements of resistance were made with the platinum, sufficient to give the most important temperature coefficient. The resistance curves for the cobalt and the platinum are shown in the diagram, Nos. 1 and 2. All corrections have been carefully applied and the resistances are in legal ohms. By interpolation amongst a number of contiguous measure- ments, the resistances corresponding to the temperatures 100°, 140°, 180°, and 220° C. were calculated. They are given in Table I., together with the measured resistance at the tempera- ture of the air. Table I .—Resistance of a Cobalt Strip in Legal Ohms at Different Temperatures. Temperature. Resistance. First Diff. Ratio. 7°‘5 C. 100 140 180 220 0-09604 •12340 •13694 •15210 T6859 •01354 •01516 •01649 ' 1T097 1-1109 ! 1-1084 i 1 1890-91.] Prof. C. G. Knott on Electric Resistance of Cobalt. 305 Since the second differences have appreciably different values, it is impossible to represent the law of change by means of a parabolic function. But the remarkable constancy of the ratios of successive pairs of resistances suggests an exponential function of the tem- perature as the expression for the resistance. Thus we may put, r = aeu from which we find, if t is the temperature in degrees centigrade, k — '002605 a= -09511 According to this formula, which strictly applies only to tempera- tures above 100°, the resistance at 7°*5 should be *09698, almost exactly 1 per cent, too high. In the paper already referred to, I found that the same form of expression held very approximately for the case of one of the nickel wires, the only essential difference being in the value of k, which for nickel was *003. The resistance of cobalt there- fore does not change so quickly with temperature as does the resistance of nickel. In the second series of experiments, the lower ends of the rods, with their connecting wires, were inserted into a porcelain vessel. Asbestos was wrapped round the wires ; and the whole was heated in a charcoal furnace. The observations of resistance were made as the system was cooling, the cobalt and platinum being thrown alternately into the Wheatstone Bridge. The instants at which the balancings were effected were carefully noted, so that it was an easy matter to interpolate between two successive measurements for the one wire that resistance which corresponded to the inter- mediate measurement for the other wire. In this way, for every measured cobalt resistance, the corresponding resistance of platinum was calculated by a simple interpolation. After all corrections were applied, every resistance was divided by the resistance of the same wire at 7° C. By this treatment the results of the four different experiments were reduced to identically the same condition, so that direct comparison was possible. Each single experiment contained from 20 to 30 distinct pairs of measurements. These numbers were then classified into groups, 306 Proceedings of Royal Society of Edinburgh. [sess. and by a rigorous process of interpolation, the cobalt resistances corresponding to assumed values of the platinum resistances were calculated. These are the numbers given in Table II., which epitomises the results of the four distinct experiments. The first column contains the platinum resistances, taken as convenient multiples of the resistance at 7° C., measured after the experiment. These virtually serve as a temperature scale. The other columns give in order the corresponding resistances of the cobalt, likewise all expressed in terms of the cobalt resistance at 7° C., measured after each experiment. Table II. Platinum Resistances. Cobalt Resistances. Experiment Experiment Experiment Experiment I. II. III. IV. 2-0 5-8047 5-7996 5-9748 6-0361 1-8 4*5101 4-3423 4-4511 4-4580 1-6 3-1822 3-0536 3-0932 3*2216 1*4 2-2029 2-1795 2-1111 2-2602 1-2 1 -5329 1-5337 1-5050 1*0 1-0000 1-0000 1-0000 1-0000 If we assume that the changes in the platinum resistance follow the same law as in the earlier experiment with the oil, the rise of temperature, which will just double the resistance, is about 680° C. ; and the interval from 1 to 1*2 may be taken as corresponding to a rise of temperature of 136° C. According to the experiment in oil, this rise of temperature would have increased the resistance of the cobalt in the ratio 1*425 to unity. It is apparent then, that under the influence of the first excessive heating, the cobalt has been considerably altered in its properties, so that the average temperature coefficient for resistance up to 150° C. has been increased by a quarter. The only other pos- sible explanation of this discrepancy is that the corrections to be applied for the resistances of the connections or contacts may have been underestimated in the second series of experiments, or overestimated in the first. There could, however, be no doubt as to the resistances of the connections, which were the same in 1890-91.] Prof. C. G. Knott on Electric Resistance of Cobalt 307 all experiments, and were measured with great care. If again the resistances of the contacts had changed to any great extent, this would declare itself in the measured resistances at 7° C. made before and after the first severe heating. In Table III. these measured resistances, corrected for connections, are given. They were all made at 7° C., except the first pair (taken immediately before the first heating), for which the temperature was 7° ’5 C. Table III. Resistance in Legal Ohms of When measured. Platinum. Cobalt. •8525 •09724 Before 1st heating. •85028 •09135 After 1st ,, •85028 *09354 „ 2nd ,, •85013 •09674 „ 3rd „ •85232 •09978 , , 4th , , The fall in resistance after the first heating is probably due to some change in the contact resistances — decrease evidently. But even if this were large enough to sensibly affect the second sig- nificant figure in the calculated value of the temperature coefficient, its effect would be to diminish this coefficient. Consequently, we must accept the conclusion that the first excessive heating has profoundly influenced the qualities of cobalt as regards its change of resistance with temperature. Table III. shows us also that whereas the platinum resistance at 7° C. has not been changed at all by the second heating, and only slightly by the third, the cobalt resistance goes on steadily increasing. After the experiments were completed, the cobalt was indeed found to be much altered by oxidation. It had become exceedingly brittle, and broke into small pieces when it was being detached from the copper rods. This steady deterioration in condi- tion of the cobalt explains the inferiority in point of regularity of the third and especially the fourth experiment, as compared with the first and second. It is matter of surprise that, in spite of the great alteration in structure taking place in the cobalt strip, the general behaviour of 308 Proceedings of Royal Society of Edinburgh . [sess. the cobalt, as shown in the first three experiments, is essentially the same. This is well shown by tabulating the rates of change themselves. These quantities were calculated from the observa- tions by the same general method of interpolation as was used in calculating the numbers of Table I. They are given in Table IV., of which the first column contains the platinum resistances to which the tabulated rates of change correspond. Table IV. Platinum Resistance (or Rates of Change of Cobalt Resistance per Unit Change of Platinum Resistance. Temperature). Experiment Experiment Experiment Experiment I. II. III. IV. 2*0 7*02 7-30 10-33 9-15 1*8 6-19 7-24 6-74 5-09 1-6 5-45 5-57 6-63 6-10 1-4 3-76 3-58 3-65 3-66 1-2 3-58 3*23 2-78 I have thought it sufficient to give the condensed numerical results as contained in Tables I., II., and IV. The individual ob- servations upon which these results are based are entered graphi- cally in the diagram. Curves 1 and 2 have already been mentioned. They show the march of resistance with temperature as measured on a mercurial centigrade thermometer. In curve 3, the platinum resistances are the abscissae, and the ordinates are the corresponding cohalt resistances. The points belonging to the various experiments are distinguished by special mark. In one particular, cohalt resembles iron and nickel in its behaviour. There is a rapid increase in the steepness of the curve at higher temperatures. In iron and nickel, however, this rapid increase is followed at still higher temperatures by a distinct decrease, the curves bending so as to present a concavity towards the temperature axis. Neither Table IV. nor the curves give any hint of such a tendency in cobalt. It will be seen that Experiments I. and II. are in fair agreement throughout; and that all four experiments point to the existence of a critical temperature at which the re- COBALT RESISTANCE • SCALE FOR (3) PROFESSOR KNOTT ON THE RESISTANCE OF COBALT. 