PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. irobrf i PROCEEDINGS THE ROYAL SOCIETY OF EDINBURGH. VOL. XXIX. NOVEMBER 1908 to JULY 1909. EDINBURGH: PRINTED BY NEILL AND COMPANY, LIMITED. MDCCCCIX. CONTENTS. The Shift of the Neutral Points due to Variation of the Intensity of Mechanical Vibrations or Electric Oscillations superposed upon Cyclic Magnetisation in Iron. By James Russell. Issued separately November 16, 1908, The Effect of Load and Vibrations upon Magnetism in Nickel. By James Russell. Issued separately December 5, 1908, ...... On the Recalescence Temperatures of Nickel. By T. A. Lindsay, M.A., B.Sc., Carnegie Scholar, Edinburgh University. Communicated by Professor J. G. MacGregor. Issued separately December 22, 1908, . On a Question in Absorption Spectroscopy. By Robert A. Houstoun, M.A., Ph.D., D.Sc., assisted by Alexander S. Russell, M.A. Communicated by Professor A. Gray. Issued separately December 22, 1908, . Dissymmetrical Separations in the Zeeman Effect in Tungsten and Molybdenum. By Robert Jack, M.A., B.Sc., Ph.D., 1851 Exhibition Research Scholar. Com- municated by Professor A. Gray. Issued separately December 30, 1908, . On the Reducing Action of Electrolytic Hydrogen on Arsenious and Arsenic Acids when liberated from the Surface of Different Elements. By William Thomson, F.I.C. Issued separately January 21, 1909, . . . . . Preliminary Note on the Action of Nitric Anhydride on Mucic Acid. By Professor A. Crum Brown, F.R.S., and G. E. Gibson, B.Sc. Issued separately February 19, 1909, .......... Temperature Observations in Loch Garry (Inverness-shire). With Notes on Currents and Seiches. By E. M. Wedderburn, LL.B., VV.S. Issued separately March 1, 1909, ......... On the Conditions for the Reversibility of the Order of Partial Differentiation. By W. H. Young, Sc.D., F.R.S. Communicated by J. H. Maclagan Wedderburn, D.Sc. Issued separately March 2, 1909, ...... Laboratory Note on a Study of Polarisation by means of the Dolezalek Electrometer. By A. F. Ewan, Physical Laboratory, Edinburgh University. Communicated by Professor J. G. MacGregor. Issued separately April 12, 1909, A Special Form of Photographic Camera for Recording the Readings of the Scales of Scientific Instruments. By James Robert Milne, D.Sc. Issued separately April 17, 1909, . . . On an Improved Form of Magnetometer and Accessories for the Testing of Magnetic Materials at Different Temperatures. By James G. Gray, B.Sc., Lecturer on Physics in the University of Glasgow, and Alexander D. Ross, M.A., B.Sc., Assistant to the Professor of Natural Philosophy in the University of Glasgow. Communicated by Professor A. Gray, FfRS. Issued separately April 17, 1909, . PAGE 1 38 57 68 75 84 96 98 136 165 176 182 VI Contents. Life and Chemical Work of Archibald Scott Couper. By Richard Anschutz, Ph.D., LL.D., Professor of Chemistry in the University of Bonn. Translated and com- municated by Emeritus-Professor A. Crum Brown, M.D., D.Sc., LL.D. (With Two Plates.) Issued separately April 30, 1909, . On the Magnetic Properties of certain Copper Alloys. By Alexander D. Ross, M.A., B.Sc., Assistant to the Professor of Natural Philosophy in the University of Glasgow, and Robert C. Gray, Thomson Experimental Scholar in the University of Glasgow. Issued separately May 3, 1909, , . Low Temperature Experiments in Magnetism. By James G. Gray, B.Sc., Lecturer on Physics in the University of Glasgow, and Hugh Higgins, M.A., Thomson Experimental Scholar in the University of Glasgow. Communicated by Professor A. Gray, F.R.S. Issued separately May 11, 1909, . On the Discharge of Water from Circular Weirs and Orifices. By G. H. Gulliver, B. Sc., A.M.I.Mech.E., Lecturer in Engineering in the University of Edinburgh. Issued separately May 11, 1909, ....... The Electromotive Force of Iodine Concentration Cells with One Electrode saturated with Iodine. By A. P. Laurie, D.Sc., M.A. Cantab. Issued separately May 11, 1909, . . . . . . . . . Cynomacrurus Piriei , Poisson abyssal nouveau recueilli par l’Expedition Antarctique Nationale Ecossaise. Note preliminaire, par Louis Dollo, Sc.D. (Cantab.), For.Mem.G.S., C.M.Z.S., a Bruxelles (Musee). Presentee par M. R. H. Traquair, M.D., F.R.S. , Y.P.R.S.E. Issued separately May 13, 1909, On Lagrange’s Equations of Motion, and on Elementary Solutions of Gyrostatic Problems. By Professor Andrew Gray, F.R.S. Issued separately May 13, 1909, On Energy Accelerations and Partition of Energy. By C. W. Follett. Com- municated by Professor W. Peddie. Issued separately May 15, 1909, The Systematic Motions of the Stars. (Second Paper.) By Professor Dyson. Issued separately May 15, 1909, ........ Flexural Vibrations of Thin Rods. By George Green, M.A., B.Sc., Assistant to the Professor of Natural Philosophy in the University of Glasgow. Communicated by Professor Gray. Issued separately April 30, 1909, .... A Negative Attempt to detect Fluorescence Absorption. By Robert A. Houstoun, M.A., D.Sc., Ph.D., Lecturer on Physical Optics in the University of Glasgow. Communicated by Professor A. Gray, F.R.S. Issued separately July 8, 1909, Experiment with the Spark Gap of an Induction Coil. By Dr Dawson Turner. Issued separately July 8, 1909, ....... Strophantlius sarmentosus : its Pharmacological Action and its Use as an Arrow Poison. By Sir Thomas R. Fraser, M.D., F.R.S. L. and E., Professor of Materia Medica in the University of Edinburgh ; and Alister T. Mackenzie, M.A., M.B., Ch.B., Carnegie Research Scholar. (Abstract.) Issued separately July 9, 1909, . On the Histological Changes in the Liver and Kidney after Chloroform administered by Different Channels. By G. Herbert Clark, M.B., D.P.H. ( From the Physiological Laboratory of the University of Glasgow.) (With Three Plates.) Issued separately July 9, 1909, ....... PAGE 193 274 287 295 304 316 327 349 376 393 401 414 415 418 Contents. Vll PAGE On the Effect of Internal Friction in Cases of Compound Stress. By G. H. Gulliver, B.Sc., A.M.I.Mech.E., Lecturer in Engineering in the University of Edinburgh. Issued separately July 9, 1909, ....... 427 On the Friction at the Extremities of a Short Bar subjected to a Crushing Load, and its Influence upon the Apparent Compressive Strength of the Material. By G. H. Gulliver, B.Sc., A.M.I.Mech.E., Lecturer in Engineering in the University of Edinburgh. Issued separately July 16, 1909, ..... 432 On Group-Velocity and on the Propagation of Waves in a Dispersive Medium. By George Green, M.A., B.Sc., Assistant to the Professor of Natural Philosophy in the University of Glasgow. Communicated by Professor A. Gray, F.R.S. Issued separately July 16, 1909, ....... 445 On a Simple Radioscope and a Radiometer for showing and measuring Radio- activity. By Dr John Aitken, F.R.S. Issued separately July 21, 1909, . 471 Nematonurus Lecointei, Poisson abyssal de la “Belgica” retrouve par l’Expedition Antarctique Nationale Ecossaise. Note preliminaire, par Louis Dollo, ScD. (Cantab.), Ph D. (Giessen), Min. et Geol. D. (Utrecht), a Bruxelles (Musee). Presentee par M. R. H. Traquair, M.D., LL.D., F.R.S., V.P.R.S.E. Issued separately August 5, 1909, ....... 488 The Theory of Jacobians in the Historical Order of Development up to 1860. By Thomas Muir, LL.D. Issued separately August 6, 1909, . . . 499 Motion of Neptune’s Satellite. By David Gibb, M.A., B.Sc. Communicated by Professor Dyson. Issued separately August 23, 1909, . . . .517 The Pathogenesis of Micrococcus melitensis. By J. Eyre, M.D., Bacteriologist to Guy’s Hospital, Member Advisory Board of Mediterranean Fever Commission, and Chairman of the 1906 Working Party in Malta. Issued separately September 7, 1909, . . . . . . . 537 The Development of the Auditory Ossicles in the Horse, with a Note on their possible Homologues in the Lower Vertebrata. By Ray F. Coyle, B.S. ( From the Zoological Department of the University of Edinburgh.) Communicated by Professor J. C. Ewart, M.D., F.R.S. (With Six Plates.) Issued separately September 9, 1909, ........ 582 Dr O. Pettersson’s Observations on Deep Water Oscillations. By E. M. Wedderburn, W.S. (With a Plate.) Issued separately August 14, 1909, . . . 602 Mendelian Action on Differentiated Sex. By D. Berry Hart, M.D., F.R.C.P.E., Lecturer on Midwifery, Surgeons’ Hall, Edinburgh ; Carnegie Research Fellow. {From the Laboratory of the Royal College of Physicians.) (Abstract.) Issued separately September 29, 1909, ....... 607 Observations with a Current Meter in Loch Ness. By E. M. Wedderburn, W.S., and W. Watson, M.A., B.Sc. Issued separately October 1, 1909, . . 619 Hydrolysis of Salts of Amphoteric Electrolytes. By Miss Heather Henderson Beveridge, B.Sc., Carnegie Research Scholar. Communicated by Professor James Walker. Issued separately October 14, 1909, ..... 648 The Superadjugate Determinant and Skew Determinants having a Univarial Diagonal. By Thomas Muir, LL.D. Issued separately October 15, 1909, 668 Vlll Contents. PAGE The Skeleton of a Sowerby’s Whale, Mesoplddon bidens , stranded at St Andrews, and the Morphology of the Manus in Mesoplodon, Hyperoodon and the Delphinidae. By Sir Wm. Turner, K.C.B., D.C.L., F.R.S., President of the Society. Issued separately October 14, 1909, ....... 687 The Atomic Weight of Platinum. By E. H. Archibald. Communicated by Professor MacGregor. Issued separately December 2, 1909, . . . .721 On the Development of Mixed Cultures of Bacteria and Lower Fungi in Liquid and Solid Media. By Emil Westergaard, Lecturer on Technical Mycology, Heriot- Watt College, Edinburgh. (Preliminary Notice.) Issued separately December 2, 1909, .......... 748 Obituary Notice, ......... 749 Appendix — Proceedings of the Statutory General Meeting, 1908, .... 753 Proceedings of the Ordinary Meetings, Session 1908-1909, . . .754 Laws of the Society, . . . . . . . .759 The Keith, Makdougall-Brisbane, Neill, and Gunning Victoria Jubilee Prizes, . 764 Awards of the Keith, Makdougall-Brisbane, Neill, and Gunning Victoria Jubilee Prizes, . . . . . . . . . .766 The Council of the Society, 1909-1910, . . . . . .771 Alphabetical List of the Ordinary Fellows of the Society, . . .772 List of Honorary Fellows of the Society, . . . . . . 788 List of Ordinary Fellows of the Society elected during Session 1908-1909, . 789 Ordinary Fellows deceased and resigned during Session 1908-1909, . .790 Abstract of Accounts of the Society, Session 1908-1909, . . . .791 Index, .......... 797 PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SESSION 1908-9. Part I.] VOL. XXIX. [Pp- 1-64. CONTENTS. NO. PAGE I. The Shift of the Neutral Points due to Variation of the Intensity of Mechanical Vibrations or Electric Oscillations superposed upon Cyclic Magnetisation in Iron. By James Russell, . 1 {Issued separately November 16, 1908.) II. The Effect of Load and Vibrations upon Magnetism in Nickel. By James Russell, ...... 38 ( Issued separately December 5, 1908.) III. On the Recalescence Temperatures of Nickel. By T. A. Lindsay, M.A., B.Sc., Carnegie Scholar, Edinburgh University. (< Communicated by Professor J. G. MacGregor), . 57 ( Issued separately , 1908.) EDINBURGH : Published by ROBERT GRANT k SON, 107 Princes Street, and WILLIAMS k NORGATE, 14 Henrietta Street, Covent Garden, London. MDCCCCVIII. Price Four Shillings. REGULATIONS REGARDING THE PUBLICATION OF PAPERS IN THE PROCEEDINGS AND TRANSACTIONS OF THE SOCIETY. The Council beg to direct the attention of authors of communications to the Society to the following Regulations, which have been drawn up in order to accelerate the publication of the Proceedings and Transactions, and to utilise as widely and as fairly as possible the funds which the Society devotes to the publication of Scientific and Literary Researches. 1. Manuscript of Papers. — As soon as any paper has been passed for publication, either in its original or in any altered form, and has been made ready for publication by the author, it is sent to the printer, whether it has been read or not. The ‘ copy ’ should be written on large sheets of paper, on one side only, and the pages should be clearly numbered. The MS. must be easily legible, preferably typewritten, and must be absolutely in its final form for printing ; so that corrections in proof shall be as few as possible, and shall not cause overrunning in the lines or pages of the proof. All tables of contents, references to plates, or illustrations in the text, etc., must be in their proper places, with the page numbers left blank; and spaces must be indicated for the insertion of illustrations that are to appear in the text. 2. Illustrations. — All illustrations must be drawn in a form im- mediately suitable for reproduction ; and such illustrations as can be reproduced by photographic processes should, so far as possible, be preferred. Drawings to be reproduced as line blocks should be made with Indian ink (deadened with yellow if of bluish tone), preferably on fine white bristol board, free from folds or creases ; smooth, clean lines, or sharp dots, but no washes or colours, should be used. If the drawings are done on a large scale, to be afterwards reduced by photography, any lettering or other legend must be on a corresponding scale. If an author finds it inconvenient to furnish such drawings, the Society will have the figures re-drawn at his expense ; but this will cause delay. When the illustrations are to form plates, a scheme for the arrangement of the figures (in quarto plates for the Transactions, in octavo for the Proceedings) must be given, and numbering and lettering indicated. 3. Proofs. — In general, a first proof and a revise of each paper will be sent to the author, whose address should be indicated on the MS. If further proofs are required, owing to corrections or alterations for which [■ Continued on page in of Cover. PROCEEDINGS X'- OF THE ROYAL SOCIETY OF EDINBURGH. YOL. XXIX. 1908-9. I. — The Shift of the Neutral Points due to Variation of the Intensity of Mechanical Vibrations or Electric Oscillations superposed upon Cyclic Magnetisation in Iron. By James Russell. (Read November 18, 1907. MS. received July 18, 1908.) CONTENTS. Introduction and Objects of Investigation I. Mechanical Vibrations. II. Electric Oscillations. Apparatus page 3 page 14 Experimental Methods 55 4 55 15 Intensity of Vibrations or Oscillations . 55 5 55 17 Diagrams .... 55 5 * ’ ' • 55 17 Cyclic Field | ^ata 5’ 5 • • • * 55 17 l Results 55 10 * * • • 55 24 Cyclic Residual ( Data '5 12 } Magnetisation \ Results 5) 12 ) • • * * 55 Results with Cyclic Field AND Cyclic Residual Magnetisation IN Terms of Field Change .... IV. Dr Eccles and Professor Maurain’s Results V. Molecular Theory Conclusion PAGE 1 26 28 30 34 When mechanical vibrations or electric oscillations are superposed at all points of a normal hysteresis loop, the induction at the cyclic extremes is increased, the residual magnetisation decreased, and those differences of magnetic condition to which hysteresis gives rise lessened. The curves delineating these changes form a continuous loop, and neutral points occur where vibrations superposed upon decreasing cyclic field produce no induction change whatever. VOL. XXIX. 1 2 Proceedings of the Royal Society of Edinburgh. [Sess. In a former communication * it was found that the position of the neutral points in the first and third quadrants depends not only upon the cyclic amplitude, but upon the intensity of the vibrations. To quote : “ The smaller the cyclic field ” (amplitude) “ and the greater the vibrational intensity, the closer is the neutral point thrust towards the vertical axis ; the higher the cyclic field and the less the vibrational intensity, the closer is the neutral point thrust towards the cyclic extreme.” For any given loop, therefore, the position of the neutral points depends wholly on the intensity of the vibrations. In a recent paper, Maurain,j* experimenting with electric oscillations, obtained a different result. He found that the position of the neutral points in the first and third quadrants is where “ la courbe d’ aimantation stable ,” as defined, cuts the particular hysteresis loop upon which the oscillations are superposed. Their position, thus definitely fixed, is, according to these experiments, independent of the intensity of the oscilla- tions. On the other hand, Dr Eccles,J also experimenting with electric oscillations produced by single minute sparks, obtained yet another result. Although the “ spark effect ” increases the induction at both cyclic extremes, the first recorded readings, as these positions are departed from, show in all cases decrease of induction. There is here no evidence of neutral points, and the curves plotted from the observations are discontinuous in the same way that dB/dH plotted against cyclic field produces curves discontinuous at the cyclic extremes. Further, in an earlier series of experiments, Garibaldi found that Hertzian waves increased or decreased the permanent magnetism of steel according as it had or had not been previously subjected to a demagnetising field immediately withdrawn. On the other hand, Maurain, in the paper above referred to, obtained a result which he describes as “ presqwe nulle” when oscillations are superposed upon residual magnetisation which had been reached by the same process of withdrawing a demagnetising field. The author of a paper § which I have been unable to refer to wrote me as follows : — I found that if a piece of iron or steel is magnetised by a direct current , and then demagnetised by reversing the current , the effect * “ The Superposition of Mechanical Vibrations (Electric Oscillations) upon Magnetism, and conversely, in Iron, Steel, and Nickel,” Trans. R.S.E., vol. xlv., part ii., p. 510. Phil. Mag ., Oct. 1907. Electrician , July 5, 1907. t “ Les Detecteurs magnetiques et faction des Oscillations electriques sur f aimantation,” Journal de Physique , Janvier 1907. f Proceedings of the Physical Society of London, vol. xx. Phil. Mag., August 1906. § Note presented at the Meeting of the American Association for the Advancement of Science, by G. F. Stradling. (Reports have not been received by the R.S.E. for several years.) 1908-9.] Vibrational Neutral Points in Magnetised Iron. 3 of a series of taps is first to cause the development of magnet ic poles in the sense of those produced by the magnetising current. The strength of the poles reaches a maximum and diminishes. I was not able to get this effect by tapping the iron after the magnetising current was broken, but only when the iron was at least approximately demagnetised. Fromme seems to have found this effect, though he says very little about it.” Eccles connects the magnitude of the spark effect “ at any point ” with the slope of the hysteresis loop ; Maurain, with the whole magnetic history of the iron. According to the latter, the direction of the induction change depends upon the position of the point where oscillations are superposed relative to “ la courbe d’ aimantation stable ” ; according to Garibaldi and Stradling, it must depend also on how that point had been reached. None of these apparently discordant results are, however, complete statements of the whole facts as observed by the author. All alike have failed to recognise the shift of the neutral points with the intensity either of the mechanical vibrations or electric oscillations, which implies that within the limits of the range of shift their intensity determines whether the induction will be increased or decreased. I shall endeavour to show that the introduction of this factor, which the present investigation fully confirms and extends, co-ordinates the apparently discordant results; is not only in harmony with the molecular theory of magnetism, but a necessary deduction from it. I. Mechanical Vibrations. Apparatus. The mild steel wire (100 cms. long and ’092 cms. diameter), one of the wires with which the former experiments had been made, was, after demagnetisation by decreasing reversals, reannealed by passing a bunsen flame along its entire length. It was wound with a few turns of soft woollen yarn and inserted in the axis of the horizontal magnetising coil, 41 cms. long, placed at right angles to the earth’s magnetic field. One of its ends was soldered to the edge of the gong of the electric bell, the whole apparatus, as previously described, being suspended from the roof by means of india-rubber tubing to prevent as far as possible any external disturbances reaching the wire. The damped trains of mechanical vibrations were produced in the wire by a steel ball so arranged as to strike the gong once after rolling down the angle between two inclined planes. An exploring coil and ballistic galvanometer (11 seconds complete period), with com- 4 Proceedings of the Royal Society of Edinburgh. [Sess. pensating coils, measured as before the change of magnetic intensity at approximately the central portion of the wire. Experimental Methods. Cyclic Field. — After demagnetisation by decreasing reversals (the revolving commutator being used), the Held, put on by steps of increasing reversals, is reversed about forty times at some pre-arranged extreme value. One-half the average of two consecutive readings determines the induction at this cyclic extreme ; from which steps (the first being zero) are then taken to a sufficient number of points in the first and third quadrants from positive and negative amplitudes respectively, the induction change being noted. At each point the galvanometer readings are again noted, on the superposition of a series of nine damped trains of vibrations of increasing intensity, produced by increasing the heights through which the steel ball falls in arithmetical progression. On the completion of each series, the field is put off in steps of decreasing reversals. In no case are further vibrations superposed at the same or any other point until the demagnetising process, followed by reversals at the cyclic amplitude, has intervened. Cyclic Residual Magnetisation.— After about forty reversals at a high value of field amplitude, the induction is first determined as above described. Noting the galvanometer reading on withdrawing the field determines the residual magnetisation, which is now subjected to various values of a reversed field, so selected that when withdrawn the steel wire is left residually magnetised in zero field at a sufficient number of points of what may very well be called cyclic residual magnetisation between positive and negative maxima of residual magnetisation in the usual sense. A number of these points are shown in the reference diagram accompanying figs. III. and IV., and their positions on the vertical axis are determined by noting the two galvanometer readings when the reversed field is put “ on ” and "off,” taken in conjunction with the value of the residual magnetisation previously determined. At each point the galvanometer readings are again noted on the superposition of the nine damped trains of mechanical vibrations of increasing intensity produced as above described. On the completion of each series the cyclic extreme is again reverted to, and in no case are further vibrations superposed at the same or any other point until after forty reversals of the cyclic field, followed by the cyclic field process as above described. Owing to the high field amplitude, de- magnetisation by decreasing reversals was considered unnecessary. 1908-9.] Vibrational Neutral Points in Magnetised Iron. 5 Intensity of Vibrations. The intensity of the mechanical vibrations may be increased either by increasing the weight (W) of the steel ball or the vertical distance (D) through which it falls before striking the gong to which the experimental wire is soldered. When W and D are varied simultaneously so that the product of W x D° 7 is not changed, it is found that, under the same conditions, the induction change in the wire as measured by the ballistic galvanometer also remains unchanged within the limits of accuracy attainable in these experiments. The intensity of the vibrations is used in the sense that it varies with the function W x D0-7. In any series of experiments the same ball is used, the distance through which it falls alone being varied. Diagrams. Field (H), induction (B), and induction change (dB) are in C.G.S. units in all the diagrams. The intensity of the vibrations is proportional to W x D0’7, the weight (W) of the steel ball being in grams, the vertical distance (D) through which it falls in cms. All the points plotted are obtained by averaging the readings taken at symmetrical points in reference to the positive and negative cyclic extremes. They are, however, represented in all the diagrams as if taken in reference to the positive extremes. This applies both to cyclic fields and cyclic residual magnetisation. Cyclic Field. Experimental Data. — In fig. I. a series of nine trains of damped mechanical vibrations increasing in intensity are superposed in succession upon a sufficient number of points of that part of the hysteresis loop decreasing for H — 1*9, B = 3170 (cyclic extreme) to H = 0, B = 2000. The abscissae represent the intensity of the vibrations, increasing from W x D0'7 = 2*2 to 10'4, superposed at eight values of field, viz. H = T9, 172, 1*6, F34, IT, 095, 052, and 0; the ordinates, the summation of the induction changes following thereon. Fig. I. taken in conjunction with Table I. which supplies the actual data from which two of the curves, viz. H = 1’34 and I T, have been plotted, is, without further explanation, self-explanatory. Fig. I.a shows the same curves drawn to a slightly contracted horizontal scale, to a largely expanded vertical scale, in so far as they can be shown within the limits of about B = zk 60. The rectangles in dash lines show the contraction and expansion of the horizontal and vertical ordinates 6 Proceedings of the Koyal Society of Edinburgh. [Sess. 1908-9.] Vibrational Neutral Points in Magnetised Iron. 7 Table I. — Decreasing Cyclic Field. Mechanical Vibrations. r- * V ibrations superposed upon Vibrations regarded as superposed upon H = + T34. o Q X £ H = +T34 reduced from H= + T9. H= - T34 reduced from H= -D9. Average readings. Summation. Summation x 2’95 = Total change of B. 2*2 -3 3 -3 - 3 - 9 3-6 -0-5 0-5 -0-5 - 3 5 - 10-5 4-8 2 - 3 2*5 - 1 - 3 5-9 4 - 6 5 4 12 69 11 - 9 10 14 41 7-8 14 -10 12 26 77 8-7 12 - 18 15 41 120 9-6 22 - 24 23 64 189 10-4 26 - 18 22 86 254 i>- * Vibrations superposed upon Vibrations regarded as superposed upon H = + IT. o Q X & H= + ri reduced from H= +T9. H= - IT reduced from H= -1-9. Average readings. Summation. Summation x 2’75 = Total change of B. 2-2 -5 5 -5 - 5 - 15 3-6 -3 3 -3 - 8 -24 4-8 -2 1-5 - 1-75 - 9-75 -29 5-9 - 1 -0-5 -0’25 - 10 -30 6-9 1 -1 1 - 9 -27 7-8 4-5 -3-5 4 - 5 - 15 8-7 2 -4 3 - 2 i 6 9*6 6 -8 7 5 15 10-4 9 -7 8 13 38 Curve H = 1T of fig. I. Curve H = D34 of fig. 8 Proceedings of the Royal Society of Edinburgh. [Sess. respectively in fig. La as compared to fig. I. Fig. I.a also shows a second series of experiments, conducted in exactly the same way, in which, by means of a smaller steel ball (0252 grams instead of 1*475 grams), nine trains of vibrations of increasing intensity are superposed in succession between the values of WxD°'7 = 0*38 and 1*8 for the various values of H shown. Had these curves been drawn to the same scale as that adopted in fig. I., they would have fallen within the area of the small rectangle shown with that figure. Fig. I.a therefore enables the curves to be more readily traced closer to the vertical axis, the lowest value of W x D° 7 (038) being twenty-seven times less in intensity than the highest value (104). Note that the curves for the same values of H in the two series of experiments are not in all cases continuous. The conditions are different. Thus it is obvious from the discontinuity of the curves when H — T34, 052, and 0, that the demagnetising effect of nine vibrational trains of increasing intensity superposed in succession between the limits of W x D° 7 = 0*38 and 1*8 is greater than that of the initial single vibrational train W x D0’7 = 2*3 of the first series of experiments. On the other hand, when H=l*72 and 1*6 the curves appear to be quite continuous, notwithstanding the dissimilarity of the conditions. The experiments illustrated in fig. I. were repeated for a lower and a higher value of cyclic amplitude, and all the results are shown in the three diagrams of fig. II., the field and induction at cyclic amplitudes being H — 125, 19, 2*7, and B = 1270, 3170, 10,400 respectively. The induction changes are in this instance not plotted against W x D0"7 for various values of field as in fig. I., but against field (decreasing from the positive cyclic extreme) as abscissse for various values of W x D0*7. The curves of the middle diagram are thus derived from the same experimental data as those of fig. I. In the latter case each curve represents one series of readings obtained consecutively ; in the former case each curve is obtained by selecting the same particular values of W x D0'7 from eight distinct series of readings. The curves for the vibrational intensities W x D°‘7 — 3*6, 5 '9, 7'8, and 9*6 have been omitted in these diagrams to avoid unneces- sary crowding. The openness of the vertical scale shows clearly the regular sequence in which the curves cross each other, and also the shift of the neutral points where each curve crosses the horizontal axis ; but it precludes the delineation of the complete curves, with the exception of those for the lowest vibrational intensity in each case, viz. W x I)0’7 = 2*2. It majq however, be stated that the curves do not appear to cross each other at any other points than those shown in these diagrams, nor do they cross each other at any point whatever when induction change is plotted against 1908-9.] Vibrational Neutral Points in Magnetised Iron. 9 DECREASING CYCLIC FIELD. MECHANICAL VIBRATIONS. 10 Proceedings of the Royal Society of Edinburgh. [Sess. W x D° 7 for the various values of held decreasing from the cyclic extremes (%■ L)- The broken line curve of the middle diagram of hg. II. has not yet been referred to. It is derived from the same experimental data from which the second series of curves (within the dash line rectangle) of hg. I.a were plotted, by selecting from eight distinct series of experiments for various values of H the readings obtained upon the superposition of the initial single vibrational train only in each case. These readings are given fully in Table II. The intensity of the vibrations is represented by W x D° 7 = 0*38, and the necessity of taking readings at values of decreasing held close to the cyclic extreme, for this the lowest vibrational intensity used in these experiments, may be noted. Table II. — Decreasing Cyclic Field. Mechanical Vibrations. w c+H o | TJ1 Vibrations super- posed upon . Vibrations regarded as superposed upon + H. oo CD O 4 + > H + . H - . Average readings. x2-95 = change of B. CO 6 II © Q T9 3*0 -3*5 3-25 9-5 X is 1-86 1-25 -075 DO 3 i—5 i — i 1*83 0-25 -0-25 0-25 0-75 bb cpi 1-72 -0-5 0-25 - 0-375 -1 P p o 1-6 - 1*0 0-75 -0-875 -2-5 o> £ 1-34 - 1*0 1*0 -DO - 3 Pi CD o Pi pq 0-52 - 1-75 1-75 - 1*75 -5 0 -2-75 1-75 -2-25 -6-5 Results. — When damped trains of mechanical vibrations of increasing intensity are superposed upon that part of a normal hysteresis loop when the held is decreasing, the induction is for various values of held neither at nor too far removed from the cyclic extremes, first decreased, afterwards increased. The curves representing these changes (hgs. I. and I.a) hrst fall somewhat below, afterwards may rise largely above, the horizontal axis. Any one of these curves is sufficient to show that the direction of the induction change is not independent of the vibrational intensity, while a comparison of the curves confirms the conclusion previously arrived at 11 19 08-9. J Vibrational Neutral Points in Magnetised Iron. (by a different experimental method) that for any given normal loop the neutral points are thrust from or towards the cyclic extremes according as the vibrational intensities are greater or less. Thus for a cyclic ampli- tude of H = T9, B = 3170 (fig. I.a), the neutral points for the following ascending values of the decreased cyclic field, viz. H = 1T, T34, 1*6, and 1*72, occur with vibrations of decreasing intensity of approximately W X D07 = 9, 5, 2, and 1 respectively. It is also further evident that the neutral points are not only thrust towards the cyclic extremes the weaker the vibrations, but that they may occur quite close to it, provided the vibrational intensity is sufficiently reduced. For instance, with a field value of H = T83 removed from the cyclic extreme by so small an amount as 0*07, although the curves fail to fall below the horizontal axis, it has every appearance of doing so had the intensity of the initial vibrational train been only a little less than W x D07 — 0*38 (fig. I.a). In any case, a higher limiting value of the neutral points occurs well within II = 01 of the cyclic extremes, for this particular value of the amplitude, if the mechanical vibrations are weak enough (see also broken line curve, fig. II.). On the other hand, the neutral points are thrust from the cyclic extremes the greater the vibrational intensity, until a lower limiting value of the decreased cyclic field is reached, beyond which vibrations of all intensities produce only induction decrease (fig. I., H = 0*95, 0*52, also the middle diagram of fig. II.). The above results apply to a cyclic amplitude of H — 1*9, B = 3170. At lower and higher amplitudes, viz. 11 = 1*25, B = 1270, and H = 2*7, B = 10,400, the various neutral points with different vibrational intensities occur at lower and higher values of field respectively, and each corre- sponding neutral point for any given vibrational intensity is thus thrust from the vertical axis the higher the amplitude (fig. II.). At these three increasing values of cyclic amplitudes, the range of field through which the neutral points may shift with intensity, viz. H = 0*43, 0*54, and 0*67 respectively, is also increased as the amplitudes are increased (fig. II.), but this must again contract as saturation values are reached. To sum up, the conclusions may now be stated more definitely and fully than in the previous communication. The neutral points which occur when vibrations are superposed upon the decreasing cyclic field symmetrical about the origin are thrust towards the vertical axis the less the cyclic amplitude and the greater the vibrational intensity, towards the cyclic extreme the greater the cyclic amplitude and the less the vibrational in- tensity. There are thus lower and higher limiting values of the decreasing field through which the neutral points may shift, and both must vanish in 12 Proceedings of the Royal Society of Edinburgh. [Sess. the origin or the cyclic extremes according as the amplitude is sufficiently decreased (zero amplitude at the origin) or sufficiently increased (saturation values of induction at the extremes). The maximum range of possible shift, which may be extensive, occurs between these two extremes. Between the lower and higher limiting values of the range of shift, vibrations in- crease or decrease the induction according as the vibrations are sufficiently increased or sufficiently decreased. Below the lower limiting value vibra- tions of all intensities, however great, decrease the induction. Above the higher limiting value, vibrations of all intensities, however weak, increase the induction. In Section III. these results will be co-ordinated with the immediately preceding field change. Cyclic Residual Magnetisation. Experimental Data. — In fig. III. the series of nine trains of damped vibrations, increasing in intensity, are superposed in succession upon a sufficient number of values of cyclic residual magnetisation as already defined, between the limits of B= +9100 and —9100, the field being zero. The reference diagram shows these values as reached from the positive cyclic extreme, viz. H — 2 7, B = 10,400, just as the results for cyclic field have been represented as occurring with the decreasing positive field. The abscissm (fig. III.) represent (as in fig. I.) the intensity of the vibrations in- creasing from W xD°'7 = 2,2 to 10*4 superposed upon eight values of cyclic residual magnetisation, viz. B = + 9100, +8700, +8020, +7500, +4570,0, — 3390 and — 9100 ; the ordinates, the summation of the induction changes following thereon. In fig. IV. the induction changes from the same experimental data are plotted, not against W x D0'7 for various values of cyclic residual magnetisa- tion, as in fig III., but against cyclic residual magnetisation as abscissae for the following values of vibrational intensity, viz. WxD07 = 2'2, 4'8, 6*9, and 10*4. The curves for the other five values of vibrational intensities have been omitted, to avoid confusion. Obviously figs. III. and IV. for cyclic residual magnetisation correspond to figs. I. and II. respectively for decreasing cyclic field. Results. — When damped trains of mechanical vibrations are superposed at the extreme values of cyclic residual magnetisation, the resulting induction changes are, for reasons of symmetry, the same quantitatively, but of reversed sign — negative in reference to positive magnetisation, positive in reference to negative magnetisation. In other words, the residual magnetisation is for all values of vibrational intensity reduced. In fact, the extreme values of 1908-9.] Vibrational Neutral Points in Magnetised Iron. 13 CYCLIC RESIDUAL MAGNETISATION. 10 4 14 Proceedings of the Royal Society of Edinburgh. [Sess. cyclic residual magnetisation are reached in the ordinary way by with- drawing the field at the cyclic amplitudes. But as these extreme and symmetrical positions are departed from, the curves for the same inter- mediate values of positive and negative cyclic residual magnetisation plotted against increasing values of W x D0'7 become wholly unsymmetrical. To so great an extent is this the case that the decrease of the cyclic residual magnetisation has, for the lowest value of vibrational intensity, viz. W x D0'7 — 2*2, wholly vanished when B= +8700 is reached, to be immedi- ately replaced by increase at only slightly lower values, viz. B = + 8020 and +7500 (fig. III.). These curves further show that the direction of the induction change is not independent of the vibrational intensity. They first rise somewhat above, afterwards may fall largely below the horizontal axis. The neutral points which therefore occur are thrust from or towards the positive extreme of residual magnetisation according as the vibrational intensities are greater or less. Thus, for values of cyclic residual mag- netisation between the limits of B = zb 9100, the neutral points for the following ascending values of B— +7200, +7700, +8020, and +8700 occur with vibrations of decreasing intensity, viz. W x D0'7 = 10'4, 6*9, 4*8, and 2*2 (fig. IV.). Thereafter, vibrations of all intensities between the above experimental limits increase the cyclic residual magnetisation to a greater extent the less its value. When the zero of residual magnetisa- tion is passed, the positive induction change, now decrease in reference to the negative magnetisation, continues at somewhat increased values until the negative extreme is reached. These results do not differ essentially from those obtained with cyclic field. The shift of the neutral points is subject to essentially the same laws, although the direction of the induction changes is opposite in the two cases. At a later stage (Section III.) it will be shown that even these apparently opposite effects disappear when the results for cyclic field and cyclic residual magnetisation are expressed, not in terms either of magnetisation or of field, but of field change. II. Electric Oscillations. Apparatus. Experiments were in the first place tried with the mild steel wire *092 cms. diameter, already used, and the results obtained for transverse oscillations will be given later. Owing to the effect of the oscillations being mainly confined to the surface of the wire, the galvanometer readings were, 15 1 908—9.] Vibrational Neutral Points in Magnetised Iron. as anticipated, much less than with mechanical vibrations. Lengths of iron wires 100 cms. long and 0*028 cms. diameter, annealed and varnished, were therefore made up into bundles of five wires each. Four of these bundles could be inserted into either of two narrow glass tubes 41 cms. long. Round the first, five silk-covered copper wires 0*056 cms. diameter were closely wound in a single layer, through which oscillations could be passed in parallel. This formed oscillation solenoid No. 1, with three (15/5) effective turns of wire per cm. of length. The second glass tube was wound with a single silk-covered copper wire of the same diameter, also in a single layer throughout its entire length, through which oscilla- tions could be passed in series. This second glass tube formed oscillation solenoid No. 2 with fifteen (effective) turns per cm. of length. Either of these solenoids, after insertion in the magnetising coil at right angles to the earth’s field and as previously described, could be con- nected with the secondary of an air oscillation transformer consisting of eights turns of copper wire 0*264 cms. diameter, insulated from its supports by means of india-rubber tubing. The radius of the secondary was 8*7 cms., and it was earthed at a point approximately equidistant from its terminals.* The primary, consisting of one turn of copper wire insulated in the same way, 0*264 cms. diameter and 15 cms. radius, was connected with the terminals of a small Wimshurst machine (8-inch plates) with one of its small Leyden jars in series. A row of spark gaps, each 1 mm. in length, formed a shunt across the terminals of the Wimshurst, and any number from one to ten could be introduced into this parallel circuit by means of a sliding wire connection, pointed at one of its ends so as to rest securely in small holes drilled in the spark balls. These were of brass, 1*2 cms. diameter, and only approximately spherical. They were cemented to vertical glass supports. The above description is illustrated in fig. V., which may be regarded as a plan of the apparatus drawn to scale. In the preliminary experiments with the single steel wire (*092 cms. diameter) a single micrometer spark gap was used. It could be increased in length from 1 to 12 mm. Experimental Methods. Cyclic Fields. — The sequence of operations observed and the galvano- meter readings taken were entirely similar to those which have been fully described for mechanical vibrations, with the following exception. It was * This was found to be absolutely necessary. Without the earth connection, the spot of light moved over a large part of the scale, more especially just before the passage of the spark ; with the earth connection, a sharp deflection was obtained on the passage of the spark, in the vast majority of cases from a steady zero position. 16 Proceedings of the Royal Society of Edinburgh. [Sess. not considered necessary, with the high induction amplitude alone used, viz. B = 8000, that demagnetisation by decreasing reversals should follow upon the completion of each series of readings. In no case, however, were further trains of oscillations of increasing intensity superposed at the same or any other point until about forty reversals of field at the cyclic amplitude had intervened. The superposed trains of damped secondary electric oscillations were increased in intensity by progressively increasing either the number of 1 mm. spark gaps in series or the length of the single micrometer spark gap. In the former case, oscillation solenoids No. 1 and No. 2 were used, which subjected the bundles of fine iron wires to oscillations co-directional with the magnetising cyclic field; in the latter case the steel wire ’092 cms. diameter was subjected to transverse oscillations, its ends being directly connected with the secondary of the air transformer. With co-directional oscillations it was found necessary to reverse the connections between the secondary of the oscillation transformer and either of the oscillation solenoids. Under these conditions the Wimshurst machine did not reverse its polarity during any series of continued experiments, although it might do so from day to day. The results obtained by reversing the connections between the oscillation primary and the Wimshurst could only be explained by the polarity of the latter reversing in an erratic manner. This method was therefore discarded from the first. 