1890-91.] Prof. C. G. Knott on Electric Resistance of Cobalt. 309 sistance begins to increase rapidly with rise of temperature. This critical temperature is about the stage 1*5, which corresponds ap- proximately to 350° C. The phenomenon may be broadly stated in these terms. Between temperatures 400° C. and 700° C. the resistance of a cobalt strip increases on the average at a rate nearly twice as great as the average rate of increase between 0° and 300° C. 2 o VOL. XVIII. 12/9/91. 310 Proceedings of Boy al Society of Edinburgh. [sess. The Thermoelectric Positions of Cobalt and Bismuth. By Professor Cargill G. Knott, D.Sc., E.R.S.E. (Read July 6, 1891.) So far as I know, the only satisfactory determination of the position of the cohalt line on the thermoelectric diagram was made by Professor Tait’s students in the Physical Laboratory of Edinburgh University some fifteen years ago. The position of the cohalt line, so found, was given along with the positions of certain alloys in a paper by Professor J. Gordon MacGregor and myself, published in the Transactions of the Royal Society of Edinburgh , vol. xxviii. (1878). The particular specimen of cobalt used in these early experiments was a short rod obtained by electrolytic decomposition. The noteworthy facts regarding its thermoelectric line were that it lay below nickel on the diagram, and that its inclination to the lead line was much greater than the inclinations of the iron and nickel lines. As a laboratory exercise, I gave to Mr Sawada, one of our students of physics, the task of studying the thermoelectric properties of the cobalt described in the preceding paper on electric resistance. The plan adopted was to form a multiple arc of palladium and bismuth, and, by proper adjustment of the resistances in these branches, to obtain an intermediate line which should cut through the cobalt line at temperatures within easy reach. Such an intermediate line passes through the neutral point of the component metals. It divides the region between their lines so that any transversal is cut into portions which are directly as the resist- ances in the branches of the multiple arc. Thus, by varying the ratio of the resistances in these branches, we may sweep through the region between the two corresponding diagram lines, interpolat- ing, so to speak, any intermediate line suitable for our purpose. The extreme accuracy with which we can measure electric resistance enables us to fix the position of this intermediate line as accurately as the positions of the component lines are known. In the present case, the low position of cobalt on the diagram very much circumscribed the choice of metals for the multiple arc. 1890-91.] Prof. C. G. Knott on Cobalt and Bismuth. 311 Bismuth had to be one of them, as it alone was known to lie below cobalt. The other metal fixed upon was palladium, a substance convenient in every way. Its diagram line is straight up to high temperatures ; and its character does not perceptibly change even after severe heatings. Unfortunately, however, the use of bismuth limited the investigation to moderate temperatures only. The bismuth was broken up into small pieces, which were packed tightly into the bore of a siphon-shaped glass tube. Gentle heating in a Bunsen flame sufficed to melt the metal, which ran together and solidified on cooling into a fairly uniform rod. The junction wires were fused into the ends of the bismuth rod. As finally set up, the apparatus consisted of a triple cobalt palladium bismuth junction dipping in oil. This formed the “hot junction.” Besistance boxes were included in the palladium and bismuth branches. Because of the magnitude of the thermoelectric forces between these three metals and copper, great precaution was necessary in keeping the various cold j unctions at the same tem- perature. The palladium branch always contained 100 ohms resist- ance j and the bismuth branch never contained less than 200. For each of the seven selected ratios of resistance, a careful series of thermoelectric observations was made. A delicate high-resistance galvanometer was used ; and the temperatures were measured by a mercurial thermometer. The electromotive forces between the cobalt and each intermediate “ equivalent metal ” were in this way measured directly. From these the thermoelectric powers at chosen temperatures could be calculated. But one of these equivalent metals was palladium itself, obtained by making the resistance of the bismuth branch infinite. Thus, by a simple process of subtraction, we obtained the thermoelectric powers between palladium and all the others. These quantities, calculated for 0° and 100° C., are given in the following table. The symbols Bi, Co, Pd stand for the metals bismuth, cobalt, and palladium respectively. The various equivalent metals are represented by the symbol Pd Biw, where the number n represents the ratio of the resistances in the bismuth and palladium branches. Thus Pd Bi2 means that, since the palladium branch always contained 100 ohms, the bismuth branch contained in this case 200 ohms. The electromotive forces, from which these values were calculated, were measured in microvolts. 312 Proceedings of Royal Society of Edinburgh. [sess. Thermoelectric Powers referred to Palladium. Metal. Thermoelectric Power at Neutral Point with Cobalt. 0° C. 100° C. Co, . 7*00 17-31 Pd Bi13, 5-98 6-46 - 10° '*4 C. Pd Bi8, 9-38 9-96 + 24°"5 Pd Bi5, 14*45 14-69 74°-l Pd Bi4, ...... 17-44 17-44 101°-4 Pd Big 21-73 22T3 148°-9 Pd Bi2 29-10 29-55 224°-0 Bi, . . . . . . . 86-0 8S-8 The numbers in the last row have been calculated from the numbers in all the six Pd Bi rows. For if p is the thermoelectric power between Pd and Bi, and pn the same between Pd and Pd BiW) we know that P~Pn_nj Pn 1 or p = (n+ l)pn. Thus, from the six sets of values corresponding to pn we obtain the following values for p at 0° C. and 100° C. : — n+ 1. p at 0° C. p at 100° C. 14 83-7 90-4 9 84-4 89-6 6 86-7 88-1 5 87-2 87-2 4 86-9 88-5 3 87-3 88 -7 Means, . . 86-0 0-8 88-8 0-7 This table is obviously an indication of the accuracy of the experiment. And now, referring everything to the lead-line, and expressing the thermoelectric power in the form p = A + IB,. 1890-91.] Prof. C. G. Knott on Cobalt and Bismuth. 313 we obtain for the coefficients A and B the following values : — A B.102. Lead, . . 0 0 Palladium, . - 6-18 - 3-55 Cobalt, -13-18 -13-9 Bismuth, -92-2 - 6-4 According to the numbers deduced by Fleeming Jenkin from Matthiesen’s experiments, bismuth lies four times further from lead than does cobalt. Here we have it seven times. Professor Tait’s electrolytically-deposited cobalt lies four and a half times further from lead than does palladium. Here we have it a little over two times. According to Becquerel’s numbers, given at the end of the English translation of Mascart and Joubert’s Electricity and Magnetism , the ratio at 50° C. of the thermoelectric powers of palladium and bismuth relatively to lead is as 7 to 40. Here we have it 1 to 16. These discrepancies are not surprising. We know* how variable are the thermoelectric properties of stable alloys intended to have the same composition, and how a very slight change in composition may be accompanied by a very large change in thermoelectric quality. The present experiments must therefore be judged of altogether on their own merits. Now, a simple comparison shows that Professor Tait’s electrolytically deposited cobalt will fit in to the region between lead and bismuth very much as Matthiesen’s cobalt fits in to his own series. Thus the cobalt investigated here seems to differ from the other specimens in much the same way. The new cobalt, indeed, has its diagram line at ordinary atmos- pheric temperatures above the line of Tait’s nickel, for which A=— 21 ‘8. This unexpected result was at once tested. A rough experiment was made with a nickel cobalt couple, and a neutral point was obtained at a moderately low temperature. The cobalt line, therefore, begins above the nickel line, but because of its greater downward inclination gets below it at temperatures above 100° C. * See the paper by MacGregor and myself, already referred to ; also my paper on “ The Electrical Properties of Hydrogenised Palladium” {Trans. Roy. Soc. Edin vol. xxxiii., 1886). 