1908-9.] Vibrational Neutral Points in Magnetised Iron. 17 Intensity of Electric Oscillations. In the first part of this paper a very definite meaning could be attached to the intensity of the mechanical vibrations. It was found that their intensity varied with a function of the weight (W) of the ball and the distance (D) through which it fell, the function being approximately W x D0-7. With electric oscillations the same definite signification does not apply. It is assumed that the intensity of the resultant trains of damped oscillations in the secondary of the air transformer is increased or decreased as the number of 1 mm. sparks in series or the length of the single spark is increased or decreased. Diagrams. These are plotted from the experimental data in the way already described for mechanical vibrations, the intensity of the electric oscillations being represented by the number of 1 mm. sparks in series or the length of the single spark, for co-directional and transverse oscillations respectively. Field (H), induction (B), and induction change (dB) are likewise in C.G.S. units. Cyclic Field. Experimental Data. — In fig. VI. a b and fig. VII., with the twenty iron wires, (H)28 cms. diameter, inserted in oscillation solenoids Nos. 1 and 2 re- spectively, a series of ten trains of damped electric oscillations, increasing in intensity and co-directional with the magnetising field, are superposed in succession upon a sufficient number of points of that part of the normal hysteresis loop decreasing from H = 20, B = 8000 (cyclic extreme), to H — 0, B = 6900. The abscissae represent the number of 1 mm. sparks in series, increasing from one to ten, superposed in the case of figs. Vl.a b at six values of field, viz. H = 20, 1 7*3, 15T, 11*2, 7*8, and 0, and in the case of fig. VII. at eight values of field, viz. H = 20, 112, 7-8, 5*9, 4*4, 3'4, 2*0, and 0 ; the ordinates, the induction changes following thereon. Observe that for each value of field there are pairs of curves, represented in the case of each pair by the continuous and dash line curves respectively. Tables III. and IV. show how one of the pairs of curves in figs. Vl.a b (curves H — 15T) and in fig. VII. (curves H = 44) respectively have been obtained from the experimental data. If, when the field is positive, the connections between the secondary of the air transformer and the oscillation solenoid are not crossed, it is found necessary to reverse or cross them to obtain approximately the same readings when the experiments are repeated with negative field. On the other hand, if the oscillation connections are crossed VOL. xxix. 2 18 Proceedings of the Royal Society of Edinburgh. [Sess DECREASING CYCLIC FIELD, ELECTRIC OSCILLATIONS. 1908-9.] Vibrational Neutral Points in Magnetised Iron. 19 Table III. — Decreasing Cyclic Field. Co-directional Oscillations. Oscillation Solenoid No. 1. 1 2 3 4 5 6 7 8 9 10 m Ph cS PL . to Oscillations superposed upon P3 Ph pi u a « H=+15T H= -15T o ,rH reduced from reduced from o' £5 H= +20. H= -20. co co O PH O £ co Pi O • rH o co CO O co PI O • rH o H O 5 pi pi - 3 4 5 o o pi o 6 o • 2 Pi o - 5 3*5 8-5 • rH 7 • rH o 4 c3 r~H - 7 5-5 14 m O o m 8 3 o - 7 5 19 9 ?h 4 Ph oi ^d - 5 4-5 23-5 10 o o Tog s 5 • rH m g «4H . Oscillations superposed upon Oscillations regarded as superposed upon H = + 0*9. °.3 -4—^ ' _ too 5 p Cu H O, a) t-1 H= +0-9 reduced from H— + 1*9. H= -0*9 reduced from H= -19. Average readings. Summation. 1 Summations x 2-34 = Total change of B. 1 -0-25 0-5 -0-375 -0-375 -0-9 2 0 0 0 -0-375 -0-9 3 0-5 -0-25 0-375 0 0 4 0-75 -0-75 0-75 0-75 1-7 5 075 -0-75 0-75 1-5 3-5 6 0-75 -0-75 0-75 2-25 5-3 7 0-75 -0-75 0-75 3-0 7-0 8 DO -1-0 1-0 4-0 9-3 9 1-0 -1-0 1-0 5-0 11-7 10 TO - 1-25 1-125 6-125 14-3 11 1-25 - 1-25 1-25 7-375 17-2 Oscillations superposed 2 upon " m £3 Length o spark in H= +0-65 reduced from H=+l-9. H= - 0-65 reduced from H= -1-9. 1 -0-75 0-75 2 -0-25 0-25 3 0 0-25 4 0-25 -0-25 5 0*5 0 6 0-5 -0-5 7 0-75 -0-25 8 0-5 -0-5 9 0-5 -0-75 10 0-75 -0-75 11 0-75 - 0-75 12 0-75 - 0-5 Oscillations regarded as superposed upon H= +0*65. Average readings. Summation. Summations + 2‘34 = Total change of B. -0-75 -0-75 -1-7 -0-25 - i-o -2-3 -0-125 - 1-125 -2-6 0-25 -0*875 -2-0 0-25 -0-625 -1-4 0-5 -0-125 -0-3 0-5 0-375 0-9 0-5 0-875 2-0 0-625 1-5 3-5 0-75 2-25 5-3 0-75 3-0 7-0 0-625 3-625 8-5 Curve H = 0'65 of fig. IX. Curve H — 0*9 of fig. IX. 24 Proceedings of the Royal Society of Edinburgh. [Sess. Figs. IX. and X. show the results obtained when the secondary terminals of the oscillation transformer were connected directly with the ends of the single steel wire (transverse oscillations). In these experi- ments the length of a single spark is increased from 1 mm. to 11 or 12 mms. by increments of 1 mm. Fig. IX. shows for the following values of decreasing positive cyclic field, viz. H = 133, 0'9, 0’65, 048, 0*3 and 0, the results when the induction change due to superposed transverse oscillations increasing in intensity by the means above indicated are plotted against the length of the spark as abscissae. Table YI. shows the experimental data from which two of the curves, viz. H — 09 and 065, have been plotted. Observe that the galvanometer readings are very small, and have been read to 0‘25 of a mm. division of the scale ( i.e . to B — 06). Notwithstanding this, the readings obtained with positive and negative fields are nearly the same throughout (as a rule identical), so that with transverse oscillations it is unnecessary, for obvious reasons, to reverse the oscillation connections to obtain similar curves differing only in sign, as was found absolutely neces- sary with co-directional oscillations. Fig. X. shows from the same experimental data the induction changes plotted against the decreasing cyclic field as abscissm for various oscillation intensities corresponding to spark lengths of 1, 2, 3, 5, 8 and 11 mms. In these experiments the cyclic amplitude is H = 1‘9, B = 3l70 and the residual magnetisation B — 2000 when H = 0. Figs. IX. and X. for transverse oscillations exhibit differences when zero field is approached, not observed either with co-directional oscillations or mechanical vibrations, but not such as to affect the general results. Compare these two figures with figs. VII. and VIII. for co-directional oscillations, and with figs. I. and II. for mechanical vibrations. Results. — When damped trains of electric oscillations are superposed upon magnetisation, it is necessary to distinguish between co-directional and transverse oscillations. In the latter case the oscillation phase neither directly assists nor directly opposes the magnetisation change, and the same results are obtained if the secondary oscillation connections are reversed relative to either positive or negative magnetisation. In the former case the oscillation phase must either directly assist or directly oppose the mag- netisation change. If it could be assumed that L1\e initial amplitude of each damped train of secondary oscillations was invariably greater than that of succeeding amplitudes, it might be anticipated that the curves representing the induction changes due to oscillations superposed upon that arm of the hysteresis loop decreasing from the positive extreme would fall above or below each other according as the phase of the first amplitude 1908-9.] Vibrational Neutral Points in Magnetised Iron. 25 opposed or assisted respectively the magnetisation change. But no such assumption can be made. The oscillation constants of the primary and secondary of the air transformer vary with the number of 1 mm. sparks in series, with oscillation solenoids No. 1 and No. 2, and with the permeability of the iron wires. Hence there may be an alternate rising and falling resultant of the damped oscillations in the secondary citcuit. The amplitude of the first secondary oscillation may therefore be less than a succeeding amplitude of opposite phase. When, however, the number of 1 mm. sparks in series are sufficiently increased, the large amount of damping thus introduced into the primary circuit may become the dominating factor, independent to a large extent of any other. A comparison of tig. Vl.ab (oscillation solenoid No. 1) and fig. VII. (oscillation solenoid No. 2) supports this assumption. For strong oscillations, the curves with uncrossed oscillation connections relative to the decreasing positive field are in both cases invariably higher than those obtained with crossed connections. It is therefore highly probable that the amplitude of the first oscillation is greater than that of those which follow, and that its phase opposes the magnetisation change. On the other hand, the relative position of these curves is reversed for weak oscillations when solenoid No. 2 is used (fig. VI.). This result is at least not unintelligible in view of a rising and falling resultant of the damped secondary oscillations under the varied resonance conditions under which the experiments were made. In any case, it is obvious that the induction change in the iron wires is sensibly affected in a very definite way by the conditions under which the damped secondary oscillations are produced. Notwithstanding these differences, the conclusions arrived at relative to the shift of the neutral points when the cyclic field is decreasing, and the consequent dependence, within the limits of the range of shift of the direction of the induction change upon intensity (see p. 11), are fully applicable to electric oscillations, whether co-directional or transverse. This is sufficiently evident from a cursory comparison of the diagrams in each case, without again entering into details. Figs. Vl.a b and fig. VII. (co-directional oscillations) and fig. IX. (transverse oscillations), showing the induction changes due to superposed oscillations of increasing intensity for various values of decreasing cyclic field plotted against the number of 1 mm. sparks in series as abscissa3, are entirely similar in their main features to figs. I. and I.a showing the induction changes due to superposed mechanical vibrations of increasing intensity for various values of the decreasing cyclic field plotted against W x D0'7 as abscissae. So also are fig. VIII. (co-directional oscillations), fig. X. (transverse oscillations), and fig. II. (mechanical vibrations) entirely 26 Proceedings of the Royal Society of Edinburgh. [Sess. similar in their main features, in which the induction changes are plotted against decreasing values of field as abscissae for various intensities represented as the case may be by the number of 1 mm. sparks in series for co-directional oscillations, the length of the single spark for transverse oscillations, and the function W x D° 7 for mechanical vibrations. It may be noted, however, that the range of decreasing cyclic field over which the neutral points may shift with variation in the intensity of the oscillations (fig. VIII. co-directional oscillations, fig. X. transverse oscillations) is much greater than that obtained with mechanical vibrations, fig. II. Cyclic Residual Magnetisation. — Garibaldi obtained increase, Maurain a very small decrease,* of cyclic residual magnetisation upon the super- position of electric oscillations. These isolated results are in harmony with those obtained with mechanical vibrations. Any elaborate experiments were therefore considered superfluous with electric oscillations. III. Results with Cyclic Field and Cyclic Residual Magnetisation in Terms of Field Change. The experimental results for cyclic field and cyclic residual magnetisation now fall to be compared, the one with the other. The comparison will be facilitated if the starting-point be made from one or other of the cyclic extremes in both cases, say from the positive extreme, as represented in all the diagrams. In the former case, when vibrations or oscillations are superposed at all points of the descending arm of the normal hysteresis loop, the induction change at the cyclic extreme is positive, as the cyclic extreme is just departed from also positive, afterwards negative or positive as the intensity of the vibrations or oscillations is weak or strong, beyond the lower limiting value of the neutral points and until zero field is reached negative, between zero field and the negative cyclic extreme also negative. In the latter case, where vibrations or oscillations are superposed at all, values of cyclic residual magnetisation reached by the cyclic field process from the positive amplitude, the induction change at the residual extreme is negative, as this position is just departed from also negative, afterwards positive or negative as the intensity of the vibrations or oscillations i& weak or strong ; beyond the lower limiting value of the neutral points (for the strongest intensity used) and until zero magnetisation is reached positive, and finally between zero magnetisation and the negative extreme of cyclic residual magnetisation also positive. With cyclic field and cyclic residual magnetisation alike, the shift of the * u presque nulle ” ; see p. 2. 1 908-9 J Vibrational Neutral Points in Magnetised Iron. 27 neutral points, therefore, is from or towards the jDositive extremes according as the vibration or oscillation intensity is strong or weak. In both cases the neutral points may occur close to the positive extremes if the intensity is sufficiently reduced, towards the lower limiting value of the neutral points if the intensity is sufficiently increased. On the other hand, the direction of the induction change due to superposed vibrations or oscillations is at all corresponding points reversed for cyclic residual magnetisation as compared with cyclic field. This reversal can neither be co-ordinated with the induction nor with the presence or absence of the field. It can, however, be directly co-ordinated with the field change immediately preceding the superposition of vibrations or oscillations, which is of opposite sign in the two cases. The results in both cases may now be stated as follows : — When vibrations or oscillations are superposed at the cyclic field amplitudes or at the extreme values of cyclic residual magnetisation, the direction of the induction change due to superposed vibrations or oscillations corresponds with that of the immediately preceding field change. As these extreme positions are departed from, the direction of the induction change is first opposed to, afterwards corresponds with, that of the immediately preceding field change, and continues to do so until the opposite extremes of cyclic field amplitude or cyclic residual magnetisation are reached. The position of the neutral points depends upon the intensity of the vibrations or oscillations, and it is thrust from the extremes the greater their intensity, but reaches a lower limiting value before zero field in the one case or zero magnetisation in the other case is reached. On the other hand, the neutral points are thrust towards an upper limiting value the weaker the intensity of the vibrations or oscillations, which may occur close to but not at the cyclic field amplitude in the one case, or close to but not at the extreme value of cyclic residual magnetisation in the other case, provided always the vibrations or oscillations are sufficiently weak. Within the upper and lower limiting values of the neutral points, the directional of the induction change may either correspond with or be opposed to the immediately preceding field change according as the intensity of the vibrations or oscillations are weak or strong. In both cases, also, the direction of the induction change therefore will correspond with that of the immediately preceding field change throughout a wider and wider range the weaker the vibrational or oscillational intensity, but never quite throughout the whole range. 28 Proceedings of the Royal Society of Edinburgh. [Sess. IV. Dr Eccles and Professor Maurain’s Experimental Results. Dr Eccles plots the induction changes due to superposed oscillations produced by single minute sparks against cyclic field as abscissae. The curves are discontinuous in the same way that the curves obtained by plotting dl/dH against cyclic field are discontinuous at the cyclic extremes. My previous paper showed that the curves representing the effect of vibrations or oscillations superposed at all points of a normal loop form a continuous loop. In this respect Professor Maurain’s experiments and those of others agree with my own. It was also pointed out that the neutral points are thrust towards the cyclic extremes the less the intensity of the vibrations or oscillations. The present paper shows how very close the neutral points may approximate the cyclic extremes, but they can only vanish there when the effect of vibrations or oscillations superposed at the cyclic extremes is zero. My own experiments, however, differ from those of Eccles to a less extent than those of Maurain, who varies the conditions of the former’s experiments. Eccles superposes oscillations of the same intensity through- out upon hysteresis loops of various amplitudes. Maurain superposes oscillations of four different intensities upon the same loop throughout. One of the results is that “ plus les oscillations agissantes sont faibles , plus le maximum de leur action seloigne du maximum de la courbe des distances D et se rapproche du maximum de dl/dH.” This is clearly shown in fig. 3 of the paper, as also that the maximum of each curve is thrust from the maximum of dl/dH in the direction of the vertical axis the stronger the intensity of the oscillations. Maurain continues: — “ En somme, la consideration de la distance D a la courbe d’ aimantation stable , qui permet dejd de prevoir le sens de V action des oscillations, est importante egalement pour prevoir Vintensite de cette action, et cela d’autant plus qui les oscillations sont plus intenses .” In fact, Maurain’s curves (fig. 3) show (1) that dl/dH becomes a more and more important factor than the distance D in determining the maximum of the curves due to oscillations the weaker their intensity ; and, conversely, (2) that the distance D becomes the more important factor the stronger their intensity. Thus it is that Eccles’ results obtained with minute sparks approximate more nearly to Maurain’s result (1) with “ tres faibles ” oscillations than to result (2) when the intensities are taken stronger and stronger. They approximate still more closely to my own results with the weakest vibrations or oscillations used, because under these conditions, with the neutral points thrust in my case close 1908-9.] Vibrational Neutral Points in Magnetised Iron. 29 to the cyclic extremes, the direction of the induction change coincides with that of the immediately preceding field change throughout a very much wider range of cyclic field. Consequently a greater opportunity is. afforded for at least a general correspondence between the magni- tude of the “spark effect” and the slope of the hysteresis loop which Eccles sought to establish. Between the upper limiting value of the neutral point and the cyclic extreme this correspondence is impossible, because the direction of the “ spark effect ” according to my results is opposed to that of the field change. The direction of the induction changes due to superposed oscillations is, however, according to Maurain, wholly independent of their intensity, and is determined by “ la consideration de la distance D a la courbe d’aimantation stabled These differences therefore appear to be more fundamental than those between Eccles’ results and my own. In the series of experiments above referred to, Maurain starts with oscillations sufficiently strong to completely annul the hysteresis. Curve 1 is thus obtained. Curve 2 results from oscillations rather less strong;. Curve 3 is obtained with oscillations described as “ plus faibles ,” and curve 4 with oscillations “ tres faibles d On the other hand, my experiments begin with the weakest intensity, producing in the case of mechanical vibrations and electric oscillations an induction change of B = 10 and 25 respectively at the cyclic extremes. In the latter case the maximum induction change obtained where approxi- mately the slope of the loop is steepest (and consequently not given in the tables) was B=1Q0. Maurain’s maximum induction change under the same conditions appears to have been of the order of B — several thousands for the weakest intensity of oscillations (curve iv. fig. 2, Maurain). My experiments end with the strongest vibrational or oscillational intensity used, which appears to have reduced the residual magnetisation to a rather less extent than the induction obtained with the intensity of oscillations described as “ plus faibles ” (curve iii. fig. 2, Maurain). Curve iv., obtained with the weakest oscillation with which Maurain experimented, is therefore the only curve which may probably fall within my range of intensities, either for mechanical vibrations or electric oscillations. I found it impossible, however, to show with accuracy, or even to show at all, the gradual shift of the neutral points towards the cyclic extremes in a diagram which also exhibits, as in Maurain’s case, the normal hysteresis loop. The angles which the curves make with the horizontal axis become much too small as the intensities of the oscillations are reduced. In fig. VIII. (present paper), for instance, the ordinate scale has been 30 Proceedings of the Royal Society of Edinburgh. [Sess. expanded 100 times in comparison with that usually adopted for hysteresis loops. Maurain, commenting on Eccles’ results, says : “ Les courbe qui, dans le memoire de M. Eccles representent V action des oscillations anx diff events points d’une des branches d’un cycle d’aimantation, paraissent comporter une discontinuity dans les valeur de cette action autour du sommet d’un cycle ; je nai pu me rendre compte de la cause de cette difference entre ses resultats et les miens.” Between the upper and lower limiting values of the neutral points, which, as has been shown in this paper, may cover a very wide range of decreasing cyclic field, Eccles obtains only induction decrease when oscillations of very weak intensity are superposed ; Maurain, experimenting in all cases with oscillations of much greater intensity, only induction increase. In the former case the neutral points are thrust towards their upper limiting values, which may occur quite close to the cyclic extremes, and the curves are discontinuous, because readings do not appear to have been taken between these two positions. In the latter case the neutral points are thrust from the cyclic extremes towards their lower limiting value, where the curves crowd together as the intensity of the oscillations are more and more increased. The lower limiting value of the neutral point may correspond to “ la courbe d’aimantation stable.” In the view of the author, the molecular theory of magnetism lends no support to the possibility that the positions of the neutral points (where vibrations or oscillations superposed upon cyclic fields produce no induction change) are independent of their intensity, nor that within definite limits vibrations or oscillations may not, when superposed at the same point, pro- duce induction change in opposite directions, according as their intensities are sufficiently weak or sufficiently strong. V. Molecular Theory. It now remains to be shown whether the whole of the experimental results obtained with mechanical vibrations (Section I.) and with electric oscillations (Section II.), and restated in terms of field change irrespective of the presence (cyclic field) or absence (cyclic residual magnetisation) of the field (Section III.), are not only in harmony with, but a necessary deduction from, the molecular theory of magnetisation. It will be convenient that the word vibrations when used alone signifies in the remainder of this paper either mechanical vibrations or electric oscillations. 1908-9.] Vibrational Neutral Points in Magnetised Iron. 31 With field increasing towards a cyclic extreme, the molecular groups will tend to place themselves more and more in alignment with the direction of the field, so that when (say) the positive cyclic extreme is reached, the superposition of vibrations will assist the rotation of the molecules of very different degrees of stability, and the induction will be increased. This induction change will necessarily coincide in direction with that of the immediately preceding field change, and it will be independent of the intensity of the vibrations. When the field is decreased, the decre- ment may obviously be made so small that even the least stable molecular groups will remain unaffected, and the rotation of the molecules will, on the superposition of vibrations, remain unchanged in direction. But the induction change will now be against the immediately preceding field change, and this result also will be independent of the vibrational intensity. If, however, the field decrease had been a little greater than above indicated, by an amount sufficient to rotate negatively the more favourably placed molecules of the least stable groups, their rotation with the field change will also be assisted, and the induction change due to superposed vibrations will now be definitely reduced in amount. On a further field decrease the reduced positive induction change will more readily pass into negative induction change if the intensity of the vibrations is weak enough to leave uninfluenced the more stable molecular groups, the less stable molecules rotating negatively in response to the negative field change alone being- assisted. The induction change will now be with the field change, and once this has been established, will continue to be so for all greater decre- ments of field, provided the vibrational intensity be not unduly increased. But the decrease of field remaining as before, if the vibrations had been of a somewhat greater intensity to influence also a few of the more stable molecular groups not yet sensibly effected by the comparatively small field decrease, and whose last rotation was in the direction of the field (i.e. of the field change before the positive extreme was departed from), their tendency to rotate positively would also be assisted. Obviously the intensity of the vibrations could be adjusted so that their superposition at this particular value of decreasing field would produce no induction change whatever, the negative rotations of the less stable balancing the positive rotations of the more stable molecular groups. Further, if the vibrations had been of yet greater intensity, groups of yet greater stability, whose last rotation was positive, would have been brought into action, the molecular balancing would be upset, and the induction change would again be against the field change, a reversion to what took place at a smaller field reduction with weaker vibrational intensity. To re-establish a balance for 32 Proceedings of the Royal Society of Edinburgh. [Sess. this greater vibrational intensity, a larger proportion of the molecules must tend to rotate negatively, and this could be accomplished by a further increase of the field decrement. The position where the opposing molecular rotations balance (induction change neutral point) is therefore thrust from the cyclic extreme the greater the vibrational intensity. If the intensity of the vibrations be further increased, the molecular balancing would be again upset by bringing into play yet more stable groups tending to rotate positively, and the induction change would for the third time oppose the field change. Ultimately, however, this alternating process must cease when, under the influence of a sufficiently large decrement of field (or even increment of negative field, which this argument does not exclude), the increasing number of molecular groups tending to rotate negatively could just be balanced, and no more, by all the available remaining molecules still tending positively. Thereafter, negative rotation of the molecules would predominate, and the direction of the induction change would, on the superposition of vibrations of all intensities, however great, coincide with the direction of the field change. This process would continue until, with a sufficiently large incre- ment of negative field, all the molecular groups would tend to place themselves more and more in alignment with the direction of the field as the negative cyclic extreme is approached. The induction change due to superposed vibrations would coincide with that of the immediately preceding field change, the condition of things from which this hypothesis started at the positive cyclic extreme. The above deductions from the molecular theory of magnetisation are obviously in harmony with the experimental results obtained for cyclic field symmetrical about the origin. The shift of the neutral points within definite limits, and the correspondence between the direction of the induction change and that of the immediately preceding field change throughout a wider and wider range of cyclic field the weaker the intensity of the superposed vibrations or oscillations, are rendered im- mediately intelligible. It will be readily perceived that these deductions are not confined to cyclic fields symmetrical about the origin. It need only be supposed that a preponderance of the molecules are rotating in the direction of the field change as the cyclic amplitudes (not even necessarily of opposite sign) are reached for the above deductions to become fully applicable. The area of a large normal hysteresis loop may, for instance, be mapped out by a series of loops unsym metrical about the origin between the cyclic limits of, say, the positive extreme and increasing values of the negative field, as shown in 1908-9.] Vibrational Neutral Points in Magnetised Iron. 33 diagram XI. In the descending curve A R the long arrow represents the theoretical shift of the neutral points towards A the weaker the vibrational intensity. According to the above deductions, the shift of the neutral points is towards the cyclic extreme where the last reversal of field change took place, and consequently in the ascending curve R A it will be towards R the weaker the vibrational intensity. In the two branches of this little loop, therefore, between which the induction does not differ greatly, the shift of the neutral points will be in opposite directions, as indicated by the arrows, and is therefore independent of the values either of the field or of the induction. Similarly, in all the other ascending curves the shift of the neutral points will be towards the negative field extremes of their respective loops the weaker the intensity of the vibrations, until finally the last of the series Al Rx A becomes symmetrical with A R A1? the curve descending from the positive extreme. F urther, the ascending branches of these and all other intermediate loops cut either the vertical or horizontal axis, or both, at all points in a positive direction ; while the descending branches, which coincide with one another, cut the vertical and horizontal axes only at their positive and negative extremes respectively. Hence the direction of the induction change due to vibrations superposed at all points of the axes included within the large VOL. xxix. 3 34 Proceedings of the Royal Society of Edinburgh. [Sess. symmetrical loop will be positive throughout a wider range of either the less the vibrational intensity, but never quite throughout the whole range. The direction of the shift of the neutral points represented by the large arrows will be towards the negative extreme Hx of the horizontal axis and towards the positive extreme R of the vertical axis the less the vibrational intensity, because a nearer approach is in both cases made to the negative cyclic extremes of the unsymmetrical loops at which the last reversals of field change took place. These deductions relative to cyclic residual magnetisation (vertical axis-zero field) and what may similarly be called cyclic zero induction (horizontal axis) are inseparably connected with each other. In the former case residual magnetisation is not necessarily decreased by vibrations. In neither case can the sign of the induction change due to superposed vibrations be determined apart from (1) the direction of the path by which the points on either axis have been reached, nor apart from (2) the vibrational intensity. The experimental results with cyclic residual magnetisation show the wide range throughout which these conclusions deduced from the molecular theory of magnetisation are applicable. Vibrations may increase the residual magnetisation within the limits of B = 0, and a point, B — 8700, not far removed from the extreme possible limit under the conditions, viz. B = 9100. Conclusion. The above deductions from the molecular theory of magnetisation depend primarily, therefore, upon the molecular condition in which the iron is left when the cyclic field process is arrested at any point, and not upon the actual values of the induction or field, either or both of which may be zero. If the cyclic field change be large enough a preponderance of the molecules must be rotating in the direction of the field change as the cyclic amplitudes, not necessarily symmetrical about the origin, are approached. On a reversal of field change the most favourably placed molecules of the least stable molecular groups must be the first to experience a reversal of their rotation, followed by those of more and more stable groups as the field change is taken greater and greater. Finally, the opposite cyclic extremes will be reached. The intensity of vibrations superposed at any point will necessarily differentiate between molecular groups of various degrees of stability whose molecules have been arrested in their passage from positions of less to positions of greater stability under the conditions. The rotation of the molecules of a greater number of molecular groups of all degrees of stability 35 1908-9.] Vibrational Neutral Points in Magnetised Iron. will be assisted in the direction of their last rotations, which may or may not coincide with that of the immediately preceding field change, the stronger the vibrational intensity. On the other hand, the rotation of the molecules of the least stable groups, to the exclusion of those of greater stability, will be assisted in the direction of their last rotations the weaker the vibrational intensity. But as these are the first to rotate in the direc- tion of the cyclic field change after reversal, it follows that the induction change due to superposed vibrations will coincide in directional with that of the immediately preceding field change throughout a wider range of cyclic field the less their intensity. According to this hypothesis, neutral points occur where the rotations of the molecules in opposite directions balance, and these positions must be thrust towards the cyclic extreme at which the last reversal of field change took place the weaker the vibrational intensity. The above deductions due to a complex magnetic seolotropy produced by reversals of field change are thus in harmony with the experimental results obtained for cyclic field and cyclic residual magnetisation with mechanical vibrations and electric oscillations, and summarised in terms of the immediately preceding field change in Section III. of this paper. In cyclic fields symmetrical about the origin there are higher and lower limiting values of the decreasing cyclic field between which the neutral points may shift. These vanish in the origin or the cyclic extremes accord- ing as the amplitude is sufficiently decreased (zero amplitude at the origin) or sufficiently increased (saturation values of induction at the extremes). The locus of the lower limiting value of the neutral points may approximate to the stable curve of Duhem (theoretical) or Maurain (experimental). The locus of the higher limiting value of the neutral points approximates to the cyclic extremes, but can only vanish there when the effect of the vibrations superposed at the extremes is zero. Between these loci, which may thus cover a very wide range of the decreasing cyclic field, neither unduly increased nor decreased, superposed vibrations may either increase or decrease the induction according as the vibrational intensity is sufficiently strong or sufficiently weak. With cylic residual magnetisation (zero field) there are also lower and higher limiting values between which the neutral points may shift. The direction of shift is towards the higher limiting values, which may occur close to but not at one or other of the extremes of residual magnetisation, the less the vibrational intensity. It will be towards the positive extreme if the slope of the unsymmetrical loops by which points on the vertical axis were reached be positive, and vice versa, because a nearer approach is 36 Proceedings of the Royal Society of Edinburgh. [Sess. thereby made to those points of the loops where the last reversal of field change took place. It may therefore be repeated, that residual magnetisa- tion is not necessarily decreased by vibrations. The sign of the induction change cannot be determined apart from the direction of the path by which points on the vertical axis (cyclic residual magnetisation) have been reached,, nor apart from the vibrational intensity. In this short summary of deductions from the molecular theory of magnetisation and of the experimental results the word “ vibrations ” refers both to mechanical vibrations and electric oscillations (co-directional and transverse). In the former case the intensity of the mechanical vibrations was found to be proportional to a definite function (W x D0'7) of the weight (W) of the steel ball and the distance (D) through which it fell. The accuracy of this experimental method is obvious, and no difficulty was experienced in obtaining as many as twenty distinct curves between the limits of W x D0'7 = 038 and 104 (measured in gram-centimetres), from which the conclusions are drawn. Although, in the latter case, a similar definite signification would be less readily obtained, the same general conclusions are equally applicable to both. With damped electric oscillations the experimental results are necessarily more complex. The induction changes due to superposed oscillations are the resultant of the irreversible * (vibrational) effects, and the reversible effects of the oscillatory current, just as the induction changes due to loading and unloading (or vice versa), are the resultant of the irreversible (vibrational) effects (due to a complex molecular seolotropy in cyclic field) and the reversible effects of the “ ons ” and “ offs ” (or vice versa) of the load.f The irreversible effects are subject to the same laws which govern the induction changes due to superposed mechanical vibrations in cyclic fields. In fact, these results may be taken to be general, not only applying to electric oscillations, weak alternating currents, and the * This compounding of the irreversible with the reversible effects may very easily be lost sight of. The following appears to be worth further consideration. Professor Rutherford,1 in his determination of the damping of oscillations by the magnetic method, assumes that if the initial phase of the oscillation train be such as to increase the magnetisa- tion of the bundle of steel needles, it will produce no magnetic effect, because these have been magnetised to saturation. That is to say, as the initial phase increases to a maximum the magnetisation will increase, and as the initial phase falls to zero the decrease of magnetisation will not exceed the previous increment. But the irreversible (vibrational) effect opposes the increase and assists the decrease, hence the residual magnetisation may fall below its original value. The proof as stated would therefore appear to be incomplete. t “The Effect of Load and Vibrations upon Magnetism in Nickel,” pp. 38-56. Read in conjunction with this paper. l “ On a Magnetic Detector of Electric Waves, and some of its Applications,” Phil. Trans. Roy. Soc., London, A., 1897, vol. clxxxix., p. 1. 1908-9.] Vibrational Neutral Points in Magnetised Iron. 37 irreversible effects of loading and unloading, but to the irreversible effects of all other disturbances, whether produced by electric, mechanical,* or thermal means (temperature change). Wherever these are associated with a complex magnetic aeolotropy such as .may be impressed upon the magnetic material by cyclic field change, there the shift of the (vibrational) neutral points, and the consequent dependence of the direction of the irreversible induction change upon the intensity of the disturbance, independent of the values of the magnetisation or the field, either or both of which may be zero, will be in evidence. As on former occasions, I desire to thank the Royal Society of London for placing at my disposal Government grants for furthering these researches. * In a later communication than that already referred to (p. 2), Professor Maurain states that “la courbe normale depend un peu clu l’amplitude des cycles de torsion.” See “Sur Faction de la torsion sur l’aimantation,” Journal de Physique , May 1907. In other words, the vibrational neutral points shift with the intensity of the torsional disturbance. ( Issued separately November 16, 1908.) 38 Proceedings of the Royal Society of Edinburgh. [Sess. II. — The Effect of Load and Vibrations upon Magnetism in Nickel. By James Russell. (MS. received April 13, 1908. Head November 18, 1907, and March 2, 1908. Q CONTENTS. Objects of Investigation . Apparatus and Methods . Cyclic Fields Cyclic Residual Magnetisation 1 Increasing Fields . Discussion and Summary . page 38 55 39 Data, page 40 ; Results, „ 46 • 55 55 ’ 5 5 5 5 48 • 5> 55 ? 55 55 • * * 55 43 47 49 52 The initial irreversible effects of applying or of removing stress resemble those produced by vibrations, although these processes “ may be conducted in such a way that no actual vibration takes place.” * Ewing has investi- gated the initial effects of tension in iron,-)- Cree the initial effects of pressure in cobalt.^ In iron and cobalt, tension and pressure respectively increase the induction before the Villari reversal in both metals is reached. Vibrations also in non-cyclic fields increase induction. Consequently in low fields the initial irreversible and final reversible effects of tension and pressure in iron and cobalt respectively augment each other. In nickel, on the other hand, the irreversible and reversible effects of tension must oppose each other ; the latter effect lowering the induction at all stages of field increasing from zero.§ In Ewing and Cowan’s paper, however, no mention is made of any initial effects tending towards induction increase. Nickel has therefore been selected as the subject of these experiments, and annealed nickel, because in this condition the effects of mechanical vibrations are large, and in comparison with quenched nickel entirely normal in character. || The irreversible and reversible effects of load with and without permanently acting mechanical vibrations are investigated (1) in fields increasing from zero; (2) in cyclic fields; and (3) in zero field with what may be called cyclic residual magnetisation, which will be defined later. To differentiate these effects the loads used must be small. * Magnetic Induction in Iron , Ewing, 3rd edition, p. 216. t Phil. Trans., 1885, p. 603. % Phil. Trans., 1890, p. 329. § Lord Kelvin, “Electro-Dynamic Qualities of Metals,” part vii., Phil. Trans., 1879; Reprint of Papers, vol. ii., pp. 332-407. “Magnetic Qualities of Nickel,” Ewing and Cowan, Phil. Trans., 1888, pp. 325-333. || “ The Superposition of Mechanical Vibrations upon Magnetisation,” etc., Trans. Roy. Soc. Edin., xlv. p. 491. 1908-9.] Load and Vibrations upon Magnetism in Nickel. 39 Apparatus. One end of the annealed nickel wire, 100 cms. long and 092 cm. diameter, formerly used, was soldered to the gong of the electric bell, while its other end was linked by means of a short length of thread (to prevent torsion) to the vertical arm of an L-shaped lever. Its horizontal arm carried a light scale pan, counterpoised so that when empty the wire was entirely free from load. To prevent vibrations in the ordinary sense when load was put “on” or “off,” the scale pan was cushioned with india-rubber, and a soft woollen thread was, for the same purpose, wound round the nickel wire in a loose spiral. The whole apparatus, which has previously been more fully described, || was suspended from the roof by means of india-rubber tubing, to prevent external vibrations reaching the nickel wire. The wire was in a horizontal position, at right angles to the earth’s magnetic field, and coincided with the axis of the magnetising solenoid 41 cms. long. An exploring coil and ballistic galvanometer (complete period eleven seconds) measured the magnetic intensity at approximately the central position of the wire. Superposition of Field, Load, and Vibrations. The above apparatus- enabled the relative superposition of load, field, or cyclic residual magnetisation, as distinguished below, to be performed either with or without permanently acting vibrations. In the former case the nickel wire was kept in a state of continuous vibration by ringing the electric bell. A conditions. — Loading, followed by repeated “ offs ” and “ ons ” of load, may be superposed at a sufficient number of points on the normal BH curve obtained at each point by field reversals increasing from zero (Al), or on the normal hysteresis loop (A2). This latter case may, when so stated, include the superposition of “ offs ” and “ ons ” of load on a hysteresis loop performed with permanent load. Loading and unloading may also be superposed, field being zero at all values of cyclic residual magnetisation between positive and negative maxima (A3)— the cyclic residual magnetisa- tion being produced, as shown in fig. V., by withdrawing the cyclic field increasing negatively (positively) always after the positive (negative) cyclic extreme has been departed from. Loading and unloading may be per- formed in steps. In all these cases each set of observations performed at any given point is independent of those performed at any other point. Reference previous page. 40 Proceedings of the Royal Society of Edinburgh. [Sess. Either demagnetisation by decreasing reversals intervenes, or under condi- tions (A2) and (A3) and only where expressly stated many reversals of high amplitude alone may intervene. B conditions. — After demagnetisation by decreasing reversals, the nickel wire being loaded, field reversals increasing from zero may be superposed (Bl). When the loading is zero the normal BH curve is obtained. In this paper the A and B conditions refer exclusively to the relative superposition of load and field. Mechanical vibrations are never super- posed ; they either are or are not permanently acting. Diagrams. Field (H), induction (B), and induction change (dB) are in C.G.S. units in all the diagrams. The curves are either obtained from the average readings taken with both positive and negative fields increasing from zero ; or in the case of cyclic fields, the results plotted for each arm of a hysteresis loop are obtained from the average results taken with both arms ; the same method being adopted for cyclic residual magnetisation. The occurrence of Yillari reversals, found to exist with cyclic fields and with cyclic residual magnetisation, appears to offer the explanation that results not so easy of satisfactory repetition obtained in very low fields in- creasing from zero may be fully accounted for by the difficulty of reaching in every case an absolutely neutral position by the method of demagnetisa- tion by decreasing reversals in nickel. For this reason the data and conclusions relating to cyclic fields and cyclic residual magnetisation will be taken first ; fields increasing from a neutral magnetic zero last. Cyclic Fields. Experimental Data. — Fig. I. shows the effects of the first “ on ” and of the seventh “on ” and “off” of a load of 11 ozs. (05 kilos per square mm. of sectional area), superposed under the A2 conditions, at a sufficient number of points, upon the normal hysteresis loop without load. Fig. II. shows the effects of the first “off” and of the seventh “off” and “on” of the same load, superposed under the same conditions, upon the hysteresis loop performed with load “ on.” In both cases the value of the field H = T23 at cyclic extremes is the same. In both cases nearly final results are reached with the seventh “on” and “off” of load. The series of small diagrams show the inductive changes (dB) which occur between the first 41 1908-9.] Load and Vibrations upon Magnetism in Nickel. and seventh “ ons ” and “ offs ” (fig. I.a) and between the first and seventh “ offs ” and “ ons ” (fig. Il.a) for a sufficient number of field values between H=+T23 and — 123, i.e. as if the observations had been taken on the descending arms of the loops. The induction changes (dB) are plotted as ordinates; the number of times the load has been put “on” and “off” as abscissae. CYCLIC FIELD. A 2 CONDITIONS. -1-23 Figs. I. and I.a must thus be taken together, as also figs. II. and Il.a. In fig. I.a when H=+1'23, for instance, the positive reading obtained with the first “ on ” (dash line curve), corresponds with the increase of induction at the cyclic extreme of fig. I. for the first “ on.” The ordinate difference in the latter fig. between the seventh “on” and the seventh “off” corresponds to the readings obtained at the extreme right of fig. I.a (H= +1*23), as measured by the distance between the horizontal axis and either the “on” curve (dash line) or the “off” curve (full line). Again, in 42 Proceedings of the Royal Society of Edinburgh. [Sess. fig. I.a when H= + 0'43 the “ons” and the “offs” decrease and increase the induction respectively by nearly equal amounts from the first, and either of these amounts corresponds to the difference between the “ on ” and “off” curves of fig. I. at this particular value of field, irrespective of whether the first or the seventh “ on ” curves be taken. When these experiments are repeated with permanently acting vibra- tions, fig. I.v shows the curves representing the fourth “on” and “oft1” of load superposed on a loop without load, fig. II. v the curves representing the fourth “off” and “on” superposed upon a loop performed with permanent load. Under these conditions the first “ on ” differs very little from the fourth “on” (fig. I.v), and the first “off” very little from the fourth “off” (fig. II. v). These figures are the experimental results obtained for the same amplitude of cyclic field as in figs. I. and II., but the scale is three times closer. For approximately the same induction amplitude, and consequently lower field amplitude, the crossings of the curves remain essentially the same. In the above diagrams the curves representing the (practically) final “ ons ” or “ offs ” of load are obtained by the summation of .all the readings. In those now to be described, where “ ons ” and “ offs ” of load are super- posed forty times in succession, this method becomes wholly inapplicable. If the cyclic amplitude be sufficiently increased, the induction at cyclic extremes may be assumed to be independent of the “ ons ” and “ offs ” of load superposed during the cyclic. That this assumption is sufficiently correct is supported by the fact that there is no “ sagging ” in either direction when the field is reversed several times on the conclusion of any series of readings. The actual position of each final “off” of load may therefore readily be obtained by noting the induction change ivhen a single step is taken to the opposite cyclic extreme to that from which the observations started. This also fixes the position of the immediately preceding “ on ” of load. Fig. III. shows the curves, obtained in this manner, representing the fortieth “on” and the fortieth “off” of the 11 ozs. load (05 kilos per mm.2) superposed under the A conditions upon the normal hysteresis loop, the values of field and induction at cyclic extremes being respectively H = 11T and B = 4200. The series of smaller diagrams (fig. Ill.a) show the instantaneous induction changes which occur between the first and fortieth “ ons ” and “ offs ” of load for various values of field between H = + 11 1 and H = — 11 1. In figs. IV. and IV.a the corresponding results are recorded when mechanical vibrations are permanently acting. Figs. III. and IV. eliminate not only possible errors very liable to occur 1908-9.] Load and Vibrations upon Magnetism in Nickel. 43 where the curves are obtained by the summation of a series of readings as in figs. I. and II., but also the effects of magnetic viscosity. The same results, however, are obtained in both cases. In figs. Xll.a and IV.a the induction changes (dB) are plotted as ordinates; the number of times the load has been put “on” and “off” as abscissae. The curves of these figs., and those of figs. La and Il.a, are merely introduced to show the general nature of the sequence of changes which occur when “ons” and “offs” of load (in the case of Il.a “offs” and “ ons ” of load) many times repeated are superposed at all stages of that arm of the loops descending from the positive to the negative cyclic extreme. Results. — The effects of the first “ on ” and the first “ off” of load super- posed at all points of hysteresis loops not unduly increased, without (fig. I.) and with (fig. II.) load respectively, are essentially vibrational in character. In other words, induction at cyclic extremes is increased, residual magnetisa- tion decreased, neutral points occur in the first and third quadrants, and, generally speaking, those differences to which magnetic hysteresis gives rise are reduced, irrespective of whether “ on ” is superposed upon a normal loop without load, or load “off” superposed upon a loop performed with load. The differences between the curves representing the first “ on” (fig. I.) and the first “off” (fig. II.) might have been anticipated from the known effects of load in nickel. Load “ on ” (tig. I.) increases the induction to a less extent, decreases the residual magnetisation to a greater extent, than load “ off” (fig. II.). Load “ on ” therefore thrusts the neutral point towards, load “ off ” from, the cyclic extreme. These neutral points are not Villari critical points due to load, but irreversible vibrational effects inseparable from the putting “ on ” or “off” of load. Although it is the first “ on ” (figs. I.a, Ill.a) or the first “ off” (fig. Il.a) superposed upon hysteresis loops without and with load respectively which produces the most marked irreversible induction changes, repeated loading and unloading, as these figures show, also produce irreversible effects by no means negligible. These, however, gradually disappear, leaving finally equal and opposite induction changes due to “ ons ” and “ offs ” when the process is sufficiently often repeated. A study of these diagrams shows that these combined changes occur at all stages of the loop in orderly sequence, and that both effects consequently may readily be distinguished from each other. Repeated loading and unloading therefore accentuate all the vibrational effects already mentioned due to the superposition of the first “on” (fig. I.) or the first “off” (fig. II.). The induction at cyclic extremes is further increased, and the differences due to magnetic hysteresis 44 Proceedings of the Royal Society of Edinburgh. [Sess. further reduced. The former effect tends to disappear as the cyclic amplitudes are sufficiently increased, and, as in fig. III., the final “off” curve alone exceeds the normal induction at the cyclic extreme, the final “ on ” not being increased sufficiently to rise above the normal cyclic CYCLIC FIELDS. A 2 CONDITIONS-continued. ORDINATES. CHANGES OF B-ABSCISSAE. 1st TO 40th "ONS" AND "OFFS OF LOAD. amplitude as in figs. I. and II. at lower amplitudes (see “ Fields increasing from Zero,” p. 48). But there are points in the first and third quadrants, when the cyclic extremes are being departed from, where the irreversible effects vanish, and loading and unloading decrease and increase the induction by practi- 1908- 9.] Load and Vibrations upon Magnetism in Nickel. 45 cally equal amounts from the first to the linal “on” and “off” of load. These points occur with small induction amplitudes, as in fig. I., when H^O'43 (fig. I.a) ; at higher amplitudes, as in fig. III., not quite at but near the cyclic extreme (fig. Ill.a). They are thrust towards or from the cyclic extremes as the amplitude is greater or less, and in this respect are subject to the same laws which govern the superposition of mechanical vibrations and other forms of disturbances superposed under the A conditions. || The positions where the initial irreversible effects of repeated loading and unloading vanish are therefore vibrational (but not load) neutral points. It may be observed that in figs. II. and Il.a the vibrational neutral points, as above defined, are not quite so perfectly marked, and occur much closer to the vertical axis, just as is the case with the actual neutral point already referred to when “off” is first superposed upon the loop performed with permanent load, the reason in each case being the same. Passing now from these irreversible changes essentially vibrational in relation to the loops upon which loading and unloading are superposed, the curves representing the final effects in relation to each other may now be considered. Load “on” invariably decreases, load “off” invariably increases, not only the induction at cyclic extremes, but the residual magnetisation. At points in the second and fourth quadrants, where induction and field oppose each other, loading and unloading produce (after the initial vibrational effects, which may be considerable, are over) no induction change whatever. Thereafter, until zero induction is reached, loads “ on ” and “ off” increase and decrease induction respectively. There thus exist in cyclic fields well-marked Villari reversals in nickel. Fig. III. may more especially be referred to. Fig. Ill.a shows how the Villari critical point is reached. It occurs at some definite field value between H = 0'78 and H^O’95. The curves, after forty “ons” and “offs” of load, have practically reached asymptotic values. With a field of H=— 078 (the induction being positive) it is evident that the Villari critical point will not be reached however often the loading and unloading be repeated. With a larger negative field of H = — 0*95 the critical point has been passed, but it may be observed that the crossing of these curves does not, strictly speaking, constitute a Villari neutral point, as, in the immediate neighbourhood of this point, “ ons ” and “ offs ” are both producing negative induction change. It must therefore occur at some intermediate value of field for which, after the irreversible vibrational effects are over, repeated “ ons ” and “ offs ’ would give rise to no induction change whatever. With lower cyclic amplitudes the Villari reversal occurs closer to the vertical || Reference p. 38. 46 Proceedings of the Royal Society of Edinburgh. [Sess. axis (figs. I. and I.a), and when the hysteresis loop is performed with load “ on ” apparently closer still (figs. II. and Il.a). Results with permanent vibrations. — The great differences which occur between the curves representing the effects of “ ons ” and “ offs ” of load superposed upon a normal loop (fig. I.), and “offs” and “ ons ” superposed upon a loop performed with permanent load (fig. II.), to a large extent dis- appear when the nickel wire is kept in a state of continuous vibration (irrespective of whether the experiments are repeated for the same field amplitude, or approximately for the same induction amplitude). This is immediately apparent on comparing figs. I. and II. without vibrations with figs. I.v and II. v with vibrations. The latter figures, taken in conjunction with the text, show that loading and unloading decrease and increase re- spectively both the induction at cyclic extremes and the residual magnetisa- tion from the first. Nevertheless, the irreversible vibrational effects have not entirely been eliminated. The relation of the fourth “off” curve (fig. I.v) and of the fourth “ on ” curve (fig. II. v) to the normal loop and to the loop performed with load upon which they are respectively superposed is obviously vibrational. The induction at cyclic extremes is in both cases slightly increased, the residual magnetisation decreased. At higher induction amplitudes, however (figs. III. and IV.), the irreversible vibrational effect of repeated loading and unloading entirely vanishes at the cyclic extremes when mechanical vibrations are acting — see fig. IV.a, H = 11T. This is not quite the case without vibrations, fig. Ill.a, H = 11T. As the cyclic extremes are departed from the irreversible effects in both cases reassert themselves, reaching maximum values, which may be opposite in sign to the final effect of load, where the slope of the cyclic curves is great. At all stages the initial irreversible effects with vibrations (fig. IV.a) are much less than without vibrations (fig. Ill.a), and in the former case are confined to a much narrower range of low field. While this is so in reference to the initial effects, the final reversible effects of load, i.e. the ordinate difference between the “on” and “off” curves, are much greater with (figs. IV. and IV.a) than without (figs. III. and Ill.a) permanently acting vibrations. Also the Villari reversals in the second and fourth quadrants remain practically unchanged although they occur at much lower values of the cyclic field. t / Cyclic Residual Magnetisation. Experimental Data. — Fig. V. shows the results obtained with what may be called cyclic residual magnetisation between the limits of B = dt 2800 1908-9.] Load and Vibrations upon Magnetism in Nickel. 47 obtained by simply withdrawing the field H — ±111. Intermediate values of residual magnetisation are, however, obtained by withdrawing the negative (or positive) cyclic field at a sufficient number of points of the loop descend- ing from the same positive (or negative) induction amplitude. The six small diagrams show the changes which take place between the first and fortieth “on” and “off” of the same load (11 ozs. = 0‘5 kilos per mm.2), as if the cyclic field had always started from the positive extreme, as illustrated in the large central reference diagram. The value of the induction given with each diagram is obtained by measuring the induction change when, after the fortieth “off” of load, a single step is taken to the opposite cyclic extreme to that from which the cyclic process started. Between each set of observations, thirty or forty reversals of the highest field used intervene. Results. — The initial irreversible and final reversible effects of loading CYCLIC RESIDUAL MAGNETISATION. A3 CONDITIONS. and unloading at the extreme values d= 2800 of residual magnetisation, shown in fig. V., must, for reasons of symmetry, be each the reflection of the other in the horizontal axis. In each case the irreversible vibrational effect lowers the induction from 2800 to 1900, while the reversible effects of loads “on ” and “off” many times repeated decrease and increase respectively the residual magnetisation. But when these positions are departed from, the symmetry of the curves between the first and fortieth “ ons ” and “ offs ” of load disappears. This is well illustrated in the next pair of curves, where, quite accidentally, the residual magnetisation is B = + 800 and B = — 800 respectively. At the former positive value of induction there is practically no irreversible vibrational effect, loading and unloading taking their final values almost at once. At the latter negative value of induction, however, the initial lowering of the residual magnetisa- tion which marks more especially the first “ on ” of load is still largely in 48 Proceedings of the Koyal Society of Edinburgh. [Sess. evidence, while the final reversible effect is distinctly greater than at the same positive value of magnetisation. If this want of symmetry be con- tinued at lower values, a point must be reached where at some positive value of residual magnetisation the final reversible effect of loading and unloading will be nil. The next pair of curves shows that such a point is reached between the values B=+200 and B=+140, which constitutes a Yillari critical point for cyclic residual magnetisation. Thereafter, until zero magnetisation is reached, loading and unloading produce increase and decrease of residual magnetisation respectively, as shown in fig. V., when B = +140. These results therefore in zero field, with cyclic residual magnetisation, do not differ essentially from those obtained in cyclic fields. The absence of the initial irreversible effects at a comparatively large value of residual magnetisation constitutes a vibrational neutral point, and corresponds to that which occurs in the first (and third) quadrants with cyclic fields where the effects of loading and unloading assume their final values at once. The absence of the final reversible effects (after the irreversible effects are over) at a smaller value of residual magnetisation constitutes a Villari critical point, and corresponds to that which occurs in the second (and fourth) quadrants with cyclic fields where the final reversible effects of loading and unloading are nil. The asymptotic nature of the curves are equally well marked in both cases (figs. V. and Ill.a). Fields increasing from Zero. ExjJerimental Data. — Figs. VI. and VII. show the induction changes (ordinates) due to the first superposition of loads of 3, 11, and 20 ozs., corresponding to 0T4, 05, and 0'9 kilos per sq. mm. of sectional area, for values of induction (abscissae) increasing from zero without and with permanently acting vibrations respectively. Figs. VIII. and IX. show the effects of cyclic load (abscissae) without and with vibrations respectively. In both cases the same value of field supports an induction of B = 650 before the superposition of load. A total load of 14 ozs. (0‘64 kilos per sq. mm.) is put “on” in steps of 3, 3, 2, 2, and 2 ozs., and “off” in inverse order. The first two complete load cycles, and a practically closed loop obtained after ten such cycles have been performed, are shown without (fig. VIII.) and with (fig. IX.) permanently acting vibrations. When load is superposed under the A conditions many distinct curves may be obtained, showing the irreversible effects of the first, second, etc. “ ons ” and “ offs.” The effects of the first “ on ” have been shown in figs. 1908-9]. Load and Vibrations upon Magnetism in Nickel. 49 VI. and VII., plotted against induction. When “ ons ” and “ offs ” are repeated a sufficient number of times, equal magnetic changes occur in either case. The full and faint dash line curves of fig. X. show respectively for all values of field the induction reached when load is put “off” and “on” for the fortieth time, without vibrations. These curves represent the final reversible results with a load of 11 ozs. (0*5 kilos per sq. mm.) under the A conditions. The other two pairs of curves in this diagram are obtained under the B conditions, the load used being the same. The full and faint continuous lines are respectively the normal BH curve without load and the BH curve with load. The full and faint dotted lines show the corresponding curves without and with load respectively, but with permanently acting vibrations. The ordinate differences between each of the above three pairs of curves with and without load are in fig. XI. plotted against induction. The dash line curves show this load effect under the A conditions without mechanical vibration, while the continuous line curve represents within the limits of experimental error the load effects under the B conditions irrespective of whether vibrations are or are not permanently acting. Fig. XII., without vibrations, shows for three different values of induction the changes due to loading and unloading which take place between the first and fortieth “ ons ” and “ offs ” of load, plotted from the experimental data from which the dash line curves of fig. X. were obtained. The remaining diagrams of the fig. show for three very similar values of induction the corresponding changes under the same A conditions, but with permanently acting vibrations. The induction values given with each figure are obtained after the fortieth “off” of load by taking a single step to a sufficiently high value of field, as already explained. Results. — In fields increasing from zero, the effect of the first “ on ” of load superposed under the A conditions is to increase or decrease induction as field (induction) is low or high ; within the experimental limits, the less the load the greater is the increase in low fields ; the greater the load, the greater is the decrease in high fields. The neutral points are thrust towards the origin the greater the load, from the origin the less the load (fig. VI.). Although in this respect the initial irreversible effect of load in nickel is similar to the final reversible effect of load in iron, the resemblance is in appearance only. With permanently acting vibra- tions the initial effects nearly vanish, the first superposition of load decreasing the induction (almost) from the origin (fig. VII.). It thus becomes apparent that these initial effects of load are at all stages the result of the vibrational effect due to the first superposition of load which is always VOL. xxix. 4 50 Proceedings of the Royal Society of Edinburgh. [Sess. positive, and the reversible effect which is always negative. At low values of field and induction the former predominates, at high values the latter. Successive positive induction changes may be obtained with successive VALUES OF B. AT FORTIETH "OFF” OF LOAD ORDINATES, CHANGES OF B.-ABSCISSAE, 1st TO 40th “ONS" AND "OFFS OF LOAD. increments of load, but this possibility is limited with fields increasing from zero to a very narrow range (fig. VI.). In general, the second and further increments of load will either produce no effect or lower the induction (fig. VIII.). Successive “ ons ” and “ offs,” however, augment the 1908-9.] Load and Vibrations upon Magnetism in Nickel. 51 irreversible vibrational effect observed upon the first superposition of load. The increase of induction due to this cause is not so completely eliminated with permanently acting vibrations as the increase due to the first super- position (figs. IX. and VII.). Permanently acting vibrations, while increasing the induction change due to load, decrease the area of the loops formed during a cyclic load process, and observed in these figures when loading and unloading is performed in steps. A comparison of fig. VIII. with, say, fig. 108 given on p. 218 of Ewing’s Magnetic Induction, 3rd ed., shows that the irreversible vibrational effect of cyclic loading does not differ from the same effect in iron, except that it is the first increment of load that in general gives rise to induction increase, and not successive increments as in iron. This is due to the fact that in nickel the irreversible vibrational and the reversible effects of load oppose each other, while in iron they assist each other. Nevertheless, the vibrational effect of repeated loading and unloading tends towards induction increase in nickel as in iron. This latter effect is especially marked in low fields (fig. X., dash line curves). The final “off” curve is for all values of field the higher of the two, but lower than that obtained under the B conditions with permanently acting vibrations of sufficient intensity. The final “ on ” curve (A conditions) and the permanent load curve (0*5 kilos per mm.2 — B conditions) with vibra- tions fall above or below the normal BH curve as the fields are low or high respectively. The permanent load curve without vibrations (B conditions) is the lowest throughout of the six curves compared, that with permanently acting vibrations of sufficient intensity without load (B con- ditions) the highest; the load curves therefore fall below the corre- sponding curves without load. This almost universally recognised result is irrespective of whether mechanical vibrations are or are not acting. Permanently acting vibrations, however, eliminate in fields increasing from zero the irreversible first effects of loading and unloading to a greater extent that at some stages of cyclic field (fig. XII. and figs. Ill.a, IV.a respectively). But the load effect, i.e. the ordinate differences between each pair of curves, is at all values of induction decidedly less under the A conditions without vibrations than under the B conditions irrespective of whether vibrations are or are not acting. It may be noted that the approximation of the load effect under the A conditions with vibrations to the load effect under the B conditions will depend upon their intensity. 52 Proceedings of the Royal Society of Edinburgh. [Scss. Discussion and Summary. Loading and unloading may be superposed upon magnetisation (A conditions) with field increasing from zero (Al), with cyclic field (A2), or with zero field, cyclic residual magnetisation (A3) alone being dealt with. Reversals of field increasing from zero may also be superposed (B1 con- ditions), the nickel wire being either loaded or unloaded. Under the A conditions, the magnetic changes following upon load changes are compounded of (a) the irreversible vibrational effects due to molecular instability and ( b ) the reversible effects of loading and unloading. In general, the initial effects (a) are most marked on the first superposition of load (or on the first superposition of load “ off” if the nickel wire be already loaded). They decrease and finally vanish when “ ons ” and “ offs ” of load are sufficiently often repeated, leaving only the final reversible effects ( b ). Both effects are clearly distinguishable from each other and traceable in regular sequence at all stages of increasing field (Al), cyclic field (A2), or cylic residual magnetisation (A3). Permanently acting vibrations lessen or eliminate the irreversible effects (a), but increase the reversible effects (b). The curves representing the first “ on ” of various loads under conditions Al are of interest. The irreversible vibrational effect (a) increases the in- duction, while the reversible effect ( b ) decreases the induction to a greater extent, the greater the load. At low inductions the former predominates. Hence the first “ on ” curve falls above or below the normal BH curve as the field is low or high, and the neutral points are thrust towards the origin the greater the load, from the origin the less the load, just as the Yillari critical points are in iron. Under conditions A2 (cyclic field), the first “ on ” or the first “off” of load increases the induction at cyclic extremes (not unduly increased), decreases the residual magnetisation, and lessens those differences to which hysteresis has given rise, irrespective of whether “on” is superposed upon a normal loop without load, or load “off” is superposed upon a loop performed with load. The irreversible changes (a) due to repeated loading and unloading under conditions Al (increasing field) accentuate the induction increase due to the first superposition of load. This increase is especially well marked in low fields, but tends to vanish as field is sufficiently increased. Under con- ditions A2 (cyclic fields) also, the results mentioned immediately above as due to the first superposition of load “on” or “off” are further increased. The vibrational neutral points in the first and third quadrants are where the changes due to loading and unloading (induction decrease and increase 1908-9.] Load and Vibrations upon Magnetism in Nickel. 53 respectively) assume their final reversible values from the first — the (a) effect being zero. These neutral points are thrust towards or from the cyclic extremes as the amplitudes are greater or less. Under condition A3, a neutral point as above defined (where the changes due to loading and un- loading assume their final reversible values from the first) occurs at a comparatively large value of cyclic residual magnetisation, which will be positive or negative as the cyclic field process has been conducted from positive or negative extremes respectively. At all other values the residual magnetisation will be either increased or decreased according as these values lie between or beyond the limits of the neutral point and the zero of cyclic residual magnetisation. Further, the irreversible increase (a) due to loading and unloading betiveen these limits will be positive or negative according as the immediately preceding field change had been positive or negative. But it has been shown in the preceding paper,* read in con- junction with this communication, that a phenomenon of this kind can be co-ordinated with the shift of the neutral points in a cyclic field from or towards the extreme at which the last reversed took place according as the vibrational intensity is strong or weak. Permanently acting vibrations eliminate the irreversible effects (a) to a greater extent under conditions A1 than under conditions A2 where the cyclic fields are steepest. Under all the above conditions, therefore, the irreversible effects (a) are subject to the same laws which govern the superposition of mechanical vibrations. They depend in cases A2 (cyclic field) and A3 (cyclic residual magnetisation) upon the tendency of different molecular groups of unequal stability to rotate in opposed directions, consequent upon the nickel wire having been previously subjected to at least one reversal of field change, as fully discussed in the paper referred to above.* Under the Al con- ditions, the magnetic aeolotropy is less complex, no such opposing tendencies having been impressed upon different molecular groups, the field change having been in one direction only. On the other hand, the reversible effects (b) are such that, under the Al conditions (increasing field), loading and unloading sufficiently often repeated decrease and increase the induction by equal amounts respec- tively. This cyclic load process encloses an area, the curve for loading, as pointed out by Ewing, everywhere lying above that for unloading. This statement, however, only holds true after the reversible effects (a) * “ The Shift of the Neutral Points due to Variation of the Intensity of Mechanical Vibrations or Electric Oscillations superposed upon Cyclic Magnetisation in Iron,” pp. 1-37. Read in conjunction with this paper. 54 Proceedings of the Royal Society of Edinburgh. [Sess. producing induction increase are over. Permanently acting vibrations increase the range of magnetic change due to load change, but decrease the area of the loops formed during the cyclic load process. The load effect is thus negative if the induction be regarded as positive, and when plotted against the latter as abscissae the resultant curve is concave upwards. Consequently Villari critical points have been looked for at very small and very large values of induction.* Hydweiller,f contrary to the almost universally accepted view, claimed to have found such a result at low values of field with various small loads, essentially similar to the Villari reversal in iron. Messrs Honda and Shimizu J have, however, recently repeated these experiments, and they find that no such reversal exists. They maintain that Hydweiller never reached a magnetic zero, the necessary initial starting-point from which such experiments must be conducted. In any case, the experiments described under A2 and A3 conditions show that the latter’s method of demagnetisation by a combined process of field reduction and tapping might itself create a molecular condition favourable to the occurrence of a Villari reversal in nickel, even although a magnetic zero, as measured by magnetometer methods, had been reached. The results of: the comparisons instituted between the curves repre- senting the final reversible effects of “ ons ” and “ offs ” of load and those obtained under the Bl conditions with and without permanently acting vibrations need not be repeated in detail. They may, however, be shortly summarised as follows-. The curves obtained under the Bl conditions without vibrations exhibit magnetic but not load hysteresis ; those under the A1 conditions exhibit load hysteresis, but eliminate to a large extent magnetic hysteresis ; while the curves with permanently acting vibrations eliminate both magnetic and load hysteresis. The load curve always falls below the corresponding curve without load. The reversible effects ( b ) under conditions A2 and A3 are more complex. At points in the second and third quadrants where induction and field oppose each other, loading and unloading produce, after the irreversible changes due to molecular instability are over, no induction change whatever. Thereafter, until zero induction is reached, loads “ on ” and “ off” increase and decrease induction respectively. There is thus in cyclic fields well-marked Villari reversals in nickel. With cyclic residual magnetisation (A3 conditions, zero field) essentially similar phenomena are * Kelvin ( loc . cit.). t Wied. Ann., lii. 1894, p. 462. Phil. Mag., (5) xxxv., 1893, p. 469. f Physikalische Zeitschrift, 5, 1904, p. 254 and p. 631. 1908-9.] Load and Vibrations upon Magnetism in Nickel. 55 observed. The reversals occur at somewhat lower values than the vibra- tional neutral points where “ons” and “offs” of load assume their final values from the first, just as the Villari critical points occur at lower values of induction (second and fourth quadrants) than the vibrational neutral points (first and third quadrants) with cyclic fields. Permanently acting vibrations increase the irreversible effects (b) under the A2 as under the A1 conditions. The Villari critical points remain. These Villari reversals, occurring as they do under both the A2 and A3 conditions, depend therefore upon the molecular condition impressed upon the nickel by the cyclic field process, independent of the presence of the field itself. To distinguish from the Villari critical points which occur in iron and cobalt in opposite senses, apart altogether from cyclic con- ditions, these phenomena may more appropriately be called the cyclic Villari reversals in nickel. Obviously, the effects of loading and unloading under cyclic conditions must be more complicated in iron and cobalt than in nickel. Just as the initial irreversible effects (a) can be co-ordinated under the A2 and A3 conditions with molecular groups of unequal stability tending to rotate in opposite directions, see p. 53, so may the reversible effects (b) of loading and unloading be co-ordinated with the molecular groupings which have, in continuation of this process, actually assumed opposite polarities, as Professor Hughes * found to be the case when zero magnetisation was reached or approximated to. In comparison with so essentially an isotropic process (isotropic co-directionally, not transversely, in reference to the field) as that of demagnetisation by decreasing reversals, the methods of reaching a magnetic zero by a reduced field reversal under the A2 conditions, or by subsequently withdrawing a slightly greater value of reduced field reversal under the A3 conditions, do not differ essentially from those adopted by Hughes, who reached a position of neutrality or approximate neutrality by tapping or by heating to redness an iron wire left residually magnetised. He showed that as the surface was dissolved away by means of nitric acid the successive longitudinal layers were of opposite polarities, and that it is the summation of these opposing layers which under such conditions constitute magnetic neutrality. Under both the A2 and A3 conditions the demagnetising process precludes perfect symmetry of the molecular groupings of opposite polarities. It therefore follows that the conditions constituting magnetic neutrality will not be such that the final effects (6) of loading and unloading can possibly be zero. Such a condition — where the summation of the positive and negative magnetic changes due to * “Magnetic Neutrality and Polarity,” Proc. Roy. Soc., London, xxxvi., 1883-4, p. 405. 56 Proceedings of the Royal Society of Edinburgh. [Sess. loading, and of the negative and positive changes due to unloading, on the molecular groups of opposite polarities respectively, is zero — must occur at some other position than that of magnetic neutrality. If this hypothesis be correct, then, after the irreversible vibrational effects (a) have secured permanent stability under the conditions of the various molecular groups, these positions, where this nice balancing of the opposing magnetic changes due to loading and unloading occurs, constitute cyclic Villari critical points in nickel. I desire to express my indebtedness to the Royal Society of London for placing at my disposal Government grants to prosecute these researches. ( Issued separatelij December 5, 1908.) 1908-9.] On the Recalescence Temperatures of Nickel. 57 III. — On the Recalescence Temperatures of Nickel. By T. A. Lindsay, M.A., B.Sc., Carnegie Scholar, Edinburgh University. Communicated by Professor J. G. MacGregor. (Read July 20, 1908. MS. received September 25, 1908.) The object of the experiments described in this paper was to study the cooling of nickel, and to endeavour to get recorded any recalescence which might occur. A specimen of pure nickel could not be obtained, but the nickel worked with, supplied by Messrs Johnston & Sons, con- tained less than 2 per cent, of impurities. The critical ranges of nickel, or the temperature ranges over which changes in certain of the physical properties of nickel occur, have for long been a subject of investigation, and various workers have attempted to get evidence of evolution of heat or “ recalescence ” at these temperatures, but no successful attempt seems to be on record. Take,* reviewing the work done in this direction, says : “ It may be stated that neither anomalous changes of length nor recalescence phenomena have been observed in the case of nickel.” In the most recent work on the recalescence of metals the “ differential ” method introduced by Roberts- Austen has been adopted, and Rosenhain,j- in a discussion of the various methods of taking cooling curves, indicates that this “ differential ” method is the best. In my preliminary experi- ments I used the Roberts- Austen arrangement, but abandoned it for the simpler modification used by Carpenter and Keeling J in their work on iron- carbon alloys, as I found the latter gave more readily interpretable results. In the method as used by Carpenter and Keeling, blocks of the metal under observation and of a metal which cools regularly without recalesence are placed close together in a furnace ; thermo-electric junctions of the same kind of wires are inserted in the metal blocks, and so connected to a galvanometer that when heated they send current through the galvano- meter in opposite directions, and in this way the galvanometer indicates any difference of temperature between the two metals ; another thermo- couple inserted in the metal under observation is connected to another * Magnetische Untersuchungen, Biss. Marburg , 1904, p. 88. t Physical Society of London, Jan. 24, 1908. X Journal Iron and Steel Institute , 1904, vol. i. p. 224. 