314 Proceedings of Royal Society of Edinburgh. [sess. As regards the inclination of the cobalt line, the present result agrees as well with the earlier result as could reasonably be ex- pected with two quite different specimens of the metal. Thus, expressed in the same units, the thermoelectric power of Tait’s electrolytically-deposited cobalt is -26-3-0T16*, while for the present specimen p= — 13*2 - 0*139£ . With the exception of the sharp upward bend in nickel, this gives the greatest inclination yet obtained for a thermoelectric line. The downward trend and comparatively large inclination of the bismuth line are also worthy of note. Because of the position of the line, as a whole, lying far below the lines of all other metals, this large inclination does not greatly influence the electromotive forces, so that with bismuth couples the electromotive force is very approximately proportional to the temperature. This fact, of course, prevents us from making a very accurate determination of the coefficient B, which in the present experiment has a large pro- bable error. The mean value is a little larger than that indicated by Battelli’s direct measurements of the Thomson effect in bis- muth.* Righi has shown f that the electric resistance of bismuth is altered in a strong magnetic field. To find if any thermoelectric change accompanied magnetisation of bismuth, a bismuth palladium couple was set up between the poles of a powerful electromagnet. No effect whatever was observed, although the arrangement (slightly modified) was sensitive enough to show with great ease the thermo- magnetic effect discovered by v. Ettingshausen and Nernst.J * See Wied. Beibl., vol. xi., 1887. t See Wied. Beibl., vol, viii., 1884. | See Wied. Ann., vol. xxix., 1886. 1890-91.] Prof. C. G. Knott on Magnetic Strains. 315 On the Effect of Longitudinal Magnetisation on the Interior Volume of Iron and Nickel Tubes. By Professor Cargill G\ Knott, D.Sc., F.R.S.E. (Read July 20, 1891.) The following results in magnetic strains are, so far as I am aware, new. They supplement in an interesting way Joule’s old result of no change of volume in an iron rod when it is magnetised. What is given here is only preliminary, and suggests many lines of research which I hope to be able to follow out later. The broad fact established is, that the internal capacity of certain iron and nickel tubes alters appreciably when the tubes are magnetised longitudinally. The tubes were 34’8 cm. long, and were all about 3 cm. external diameter. One iron tube had an internal diameter of 1 cm., and another of 2 cm. These I shall call and A2 respectively. A3 represents the third iron tube, whose wall was about 1 mm. thick. The nickel tube (B) had its wall 03 mm. thick. When experimented with, each tube was tightly corked at both ends, and through the one cork a fine capillary glass tube projected. The tube was filled with alcohol coloured with cochineal. The changes of volume were measured by the movement of the end of the liquid column in the capillary tube. This was viewed through a microscope. A movement in the tube through a distance equal to one division of the microscope micrometer meant a change of volume of 7'2 x 10-6 cub. cm. As an example, take the case of A1? the small bored iron tube, in a field of 250. The sudden outward movement of the liquid meniscus showed a total compression (change per unit volume) of 21 x 10-7 in the region inside the tube. But we know that in this field ordinary wrought iron lengthens ; and in virtue of this lengthen- ing the internal volume will be increased. It is clear, then, that the transverse contraction of the walls of the tube has overbalanced the longitudinal extension. If A. /x represent the elongations parallel to and perpendicular to the axis of the tube along the inner surface of the bore, the dilatation will be A, -i- 2/x. Now, in field 250 Bidwell 316 Proceedings of Royal Society of Edinburgh. [sess. finds A = + 5 x 10'7; hence at once p = - 13 x 10 7. I give a few results for the different tubes in various fields. In Field 50. Tube. X + 2/x observed. A Bid well. V- calculated. Ax - 1*84 x 10-7 + 10 x 10-7 - 5*9 x 10-7 a2 -2T ? ? - 6T x 10-7 a3 -1*2 -5-6x10-7 In Field 125. Tube. A + 2 fJL A r- A, - 6 "6 x lO-7 + 18 x 10-7 -12-3x10-7 A2 -8-4 „ ? 5 -13-2x10-7 As -3 -10-5x10-7 In Field 250. Tube. A + 2 ix A -21 x 10~7 + 5x10-7 i 00 X o <1 A., - 7 x 10 ~7 5 9 - 6 x 10 —7 a; - 2-6 ,, ? - 7*6 x 10~7 Unfortunately I possessed no nickel tubes shaped like the iron ones, so had to content myself in the meantime with a thin walled tube formed by rolling up a sheet of ordinary commercial nickel to the convenient size. The results for this tube were of great interest. Up to a field of 50, the compression of the inside space varied uniformly with the field, the dilatation being given by the formula A+2/* = - l-8 x 10_8H, where H is the longitudinal field. Now BidwelFs results give up to the same field the following expression for A: — A = -18 x 10_8H. Ijl= + 8-1 x 10“8H. Hence .1890—91.] Prof. C. G. Knott on Magnetic Strains. 317 For fields higher than 50 the following remarkable results were obtained Field. A + 2 p r 60 - 97 x 10-7 - 100 x 10~7 + 457 x 10~7 100 -8-0 „ -140 ,, + 66 135 0 -163 „ + 81-5 „ 240 + 4*0 „ -190 ,, + 97 260 1 + 9*0 „ ? -202 „ + lOo ‘5 , , Thus, for the iron tubes, the transverse contraction always exceeds the longitudinal extension, so that there is on the whole a diminution of the internal space. There is evidence of the contraction attaining a maximum, which, in the case of the thinner walled tubes (A2 and A3), occurs in a field not far removed from the field which produces the maximum extension. For the nickel tube, the transverse expansion differs so slightly from the longitudinal contraction, that the change of volume of the internal space, though of the same order of quantity as the correspond- ing change in the iron tubes, is a very small fraction indeed of the change that would result from the longitudinal contraction acting alone. In low fields, the longitudinal contraction overbalances the transverse expansion, causing a compression. This compression reaches a maximum about field 60, and then falls off first slowly, then more rapidly. About 140 it becomes zero, and changes sign in higher fields. In field 260 a very distinct dilatation is produced about equal to the maximum compression obtained in field 60. The rapid changes of temperature of the liquid in the heart of the magnetising coil, when the high currents were used, made accurate measurements of the changes of volume impossible ; but there was no doubt as to the fact of the change of sign in the compression when the field was taken high enough. It should be mentioned that, in an experiment with a glass tube substituted for the iron or nickel tube, no effect was produced ; so that the alcohol itself was uninfluenced by the magnetising force. An experiment was also tried with a current of seven amperes passed along the iron tubes, so as to cause a circular magnetisation of the outer circumference. No change of volume was observed, however, probably because of the comparative smallness of the fields involved. 