58 Proceedings of the Royal Society of Edinburgh. [Sess. galvanometer and thus determines the temperature of this metal. Carpenter and Keeling used platinum as the “ blank ” metal or metal without recalescence ; but as platinum was not available, and I did not wish to work above 1000°, I used pure copper as being suitable for this purpose. A diagram of my arrangement is shown in tig. 1. FF represents the lagging of the furnace, and AB its porcelain tube ; C is a copper block, drilled with a hole for the insertion of a thermo-couple, and N the nickel block with two holes for thermo-couples ; D is the galvanometer for the double thermo-couple or “ differential ” circuit ; and T the galvanometer indicating temperature of N. An electrical resistance furnace made by the Cambridge Scientific Company was used ; it consists of a tube of English porcelain 62 cm. long, of diameter 4 cm., and lagged with asbestos to a diameter of 19 cm., this tube being heated electrically by a coil of platinum foil. The metal blocks were 2 cm. long and 3J cm. in diameter, drilled with holes 1‘3 cm. deep and *6 cm. in diameter; these were placed about •6 cm. apart in the centre of the furnace tube, the rest of the tube being loosely packed with asbestos, and under these conditions a cooling from 900° to 180° occupies about 3J hours, the heating current being completely shut off. The thermo-junctions were of platinum and platinum-iridium wires welded together in the blowpipe; the wires of the “ differential ” circuit were ‘005 cm. in diameter, and those of the “ temperature ” circuit ‘02 cm. in diameter ; in each case the wires were insulated by means of thin porcelain tubes, and were soldered to copper leads to their respective 59 1908-9.] On the Kecalescence Temperatures of Nickel. galvanometers, these copper junctions being kept in test-tubes of alcohol surrounded by melting ice. The galvanometers were both of the D’Arsonval type. The one used in the differential circuit was of 1098 ohms resistance, and of such sensitive- ness that it gave a deflection of inch with 1 volt on 3950 megohms at 40 inches distance from the scale, and although not aperiodic it was not far from being so. The galvanometer of the temperature circuit was more sensitive than I required, and was therefore used with an external resistance, as its scale had to register from 100° to 1000°. Preliminary experiments showed that the nickel did not oxidise in the furnace to an extent likely to affect any exhibition of recalescence, so I did not think it necessary to keep the metal in a non-oxidising gas. The scale of the temperature galvanometer was calibrated by making use of the known boiling-points of water, naphthaline, and sulphur, and determining the position of these known temperatures on the scale, the error limit amounting to ±T nun., or less than * 5 °. The boiling-point of naphthaline was taken as 218°, and that of sulphur as 444‘5°. An open V. Meyer tube 48 cm. long, with a bulb 8 cm. in diameter, and jacketed outside with asbestos, was used to boil the naphthaline and sulphur in, and the thermo-junction, protected by a thin- walled Bohemian glass tube, was lowered to within 4 cm. of the boiling liquid. The vessel used for the water was a wide-necked flask 17 cm. in diameter, fitted with an escape tube and lined outside with asbestos ; precautions to prevent bumping were observed, and the thermo-junction inserted as before. A curve drawn through these three determinations, as plotted on a temperature deflection diagram, then furnished the means of getting the temperature corresponding to any deflection on the galvanometer scale. The general procedure was to heat up the furnace and contents slowly in about If hours to about 1000°, then shut off heating current and connect up galvanometers. During the cooling, readings of the two galvanometers were taken simultaneously at equal falls of temperature — about 4J° — as registered by the temperature galvanometer, photographic or other self- recording appliances not being available. In the cooling curves drawn to detect recalescences, the deflections of the differential-circuit galvanometer were plotted as abscissae, and as ordinates the actual temperatures of the nickel determined by the deflec- tions of the temperature galvanometer. These curves are rather complex in form, and as they might be expected to be simpler the more uniform the temperature of the furnace at the beginning of the cooling, I at first kept the furnace at its maximum temperature for about half an hour, in order to 60 Proceedings of the Royal Society of Edinburgh. [Sess. get the thermal conditions as steady as possible ; but this was not found to simplify the form of the curves, and subsequently, and in the case of the curves illustrated, the cooling was started immediately after the maximum temperature was reached. The general form of the cooling curves may now be discussed. Under ideal conditions, with two similar pieces of the same metal, similarly situated in a furnace cooling uniformly, and initially at a uniform tempera- ture throughout, the metals will always be at the same temperature during cooling, and the galvanometer of the differential circuit will be continuously at zero, so that the curve will coincide with the temperature axis. If we consider, however, the actual conditions under which I worked, we see that with two pieces of different metals, though neither of them metals which exhibit recalescence, in general there will be a difference of temperature between them throughout the cooling, as the furnace is not initially uniform in temperature throughout. Also this difference will be of different magni- tude and sign according to the actual distribution of temperature in the furnace, while it will also be affected by the relative sizes and natures of the bodies, position in the furnace, and surroundings generally, so that the exact form of the curve cannot be foreseen. We can, however, say that (1) the initial abscissa will in general differ from zero, since there will in general be an initial difference of temperature between the metals ; (2) the curve must finally arrive at the temperature axis, since the two metals must finally both come to room temperature ; (3) if one of the metals cools more rapidly than the other, and is initially at the higher temperature, the curve may run down more or less steadily to the temperature axis, or it may cut the axis before the final temperature, and attain a maximum on the other side, before returning to the temperature axis again at the room tempera- ture ; (4) if the metal which cools more slowly is initially at the higher temperature, this difference of temperature may increase at first, though finally it must become zero at room temperature as before ; (5) the maximum points indicated above will not occur at any definite temperature, but may correspond to a high or low temperature ; in fact, the maximum difference of temperature between the metals will depend on their initial difference of temperature and on the conditions under which the cooling occurs, which will vary according to the distribution of temperature in the furnace. The result of the occurrence of recalesence in one of the metals may be a rise in temperature of that metal, or at least a slower rate of fall than there would otherwise have been, and the effect in the curve will be a more or less sudden change of slope. If the recalescence be of small range, the curve will immediately return to approximately its former slope, and the result 61 1908-9.] On the Recalescence Temperatures of Nickel. will be a more or less pronounced but small hump on the curve ; but if it be of large range, the result will be either a large hump or a long-drawn-out and flat hump, according to the rate of evolution of heat. Under actual conditions these humps may not be readily recognised, being concealed by the sinuosities of the curve due to errors of observation ; but as these sinuosities differ from experiment to experiment, while the recalescence humps preserve their position, except in so far as it may be altered by repeated heatings, it is quite possible to recognise a recalescence hump even of comparatively small size, by comparing with one another a series of cooling curves. Fig. 2 shows typical specimens of curves with no recalescence humps ; they are taken with two pieces of copper of different size, and are approxi- mately straight lines, except for the slight sinuosities, which give an idea of the limits of size within which humps could not be interpreted as recales- cences. In these cases the galvanometer indicated a difference of temperature between the two pieces of metal initially, and the curve is constantly running down towards the temperature axis so far as it is recorded. 62 Proceedings of the Eoyal Society of Edinburgh. Fig. 3a shows curves obtained with nickel and copper in successive heatings of a new specimen of nickel. Here the galvanometer indicated that the metals had started at about the same temperature,, but the copper cooling more quickly than the nickel, probably on account of its smaller specific heat, we get a difference of temperature established, which grows to a maximum just above A (most of the curves just begin to be recorded here, but Nos. 1 and 3 show part of this maximum), and thereafter the curves tend to get back to the temperature axis, except where they are interfered with by recalescences, the general trend of the curves being from right to left. These curves show two small humps, Iq and R2, occurring at the same temperatures, about 660° and 525° respectively, in all cases ; also a large hump occurring within the same temperature range in all cases, viz. 440°-285°, being very evident as a change of slope at R, the original slope being regained at B. The large recalescence consists of two distinct parts, as at R1 the slope again abruptly changes till the curve is nearly horizontal, indicating that heat is being given out at the greatest rate ther.e ; the first part, from R to R1, extends from 440°-370°, and the latter part, R1 to B, from 370°-285°. The general slope of the curves is seen above Rx and again from B to C, while between R1 and R2 and between R2 and R the curve has not regained this slope, showing a small and gradual evolution of heat here also. Fig. 3b shows the next two coolings taken of the same nickel and copper ; here the galvanometer indicated that the copper had started at a higher temperature than the nickel, and the general trend of the curve is therefore from left to right towards the temperature axis, which was crossed during the large recalescence, and when this is finished at B the curve turns back again towards the temperature axis. These curves again show the recalescences in same places, R1? R2, and R to R1 and B, though they have a less marked effect in changing the slope of the curve, owing to its general trend being from left to right. It may be noted here that the recalescence temperatures mentioned above cannot claim to be closer than to 5°, as I was only able to take readings of galvanometer deflection at intervals of 4J° or 5°. A large number of coolings were taken of the specimens, partly to gain experience in interpreting and partly to test the uniform occurrence of the recalescences, and the curves shown are a few typical specimens. Fig. 4 shows the effect of repeated heatings on the nickel ; these curves were taken after the specimen had been subjected to from fifty to sixty coolings. The effect is apparently that the temperatures at which the recalescences occur are unaltered, but Rx at 660° is disappearing — it is just TEMPERATURE Fig. 3a. 64 Proceedings of the Royal Society of Edinburgh, [Sess. evident as a slight bulge in the curve— and that at 525° is getting smaller in size also, while the gradual evolution of heat from Rx to R2 seems also to have disappeared, though this is not quite certain. These results are corroborated in fig. 5, these curves being also taken at about the same time. In the case of fig. 4 curves, the metals had started about the same tempera- ture and attained maximum difference of temperature just above A, and there- after tended towards the temperature axis just as the curves in fig. 3a did. Rosenhain * has found that recalescence occurs in silica porcelain at about 550°, and as this is present in some furnaces, it gives rise to mislead- ing results. No such indication of recalescence is given in my curves of copper and copper in fig. 2 ; but to find whether or not my results were due to recalescence of the materials of the furnace used, I took coolings in a fireclay gas muffle, packing the specimens in loosely with asbestos. The curves got are shown in fig. 5, and are in agreement with the other curves in their recalescence indications ; it will be noticed that curves 1 and 2 have the humps smaller, but this is due to the galvanometer being shunted * Physical Society of London, January 24, 1908. Ill the printer is not responsible, the expense of such proofs and corrections will be charged against the author. All proofs must, if possible, be returned within one week, addressed to The Secretary , Royal Society, Mound, Edinburgh , and not to the printer. To prevent delay, authors residing abroad should appoint some one residing in this country to correct their proofs. 4. Additions to a Paper after it has been finally handed in for publication, if accepted by the Council, will be treated and dated as separate communications, and may, or may not, be printed immediately after the original paper. 5. Brief Abstracts of Transactions Papers will be published in the Proceedings, provided they are sent along with the original paper. 6. Separate Issue of Reprints; Author’s Free and Additional Copies. — As soon as the final revise of a Transactions paper has been returned, or as soon as the sheet in which the last part of a Proceedings paper appears is ready for press, a certain number of separate copies or reprints, in covers bearing the title of the paper and the name of the author, are printed off and placed on sale. The date of such separate publication will be printed on each paper. The author receives fifty of these reprints free, and may have an} reasonable number of additional copies at a fixed scale of prices which will be furnished by the printer, who will charge him with the cost. To prevent disappointment, especially if the paper contains plates, the author should, immediately after receiving his first proof, notify to the printer the number of additional copies required. 7. Index Slips. — In order to facilitate the compilation of Subject Indices, and to secure that due attention to the important points in a paper shall be given in General Catalogues of Scientific Literature and in Abstracts by Periodicals, every author is requested to return to the Secretary, along with his final proof, a brief index (on the model given below), of the points in it which he considers new or important. These indices will be edited by the Secretary, and incorporated in Separate Index Slips, to be issued with each part of the Proceedings and Transactions. MODEL INDEX. Schafer, E. A. — On the Existence within the Liver Cells of Channels which can be directly injected from the Blood-vessels. Proc. Roy. Soc. Edin., vol, 1902, pp. Cells, Liver, — Intra-cellular Canaliculi in. E. A. Schafer. Proc. Roy. Soc. Edin., vol. , 1902, pp. Liver, — Injection within Cells of. E. A. Schafer. Proc. Roy. Soc. Edin., vol. , 1902, pp. p The Papers published in this Part of the Proceedings may be had separately, on application to the Publishers, at the follow- ing prices: — No. I., . . Price 2s. 2d. No. II., . ,, Is. 2d. No. III., . 8d. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SESSION 1908-9. Part II.] VOL. XXIX. [Pp. 65-128. CONTENTS. NO. IV. On a Question in Absorption Spectroscopy. By Robert A. Houstoun, M.A., Ph.D., D.Sc., assisted by Alexander S. Russell, M.A. {Communicated by Professor A. Gray), {Issued separately December 22, 1908.) Y. Dissymmetrical Separations in the Zeeman Effect in Tungsten and Molybdenum. By Robert Jack, M.A., B.Sc., Ph.D., 1851 Exhibition Research Scholar. {Communicated by Professor A. Gray), ...... {Issued separately December 30, 1908.) YI. On the Reducing Action of Electrolytic Hydrogen on Arsenious and Arsenic Acids when liberated from the Surface of Different Elements. By William Thomson, F.I.C., . {Issued separately January 21, 1909.) PAGE 68 75 84 YII. Preliminary Note on the Action of Nitric Anhydride on Mucic Acid. By Professor A. Crum Brown, F.R.S., and G.*E. Gibson, B.Sc., ...... 96 {Issued separately February 19, 1909.) {Continued on page iv of Cover. EDINBURGH : Published by ROBERT GRANT & SON, 107 Princes Street, and WILLIAMS & NORGATE, 14 Henrietta Street, Covent Garden, London. MDCCCCIX. % Price Four Shillings and Fourpence. $ 190S REGULATION S REGARDING THE PUBLICATION OF PAPERS IN THE PROCEEDINGS AND TRANSACTIONS OF THE SOCIETY. 1, The Council beg to direct the attention of authors of communications to the Society to the following Regulations, which have been drawn up in order to accelerate the publication of the Proceedings and Transactions, and to utilise as widely and as fairly as possible the funds which the Society devotes to the publication of Scientific and Literary Researches. 1. Manuscript of Papers.— As soon as any paper has been passed for publication, either in its original or in any altered form, and has been made ready for publication by the author, it is sent to the printer, whether it has been read or not. The ‘ copy 5 should be written on large sheets of paper, on one side only, and the pages should be clearly numbered. The MS. must be easily legible, preferably typewritten, and must be absolutely in its final form for printing ; so that corrections in proof shall be as few as possible, and shall not cause overrunning in the lines or pages of the proof. All tables of contents, references to plates, or illustrations in the text, etc., must be in their proper places, with the page numbers left blank ; and spaces must be indicated for the insertion of illustrations that are to appear in the text. 2. Illustrations. — All illustrations must be drawn in a form im- mediately suitable for reproduction ; and such illustrations as can be reproduced by photographic processes should, so far as possible, be preferred. Drawings to be reproduced as line blocks should be made with Indian ink (deadened with yellow if of bluish tone), preferably on fine white bristol board, free from folds or creases ; smooth, clean lines, or sharp dots, but no washes or colours, should be used. If the drawings are done on a large scale, to be afterwards reduced by photography, any lettering or other legend must be on a corresponding scale. If an author finds it inconvenient to furnish such drawings, the Society will have the figures re-drawn at his expense ; but this will cause delay. When the illustrations are to form plates, a scheme for the arrangement of the figures (in quarto plates for the Transactions, in octavo for the Proceedings) must be given, and numbering and lettering indicated. 3. Proofs. — In general, a first proof and a revise of each paper will be sent to the author, whose address should be indicated on the MS. If further proofs are required, owing to corrections or alterations for which [ Continued on page iii of Cover. 65 1908-9.] On the Recalescence Temperatures of Nickel. in these curves. The explanation of the form of these curves is the same as in the case of fig. 3b. The insulation of the thermo-couple wires was also changed to asbestos, but this also had no effect on the exhibition of recalescence. The results recorded by different workers on the transition tempera- tures of nickel differ somewhat, probably due to the fact that the specimens used were different in composition. Harrison * using the same specimen of nickel throughout, correlates the changes which occur in the magnetic, thermo-electric, and electrical resistance properties, the results being : — Range of temperature extending from sudden drop in magnetic permeability to its vanishing-point : 320°-374° ' 300°-373° ■ 310°-374° according to previous thermal treatment. Range in which Peltier coefficient undergoes change, 290°-375°. Range in which change in slope of the resistance-temperature curve occurs, 320°-375°. * VOL. XXIX. * Phil Mag. (6) 8, 179, 1904. 5 66 Proceedings of the Royal Society of Edinburgh. [Sess. Fig. 1908-9.] On the Recalescence Temperatures of Nickel. 67 Now, the range of temperature over which I have found heat is given out at the greatest rate, viz. the latter part of the large recalescence, is from 370°-285°, and this corresponds very well with the ranges given for the changes noted above, by Harrison. My conclusion, then, is that nickel (98 per cent.) in cooling from 900° to 180° gives out heat gradually over a long range (roughly speaking, from about 700° to about 285°), but in addition there are three places where heat is given out at a greater rate. We have recalescences of small extent at about 660° and at about 525°, and to a much larger extent from 440° to 370°, and again to a larger extent from 370° to 285°. Also the range over which we have greatest evolution of heat corresponds to that range over which we have the well-known changes in the magnetic and thermo-electric properties of nickel occurring. I hope to repeat these experiments with a purer specimen of nickel, to determine whether or not the recalescences observed occur in the nickel itself or are due to impurities. The expenses of this research were defrayed in part by a grant from the Tait Memorial Fund. (. Issued separately December 22, 1908.) 68 Proceedings of the Royal Society of Edinburgh. [Sess. IV. — On a Question in Absorption Spectroscopy. By Robert A. Houstoun, M.A., Ph.D., D.Sc., assisted by Alexander S. Russell, M.A. Communicated by Professor A. Gray, F.R.S. (MS. received October 12, 1908. Read November 2, 1908.) [n the third volume of his Spectroscopic, p. 91, Kayser has raised the question whether on mixing two coloured solutions which do not act on one another chemically the absorption spectrum of each of the components remains unchanged. Melde thought he had discovered such an effect ; he stated that when a solution of carmine in ammonia which has two sharp bands in the green, was added to a solution of potassium dichromate which absorbs the violet end of the spectrum, or to an ammoniacal solution of copper sulphate which absorbs the red end, that the carmine bands were in each case displaced towards the end absorption in question. He ascribed this to a physical action between the molecules. It was, however, pointed out by Schuster that a shift of this nature would be seen if, instead of mixing, the one solution was merely placed behind the other. Bostwick * and Kriiss f repeated Melde ’s work, and came to the conclusion that there was a real shift in addition to the apparent shift pointed out by Schuster. Since then additional evidence has been adduced by FormanekJ and has been quoted by Kayser in the section cited above. The object of the research recorded in this paper was to investigate those cases with the most accurate means possible, and, if a shift was established, to decide if it was physical. We have theoretical grounds for expecting such a shift. Suppose that we have an electric doublet vibrating according to the equation <*> where x specifies the position of the negative electron relatively to the * A. E. Bostwick, “ Preliminary Note on the Absorption Spectra of Mixed Liquids,” Amer . J. (3), xxxvii., pp. 471-473 (1889). t G. Kriiss, “ Ueber die Constitution von Losungen,” Ber. Chem. Ges., xv., pp. 1243-1249 (1882). f J. Formanek, “ Untersuchung und Nachweis Organischer Farbstoffe auf Spectroscopi- scbem Wege,” Zs. f. Farben- u. Textil-Chemie, i. Heft 11 (1902). 69 1908-9.] A Question in Absorption Spectroscopy. positive one, which is regarded as fixed. Let a second doublet of co-ordin- ate x± and different free period commence vibrating near the first. It will act on the first electron, and this action may be represented by intro- ducing a new term lx1 in equation (1), l being small in comparison with k. On account of their rapidity we may regard l as a constant as far as the light vibrations are concerned. Equation (1) now runs, m^ + h^ + Jcx + lx^ 0 (2) at “ at We have a similar equation for the second doublet. On solving, we find that the mutual action has slightly altered the periods of both vibrations. As an absorption band corresponds to a free period, absorption bands might thus affect one another. The effect of the mutual actions of the electrons on the theory of dispersion and absorption has been fully worked out by one of the authors.* On the other hand, we should expect this shift to be too small to observe. The absorption bands of organic colouring matters usually appear at different positions in the spectrum when different solvents are used. Thus the fuchsine band in water is at 540 /u/x, while in alcohol it is at 555 /a/a. Kundt stated the law that the absorption band is farther to the red the greater the dispersion of the solvent; but investigation has shown that this law is as often as not disobeyed. It is nevertheless still given in the text-books. This dependence of the position of the absorption band on the solvent — the “ Kundt effect ” — is supposed to be due to a physical action between the molecules of the solvent and the molecules of the colouring matter. If changing the whole medium in which the doublet is placed displaces the band only by something of the order of 15 fxfj., then adding a small quantity of another colouring matter in the proportion of at the most 5 gms. per litre should have no appreciable effect. The apparatus was a spectrophotometer which has been described in an article in the Phil. Mag.f This instrument has two slits, one about 7 mm. vertically above the other. Both slits are illuminated by the same source, and the liquids, the absorption of which is to be compared, are placed one in front of each slit. The nicol eyepiece in the telescope may be replaced * R. A. Houstoun, “ Untersuchungen fiber den Einfluss der Temperatur auf die Absorp- tion des Lichtes in isotropen Korpern,” Diss. Gottingen, 1906, Ann. d. Phijs. (4), xxi. (1906), p. 535. t Ibid ., “A New Spectrophotometer of the Hiifner Type,” Phil. Mag., February 1908. 70 Proceedings of the Royal Society of Edinburgh. [Sess. by an ordinary eyepiece with cross-wires and the instrument used as a spectroscope. First of all the effect was tried of mixing uranyl nitrate in succession with cobalt chloride, copper sulphate, potassium dichromate, and nickel sulphate, and of mixing cobalt chloride in succession with copper sulphate, potassium dichromate, and nickel sulphate. In order to obtain the greatest accuracy, a differential method was used. Double glass cells of the form shown in the diagram were made for us by Leybold’s Nachfolger, Cologne, each compartment measuring 2x2x1 cm. inside. Solutions of the two salts to be mixed were prepared of a suitable strength. One compartment of each cell was filled with the one solution and the other compartment with the other solution. The cells were then placed above one another, one before each slit, so that the light passed through both solutions in each cell, and the position of the nicol read carefully for different wave-lengths. It was, of course, practically the same for all colours. Then the top cell was emptied. // // 77 y a mixture prepared of equal parts of the two solutions, and both compart- ments of the cell filled with this mixture. The cell was then replaced and the nicol again read. Any difference in the nicol readings could thus be due only to the mixing. The effect of mixing was also examined spectroscopically. This method is most suitable when dealing with sharp bands, the centres of which can be measured with the cross-wires. In this case light which passed through the mixed solutions was compared straight away with light which had passed through the solutions in succession. If c denote the concentration of the solution in gram-molecules per litre and d the thickness of solution passed through, then A the “ molecular extinction coefficient ” is defined by i = i0io-Acd, where I and I0 are respectively the intensities of the light before and after passing through. 71 1908-9.] A Question in Absorption Spectroscopy. The molecular extinction coefficients of the five salts were found to he as follows : — CuS04 *5H20. CoC12*6H20. NiS04 •7H20. K2Cr207. U02(N03)2-6H20. A A a A A A A A A A 598 •883 633 *514 693 2-112 697 •14 630 •035 590 •672 620 •518 660 1-951 633 •46 567 •039 572 •399 598 •527 630 1-493 588 •68 521 •044 537 •122 591 •552 617 1-092 568 1-10 498 •0605 450 •026 584 •620 596 •672 552 2-11 491 •181 576 •738 586 •445 544 3-69 488 •404 568 •970 567 •259 537 7-06 485 •413 552 1*817 550 •185 529 12-75 483 •355 537 3-120 535 •158 521 23-47 480 •361 522 4*561 521 •114 510 65-69 475 •421 515 4-827 509 •097 499 119-3 470 •902 510 5-238 498 •085 489 179-1 466 •941 504 5-509 488 •104 480 251-9 455 1-445 499 5*172 479 •186 471 322-6 470 •293 463 394-4 462 •381 448 •562 In the case of uranyl nitrate with cobalt chloride and potassium dichro- mate and in the case of cobalt chloride with copper sulphate, potassium dichromate, and nickel sulphate, no change could be detected as a result of mixing. Different strengths were used, and about seven points in the spectrum were examined. An alteration of of the intensity transmitted could have been detected in the most favourable cases. It was different in the case of uranyl nitrate with copper sulphate and nickel sulphate. The spectrum of uranyl nitrate consists of bands in the violet, the first two of which at 486 and 473 are very easily seen with the eye although the table of molecular extinction coefficients does not show the second well. On mixing, in each of the above cases, both these bands were displaced towards the red. The shift varied with the strengths of the solutions used ; it seemed to be proportional to the quantity of sulphate present divided by the quantity of nitrate. As the first two bands of uranyl sulphate are at 491 and 477, as no shift was produced by mixing copper nitrate and uranyl nitrate and as the same shift was produced by adding sulphuric acid to uranyl nitrate, there seems no doubt that the shift is chemical. We next repeated Melde’s work with carmine. This was done only spectroscopically. A solution of carmine in ammonia which has bands at 72 Proceedings of the Royal Society of Edinburgh. [Sess. 570 and 528 and then slowly increasing absorption in the bine and violet, was mixed with an ammoniacal solution of copper sulphate. The strength of the carmine solution was 0T5 gms. per litre. The strongest copper sulphate solutions had about 10 gms. copper sulphate per litre. Strengths down to d^nd of this were used. A definite shift of both bands to the red was obtained, amounting as a rule to 20 Angstrom units which seemed to remain pretty much the same as the concentration of the copper sulphate was diminished. The measurements were always made on the centre of the bands. The bands were so ill-defined that 10 Angstrom units was the smallest shift one could be sure about. In this case there is nothing to show whether the change is physical or chemical. The effect was tried next of mixing the ammoniacal solution of carmine with potassium dichromate. The strength of the latter solution was 4 gms. per litre and less. We could not say whether there is a shift to the violet or not. If there is one it cannot be more than 5 Angstrom units. But there is no doubt whatever that the ammonia acts on the dichromate, changing it into the chromate, and pushing back the beginning of the continuous absorption much further into the violet. Bostwick, it must be o noted, obtained a definite shift in both cases of the order of 40 Angstrom units. It is difficult to say what the discrepancj^ is due to. We varied our conditions repeatedly but cannot explain it. We finally repeated some of Formanek’s experiments. Here we had trouble with the cells. The cement absorbed the aniline dyes used, some- times rapidly, sometimes just appreciably. Cells made by Leybold, cells of unknown manufacture, and home-made cells were alike unsatisfactory ; and cells made without cement, of plate glass held together with rubber bands, leaked. It was therefore necessary, to do the work thoroughly, to have cells made without cement by R. & J. Beck, Limited, with first quality glass surfaces, the different pieces being kept together by a brass frame. The figures show how this was done. The cells were double and were used 73 1908-9.] A Question in Absorption Spectroscopy. in the same way as the other double cells, and the compartments had the same internal dimensions. Each cell consisted, in addition to the frame, of five pieces of glass, three plates and two pieces of square tubing with the top side ground off. They were satisfactory, but had to be put together with very great care. The effect of the cement on the dyes does not seem to have been mentioned by other workers, and may explain some effects observed in the photometry of the aniline colouring matters. In the article cited, Formanek gives five cases where on mixing dyes the bands affect one another. In his book he gives the sources from which his dyes were obtained, but we were able only to obtain those necessary for four of these cases. These cases are as follows : — (1) The bands of malachite green and brilliant green in water (6183, 6255) run together on mixing. A new band is formed which lies between 6183 and 6255. (2) If a little malachite green (band at 6183) be added to a suitably diluted solution of methylene blue (chief band at 6678, subsidiary band at 6081) in water, the subsidiary band of the methylene blue at 6081 runs together with the band of malachite green, and in the spectrum we see only the chief band of methylene blue in its original position and the band of malachite green somewhat displaced. If malachite green be added until the proportions of both colouring matters are about the same, the absorption band of malachite green returns to its original place. (3) If Nile blue A (band at 6448) and methylene blue are mixed in water, we obtain only one band which lies near the position of the Nile blue band. (4) On mixing methylene blue and methyl violet 6 B, which has a band at 5935, the methyl violet band is displaced towards the red. We first of all examined these cases spectroscopically taking different strengths. In no case did we see the slightest displacement as a result of mixing nor coidd any alteration of intensity be detected. The spectro- photometric method was then employed, one critical point in the spectrum being taken for each case, e.g., a point was taken between the bands if they were expected to move together on mixing. In the second case only could a small change of intensity be detected, which was not very consistent ; as it was about -^th of the intensity it was too small to be investigated. It could not in any case be detected by the spectroscopic method, which was the method employed by Formanek. Formanek seems to have used only test-tubes for the liquids under exam- ination, and we are forced to the conclusion that the shift he observed is merely an apparent one caused by the one maximum being on the slope of 74 Proceedings of the Royal Society of Edinburgh. [Sess. the other. It is in fact the effect pointed out by Schuster. There is no action between the molecules. We have thus met with no evidence in favour of the existence of an effect of the nature mentioned by Kayser. The research was carried out in the Physical Laboratory of the Uni- versity of Glasgow with the aid of a grant from the Carnegie Trust for the Universities of Scotland. ( Issued separately December 22, 1908.) 1908-9.] Dissymmetrical Separations in the Zeeman Effect. 75 V. — Dissymmetrical Separations in the Zeeman Effect in Tungsten and Molybdenum. By Robert Jack, M.A., B.Sc., Ph.D., 1851 Exhibition Research Scholar. Communicated by Professor A. Gray, LL.D., F.R.S. (MS. received October 12, 1908. Read November 2, 1908.) It has been mentioned by Professor Voigt of Gottingen in his newly pub- lished book * and by Professor Zeeman of Amsterdam in the Physikalische Zeitschrift ,f that I have found examples of strongly marked dissymmetry in studying the Zeeman Effect in tungsten and molybdenum. Professor Zeeman has also discovered and published such cases of dissymmetry in other elements. Not only have many examples of normal dissymmetry been found, but almost as many cases of abnormal dissymmetry. To explain those terms, normal and abnormal , let us consider that the single spectrum line is broken up, when the light is in the magnetic field, into the three com- ponents, 1, 2, 3, where the numbers begin from the component which has the shortest wave-length. In the normal dissymmetrical triplet the middle component is nearer the component on the red side than that on the violet one, i.e. for the normal type the interval 1-2 is greater than the interval 2-3, but in the abnormal dissymmetrical triplet 2 is nearer to 1 than to 3. These observations of Professor Zeeman and myself, which were made at the same time in the Universities of Amsterdam and Gottingen, having been com- municated to Professor Voigt, he wrote and published in the above-mentioned book an extension to his and Professor H. A. Lorentz’s theories of the Zeeman Effect. In his original theory Professor Voigt had shown that, considering the electrons as uncoupled, cases of normal dissymmetry might arise among the Zeeman triplets, this dissymmetry being accompanied by a greater intensity of the red component than the violet one. J He pointed out also that the “ absolute ” dissymmetry or the difference between the absolute displacements of the red and violet components should be independent of the magnetic field strength used to produce the Zeeman Effect. To explain the large numbers of complicated types of Zeeman Effect which have been found — in the study of the Zeeman Effect in tungsten I discovered lines with no * W. Voigt, Magneto- und Elektrooptih. + P. Zeeman, Phys. Zeit., x. 340, 1908 ; W. Voigt, Phys. Zeit., xi. 353, 1908. | Thus normal dissymmetry is the more simply explained and first discovered type, whereas abnormal dissymmetry requires a more complicated theory, and when first observed was contradictory to any existing theory. 76 Proceedings of the Royal Society of Edinburgh. [Sess. fewer than 17 to 19 components, the largest numbers hitherto found — Professors Voigt and Lorentz made use in their theories of couplings between electrons of the same vibration frequencies. The latest step taken by Professor Voigt as a result of these newest observations on dissymmetry is to introduce couplings between two electrons of different vibration frequencies. The theory shows that cases of normal and abnormal dissym- metrical triplets arise, that the intensities of the two outer components are the same, and that the displacement of the lines which produces the dissymmetry is proportional to the square of the magnetic field strength used. All these conclusions may be compared with the results arrived at for the uncoupled electrons. Thus the subject of the dissymmetry of the components is important, as it may lead to a more accurate knowledge of the grouping of the electrons and the constitution of the atom. While Professor Voigt’s book was being printed, observations appeared by P. Gmelin * showing that in the case of the dissymmetrical triplet, A — 5790,f of the mercury spectrum, the displacement of the middle line was propor- tional to the square of the field strength. In the following my observations are given, and an attempt is made to show that in addition to the possibility of the presence of such couplings in some cases, as Professor Voigt has assumed, there is evidently some con- nection between the rotation of the plane of polarisation produced by the concave grating apparatus used and the dissymmetry observed in many of the cases. There are, however, also examples of dissymmetry which are exceptions to such a rule ; and further, there are symmetrical separations which seem to be wholly uninfluenced by the rotation of the plane of polarisation. With the concave grating apparatus of the Physical Institute, University of Gottingen, photographs of the transversal Zeeman Effect were in the first place taken, i.e. the light at right angles to the magnetic lines of force was used, and hence in the case of triplets all three components were present. From these photographs both the type and the amount of the dissymmetry were observed, but one could decide nothing about the displacement of the components which had caused the dissymmetry. The variation in the separations of the components is very striking, the difference between the separations towards red and violet amounting in some cases to over 25 per cent. The grating apparatus in that laboratory has already been described.^ * P. Gmelin, Phys. Zeit ., ix. 212, 1908. t All wave-lengths will be given in angstroms. % Phys. Zeit., vi. 25, 1905. 1908-9.] Dissymmetrical Separations in the Zeeman Effect. 77 To obtain the light, a thin layer of the salt to be used is put on strips of carbon, 1 mm. thick and 5 mm. long ; these are placed against the poles of the magnet, and a spark is passed between these electrodes. To focus the light of the spark on the slit a quartz lens is used, as glass absorbs the violet rays. The maximum thickness of the lens used is 6*6 mm. The light passing through the slit and falling on the grating comes from a portion of the lens 4 cms. in diameter, which, if spark, lens and slit are in a line, and the lens at the proper height, is at the middle of the lens, and then the difference between the maximum and minimum thicknesses used is about 2 mm. Zeeman has shown * that the intensities, when a diffraction grating is used, depend on the angle which the plane of the vibrations makes with the lines of the grating. By introducing quartz plates of thick- nesses to give different rotations, he was able to vary the intensities in the case of a triplet, from having a strong middle component with weak side components, to the reverse distribution of intensity. When the plane of vibration is parallel to the lines of the grating the intensity is a maximum, and when at right angles to this the intensity is a minimum. The influence of the magnetic field gives vibrations in two planes at right angles to each other, and by rotation first one plane of vibration and then the other can be brought parallel to the ruled lines, and so the maximum and minimum for each kind of vibration got. When the planes of vibration make 45° with the lines, then the vibrations are in the same relative positions to the rulings, and then it was found that in the case of triplets the intensities were as Lorentz had predicted, namely, the middle component twice as strong as the side components. In the apparatus used the quartz lens produces rotation. When the lens is placed as mentioned above it has the same effect as a quartz plate of about 1 mm. thickness. Thus, for approxi- mately A = 3450 the middle component was twice as strong as the side components, that is, the planes of vibration made 45° with the rulings. As the amount of the rotation varies with the wave-length for the region A = 2800 to A = 2900, the planes had been rotated through 45°, and now the middle component had a minimum intensity. The cycle of variations is passed through more quickly as one proceeds further towards the violet, on account of the greater variation in rotation there. Thus the relative intensities of the components in the Zeeman triplets give an indication of the amount of the rotation of the plane of polarisation produced by the quartz lens for the different parts of the spectrum. In the case of over- lapping spectra of different orders, it was quite easy, by means of this property, to distinguish the lines belonging to the same order, for the * P. Zeeman, K. Akad. v. Wet., Amsterdam, Oct. 1907. 78 Proceedings of the Poyal Society of Edinburgh. [Sess. different wave-lengths overlapping had different rotations, and hence different relative intensities for their components. In the following table the examples of symmetry found in tungsten are Table I.— Tungsten. Field strength = 24, 650 gauss. Wave- length. Dissym. 2488*89 n 2522*14 n 2555*23 n 2580*63 n 2606*50 a 2633*24 n 2697*81 n 2774*12 n 2774*60 n 2792*85 n . CO _ sag si g . >> -1-3 <£ 1 , h=s' + o P cS CO in c6 rj ll a: 4-2 4^ go *rH ps QO -0-142 0 + 0-123 -0-149 0 + 0162 -o-ioo 0 + 0-122 -0-160 0 + 0-150 -0-110 0 + 0-131 -0-160 0 + 0-188 -0-141 0 + 0-144 >> 4^> • rH CA n a> Remarks. Min. inten- sity of mid. compt. Wave- length. 3087*73 3826-85 3951-15 4050-25 4051*35 420072 £ m a a n n n n n T3 in £ o * O £ I _ + © a> 3 p- ® -£ g o »i-4 °> CO QO -0-178 0 + 0-217 -0-196 0 + 0-201 -0-249 0 + 0-244 -0*145 0 + 0-122 -0-122 0 + 0-101 -0-112 0 + 0-097 -0*230 0 + 0*205 Remarks. Edge of plate. Middle of plate. Different rotations. Mid. compt. twice as strong. Again the concurrent changing of the dissymmetry with that of the intensities is striking. There are further exceptions also. The line A = 3087*73 is interesting. At the centre of the plate the light had passed through the centre of the lens, but at the edge of the plate the light was 1908-9.] Dissymmetrical Separations in the Zeeman Effect. 81 mainly from a part nearer the edge of the lens. Due to the difference in rotation thus produced, a difference in the relative intensities of the com- ponents was observed, and at the same time a difference in the dissymmetry. The measurements show that these changes are in no way due to a differ- ence of field strength acting on the light which falls on these two parts of the plate. Such a difference between the middle and the edge often occurs. These results tend to confirm the connection between the rotation and the dissymmetry produced by the apparatus used. The exceptions show that this does not explain everything. The problem was now to discover what component or components moved to produce the dissymmetry. Photographs of the same lines in tungsten were made in such a way that on the upper half of the plate came the spectral lines without separation, and under these were the separated com- ponents produced under the influence of the magnetic field. By means of a sheet, first the one half and then the other was covered. The same was also done with the lines in the iron spectrum. All the observations show that the centre component may sometimes remain stationary, and at other times be moved towards the red, or again towards the violet. The same is also true of the mean of the outer components. In the following table the results for tungsten are given : — Table III. — Tungsten. Field strength = 22, 000 gauss. Wave- length. S >» C/2 C/2 • rH Distance from Spectral line ( - towards Violet, + towards Red). Q (mm.) o (Angstrom.) 2488-89 n ( -0-117 I +0-004 [ +0-118 - 0-114 + 0-003 + 0-115 2522-14 n f -0-116 ] +0-003 ( +0-117 -0-112 + 0-003 + 0-114 2555-23 n f -0-122 ] +0-006 { +0-127 -0-119 + 0-006 + 0-123 2697-81 a f -0-141 ] -0-005 ( +0-155 -0-137 -0-005 + 0-151 Intensity. Wave- length. n 2774-12 5/ 4 1 2 r 2774-60 4 J 5 ) 3 r 2856-20 5/ 6 ) 4 f 3049*80 6 J c/2 C/2 a a a Distance from Spectral line ( - towards Violet, + towards Red). (mm. ) O (Angstrom.) f - 0*138 4 -0-005 [ +0-143 -0-135 -0-005 + 0-140 f -0-126 4 -0-006 t +0-130 -0-124 -0'006 + 0-128 f -0-131 -o-oio ( +0-133 -0-129 -o-oio + 0-130 f -0-246 4 -o-oii t +0-255 -0*242 -0-011 + 0-251 -4-3 In this experiment the lens was moved a little distance from its former position (Table I.), which gave a difference in rotation and an accompanying VOL. xxix. 6 82 Proceedings of the Royal Society of Edinburgh. [Sess. change in dissymmetry. The distances are here given from the unseparated spectral line, and these measurements have been transformed to angstroms to show the alteration in wave-length produced. The field strength was slightly smaller than before, being 22,000 gauss. It will be seen on compar- ing this with Table I., that the amounts of dissymmetry have changed, and that some cases of normal dissymmetry have even become abnormal, owing to the new arrangement of the apparatus. The motions of the centre com- ponents and of the mean of the outer components from the original position of the spectral line are in some cases quite appreciable, and beyond the range of the errors of measurement. A further experiment was made, in which the light, in addition to passing through the quartz lens, was made to penetrate a quartz plate, 5 mm. thick. The distances of the outer components from the middle component are given. In this case the field strength was a little higher, being now equal to 25,700 gauss. Table IV. — Light through Quartz Plate, 5 mm. thick. Field strength = 25, 700 gauss. Remarks. Min. intensity of mid. compt. A = 2630 approx. Max. intensity of mid. compt. A = 2750 approx. Min. intensity of mid. compt. A = 2960 approx. Wave- length. • m t3 tj a in in 3025-01 3041-96 3049-80 3311-53 3361-25 n a n n n oS r< £ £ «-8 b . p C5 1 , rO + 03 § . -P5 !=; -+-3 g o .2 or QO^ I -0-157 0 + 0-146 -0 141 0 + 0-130 Intensity. Remarks. 4 1 3 J- 4j 3 l 4 r 3 J 4 1 Components 4 r broadened and 1 1 difficult to 4 J measure. 4 1 8 r 4 J 2 4 3 r 2 J As there is now a much greater thickness of quartz, the amount of rotation is much increased, and hence the cycle of changes in the intensities is passed through very much more quickly. From observing all the lines 1908-9.] Dissymmetrical Separations in the Zeeman Effect. 83 on the plates, the turning points in the intensity of the middle component are approximately as stated in the table. It will be seen that correspond- ing to this more rapid variation in intensities, there is a similar variation in the character of the dissymmetry found in the lines. Again, there are exceptions to the rule that the dissymmetry depends on the amount of the rotation of the plane of polarisation. These experiments show that in using a quartz lens and a concave grating to obtain the Zeeman Effect cases of dissymmetry arise which are due to the angle between the planes of vibration of the components and the lines of the grating, for this dissymmetry varies with the intensities, which, in their turn, vary with that angle. That all cases of dissymmetry cannot be so accounted for is shown by the exceptions to this rule where abnormal dissymmetry is found instead of the normal which might be expected, and vice versa. These point to the possibility of the presence of the couplings between electrons of different vibration frequencies assumed by Professor Voigt, in consequence of which the two triplets containing the coupled electrons become respectively an abnormal and a normal dissymmetrical triplet. The intensities of the outside components are in most cases the same, and this also is in accordance with the theory. In the photographs of these substances, tungsten and molybdenum, are also to be found many other examples of dissymmetry among lines which break up into many components. This research was carried out in the University of Gottingen, and I take this opportunity of expressing my gratitude to Professor Voigt, and the pleasure I had in having the apparatus there, which is so splendidly adapted for such research, set at my disposal. { Issued separately December 30, 1908.) 84 Proceedings of the Royal Society of Edinburgh. [Sess. VI. — On the Reducing Action of Electrolytic Hydrogen on Arsenious and Arsenic Acids when liberated from the Surface of Different Elements. By William Thomson, F.I.C. (Read June 15, 1908. MS. received July 12, 1908.) This research was commenced with a view to find the velocity at which arsenic was liberated as arseninretted hydrogen from cathodes of different elements : (a) From arsenic in the form of arsenious acid. (b) „ „ „ „ arsenic acid. The experiments were carried out in the apparatus already described by me* which consists of a porous pot containing 30 c.c. of dilute sulphuric acid (one of strong acid to six of water by volume), with the cathode, when that was possible, in the form of a cylinder 60 mm. long and 10 mm. diameter, immersed to a depth of 27 mm., giving a surface exposed to the electrolyte of 8*48 square centimetres, the end passing through an india-rubber cork fitted into an opening in the glass stopper, which was accurately ground into the mouth of the porous pot and made air-tight with vaseline ; the liberated hydrogen was passed from a glass tube fused into the same glass stopper, which ended in a two-way tap and T-piece. Another similar apparatus was placed in series with the first-mentioned, so as to liberate hydrogen from pure dilute sulphuric acid. This apparatus was also provided with a two-way tap and T -piece, so that a stream of pure hydrogen, dried through a calcium chloride tube and passed over a small roll of dry basic lead acetate paper to remove any trace of H2S, could be passed through one or other of two drawn-out hard glass tubes which were heated to redness near to the drawn-out ends to receive the arsenic mirrors. These were deposited on the drawn-out part, the diameter of which was graduated by inserting a wire, the one end being F6 mm., the other IT mm. diameter, the length between these two points being 2 mm., the tube being cooled from the larger diameter. This apparatus was capable of easily detecting 0*000,000,541,3 gramme (roughly about 2000000 a gramme) of elemental arsenic when contained in the 30 c.c. of acid in the porous pot. This * Memoirs and Proceedings of the Manchester Literary and Philosophical Society, vol. xlviii. part iii., No. 17. 1908-9.] On the Reducing Action of Electrolytic Hydrogen. 85 quantity was taken as a unit, and for each experiment 5 c.c. of a solution containing 0-000,005,413 grammes per c.c. was taken in the form of : (a) Arsenious acid. ( b) Arsenic „ This makes 50 units, each of which can be easily detected. This amount was deduced from another standard in which 50 c.c. of a liquid containing ToVo‘th of a grain per gallon produces a well-defined mirror of arsenic on the cooled drawn-out part of the glass tube. Having filled the apparatus with hydrogen by passing a current of 3 amperes through 10 c.c. of dilute sulphuric acid in the porous pot, 5 c.c. of the standard solution of arsenic above mentioned is made up to 15 c.c. with dilute sulphuric acid and poured into the apparatus by a funnel fused into the glass stopper of the porous pot, stoppered by a glass rod at the bottom, the funnel being rinsed into the porous pot with 5 c.c. of the same dilute acid. After the apparatus has worked for 2 k minutes and a mirror has been deposited, the two-way tap is turned so that the hydrogen from the apparatus in series generating pure hydrogen sweeps the tube for a few moments. The tube is then removed and another inserted to receive a fresh mirror, the second mirror being produced by the two-way tap diverting the flow of the hydrogen containing arseniuretted hydrogen for 2\ minutes to the second tube, through which pure hydrogen had previously been passing, and which was heated to redness for the purpose of receiving the second mirror. In this way mirrors were received without loss of arsenic on the drawn-out portion of hard glass tubes, cooled at the point at which the mirror was to be deposited by means of cold water flowing continually over them. The mirrors thus received were sealed off in an atmosphere of dry hydrogen, and the quantity on each estimated by comparison with a series of standard mirrors examined and compared by a magnifying glass. Plotting the amounts of arsenic deposited in successive intervals of 2\ minutes as the ordinates, and the time as abscissae, curves were obtained for all these experiments. It was observed that, however carefully each experiment was repeated, no two results agreed absolutely, and this dis- agreement was greater for arsenic acid than for arsenious acid. Thirteen different elements were tested — viz., lead, zinc, cadmium, tin, silver, graphite, iron, platinum, aluminium, gold, cobalt, nickel, and palladium * * The following metals were used in the form of cylinders : — Lead, zinc, cadmium, and tin. Iron was used in a cylindrical form made by wrapping pure iron wire on a cylinder of glass, giving about the same surface exposed to the electrolyte as the metallic cylinders. The graphite electrode was cut in the form of a rectangular block giving about the same 86 Proceedings of the Royal Society of Edinburgh. [Sess. — and the order given above is the order in which they are capable of removing arsenic from solution as arseniuretted hydrogen when it exists in solution in the form of arsenious acid. This order, however, does not hold for the relative power of the different elements for removing arsenic from solution as arseniuretted hydrogen when it exists as arsenic acid in the electrolyte. Chapman and Law * suggest that the reducing efficiency of hydrogen with respect to arsenious and arsenic oxides depends largely upon the super- tension f of the cathode at which the hydrogen is liberated, and they put forward a formula to explain this, as follows : — M asHo^=^L- AsP h, “ where As represents the amount of unreduced arsenious oxide and K a constant factor. If the equation be disturbed by the addition of As, i.e. if the factor As be increased, reduction takes place or the reaction proceeds from right to left, and the same result is reached if PH is made larger. On the other hand, if PH is made smaller, As must be made larger to preserve the equilibrium. In other words, there is always left in solution after each experiment a certain residuum of unreduced arsenious oxide.” MAsh3 is a minute quantity of arseniuretted hydrogen always left in solution, and PH the potential of the hydrogen effecting the reduction. The results we have obtained contradict this hypothesis. The following table shows the relative velocities of thirteen different elements in decomposing arsenious and arsenic acids respectively, and the supertension of each element is also given when obtainable. The figures in Table I. represent units of arsenic as above described liberated in 25 minutes from 50 units (taken as 100 half-units) of elemental arsenic contained in the electrolyte (a) as arsenious acid, and ( b ) as arsenic acid. It was found that the current density had little influence on the result. The metals which could be easily melted were formed into cylinders 1 cm. surface as the cylinder, and all the others were used in the sheet form ; but it was found that the area of the cathode did not materially affect the result. * Chapman and Law on “ The Reducing Action of Hydrogen,” part ii., “ The Estimation of Traces of Arsenic by the Marsli-Berzelius Method and the Insensitiveness of Zinc,” Analyst , 1906, vol. xxxi., p. 3. t “ Supertension ” of an electrode, according to Caspari (“ Ueberspannung,” Zeit. physikal. Ghem ., 1899, xxx., 89) is the excess of electromotive force necessary for the liberation of hydrogen at that electrode over the electromotive force required for the reversible produc- tion of hydrogen on a cathode of platinised platinum. The values of the “ excess-voltage ” or supertension for different metals are given by Caspari in his paper, and also in Lehfeldt’s Electrochemistry, part i., p. 176. 1908-9.] On the Reducing Action of Electrolytic Hydrogen. 87 diameter and immersed to the depth of 2*7 cm., giving a current density of C100 = 35 (i.e. the current density was at the rate of 35 amperes dis- tributed over 100 square centimetres of surface). When the cathode had to be used as a sheet, the current density was C100 = 3'5, the surface being 10 times greater. Table I. — Showing the Relative Amounts of Arsenic removed as Arseniuretted Hydrogen from (a) Arsenious Acid and (6) Arsenic Acid from 100 Parts introduced, in 25 Minutes, when Working with 3 Amperes. Metal. (a) Arsenious Acid. (6) Arsenic Acid. Supertension (Volts). Lead .... 100 98-5 0-64 Zinc .... 100 41 0-70 Cadmium 100 27 0-48 Tin 100 18-5 0-53 Silver .... 100 0 0T5 Graphite .... 100 4 . . . Iron ..... 93 40-5 0-08 Platinum .... 88-5 0 0-09 Aluminium 82 9 • • • Gold .... 74 4 0-02 Cobalt .... 43-5 0 ... Nickel .... 42-5 0 0-21 Palladium 38 0 0-46 It will be seen that lead is the most efficient of the elements examined, and it is remarkable that it liberates arsenic as arseniuretted hydrogen (AsH3) when it exists in solution as arsenic acid almost with the same velocity as when it exists as arsenious acid. Lead has a high supertension, but not so high as zinc ; and whilst both of these metals liberate arsenic at about the same velocity from arsenious acid, lead liberates as AsH3 dooths of the arsenic present as arsenic acid in 25 minutes, whilst zinc only liberates Afo^hs of the amount present in the same time. The next remarkable metal in the series is silver, with a very low supertension of 0T5, as compared with lead 0-64 and zinc 0'70. It liberates arsenic as As] 1., from arsenious acid with about the same velocity as lead or zinc, whilst it is powerless to liberate any arsenic when it exists in the form of arsenic acid under the conditions of the experiment. Again, palladium, which has a comparatively high supertension, is at the bottom of the series as regards efficiency in decomposing either arsenious or arsenic acid. Gold, which is at the bottom of the series as regards supertension, has the power of decomposing arsenious acid to the extent of three-quarters of the most efficient elements, and it o > c c'O t— to C •>— i- a D 05 Diagram 1908-9.] On the Reducing Action of Electrolytic Hydrogen. 89 does decompose some arsenic acid, whilst palladium is powerless to decom- pose any. Iron, in this respect, is a remarkable metal, with the lowest but one supertension ; it decomposes arsenious acid nearly as rapidly as lead, and it stands second (next to lead) in its power of decomposing arsenic acid. These experiments show, I think, that the power of any element to decompose arsenious and arsenic acid is a peculiarity of the individual metal, and appears to be independent of its supertension. The diagram No. 1 shows the various elements arranged as abscissae in their relative supertension values, whilst the ordinates show the amount of arsenic liberated from each in 25 minutes. Table II. gives the results of the experiments made with the different elements as electrodes to discover the velocities at which the cathodes liberate the arsenic in periods of 2J minutes. If we take the first five elements, it will be seen that the average velocities with which they decomposed arsenious acid into arseniuretted hydrogen are : — Table II. — “Units” of Arsenic evolved as AsH3. Intervals in Minutes . Oi. *J2 5 71 1 2 10 121 15 17J 20 221 25 Totals. Lead .... 9 13 8-5 7 5-5 4 2-25 1*5 1 0-5 52*25 Zinc .... 8-5 14*5 7-5 6 4 3 2-5 1-75 2 1 50-75 Cadmium . 8*5 12*5 8*5 6*5 5 3 5 2-5 2*25 1*5 1-25 52-0 Tin .... 9 12*5 8 6-5 4*25 3-5 2-75 2 U75 1-25 51-5 Silver 6 12 10-7 7 3 5 3*8 2*7 1-3 •8 •3 49-9 It will be seen that the first figure is always lower than the others ; this was due to residual hydrogen in the apparatus, although it was made as small as possible, the total volume being 20 c.c. of air-space in tubes and apparatus with 30 c.c. of electrolyte (3 amperes liberate 21 c.c. per minute). These results are averages of two or more experiments. Allowing for experimental error, a constant is obtained for these first five metals for a unimolecular velocity reaction, and this is one of the few electro-chemical reactions in which such velocities can be measured. If a is the original concentration of the arsenious acid, and x the quantity transformed at the time t , the rate of transformation at that time will be, according to the unimolecular formula, dx v / \ — = Jc(a-x), where dx represents the very small quantity transformed in the very small RATE OF EVOLUTION FROM ARSENIOUS ACID (spun u i passajdxs) paA|OA9 oiuasjy Diagram 3 1908-9.] On the Reducing Action of Electrolytic Hydrogen. 91 interval dt starting at the beginning of the time t, and k is the coefficient of the velocity of the action. From this equation the integral calculus enables us to find a relation between x and t, the corresponding values for any stage of the reaction, in terms of the original concentration and the velocity constant. This relation has the form, 1 1 CL r — log = k. t L a - x It was observed that, if the amount of arsenic in the form of arsenic acid were increased in the cathode chamber, one arrived at a point when the cathode elements, which liberated no arseniuretted hydrogen under the ordinary conditions of the experiment, were capable of giving a small mirror on working the apparatus continually for 45 minutes, and the following Table shows the results : — Table III. — Elemental Arsenic in the Form of Arsenic Acid in 30 c.c. expressed in — 1 Units as above described. Millionths of a gramme. Nickel ..... 20 10-8 Platinum .... 90 48-7 Silver 140 75-8 Palladium .... 191 103-5 An attempt was made to measure the velocity of the reduction when using a copper cathode. No arseniuretted hydrogen was given off until the copper had become covered with a brownish -black deposit which gave by two analyses of small quantities the formula CusAs. Chapman and Law found the same deposit, which they regarded as one of elemental arsenic. On making other experiments we obtained no deposit on the copper and no arseniuretted hydrogen evolved. With an electrolyte composed of 5 per cent, sodium hydrate solution we did get arseniuretted hydrogen evolved as follows : — Minutes . . . 24 5 74 10 12| 15 174 Units obtained ..0 2 3 -5 2'5 2'5 1*5 1 = 13 We tried the element magnesium as a cathode in a similar way to the other metals, but found it dissolved rapidly in the electrolyte whilst the current was passing. Table IV. shows the results of the different experiments, with the averages for each, also additions of the quantities evolved in each experi- Table IV. — Units of Elemental Arsenic. Totals. lD © p Ip CO CO CO lOOif5 LD ©pjp cb co LD ld LO LD p O * . . . • • • . . . • Ip rH rH . . . LD p 3> rH . . . LD * p p .... . . . p rH lD ■ • • . , . p • CO rH rH . . . LD p Ip rH . . . LD • p p .... . . . • «H|C* CM . . . p 02 rH rH rH rH . . . p 02 rH rH . . . • p rH .... . . . • o HI • • • . . . . . . p p CO rH rH rH rH . . . rH rH rH . . . LD p I> rH .... . . . He* & • • • LD p jp «— * . . . p p CO rH rH rH rH • • • rH rH rH . . . p p p .... . . . p rH o CO . . . LD p 1> H • • • p p CO rH rH rH rH . . . rH rH rH . . . LD p J> rH .... p rH • He* CM CO . . . rH rH rH . . . p p CO rH rH rH rH . . . LD p 02 rH rH rH . . . LD p 3> rH .... • p rH • 30 • • • LD p Cl rH rH rH . . . p p CO rH rH rH rH . . . LD p 02 rH rH rH . p rH LD p J> rH .... • p rH • He* CM rH LD p I> 02 rH rH • p rH p p rH 02 rH rH p rH p 02 rH rH • p rH LD p 2> rH • * p rH CO ?H p H ID CM * rH LD p Ip 02 rH rH H H H p p 02 t* rH rH LD p CO rH rH rH p 02 rH rH ID p M rH rH rH rH rH rH • • p p H CO rH • H« CM CM H H H LD p 02 02 02 02 M M CM p LD rH rH 02 rH p H M iH p 02 H H LD p Jp (MHH rH rH rH p p rH rH CO CO CO • O CM p H CM H LD p Ip CO 02 02 LD p ip rH CM rH p 00 rH 02 02 rH lD lD CM CO CO CO p 02 rH rH CM CO (M HHH LD p CO rH rH rH rH p CO CO CO • I>- rH ID LD CM CO CO CO CO CO CO p M CO CM p 00 02 rH 02 rH LD CO CO CO p 02 rH rH LD p Ip CO CO 02 rH rH rH p p I>- CO CO CO CO LD p Ip CO T* CO 02 * rH H H HH ^ CO CO CO p p 02 rH 02 »H p CO H CO p 02 rH rH p CO Tft CO rH rH rH p 00 Th CO Tji co LD p p Tfi • H« (M T— 1 p CD ID LD LD LD LD H H H 02 02 02 02 lD lD lD LD p ip 02 rH rH LD p CO CO LD 'H rH rH rH lfllOlSO 10 lO lO • O rH CD 00 t>- CD CD CO CD CD CD p 02 02 02 02 02 p CD CD LD p I> 02 rH rH p CD ZD HHH p 00 p • h|N £— p CO CD GO CO CD 00 p t> 00 p p 02 02 CO 02 p CO OS GO p 02 rH rH 00 CO 00 rH rH rH ip as h co 0 rH rH rH p OS 00 00 0 lD CO CO CO rH rH rH p O CO rH rH rH rH p H LD H H H H p p 02 CO CD CO p CO CO CO rH rH rH rH rH rH p CO CO CO rH rH rH rH rH rH CO CO rH •55 .S -M) " s- - CO W <22 Si w a ® 3 X > ,.SS H Ilia'S Si'"’ W**3 H £ 0) H 0) 5*1 § Pi ® ■$£W < C/2 £ gr-HOJ +3 a 02 fl 0) .3 .5 „ bO »£ -c« CO QJ hi 02 Pi ® 3 X > .ss < 1 ^,13 d§3s z< N A o> H CD *g he A3 H r ~ c$ 5 SL S3 55 * > •2W H ? 42* ^ •rf ^ 01 fl ^ ?JrHMCO s 1 CQ pH gsx > p.SS H 3 i «! 0 -4H £ 0 £ © •3 he 5 ^ 5 £ s c X Jjj ■=w ^ 1-1 e* s ss 02 ft ? 3 X >; 0 pi] ’3 +313 l ® » c H S3 112 S3 02 • g be 52 <12 Sw H p< ® c X > ® M fl 52 «h h.2S ^ S is! a* 0 5 0 .0 5 0) tO 0 0 02 »o Hi h< © © p lOON CO CO CO no O nO (01 Hi Hi Hi ^ ^ tO p p d © © © t}< H' p cb p p p r-i CO © Hi 00 Hi CO CO CO p cb rH no OiflN © CO rH d Cl Cl to 21 0 21-5 21-25 •>* O p O 00 © © 00 00 rH rH rH rH . . . • • ■ . . . . . . .... • • . . . • .... . . . . . . . . . • • • .... . . . .... . . . • • • . . . . . . .... rH . . . p Cl . . . • .... . . . . . . . . . . . . .... 2 Omin . . . mins. . . . .... . . . . . . • • • . . . .... o # rH u 5 . . . . . . • .... • • • rH rH rH . . . . . . .... • • • • • . . . . . • • • HHH . . . . . . • .... • . . . • • .... • • • rH rH rH • • • no no • Cl o .... Cl . . . • . . . • - • WO WO Cl rH rH rH . . . * p rH .... . . . . . . • .... . . . 1*5 1 1'25 . . . * H p .... . . . • . . . p rH .... • p rH p Cl H H . . . rH rH rH • .... . . . © . . . .... 1-5 1 1-25 UO Cl rH rH . . . 1-5 1 1-25 rH • • CO rH Cl . . . . . . ■ .... 10^0 H H rl p Cl r-H rH . . . no p L- h^h rH r-H • . . . • • • .... (01 CM <01 p Cl rH rH • p l— 1 1-5 2 1-75 rH no p (01 rH rH rH •5 ' 1 •75 • •5 •25 • .... (01 (01 (01 p Cl r-H rH rH rH rH O nO (01 (01 d d • UON (01 rH rH rH HHH • to P • Cl tO p t>- CO (01 (01 wo p 3> Cl rH rH no p 1 ^ (M H H no to t>- CO d d p rH CO CO Cl <01 Cl Cl 1 1-5 1-25 • rH rH rH © no p <01 CO CO CO Cl Cl d no nO I>- CO d d CO CO CO p p no 00 CO d d Cl to to I>- r— < Cl rH © no no no rH rH rH ■ • • co rH tO p I- Hi CO CO Cl Cl Cl H< Hi Hi no nO >1 CO CO 00 rH P- no co co co no p Cl Cl Cl Cl • d Cl Cl • • p 00 Cl nO tO no Cl Cl Cl to p (01 UO lO iO Hi Hi Hi OtiuOiO p Cl CO Cl • no p !>• d co d CO CO CO CO M3 mo r- co in mo Cl Cl Cl (0(0(0 lOlOlf) p CO NOOO © p CO Hi CO p CO Hi CO © Hi Hi Hi Hi I>- L- wo p Cl Cl (M Cl p aoi rH 0(0 0 p CO © oo to © no no no © no p Cl Hi H< H1 no no to nO CO o © rH wo wo i> Cl CO Cl p © 00 00 r- a> oo © L- Hi CO Hi Hi © to no CO Cl cl no p Cl CO CO CO © p d Hi Hi rH CO © © © p p p Cl Cl Cl tO tO tO US >o o p 00 CO Cl CO Cl © rH rH rH © p to to Cl Cl Cl © p p CO CO rH d IRON— Arsenious acid. 1st Experiment 2nd ,, Average . Arsenic acid. 1st Experiment 2nd ,, Average . PLATINUM— Arsenious acid. 1st Experiment 2nd ,, Average . ALUMINIUM— Arsenious acid. 1st Experiment 2nd ,, Average . Arsenic acid GOLD— Arsenious acid. 1 1st Experiment 2nd ,, 3rd „ Average . Arsenic acid COBALT— Arsenious acid. 1st Experiment 2nd Average . .*2 o c o <^> Co NICKEL— Arsenious acid. 1st Experiment 2nd Average . Arsenic acid PALLADIUM— Arsenious acid. 1st Experiment 2nd ,, 3rd Average . Table IV.— Unit6 of Elemental 50 40 30 20 10 Inins. 7* 10 121 2 15 17; 20 22i Diagram 4. 1908-9.] On the Reducing Action of Electrolytic Hydrogen. 95 ment to show the total amounts obtained as adjudged from the estimations of the quantities represented by each mirror, when compared with standard mirrors produced by eliminating arsenic from arsenious acid by lead and by zinc cathodes each advancing by one unit of arsenic, as above described. Diagram 1 shows the elements whose supertensions were known to me arranged graphically as abscissse, the ordinates showing the amounts of arsenic liberated {a) from arsenious acid and ( b ) from arsenic acid in 25 minutes from the different elements. Diagram 2 shows the average results obtained from the different elements examined, when acting on arsenious acid ; the ordinates repre- senting units of elemental arsenic, and the abscissae the time. Diagram 3 is similar to diagram 2, with the exception that arsenic acid was used instead of arsenious acid, and it is drawn on a smaller scale than diagram 2. Diagram 4 shows in one line the curve obtained by taking the average of the four elements, lead, zinc, cadmium, and tin, adding together the mirrors obtained in the first two periods of 2 \ minutes, and taking them as a 5-minutes interval, the others being taken at 2 J -minutes intervals. The other line shows the curve obtained by calculating x for the correspond- ing periods when using the mean constant, k showing that for these four metals the reaction is practically a unimolecular one. I have to acknowledge the services of my assistant, Mr L. L. Bircumshaw, for the perseverance and industry which he has exercised continuously during the last fourteen months in carrying out this investigation with me. (. Issued separately January 21, 1909.) 96 Proceedings of the Royal Society of Edinburgh. [Sess. VII. — Preliminary Note on the Action of Nitric Anhydride on Mucic Acid. By Professor A. Crum Brown, F.R.S. and G. E. Gibson, B.Sc. (MS. received October 12, 1908. Read July 21, 1908.) In the course of his researches on mucic acid, Professor Crum Brown found that this acid could not readily be nitrated in the ordinary way. Mucic acid dissolves, to a certain extent, in a mixture of concentrated sulphuric and nitric acids, but on standing separates out again apparently unchanged. An exceedingly small quantity of a crystalline nitrate can, however, be obtained by pouring this mixture into a large volume of acid water and immediately shaking up with ether. On evaporating the ethereal layer the nitrate is obtained, but the yield is so small that this method of preparation is not practicable. With nitric anhydride, however, a good yield of a crystalline nitrate is obtained. The method is the same as that described in a previous paper for the preparation of tartaric acid dinitrate. Not more than 20 grams of mucic acid should be treated in one operation, and both the mucic acid and the nitric anhydride should be cooled in ice before mixing. If these precautions are not taken, considerable decomposition of the nitrate may take place. In one experiment, 16 ’3 grams of Merck’s pure mucic acid were mixed with about 50 grams of nitric anhydride. The mixture was left over- night in an evacuated desiccator containing solid caustic soda. It was then treated with ether in a Soxhlet tube, the filter of which had previously been weighed. The ethereal extract was evaporated at the ordinary temperature with the help of a steam -jacketed “ Geryk ” vacuum pump. Twenty-five grams of the nitrate were obtained, and 0'5 gram of unchanged mucic acid remained on the filter. If no mucic acid had been lost in the process of preparation, these figures would correspond to the formation of the trinitrate. There is, however, always some loss caused by decomposition of the nitrate, so that there can be little doubt that the substance which is obtained is the tetranitrate of mucic acid. Many different preparations were analysed, both by Walter Crum’s mercury method and by combustion in vacuo, and the results of these 1908-9.] The Action of Nitric Anhydride on Mucic Acid. 97 analyses confirm this conclusion. Tire figures vary with each new preparation, but correspond more closely with the tetranitrate than with the trinitrate. Pure tetranitrate, free from ether, has not yet been obtained. On evaporating the ethereal solution, the substance crystallises in well-defined colourless needles, hut on standing in air or in vacuo over concentrated sulphuric acid, these soon fall to a white powder. This change is appar- ently due to partial decomposition. The substance behaves in a similar manner when crystallised from alcohol. The white powder thus obtained does not decompose further if kept perfectly dry, but in the air it soon begins to decompose, with evolution of nitric acid and oxides of nitrogen. Mucic acid is one of the products of this decomposition. Tartaric acid dinitrate behaves in a similar manner when exposed to moist air, tartaric acid being the chief product of decomposition. Mucic acid tetranitrate is, in many other respects, very similar to tartaric acid dinitrate. It is readily soluble in water, alcohol, and ether, but not in chloroform or benzene. Treated with ammonium sulphydrate, crystals of the sparingly soluble ammonium mucate are obtained. On heating the nitrate it decomposes violently. When an ethereal solution of the nitrate is allowed to stand in contact with a little water, drops of a syrupy substance, which is soluble in water, separate from the ethereal layer. In the course of a few days crystals of oxalic acid separate from the aqueous layer. On the analogy of tartaric acid dinitrate, tartaric acid and tetraketo adipic acid should be formed as intermediate products of decomposition. As yet, neither of these acids has been detected. (. Issued separately February 19, 1909.) 98 Proceedings of the Royal Society of Edinburgh. Sess. VIII. — Temperature Observations in Loch Garry (Inverness-shire). With Notes on Currents and Seiches. By E. M. Wedderburn, LL.B., W.S. (MS. received November 2, 1908. Read November 2, 1908.) During the first seven months of the year 1908 I had the good fortune to be living at Invergarry in Inverness-shire, with sufficient time at my disposal to make temperature observations in Loch Garry, and, through the generosity of Sir John Murray and Mr Laurence Pullar, the funds of the Lake Survey (Pullar Trust) were put at my disposal to defray the expenses of observa- tion. I was further fortunate in securing the services of Mr Wm. Macdonald, Mount Pleasant, Fort Augustus, who was previously boatman to the Lake Survey on Loch Ness, and who proved himself a most painstaking and eager observer, and by whom by far the greater number of the actual observations were made. One reason for my anxiety to obtain observations in Loch Garry was that it is a lake of the temperate class, of considerable size, and fairly uniform basin. A description of the lake will be found in the Lake Survey Reports, Geographical Journal , vol. xxx. p. 401, October 1907. The lake is divided into two parts. The main part of the loch is about 4 miles long, and is a simple basin with a maximum depth of about 220 feet. At the eastern end there is a shallow basin cut off from the main loch by a large promontory ; the channel between the two basins is very narrow, and is so shallow that when the level of the loch is low it is difficult to get a rowing boat from one basin to the other. This smaller basin, which is about a mile in length, is little over 40 feet deep, and in summer large portions of it are covered with weeds. Nearly all the observations were made in the main basin, but occasional observations were made in the small loch for the sake of comparison, and no noteworthy differences in temperature between the basins were observed. The chief point of interest in the observations was to discover whether temperature changes similar to those found in Loch Ness occurred in such a body of water as Loch Garry. The presence of the temperature seiche in Loch Ness has been fully established, but it was considered doubtful whether a temperature seiche could occur in a lake of moderate length and depth such as Loch Garry. It was hoped that further use could be made of the electrical installation 99 1908-9.] Temperature Observations in Loch Garry. which was used in Loch Ness, so that a continuous record of the tempera- ture in the deepest part of the lake could be obtained. The Callendar Recorder was set up on the southern shore of the lake opposite the deepest part, but great difficulties were experienced with the platinum thermometer and the cable. The thermometer had been designed to stand a pressure of 300 feet of water, but it was found that the pressure at a depth of 200 feet was too much for it. A new covering was procured for the thermometer, but after that, it was found that the insulation of the cable, which was the one used on Loch Ness, had become very faulty, and the use of the Callendar Recorder had finally to be given up without any trustworthy records being obtained, and mercury thermometers had to be relied on for all observations. Observations by means of mercury thermometers were carried on every day so far as weather and circumstances permitted. Readings of the air Fig. 1.— Macdonald’s Messenger. temperature were made by a maximum and minimum thermometer (un- screened) placed on the shore of the loch. A buoy was moored over the deepest part of the loch, and most of the observations were made from a boat attached to this buoy. A light anchor was also carried in the boat, and by means of it the boat could be readily anchored at any part of the loch. In this way one person was able to make the observations, save in very stormy weather. The ordinary reversing mercury thermometer was used with a messenger designed by Macdonald, which proved admirable. The usual dividing messengers are troublesome to use in cold weather, as one or both of the parts is very liable to get lost owing to the numbness of the observer’s hands while working in cold water. Macdonald’s messenger was formed by twisting a bar of metal into a spiral which could then be screwed on to the sounding line without much fear of losing it. The construction of the messenger sufficiently appears from the photograph which forms fig. 1* * For a description of methods of thermometry, see Dr H. R. Mill’s “Clyde Sea Area,” part iii. and plate i., Tro.ns. R.S.E., vol. xxxviii. p 3. 100 Proceedings of the Royal Society of Edinburgh. [Sess. It is a great improvement on any of the messengers which I have seen, both in point of convenience and of cost. The drainage area of Loch Garry is large, being 137*33 square miles — about 78'5 times the area of the loch, whereas in Loch Ness the drainage area is only 31*6 times the area of the loch. Assuming that the average rain- fall over this area is 72 inches (a moderate estimate), the volume of water received by this drainage area in the course of a year is, roughly, 23,000 million cubic feet, and, assuming a 20 per cent, loss * by evaporation, absorption, etc., the amount of water flowing into Loch Garry in the course of a year is 18,400 million cubic feet, or nearly five times the normal capacity of the loch. These figures are given as showing the importance of rainfall in considering the temperature of lakes having a large drainage area, and in this connection it may be mentioned that the level of the loch rises as much as 25 feet above its summer level during floods. A rise of 10 feet in twenty-four hours is not uncommon. As a rule, however, the water which enters a lake is lighter than the bulk of water in the lake,*]* and spreads itself along the surface, and does not very greatly affect the abysmal temperature. Periodical observations were made of the temperature of the upper River Garry, which is by far the largest stream entering the lake. For reference these observations are given in the following table : — Table I. Temperature of Upper River Garry in 1908. Date. Temperature. Date. Temperature. Date. Temperature. Jan. 31 35*8 Mar. 16 38-0 May 27 49-5 Feb. 3 36*4 11 19 39*2 J une 2 637 11 7 39*0 11 23 40*2 „ 4 62-6 11 19 38-8 AjDr. 2 40*2 „ 11 53-4 11 29 34-0 11 6 41-0 „ 15 52*6 Mar. 3 35-9 11 17 47*0 „ 20 51*2 11 6 35-7 11 28 43*3 „ 26 63*2 ii 9 35*0 May 6 49-2 July 3 72*0 11 13 38-0 11 13 48-5 „ 8 65*1 11 14 38-5 ii 15 48-7 „ 11 57*8 The temperature of water in a shallow river responds rapidly to changes in the temperature of the atmosphere and to sunshine, and is therefore a fair guide to the quantity of heat which the lake is receiving — much more so than observations of extremes of heat and cold made with a maximum and minimum thermometer. * See Lake Survey Report, Geogr. Journal , vol. xv. p. 342, April 1900. t But see Forel’s Le Leman , vol. ii. p. 358. 101 1908-9]. Temperature Observations in Loch Garry. Approximate estimates were made of the quantity of heat stored in the lake for successive weeks during the period of observation. The method employed was to calculate roughly from the contour of the lake basin the quantity of water between the surface and a depth of 10 feet, between depths of 10 and 25 feet, 25 and 50 feet, and so on. The mean was then taken of all observations at the centre of the lake during each week, at the surface, 10 feet, 25 feet, 50 feet, etc. ; and, on the assumption that these mean values were the means for all parts of the lake, a rough calculation was made of the quantity of heat passing into or out of the lake from week to week. As the observations from which the means were taken were all made about the centre of the lake, it is thought that the assumption that they are typical of the whole lake is sufficiently accurate for the present purpose. Table II. gives the results of these calculations. The positive sign denotes that heat entered the lake, the negative sign that there was a loss of heat. A separate column gives the mean surface temperature for the successive weeks. Table II. Week ending Gram calories Mean Surface Week ending Gram calories Mean Surface -M010 Temperature. + 1010 Temperature. Feb. 3 -3200 38-3 Apr. 27 + 1200 41*3 „ io H-4800 37’8 May 4 + 2800 41 '5 M 17 38-6 „ 11 437 + 1500 + 8000 „ 24 -4200 38-3 „ 18 + 11700 46-0 Mar. 2 -2900 38-2 „ 25 + 13700 46*3 „ 9 372 June 1 55-0 - 1800 + 12800 „ 16 + 2100 37-0 „ 8 + 4700 56-0 „ 23 + 2600 37-7 „ 15 - 800 52-3 „ 30 + 4600 38T „ 22 + 6600 53T Apr. 6 + 4500 39-2 „ 29 + 8800 58-5 „ 13 + 4100 39-8 July 6 + 200 66-8 „ 20 + 3800 40-9 „ 13 - 1800 61-4 „ 27 41-3 „ 20 59-4 102 Proceedings of the Poyal Society of Edinburgh. [Sess. Comparing this table with the temperatures given in Table I., which are, as already explained, a rough measure of the heat supplied to the lake, it is seen that when the river temperature is below the surface temperature the lake is losing heat, and when it is above the lake is gain- ing in heat. Thus in the middle of February there was a very mild spell of weather during which there was an accession of heat, followed by very cold weather during which there was a considerable loss of heat, and the second week of March is the time at which the lake is at its coldest. There- after there is a steady accession of heat until the middle of June, the most rapid gain being during the warm and sunny weather which occurred about the end of May. About the middle of June there was actually a loss of heat. The weather during a large part of June was sunless, and during the week ending 22nd June the mean maximum air temperature was under 50° F. In the end of June and beginning of July there was again a spell of warm weather followed by an accession of heat, but during the sun] ess weather of the third week of July there was again a loss of heat. As the observations were discontinued shortly thereafter, I cannot say whether this loss was arrested, or whether the lake continued to lose heat during the autumn. During the period of observation the difference between the greatest and least quantity of heat in the lake is about 9 X 1014 gram calories, which may be considered as the quantity of heat stored up in the lake during spring and summer. For Loch Ness I calculated that the quantity of heat stored up was 1*9 X 1016 gram calories, which is more than twenty times as much as in the case of Loch Garry, while the area of Loch Ness (through which the heat enters the lake) is only twelve times that of Loch Garry. According to Knott the solar energy supplied is equivalent to 60-73x 1014 gram calories. The disparity between the ratios of surface area to quantity of heat in Loch Ness and in Loch Garry may appear at first surprising, but when the quantity of water passing through Loch Garry, and the fact that it is the warmest surface water which flows out of the loch, is considered, it is apparent that more heat is lost by this means in the case of Loch Garry than in the case of Loch Ness, where the outflow is comparatively very small. Another reason for the smallness of the ratio in the case of Loch Garry is that owing to the less bulk of water the surface water rises in temperature much more rapidly than in Loch Ness, and accordingly the date at which the lake ceases to gain in temperature by conduction is much earlier. Moreover, though no sunshine observations are available, I think it is safe to state that the average amount of sunshine over Loch Garry is 103 1908-9.] Temperature Observations in Loch Garry. less than over Loch Ness. The period of observation in Loch Garry was particularly sunless. Some interesting observations on the freezing of the lake were made during the spring of the year. It does not follow that because a lake is of the temperate class that it will become frozen over every year. The classification depends solely upon the temperature of the water reaching* the maximum density point. When that point is reached the lake is in a suitable condition for freezing, for water which is cooled at the surface by conduction from the atmosphere or by radiation remains at the surface and does not sink. In point of fact, however, the water in a lake is usually cooled considerably below the maximum density point before freezing occurs. There is usually an interval of time between the date at which the temperature of the water in a lake reaches the maximum density point and the date at which the temperature of the atmosphere falls sufficiently to cause freezing ; and during this time the water all through the lake is falling in temperature, owing to the circulation of the water produced by winds ; and though, as will be seen from Table II. , the surface temperature fell as low as 37 F., freezing all over the lake did not take place. On several occasions, however, notably in the month of March, during frosty, clear nights large irregular patches of ice were formed in a single night, with a thickness in one case of as much as half an inch. Isolated patches of ice were formed in mid lake, and when observed in the early morning these appeared not to be connected with the shallow shore waters, where one would naturally expect freezing to take place most readily. These patches rapidly disappeared whenever a breeze sprang up to mix the thin surface layer, which had been rapidly cooled during the night, with the warmer waters below. It is thought that the irregularity of the patches of ice formed may be due to differences of surface tension in the lake, which would have an effect on the ripples produced by light winds, and thus on the mixing of the surface layers of the lake. Local differences at the surface may also cause differences in the rate of radiation from the lake and evaporation at the surface, and further contribute to the irregular formation of ice. In lakes with shallow shores and bays, freezing would probably occur first by the formation of a shore fringe of ice, gradually extending* out into the lake ; but the shores of Loch Garry are for the most part steep, and it is probable that when the lake becomes covered with ice (as it does in any ordinary winter) it will be covered all over by a thin sheet of ice in a single night in calm weather, and that if the weather continues calm this sheet will gradually grow thicker by conduction. For further discussion of the observations on formation of ice in Loch Garry, reference is made to 104 Proceedings of the Royal Society of Edinburgh. [Sess. a paper on the “ Freezing of Lakes ’’published in the Scottish Meteorological Society’s Journal for 1908.