318 Proceedings of the Royal Society of Edinburgh, [sess. On some Relations between Magnetism and Twist. Parts II., III. By Cargill G. Knott, D.Sc. Edin., F.R.S.E., Professor of Physics, Imperial University , Tolcyo, Japan. (Read June 1st, 1891.) (Abstract.) Part II. contains a continuation of former experiments on the twists produced in the magnetic metals when they are under the combined influence of circular and longitudinal magnetisations. It is established that a cobalt rod of rectangular section twists left-handedly when a current is passed along it in the direction of magnetisation. That is, cobalt behaves like nickel. Iron, on the other hand, twists right-handedly, until very high fields are employed. These results seem to have a close connection with the magnetic changes of length in these metals; for iron expands in moderate fields, while nickel and cobalt contract, the former always, and the latter till high fields are reached. In the case of nickel an evident maximum twist is obtained for intermediate values of field. The occurrence of this maximum finds a ready explanation in terms of the theory suggested. In all cases the amount of twist produced by reversing one of the magnetising forces depends on which one is reversed. Generally the twist is greater when the longitudinal field is reversed than when the current along the wire is reversed. For low fields in the case of iron and nickel it is, however, the current reversal that pro- duces the greatest twist. These various phenomena give very instructive illustrations of the magnetic after-effect or hysteresis. In Part I. an expression was given for the twist in terms of the elongations in a thin walled tube of given radius, under the com- bined influence of given circular and longitudinal magnetisations. From the observed maximum twists in iron and nickel wires now given, a comparison is made between the elongation coefficients which enter into the formula for the tubes of equal diameter. The comparison is in remarkable accordance with the direct comparison of elongations as furnished by Mr Bidwell’s measurements. Part III. contains a discussion of the magnetic consequences of 1890-91.] Prof. C. G. Knott on Magnetism and Tivist. 319 twisting a magnetised wire, more especially a wire magnetised circularly by a current passing along it. The peculiar manner in which the magnetic change sometimes lags behind the stress, some- times shoots ahead of it, is fully investigated. This magnetic “ lagging ” or “ priming ” is found to depend upon the strength of the current, upon the amount of twist, and upon the amount and degree of tapping to which the wire is subjected. The longitudinal polarity acquired by a current-bearing wire when it is twisted is relatively very high as compared with the probable intensity induced at the circumference of the wire. Further, the longitudinal intensity so acquired is reversed, more or less com- pletely, when the current is reversed. These facts are not easily explained in terms of the usual theory of magnetic seolotropy, or in terms of any simple hypothesis of rotatable molecules. They rather hint at the existence of complex molecular groupings, which assume new configurations under the influence of a changing stress or a changing magnetic force. Certain experiments on the effect of slightly twisting a wire, which by superposed magnetisms has been reduced to an apparently demagnetised condition, show how easy it is to destroy the apparent magnetic balance. There is a strong suggestion that a magnetised wire may, under certain circumstances, consist of alternating layers of opposite polarities. Any mechanical stress which acts differently on these different layers will almost, as a matter of course, power- fully affect the average resultant action which is measured on the magnetometer. From the experiments recorded in the paper, and from the experi- ments of other investigators into the complex relations of magnetism and twist, the general conclusion may be drawn that the first effect of a shearing stress upon the molecular groupings is not only to increase the average intensity in the direction of the magnetising force, but also to bring into prominence a relatively high intensity in directions at right angles thereto. 320 Proceedings of Royal Society of Edinburgh. [sess. On the Gravimetric Composition of Water. A Preliminary Communication. By W. Dittmar. (Read February 3, 1890.) On the strength of Dumas’ famous Recherche sur la Composition de VEau * and adopting the great master’s own interpretation of his results, all chemists, until lately, agreed in assigning to the atomic weight of oxygen the value 0 = 16 (H=l); and it is on the strength chiefly of the same experiments that many of us now hold that 0 = 15*96 is a closer approximation to the truth ! In these circumstances it surely is worth while to look into Dumas’ work with the help of critical experiments, and try to see whether he was not right in thinking that — all his great efforts notwithstanding — the difference lies within the influence of his method-errors ; the more so, as all these errors (as far as one can see without experimenting) tend to raise the experimentally ascertained value of the ratio H : 0 above its true value. I accordingly, some time ago, caused my private assistant, Mr Henderson, to join me in this inquiry, and, thanks to his youthful energy and indefatigability, we have already made considerable pro- gress in our work, and hope before long to lay a complete account of it before the Society. Meanwhile, I content myself with stating that we have succeeded in so modifying Dumas’ modus operandi as to give a higher degree of constancy to the weighings, and to reduce the trouble and loss of time involved to far less than it was with the original form of the method. The principal object of the present notice, however, is to direct attention to an oversight which Dumas made himself guilty of, and which, as far as I am aware, has never been noticed before. What I allude to is that Dumas, while weighing his oxygen (virtually) in vacuo , weighs his water in air, and forgets to reduce this latter weight to the vacuum. That the correction tells very considerably upon the calculated weight of the hydrogen a very little reflection is sufficient to show ; * Ann. Chim. Pliys. (3), vol. viii. p. 189. 321 1890-91.] Mr W. Dittmar on Composition of Water. I prefer to give at once the results of my recalculation of Dumas’ experiments, and apply the correction to the most “ probable value” as calculated by me. In his tabular statement of results Dumas gives, in the case of each of his nineteen experiments, two values for what he calls the “equivalent of hydrogen” (the term with him meaning the weight of hydrogen which combines with 10,000 parts of oxygen into water) — viz., firstly, the value as calculated from the uncorrected weights of water and oxygen ; and, secondly, the “ equivalent * as corrected for the air in the sulphuric acid ” (used for the evolution of the hydrogen from zinc). For reasons, which will be stated in the memoir, I have left these corrected values on one side, and recalculated and reduced only the “ equivalents hruts” Taking S as a symbol for the weight of oxygen consumed in a given experiment, and W for the uncorrected weight of water pro- duced, I formed the equations = 81 W2-K2 = 82 W3-*S3 = S3 and solved the nineteen equations in respect to Jc — firstly, in the way which reduces the algebraic sum of all the errors 8 to nil ; and, secondly, so as to reduce the sum of the squares of the errors 8 to its minimum. The first method gave &=1T25 43; the second gave &=1T25 47. The two values, as we see, are practically identical. Adopting the second, it may be read as stating that 1000 grammes of oxygen take up hydrogen to form a quantity of water whose apparent weight in air is 1 1 25*47 grammes. But, assuming the air to have the density corresponding to 15° and 760 mm. (which probably is not far removed from the air-density which actually prevailed during Dumas’ work), the air displaced by the water amounts to 1*38 grammes ; hence we have, in reference to any given quantum of water, the following relative values for the weights of * As already pointed out by Lothar Meyer and Seubert, Dumas’ table of results includes quite a number of misprints. These, however, are all easily discovered, and set right without much fear of error. 322 Proceedings of Royal Society of Edinburgh. [sess. Oxygen. Hydrogen. Water. 1 0-126 85 1-126 85 8 1-014 8 = “H” 15 767 = “ 0” 2 = “ H2” The results of our own work enable me to say that the true value of “ H ” (0 = 16) is probably not quite so high as 1-0148, but it is higher than the 1*0024 demanded by the customary “0 = 15-96.” I venture to hope that the publication of this notice will cause those chemists who hitherto ( after having become convinced that O : H is less than 16) have persisted in referring their atomic weights to H= 1, will give up this absurd practice, and, like other people, adopt 0 = 16 as their standard. The sixteenth part of the atomic weight of oxygen, surely, is as good a unit as one could desire to have. 1890-91.] Mr E. Sang on NicoVs Polarising Eye-Piece. 