* The chief point of interest of the observations in the early months of the year, apart from the freezing of the lake, was the great uniformity in the temperature of the lake from top to bottom, even although considerable changes of temperature of the water took place from day to day. Table III. Date. Temperature, ° F. Difference. Surface. 200 Feet. 1908. Jan. 30 38-3 38-2 - T Feb. 5 37-8 37-7 - T „ 12 38-5 38*7 + -2 „ 19 38-7 38-8 + T „ 28 38-0 38-2 + -2 Mar. 3 37*8 37-7 - T „ 10 37-0 37*5 - -5 „ 11 36-5 375 - TO „ 12 37-2 37-5 + -3 ,, 13 37-5 37-5 •o „ 23 38-0 38-0 •o Apr. 2 { (10 a.m.) ( 38-8 38-8 •o Apr. 2 \ (3 p.m.) J 38-9 38-9 •o Apr. 3 39-0 39-0 •o Table III. gives a few observations which illustrate this point, and the explanation is to be found in the mixing of the water due to winds. Thus on 10th and lltli March there was a calm, with the result that we do not find this uniformity of temperature from top to bottom. The surface water has been cooled down, and has not mixed with the rest of the water in the lake. On the other hand, on 2nd and 3rd April there were strong winds, and the observations show how rapidly the heat which enters at the surface is distributed over the whole lake. This is, I think, very good evidence that the currents produced by wind are appreciable to the bottom of the lake in the spring of the year. On to the end of April there was never any great variation in tempera- ture from the surface to the bottom. On 29th April, observations at the surface gave a temperature of 41 T° and at the bottom 41 ‘0°. There had, prior to that, been variations of as much as 1°, but these differences always disappeared before a strong wind. A reference to Table II. will show that * Yol. xiv. p. 219. 105 1908-9.] Temperature Observations in Loch Garry. in May the rate at which heat' enters the lake begins rapidly to increase, and at the same time the temperature gradient in the lake increases, indicating that when the rate of heat-supply is sufficiently great, wind currents are not sufficiently strong to produce a thorough mixing of the water. Increasing differences of density also tend to make wind-produced currents less far-reaching, and the temperature gradient in the lake rapidly increases. On 6th May the temperature at the surface and 200 feet was respectively 44'5° and 41 '2°, there having been little variation in the bottom temperature during the previous ten days. Owing to stormy weather no observations were made on the 7th, but on the 8th the bottom temperature had risen to 42° — a rise of *8° — showing the influence of currents produced by winds. A more marked case occurred about a week later. On 15th May the surface temperature was 46'3° F., and at the bottom 42'3° ; again there had been very little variation in the bottom temperature. On the 16th and 17th the wind was very strong and no observations could be made, but on the 19th it was found that the bottom temperature had risen l-7° to 44’0°. There was a continuance of moderately strong winds, with the result that the bottom temperature had risen to 44-5° by 22nd May, and to 45‘0° by the 27th. Variable winds were experienced till the 5th of June, when the bottom temperature was only 45*2°, showing little variation for the previous nine days, but the wind increased on the 5th, and observations on 6th June showed a bottom temperature of 45'5°, and on the 10th 46'0°. As will be seen in Table II., about the middle of June the lake, instead of gaining in heat, began to lose it. The result is the formation of a slight temperature discontinuity. Table IV. Observations at Centre of Loch Garry , June 1908. 6th. 8tli. 9th. 10th. 11th. 12 th. 13 th. 15th. 16th. 17th. 18th. 19th. 20th. Surface 56-8 52-2 53T 52-8 52-8 52-0 51-9 51-8 51*4 51-9 52-0 52-2 52-0 25 50-5 51-5 50-0 52-0 5T9 52-0 51-8 51-5 5T2 51-3 51T 51-4 5T5 50 48*0 50-9 48-9 48-7 49-0 50-4 51-0 51-3 51T 51-0 50-5 50-5 50-9 75 47-0 49-0 47*0 47-0 46-7 47-0 46-8 46-7 47*6 47-0 47-6 47-5 47-3 100 46-0 45-9 46-4 46-2 46-2 46-4 46-3 46-3 46*0 46-3 46-2 46-4 46-2 150 45-8 45*7 45-9 46-0 46-0 46-0 46-0 46-0 46-0 46*0 46-0 46-0 46-0 200 45-5 45*5 45-8 46-0 45-8 459 45-9 46-0 46-0 46-0 46-0 46-0 46-0 Table IV. gives some of the observations made at this time, and they show the gradual appearance of a discontinuity between 50 and 75 feet, 106 Proceedings of the Royal Society of Edinburgh. [Sess. and confirm the opinion I have previously expressed,* that the discontinuity makes its appearance whenever there is no further gain of heat. During the time covered by the observations given in Table IV. the winds were light and variable, and this may have favoured the formation of the dis- continuity. The bottom temperature remained about 46 '0° until the end of June, and during the month of July there was a gradual and fairly con- tinuous rise to 46’5°, with moderate and variable winds. On 6th September, when an isolated observation was made, the temperature at the bottom was 47*0°, showing that the gradual rise in bottom temperature was continued. The rise in bottom temperature after the formation of the discontinuity is very gradual, whereas before its formation changes in bottom temperature took place by small leaps following high winds. This gradual rise is prob- ably due to the very slow currents which I believe to exist at the bottom of stratified lakes, and also to convection currents started by the tempera- ture seiche. It also indicates that after the formation of the discontinuity layer in a lake the direct return currents take place above the discontinuity. Otherwise there would still be spasmodic increases of temperature follow- ing high winds. It is unfortunate that I was unable to continue my observations on into the autumn, for though the discontinuity made its appearance during the cold weather of June, it did not become very distinct, and was masked somewhat by the warmer weather of July which followed. That the dis- continuity did become more marked in the autumn is shown by an observation which I caused to be taken on 6th September, which shows a steep temperature gradient between 75 and 85 feet (see Table V.). Table V. Temperature on Loch Garry , 6th September 1908. Surface 54-0° 25 feet 53-8 60 „ 53 7 70 „ 52*4 75 „ 51*2 80 „ 50-0 85 „ 48-0 100 „ 473 150 „ 47-0 200 „ 47-0 Observations made in August and September would probably have given good examples of the temperature seiche. As it was, hourly or two-hourly * Proc. R.S.E. , vol. xxviii. p. 7. 107 1908-9.] Temperature Observations in Loch Garry. observations were made at one end of the lake for consecutive days and nights on 10th and 11th July, and again from 23rd to 25th July. These observations are shown in figs. 2 and 3, and that there is an oscillation in progress with a period of about twelve hours is apparent. The 7 8 9 10 II 12 13 14 15 16 /7 18 19 20 21 22 23 24^! 2 54-56789 !0 1/ i2 !3 14 15 IS 17 18 HOURS, V v ^ — - ■ V f LOCH GARRY 1908 10™ JULY IIth JULY EAST END OF LOCH Fig. 2. oscillations may appear to be very irregular, but the wonder is that they should exist at all, when the indefiniteness of the discontinuity is taken into consideration. The majority of the observations were made at the centre of the lake, and thus at the node of the temperature seiche. Temperature oscillations 108 Proceedings of the Royal Society of Edinburgh. [Sess. were, in fact, not observed there, which is additional evidence of the nature of the temperature changes. It was unfortunate that more continuous observations were not made at the ends of the lake, but the difficulty of observing day and night, with only two observers, in an open boat, and usually in pouring rain, was great. From the point of view of the tempera- ture seiche it was unfortunate that most of the observations were made at the centre of the lake, but I was anxious to observe in as deep water as possible so as to follow the bottom temperature changes. It was intended by observing at both ends of the lake to show opposition in phase at the two ends, but the loss of a thermometer at the beginning of this series of 109 1908-9.] Temperature Observations in Loch Garry. observations upset the experiment. By bicycling from one end of the lake to the other, however, and making observations alternately at the two ends of the lake, rough opposition in phase was shown. A change of wind during this series of observations further spoilt the experiment. A rough calculation from the approximate formula of the period of the temperature seiche gives a value of the same order as the observed value. The important points in the Loch Garry observations may be sum- marised as follows : — 1. They give a complete series of observations in a temperate lake for the portion of the year during which the lake is gaining heat, and are comparable to the observations in Loch Ness, which is a tropical lake. 2. They show the apparently fortuitous manner in which freezing may take place in the larger temperate lakes. 3. They show how strong winds have the effect of producing currents at considerable depths. 4. They indicate that the formation of the discontinuity layer in a lake takes place whenever the surface layer begins to cool. 5. They indicate that after the formation of the discontinuity the return current is not directly appreciable at the bottom of a lake. 6. They show that the temperature seiche is not a phenomenon peculiar to Loch Ness or to very deep lakes; but that it is possible to have temperature oscillations even in small temperate lakes, and even when the discontinuity is not pronounced. The observations suggest lines on which observations in other lakes of moderate size may be made. As a rule, observers have contented themselves with observations at wide intervals of time. It is difficult to interpret properly such isolated observations, and they may be very misleading ; but when consecutive observations are made at near intervals of time the temperature changes can be closely followed, and a number of such series of observations in different lakes would be invaluable for the purpose of comparison. The observations in Loch Garry are given in the Appendix to this paper, so that they may be available for reference to other observers. Observations with Current Metre. With a view to measure directly the currents occurring in a lake, I procured one of Ekman’s propeller current metres.* The instrument * The cost of this apparatus and the necessary gear was partially defrayed by a grant from the Moray Bequest of the University of Edinburgh. 110 Proceedings of the Kc^al Society of Edinburgh. [Sess. and the method of working will be described in a subsequent com- munication to the Society dealing with observations on Loch Ness. One or two preliminary observations were made in Loch Garry to test the working of the metre, and as they are not without interest they may be summarised here. I. 26th March 1908. Light N.E. Wind. Depth. Velocity of Current. Cm. sec. Direction (Mean). 1 foot 1-8 1 ft. 6 in. 2-3 S. 60° E. 200 ft. 1-5 N. 50° W. Showing current at bottom in direction opposite to current at surface. II. 28th March 1908. West Wind of Moderate Strength. Depth. Rate of Current. Cm. sec. Direction. 24 feet 4-8 25 „ 2-1 N. 30° E. 100 „ 4-8 S. 65° E. 200 „ 3-3 E. Showing distinct current at bottom in opposite direction to the wind. III. 31st March 1908. Strong West Wind. Depth. Rate of Current. Cm. sec. Direction. Surface. 28-0 W. 1 foot 25-3 W. 22° N. 25 feet 3*9 W. 50° N. 100 „ 37 E. 50° N. 200 „ 3-1 E. 10° N. This series of observations (fig. 4) shows very clearly a current to a depth of over 25 feet in the same direction as the wind, and below that a return current in the opposite direction. 1908-9.] Temperature Observations in Loch Garry. Ill Seiche Observations. A few seiche observations were made, as occasion permitted, by means of an index limnograph. Six of the best of these observations are shown in fig. 5, and it will be seen that the curves are most disappoint- ingly irregular, and on several other occasions when observations were made there were no oscillations to measure. The period of the uninodal seiche is from 10 '5 to 11*1 minutes, and of the binodal about 5 '5 minutes. The greatest amplitude observed was 3 inches. The basin of Loch Garry is pretty regular, and its axis is practically straight ; so that it is difficult to assign any cause for the behaviour of the lake. It may have been my misfortune always to observe at a time when seiches were irregular or absent, and of course with the index limnograph it is impossible to observe in stormy weather. But if the observations had been made in Loch Earn, it would hardly have been possible to observe on six occasions with such barren results as we had in Loch Garry. It may be that the small basin 112 Proceedings of the Koyal Society of Edinburgh. [Sess. Fig. 5. 113 1908-9.] Temperature Observations in Loch Garry. at the east end of Loch Garry has a disturbing and damping effect, but the channel between the two basins is so narrow and so shallow that I do not think this likely. The lake runs almost due east and west, and the east end of the lake is little more than a mile from the line of the Great Glen, and the inter- ference of disturbances passing along Glen Garry and the Great Glen may explain to some extent the irregular behaviour of the lake.* * Since the above communication was made to the Society, I have received a copy of Dr F. M. Exner’s paper, “ Uber eigenttimliche Temperaturschwankungen von eintagiger Periode im Wolfgangsee” (Sitz. Akad. der JViss. Wien, math.-nat. Kl Bd. cxvii., Jan. 1908), in which the author discusses observations made by electrical means in St Wolfgangsee which show a temperature seiche having a period of one day. In the case of this lake there appear to be three fairly distinct layers of water, with the result that the oscillations are rather complicated. There appears to be an oscillation of the uppermost layer of opposite phase to the oscillation in the lowest layer, while the middle layer acts as a sort of buffer between the top and bottom layers. [Appendix — Ta bles. 8 VOL. XXIX. 114 Proceedings of the Royal Society of Edinburgh. [Sess. APPENDIX. Note. — A map of the lake is published in the Geographical Journal for October 1907. In the following Tables the points of observation are denoted by letters, the positions of which are shown in fig. 6, representing a cross- section of the lake. The temperatures are measured in degrees Fahrenheit, but for convenience of those accustomed to deal with the Centigrade scale, a conversion table is prefixed. A number appearing in brackets below an observation indicates the depth at which the observation was made, being different from the depth given at the head of the column. The wind force Avas estimated according to the Beaufort scale. 1908-9.] Temperature Observations in Loch Garry. 115 Table for Conversion from Fahrenheit to Centigrade Scale. ° F. 0. •1. •2. •3. •4. •5. •6. •7. •8. •9. °C. °C. °c. °C. ° P OQ °C. °C. °C. 35 1-7 1-7 1-8 1-8 1-9 1-9 2-0 24 2'1 2-2 36 2-2 2-3 2-3 2-4 2-4 2-5 2-6 2-6 2*7 2'7 37 2-8 2-8 2-9 2-9 3-0 3-1 3-1 3'2 3'2 3 3 38 3%3 34 3 4 3-5 3-6 ! 3-6 3-7 3'7 3'8 3-8 39 3-9 3 9 4-0 4*1 4-1 4*2 4-2 4'3 4'3 4'4 40 4-4 4-5 4-6 4-6 4-7 4*7 4-8 4-8 4'9 4'9 41 5-0 5-1 5-1 5-2 5-2 5-3 5 3 5-4 5'4 5'5 42 5-6 5-6 5-7 5-7 5-8 5-8 5-9 5'9 6-0 6'1 43 6'1 6-2 6-2 6 3 6-3 6-4 6-4 6 5 6'6 6-6 44 6-7 6*7 6-8 6-8 6-9 6-9 7-0 71 7-1 7 '2 45 7-2 7-3 7*3 7-4 7-4 7-5 7-6 7-6 7-7 7'7 46 7-8 7-8 7-9 7-9 8-0 8*1 8T 8-2 8'2 8'3 47 8-3 8-4 8-4 8-5 8-6 8-6 8-7 8-7 8'8 8'8 48 8-9 8-9 9-0 9-1 9T 9-2 9-2 9*3 9'3 9'4 49 9-4 9-5 9-6 9-6 9-7 9 7 9-8 9'8 9'9 9'9 50 10*0 10-1 10T 10-2 10-2 10 3 10-3 10'4 10'4 10'5 51 10-6 ' 10-6 10-7 10-7 10-8 10-8 10-9 10'9 11-0 11 *1 52 11-1 11-2 11*2 11-3 11-3 11*4 11-4 11'5 11-6 11-6 53 11-7 11-7 11-8 11-8 11-9 11-9 12-0 121 121 12'2 54 12-2 12-3 12-3 12-4 12-4 12-5 12-6 12*6 12-7 12*7 55 12-8 12-8 12-9 12-9 130 13-1 13*1 13 '2 13 2 133 56 133 13-4 13-4 13-5 13 6 13-6 13-7 13'7 13-8 13-8 57 13-9 13-9 14-0 144 14-1 14*2 14*2 14'3 14'3 14'4 58 14-4 14-5 14-6 14-6 147 1 4*7 14-8 14'8 14'9 14-9 59 15-0 15*1 15-1 15-2 15-2 15*3 15-3 15'4 15'4 15 '5 60 15-6 15-6 15-7 15-7 15-8 15-8 159 15-9 16'0 164 61 16-1 16-2 16-2 16-3 163 16-4 16-4 16'5 16'6 16-6 62 16-7 16-7 16-8 16-8 169 16-9 17-0 17'1 17'1 17'2 63 17-2 173 173 17-4 17-4 17-5 17-6 17 6 17-7 17'7 64 17-8 17-8 17-9 17-9 18-0 18-1 18'] 18'2 18-2 18-3 65 18-3 18-4 18-4 18-5 18-6 18-6 18-7 18'7 18'8 18-8 66 18-9 18-9 19-0 19-1 19T 19-2 19'2 19'3 19'3 19'4 67 19-4 19-5 19-6 19-6 19-7 19 7 19-8 198 19'9 19'9 68 20-0 20-1 20T 20-2 20-2 20-3 20'3 20'4 20-4 20'5 69 20-6 20-6 20-7 20*7 20-8 20-8 20'9 20'9 2D0 21*1 116 Proceedings of the Royal Society of Edinburgh. [Sess. Loch Garry. Date. Hour. Position. Wind. Surface. 5 10 15 20 1 25 30 i 35 1908. Jan. 28 1.40 p.m. Buoy. 38-7 „ 29 10.30 a.m. 55 383 ... ... ... . . . . . . „ 30 2.45 p.m. 55 W.N.W. 38-3 . . . ... ... . . . „ 31 12.40 „ F. Calm. W. 4. 36-5 „ 31 2.30 „ East end. W. 4. 37-0 ... ... ... Feb. 3 12.45 ,, F. W. 4. 38-0 ... ... ... ... ... . . • ... „ 3 2 15 Buoy. • . • 38-0 . . . • . . . . . . . . . . . „ 3 4.45 „ East end. • . • 36*8 « • • ... ... ... . . • 4 1 55 10.0 a.m. Buoy. Calm. 37-5 ... ... ... ... 55 4 1.0 p.m. East end. 37-4 ... ... . . • „ 5 2.0 ., Buoy. W. 4. 37-8 37*8 . . . . . . . . . . . . „ 5 3.45 „ Small loch. ... 38*0 ... ... ... ... 37'8 . . . ... „ 6 11.40 a.m. Buoy. W. 4. 37-8 • . . . . . . . . . . . . . . „ 6 4.30 p.m. „ . . . 37*5 • . • . . • . . . . . . . . . „ 6 5.15 „ East end. Airs. . . . ... . . . . . . . . . ... „ 7 9.40 a.m. 55 ... 37-8 ... ... ... „ 7 1.40 p.m. . F. W. 3. 38-0 . . . 38-0 „ 7 3-0 „ Buoy. 38-0 . . . . . . . . . „ 7 3.50 „ East end. . . . ... ... ... • . . „ 8 2.10 „ Buoy. W. 3. 38-0 • . • . . . . . . . . . „ 11 5.0 „ 55 W. 2. 38-3 . . . ... ... ... . . . ,, 12 10.30 a.m. 55 Calm. 38-3 ... ... ... „ 12 4.0 p.m. 55 ,, 38-5 . . . . . . . . . . . . . . . „ 13 2.30 p.m. 55 Variable. 383 . . . . . . . . . „ 14 11.0 a.m. F. W. 2. ... ... ... ... ... „ 14 11.45 p.m. Buoy. W. 5-6. . . . . . . . . . . . . . . • „ 14 2.30 „ East end. • • • 38*2 ... ... ... • . . „ 15 10.20 a.m. 55 W7. 2. 38-2 ... ... ... ... ... „ 15 Noon Buoy. W. 4. 38-8 . . . . . . . . • ... . . . . . . . . • „ 15 2.0 p.m. F. W. 3. 39-0 ... ... ... ... . . . „ 17 Noon Buoy. W. 1. 38-8 . . . ... ... 38-9 . . . „ 17 2.0 p.m. C. W. 2. 38-5 ... ... ... 38*ft ... „ 17 2.45 „ B. W. 3. 38*5 ... ... ... ... 38-5 ... 1 „ 17 3.15 „ A. W. 3 38-5 ... 38-5 ... „ 18 12.30 „ Buoy. W. 3-4. 39-0 ... ... ... 39-0 „ 19 Noon F W. 2. 38-8 ... ... ... 38-8 „ 19 12.45 p.m. E. ... 38-8 ... ... ... ... 1 38-8 ... ... | „ 19 1.0 „ D. W. 1. 38-1 ... ! - ... ... ... „ 19 2.0 „ Buoy. W. 1. 38-7 ... „ 19 3.15 „ C. ... 38-7 ... ... ... ... ... ... i „ 19 3.45 „ A. 38-7 „ 19 4.0 „ East Bay. 38-7 • . . . o . . . . 38-7 . . . . . . „ 20 10.30 a.m. A. Calm. 38'8 ... ... ... 38-8 ... „ 20 11.30 „ Buoy. W. 1. 38-8 38-8 ... ... 1 „ 20-' ' 12.30 p.m. D. W. 3. 38 8 ... ... ... ... ,,’24 1.45 „ F. W. 1. 386 ... 24 ,, 2.20 „ E. W. 1. 38-6 ... ... ... ... 1 * On 21st and 22nd February 117 1908-9.] Temperature Observations in Loch Garry. Loch Garry. 40 45 50 55 60 65 70 75 80 85 90 100 125 140 150 175 200 ... ... 38-3 38-0 37-3 37-8 37-8 37- 6 38- 0 37- 7 38*0 38- 0 38'0 38-3 38-5 38-5 38-2 38-8 38- 8 39- 0 38-5 38-4 38- 6 39- 0 38-8 38-8 38-8 38-7 38-7 38-7 38-8 38-8 38-8 38-6 38-6 ... ... ... ... 39-0 38-8 387 . . . * . . . 38-8 (86) 38-6 37-5 37-8 37- 8 37*7 38- 3 38-8 38- 8 39- 0 38-0 38-2 38-7 38 ’8 38-8 38-8 38- 8 38 8 39- 0 (96) 38-8 38-8 38-8 38'8 38-8 38-8 " * • 1 ... ... . . . • . . ... ... 38-8 38-5 38-5 37'5 38-0 38- 8 39- 0 39-0 39-0 39-0 38-8 38- 8 39- 0 (168) 38-8 38-8 (143) 38-8 38-8 (170) 38-6 (160) 38-8 (180) 38-5 38*2 37-6 37-7 37-7 37*5 37- 7 38- 0 383 38-6 38- 7 39- 0 39-0 38-8 38-8 38-8 38-8 there was a west gale, force 6-9. 116 Proceedings of the Royal Society of Edinburgh. [Sess. Loch Gaeey. Date. Hour. Position. Wind. Surface. 5 10 ^ l 20 25 30 35 11908. Jan. 28 1 1.40 p.m. Buoy. 38'7 „ 29 10.30 a.m. 38-3 ... „ 30 j 2.45 p.m. W.N.W. 38 3 ... ... Calm. „ 31 12.40 „ F. W. 4. 365 31 2.30 ., East end. W. 4. 37-0 Feb. 3 i 12.45 „ F. W. 4. 38-0 „ 3 2.15 „ Buoy. 38-0 „ 3 4.45 „ East end. 36-8 .. 4 10.0 a.m. Buoy. Calm. 37*5 ... «... „ 4 1.0 p.m. East end. 37 4 2.0 ., Buoy. W. 4. 37 8 37 8 ... 5 3.45 „ Small loch. 38-0 37-8 „ 6 11.40 a.m. Buoy. W. 4. 37'8 „ 6 4.30 p.m. „ 375 „ 6 5.15 „ East end. Airs. 9.40 a.m. 37 8 7 1.40 p.m. F. W. 3. 38-0 38-0 7 3.0 „ Buoy. 380 7 3.50 „ East end. „ 8 2.10 „ Buoy. W. 3. 380 „ 11 5.0 „ W. 2. 38-3 „ 12 10.30 a.m. j, Calm. 383 12 4.0 p.m. „ 38-5 13 2.30 p.m. „ Variable. 383 „ 14 11.0 a.m. F. W. 2. 14 11.45 p.m. Buoy. W. 5-6. 14 2.30 „ East end. 38-2 ... 15 10.20 a.m. W. 2. 38-2 „ 15 Noon Buoy. W. 4. 38-8 „ 15 2.0 p.m. F. W. 3. 39-0 „ 17 Noon Buoy. W. 1. 38-8 38-9 „ 17 2.0 p.m. C. W. 2. 38-5 38-f 17 2.45 „ B. W. 3. 38-5 38-5 „ 17 3.15 „ A. W. 3. 38-5 38-5 ., 18 12.30 „ Buoy. W. 3-4. 390 39-0 ... „ 19 Noon F. W. 2. 38-8 38-8 ... „ 19 12.45 p.m. E. 38-8 ... 386 ... „ 19 1.0 „ D. W. 1. 38-1 ... „ 19 2.0 „ Buoy. W. 1. 38-7 „ 19 3.15 „ C. 387 ... 19 3.45 „ A. 38-7 ... „ 19 4.0 „ East Bay. 38-7 38' „ 20 10.30 a.m. A. Calm. 388 ... 38- ... „ 20 11.30 „ Buoy. W. 1. 38-8 38' ... „ 20 * 12.30 p.m. D. 1 W. 3. 38 8 i „ '24 1.45 „ F. 1 W. 1. 386 ’ „ 24 2.20 „ E. W. 1. 38-6 1 On 2l8t and 22nd February 117 1908-9.] Temperature Observations in Loch Garry. Loch Gaeey. there was a west gale, force 6-9. 118 Proceedings of the Royal Society of Edinburgh. [Sess. Loch Garry Date. Hour. 1 j Position. Wind. Surface. 5 10 15 20 25 30 | 35 j 1908. Feb. 24 3.0 p.m. D. • . . 38-6 . . . . . . . . . . . . „ 24 3.30 „ Buoy. W. airs 38-7 „ 24 4.45 „ C. W. 1. 38-6 ... ... ... ... ... „ 24 5.0 „ B. 55 386 ... ... ... 1 ... ... „ 24 5*45 „ Small loch. Calm. 38-6 ... ... ... ... 384 » 25 4.0 „ Buoy. W. 2-5. 38 -G ... ... ... ... ... ... „ 28 Noon 55 W. 2-4. 38-0 ... ... ... ... „ 28 12.45 p.m. A. ... 37-9 ... ... ... ... • . • » 29 11.30 a.m. F. N. 2-3. 375 ... ... „ 29 Noon E. N.E. 2. 376 ... „ 29 12.45 p.m. D. ... 38-0 . . • ... ... ... ... „ 29 1.30 „ Buoy. N. 2. 38-0 . . . . . . ... ... ... . . . „ 29 2.15 „ C. N. 2-3. 38-0 ... ... ... ... Mar. 3 2.0 „ D-E. E. 1. 1 37-5 ... ... „ 3 3.0 „ F. E. 1-2. 36-4 ... ... . ! » 3 3.5 „ 55 . . . 36-3 , . . • . . . . . ... ... ... » 3 10.30 a.m. A. 37-9 ... ... ... ... „ 3 11.0 „ C. 37-8 ... ... 1 „ 3 11.30 „ Buoy. • . . 37 8 ... ... 1 • • • ... ... » 5 2.30 23.ni. 55 Calm. 36-7 ... 37-0 37-3 • • • „ 5 4.45 „ A. E. airs. 373 ... ... ... o • • 37-6 ... „ 6 10.0 a.m. 55 37-8 ... » 6 Noon F. ... 36-4 ... 37-0 » 6 1.0 23.ni. E. 37-0 ... . 372 . . . „ 6 2.0 „ D. Calm. 37-0 ... ... ... » 6 4.0 „ Buoy. 37-2 37-4 „ 6 5.0 „ B. Calm. 38-0 „ 7 10.45 a. m. Buoy. W. airs. 1 36-9 „ 9 4.0 23.ni. 55 W. 3-4. 372 ... „ 9 12.45 p.m. F. W. 3. 37-5 ... . . • ... » 9 1.0 „ E. 37-5 ... . . „ 10 3.30 „ Buoy. N. 1. 37.0 ... ... ... 37-0 ... ,, 11 10.30 „ 55 Calm. | 36A ... ... 37-0 » 11 12.45 „ D. 55 37-0 ... ... ... ... 37-0 | » 11 2.30 „ Buoy. 55 37‘0 37-0 „ 11 3.30 „ C. 55 37-4 ... ... ... ... ... „ 11 4.0 „ B. 55 37*5 • . . ' „ 11 4.30 „ A. 55 37-3 ... ... „ 12 11.0 a.m. 55 55 363 37-0 „ 12 Noon B. 36-7 ... „ 12 4.30 p.m. Buoy. W. 1. 37-2 ... 1 ... „ 13 9.45 a.m. 55 Calm 37-0 ... 37*1 „ 13 10.30 „ D. 55 37*0 ... ... ... ... 37-4 ... ... „ 13 11.30 „ E. 55 37-6 37-5 „ 13 Noon F. 5> 37-9 37-8 „ 13 4.0 p.m. Buoy. E. 1. 37-5 ... ... ... 37*3 ... | ... „ 14 10.0 a.m. 55 Calm. 36-4 ... ... 37-2 „ 14 12.30 23.m. F. 55 38-0 ... ... • • • ... ... ... ... „ 14 1.15 „ D. 55 37-8 ... ... ... „ 34 2.30 „ Buoy. E. airs. 1 37 3 ... ... | ... ... • • • ... 1908-9.] Temperature Observations in Loch Gariy. 119 — cont inued. 40 45 50 55 60 65 70 75 80 85 90 100 125 140 150 175 200 ... . . . 38-6 38-7 38-6 38-6 38-6 38-0 38-0 38-0 38-0 38*0 37- 8 38- 0 37-4 37-0 37-9 37-8 37-7 37-8 379 37-5 37-4 37-5 37- 9 38- 0 37-8 37-5 37-7 37-2 37*0 37*3 37-0 373 375 373 37-0 37*0 372 37*2 37-5 37-9 37-3 373 37-7 37-4 ... ... 38-0 37-5 37-8 37-4 37*5 37- 6 38- 0 38*7 38-6 38-6 38-6 38-0 38-0 38*0 38-0 37- 8 38- 0 37-4 37- 4 38- 0 37-8 37-7 37- 8 38- 0 37-8 37- 7 38- 0 38-0 37*9 37’5 37-5 37-4 37-2 37-5 37-4 375 37-5 37*5 37-4 37-4 37-5 37-5 37-4 37-5 375 37-4 38*6 37-5 (130) 38-7 37-8 ... ... . . • 38-7 38-6 38-6 38-0 38-0 38*0 37- 8 38- 0 37-5 37-9 37-8 37-8 37-8 37-9 37-9 37-5 37-8 37-5 37-4 37-5 37-5 37-7 37-4 37-4 37*5 37-5 37-5 37-5 37-6 37-8 38-7 (180) 38-6 38*0 (180) 37-5 (190) 37-8 (195) 38-7 38-2 37-8 377 37- 8 38- 0 379 37*7 37*5 37-5 37-4 37*5 37*7 37*5 37*8 375 Proceedings of the Royal Society of Edinburgh [Sess. Loch Garry Date. Hour. Position. Wind. Surface. 5 10 15 20 25 30 35 1908. Feb. 24 3.0 p.m. D. 38 6 ,, 24 3.30 „ Buoy. W. airs 38'7 „ 24 4.45 „ C. W. 1. 38 b » 24 24 5.0 „ 545 „ B. Small locli. Calm. 38 b 386 386 25 4.0 „ Buoy. W. 2-5. 38 b „ 28 Noon W. 2-4. 38-0 „ 28 12.45 p.m. A. N. 2-3. 37 9 - „ 29 1 1.30 a.ui. F. „ 29 Noon E. N.E. 2. 37 b ... ... „ 29 12.45 p.m. D. N. 2. „ 29 1.30 Buoy. 38 0 „ 29 2.15 „ C. N. 2-3. 38 0 Mar. 3 2.0 D-E. E. 1. 375 3.0 „ F. E. 1-2. 3b 4 „ 3 3.5 „ „ 3b 3 „ 3 10.30 a.m. A. 37-9 „ 3 11.0 „ C. 37-8 „ 3 11.30 „ Buoy. 37 8 37-0 373 ... „ 5 2 30 p.m. Calm. 367 „ 5 4.45 „ A. E. airs. 373 „ 6 10.0 a.m. 37-8 370 ... " 6 F. 3b-4 ;; e 1.0 p.m. E. 37-0 372 ... „ 6 2.0 „ D. Calm. 37 0 „ 6 4.0 „ Buoj-. 372 374 ... „ 6 5.0 „ B. Calm. 380 10.45 a.m. Buoy. W. airs. 36 9 „ 9 4.0 p.m. W. 3-4. 372 „ 9 12.45 p.m. F. W. 3. 37 5 ... 9 1.0 „ E. 37 5 37 0 ... 10 3.30 „ Buoy. N. 1. 37.0 „ 11 10.30 „ Calm. 365 37-0 ... „ ii 12.45 „ D. 37 0 370 ... „ 11 2.30 „ Buoy. 37’0 37-0| ... » H 3.30 „ c. 374 ... ... „ 11 4.0 „ B. 375 „ 11 4.30 „ A. 37 3 „ 12 11.0 a.m. „ 363 370 ... „ 12 Noon B. 367 „ 12 4.30 p.m. Buoy. W. 1. 37 2 37-1 ... „ 13 9.45 a.m. Calm 370 „ 13 10.30 „ D. » 37-0 37-4 ... „ 13 11.30 „ E. 37-6 sH 13 Noon F. „ 379 37'8 ... 13 4.0 p.m. Buoy. E. 1. 37-5 373 ... „ 14 10.0 a.m. Calm. 36-4 372 ... 14 12.30 p.m. F. „ 38 0 ... ... ,, 14 1.15 „ D. „ 37-8 ... ;; i-i 2.30 „ Buoy. E. airs. 37 3 119 1908-9.] Temperature Observations in Loch Garry. — coni inued. 37 -i 37-9 3-0 ... 37-8! ... 37-7 372 370 37 3 37-0 373 375 373 37-0 37-0 372 372 37-9 373 37-4 37-5 100 125 140 150 i 175 200 37 e 37-7 37-5 374 37f 37-5 37-4 37-5 375 37'4 ! 375 (130) 38-7 (180) I 38-7 38-6 38 6 38 •( 38-0 ; I 38-0 38-0 378 38 0 375 37-9 37'8 37-8 377 37-8 38-0 (180) 379 37-5 37-8 37-5 37-4 375 37 £ 37-1 379 377 375 37-5 375 (190) 37-8 1 (195), 1 375 37-81 120 Proceedings of the Royal Society of Edinburgh. [Sess. Loch Garry Date. Hour. Position. Wind. Surface. 5 10 15 20 25 30 35 1908. Mar. 16 10.30 a.m. Buoy. Calm. 370 55 16 12.15 „ F. E. airs. 37-6 . . . • . . ... 5 5 16 12.45 „ E. ... 37-4 ... ... ... 55 16 1.0 „ D. ... 37-5 ... ... ... 55 16 2.45 „ Buoy. W. airs. 37-4 55 16 4.30 „ C. 55 37*4 ... ... 55 16 5.0 ,, B. Calm. 37*5 ... ... ... 55 16 5.20 „ A. W. airs. 37-5 ... ... 55 17 3.0 „ Buoy. • . . 37-6 . . . • . . 55 18 10.15 „ 55 E. 1. 37-5 • . . ... 55 18 1.15 p.m. 55 55 37-7 . . • . . • . . • 55 19 10.0 a.m. A. Calm. 36-8 ... 37*4 55 19 10.30 „ A. B. ... 37-0 ... ... 37*3 55 19 11.0 „ B. E. airs. 37-4 37*4 55 19 11.30 „ C. 55 37-0 ... ... 37*5 55 19 Noon Buoy. 55 38-0 37*5 55 19 1.30 p.m. D. E. 1. 38-0 ... 37*8 55 19 2.15 „ E. ... 37-9 ... ... 38*0 55 19 2.45 „ F. E. 1. 38-0 ... ... 38*0 55 20 9.30 a.m. Buov. 55 37-5 ... ... ... 55 20 11.0 „ D. S. 2. 37-7 ... ... 55 20 Noon E. E. 2. 38-0 55 20 12.30 p.m. F. • . • 38-4 , . . ... 38*0 55 20 5.0 „ Buoy. Calm. 37-8 ... ... . . . 55 21 10.0 a.m. 55 55 36-8 ... ... 55 21 Noon C. W. 1. 37*7 ... ... 55 21 12.30 p.m. B. 37-8 55 21 12.45 „ A. ... 37-8 ... 55 23 11.0 a.m. Buoy. W. 3. 38-0 ... ... ... 55 23 2.45 p.m. F. W. 2. 400 ... 38*2 55 23 3.30 „ E. ... 38-0 ... ... ... 55 23 3.45 „ D. 38-0 55 23 4.15 „ Buoy. W. 3. 38-0 ... ... ... . . . 55 23 5.0 „ C. ... 38-0 ... ... ;5 23 5.15 „ A. ... 38-0 ... 55 24 12.30 p.m. Buoy. W. 2-3. 38-0 ... ... 55 24 4.15 „ 55 W. 2-3. 37-0 ... ... ... 55 26 11.0 a.m. 55 E. 1. 38*0 ... 55 28 11.30 „ 55 W. 3-4. 38*2 55 28 3'15 p.m. 55 W. 4-5. 38*3 . . . ... ... 55 31 3.30 „ 55 W. 3-4. 38*8 ... Apr. 2 9.45 a.m. 55 W, 2. 38*8 55 2 12.30 p.m. F. W. 4. 39*0 . . . ... 39*0 55 2 3.0 „ Buoy. W. 4-5. 38*9 . • • ... ... 55 3 2.30 „ 55 W. 2-3. 39*0 ... ... 55 6 11.0 a.m. A. W. 1. . 39*7 39*0 55 6 11.15 „ B. Calm. 39*4 55 6 11.45 „ 1 C. ... 39*6 • * * . . . * ' * 1908-9.] Temperature Observations in Loch Garry. 121 . — continued. 40 45 50 55 60 65 70 75 80 85 90 100 125 140 150 175 • . . ... . . . . . . 37-4 37-8 37-7 37-4 37-3 37-4 37-4 37-5 37-6 37*5 37-5 37*5 37-4 37-4 37-5 375 37-8 37- 8 38- 0 37-7 37- 8 38- 0 38-0 37-8 37'0 37-8 37'8 37-8 37- 8 38- 1 37- 9 38- 0 38-0 38-0 38-0 38-0 38-0 38'0 38-2 38-3 38-8 38- 8 39- 0 38- 9 39- 0 39-0 39 0 39-0 ... 38*0 . . . 37-5 37- 7 38- 5 38-0 38-0 38-0 37-5 37-7 37*5 37-5 37*5 37-4 37-5 37-5 37-4 37-5 37-5 37-8 37-8 37’9 37-8 37- 8 38- 0 37-8 37*8 37-8 37-8 37-8 37- 9 38- 0 38-0 38-0 380 38-0 38-0 38-1 38-2 38-2 38-8 38-8 38- 8 39- 0 39-0 39-0 390 37*6 (120) 38-0 37'5 37-5 37- 9 38- 4 37- 8 (130) 38- 0 37-8 (130) 38*0 39- 0 39-0 (130) 37-6 37-5 (170) 37-5 37-7 37 7 37-7 37- 6 37 7 (145) 38- 0 37-8 37-8 37-8 37- 9 38- 0 37- 9 38- 0 38-0 38*0 38-0 38-2 38-2 38-2 38-7 38-8 38- 8 39- 0 37'9 (180) 200 37-7 37-6 37-8 38'0 37-8 38-0 37*9 38-0 37 8 37-8 380 38 0 38 0 38-2 38-2 38*2 38-7 38-8 38- 9 39- 0 120 Proceedings of the Royal Society of Edinburgh. [Sess. Loch Garry Date. Hour. Position. Wind. Surface. 5 10 15 20 25 30 35 1908. Mar. 16 10.30 a.m. Buoy. Calm. 370 ... 16 12.15 „ F. E. airs. 37-6 „ 16 12.45 „ E. 37-4 „ 16 1.0 „ D. 37-5 „ 16 2.45 „ Buoy. W. airs. 37-4 „ 16 4.30 „ c. 37-4 „ 16 5.0 ,. B. Calm. 37-5 16 5.20 „ A. W. airs. 37 5 17 3.0 „ Buoy. 37-6 „ 18 10.15 „ E. 1. 375 18 1.15 p.m. „ „ 377 „ 19 10.0 a.m. A. Calm. 36 8 37-4 „ 19 10.30 „ A. B. 37-0 37-3 19 11.0 „ B. E. airs. 37-4 374 „ 19 11.30 „ C. 370 37-5 „ 19 Noon Buoy. 380 375 „ 19 1.30 p.m. D. E. 1. 38-0 37-8 19 2.15 „ E. 37-9 38-0 „ 19 2.45 „ F. E. 1. 380 38-0 20 9.30 a.m. Buov. 375 „ 20 11.0 „ D- S. 2. 37-7 „ 20 Noon E. E. 2. 38-0 „ 20 12.30 p.m. F. 38 4 380 „ 20 5.0 „ Buoy. Calm. 37-8 „ 21 10.0 a.m. 36-8 „ 21 Noon C. W. 1. 37-7 21 12.30 p.m. B. 378 „ 21 12.45 „ A. 37-8 » 23 11.0 a.m. Buoy. W. 3. 38-0 „ 23 2.45 p.m. F. W. 2. 400 382 23 3.30 „ E. 38-0 „ 23 3.45 „ D. 380 „ 23 4.15 „ Buoy. W. 3. 38-0 „ 23 5.0 „ C. 380 „ 23 5.15 „ A. 38-0 ,, 24 12.30 p.m. Buoy. W. 2-3. 38-0 „ 24 4.15 „ „ W. 2-3. 37-0 „ 26 11.0 a.m. E. 1. 38-0 „ 28 11.30 „ W. 3-4. 38-2 „ 28 3‘15 p.m. „ W. 4-5. 38-3 „ 31 3.30 „ W. 3-4. 38-8 Apr. 2 9.45 a.m. W. 2. 38-8 „ 2 12.30 p.m. F. W. 4. 390 39-0 „ 2 3.0 „ Buoy. W. 4-5. 38-9 „ 3 2.30 „ W. 2-3. 39 0 „ 6 11.0 a.m. A. W. 1. 39-7 390 » 6 11.15 „ B. Calm. 394 „ 6 11.45 „ C. ... 39-6 1908-9.] Temperature Observations in Loch Garry. — continued. 40 I 45 ‘ 50 I 55 37 4 37-8 377 37-4 373 37-4 374 375 37-6 37-5 37-5 37-5 374 374 37-5 37-5 37'8 j 37-8 | 38-0 37-7 37- 8 38- 0 !38'0 37-8 37-0 37-8 37-8 37-8 37- 8 ,38-1 379 38- 0 38-0 380 38-0 38-0 38-0 380 60 65 70 75 85 90 100 125 I 140 150 175 375 37 5 37-8 37-8 37-9 37-8 37-8 37- 8 (130) 38- 0 37 (170) 37-5 37- 6 j 37'7 I (145) 38- 0 j 37-8 37-8 ... 37-8* 37-9 (180) 38-0 38-0 38-2 38-3 .. 38 8 .. 38 8 .. 39 0 .. 38 9 .. 39 0 .. 39 0 .. 39 0 .. 39 0 .. 38-2 38-8 38-8 382 38-7 38-8 38-8 390 390 390 390 390 3901 (130) 38-8 ... 390 ... 121 200 ! 37-7 37-6 37 8 380 378 380 379 38-0 37 8 378 380 38 0 I 38 0 382 38-2 38-2 38-7 38-8 38-9 39 0 122 Proceedings of the Royal Society of Edinburgh. [Sess. Loch Garry Date. Hour. Position. Wind. Surface. 5 10 15 20 25 30 35 1908. Apr. 6 12.30 p.m. Buoy. W. 1. 40-0 39-2 55 6 4.0 „ F. ... 39-8 55 6 4.20 „ E. ... 40-0 ... 55 6 4.45 „ D. 40'0 ... ?? 6 5.45 „ Buoy. W. 2. 39-5 53 7 2.0 „ 55 W. 3-4. 39-3 . . • 55 8 4.0 „ 55 Calm. 40-0 . • • 55 9 9.45 a.m. 55 W. 1-2. 398 ... 55 9 3.15 p.m. 55 N. 1. 40-0 . . • 51 10 10.45 a.m. 55 W. 1. 39-9 55 13 3.30 p.m. 33 E. 0. 40 0 . . . ... 55 14 11.45 a.m. 55 E. 1. 40-4 55 15 10.0 ,. •5 E. 1-2. 40-3 ... 55 16 11.30 „ 55 E. 1-2. 41*1 55 16 2.30 p.m. 33 E. 2-3. 4P0 55 17 10.45 a.m. A. W. 1. 40-5 55 17 11.15 „ B. W. 1. 40-8 40-0 55 17 11.45 „ C. ... 40-8 40'0i ... 55 17 3.0 p.m. F. W. 2-3. 42-4 42-0: ... 55 17 3.30 „ E. ... 41-8 55 17 4.0 „ D. ... 4P2 33 17 4.30 „ Buoy. W. 2-3. 4F8 ... 33 20 3.30 „ 55 W. 2. 41-0 ... 55 21 11.15 a.m. 55 N. 0. 4D4 1 33 22 12.45 p.m. 55 N. 0. 41*8 55 24 10.0 a.m. 55 E. 2-3. 41*1 55 25 Noon. 55 W. 2-3. 41-0 . . • 55 27 Noon. 55 E. 2-3. 41-0 55 28 8.15 a.m. A. E. 2. 40-9 33 28 8.45 „ B. ... 41 -0 33 28 9.15 „ C. ... 41-0 ... 55 28 9.45 „ Buoy. E. 2-3. 4P0 33 28 10.15 D. ... 4D2 55 28 10.45 „ E. 4D5 33 28 11.15 „ F. 41*7 33 28 2.30 p.m. Buoy. E. 2-3. 4P6 4P3 33 29 9.30 a.m. 55 E. 2-3. 4P1 33 30 12.20 p.m. 55 Calm. May 1 1 1.45 a.m. 55 W. 2. 42-0 55 4 2.15 p.m. 55 E. 1. 417 55 5 9. 15 a.m. 55 E. 1. 42 '2 ... ... 55 6 10.45 „ A. ... 42-3 41-6 ... 55 6 11.15 „ C. ... 42*0 41-9 . . . 33 6 12.15 p.m. Buoy. Variable. 45-0 42-4 33 6 1-30 „ D. ... 45 -5 ... 55 6 3.30 „ F. 44*5 42-9 33 6 4 15 „ E. ... 45-0 42-8 33 6 5.0 „ Buoy. W. 2-3. 44-5 • . . 55 8 10.30 a.m. 55 Variable. 43 2 ... ... ... 1908-9.] Temperature Observations in Loch Garry. 123 — continued . 40 45 50 55 60 65 70 75 80 85 1 ... ... ... ... ... | ... 397 39-2 39-2 397 39*4 39-3 39-5 39-6 397 39 8 : 40*0 39- 9 40*0 40*6 40- 4 40-0 40-0 40- 0 41- 4 41-0 41-0 39- 8 40- 9 41- 2 41-0 417 41-0 41-0 40- 9 41 '0 41- 0 41-0 4M 41-3 41-5 41*0 41-0 41*3 41-6 41-5 41- 4 4] -8 42*0 42- 0 42-5 42-2 ... ... ... ... ... * 1 40*4 417 ... ... . . . ■ ■ ■ j ... ’’’ | 1 100 125 140 150 39-0 39-2 39-2 ... 39-5 ... 393 39-2 ... 39-2 390 39-0 39-4 ... 39-4 39 7 40*0 39-4 ... 39-4 39'4 ... 39-4 39-6 39-4 39-8 39-8 39-8 39-8 40-0 39-8 40-2 40-0 40-2 ... 40-0 40-0 • . . 40-0 40-0 40-0 40-0 40-2 40-0 407 ... 40-0 40-0 40-0 40-9 40-8 40-9 40-8 40*8 40-8 41-0 40-6 40-8 ... 40-8 41-0 40-9 40-9 ... 41-0 ... 41-0 41-0 (130) 40-9 41-0 (130) 41-0 41-0 ... ... 41-0 41-0 41*0 41-1 ... ... 41-0 . . . ... 41-0 41-0 ... 41 0 414 41-0 41-5 41-4 41-4 ... ... 41-2 414 ... ... 41-3 • . . 410 41-4 (130) 41-3 41-4 ... ... 41-2 41-2 ... 41-2 175 39-2 (180) 41-0 (190) 41-2 (180) 200 39-2 39- 0 39*4 40- 0 39-4 39-3 393 39-4 39*7 39- 7 40- 0 40 0 40-0 40-6 40-5 40-6 40-6 407 40-8 41-0 414) 41-0 41*0 4J-0 417 41-2 41-2 41-2 427 122 Proceedings of tlie Royal Society of Edinburgh. [Sess. Loch Garry Date. Hour. Position. Wind. Surface. 5 10 15 20 25 30 35 1908. Ayr. 6 12.30 p.m. Buoy. W. 1. 400 39-2 „ 6 4.0 ,. F. 39-8 „ 6 4.20 „ E. 40-0 6 4.45 „ D. 400 „ 5.45 „ Buoy. W. 2. 395 2.0 „ W. 3-4. 39-3 „ 8 4.0 „ Calm. 40-0 „ 9 9.45 a.m. W. 1-2. 398 ... 3.15 p.m. „ N. 1. 40-0 „ io 10.45 a.m. W. 1. 39 9 ., 13 3.30 p.m. „ E. 0. 400 „ 14 11.45 a.m. E. 1. 40-4 „ 15 10.0 .. E. 1-2 40-3 „ 16 11.30 „ E. 1-2. 41-1 „ 16 2.30 p.m. E. 2-3. 41-0 „ 17 10.45 a.m. A. W. 1. 40-5 „ 17 11.15 „ B. W. 1. 408 400 ... » 17 11.45 „ C. 40-8 40-o: ... „ 17 3.0 p.m. F. W. 2-3. 42-4 42-0 „ 17 3.30 „ E. 41-8 17 4.0 „ D. 41-2 „ 17 4.30 „ Buoy. W. 2-3. 41-8 „ 20 3.30 „ W. 2. 410 „ 21 11.15 a.m. N. 0. 41-4 12.45 p.m. „ N. 0. 41-8 24 10.0 a.m. E. 2-3. 41-1 „ 25 Noon. W. 2-3. 41-0 Noon. E. 2-3. 41-0 „ 28 8.15 a.m. A. E. 2. 409 „ 28 8.45 „ B. 41-0 „ 28 9.15 „ C. 410 „ 28 9.45 „ Buoy. E. 2-3. 41-0 „ 28 10.15 „ D. 41-2 „ 28 10.45 „ E. 41-5 „ 28 11.15 „ F. 41-7 „ 28 2.30 p.m. Buoy. E. 2-3. 416 41-3 21) 9.30 a.m. E. 2-3. 411 „ 30 12.20 p.m. „ Calm. May 1 1 1.45 a.m. W. 2. 42-0 ... „ 4 2.15 p.m. „ E. 1. 41-7 ... „ 5 9.15 a.m. E. 1. 42-2 6 10.45 „ A. 423 41-6 „ 6 11.15 „ C. 42-0 41-9 j. 6 12.15 p.m. Buoy. Variable 45-0 424 » 6 1-30 „ D. 45-5 330 „ F. 44-5 42-9 ... v 8 4 15 „ E. 45 0 42-8 6 5.0 „ Buoy. W. 2-3. 44-5 1 „ 8 10.30 a.m. ” Variable 43-2 | ... J 1 1908-9.] Temperature Observations in Locli Garry. — continued. 123 40 4.r) 50 55 60 65 70 75 80 392 39 3 393 392 39- 4 393 395 39 6 39 39 8 40- 0 399 lo-o 40-6 40-4 40-0 urn 40- 0 41- 4 41-0 41-0 398 40- 9 412 41- 0 4M 41-0 41-0 40- 9 41- 0 41 0 41 0 41 *li 413 41-5 41-0 410 4 i 3 41-6 41-5 41-4 41- 8 42/0 42- 0 90 100 125 39-0 392 395 39-2 39 0 39 4 397 39- 4 394 396 398 | 39-8 40- 0 40-2 40-2 40 0 j 40-0 | 40-0 j 40-2 | 40-1 I I 40 0 i 40-9 409 40- 8 i 41- 0 40- 8 41- 0 40- 91 410 ; 41- 0 410 (130) 1 409 (130) 41-0 411 410 41 0 41-4 41-1 41-3 41-4 41-4 410 (130) 140 150 175 393 392 392 (180) 390 39- 4 40- 0 39-4 394 39-4 39-8 398 39- 8 40- 0 40 0 39 0 394 40-0 39-4 393 393 39-4 39-7 39- 7 40- 0 40 0 40-0 406 40-5 40-6 40-6 407 40-8 41-0 (190) 41-0 410 41-0 41-0 41-1 41-2 (180). 41- 2 42- 1 I 124 Proceedings of the Royal Society of Edinburgh. [Sess. Loch Garry Date. Hour. Position. Wind. Surface. 5 10 15 20 25 30 35 1908. May 8 1 1.15 a.m. D. Calm. 43-0 . . . 42-3 . . . . . . 53 8 Noon E. 55 42-5 ... ... ... 42-0 ... ... 55 8 12.30 p.m. F. 433 ... 420 33 8 1.30 „ Buoy. Calm. 44-0 . . . . . . . . . ... 42-7 . . . 55 8 4.30 „ C. ... 44*0 ... ... ... 43-2 ... ... 55 8 5.0 „ A. E. 1. 44-4 43-0 55 9 9.0 a.m. Buoy. W. 3-4. 43*3 . . • ... ... . . • 43-2 . . . 55 12 10.0 „ 55 Calm. 45-0 . . . ... ... 44-4 33 12 12.30 p.m. 55 55 46-0 . . . . . . . . . . . . 44-4 . . . 55 12 2.15 „ 55 E. airs. 45-7 . • • . . • 44*3 ... 55 12 3.45 „ B. ... 45*2 ... ... ... ... 44-5 ... ... 55 12 4.15 „ A. 45-3 44‘4 55 13 11.30 a.m. 55 W. 1. 45-6 • . . • • • ... 44*3 . • • 55 13 Noon B. ... 45-7 ... ... 44-4 . . . . . * 33 13 12.30 p.m. C. . . . 46-0 . . . . . . . . . . . . 44-2 . . . . • . 33 13 1.45 „ Buoy. N. 1. 47-0 . . . • . . . . . . . . 44-5 . . . . . . 55 13 3.15 „ D. ... 47-1 ... ... ... ... 33 13 4.0 „ E. 49‘0 44-2 5i 13 4.30 ,, F. , . . 48-7 ... ... ... 44*2 . . • . . • 55 14 10.30 a.m. Buoy. E. 1. 46 '3 . . . . . . . • . 44-6 . . . • • • 33 14 3.0 p.m. 55 45-9 . . . . . • ... 44-1 . . . . . • 55 15 10.30 a.m. 55 E. 1. 46-3 ... . . . ... ... 44-5 . . • . . • 55 15 Noon D. E. 2. 47-0 ... ... ... ... 46-1 ... ... 33 15 12.45 p.m. E. E. 1-2. 47-8 • • • 46-0 ... ... 55 15 1.30 „ F. E. 1-2. 48-8 • . . ... ... 47-8 • . • . . • 55 19 10.15 a.m. Buoy. W. 2-3. 46-3 . • • . • . ... 46d . . . . . • 33 19 4.45 p.m. 55 W. 3-4. 45*8 . . . . . . . . . . . . 45-8 . . • . . . 33 21 1.30 „ 55 W. 2-3. 46*2 . . . . . • 46-0 . . . . . . 33 21 6.15 „ 55 W. 1-2. 46-2 . . . . . . - - • 46-1 . . . • . • 55 22 8.30 a.m. 55 W. 2-3 460 . • • ... . . # ... 46-0 . . • • . • 33 22 5.0 p.m. 55 W. 2-3. 46-7 . . • . . . . . . . . . 46*6 . . . . . • 55 23 10.45 a.m. 55 W. 1-2. 46-5 . . . . . . . . . 46 4 . . . . . . 55 23 11.30 „ C. 47-0 . . • ... ... ... 46*8 . . . . . . 33 23 12.15 p.m. A. ... 47-1 ... ... 46*5 ... ... 55 25 12.15 „ Buoy. W. 3-4. 46-8 46*7 55 27 11.30 a.m. F. W. 1. 47'7 ... . . . . . • ... 46*0 . . . . . . 55 27 12.15 p.m. E. 47-0 . . . . . . . . . 46*4 . . . . . . 55 27 1.0 „ D. ... 47-0 46*8 ... 55 27 2.15 „ Buoy. W. 1-2. 47-5 47*3 ... 55 27 3.0 „ C. ... 47-8 ... ... ... 47*4 ... 33 27 3.30 „ B. ... 48 '2 ... ... ... ... 47*5 . . . ... 55 27 4.10 „ A. 48-4' 48 *C ... 55 28 12.15 „ Buoy. W. 1. 49-7 . . . . . • . . . 47 *4 ... . . • 55 28 5.45 „ 55 E. 1-2. 52-3 . . . 47 *£ . . • 55 29 Noon n E. airs. 54-4 ... ... 47*/ ... 1908-9.] Temperature Observations in Loch Garry. 125 — continued. 40 45 50 55 60 65 70 75 80 I 85 90 100 125 140 150 175 200 423 42-3 42-0 42-0 42-0 42-0 41-9 (170) 42-0 41-9 (130) ... 42-5 ... ... 42-4 42'3 ; 42-0 43-0 ... ... ... ... 42*7 42*2 42-8 (130) 43-0 . . . ... 42*2 ... 42-0 ... 41-9 43-8 ... ... 42-4 42-3 42-3 42-1 44-0 ... ... 42-4 42-4 ... 42-4 42-1 ... 44-0 ... ... 42-5 42-3 421 43-5 ... ... 42-4 ... 42 -J ... 43-0 42-3 (145) 44*0 ... ... ... 42-4 . . . ... 43-2 42-4 ... 42-2 43'3 ... ... 42-3 421 ... ... 43-7 ... ... 42-8 ... 42-5 42-4 43-7 ... I ”... ... 42-4 42-4 42 '4 43-5 42-5 42-4 (170) ... 43'9 ... ... 42-4 . . . . . . 43-9 ... 43-0 ... ... 42-5 42-5 42*4 42-4 42-3 ... 44-0 ... ... ... 42-8 . . . 42-5 42-4 42-4 42-3 42-3 43-9 ... ... 43-0 ... ... 42-6 42-5 42-4 ... 42-3 444 ... ... 42-5 42-3 42 3 44-4 42-4 42-3 (170) ... 44-9 43-4 ... ... 42-4 45-5 . . . ... ... ... 45-0 ... 44-6 . . . 44-0 • • • 45-8 ... 45-0 44-5 44-0 45-9 ... ... ... 45-4 ... 44-5 44-4 ... 46-0 ... ... 45-4 ... 44-5 44*2 46-0 ... . . . 45-3 44-9 44-3 ... ... 46-2 ... ... ... ... ... 45-6 ... 44-8 44-5 ... 462 ... ... ... 46-0 ... 45-0 . . . 44-8 ... 44-5 ... 46-2 . . . ... ... ... 46-0 44-7 44-7 ... 46-3 . . . ... ... ... . . . ... 45*1 44-8 46-7 45-9 (120) 45-0 44-3 45-4 ... 45-1 ♦ ... ... 45 0 ... .... 46-2 ... ... ... 46-0 ... ... 45-5 45-0 ... 45-0 46*5 ... ... ... ... 46-0 45-3 ... 45-1 45*0 46-8 46-6 45-6 45-0 (170) 45*0 ... 46-8 © • . ... 46-7 45-4 45*0 ... ... 47-0 46-7 45-5 (130) 45-0 47-C ... 46-7 46-0 j (130) • . . ... 46'g ... ... ... 45-8 ... 45-6 ... 45-3 ... 45-0 • . . ... 464 ... ... ... ... 464 ... 45-9 ... 45 ‘5 . . . 45-2 ... ... 464 ... ... ... ... ... ... ... 45*9 ... 45-2 1 45-2 124 Proceedings of the Royal Society of Edinburgh. [Sess. Loch Garry Date. Hour. Position. Wind. Surface. 10 15 20 25 30 35 1908. May 8 11.15 a.m. D. Calm. 43-0 42-3 „ 8 Noon E. 42-5 420 „ 8 12.30 p.m. F. 43-3 420 „ 8 1.30 „ Buov. Calm. 44-0 42-7 „ 8 4.30 „ C. 44-0 432 „ 8 5.0 „ A. E. 1. 44-4 430 „ 9 9.0 a.m. Buoy. W. 3-4. 433 432 „ 12 10.0 „ Calm. 45-0 44-4 „ 12 12.30 p.m. „ „ 46-0 44-4 „ 12 2.15 „ E. airs. 45-7 443 „ 12 3.45 „ B. 45-2 445 12 4.15 „ A. 453 44-4 „ 13 11.30 a.m. ,, W. 1. 45-6 44-3 13 Noon B. 45-7 444 „ 13 12.30 p.m. C. 46-0 44-2 „ 13 1.45 „ Buoy. N. 1. 470 44-5 „ 13 3.15 „ D. 47-1 „ 13 4.0 „ E. 49 0 44-2 „ 13 4.30 „ F. 48-7 44-2 14 10.30 a.m. Buoy. E. 1. 46-3 446 „ 14 3.0 p.m. 45-9 44-1 „ 15 10.30 a.m. „ E. 1. 463 44 5 „ 15 Noon D. E. 2. 47 0 46-1 „ 15 12.45 p.m. E. E. 1-2. 47-8 460 „ 15 1.30 „ F. E. 1-2. 48-8 47-8 „ 19 10.15 a.m. Buoy. W. 2-3. 46-3 461 „ 19 4.45 p.m. W. 3-4. 45-8 45- 81 ... 46- 0 ... 21 1.30 „ W. 2-3. 46-2 „ 21 6.15 „ W. 1-2. 46-2 461 „ 22 8.30 a.m. , W. 2-3 460 460l ... „ 22 5.0 p.m. W. 2-3. 46-7 46-6 „ 23 10.45 a.m. „ W. 1-2. 46-5 46 4 „ 23 11.30 „ C. 47-0 46-8 „ 23 12.15 p.m. A. 47-1 46-5 „ 25 12.15 „ Buoy. F. W. 3-4. 46-8 46-7 „ 27 11.30 a.m. W. 1. 47-7 460 „ 27 12.15 p.m. E. 47-0 46-4 „ 27 1.0 „ D. 47-0 468 „ 27 2.15 „ Buoy. W. 1-2. 47-5 47-3 „ 27 3.0 „ C. 47-8 47-4 „ 27 3.30 „ B. 48-2 47-5 „ 27 4.10 „ A. 48-4' 48-C 28 12.15 „ Buoy. W. 1. 497 47-4 „ 28 5.45 „ E. 1-2. 52-3 47 T „ 29 Noon ” E. airs. 544 47‘" 1908-9.] Temperature Observations in Loch Garry. — continued. 125 43 0 438 43 - l) 44- 0 43-5 43 9 43- 9 44- 0 43 9 441 44'4 444) 46-0 46 0 46-2 462 46-2 46-3 46-7 45- 4 46'2 46- 5 46'8 46-8 46'9 46 9 43-0 I 4-2-8 i 43-0 85 ; 90 100 125 42-0 41-9 j (130) 42-4 J ... 42-7 42-2 (130) 42-4 42-4 42-5 424 42-3 42-4 42-4 42-3 42-8 42-4 42-5 42-4 42-5 42-5 426 42-5 46-6 46-7 46-7 ! 45-8 46-5 42 4 42-4 45-0 45-0 45-4 45-4 453 45- 6 450 46- 0 45-1 45-6 45-4 42-1 (145) 46-0 456 45-9 459 44-7 44-8 (120) 450 (130) 45 0 (130) 150 175 200 42-0 i 42 0 | 1170) 42 0 42-3 | 42-4 423 419 42-1 42-1 421 421 ... 42-5 ... -12-4 424 42 4 (170) 42-4 42 4 42 3 ! 42-41 42-3 42-3 I 42-4 1 ... 42-3 42-3 423, ... (170) 42-3 ... 1 ... 44-6 44-5 44-5 44 -5 ; 449 44-8 44-8 4501 44 0 44-0 ; 44-4 44-2 44-3 44-5 44-5 | 45-0 45-1 1 45-0 (170) 45-0 45 3 45-5 452 45-0 45-2 452 126 Proceedings of the Royal Society of Edinburgh. [Sess. Loch Garry Date Hour. Position. Wind. Surface. 5 10 ! is 20 25 30 35 1908. May 29 3.0 p.m. Buoy. . . . 6P0 49-4 47 ‘5 • . . 5? 30 9.45 a.m. 55 Calm. 57-4 50*0 47-4 ... ... 55 30 1.15 „ 5 5 E. 1. 59-4 ... 49-5 . . . 47*3 55 30 6.15 p.m. 55 Calm. 56-1 48-0 47-3 . . . June 1 10.0 a.m. 55 E. 1-2. 55-3 . . • 53'4 48-4 . . • 55 1 12.15 p.m. D. E. 2-3. 56-0 . . . 55*4 48-6 . . . 1 55 1 6.30 „ Buoy. E. 1-2. 56*6 . . . 52-2 . . . 49-0 . . . 55 2 9.0 a.m. 55 E. 1. 57-3 53-8 . . . 501 ... 55 3 10.0 „ 55 W. 1-2. 57*4 56-2 ... 49-4 ... . . . *5 3 3.30 p.m. D-E. W. 0-1. 60-1 55-0 50*1 49-0 55 n O 4.45 „ Buoy. W. airs. 60-3 . . . 57'9 . . . 49-5 . . • . . • 1 5 4 3.30 ,, 55 W. 3-4. 56'5 • . • 55-3 • . • 54-0 . . . 55 5 1.0 „ 55 W. 3. 53-0 ... 53-0 . . • 5D4 ... 5 5 5 3.0 „ E. W. 3. 49-0 48-4 48-0 ... ... ‘5 5 4.0 „ D. W. 4. 52-2 49-6 ... 49-2 ... * 5 6 10.0 a.m. D. E. 1 560 53*4 ... 51-0 ... 55 6 11.0 „ E. 56-0 54-0 ... ... 52-7 ... 55 6 Noon F. W. 1. 55-3 54*1 53-7 55 6 1.30 p.m. Buoy. W. 1. 56-8 53*6 . . . 50-5 . . . 55 6 2.30 „ C. ... 56-0 52-8 49-6 . . . 55 6 3.30 ,, B. ... 57A 53-0 50-2 . . . 55 6 4.0 „ A. 57*6 , . . 53-0 . . . 50-5 . . . 55 0 4.15 „ A-E. end • • • 57-3 55-2 ... 50-7 ... 49-5 55 8 8.0 a.m. Buoy. W. 3. 52-9 ... 52-9 ... 52*8 . . . 55 8 7.30 p.m 55 W. 2. 52-2 52-2 ... 51-5 5 5 9 11.30 a.m. A. W. 1-2. 54-0 535 ... 545 '5 9 Noon. B. W. 2-3. 53-7 ... 53*3 49-8 ... ... 55 9 4.0 p.m. Buoy. W. 2-3 53-1 52-8 50-0 55 10 10.0 am. 55 W. 2-3. 52-4 52-3 52*2 , . . 52'2 ... 55 10 1.0 p.m. 55 W. 3. 52-8 52-3 52-2 ... 52-0 5 5 10 2.30 „ D. W. 3-4. 51*4 51-2 51-2 ... 5P1 • . . 10 5.0 „ Buoy. W. 3-4. 52'5 52-4 52-3 ... 5P8 ... 11 8.30 a.m. 55 W. 1. 52*8 52-7 52-5 ... ... 51-9 ... 11 11.0 „ F. W. 1. 51-2 51-0 5P0 ... 50-9 • . . 5) 11 Noon. E. W. 1. 5D8 51-7 5D5 ... ... 51-0 ... 55 11 1.0 p.m. D. W. 2. 52-0 5P8 51-8 ... ... 51-4 ... 5) 11 2.0 „ Buoy. W. 2. 52-0 52-0 51-8 5P9 11 3.0 „ C. W. 2. 52-8 52*9 52-9 ... 52-4 11 4.0 „ B. W. 2-3. i 53-4 53*3 53*2 53-0 ... 11 5.0 „ A. W. 1. 54-0 53-8 53*6 ... ... 53-0 ... 12 11.0 a.m. Buoy. W. 2-3. 52-0 52*0 52-0 ... 52-0 ... 55 12 5.30 p.m. 55 W. 3-4. 52-0 . • • . . . . . . 52-0 . . . 13 8.0 a.m. 55 W. 3-4. 5P9 51-9 5D9 5D8 ... 13 Noon 55 W. 3-4. 5P9 5P9 51 '9 ... 5D8 ... 15 10.0 a.m. 55 W. 1. 51 -8 51-8 51-7 51-5 ... 15 11.0 „ D. ... 51-8 51-7 51-5 5P4 ... 15 Noon E. 5P8 51-6 5D5 51-0 15 1.0 p.m. E. E. 1. 52-0 51-9 51-5 ... 51-1 ... 55 15 5.0 „ Buoy. E. 2-3. 52-0 51-8 518 ... 5D5 ... 1908-9.] Temperature Observations in Loch Garry. 127 — contimied. 40 45 50 55 60 65 70 75 80 85 90 100 125 140 150 175 200 46-9 45-9 45-2 451 46-9 ... ... 46-1 ... . . . 45*4 . . . 45-1 . . . 45*1 46-6 46-0 ... ... ... 45-4 . . . 45-1 45-0 46-7 ... ... ... . . . 45-8 . . . 45-2 45-1 47-1 46-2 ... i ... 45-4 45-2 . . . 45 ‘2 45-2 46-9 ... ... 45-9 ... . . . 45-4 . . • . . . 45-0 . . . . . . 47-0 ... 46-3 ... . . . 45-8 ... 45-2 45-1 47-0 46-3 ... 456 . . . 453 45-1 47-0 46-3 ... ... ... 45-6 45-4 45-2 45*2 45-1 47-0 45-9 45*3 45-1 ... 47-0 46-3 ... ... 45-5 45-3 . . . 45-2 . . . 45-2 48-4 46-5 ... ... . . . 45-7 • . . 45-3 . . . 45-1 47-4 ... ... 46-2 ... ... . . • 45-5 . . . 45-3 . . . 45-2 46-4 ... ... 45-7 ... ... . . . 45-5 45-4 . . . . . . . . . ... ... 47-8 ... ... ... ... 47-1 ... 46-0 ... ... 45-4 ... 45-7 (160) 45-2 (195) ... 48-5 ... ... ... 47-2 ... 46-2 45-9 ... 45-8 ... ... 47-8 ... ... ... 46-2 ... 46-0 46-0 ... 45-4 45-4 (160) ... 480 • • • ... 46-2 . . . ... . . • 45-9 . . . . . . . . . 48*0 ... ... 47*0 ... ... 46-0 45-8 45-8 45-5 45-5 48-0 ... 47-0 ... ... . . . 463 45*3 45-1 . . . ... 49-0 ... 47-3 ... ... 46-9 46-0 45-5 . . . . . . ... ... 48-8 ... ... 47'3 ... 46-8 ... ... * * * 47-2 * * * 45-7 45-6 45-5 50-9 ... ... 49-0 ... ... 45-9 . . . 45-7 45-5 49-5 ... ... 47-6 ... 467 . . . . . . 48-1 ... ... ... ... 46*8 ... ... 46-0 45-5 45-5 (135) ... , 48-9 ... . . . 47-0 46-4 45-9 . . . . . . 45-8 48-3 ... ... ... ... ... 46-0 46-0 45-9 45-9 45-9 48-7 ... 47-0 ... ... 46-2 46-0 46-0 46 '0 46-0 48-7 ... 46-4 ... 46-2 46-0 45-9 45 9 51-2 ... 48-0 ... ... 46-4 46-0 45-9 45-9 45-9 49-0 46-7 ... ... ... 46-2 46-0 46-0 45-9 45-8 48-0 ... ... 46-8 ... 46-7 ... ... ... . . . . . . ' * * ’ 48-7 ... ... ... ... 46*6 ... 46‘0 45*9 45*9 (145) ... 49-0 ... ... ... 46-9 ... ... ... 460 45-9 45‘7 45-7 (170) 50*0 ... ... ... . . . . . • . . . . . . 46-4 • . . ... 46-0 45 '9 50-6 ... 47-3 ... ... 46-1 ... 45-8 ... 51-0 < ... ... ... 47*7 . . . ... ... 46-4 46-0 45-8 ... ... 51-0 * • . ... 47-7 • . . . . , 46*4 . . . ... . . . ... 50-4 ... ... . , . 47-0 ... ... 46*4 46-0 46-0 45-9 45-9 51-8 ... 47*2 ... 46*5 46-0 46-0 46-0 45-9 51-C ... 47-8 46-8 ... ... 46*3 46-0 46-0 45-9 45-9 51-5 . . . 49-5 470 ... ... 46-4 46-0 46-0 45*9 45-9 51-3 ... ... 47-0 46*7 ... ... 46-3 46-1 46-0 ... 46-0 • • • 51-2 49-4 46-7 ... 46-2 46-0 • « o 46-0 ... 46-0 50-C ... 48-0 ... ... 46-7 ... 46-4 46-0 ... 46-0 49 -4 ... 47-8 47 -C ... ... ... 46-2 ... ... ... , . . ... 51-C ... 47-9 ... ... 46*E ... ... 46-1 460 ... 46-0 46-0 46-0 126 Proceedings of the Royal Society of Edinburgh. [Sess. Loch Garrv Date Hour. Position. Wind. Surface. 5 10 .5 20 25 30 35 1908. May 29 3.0 p.m. Buoy. 610 ... 494 47‘5 „ 30 9.45 a.m. Calm. 57-4 50-0 47-4 „ 30 1.15 „ E. 1. 59 4 49-5 47-IS „ 30 6.15 p.m. Calm. 561 48-0 47 3 June 1 10.0 a.m. E. 1-2. 55-3 534 48-4 „ 1 12.15 p.m. D. E. 2-3. 56-0 55-1 48-6 1 6.30 „ Buoy. E. 1-2. 56-6 52-2 49-0 9.0 a.m. E. 1. 573 538 50 1 „ 3 10.0 „ W. 1-2. 57 4 56-2 oo-l 49-4 3 3.30 p.m. D-E. W. 0-1. 60-1 55 0 490 4.45 „ Buoy. W. airs. 60-3 57-9 49-5 4 3.30 „ W. 3-4. 56-5 55-3 54'0 1.0 „ W. 3. 53-0 530 51-4 „ 5 3.0 „ E. W. 3. 490 48 4 48-0 5 4.0 „ D. W. 4. 52-2 49-6 49-2 . 6 10.0 a.m. D. E. 1 56 0 534 510 ... „ 6 11.0 „ E. 56 0 54-0 „ 6 Noon F. W. 1. 55-3 541 537 „ 6 1.30 p.m. Buoy. W. 1. 56-8 53-6 50-5 6 2.30 „ c. 56-0 52-8 49-6 „ 6 3.30 „ B. 57'5 530 50-2 i, 6 4.0 „ A. 57-6 530 50-5 „ o 4.15 „ A-E. end 573 552 50-7 49 5 8 8.0 a.m. Buoy. \V. 3. 529 529 ... 52-8 „ 8 7.30 p.m W. 2. 52-2 52‘2 51-5 „ 9 11.30 a.m. A. W. 1-2. 54-0 ... 53 5 ... 545, ... 9 Noon. B. W. 2-3 53-7 ... 53-3 49-8 ... 9 4.0 p m. Buoy. W. 2-3 53-1 52-8 50'0 10 10.0 a m. W. 2-3. 52-4 523 52-2 52 -2 „ 10 1.0 p.m. W. 3. 52-8 52-3 52 2 52-0 „ 10 2.30 „ D. W. 3-4. 51-4 51-2 51-2 511 „ 10 5.0 „ Buoy. W. 3-4. 52’5 52-4 52-3 51-8 „ 11 8.30 a.m. W. I. 52-8 52'7 52-5 519 „ 11 11.0 „ F. W. 1. 51-2 51-0 51-0 50-9 „ 11 Noon. E. W. 1. 51-8 51-7 51-5 51-0 „ 11 1.0 p.m. D. W. 2. 520 518 51-8 51-4 „ 11 2.0 „ Buoy. W. 2. 52-0 52-0 51-8 51-9 11 3.0 „ c. W. 2. 52-8 52 9 52 9 52-4 „ 11 4.0 „ B. W. 2-3. 53 4 53 3 53-2 53-0 „ 11 5.0 „ A. W. 1. 54-0 53-8( 53-6 53'0 12 11.0 a.m. Buoy. W. 2-3. 52-0 52-0, 52-0 52-0 „ 12 5.30 p.m. W. 3-4. 52-0 ... 52-0 „ 13 8.0 a.m. „ W. 3-4. 51-9 51-9 51-9 51-8 13 Noon „ W. 3-4. 51-9 51-9 51-9 51-8 „ 15 10.0 a.m. „ W. 1. 51 "8 51-8; 51-7 51-71 51 ’5 51-5 15 n.o „ D. 51-8 51-4 „ 15 Noon E. 51-8 51-6 51-5 51 0 „ 15 1.0 p.m. F. E. 1. 52-0 519 51-5 51 1 „ 15 5.0 „ Buoy. E. 2-3. 520 51-8 51 8 51-5 1908-9.] Temperature Observations in Loch Garry. 127 — continued. 40 45 50 55 60 65 70 75 80 85 90 100 125 140 150 175 200 46'9 459 ... 45-2 451 46-9 461 45-4 45-1 45-1 466 46-0 45-4 45-1 45 0 46-7 45-8 45-2 45-1 47-1 46-2 45-4 452 45-2 45-2 46-9 45-9 45-4 45 0 47-0 463 45-8 45-2 45-1 47-0 46-3 45 6 453 451 47-0 463 456 45-4 45-2 45-2 45-1 47-0 45-9 45-3 45-1 47-0 46-3 45 o 45 3 45-2 45-2 48-4 46-5 45-7 45 3 45-1 474 46-2 45-5 45 3 45-2 46-4 45-7 45 "5 45-4 47-8 47-1 ... 461) 45-4 45-2 (195) 48-5 47-2 462 459 45-8 457 (160) 478 46-2 46 0 46 0 45-4 45'4 (160) 480 46-2 45-9 48-0 47-0 460 45-8 45-8 45-5 45-5 48-0 47-0 46 3 45-3 45-1 490 47-3 46-9 460 45-5 48-8 473 46-8 47-2 45'7 456 45 5 50-9 49-0 45-9 45-7 45'5 49-5 47-6 467 48 1 46-8 46-0 455 45-5 (135) 48-9 47-0 46-4 459 45-8 48-3 46-0 46-0 45 9 45 9 459 48-7 470 462 46-0 460 46-0 460 48'7 46'4 46-2 460 45-9 45 9 51-2 48-0 46'4 460 459 459 45 9 49-0 467 46-2 460 46-0 459 45-8 48-0 46-8 46-7 48-7 46-6 16-0 45-9 459 (145) 49-0 46-9 46-0 45-9 45-7 45-7 (170) 50-0 464 46-0 45-9 50-6 47-3 46-1 458 51-0 47-7 464 460 45-8 5 10 47-7 46-4 50-4 47-0 46-4 460 46-0 45-9 45-9 51-8 47-2 465 460 460 46-0 459 51-0 47-8 46-8 46-3 460 46-0 45-9 45-9 51-5 49-5 47J 464 46-0 460 45-9 45-9 513 47-0 46-7 46-3 46- 1 46'0 460 51-2 49-4 467 462 460 460 460 500 48-0 467 464 460 460 49-4 47-8 47-0 46-2 51-0 47 9 46-5 461 46 0 460 460 460 128 Proceedings of the Royal Society of Edinburgh. [Sess. Loch Garry Date. Hour. Position. Wind. Surface. 5 10 15 20 25 30 35 1908. June 16 9.30 a.m. Buoy. W. 2-3. 51-4 51-4 5P2 51-2 V 16 Noon C. W. 3-4. 51-5 51-4 51-4 ... 51 '4 ... 55 16 1.0 pan. B. ... 52-2 52-0 52-0 ... 51-9 55 16 1.30 „ A. 52-3 52-2 524 52*0 55 16 4.30 „ Buoy. W. 1-2. 52-0 51-9 5P8 ... 5D2 55 17 9.0 a.m. 55 E. 1. 5D9 51-9 5F8 ... 51-3 ... 55 17 5.0 p.m. 55 E. 1. 52-0 52-0 520 5P9 55 18 9.0 a.m. 55 W. airs 52-0 52-0 5P7 51 '1 55 18 1.30 p.m. 55 W. 1. 5P8 5P0 ... 55 18 4.0 ,, D. 55 5 1 *5 . . • 51 '5 5P3 ... 55 ] 8 5.0 „ Buoy. 51‘5 ... 51-5 . . . ... 55 19 10.0 a.m. D. E. airs 5D7 . . . 5P5 ... 55 19 2.0 p.m. Buoy. W. 1. 52-2 51*5 ... 5D4 ... 55 19 5.0 „ D. E. 1. 52-0 51*9 51-9 ... 55 19 6.0 „ Buoy. E. airs 52-0 52-0 5P4 55 20 7.30 a.m. 55 Calm. 52-0 5P9 5P9 51-5 55 20 10.30 „ F. 55 53-3 5P8 51*5 ... 5P1 ... 55 20 11.0 „ E. E. airs 53-8 52-0 51-8 ... 5P1 55 20 Noon D. 54-8 52-0 5F8 5P4 ... 55 20 1.0 p.m. Buoy. Calm. 56-0 52-0 51*8 5P4 55 20 2 0 55 C. 59*4 53-7 52-2 51 8 55 20 3.0 „ B. Variable. 56-0 52-8 52-0 5P2 ... 55 20 3.30 p.m. A. ... 56-8 52-6 52'0 5D5 55 20 5.0 „ Buoy. Calm. 58-0 52-4 52-0 5D4 55 22 10.0 a.m. 55 W. 1. 55-1 54*8 54-2 52-8 5D2 55 22 1.0 p.m. 55 W. 2-3. 54-7 54 A 53-7 51*1 55 22 5.30 ,, 5> W. 2-3. 54-0 53-7 53-4 53-3 51-8 55 23 9.30 a.m. 55 W. 1. 556 55-2 54-2 53-8 53-3 52-0 55 23 1.30 p.m. 55 W. 1. 56-0 55-9 54 8 53-4 53-0 51-9 55 23 3.30 „ E. W. 1-2. 54-0 53-8 53-3 53-0 52-4 51-8 >5 23 4.30 „ D. W. 1-2. 548 54-5 54-2 53-5 52-8 ... 52-0 55 23 5.30 ,, Buoy. AV. 2-3. 55*1 55-0 55-0 54-6 52-8 55 23 8.15 „ 55 54-5 . . . 54-4 53-9 ... 1 55 24 1.0 „ 55 AV. 1. 56-2 56-0 55-5 54-2 53,8 532 ... 55 24 3.30 „ C. W. 2-3. 56-6 56-4 56-2 56-0 544 54-0 ... 55 24 6.0 pin. Buoy. AV. 3. 55-2 55*2 55-0 54-2 . . . 54-0 . . . 55 25 12.30 „ 55 W. 1-2. 55*0 ... 55*0 54-9 54-4 54-0 55 25 4.30 „ D. W. 1-2. 54-6 54*5 54-3 53-5 53-3 ... 55 25 6.0 „ Buoy. W. 1. 55-3 55-2 55-2 55*0 55 26 8.0 a.m. 55 Calm. 58*0 56*5 55-4 55-0 54-8 54J 53-4 52-0 55 26 Noon F. 55 60-0 55-6 55-1 ... 54-5 ... 55 26 1.0 p.m. E. 55 64-0 56-7 55*8 ... 54-8 53-7 ... 55 26 2.0 „ D. 62-0 57-8 56-2 54-9 54*7 53-5 ... 55 26 4.0 „ Buoy. Calm. 64-3 56-3 55*3 54-5 . . . 53-4 55 26 5.0 „ C\ 63-0 56-4 55-1 ... 54-4 ... 52-9 ... 55 26 5.30 „ B. E. airs. 66-5 56*3 55-3 54-9 52*5 ... Ill the printer is not responsible, the expense of such proofs and corrections will be charged against the author. All proofs must, if possible, be returned within one week, addressed to The Secretary , Royal Society , Mound, Edinburgh, and not to the printer. To prevent delay, authors residing abroad should appoint some one residing in this country to correct their proofs. 4. Additions to a Paper after it has been finally handed in for publication, if accepted by the Council, will be treated and dated as separate communications, and may, or may not, be printed immediately after the original paper. 5. Brief Abstracts of Transactions Papers will be published in the Proceedings, provided they are sent along with the original paper, 6. Separate Issue of Reprints; Author’s Free and Additional Copies. — As soon as the final revise of a Transactions paper has been returned, or as soon as the sheet in which the last part of a Proceedings paper appears is ready for press, a certain number of separate copies or reprints, in covers bearing the title of the paper and the name of the author, are printed off and placed on sale. The date of such separate publication will be printed on each paper. The author receives fifty of these reprints free, and may have any reasonable number of additional copies at a fixed scale of prices which will be furnished by the printer, who will charge him with the cost. To prevent disappointment, especially if the paper contains plates, the author should, immediately after receiving his first proof, notify to the printer the number of additional copies required. 7. Index Slips. — In order to facilitate the compilation of Subject Indices, and to secure that due attention to the important points in a paper shall be given in General Catalogues of Scientific Literature and in Abstracts by Periodicals, every author is requested to return to the Secretary, along with his final proof, a brief index (on the model given below), of the points in it which he considers new or important. These indices will be edited by the Secretary, and incorporated in Separate Index Slips, to be issued with each part of the Proceedings and Transactions. MODEL INDEX. Schafer, E. A. — On the Existence within the Liver Cells of Channels which can be directly injected from the Blood-vessels. Proe. Roy. Soc. Edin., vol, 1902, pp. Cells, Liver, — Intra-cellular Canaliculi in. E. A. Schafer. Proc. Roy. Soc. Edin., vol. , 1902, pp. Liver, — Injection within Cells of. E. A. Schafer. Proc. Roy. Soc. Edin., vol. , 1902, pp. IV CONTENTS. NO. PAGK VIII. Temperature Observations in Loch Garry (Inverness-shire). With Notes on Currents and Seiches. By E. M. Wedderburn, LL.B., W.S., . . ... . .98 {Issued separately , 1909.) u The Papers published in this Part of the Proceedings may be had separately, on application to the Publishers, at the follow- ing prices: — - No. IV., Price 6d. No. V., . ,, 6d. No. VI., 00 No. VII., . ,, 6d. No. VIII., . ,, 2s. 2d. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SESSION 1908-9. Part III.] VOL. XXIX. [Pp. 129-192. CONTENTS. NO. PAGE IX. On the Conditions for the Reversibility of the Order of Partial Differentiation. By W. H. Young, Sc.D., F.R.S. ( Com- municated by J. H. Maclagan Wedderburn, D.Sc.), . 136 {Issued separately March 2, 1909.) X. Laboratory Note on a Study of Polarisation by means of the Dolezalek Electrometer. By A. F. Ewan, Physical Laboratory, Edinburgh University. ( Communicated by Professor J. G. MacGregor), . . . . . . .165 {Issued separately April 12, 1909.) XI. A Special Form of Photographic Camera for Recording the Readings of the Scales of Scientific Instruments. By James Robert Milne, D.Sc., . . . . . . 176 {Issued separately April 17, 1909.) XII. On an Improved Form of Magnetometer and Accessories for the Testing of Magnetic Materials at Ditferent Temperatures. By James G. Gray, B.Sc., Lecturer on Physics in the University of Glasgow, and Alexander D. Ross, M.A., B.Sc., Assistant to the Professor of Natural Philosophy in the University of Glasgow. {Communicated by Professor A. Gray, F.R.S.), ...... 182 {Issued separately April 17, 1909.) EDINBURGH : Published by ROBERT GRANT & SON, 107 Pkinces Street, and WILLIAMS k NORGATE, 14 Henrietta Street, Covent Garden, Lon MDCCCCIX. Price Three Shillings and Sixpence. REGULATIONS REGARDING THE PUBLICATION OF PAPERS IN THE PROCEEDINGS AND TRANSACTIONS OF THE SOCIETY. The Council beg to direct the attention of authors of communications to the Society to the following Regulations, which have been drawn up in order to accelerate the publication of the Proceedings and Transactions, and to utilise as widely and as fairly as possible the funds which the Society devotes to the publication of Scientific and Literary Researches. 1. Manuscript of Papers. — As soon as any paper has been passed for publication, either in its original or in any altered form, and has been made ready for publication by the author, it is sent to the printer, whether it has been read or not. The ‘ copy ’ should be written on large sheets of paper, on one side only, and the pages should be clearly numbered. The MS. must be easily legible, preferably typewritten, and must be absolutely in its final form for printing ; so that corrections in proof shall be as few as possible, and shall not cause overrunning in the lines or pages of the proof. All tables of contents, references to plates, or illustrations in the text, etc., must be in their proper places, with the page numbers left blank ; and spaces must be indicated for the insertion of illustrations that are to appear in the text. 2. Illustrations. — All illustrations must be drawn in a form im- mediately suitable for reproduction; and such illustrations as can be reproduced by photographic processes should, so far as possible, be preferred. Drawings to be reproduced as line blocks should be made with Indian ink (deadened with yellow if of bluish tone), preferably on fine white bristol board, free from folds or creases ; smooth, clean lines, or sharp dots, but no washes or colours, should be used. If the drawings are done on a large scale, to be afterwards reduced by photography, any lettering or other legend must be on a corresponding scale. If an author finds it inconvenient to furnish such drawings, the Society will have the figures re-drawn at his expense ; but this will cause delay. When the illustrations are to form plates, a scheme for the arrangement of the figures (in quarto plates for the Transactions, in octavo for the Proceedings) must be given, and numbering and lettering indicated. 3. Proofs. — In general, a first proof and a revise of each paper will be sent to the author, whose address should be indicated on the MS. If further proofs are required, owing to corrections or alterations for which [Continued on page iii of Cover. 1908-9.] Temperature Observations in Loch Grarry. 129 — continued. 40 45 50 55 60 65 70 75 80 85 90 100 125 140 150 175 200 51-1 51-0 48-2 47*6 460 46-0 46-0 46-0 46-0 ... ... 51-2 ... 51-2 ... 50-0 47-0 ... 46-2 46-1 45*4 ... • • • ... ... 51-6 ... ... 49-1 ... 46-3 46-0 (135) ... ... ... . . . 51-8 . . • . . . ... . . . 500 ... 46*5 ... • . • ... 510 ... 50-8 ... ... 47*1 46-1 46-0 45-9 ... 45-9 ... ... 51*0 ... 49-0 ... 47-5 47-0 463 46-0 46*0 46-0 46-0 ... 51-0 ... 49*0 ... ... 47-8 ... 46-4 46-0 46-0 ... 46-0 ... 50-5 ... 49*1 48-5 47'6 46'2 46-0 46-0 46-0 46-0 ... 50*5 ... 49-0 48-5 47-4 46-2 46-0 ... ... 46-0 51-0 ... 48-9 47 2 46-5 46 '2 46-1 46-0 ... 46 0 ... 49-8 ... 495 49-0 47-2 46-4 46-0 46-0 ... 46-0 ... 50*2 ... ... ... 47*1 46-3 46*0 ... ... 46-0 ... 50-5 ... 49*4 48-5 47-5 47-5 46*4 46-0 ... ... 46-0 ... 49-9 ... 49-1 ... 47-8 474 ... 46-0 ... ... ... 46-0 (190) ... • . • . . . 50-6 • . . ... 49-4 48-0 47-4 46-4 46-0 ... ... ... 46-0 ... ... 50-9 ... 49-1 48-5 47-3 ... 46*2 46-0 46*0 . . . 50-6 47*4 ... 46*2 46-2 ... . . . ... ... 50-5 47-7 ... 465 46-2 46-0 46-0 (145) . . . ... 50-8 49-3 ... 46 5 ... 46-1 46-0 ... 46-0 (190) . . • . . . 50-8 . . . 49-1 ... . . . 47-5 46-3 46-0 ... . . . ... 46-0 . . . 50*3 ... 49-5 ... ... 47-8 ... 46-6 46-0 46*0 . . . ... 50-4 ... 49-2 ... 47-4 46-2 46-0 46-0 (135) ... . . . ... ... 49-1 48-8 ... 47'0 (95) ... ... ... • . • 50*0 49*5 ... ... 47-2 ... 46-2 46-0 ... ... 46-0 ... . . . 49-8 ... 48-1 ... 47-3 ... 46-2 46-2 46-2 46-0 46-0 • . . 50-6 ... ... 49-0 ... 484 ... 46*4 46-2 46-0 46-0 46-0 ... ... 50-6 ... 49-8 ... 48-3 ... 46-4 46-2 46 0 46-0 46-0 . . . . . . 50-4 ... ... 48-5 ... 47-6 ... 463 46-2 46*0 46-0 46-0 ... . . . 50%3 ... ... 48-5 ... 47*7 ... 46-3 46-1 460 46-0 46-0 ... . . . 49-3 ... ... 47-0 46-9 ... 46-3 46*0 ... . . • 52-0 ... 50-0 ... 48-9 ... ... 46*8 ... 46-2 46-1 46-0 46-0 46-0 (185) 51-4 . . . 50-0 ... ... ... ... 47*6 46-4 46-2 46-0 46-0 46-0 ... ... 50'6 ... ... ... ... 47*1 46-3 ... ... ... 46*1 51-1 ... 50-4 ... 498 ... ... 47’6 46-3 46*1 461 46.0 46-0 51-7 ... 50-9 ... 49-9 ... ... 48-2 46-3 46-2 46-0 46-0 • . . 51*0 ... 50’8 ... 49-2 ... ... 47’5 ... 46-3 46’2 460 46*0 46-0 52 5 50-4 ... ... 48-3 ... 47-0 ... 46-1 46-1 46-0 ... 46-0 51-8 ... 49 5 ... 48-0 ••• • 47*0 ... 46-3 46*1 46-0 46-0 (190) ... 53*5 ... 50-5 ... 48-7 ... ... 47-0 46-2 46-1 46-0 . . • 46-0 51*0 50-3 50*0 49-5 48*5 48-1 47-4 47*0 46-3 46-1 460 460 46-0 53-0 504 48*4 47-5 46-7 ... ... 46-4 46*2 ... . . , ... . . . . . . 52*2 ... 50-0 49*0 ... 47-0 ... 46-8 46-3 ... 46-0 ... ... 52-1 ... 50-1 49-2 ... 47-8 46-8 46-1 ... 46-0 46-0 . . . 51-0 ... 50-2 ... ... 48-0 47*2 46-1 46-0 ... ... 46*0 51*0 ... 50-0 ... 48-9 ... ... 47*7 ... 463 46*1 46-0 (165) ... ... 51-0 ... 50-0 ... 48*8 . . . ... 47*0 ... ... . . . 46-1 46-0 (135) . . . . . . • • * VOL. XXIX. 9 130 Proceedings of the Royal Society of Edinburgh. [Sess. Loch Garry Date. Hour. j Position, Wind. Surface. 5 10 15 20 25 30 35 1908. June 26 6.30 p.m. A. 65-8 56-0 55-0 54*0 52-3 55 27 10.0 a.m. Buoy. Calm. 65-6 57-9 55-4 55*0 54-8 54-0 533 52-7 >> 27 4.0 p.m. 55 W. 1. 64*0 59-8 ... 54-9 54*4 54-0 53-4 52-8 55 28 2.0 „ Buoy. E. 1-2. 59-5 59-5 57-5 55*7 54-8 53-9 53-3 52-0 55 29 10.0 a.m. 55 E. 1. 62-2 60-5 59-1 58-0 55-4 54-8 53-0 51*8 5? 29 4.0 p.m. 55 E. 3. 60-8 60*4 59-0 57-9 56-0 55-0 53-9 , . . 55 30 11.30 a.m. 55 E. airs. 63-4 62*0 6F7 58-5 55-9 55-0 53-2 52-8 55 30 3.30 p.m. 51 E. 1. 64*0 63-0 60-7 58 0 ... 54-9 ... 52-5 July 1 9.30 a.m. 55 rH|0‘ 1 o 66-6 63-3 62-8 59-0 56-0 54-2 53-0 51*2 55 1 3.30 p.m. D. Calm. 72-0 64-0 59-2 57-4 56-0 55-0 540 53 0 *5 1 5.30 „ Buoy. W. 1-2. 704 63-8 60-4 57*9 56-2 55-0 54*4 52-7 5? 2 8.30 a.m. 55 Calm. 67*4 65-8 63-0 57-8 55-4 54-7 54-0 52-3 55 2 11.15 „ 5i 55 70-2 65-6 62 *0 57-6 56-0 55-0 54*0 53-0 i 5 3 10.30 „ F. E. 1. 69*7 69*4 69-0 58-8 56-9 55-3 54*1 530 55 3 Noon. E. E. 2. 69‘8 69-5 62 6 58-0 56-5 55-4 54-3 53-8 55 3 1.45 p.m. D. ... 69-0 68-8 63-0 58-1 57*0 55*3 545 533 55 3 3.45 „ Buoy. E. 3. 66-5 65*4 59-3 57-2 56 8 55-0 52-6 51-5 55 3 6.0 „ C. E. 2-3. 64*6 46-2 62-0 57 '1 55*3 53-7 52-3 5F8 55 4 10.15 a.m. A. E. 1. 66-4 66-0 64-0 60*5 53-9 • . . 5 5 4 11.0 „ B. E. 2. 66-4 ... 63-5 ... 56-9 53-7 ... I ” 4 N oon C'. E 2-3. 67-1 67*0 62-7 58*7 56-0 53-6 52-0 51*0 55 4 3.0 p.m. Buoy. E. 3. 65-6 65-4 62-6 57*8 56-1 54*8 53-7 53-0 5 5 4 4.30 „ D. E. 3-4. 65*8 65-8 65-5 62-8 58-8 55*9 54-5 52-8 55 6 9.45 a.m. Buoy. Calm. 66-6 65*3 64*5 60-9 59-0 55*1 52-6 52-3 55 6 1.15 p.m. 55 55 68*3 65-8 63-0 6F3 58-4 555 53-5 52-8 ” 6 4.0 „ O'. E. 1. 67-7 65-5 63-5 62-4 59-0 55 0 53-2 52-0 55 7 10.0 a.m. Buoy. 55 64-5 64-1 63*5 60-7 59-9 55-2 53-8 52*0 111 5 5 7 Noon D. Calm. 65*1 64-6 63-1 6F3 60*4 55*4 54-6 53-2 55 7 5.0 p.m. C. W. airs. 64-6 64*5 64-0 60-8 60-0 57 3 55-0 53*9 V 8 7.0 a.m. D. E. airs. 63-8 63-8 637 61*3 58-4 550 54-0 530 8 8.30 „ E. E. 1. 64-4 64*3 64*3 61*1 60-0 55-0 53-5 52-2 55 8 10.0 „ F. E. airs. 64-3 64-3 63-6 62-3 59-7 55*0 537 52-4 55 8 2.30 p.m. Buoy. O'. E. 1. 63*7 63-7 63*4 59-4 55*1 53-1 52-4 55 8 3.45 „ E. 2. 63-0 63-0 62-3 58-0 56-9 54*5 53-0 52-1 5J 8 5.30 „ B. E. 2. 62*4 62-0 590 58-7 55-3 53*3 52-2 51-5 55 8 6.45 „ A. E. 1. 62-0 62-0 58-0 56-0 55-3 53-4 52-6 51-5 55 9 9.30 a.m. B. E. 1. 61-0 61-0 61-0 60-9 58-5 55*9 54-0 52-1 55 9 11.30 „ ,, E. airs. 6F0 61*0 6F0 60*0 57-8 55*7 54-0 53-3 55 9 1.30 „ 55 E. airs. 6F9 6F3 61 *0 60-5 58-9 56*7 54-7 53*4 55 9 4.0 p.m. Buoy. E. 1. 62*7 ... 6F9 56-4 54-6 • • . 52*2 55 9 5.30 „ B. E. 1. 61-5 • • • ... 60*0 57-1 54-8 ... 52-0 55 10 7.0 a.m. „ E. 1. 60-6 60-6 60-5 59-2 55-8 52-6 52-0 50-7 55 10 8.0 „ 55 E. 2-3. 60-5 60-5 60-4 58*7 54-0 52-0 50-9 50*5 55 10 9.0 „ 55 E. 2. 60*3 60*2 60-1 55-0 53-0 52-0 50*3 50*0 55 10 10.0 „ 55 E. 3. 60-0 60-0 59-8 53*4 52-0 5 10 505 49-0 55 10 n.o „ 55 E. 2-3. 59-5 59-4 53*8 52-0 51*2 50-5 49*8 502 55 10 Noon. 55 E. 2. 58-3 58*0 58*0 52-0 51-0 50 8 49-9 49*0 55 10 1,0 p.m. 55 E. 1. 55*5 55-2 54:9 54-0 53-6 51-2 51*0 50-8 55 10 2.0 „ 55 E. 1-2. 57*5 55*9 543 54*1 54-0 53-0 5F4 51*2 55 10 3.0 „ 55 E. 2. 56*6 55'5 54-3 54-0 53-9 53-7 52-0 520 1908-9.] Temperature Observations in Loch Grarry. 131 — continued. 40 45 50 55 60 65 70 75 80 85 90 100 125 140 150 175 200 51-1 50-0 490 470 ... 51-5 ... 50-4 490 480 ... 460 ... ... ... 46-4 46*1 ... 460 460 460 51-1 499 49-2 470 ... 460 ... ... ... 46-3 46-2 ... ... 460 460 50-9 ... 50 0 49-4 48-2 47 -4 ... 46-5 46*2 ... 460 460 460 50-7 50-3 494 480 47-4 470 46*7 ... ... 46-4 46*2 ... 46-1 460 460 51-0 50-8 50-0 480 470 46-8 ... 463 46-2 ... 461 ... 460 51-5 50 1 50-0 490 480 47-9 47-1 47-1 ... 46-5 46-3 46 0 460 460 ... 498 48-8 480 ... ... 470 ... ... 46-4 46-4 ... 46-2 46-1 510 50-1 49-4 48-8 480 47-7 47-5 470 ... ... 470 46'2 ... 46-2 46-1 46-1 514 50-8 500 493 480 47-9 47-2 46-8 ... 46-4 46-2 ... 46-1 460 ... 514 50-5 500 48*8 48-3 47*4 47-1 46-7 ... 46-4 46-2 ... 46-2 46-1 461 510 50-5 50-2 49-5 48-8 47-8 47-3 46-3 ... 46-2 46-1 ... 464 46-1 46-1 51-7 51-0, 50-4 49-8 49-4 ... ... 47-1 . . c 46-5 . . . ... 46-1 ... 52*8 52-0l 51-0 500 50*4 49-3 480 460 ... 46-7 ... . . . ... ... ... 53-0 52 3 510 50-5 49-7 490 484 47-3 ... ... ... 46-4 46-3 ... ... ... ... 53-0 51-0 504 49-4 480 47-5 ... 470 . . . ... ... 460 ... 46*3 ... ... 51-2 50-4 500 490 48-4 47-7 47-5 470) . . . 460 46-2 ... 46-2 46-1 46-1 51-0 50-8 500 490 48-8 48-5 47*8 470 . . . ... 470 46-5 46-4 ... ... ... 49-0 470 460 . . . 46-7 ... ... ... ... ... 49-8 47-4 46-8 46-5 ... . . . 46 ‘5 46-3 ... ... 50-7 50-0 490 480 47-1 470 460 460 ... ... 46*5 46-3 ... 46-2 46 2 ... 52-0 50-7 500 480 48-2 47-7 47-5 47-2 46-7 46-5 46 3 (165) 46-2 46-2 51-7 50-3 490 48-2 470 470 460 460 . . . ... 46-7 46-5 ... 46-3 46*2 ... 51*4 50-6 49'5 48-8 47*4 47-4 470 460 464 46-3 ... 46-3 46'2 46-2 51-6 50*5 49-4 480 470 47-8 47-3 47-1 ... 460 460 ... 46-3 46-2 46*2 51-6 50-6 493 49-2 48-2 47 8 470 470 ... ... 46*5 46-4 ... 46-2 46*2 ... 520 51-0 49-7 490 47-8 47*3 470 470 465 46-3 46-3 (170) 46-2 46-2 52-8 51-7 510 500 48-9 48-2 470 470 ... ... 46*7 46-5 ... 46-5 463 ... 53-0 520 50-4 49-7 490 480 470 474 46-5 46-2 ... o • • ... ... 51*5 51-0 50*2 490 480 47-7 47-4 470 ... 46-8 46-5 ... 46-4 46-3 ... 52-0 51-0 500 48*8 48-2 480 460 46-8 46-5 46-4 (180) 52-0 50-8 490 480 480 47-8 470 47 0 ... ... ... 46-5 ... 51-4 51-0 50’] 49-5 48-7 480 47-5 470 (95) 46-5 46-4 46-4 46-3 46-3 51-9 51-0 500 49-1 48*4 480 47-3 46*9 ... ... ... 46-4 46*3 ... 46-3 ... ... 51-0 50-6 500 490 484 470 47-4 470 ... ... 46-5 463 ... ... 51-0 50*2 500 49-2 480 48 0 (135) 51-9 50-7 500 48-7 47-4 47-2 470 470 ... ... ... 53-1 52-0 50-3 49-5 48-5 48-1 47-1 460 ... ... ... 53-0 52-0 50-8 49-5 490 480 47-4 470 ... ... ... ... 50-8 50-2 49-8 ... 48-3 ... 47-4 ... ... 460 ... ... 46*1 • • . 50'8 49-2 490 ... 474 ... 46-2 ... ... ... 50-1 49’8 480 470 47*3 470 460 460 ... ... 460 ... 50-2 49*4 480 470 ... 47-2 46-7 ... ... ... 49-9 48'5 470 47*3 ... 470 470 ... ... 50-0 48-6 480 47-4 ... 470 ... 46-7 ... ... ... ... ... 48-8 48-0 47*4 470 ... 46-8 460 ... 46-3 49-0 48-8 48-2 470 ... 470 460 ... 46*4 ... ... ... 50-6 50-0 48-9 47-9 47-1 46-8 ... ... 46-5 ... ... 51 "1 509 50-3 480 ... 480 ... 47-4 ... ... 46-7 ... ... 52-0 51-4 50-8 50-3 49-8 490 ... 470 ... ... 470 ... ... ... ... ... 130 Proceedings of the Royal Society of Edinburgh. [Sess. Loch Garry I Date. Hour. Position. Wind. surface. 1908. 6.30 p.m. A. Calm. 65-8 „ 27 10.0 a.m. Buoy. 65‘6 27 W. 1. 64-0 28 2.0 „ Buoy. E. 1-2. 595 29 10.0 a.m. E. 1. 62*2 " 29 4.0 p.m. „ E. 3. 60-8 „ 30 11.30 a.m. „ E. airs. 63-4 30 July 1 ,. 1 3.30 p.m. 9.30 a.m. ” E. 1. E. 0-4. 64-0 66-6 3.30 p.m. L). Calm. 72-0 5.30 „ Buoy. W. 1-2. 70 4 2 8.30 a.m. Calm. 674 " 2 11.15 „ „ 70-2 ., 3 10.30 F. E. 1. 69-7 3 Noon. E. E. 2. 69-8 3 1.45 p.m. D. 69-0 „ 3 3.45 ,, Buoy. E. 3. 66-5 „ 3 6.0 C. E. 2-3. 64-6 „ 4 10.15 a. in. A. E. 1. 66-4 „ 4 11.0 .. B. E. 2. 66-4 „ ^ Noon C'. E 2-3. 67-1 V 4 3.0 p.m. Buoy. E. 3. 656 „ 4 4.30 „ D. E. 3-4. 65-8 „ 6 9.45 a.m. Buoy. Calm. 666 „ 6 „ 6 1.15 p.m. 4.0 „ c” E.”l. 683 67-7 7 10.0 a.m. Buoy. 64-5 7 Noon D. Calm. 65-1 ' 7 5.0 p.m. C. W. airs. 64-6 8 7.0 a.m. D. E. airs. 63-8 „ 8 8.30 .. E. E. 1. 64-4 ” 8 10.0 „ F. E. airs. 64-3 i » 8 2.30 p.m. ; Buoy. E. 1. 63-7 „ 8 3.45 C'. E. 2. 63 0 s 5.30 „ B. E. 2. 62-4 6.45 „ A. E. 1. 62 0 „ 9.30 a.m. B. E. 1. 61 0 11.30 „ E. airs. 61 0 1.30 „ E. airs. 61-9 „ 4.0 p.m. 5 Buoy. E. 1. 627 5.30 „ B. E. 1. 61-5 i, v K 7.0 a.m. i ,, E. 1. 606 1( 8.0 „ • E. 2-3. 605 1( 9.0 „ „ E. 2. 60-3 „ 1 10.0 „ E. 3. 60-0 „ 1 11.0 „ „ E. 2-3. | 595 „ 1 Noon. E. 2. 583 1 1.0 p.m. „ E. 1. 55*5 „ 1 2.0 „ „ E. 1-2 57-5 1 » 1 3.0 „ ” E. 2. 56-6 5 10 15 20 25 30 35 — 560 55-0 54-0 52-3 57-9 55-4 55-0 54-8 54'0 53 3 52-7 59-8 54-9 54-4 541 53 4 52-8 595 57 5 55-7 54-8 53-9 53 3 521 60-5 59-1 58-0 55 4 54-8 531 51-8 60-4 59-0 57-9 56-0 55-0 539 62-0 61-7 58 5 55 9 55 D 532 52 8 630 60-7 58 0 ... 54-9 52-5 63-3 62-8 59-0 56 0! 54 2 531 51-2 64-0 592 57-4 56-0! 55-0 541 53 0 63-8 60-4 57-9 56‘2 551 54 4 527 65 8 630 57-8 55-4 54-7 541 523 65-6 62-0 57-6 561 551 541 531 694 690 58-8 56-9 553 54-1 530 695 02 58-0 56 '5 5 5 '4 543 53-8 68-8 63 0 58-1 571 55-3 545 533 654 593 57-2 56 8 551 52-6 51-5 46-2 620 57-1 553 537 52 3 51-8 66-0 64-0 60-5 531 635 561 537 67-0 62 7 58-7 561 536 521 511 65-4 62-6 67-8 56- 1 54-8 537 531 65-8 655 62-8 58-8 551 54-5 528 65 3 64 5 60-9 59-0 55 ‘1 j2'6 523 65-8 63-0 613 584 555 535 52-8 655 63-5 62 4 591 551 532 521 64-1 63-5 60-7 599 551 53-8 521 64-6 63- 1 61 3 60'4 55- 54-6 532 64-5 64-0 60-8 601 57 3 551 531 63-8 637 613 58-4 55 0 541 530 64-3 64-3 61 1 601 551 53 5 52 2 643 63 6 623 597 551 53-7 52-4 63-7 63 4 594 551 531 52-4 63 -C 62-3 58-0 561 54-5 53 0 521 62 -C 59C 58-7 553 53 3; 521 51-5 62-C 581 561 55-3 53 4. 521 515 611 611 601 58-5 551 541 521 611 611 601 57 8 557 541 53 3 61 1 611 601 581 56-7 54 " 53 4 611 56‘< 54-6 52-2 601 57' 54-8 521 60- 60- 595 551 52 6 521 507 1 60- 60- 58- 541 521 50- 50-5 60- 60- 55- 531 521 50- 501j 60- 59- 53- : 521 511 50- 491 59- 53- 52- 511 50-5 49- 50 2 58- 58- 52- 511 50 8 49' 491 55- 54 54' 53- 512 51- 50-8 55- 9 54 54‘ . 54- 531 51- 51-2 55*5 54- 3 54- 53- 53-7 52- 521 1908-9.] Temperature Observations in Loch Garry. — continued. 131 40 45 50 55 60 65 70 75 80 85 90 100 125 140 150 175 200 51-1 501 491 47 0 51-5 50-4 491 481 46 9 46-4 46-1 461 461 46-0 51 -1 491 49-2 471 461 46-3 462 461 461 501 50 C 48-2 47-5 20 Noon. E. W. 1. 58*6 58-6 58-5 58-4 56-3 54-8 52-8 51*2 >> 20 2.0 p.m. D. W. 2-3. 58-8 58 *8 58-7 58*5 58-5 S 58’5 54-6 53*2 1908-9.] Temperature Observations in Loch Garry. 133 — continued . 40 45 50 55 60 65 70 75 80 85 90 100 125 140 150 175 200 51*5 51-3 51'0 50-8 50'1 49-8 49-3 48-8 47*0 52-3 51-6 51-4 51*3 50-9 50-5 50-2 50-0 ... . . . ... ... 53 0 52*3 52-0 51-9 5M 51-0 51-0 50-3 ... ... ... ... ... ... 53 7 53-7 53-0 52-7 52-2 52-0 51-3 50-0 ... 47*2 46*6 ... ... 54'0 53 9 53-1 52-6 52-0 51 ‘2 506 49-0 ... 47*2 ... ... ... ... ... 53 7 537 53-0 52-3 51-3 51-2 48-9 47-8 47-2 47*1 47*0 ... ... ... ... 53-1 53-0 51-2 • . . 49-0 48-2 48*2 47*7 47-0 46*8 46*8 ... ... ... ... 50-8 50-5 497 48-3 48-0 47-1 47-1 474 47*1 46*8 46*7 ... ... ... ... 51-7 51-3 50-7 49-0 48-2 47-3 47-0 47-0 46-8 46*8 467 ... ... 533 53-2 51-7 50-4 49-0 47*7 47-3 47-1 47-0 46*9 46*5 ... ... 54-2 53-8 52-0 51 '0 49-9 48-2 47-4 47-2 47-0 46*9 46*7 ... ... 54-2 53-0 52-3 51-1 490 48-2 47-4 47-1 ... 47*0 46*7 ... ... ... ... 52-9 51-8 51-0 49-9 48-5 47-7 471 47-0 46-9 46*8 46*5 ... ... ... 52*0 51*9 50-3 49-0 47-5 47-2 ... 47-0 469 46*8 46*5 46*5 ... ... ... 51-5 50-0 48-9 47*7 470 47-0 47-0 47*0 47-0 46*7 46*5 ... ... ... ... 50'2 48-8 48-3 47-2 47-0 47-0 47-0 47-0 47*0 46*8 46*5 ... ... ... ... 49-0 48-1 47-9 47*8 47-2 47-0 46-9 46 9 46-9 46*9 46*5 ... ... . . . 49-0 47-5 47 4 47-1 47-0 47-0 46-9 46-9 46-8 46*8 46*5 ... ... 49-0 48-9 47-4 47-2 47-0 47*0 470 47-0 47-0 46*7 46*5 46*4 ... ... ... 49-0 48-5 47-6 47-3 47-0 46*9 46-9 46-8 46-7 46*7 46*5 ... ... ... ... 49-0 48-9 48-0 47*4 47-1 47-0 46*9 46-9 46-9 46*8 46*5 ... ... ... ... 50 2 50-0 49'6 49-0 48-0 47-3 47-1 47-0 47-0 46*7 46*5 ... ... 51-2 51-2 50-5 50-0 49-5 48-0 47-4 47-0 46-9 46*9 46*5 ... ... ... ... 51-4 51-3 51-0 50-8 50-2 49-8 49-2 48-3 47-2 47*0 46*8 ... ... ... ... 51-9 50-8 50-2 49-4 48*8 47*7 47-3 47-0 47-0 47*0 46*6 46*6 46*4 46*4 46*4 51-2 50-7 50-2 49-3 48-2 47-8 47-3 470 47-0 47*0 46*7 46*4 46*3 46*3 46*3 51-8 50-7 50-2 49-4 48-2 47-9 47-3 47*2 47-0 46*9 46*7 ... ... ... ... 53-4 51-7 50*5 49-7 48-8 47-5 47*2 47-2 47-0 47*0 46*8 46*8 46*4 ... 46*3 52-7 51-1 50-4 49-8 48-7 47*4 47*1 47-1 47-0 47*0 ... 46*7 ... ... ... ... 52-5 51-2 50-8 49-4 48-2 47 '5 47-2 47-0 470 47*0 46*7 ... ... ... 52-8 509 50-6 49-5 48-0 47-8 47-6 47-2 47-0 47*0 46*7 ... ... ... ... 51 *4 50-3 50-2 ... 48-9 48-4 48-0 47-7 47-3 47*0 46*7 ... ... ... 52-4 . . . 50-7 . . . 49-3 ... 47-9 ... 47-2 47*0 47*0 ... ... 51-7 51-0 50-9 50-1 49-4 48-7 47-9 47-7 47-5 47*0 46*7 46*5 46*5 46*4 46*4 51-8 50*7 50-7 49-9 48-6 48*4 47*8 47-3 47-2 47*0 46*5 ... ... ... ... 52-2 51-2 . . . 50-7 50-0 ... 47*4 47*0 ... ... ... 52-5 51-6 ... ... ... ... ... ... 52-7 52-4 51-0 47*3 ... 46*7 46*7 ... ... ... ... 52*0 49-6 47-3 47-0 46*6 46*6 ... ... ... 51-3 49-3 474 ... 47-0 46*8 46*8 ... ... 51-0 47-4 47-0 47-0 ... 46*9 46*6 ... ... ... ... 50-7 48*7 47-8 47-0 46*8 46*8 ... ... ... . . . 50-9 493 47-8 47-0 46*7 46*7 ... ... ... 51-5 49-8 47-8 ... 47 0 46*8 46*6 ... ... ... 51-9 49-8 48*2 47-2 ... 46-9 46*7 ... ... ... 54-0 51-0 ... 49-2 47-7 46*6 46*6 ... 50-3 ... 51 '5 51-0 50-0 49-4 48-4 47-9 47-3 47-0 47-0 469 46*4 ... ... ... 52-0 51-2 50-2 49-2 48-8 48-0 47-3 47-0 47-0 46*9 46*6 ... ... 46*4 5T2 50*4 49-6 484 47-7 47*4 47-0 47-0 47-0 46*9 46*6 46*5 46*5 46*4 46*4 516 51-4 49-0 48-0 47*5 47-2 47-0 46-9 46-8 46*7 46*5 ... ... . . . 50-2 49-6 49*4 48-4 47-3 47-0 46-8 46-7 46-7 46*6 46*6 46*5 ... ... 52-3 51-7 504 49*0 47-9 47*5 47-3 47-0 46-9 46*8 46*7 46*5 46*5 46*4 ... 132 Proceedings of the Royal Society of Edinburgh. [Sess. T.nPH frARRV Date. Hour. Position. 1 Wind. Surface. ‘ 10 15 20 | 35 30 1 35 1908. ' B. E. 2. 56-0 557 55* 54-2 54-0 539 53 0 520 E. airs. 56 5 561 559 55-0 549 54 8 53-6 52-3 6.0 ., E. airs. 58-0 57-0 563 56-0 550 53-8 53*1 53 0 Calm. 58-8 583 575 57-0 55-9 548 538 53-8 Calm. 591 58-8 57-5 57 2 568 558 55 0 54-8 9.0 „ E. 0-1. 59-0 58-8 583 58-0 57-3 55 -7 55-0 54-6 E. 0-1. 58-9 58-8 58 2 58-0 57-1 560 551 54-7 Calm. 58-8 58-6 58-0 57-8 56-8 55-0 528 51-4 ” 3.0 „ Calm. 59 0 58-8 58 3 58-0 57-0 560 54-9 52-7 4.0 " Calm. 59-0 590 58-8 586 58*0 57-3 55 8 54-8 E. 0-1. 59-7 59 3 59 0 58-5 58*2 67-3 56-5 560 6.0 „ 599 59-8 59-1 58-0 57 6 56-2 7.0 „ E. airs. 60-0 59 4 59-0 58-6 57'9 57 3 56‘5 54-7 8.0 „ E. 1. 601 59-2 58-7 58-6 58-3 57-7 57-0 54-4 9.0 „ 603 60-1 59 5 59-0 58-5 58-0 56-6 53 0 11 10.0 „ E. airs. 605 60-5 59-5 58*9 58-1 57-5 55'1 51-8 11.0 „ E. 1. 60-3 60-3 594 58’3 57-9 57-0 53*5 51-2 60-5 600 59 0 58-4 58-0 54-7 520 51-9 E. 2. 60-2 600 59-8 58-7 58-0 55-0 51-7 503 2.0 ,, E. 2-3. 60-2 60-0 59 6 583 56-8 53-0 51 0 49 5 11 3.0 „ E. 2. 59-8 59-7 59 -7 58-8 55 '5 52-9 510 49-9 4.0 „ 59-7 59-5 59-0 55 1 530 52-1 51-3 50-5 11 5.0 E. 1-2. 59-2 59-2 58-5 55 '5 53 0 523 52-0 51-4 11 6.0 „ E. 2. 590 58-9 58-7 55’5 53-3 532 52-0 518 12 10 0 a.m. Buoy. E. 1. 61-3 61-3 60 '8 606 597 58-5 55-3 53-3 E. 2-3. 589 5-89 58-8 58-8 58-8 58-7 57-0 52-5 13 4.30 „ E. 2-3. 58-8 58-8 58-8 58-8 58-8 58-7 57 4 52-9 14 11.0 a.m. Variable. 59-4 59-4 593 58-7 58-4 57-8 55-7 536 14 Noon. E. 1. 59-4 59 3 59-3 59-0 58-4 579 54-8 53-9 14 1.30 p. m. 60-0 596 59'0 58-5 583 58*0 55-4 54-0 3.0 „ E. 1. 599 59-7 594 590 58-3 58-( 55-7 53-7 14 5.0 „ Variable. 59-5 595 59 5 59 3 582 57-81 55-3 54-0 14 9.0 „ 59-4 59-4 58*3 1 55-4 15 Calm. 596 59 2 59 0 59 0 585 57 e 55-5 52-9 15 3.0 p.m. W. 1-2. 59 4 59*4 59-2 59 0 58-3 57-71 55-8 53-3 ” 16 7.0 a.m. B. Calm. 59-0 59-0 58-9 54-9 16 8.0 „ W. 2. 591 59-0 ... 59-0 ... 54 0 ", 16 10.45 „ Calm. 593 59-0 ... 590 ... 55-3 16 3.15 p.m. 59-7 59*0 ... 543 16 6.0 „ 593 59-0 ... 54-7 16 7.0 a.m. F. W. 1. 59-2 58'£ ... 57 L 56 4 16 8.0 „ W. 1. 59-2 59-f ... 57"" ... 563 16 9.0 „ W. 1. 59 3 591 59-0 ... 564 ... 16 1.0 p.m. Variable 594 59' 58-1 ... 56-r 16 1.45 „ E. airs. 59-1 59- ... 57 3 ... 56" 16 4.30 „ E. 1. 593 59-3 ... 57-9 ... 57-( ... 17 10.0 a.m. Small loch Variable 58-9 581 58' 58 -i 57 '( 56- 5155-1 51 L ” 17 1.0 p.m. F. N.E. 59-1 59 t 59- 59-C 58- 58 0 52- 51 T „ 17 5.0 „ Buoy N.E. 58-9 I 58* 58* 58' 58- 57*3| 55' 53-S 18 10.0 a.m. W. 1. 58-5 58* 58- 58-4 58- 57 9 56' 53 2C ! 10.0 „ F. W. 1-2 58-8 58- 58- 58-51 57- 57 2 55- 53 2C Noon. E. W. 1. 586 58- 58- 58-4 56- 54-8 52- 51 2C | 2.0 p.m. D. W. 2-3 58-8 58- 58- 58-5 58- 58-5, 54- 53 1908-9.] Temperature Observations in Loch Garry. 133 — continued. 40 45 50 55 60 65 70 75 80 85 90 100 125 140 150 175 200 51-5 513 510 50-8 50 1 498 49-3 48-8 47-0 52-3 51-6 51-4 51-3 50-9 50-5 50-2 500 ... 53 0 52-3 52-0 51-9 5M510 510 503 53 7 53-7 53-0 527 52-2! 52 0 51-3 500 47-2 46-6 54 0 53 9 53 1 52-6 52-0 51-2 506 490 47-2 53 7 537 53 0 52-3 51-3, 51-2 48-9 478 47-2 471 470 ... 53 1 53-0 51-2 49’0 48-2 48-2 47-7 470 46-8 468 ... i ... 50’8 50'5 497 483 48-0,47-1 47 1 471 47-1 46-8 46-7 51*7 51-3 50‘7 490 48-2 47-3 47-0 47-0 46-8 46-8 46 7 53-3 532 51-7 50-4 49-0 47-7 47-3 47-1 47-0 46-9 46-5 54-2 53-8 52-0 51-0 49 9 48-2 47-4 47-2 47-0 469 46-7 54 2 53 0 52-3 51-1 49 0 48'2 47-4 47-1 47-0 46-7 52 9 51-8 51-0 49-9 48-5; 47-7 47 l 47-0 46-9 468 465 52 0 51*9 50-3 490 47*5 47-2 47 0 469 46-8 46-5 46-5 51-5 500 48-9 47-7 47 0 47-0 47-0 47-0 47-0 46 7 46-5 50-21 48-8 48-3 47-2 47 0, 47-0 47 0 47-0 47-0 46-8 46-5 49-0 48-1 47-9 47-8 47-2 47-0 469 46 9 469 46-9 46-5 490 47-5 47 4 47-1 47-0 47-0 46-9 46-9 46-8 46'8 46-5 49-0 489 474 47-2 47-0 47-0 470 47-0 47-0 46-7 465 46-4 49-0 485 47-6 47 3 47 0 46-9 469 46-8 467 46-7 465 490 48-9 48-0 47-4 47*1 47-0 46-£ 46-9 46-9 46-8 465 50 2 50-0 49-6 490 48-0 47 3 47-1 47-0 47-0 46-7 465 51-2 51-2 50-5 50-0 49 5 48 0 47’4 47-0 46-9 469 465 51-4 51-3 51-0 50-8 50-2 49 8 49-2 48-3 47-2 47-0 46-8 51-9 50-8 50-2 49-4 48-8 47-7 47-2 47-0 47-0 470 466 46-6 46-4 46-4 46-4 51-2 50-7 50-2 49-3 48-2 47-8 47-3 470 47-0 47-0 ... 46-7 46-4 463 463 463 51-8 50-7 50-2 49-4 48-2 47 £ 47-2 47-2 47-0 46-9 ... 46-7 53-4 51-7 50-5 49-7 48-81 47-5 47-2 47-2 47-0 47-0 ... 46-8 46-8 46-4 46-3 52-7 511 50-4 41* -8 48*7 474 47-1 47-1 47-0 47-0 467 52-5 51-2 50-8 49-4 48-2 47-5 47-2 47-0 470 47-0 467 52-8 509 50-6 49-5 48-0! 47-8 47-6 47‘2 470 47-0 46-7 5 1 -4 50-3 50-2 48-9, 48-4 48-0 47-7 47'3 47-0 46-7 524 50-7 49-3 ... 47-9 ... 47-2 47'0 47-0 51-7 510 50-9 50 1 49-4 48-7 47-9, 47-7 47-5 47-0 46*7 465 465 46-4 46 4 51-8 50-7 50-7 49-9 48-6 48-4 47-8 47-3 47-2 47-0 46-5 52-2 51-2 50-7 ... 50-0 47-4 47-0 52-5 51-6 ... 52 '7 52-4 51-0 ... 47-2 46-7 46-7 52-0 49-6 473 ... 47-0 46 6 466 51-3 49-3 47-1 ... 470 46-8 46-8 51-0 47-4 47 0i ... 47-C 46-9 46-6 50-7 48-7 478 ... 47-0 46-8 46-8 50-9 49-3 47-8' ... 47 0 46-7 46-7 51-5 49-8 47-8 ... 47C 468 46-6 51-9 49-8 48-2 ... 472 46-9 46-7 54-0 51-0 49-2 ... 47-7 466 46-6 50-3 51-5 51-0 50-0 49-4 48-4 47-9 47-3 47*0 47-0 469 46-4 52-0 51-2 50-2 49-2 48-8- 48-0 47-3 47-0 47-0 46-9 46-6 46-4 51-2 50-4 49-6 48-1 47-7' 47-4 47 0j 47-0 47-0 46-9 46-6 46-5 465 46-4 46-4 51-6 51-4 49-C 48-0 47-5 47-2 47*0, 46 9 46-8 46-7 46-5 50-2 49-6 49-4 48-4 47-3 47-0 46-8; 46-7 46-7 466 466 46 5 52-3 51-7 50-1 49-0 47-9 47-5'47‘3 47 0 46-9 46-8 46-7 465 t r~ ' 20 20 20 22 22 23 23 23 23 23 23 23 23 23 24 24 24 24 24 24 24 24 24 24 24 24 25 25 25 25 25 25 25 25 6 6 6 Proceedings of the Royal Society of Edinburgh. [Sess. Loch Garry Hour. 4.30 pfm. 6.30 55 8.30 55 8.30 a.m. 11.0 55 7.0 55 9.0 55 11.0 55 1.0 p.m. 3.0 55 5.0 55 7.0 55 9.0 55 11.0 55 1.0 a.m. 3.0 55 5.0 55 7.0 55 9.0 55 11.0 55 1.0 p.m. 3.0 55 5.0 55 7.0 55 9.0 55 11.0 55 1.0 a.m. 3.0 55 5.0 55 7.0 55 9.0 55 11.0 55 1.0 p.m. 3.0 55 1.0 55 2.15 55 3.45 55 Position. Wind. Surface. 5 10 15 20 25 30 35 Buoy. W. 3. 59-4 59-4 59-3 59-3 59-3 59-3 59-3 59-3 C/ W. 1. 59-4 59-4 59-3 59*3 59-3 59-3 59*3 59-0 B. W. 1. 59-6 59-6 59-6 59-6 59*5 59-5 59-5 59-1 B. W. 1. 60-1 60-0 60-0 59*9 59-9 59-8 567 53*4 Buoy. W. 2-3. 59-5 59-5 59-5 59-5 59-5 59-4 56*8 55*1 B. W. 2. 59-9 ... 59-9 ... 59 8 ... 59-8 ... 55 W. 2. 59-9 59-9 ... 59-8 ... 59-8 ... 55 W. 1. 60-0 ... 60-0 ... 60-0 59-8 ... 55 W. 1. 60-0 60-0 ... 60-0 59-7 ... 55 W. 2. 60-1 601 ... 60*0 59-9 55 W. 2. 60-1 60-1 ... 60*0 60-0 ... 55 W. 2. 60-0 60-0 600 60-0 55 W. 0-1. 60-1 60-1 60-0 59-8 . . . 55 W. 0-1. 60*1 60-1 ... 60-0 59-6 55 W. 0-1. 60*0 60-0 59-9 ... 59\5 55 Calm. 60-0 ... 60-0 60-0 580 ... 55 Calm. 59-9 ... 1 59*9 ... 59*8 ... 56-0 55 Variable. 60-0 60-0 60-0 59-0 ... 55 W. 1. 60-0 60-0 ... 59-9 ... 57 9 55 E. airs. 60*2 60*0 ... 59-9 57-2 55 E. airs. 60-0 ... 60-0 ... 59-1 55-3 ... 55 S. 1-2. 60*0 60*0 58-9 54-3 ... 55 S. 2. 59-9 59-9 ... 59-0 54-9 ... 55 E. airs. 60-0 59-8 ... 59-0 57-2 ... 55 E. 1. 60-0 59-7 ... 58-8 ... 56*9 ... 55 Calm. 59*7 ... 59-6 ... 58-8 58-0 55 Variable. 59*7 59-6 ... 58-3 56-2 ... 55 55 59*5 59-4 ... 58-3 57-0 55 Calm. 59-4 59*3 58-4 ... 57*1 55 W. airs. 59-7 591 ... 58*1 ... 57-5 ... 55 Calm. 59-9 59-1 ... 58-3 • • • 577 ... 55 W. 1. 59-9 59-0 ... 58*4 ... 57-8 ... 55 W. 2-3. 60-0 ... 59-6 587 ... 58-0 55 W. 2. 59°8 59-8 59-7 ... 59-4 ... Buoy. W. 3. 54-0 54-0 ... 53*8 . . . B. 55 54*0 ... ... ... ... A. ... 5*40 ... ... ... ... ... ... 1908-9.] Temperature Observations in Loch Garry. 135 — continued. 40 45 50 55 60 65 70 75 80 85 90 100 125 140 150 175 200 53-6 51*6 50-0 49-0 48-4 47-9 47-8 47-3 47-0 46-8 46-7 46 '6 46-6 46-5 51-8 50-6 50-0 49-0 48*2 47-7 47-0 47-0 47-0 46-9 ... 46‘6 . . . . . . . . . 46-5 • . • 51-0 50-0 49-0 48-0 47-6 47-1 . . , 47*0 ... 46-7 ... 46’6 • . . • . . 46-5 . . . . . . 52-4 51-4 50-1 49'9 48-2 48*1 48-0 47-5 47-1 47-0 ... 46-8 46-6 » . . . . . . . . . . . 52-3 51*1 49-6 48-5 47-6 47-4 47*2 47-0 47-0 46-8 46-7 46-6 • • • 46-5 46*5 46-5 52-6 50-0 48-3 . . . 47-2 . . . 47-0 46-7 „ . . . . . . . . . . . 53-0 50-2 49-0 ... 48-0 . . , 47-1 ... 46-7 • . . . . . . . . . . . 53-5 50-6 49-1 ... 48-0 47-1 ... . . . 46-7 « . • . . . . . . . . . 51 8 50-0 48-9 ... 47-6 47-0 . . . 46-9 • • . . . . . . . . . . 51-8 ... 49-7 ... 48-5 47-6 . . . 47-0 ... ... 46-7 . . . . . . . . . • . • 51-9 49-9 ... 48-6 ... 47-6 47-0 ... 46-7 . . • • . • a . . . . . 53-0 49 9 48-8 47-2 47-0 ... ... 46-6 • • . . . . . . . . . . 52-0 ... 497 48-0 ... 47'0 46-7 ... ... 46*4 ... . . . . . . . . . 51-8 49-7 47 8 ... 