323 Investigation of the Action of Nicol’s Polarising Eye-Piece. By E. Sang, Esq. (With a Plate.) (Read February 20, 1887.) The first announcement of the construction of this important instrument appeared almost paradoxical : a piece of calcareous spar was to be cut in two, the surfaces of the section polished, and then reunited by help of Canada Balsam : and it seemed strange that from such an operation there should have resulted any change in the optical properties of the mass. Even now that the instrument has been in use for some time, the true nature of its performance is often misunderstood ; while no investigation has been made public, the object of which is to enquire into the laws of the action, and into the circumstances which determine the peculiar forms of the parts. This investigation necessarily involves operations belonging to the higher branches of algebra and geometry ; but this is not to he wondered at, when physical science has reached such a degree of development as to exhibit many of the laws of its phenomena. Before proceeding with the strict investigation, it may be con- venient to take a general review of the modifications which light undergoes in its transit through the instrument ; as by that proceed- ing we shall be better prepared for seizing the full import of the analytic results. Let, then, ABCD represent the prime section of the eye-piece, BD the thin film of balsam inserted between the halves, and EF a ray of light incident on the surface AD : that ray will be refracted in two pencils, EH that submitted to the ordinary, FA that to the extraordinary, law. Were the rhomb entire these rays would again suffer refraction at the surface BC, and would emerge in directions HI, hi parallel to the incident ray : 324 Proceedings of Boyal Society of Edinburgh. [sess. the same thing would happen were the surfaces BD in optical contact, that is, were they united by a substance having its index of refraction greater than or equal to the greater of the two indices for calcareous spar. But the index for Canada Balsam is less than that for carbonate of lime, and on this account the rays may not proceed uninfluenced. If, indeed, the ray FG fall very obliquely on the surface of the varnish it may be totally reflected, no portion of it passing into the second wedge DBC. So it may also happen with the ray Yg ; but as the two rays fall with different obliquities on the varnish, their limits of total reflection are different, and between these, the extra- ordinary light alone will find a passage. The ray E:F falls at such an angle that the ordinary pencil would barely suffer total reflection, while the extraordinary pencil would not. Any ray incident between the directions AF and EjF would transmit both its pencils through the whole instrument. The ray E2F, on the other hand, is so placed that both of its pencils suffer total reflection ; and, hence, all rays within the angle EXFE2 will transmit to the eye only that portion which has experienced the extraordinary refraction, while no ray incident in the angle E2FD will send any light through. Such is the true action of the polarising eye-piece : it does not depend, as has been thought, on the separation of the images, for in truth there is never more than one image formed, and the virtual place of that image is not affected by the film of balsam. The perfection of its action depends on the magnitude of the angle E^FEg, which magnitude regulates the extent of the field of view; and on the transmitted light passing without being at all deflected in its path. For the attainment of the latter object, the surfaces AD, BC must be so placed that a ray of extraordinary light, passing in the interior parallel to the sides AB, may not suffer refraction in escaping at either surface. By this arrangement the light proceeds from the object to the eye, so that the first and last portions of its path are not only parallel to each other, but actually in one straight line. If this adjustment be not effected, there is created a parallax similar to that occasioned by the transmission of light obliquely " through a thick plate of glass : that parallax affecting the apparent positions of near, but not those of distant, objects. The lines RST, TXJ, UO are omitted for want of room; DR. SANG ON NICOUS POLARISING EYEPIECE. Vo 1 . X V 1 1 1 Proc. Roy. Soc. Edin. 1890-91.] Mr E. Sang on Nicol’s Polarising Eye-Piece. 325 The removal of this parallax is not altogether a matter of necessity, it is one rather of convenience, for by turning on the ends of the containing box circles parallel to each other, but on different axes, the inconvenience of the parallax would be entirely removed — the adjustment, however, of these axes would be troublesome. The tendency of Iceland Spar to split in planes parallel to the faces of the primitive form renders almost unavoidable the employ- ment of rhombs whose lengths are parallel to the aretes of that form, economy in the amount of material being nearly as important as a maximum extent of field. Eegarding, then, the positions of the lines AB as determined by the cleavage, and those of AD by the condition of rectilineal trans- mission, there remains only to be determined the inclination of the plate DB of balsam. This inclination may be determined by attending to one or other of two conditions. Either we may so place this plate as to give the greatest angular field of view ; or we may so fix it that the verges of that field are equally inclined to the direction AB : practically the latter consideration is the more important. It will, then, be proper, before attempting the enquiry into the best possible form of the instrument, having regard neither to the economy of the material nor to the introduction of parallax, first to determine the form which it ought to have when influenced by these restrictions. The first thing to be determined is the angle ADC, which the diagonal AD of the end of the rhomb makes with the arete of the primitive form. Adopting the results of the elaborate investiga- tions of M. Malus, let (fig. 2) the whole crystal be imagined to occupy the point O. Suppose that KOL is the direction of the axis of crystallisation, and ON that of the arete of the primitive form, and also of that portion of the ray which is interior to the crystal. Describe from O, as a centre, a sphere with the radius OM = unit, to represent the progress of a luminous pulse in air, and the interior ellipsoide with its semi-axes '604 and ’673 to represent the luminous pulse in the interior of calcareous spar. In order to place the refracting surface OP in such a position that the pencil of extraordinary light may not be bent, we must apply tangent planes at the points M and N, and continue these VOL. xviii. 8/12/91. 2 n 326 Proceedings of Royal Society of Edinburgh. [sess. planes until they meet in the line P ; the plane passing through this line P and the point O is parallel to the required refracting surface. For the determination then of the angle POM, which is supplementary to ADC of fig. 1, we only require the operations of ordinary trigonometry. Taking the inclination of the faces of calcareous spar at 105°. . 05', as determined by the observations of Wollaston and Malus, we find the angle LOM, which the axis makes with the arete, to he 63° . . 44' . . 46", and not as Malus has it, 66° . . 44' . . 46". Log cot 52° .. 32' .. 30" =9*884 3264 Log J3 = *238 5606 Log cos 63°.. 44'.. 45"| = 9-645 7658 This error of three degrees committed by M. Malus seems to have run throughout his work, and thus throws considerable uncertainty on his determination of the refractive indices. Denoting this angle LOM by X, and the semi-axes '604, '673 by a, /3, the equation of the plane MP is xxM + yyu=l , or x cos X + y sin X = 1 (MP) ; while that of the plane NP is , yy N + or since = a/3 cos X P2 J(a2 sin A.2 + /32 cos A2) 5 J(a2 sin A2 + /32 cos A2) = 1, a/3 sin A x cos A ( y sin A aP /32 J ,J(a2 sin A2 + /32 cos A2) = i; that i is, x cos A t y sin A J(a2 sin A2 + ft 2 cos A2) + = ~~ a/3 • (NP). Hence, as the line P is common to both of these planes, we obtain by elimination . g — a ^/(a2 sin X2 + /32 cos X2) y p sm A — p _ a2 . -a + B J( a2 sin A2 + /32 cos A2) xP cos A = a /3% _"2 — 1890-91.] Mr E. Sang on Nicol’s Polarising Eye-Piece. 327 from which, equations we deduce the value of the tangent of the angle LOP, tan LOP = - £ cot X S™ U T m °°^ ^ j > a a ~P j'{a2sm X.A + (3A cos Az\ from which we obtain the numerical value supp. LOP= 41° . , 14' . . 13J" (say 14"); whence, by adding the angle LOM, we obtain MOQ = 104\.58'..59i" Say ADC (fig. 1) = 104 ..59. Now, the inclination of the arete to the face of the primitive rhomb is 109° . . 08', so that, in forming an eye-piece, the ends must be inclined 4° . . 09' less than the natural face is. This result is opposed to the instructions given by Mr Nicol in his first description of the instrument : he directs that the obliquity be increased, whereas we have found that it must be diminished 4°; and, indeed, on inspection of those eye-pieces which have been made agreeably to his instructions, it will be found that the ray bf light proceeding in the interior of the crystal parallel to the arete suffers refraction at each surface, and that the ray which does not suffer refraction passes in a direction intermediate between the line of the arete and the diagonal joining the two obtuse corners. Having now determined this element of the artificial rhomb, there remains for me the solution of another question. It is this : To place the plate of balsam so that the extent of field may be placed equally on each side of the line of sight. For this, a new element enters into the investigation ; the refractive power of the balsam. Let OK represent the direction of the plate of cement, and measure off OK to represent the velocity of light in that medium ; the limiting directions of the two pencils will be thus obtained. First, for the ordinary ray ; describe a sphere round O with the radius a, and from R apply to that sphere the tangent plane Rs, meeting the surface OP in the line t ; then from that line apply a plane touching the sphere pertaining to the air in the point u, O u is the direction of that external ray, of which the ordinary pencil 328 Proceedings of Royal Society of Edinburgh . [sess. just suffers total reflection at the surface of the balsam; this is one of the boundaries of the field of view. Again, from the same point R apply the plane RST touching the spheroide in S, and cutting the surface OP in T ; the tangent plane TU will give the direction of OU the limiting extraordinary ray. The question is to place OR, so that the angle UO u may be bisected by the line OM. For the analytic solution of this problem we have only to go into detail with the investigation for extraordinary light ; since the insertion of (3 = a in any formula for that species of light will give the corresponding formula for ordinary light. Denote the angle LOP by /x, the required angle LOR by y, and the velocity of light in Canada Balsam by y: then are the co- ordinates of the point R xR = y cos v ; yR = y sin y . But the equation of a plane passing through R, and touching the spheroide, is ± y* V(«yR + /324 - a*0$} ) > = o?yl + (32xt + + % JWyl + /32x\ - a2/?2)} J or x | /32 cosv ± y sin v sinv2 + /52 cosv2 - + y | a2 sin v + y cos v siny2 + /3 2 cosy2 a2/?2 y2. a2/52 y y(a2 sin y2 + (3 2 COS y2 From the inspection of the figure it is clear that xv = sec POU. cos /x yT = sec POU. sin g which values inserted in the above equation of the tangent plam give, after reduction, and putting e2 = j32 - a2, cos POU = e2 COS fJj COS y + a2 COS (g — y) + y sin in (/j.-v) (J8* '2)) y(a2 + e2 COS y2) The supposition /5 = a, e = 0 in this formula will give the value of tbe cosine of the limiting angle for ordinary light : thus 1890-91.] Mr E. Sang on NicoVs Polarising Eye-Piece. 329 cos PO u a cos (/x — v) + Jy2 — a 2 sin (/ x — v ) ay The object is to find a value of v which would give POU + POz* = 2(/x-A) , which would be accomplished by resolving the equation sin POU 4- sin PO u tan(/t cos POU + cos POi« ’ but the labour attending the exhibition and direct resolution of this equation would be enormous, I have, therefore, preferred the method of approximation. In making this approximation we derive a guide from the last term of the numerator of cosPOU ; which becomes imaginary when a2 e2 cos v2 is less than the known quantity —2(/32 - y2). This limit, which gives (V) = 57° . . 55', corresponds to the intersection of the ellipse with a circle described with the radius OR. I, therefore, assumed three values of v, or rather of /x — v, and com- puted thence the corresponding values of POU, POw, and of the error J(POU + POw) - (/x - A), as under /x - v v POU PO u Error 85° 53°. . 45'. . 46" 80°. . 04'. . 56" 40°. . OP. . 32" - 14°. . 57'. . 46" 90 48 . . 45 . . 46 83 . . 00. . 21 50 . . 35 . . 13 - 8 . . 13 . . 13 95 43.. 45.. 46 86 . . 48 . . 08 60 . . 03 . . 04 - 1 . . 35 . . 24 where the extent of field (POU - PO^) is observed to decrease, the greatest possible extent of field being obtained when v has the limiting value : but then this convenience of a large field is counter- acted by having it unsymmetrically placed in reference to the line of sight ; as well as by the necessity of using a very long rhomb which would give another limit to the extent of view. Computing, by the ordinary method, from these three results, that value of v which may give no error, we find v = 42° . . 33' . . 00"; but this is only an approximation. Computing from it the value of the error, we find POU = 87°. . 52'. . 39"; PO^= 62°. . 14'. . 39", 330 Proceedings of Royal Society of Edinburgh. [sess. giving an error of + 2'. . 39”, from which, we infer {u-v} = 96°. . 10'. . 48" ) V field = 25°.. 40'. {v} = 42 . . 34 . . 58 ) This value of POR, 96° . . 11', differs by six degrees from the deter- mination of Mr Uicol ; hut as the surface according to that gentleman §is inclined by seven degrees to the position assigned by theory, it follows that the value of v, or the position of the plate of balsam in reference to the axis of the crystal, is nearly the same in his instru- ment, as by the above determination. If, indeed, an eye-piece, constructed according to the directions of the inventor, be placed so that the light from any object pass in the interior parallel to the length of the rhomb, that object will he found considerably nearer the limit of the ordinary than that of the extraordinary light. The above angles are sufficient to guide the operator in the con- struction of the eye-piece. But it is to he remarked that the advan- tages sought in this construction do not balance the disadvantage of a diminished field ; and that Mr Uicol’s dimensions are preferable. Having now completed the investigation of the best form for a rhomb whose faces are obtained by cleavage, I shall proceed to investigate the absolutely best form independent of that considera- tion. In strictness, this investigation ought to he founded on the above values of POU, PO^. It ought to include the solution of the equation POU + PCh/ = 2(/x - A.) . The root of that equation determined, the value of POU - POw should he thence deduced. Then the maximum value of that field ought to he sought, g and A, being the primary variables. Or if the condition of non-refraction of the line of sight be included, /x becomes a function of A, and hence the differentiation becomes monome. This investigation however is, on account of its complexity, almost impracticable : for it I shall substitute another. Instead of seeking the maximum separation of the limiting rays exterior to the rhomb, I shall seek for that position of the plate of balsam which gives the greatest internal divergence, which depends 1890-91.] Mr E. Sang on NicoVs Polarising Eye-Piece. 331 simply on a, /3, y ; after it is determined it will tlien be proper to enquire, what position of the ends of the rhomb will give symmetry in the placing of the field of view. We must, then, determine the position of OR so that the angle SOs may be a maximum. Now, it is obvious that the angle ROs is constant, having for its cosine the ratio - : and thus we have to 7 seek only for that position of OR which gives ROS a minimum or a maximum. ROS will, in the particular state of matters, be a minimum, actually zero, when OR is a semi-diameter of the ellipse, that is, when ( v) = 57° . . 55' ; but if ROS be greater than ROs, SOs will be the excess ROS - ROs, and we must then seek for ROS a maximum, not a minimum. The equation of a plane touching the ellipse of S is a2 + /32 “ 1 ’ and since that plane must pass through R a2 + p2 ’ from which equation, and the equation of the spheroide, we may determine xS) ys, the ordinates of the point of contact, 2/32^r + Vn \J (°?y b + P2xr “ °2P2) XS~ a o 2 02 2 ’ a Vr, + ^R 2 a2yR ± xR J{a?yl + fpx\ - a2/32), «%+/s%4 in which, substituting for %, yR their values, we obtain a2 p2 cos v + sin v J{y2(a2 sin v2 + P2 cos v2) - a2 ft2} X^y a2 sin v2 + p2 cos V2 5 _ /32 a2 sin v ± cos v J {y2 (a? sin v2 + /32 cos v2) - a2p2} y a2 sin v2 + j32 cos v2 whence jr)a_fi2 a2sinv±cosv^{y2(a2sinv2 + /32cosi/2) - a2P2} an a2 j32 cos V + si n v ^ { y2(a2 sill V2 + p2 cos V2) - a2p2 } * 332 Proceedings of Royal Society of Edinburgh. [sess. (a4sim (/32cosv‘ Now, ROS is the difference between LOS and v, so that when ROS is minimum or maximum 8ROS = Sv ; that is, since §ROS(sec ROS)2 = S tan ROS Sv(sec ROS)2 = S. tan ROS. Putting- 2 sin v2 + /32cos v2 - = N , whence tanLOS = igsinyj^C°Sy; a^/P cos v + a/yJN sm v i -pnQ\2 _ a4/^4 — 2 a2/32e 2 . yN . sin v cos v + (a4 sin v 2 + /34 cos v2)y2N2 (sec KQJjj) | (a2/32 + a2yNsinv)2 3 and also s tan K0S a4/?4 + a2/32y2N2 ± a2j32y(a2 sin v2 + £2COSv2)^- = (a2/32 + a2yNsini/)2 so that the value of v will he determined by equating the numerators of these two fractions. Thus '2 - a2/32 + /34 cosv2)y2N2 ± 2a2/32€2yN sinvcosi/ = ± a2/52y(a2sini/2 + j32 cosv2)^ > ' 0 V or > 9 • 9\ 9 9at2 . o 202 9 at • _ a2/32ye2(a2 sin v2 + R2cos v2) sin vcos v } - a2sillv2)e2y2N2 ± 2a2/3VyN sm v cos v = + ' L whence, after repeated simplifications, ( - a4 sin v4 + y84 cos v4)y2 + a2/32(a2 sin v2 - j32 cos v2) ± 2a2/32y J ^a2 sin i/2 + /3 o 9 a2/^2 2COSl/2-— Y cos v sm v a2/32y(a2 sin v2 + /32 cos v2)cos v sin i/ J ( a2 sin v2 + ft2 cosi/2 - — ~- = 0 ( - a2 sin v2 + /32 cos v2)y2 | a2sinv2 + /32 cosi/2 - | 2 = + 2a2/32y cos V sin v | a2 sin v2 + /32cos v2 - | + a2/32y cos v sin v { a2 sin v2 + /32 cos v2 } = + a 2/32y cos v sin v | 3a2 sin v2 + 3/32 cos v 2 - 2— y- | 1890-91.] Mr E. Sang on NicoVs Polarising Eye-Piece. 333 whence squaring ( - a2 sin v2 + /32 cos v2)2y2(a2 sin v 2 + /32 cosi/2 - ^{3a?(/3* - /S2e2 + e4) - y2(4 /3* - e4)} + sin v2^ { 3aV - 3y2(/34 - €4) + y4(4y32 - «2) } - ^(y2 - a2)3 = 0 . Put here sin v2 = x) ,2 > and we have a3 . e2(2/32 - €2)2 + X2{ 3a2(/54 - /32e2 + e4) - y2(4£4 - €4) } + X{ 3a4e2 - 3a2y2(/32 + e2) + y4(4/32 - c2) } - (y2 - a2)3 = 0 , which becomes on substituting the numerical values for a2, /3 2, e2, y2, 334 Proceedings of Royal Society of Edinburgh. [sess. / e2 = ’088 113 ; a2 = *364 816 ; /32 = *452 929^ ] y2= *427 716 ; y2- a2 =*062 900; /32 + e2 = *541 042 l ^2^2 + e2 = *993 971 ; 2/32 - €2 = *817 745 ; 4j82 - e2 = 1*723 603 J 0-058 921 8a?3 — 0*158 3148^ + 0*097 2308^-0*000 248858 = 0. This equation has three roots, only one of which is consistent with other conditions not involved in the algebraic expression of the problem : that root is a =*0025702, whence v = 2°. . 59'. . 25", a result which gives the maximum value of EOS, and therefore the minimum of SOs ; or the maximum of - SOs. The value of EOS deduced from the above v is 24° . . 40' . . 23", while the constant value of EOs is 22° . . 32' . . 59" ; thus leaving for SOs only 2° . . 07' . . 24" as the maximum when Os falls between OS and the axis. This leaves so small a difference between the interior rays which experience total reflection at the surface of the balsam, that it is needless to pursue the investigation farther. It may be at once held as demonstrated that the best position for the plane of cement is beyond the limit which gives a coincidence to the two interior rays OS, Os ; and that we must seek for the best possible position beyond that limit. The maximum value of EOs - EOS must, since EOs is constant, accompany the minimum value of EOS, which minimum value, since both angles must always lie on the same side of OR, is zero. We might, therefore, be led to suppose that the best value of LOE is (v) = 57° . . 55'. But in reality, any value of LOE between 57°.. 55' and its supplement 122°.. 05' is accompanied by this circumstance, that no pencil of extraordinary light is intercepted by the balsam. Hence in considering the values of v between these limits, we have only to examine the condition of total reflection of the ordinary ray; this examination is a matter of comparative facility. Having thus found a wide range of angles accompanied by no interruption of the extraordinary ray, we might enquire what particular angle would give the most extensive field of view ; but 1890-91.] Mr E. Sang on Nicol’s Polarising Eye-Piece. 335 in reality, all positions of the plane OR give the same value, 22° . . 33', to the angle ROs, so that the position of OR between these limits is indeterminable by this condition. Another and remarkable condition may, however, he proposed : viz., so to place the external surface, that no ray of ordinary light entering the eye-piece may pass through it ; while at the same time not a single extraordinary ray is intercepted. The construction of an eye-piece to satisfy these conditions would seem to give every requisite desirable in such an instrument. Let AB represent the position of the plate of Fig. 3. balsam, anywhere intermediate between 57°.. 55' and 102°.. 05' from the axis. Make ABD = 22° . . 33' ; any ray of ordinary light passing in the interior between AB and DB would suffer total reflection ; no ray beyond DB would be intercepted. We wish, then, that no ordinary ray entering the substance may make with the line AB an angle greater than 22° . . 33' : in other words, a ray of light BD passing in the interior ought to suffer total reflection at the outer surface. The angle ADB, then, ought to have for its cosine the ratio a ; whence ADB = 52° . . 50'. . 35" ABD= 22 ..32.. 59 BAD = 104 ..38.. 26 Assuming AC as the limit of the rhomb, and making that coincide with the direction of the arete of the primary form, the whole instrument is defined. With this eye-piece, as a matter of course, there are no separating bands perceived. In all of these enquiries the object has been to exclude the ordinary and transmit the extraordinary pencil. But the converse question may also be proposed. At a glance it is seen that no combination similar to that which we have been considering can supply the requisite conditious. We 336 Proceedings of Royal Society of Edinburgh. [sess. must place the calcareous spar between two wedges of a medium having a greater action on light. If a plate of spar be placed between two wedges of glass, having its index of refraction just equal to the index of calcareous spar for ordinary light, no ordinary ray would be intercepted ; and there would remain the question — so to form these wedges as to exclude the extraordinary pencil, as also to determine the manner in which the slice of spar should be cut from the crystal. Supposing a glass obtained with the refractive power - = 1*655 ; a it is obvious at once that the best direction for the slice of calcareous spar is across the axis of crystallisation. The angle at which the extraordinary ray interior to the glass would suffer total reflection would have -5 for its cosine; hence, that angle would be 26°. . 10'. . 19" Let, then, AB represent a plate of Iceland Spar cut at right angles to the axis: ABD, ABC, two wedges of glass ind. ref. = 1*655. Make ABD = 26° . . 10' . . 19", and a ray of light between AB and DB would send through only the ordinary pencil ; beyond DB both would pass. Make, again, the angle BDA such that its cosine is a, that is, make it 52°. .50'.. 35", and, of course, BAD = 100° . . 59' . . 06" ; and then, while no ordinary ray is intercepted, no extraordinary one is suffered to pass. When *the refractive power of the glass employed is not the inverse of a, the computations become more intricate ; but they resemble so closely those of the first part of this paper that it is needless here' to go over them. The importance of the eye-piece as an instrument for experimental research, entitles it to a strict and minute analysis, that we may call into action the full development of its powers, and thus make sure of losing none of the benefits which it promises to confer. ZOth January 1837. 1890-91.] Prof. Tait on Dr Bang’s Paper. 33 7 Not© on Dr Sang’s Paper. By Prof. Tait. (Read November 23, 1891.) At the very urgent request of the late Dr Sang, who regarded the above paper as one of his chief contributions to science, I brought before the Council of the Society the question of its publication. From the Minute-Book of the Ordinary Meetings, I find that it was read on the 20th February 1837, though it is not mentioned in the published Proceedings of that date. On 21st July 1891 the Council finally resolved that tbe paper should be printed in the Proceedings “ if otherwise found desirable.” The reasons in favour of printing it seem to outweigh those which may, readily enough, be raised against such a course. The subject is one with which, except of course in its elements, I have long ceased to be familiar. But, from the imperfect examination which I have found leisure to make, I have come to the following conclusions. The paper contains a very important suggestion which (one would have thought) should have been forthwith published, whatever judgment might be passed on the rest of the work: — viz., the pro- posal to construct the polariser of two glass prisms, separated by a thin layer, only, of Iceland spar. In view of the scarcity of this precious substance, such a suggestion was obviously of great value. I am not sufficiently acquainted with the early history of the Nicol prism to be able to pronounce on the question of Dr Sang’s claim to priority in the explanation of its action : — but he told me that he believed himself to have been the first to demonstrate that the separa- tion effected was due to the total reflection of the ordinary ray. And it is quite certain that, long subsequent to 1837, various very singular attempts at explanation have been given in print. The inventor, himself, seems to have thought that the effect of his instrument was merely to “increase the divergency” of the two rays. The numerical error which Dr Sang has pointed out in Malus’ work seems to have been a slip of the pen only, as the minutes and seconds of the angle in question are correctly given. He supplies no reference to the passage, but I find it in the list of calculated angles at p. 125 of the Theorie de la Double Refraction. It cannot be a mere misprint, because the supplement is given along with the angle, 338 Proceedings of Royal Society of Edinburgh. [sess. and is affected by the corresponding error. But I do not think that Dr Sang’s further remark is justified, as Malus not only gives the correct expression for the cosine of the angle in question, but seems to have employed in his subsequent calculations the inclina- tion of the axis to a face , not to an edge, of the crystal : — and he gives the accurate numerical value of this quantity, as deduced from Wollaston’s measure of the angle between two faces. There is an altogether unnecessarily tedious piece of analysis in Dr Sang’s investigation of the limits within which the prism works: — and it is so even although he shortens it by the introduction of the terribly significant clause “ after repeated simplifications.” I will give below what I consider to be a natural and obvious mode of dealing with the question (one which, besides, leads to some elegant results) : — but I have reproduced Dr Sang’s manuscript as it was read , for the circumstances of the present publication seem to require literal accuracy. Dr Knott has kindly verified for me the agreement of my final equation with that of Dr Sang. In p. 331, above, it is clear that, since S is a point on the spheroid, we may put xs — a cos (fj , ys = /3 sin . But we have (p. 328) xn — y cos v, 2/r = y sin v . Hence the general relation between B and S, i.e., between c fi and v , is cos cos v sin <£ sin v 1 “ 1 t ~ 'V Also, since the angle BOS is to be a maximum, ^(tan-(Aan^)-v) = 0. Differentiating the first equation, and eliminating d)3 = — — tan v But we may put the first into the form (i). or cos v sin v , , 1 , 1 — — tan = — sec A , a P 7 (cos I/)2 1 2cos v sin v — + 7 . . . , /(sin i/)2 1 ^ tan + y—jp ^2 tan)2 = 0 . (2). 1890-91.] Prof. Tait on Dr Sang’s Paper. 339 The elimination of tan between (1) and (2) is easily effected by multiplying (2) twice over by tan, using (1) after each opera- tion. We thus avoid the radicals which make Dr Sang’s work so complicated, and we have only to eliminate tan <£ and (tan <£)2 among three equations of the first degree. The resulting equation is of the fourth degree in (sin v)2, but it contains the irrelevant factor (cos v)2 (sin v)2 + p2 [Another method of effecting the elimination, while quite as simple as that just given, has the advantage of not introducing the irrelevant factor. Write for shortness cos V =p sin v and we have p = 2 p cos + q sin tj> = — , y?(sin )3 + q( cos <£)3 = 0 . From the second of these, by the help of the first, we at once obtain p sin (f> + q cos <£ = — cos sin \y l or V + 2 cos sin y ' The following are immediate consequences : — obtained, respectively, by multiplying together the first and fourth of these equations, and by squaring and adding the first and third : — p2 + q2 + ay pq sin cos y2 p2 + q2 + ipq sin <£ cos = -^/l + (sin cf> cos <£)2 y \ From these the final result may be written by inspection, in the form 4 p2q2 1 pA + qA + =-2 i + p2q2 ( v 2 + an(l Cognate Curves. By the Hon. Lord McLaren, . . . . . . .83 The Influence of High Winds on the Barometer at the Ben Nevis Observatory. By Alexander Buchan, LL.D., ...... 88 Electrolytic Synthesis of Dibasic Acids'. Alkyl Derivatives of Succinic Acid. By Professor Crum Brown and Dr James Walker, . '. .95 Proposed Extension of the Powers of Quaternion Differentiation. By Alex- ander M‘Aul ay, Ormond College, Melbourne. Communicated by Professor Tait, . . . . . . . ... 98 On the Interaction of Longitudinal and Circular Magnetisations in Iron and Nickel Wires. (Second Note.) By Professor Cargill G. Knott, . .124 On the Composition of some Deep-Sea Deposits from the Mediterranean. By J. Y. Buchanan, F.R.S., ....... 131 On the Temperature of the Salt and Fresh Water Lochs of the West of Scotland, at Different Depths and Seasons, during the Years 1887 and 1888. By John Murray, LL.D., Ph.D., . . . . . . 139 On Silica and the Siliceous Remains of Organisms in Modern Seas. By J ohn Murray, LL.D., Ph.D.* &c., and Robert Irvine, F.O.S., . . . 229 A New Method for the Estimating the Specific Gravity of the Blood. By John Berry Haycraft, M.D., D.Sc., ...... 251 On the Estimation of Uric Acid in the Urine. A Reply to Criticisms upon the Silver Method. By John Berry Haycraft, M.D., D.Sc., . . : 255 On a Method of Observing and Counting the Number of Water Particles in a Fog. By John Aitken, F.R.S., . . . . . 259 On an Optical Proof of the Existence of Suspended Matter in Flames. By Sir G. G. Stokes, Bart., F.R.S. (In a letter to Professor Tait), . . 263 Note on the Isothermals of Ethyl Oxide. By Professor Tait, . . . 265 Ill Additional Observations on the Development and Life-Histories of the Marine Food-Fishes, and the Distribution of their Ova. By Professor W. C. M‘Intosh, F.R.S., ........ A Case of Defective Endochondral Ossification in a Human Foetus (so-called Cretinoid). By Johnson Symington, M.D., and Henry Alexis Thomson, M.D. (With Three Platbs), . . . . On the Blood of the Invertebrata. By Dr A. B. Griffiths, F.R.S.E., F.C.S., &c., A New Ship for the Study of the Sea. By His Serene Highness the Prince of Monaco, . . . The Electric Resistance of Cobalt at High Temperatures. By Professor Cargill G. Knott, D.Sc., F.R.S.E. (With a Diagram), .... The Thermoelectric Positions of Cobalt and Bismuth. By Professor Cargill G. Knott, D.Sc., F.R.S.E., . . . . On the Effect of Longitudinal Magnetisation on the Interior Volume of Iron and Nickel Tubes. By Professor Cargill G. Knott, D.Sc., F.R.S.E., . On some Relations between Magnetism and Twist. Parts II., III. By Pro- cessor Cargill G. Knott, D.Sc., F.R.S.E., . On the Gravimetric Composition of Water. A Preliminary Communication. By Professor W. Dittmar, F.R.S., Investigation of the Action of Nicol’s Polarising Eye-Piece. By Edward Sang, LL.D. (With a Plate), . . Note on Dr Sang’s Paper. By Professor Tait, ..... On the Extension of Brouncker’s Method to the Comparison of several Magni- tudes. By Edward Sang, LL.D., .... Meetings of the Royal Society — Session 1890-91, . . . Donations to the Library, . .... Obituary Notices, ... i Index, PAGE 268 271 288 295 303 310 315 318 320 323 337 341 349 357 -xxiii xxv ' I: i c