47-1 ... 46-9 ... 46-7 ... • . . . . . . . . 50-9 ... 48-9 47*6 ... 47'2 46-8 ... 46-7 • . . • . . a . • . . . 50-3 49-0 ... 47-3 469 . . . 46-8 ... 46-5 ... • . . . . . . . . 51-0 49'8 47'7 ... 470 46-8 ... 46-6 ... ... . . . . . . . . . 52-0 50-3 48-7 47*3 . . . 47*0 ... . . . 46*7 . . . . • • . . • • . . . . . 52-6 50-5 . . . 490 ... 47-7 47-1 46-7 ... . . . • • . . . . . 52-0 50-5 49-4 ... 48*4 47-0 ... ... 46-7 . . • ... . . • • . . 51-8 50-3 49 3 ... 47-9 47*1 46*7 ... ... • . • 51-9 . . . 50-1 . . . 48-8 47-5 47-0 ... 46'6 ... . . • . . • 52-0 50-5 ... 49-1 • • • 47-4 . . . 47-0 . . . 46-7 . . . ... 530 ... 51*1 ... 49-4 ... 47-6 . . . 47-0 ... ... 46-7 . . . ... . . • . . . 54-0 . . . 51-0 ... 49-3 ... 47-3 ... 47-0 ... ... 46*6 . . . ... o . . • . . 52-9 51-0 48-8 ... 47*1 . . . 46-9 ... ... 46-9 ... ... ... . . . ... 53-0 50-1 47-8 ... 47-0 . . . 46-8 ... 46-7 ... ... ... . . . 54-0 ... 50*0 48-0 ... 47-0 . . . 46-9 ... ... 46-6 . . . ... ... . . . 53-5 51-0 . . , 48-5 ... 47*1 . . . 46-9 ... ... 46-6 ... ... . . . 54 9 50-9 48-0 ... 47 0 46-9 ... 46’6 ... • . . . . • 549 50-5 ... 47-9 47 0 46-9 1 ... 46-7 ... ... . . . 54-8 50 0 ... 47-9 ... 47-0 46-8 ... ... 46'6 . . . ... • • • , . . 56-8 50-8 48-4 47*0 46-8 ... ... 46-6 . . . ... • • • 58-0 51-0 47-9 47-1 ... 46-8 ... 46-5 ... ... ... 53-7 537 ... 52-4 51-2 50-0 48-0 ... 47-3 ... 47-0 47-0 ... ... ... ... ... 54-0 (90) 47-6 (95) 47-3 47-0 ... ... ... ... 54-0 52*4 51-1 (95) 47-1 (100) I (. Issued separately March 1, 1909.) 134 Proceedings of the Royal Society of Edinburgh. [Sess. Loch Garry Date. Hour. Position. Wind. Surface. 5 10 15 20 25 30 35 1908. July 20 4.30 p.m. Buoy. C.' W. 3. 59-4 594 593 59-3 59-3 59-3 59 3 59-3 „ 20 6.30 „ W. 1. 59-4 59 4 593 59-3 593 59 3 593 59-0 ,. 20 8.30 „ B. W. 1. 596 596 596 596 59-5 59 5 595 591 „ 22 8.30 a.m. B. W. 1. 60-1 600 60-0 59-9 5 9-9 59 8 567 53-4 „ 22 11.0 „ Buoy. W. 2-3. 595 59-5 59-5 59 -5 59-5 59'4 56-8 551 „ 23 7.0 „ B. W. 2. 599 599 ... 59 8 59-8 „ 23 9.0 „ „ W. 2. 599 59-9 59-8 59-8 „ 23 11.0 „ „ W. 1. 60-0 600 600 59-8 „ 23 1.0 p.m. W. 1. 60-0 600 600 59-7 „ 23 3.0 „ W. 2. 60-1 60-1 60-0 59-9 „ 23 5.0 „ W. 2. 60-1 601 60-0 60-0 1 „ 23 7.0 „ W. 2. 60 0 60-0 600 600 „ 23 9.0 „ W. 0-1. 60-1 601 600 59-8 „ 23 11.0 „ W. 0-1. 60-1 60 1 600 59-6 „ 24 1.0 a.m. „ W. 0-1. 600 60-0 59-9 59 5 „ 24 3.0 „ Calm. 600 60 0 60-0 580 „ 24 5.0 „ Calm. 599 599 59-8 56-0 1 „ 24 7.0 „ „ Variable. 600 60-0 600 590 „ 24 9.0 „ W. 1. 60-0 600 59-9 57 9 24 11.0 „ „ E. airs. 60-2 60-0 599 57-2 „ 24 1.0 p.m. „ E. airs. 60-0 60-0 59-1 55-3 „ 24 3.0 „ „ S. 1-2. 60-0 60 0 58-9 54-3 „ 24 5.0 „ S. 2. 599 59 9 590 ... 54-9 „ 24 7.0 „ „ E. airs. 60-0 59-8 59-0 57-2 „ 24 9.0 „ „ E. 1. 60 0 59-7 58-8 56-9 „ 24 11.0 „ „ Calm. 59-7 596 58-8' ... 58-0 „ 25 1.0 a.m. Variable. 59-7 59-6 58 3 56-2 „ 25 3.0 „ „ 595 59-4 583 57 0 „ 25 5.0 „ Calm. 59 4 59-3 ... 58'4 57-1 „ 25 7.0 „ W. airs. 597 591! ... 58-1 575 „ 25 9.0 „ Calm. 59-9 591 ... 58-3 57-7 „ 25 11.0 „ W. 1. 599 59-0 58-4 57-8 „ 25 1.0 p.m. „ W. 2-3. 60-0 59-6 ... 58 7 58-0 „ 25 3.0 „ Buoy. W. 2. 59-8 59-8 59-7 59-4 Sept 6 1.0 „ W. 3. 54-0 540 53-8 „ 6 2.15 „ B. 54-0 „ 6 3.45 „ A. 5-40 135 1908-9.] Temperature Observations in Loch Garry. — continued. ( Issued, separately March 1, 1909.) 136 Proceedings of the Royal Society of Edinburgh. [Sess. IX. — On the Conditions for the Reversibility of the Order of Partial Differentiation. By W. H. Young, Sc.D., F.R.S. (Communicated by J. H. Maclagan Wedderburn, D.Sc.) (MS. received November 4, 1908. Read February 1, 1909.) § 1. In the case of a function of two variables f(x , y) there is, in general, no connection between the results of proceeding to the various limits, upper, lower, and intermediate, first with respect to x and then with respect to y, and first with respect to y and then with respect to x. We cannot even assert that the repeated upper limit obtained in one way is not less than the repeated lower limit obtained in the other way. The so-called necessary and sufficient conditions for the equality of the two repeated limits do little more than express in e-language the fact of the equality. There is, however, one simple case in which we can assert with confidence the existence of the repeated limit, this is, when a unique double limit exists. It is no accident, therefore, that the simplest and best-known set of conditions for the reversibility of the order of partial differentiation — - that associated with the names of Dini and Schwarz — is based on this property. The main object of the first of the three parts of the present paper is to obtain these Schwarz-Dini conditions in a more precise form than has yet been given to them. It is found that the axial cross through the point (a , b) considered may be omitted in obtaining the limit of the values of ~ in 17 & dy dx the neighbourhood of the point (a , b), and indeed that the existence of d_ df dy ' dx except at the point (a , b) itself. It is hoped that the mode of proof adopted, in which the e-method is avoided, will be found somewhat simpler and more concise than the usual mode of presentation. In the second part of the paper I obtain certain properties of the repeated partial differential coefficients, or, more generally, of the derivates with respect to one variable of the differential coefficient, or of the derivates, with respect to the other variable. I am thus led to state on the axial cross is nowhere required for the purposes of the proof, 1908-9.] Reversibility of Order of Partial Differentiation. 137 and prove certain extensions of the Schwarz-Dini conditions considerably less narrow than those previously given. In the third part of the paper I obtain another set of sufficient con- ditions which I believe to be hew both in the form given to them and in the mode of proof. These are as follows : — If both ^4 and ^4 are continuous functions of the ensemble (x , y) at the point (a , b) and both . 4^- and -4- . 4^- exist at the point (a , b), dy dx dx dy then these two latter repeated partial differential coefficients are equal at (a , b). Stolz in his Grundzilge der Differenzial- und Integralrechnung, vol. i. pp. 141-147, has given a set of conditions, also due to Schwarz, included in mine as a very special case. The additional demands made by Schwarz on the function consist of (1) the existence of ~ and (j . yt i m a dy ' dx dx dy closed neighbourhood of the point (a, b), and (2) the continuity of f . uf- with respect to y and of ~ . rj- with respect to x at the point dy dx dx dy (a , b). The interesting question then arises : What is the relation of these conditions to those for the equality of two repeated limits ? The method of proof adopted shows that in this case also the equality virtually depends on the existence of a unique double limit. It may be noted also that in their relation to the repeated partial differential coefficients ~ . yf- and ~ . q— , or to the repeated derivates, dy dx dx dy the new conditions are less narrow than the Schwarz-Dini conditions. They do not demand even the continuity of the derivates of derivates at the point, still less the existence and continuity of ~ . in the neighbour- hood of the point considered. dy ' dx PART I. § 2. With the object of rendering what follows as complete in itself as possible, we begin by formulating a few properties in the theory of limits, on the proper grasp of which the understanding of the subject hinges. We have first to explain exactly what we mean by a double and a repeated limit. x1 , x2, .... xn , he a series of values of a variable x, forming 138 Proceedings of the Royal Society of Edinburgh. [Sess. a sequence with a as limiting value, the value a being expressly excluded from being a possible value for any xn , and further, the series f(x i) , f(x2) , . f(xn) , . . . . has only one limiting value u (which may be + oo or — oo ), then we say that n is one of the single limits of f(x) at a , and write u = Lt fixn) = one of the L It fix). n=oo x=a The function f(x) may or may not be defined for the value x = am, but, if defined, the value fia) must be disregarded in considering the limits at a. If f(x , y) is a function of two independent variables x and y, it becomes a function of x alone when we keep y constant, and has a corresponding set of simple limits, L It fix, y) . x=a If there is only one such limit for each value of y* this limit defines a function of y , and has, as such, a set of limits for y — b\ these are called the repeated limits of f(x ,y) first with respect to x and then with respect to y , and written Lit L t fix,y). y—b *=« Similarly, if there is only one limit when y is kept constant, Lit L t fix , ?/) x=a y=b denotes the repeated limits of f(x , y) first with respect to y and then with respect to x. The idea of double limits of fix , y) is different. Let xlJx2, . . . . be a sequence of values of x having a as limit, but not including a, and yx , y2, . . . .a sequence of values of y having b as limit, but not including b, then f(x,y) has at the points (x1,y1), (x2,y2), . . . . * The same is true if a law is given by means of which one of the limits is defined for each value of y ; e.g. the maximum limit. In this case a number of quantities can be identified as limits of limits of fix , y), or repeated limits ; e.g. the upper upper limit, the upper lower limit, etc. The whole set of such limits, which may theoretically be denoted by Lit Lit fix , y), y=b x=a can only be regarded as perfectly defined when all possible laws which can be used are in some manner specified. 1908-9.] Reversibility of Order of Partial Differentiation. 139 a series of values and at (a , 6) a corresponding set of limits.* If one of these is A (which may be + oo or — oc ), then A is said to be a double limit of f (x , y) for the ensemble of values (a , b). If the variables x and y are continuous, we may regard the ensemble (x , y ) as a point of the plane. The points (x1 , yf) , (x2 , y2) , . then form a sequence with the point (a , b) as limiting point. They do not, however, form the most general such sequence, since the individual points are explicitly excluded from lying on the axial cross x — a , y = b, through the limiting point.f Lemma 1. — Any repeated limit is a double limit. For convenience we shall use F(m, n) for f(pcm , y„). By the definition of a repeated limit there is then a sequence of values of F(m , n), keeping n constant, having a unique limit v(n), when m is indefinitely increased ; and the quantities v(n), as n is indefinitely increased, have the repeated limit, say u, as one of their limits ; that is v(n) = L t F (m , n) m= oo w = one of the L It v(n). n=m First consider the quantities v(n) to be all finite. Represent the values of the various functions on a straight line, /(m , n) by the point Pm>n, v(n ) by the point Qn , u by the point Q . Then, under the given conditions, Q is the limiting point of the sequence Qx, Q2, • • • • and is, for each value of n, the limiting point of the sequence P1>n, P2>„, . . . . Since all these points, except possibly Q, are finite points, any interval d containing Q as internal or end-point determines a point Qn where n is the first integer greater than some chosen number such that Q„ lies inside d. The interval d then determines a point Pm>n such that n is the first integer greater than a chosen number, and such that Pm n lies inside d. Taking a sequence of such intervals dx , d2 having Q as sole common * These may be regarded as falling under the heading of simple limits, since they are hit F (n), where F (n) =/(&„, yn). n—oz t It is unnecessary here to enter into the modifications necessary when the point (a , b ) is at infinity. 140 Proceedings of the Royal Society of Edinburgh. [Sess. internal or end-point, we get in this manner a constantly increasing set of integers m1 , m2 , . and another n1}n2, . . . . such that Q is the sole limiting point of the points PTO . The corresponding series F(m*,?R) has then u for limit, which shows that u is a double limit of F (m,n). Q.E.D. If a finite number of the quantities v(n) are infinite, we can omit them from consideration. If, however, this is not the case, u is + oo or — oo and is equal to all but a finite number of the v(n)’a. In this trivial case it is clear that, corresponding to any v(n) = u, we can find an integer m such that F(m , n) is numerically greater than any chosen quantity, and in this way we can construct a series F(m< , nf having u as limit. Thus in any case the theorem is demonstrated. Lemma 2. — If f(x , y) has only one double limit at a point (a , b), and the simple limit L t f(a + h, b + k) h= 0 is unique for all values of k in a certain neighbourhood of the zero point , then the repeated limit L t f(a + ii , b + k) ft=0 7i=0 exists. This is an immediate consequence of Lemma 1. N.B. — If the simple limit is not unique, it follows from Lemma 1 that, however we define the limiting function as a function of y, all its limits are double limits of f(x ,y). Hence if, as in Lemma 2, f(a + h ,b + lc) has only one double limit, all the limits of all possible limiting func- tions coincide. In particular the upper upper and lower lower limits are equal. Note 1. — It may evidently happen that even when L tf(x,y) does x=a not exist as a unique limit, the upper and lower limits, and therefore all intermediate limits, have one and the same definite limit as y approaches b. If we agree with some writers to call this the repeated limit, it is evident that Lemma 2 still holds, omitting the assumption as to the uniqueness of the simple limit. Note 2. — The existence of a unique limit of f(x,y) for each fixed value of x does not, of course, involve the existence of a unique limit when y varies with x, which would be concomitant to the existence of a unique double limit. § 3. A rectangle whose axes are parallel to the axes of coordinates, and whose lower left-hand and upper right-hand corners are respec- 1908-9.] Reversibility of Order of Partial Differentiation. 141 lively the points (a, b), (a-\-h ,b-\-k), will be referred to as the rectangle ( a,b ; a + h , b + k), and its double incrementary ratio defined as follows: — m(a, b; a + h, b + /,) =f(a + h ’ h + k) ~/(a + h ’ /'i • b + k > + r' 6 + *> (2) (3) so m(a, b; a + h, b + k) is the incrementary ratio with respect to x of the incrementary ratio with respect to y of f(x , y), and similarly it is the incrementary ratio with respect to y of the incrementary ratio with respect to x. If in (2), keeping x constant, we let k approach zero in any manner, and there is only one limit, this is, by definition, the partial differential coefficient with respect to y, fy(x , b), or C- . Forming the single incrementary f ratio of ffx , b) for the pair of values x — a and x — a-\-h, if this has a unique limit as h approaches zero, this is, by definition, the repeated differential coefficient with respect first to y and then to x, and will be denoted b y/ or d df > dff dx dy dxdy If fy exists, but its single incrementary ratio has more than one limit, the various limits are the various derivates at the point ( a , b ) of fy , and may be called the repeated derivates of f(x , y) first with respect to y and then to x. If fy does not exist, the upper and lower left- and right-hand derivates which appear instead form functions whose derivates with respect to x may be treated as the repeated derivates of f(x , y) first with respect to y and then to x. The following theorem will for convenience be referred to as the Repeated Theorem of the Mean. The Repeated Theorem of the Mean. If f(x , y) is a finite continuous function of x at every point of the closed rectangle (a , b ; a + h , b + k) , and has , except possibly on the bound- ing ordinates, x—a and x — a + h , 142 Proceedings of the Royal Society of Edinburgh. [Sess. a differential coefficient fx with respect to x, which is itself a finite con- tinuous function of y with, at every internal point of the rectangle, a differential coefficient df _ df dx dydx ’ then there is an internal point of the rectangle at which the repeated differential coefficient fyx(x' , yf is equal to the double incrementary ratio of the rectangle, viz. m(a, b; a + h, b + k)=fyx(x , y) . For, applying the Theorem of the Mean to the identity (3), we get m(a , A; a + h, b + k) = ~mx(b, b + k) at some point x between a and (a + h) not inclusive _ fffi , b + k) — f fix , b) k whence the result follows by a second application of the Theorem of the Mean, since fx is continuous with respect to x on the sides y = b and y = b + k of the rectangle. Note. — Assuming the simple result that, when f(x, y) is a con- tinuous function of the ensemble (x , y) the double incrementary ratio assumes at points internal to a rectangle (a, b ; a + h , b + k ) every value between its upper and lower bounds,* this shows that if fyx then exists and is finite at every internal point of this rectangle it also assumes every value between its upper and lower bounds. § 4. Theorem 1 (on the existence of fyx at the point (a , b)). — If fx exists in a closed neighbourhood of a point (a , b), while in the completely open neighbourhood, excluding the axial cross, j* it has a differential co- efficient fyx with respect to y, then, if fyx has only one double limit as we approach the point (a , b) in any manner by means of points not on the axial cross, fyx exists also at the point (a , b) itself. For, by the Repeated Theorem of the Mean, m(a , b ; a + h, b + k) =fyx(x , y) , where the point (x' , y') does not lie on the axial cross, and has (a , b) as limiting point when h and k each approach zero in any manner without assuming the value zero. Since fyfix , y), and therefore fyfix , y'), has only one double limit at the point (a, b), the same is true of m(a , b; a + h, b + k) when h and k have * A proof of this is given in § 7 below, t That is, not on x = a nor on y = b. 1908-9.] Reversibility of Order of Partial Differentiation. 143 zero as limit. Hence, a repeated limit being a double limit (Lemma 1), all the repeated limits of m(a , b; a + h, b + k) are equal. But, by hypothesis,/^. is defined on the ordinate x = a, so that JAa ' = YJ, m(a ,b)a + h , b + k) , k h= 0 and has, therefore, by what has been shown, only one limit when k has zero as limit ; that is to say, fx has a differential coefficient fyx with respect to y at the point (a , b). Note. — It should be noticed that it does not follow that fyx is con- tinuous at (a , b) with respect to either variable, still less with respect to the ensemble ( x , y). In fact, fyx need not exist on the axial cross, except at the point (a, b) itself. It will be proved below (§8, Theorem 7, Cor. 2), however, that when it does exist on the axial cross, it is continuous at (a, b). Theorem 2 (the Dini-Schwarz Theorem). — If in addition to the require- ments of the 'preceding theorem , fy exists along the line y — b at and in the neighbourhood of the point (a, b), then fxy also exists at the point (a, b) and has the same value as fyx . For, in this case, fy(a + h , b) - fy(a , b) h U m(a , b ; a + h , b + k) , k= 0 and has, therefore, as was shown in the preceding proof, only one limit when h has zero as limit ; that is to say, fy has a differential coefficient fxv with respect to x at the point (a , 6). Since the value of fxy(a , b), like that of fyx(a , b), is thus the unique double limit of m(a , b; a + h , b-\-k), fxy(<* , b) =fyx{a , b) . Q.E.D. Note 1.— -It has nowhere been assumed that the unique limit postu- lated is finite ; it may be + oo or — oo . Note 2. — The arguments used in proving the Repeated Theorem of the Mean, as well as Theorems 1 and 2, which depend on it, being based on the Theorem of the Mean in one dimension, do not require the full assumption that fyx exists at every point internal to the rectangle. It suffices, in fact , if there is no distinction of right and left * with respect to the derivates of fx regarded as a function of y, as follows * Thinking of the representation in two dimensions, right and left with respect to y is, of course, “ up and down.” - i 144 Proceedings of the Royal Society of Edinburgh. [Sess. from the more general statement of the Theorem of the Mean given in the paper “ On Derivates and the Theorem of the Mean,” by W. H. and G. Chisholm Young, Quart. Journal of Math., Oct. 1908. Note 3. — It should be noticed that, without making any properly two-dimensional hypothesis, we can prove that fyx exists at the point (a , b) if we postulate that fyx exists and is finite along the ordinate x = a in some open neighbourhood of the point (a , b) but not at the point itself, and that it has a unique limit as we approach the point (a , b) along that ordinate. This is an immediate consequence of the Theorem of the Mean for a single variable applied to fx regarded as a function of y at points of the ordinate x = a. For this reason, as well as from the fact that the axial cross can, as we have seen, be omitted, the usual statements of the Schwarz-Dini conditions seem to leave something to be desired.* It may further be remarked that in Note 2 it is sufficient if the derivates of fx with respect to y on the ordinate x = a present no dis- tinction of right and left.f All these sets of conditions are, of course, sufficient but not necessary. It is obvious that sufficient conditions of a less restricted character can be formulated ; some of these will be found below. Note 4. — In the proof of the existence of a unique double limit for m(a , b\ a + h , b + k), the assumption (1) that fx exists in the open neighbourhood of the point (a, b), excluding the ordinate x — a, was rendered necessary in order to apply the Repeated Theorem of the Mean. This being postulated, the further assumption (2) that fx also exists on the ordinate x = a, at and in the neighbourhood of the point (a , b), is needed in order to ascribe a meaning to the expression fjp , b + k) - fx{ci , b) and so to prove the existence of fyx at the point (a , b). Similarly, without postulating (2), the existence of fxy requires the assumption (3) that fy exists on the line y = b, at and in the neighbour- hood of the point (a , b). * Stolz, Grundziige der Differencial- und Integralrechn ung, 1893, p. 147. Hobson, “Partial Differential Coefficients and Repeated Limits,” Proc. L.M.S. , 1906, series ii., vol. v. p. 234. See also Functions of a Real Variable , p. 318 and the errata. It should be noticed that the account in the book is really earlier than that in the paper, t See footnote on preceding page. 1908-9.] Reversibility of Order of Partial Differentiation. 145 The assumptions (2) and (3) are independent, and precisely of the same importance in the Schwarz-Dini conditions. Both could be omitted if we suitably enlarged our definition of a repeated differential coefficient, for without them we could still prove that the double incrementary ratio had a unique limit.* PART II. § 5. We now proceed to entirely drop the assumption as to the existence * df of a differential coefficient with respect to y of , and begin by proving (JbX certain properties of the derivates of ^ with respect to y. The following lemma is an immediate consequence of the definitions and Lemma 1. Lemma 3. — If fx exists at a rpoint (a , b) and on its ordinate in the neighbourhood, any derivate of fx with respect to y is a double limit of m(a,b; a + h, b + k). For, putting mJJ) , b + k) =/(a» & + -/(•*•. ft) m(a , b ; a + h, b + k ) = b + k)-ma(b, b + k) ^ h Therefore, by the definition of a differential coefficient, L£ m(a , b ; a + h, b + k) = ^—mib , b + k) at x — a h=0 dx fx(a , b + k) -f,(a , b) k Hence, by the definition of the derivates, L It Id m(a , b ; a + h, b + k) = the derivates of fx with respect to y at the point (a , b). Jc= 0 7i=0 Thus these derivates are repeated limits, and therefore, by Lemma 1, double limits of m(a , b; a + h , b + k). Q.E.D. Lemma 4. — If fx exists at every point of an open rectangle (a , b ; a + h , b + k), excluding the bounding ordinates, and is a finite continuous function of y at every interned point, then, if f(x , y) still exists and is a continuous function of y on the boundary, L L m(a , b ; a + h , b + k) L U, * It should be noticed that the difference between Hobson’s conditions, loc. cit., and those given by Schwarz consists in the omission of assumption (3), and that this is only possible in the light of the extended definitions suggested by Hobson. If such a definition be adopted, there is, it would appear, no reason for making the assumption (2) either. VOL. XXIX. 10 146 Proceedings of the Royal Society of Edinburgh. [Sess. where L and U are the lower and upper bounds of any derivate of fx with respect to y at points internal to the rectangle. For, since m(a, l ; a + h, b + k) - m<^b + ^ ~ m“(* ’ 6 + *> , h and the conditions of the Theorem of the Mean are satisfied, m(a , b ; a + h , b + k) ^ ) — fx(x> b) wpere a V) . g) (x-x)(y -y) where f(x , y) is a continuous and finite function of the ensemble (x,y), assumes every value between its upper and lower bounds in a closed rectangle (a , b ; c , d) at points at which an, b)-f{a, b) n=co h k _ n n==cc bk n = U m(a , b ; a + hkn, b + k) . go Thus the derivates with respect to y of the upper right-hand derivate of f{x , y) with respect to x are repeated limits, and therefore double limits, of the double incrementary ratio, so that they all coincide at {a , b) if a unique double limit exists. df As pointed out in Note 4, § 4, the existence of -A on the ordinate x = a CLOG is immaterial in the proof of the existence of a unique limit for the double incrementary ratio. Thus the assumption in question is superfluous in * Loc. cit. t Line 13, loc. cit. 154 Proceedings of the Royal Society of Edinburgh. [Sess. proving that all the derivates with respect to y of the upper right-hand derivate with respect to x are equal at the point (a , b). F or definiteness the upper right-hand derivate was taken, but it is clear that the same proof applies for any derivate. Thus, without assuming the existence of fx on the- ordinate x — a except at the point (a , b), all the derivates with respect to y of all the derivates with respect to x of fix , y) are equal at the point (a , b), so that, in Hobson’s sense, the partial differential co- efficient 7 J - exists at the point (a , b). dydx Adopting Hobson’s definition, the set of sufficient conditions for the reversibility of the order of partial differentiation discussed by Schwarz, Dini, and Hobson, reduce, in the light of what proceeds, to the following simpler form : — d2f It (D dp- exists at all ‘points in a non-axial neighbourhood of the point (a , b) ; d'2f (2) The values of in a non-axial neighbourhood of the point (a , b) have a unique limit at (a , b), finite or infinite ; df .... (3) — not only , as 'is implied in (1), exists, and is a finite and con- UX tinuous function of y in a non-axial neighbourhood of (a , b), but also exists on the abscisse y — b , cd and in the neighbourhood of (a , b) ; df (4) — exists at the point (a , b) ; dy then, in Hobson's sense, d2f and d2f dxdy both exist and are equal to the dydx unique limit specified in (2). § 11. It should, however, be noticed that the retention of the existence of the first differential coefficient in Dr Hobson’s definition of the second differential coefficient must be regarded, from the point of view adopted by him, as somewhat arbitrary. It seems not less unreasonable to assert the existence of d2f dydx when all the derivates with respect to y of all the derivates with respect to x coincide at the point (a , b) , which may, of df course, be the case without f- existing at (a , b) . ax Adopting this definition, if we know that the double incrementary ratio has a unique limit at the point (a, b) , we can easily show that all the derivates of derivates of f{x , y) are equal at (a, b). For, although the derivates of derivates are not necessarily themselves repeated limits of 1908-9.] Reversibility of Order of Partial Differentiation. 155 m(a, b; a + h, b + k), they lie between the upper and lower double limits of m(a , b ; a + h , b + k) when h and k are indefinitely diminished. To prove this let v(x , y) denote any derivate of f(x, y) with respect to x , e.g. the right-hand upper derivate ; then, for each value of y there is a sequence of values of h which determines the value of v(x , y) as a limit, viz. Therefore v(x,y) = L the derivates of v(xy) at (a , b) = hit ht ^ i /O* + hkttli b + k) — f(x, b + k) k= 0 n— co tv ( ljc,n _ f(a + ht) ; n , b + k) - f(a , b) ) K , n ^ Changing hk>n in the first fraction into h0>n , we get m(a ,b; a-\-h0n ,b-\-k). Remembering that the sequence hkn, b + k) k= 0 U— oo A a double limit of m(a , b ; a + h, b + k) A lowest double limit of m(a, 6; a + h, b + k). (1) Similarly, changing h0 if * < v , = x2 — ?/2, if x ^ y . The region considered is the square (0,0; 1,1). Here f(x , y) is a continuous function of the ensemble (x , y); its derivates are, however, discontinuous. .f-x =f x = - 1 , if x L y , = 2x if x > y . Therefore the right-hand derivates with respect to y of the left-hand derivate with respect to x is zero everywhere, but the left-hand derivate with respect to y , though zero except on the line x = y , has here the value + oo , since it is the limit of - 1 - 2x T Again, f+x=/+x= - 1 , if x< 1 , when 0 being an otherwise unknown function of h and k ; is a function of k , but not of h , which vanishes with k ; is a function of h , but not of k , which vanishes with h . Therefore h k . Let us approach in such a way that f(a + h , b + k) -f(ci + h, b) k ~f,(a , h) < ! fx(a + Oh , b + k) -ffa , b) h k + Vk , + Vh k h (1) where m is any positive quantity, finite or infinite. Then the right-hand side of the last inequality has the limit zero, therefore the same is true of the left-hand side. 1908-9.] Reversibility of Order of Partial Differentiation. 163 Since this is true for all positive values of m , it is true for all modes of approach such that j has not zero for one of its limits, which is equivalent to the statement to be proved. Theorem 10. — If fxx is a continuous function of the ensemble (x , y) at the point (a , b), and fyx exists at the point (a, b), then the double in- crementary ratio has a unique double limit whose value is fyx (a , b) for k all modes of approach other than those for which limits. For where Therefore has zero for one of its m (a, b; a + h, b + Tc) = > h - m^b ’b + k\ / v mfb , b + k) = f(r , b-\-k) — f(x^ b) d m(a , b ; a + h , b + k) = —mfb , h 4- li) for some value of x> a and ) Q<0<\ , (D and 0 is an otherwise unknown function of h and k. But since, by hypothesis, ~fx is a continuous function of the ensemble (x , y ) at the point (a , b), and ~fx exists there, we may apply the lemma. d„ But if has not zero for one of its limits, A Oh certainly has not zero for one of its limits, since, whatever function 0 is of li and k , Oh > k h Hence the lemma holding for the function ffx , y) ffei + Oh' , b + It) — f fa + Oh , b) has a unique limit, and this is fyfa, b). Hence, by (1) the same is true of m(a , b ; a + h, b + Jc) for all the specified modes of approach of h and k to zero. Theorem 12. — If fxx and fyy are both continuous functions of the 164 Proceedings of the Royal Society of Edinburgh. [Sess. ensemble (x , y) at the point (a , b), and fxy and fyx both exist at the point (a , b), then fxy(a , b) =fyx(a , b) , and m(a, b; a + li, b + k) has a unique double limit equal to both these repeated partial differential coefficients. For, since fxx is a continuous function of (x , y), and fyx exists at the point (i a , b), it follows by the preceding theorem that m(a , b ; a + h . , b + k) has a k unique limit for all modes of approach for which j has not the limit h zero, and this limit is fyx(a , b). Again, since fyv is a continuous function of (x , y), and fxy exists at the point (a, b ), it follows that m(a , b ; a + h, /> + /»;) has a unique double limit h for all modes of approach for which k has not the limit zero, and that this limit is fxy{a , b). Hence fyx(a , b) = fxy(a, b) — unique limit of m(a , b; a + h , b + k) for all modes of approach which do not make either But for modes of approach which make k h h or k k h have the limit zero, have zero for a limit. m(a , b ; a + h , b + k) has, by the above, the limit fxy(a , b), and for modes of approach which make ~ have the limit zero, it has fyx(cc , b) for limit. Hence for all modes of approach m(a , b ; a + h , b+k ) lias the unique limit fja, b) = f,s(a, b). ( Issued separately March 2, 1909.) 1908-9.] Note on a Study of Polarisation. 165 X. — Laboratory Note on a Study of Polarisation by means of the Dolezalek Electrometer. By A. F. Ewan, Physical Laboratory, Edinburgh University. (Communicated by Professor J. G. MacGregor.) (Read July 20, 1908. MS. received September 15, 1908 ; revised January 23, 1909.) The following experiments originated in a series of laboratory exercises which I performed on the use of the Dolezalek electrometer. The instrument which I used was made by Bartels, and had its needle suspended by a phosphor-bronze strip. This needle was raised to a potential of about 160 volts by being connected to one terminal of a battery of eighty small secondary cells, the other terminal of which was connected to earth. When at this potential the instrument gave, for a potential difference of 1 volt between its two pairs of quadrants, a deflection of 200 divisions on a scale 200 centimetres distant from it. The maximum deflection in the experiments described was 166 divisions, i.e. 332 cms., giving tan-1 T66 as maximum angle of deflection ; and therefore, by taking the deflection as proportional to the potential difference, a maximum error of 0*7 per cent, is introduced. Although these experiments are merely preliminary ones, I desire to give an account of the results obtained, as I am unable to go on with them at present. They refer to two subjects — (1) the variation of the electro- motive force of polarisation of a cell with the difference of potential between the electrodes, and (2) the applicability of Wiedeburg’s formula for the variation, with time, of the electromotive force of polarisation during the flow of the current. 1. Variation of the Electromotive Force of Polarisation with the Difference of Potential between the Electrodes. It is usually held that there is no such variation, but that, for a given electrolyte, given electrodes, etc., it depends only on the current density. This assumption seems never to have been tested ; and as it underlies certain methods of using the Wheatstone bridge in the measurement of the conductivity of electrolytes, a test is desirable. For this purpose I passed a current through two cells of very different resistances, but otherwise 166 Proceedings of the Royal Society of Edinburgh. [Sess. exactly similar, arranged in series. Their electrodes consequently differed considerably in potential. The differences of potential between the electrodes and the liquid in the cells immediately behind the electrodes were then measured, at observed times, by means of the electrometer and according to Fuchs’* method; and the corresponding curves were plotted for all four electrodes. The time was observed by means of the second-hand of an ordinary watch. Each cell consisted of two small rectangular troughs connected by an upturned U-tube, each U-tube being fitted, for convenience in filling, with a branch tube closed by a clip. The electrodes consisted of rectangular pieces of platinum of approximately the same area, viz. T3 square inches, with platinum wires welded to them at their upper edges. The electrolyte was connected with the electrometer by means of calomel electrodes con- structed according to the method described in Findlay’s Practical Physical Chemistry (1906), page 202. To enable me to connect the electrometer quickly to the various electrodes and the liquid in which they were placed, the opposite pairs of quadrants of the electrometer were connected by copper wires to a mercury- pool commutator, with which were also connected by copper wires the four platinum electrodes and the corresponding calomel electrodes. To make sure that the nozzles of the calomel electrodes were out of the lines of flow of the current, the platinum electrodes were so placed, and the depth of liquid in the troughs so arranged, that the electrodes almost completely filled the cross-section of the electrolyte in the troughs ; and the calomel electrodes were then placed so as to have their nozzles immediately behind the platinum plates, thus being in that part of the trough through which the current does not pass directly. The troughs were provided with glass covers to diminish evaporation and to keep out dust ; and before performing each experiment the mercury in the commutator pools was cleaned, and the electrodes were white-heated. The U-tubes of the two cells differed in length and cross-section to such an extent that the resistances of the liquid they contained were about 90,000 and 2000 ohms respectively. Thus the difference of potential of the electrodes of the one cell would be about forty-five times as great as that of the other. The electrocute used in the two cells was the same as in the calomel electrodes, viz. potassium chloride, and the concentration was the same also. Thus there would be no electromotive force at the nozzles of the calomel electrodes. * Pogg. Ann., clvi. 158, 1875. 1908-9.] 167 Note on a Study of Polarisation. Two of the more successful series of observations of the cotemporaneous variation of the potential difference between the electrodes and the electrolyte directly behind them are shown graphically in fig. 1. They are marked (a) and (b) respectively. The graphs were obtained by plotting the polarisation against the time for each of the four electrodes — the polarisation being the excess of the potential difference between the electrode and the electrolyte behind it over the potential difference just before starting the polarising current. The set of curves marked (a) was the first of the two obtained. It showed that the anode curves and cathode curves of the two cells were neither coincident nor of exactly the same form, although in the case of the cathode curves the difference in form was slight. Differences in form were to be expected, because of differences in the temperatures of the cells and in the convection currents in the neighbourhood of the electrodes, no precautions having been taken in these preliminary experiments to exclude such differences. These differences in form must prevent exact coincidence ; but there was obviously not even general coincidence, both the anode and cathode of the high-resistance cell being throughout more highly polarised than those of the low-resistance cell. This might be due either to the dependence of the polarisation on the potential difference of the electrodes or to differences in the current density at the electrodes caused by inequality of their area. If it was due to differences in the current density, interchanging the electrodes might be expected to change the relative positions of the curves. Accordingly, the anodes and cathodes respectively of the two cells were interchanged, and a set of observations represented by the curves marked (b) (fig. 1) obtained. As the polarising current in the two series of observations (a) and ( b ) would not be exactly the same, the two sets of curves might be expected on this account to differ slightly in form. It will be seen that this difference is very small in the case of the anode curves, while all the four cathode curves are of approxi- mately the same form. From the general agreement in form of the anode curves of the same cell, it would seem that the form of the curves was determined by the structure of the cell rather than by the electrode. Notwithstanding the differences in form, it is clearly seen from set (b) that after a short time (in which the disturbing influences might be expected to be most marked) the anode and cathode of the low-resistance cell are more highly polarised than those of the high-resistance cell, and approximately by the same amount as, in the case of set (a), the anode and cathode of the high-resistance cell were the more highly polarised. This shows us that the non-coincidence of the curves for the high- 168 Proceedings of the Royal Society of Edinburgh. [Sess. Fig. l. 1908-9.] 169 Note on a Study of Polarisation. resistance and low-resistance cells, which at first sight suggested variation of polarisation with potential difference of electrodes, may have been largely, and possibly wholly, due to differences in the area of the electrodes. Additional observations would need to be made, with exactly cut electrodes and more complete precautions against the sources of error mentioned above, before a test of this kind would be completely satisfactory. But it may be concluded at least that this experiment showed no evidence of variation of the electromotive force of polarisation with the difference of potential of the electrodes. 2. Wiedeburg’s Formula for the Variation of Polarisation with Time during the Flow of the Current. Wiedeburg,* making simple assumptions as to the way in which the polarisation itself occurs, and as to the occlusion and diffusion which go on at the same time, has developed the formula: _ 1 - e~yt J a - be~yt for the polarisation, as a function of the time, during the passage of the polarising current, the circuit being of constant resistance and containing a cell of constant electromotive force, and the electrodes being of ecpial area. The a, b, and y in his formula are functions of one or more of the electro- motive force of the galvanic cell, the resistance of the circuit, etc., and of the initial conditions. To test this formula, I passed a current from a secondary cell through the same circuit as in the former case ; but instead of observing all four electrodes I watched only one, thus being able to keep the electrometer permanently attached to one platinum electrode and the corresponding calomel electrode. Consequently the deflections were much more accurately determined. Three of the series of observations thus made are given graphically in fig. 2. It will be seen that, even with an ordinary watch, the curves can be followed quite a considerable distance from the bend towards the origin by means of the Dolezalek electrometer. Wiedeburg tested his formula by the aid of the law, obtained empiri- cally by Bouty,f that the polarisation within very short intervals of time from the starting of the polarising current is given by the formula : at T where a and (3 are constants. * IVied. Ann., li. 302, 1894. t G.R, cxvi. 628, 1893. 170 Proceedings of the Royal Society of Edinburgh. [Sess. He did so by showing that Bonty’s formula is a particular case of his own. For since e~yt =1 - yt + V-t2 - V * + etc., ' 1.2 1.2.3. we have, for sufficiently small values of t, e~yt = 1 - yt . Substituting this expression for e~yt into Wiedeburg’s formula, we have P= f- a -h( \ - yt) which is of the same form as Bouty’s. We may write Bouty’s formula as V +PP = <*■ , and in this form it indicates that if ^ be plotted against p, the graph obtained should be rectilinear within the time to which this law is applicable. Fig. 3 shows the curves of ~ against p, as given by my observations for the two anodes No. 1 and No. 2 of fig. 2. It will be seen that between the points corresponding to 01 and Ctl 8 min. on the one curve, and 01 and 02 min. on the other, the curvature is not appreciable. Above this the curves begin to bend as we might expect. Difficulty of observation both of time and polarisation makes it impossible for me to take points on my curves corresponding to smaller values of the time, but from these curves we can conclude that Bouty’s form of Wiedeburg’s formula holds in the cases investigated within a time range of about a fifth of a minute. For larger values of the time which necessitate the inclusion of the term J , but allow of the term y7 being excluded from the expansion of e~yt , 2x3 we have e yt = 1 - yt + //V2 Wiedeburg’s formula becomes, in that case, V t - At 2 B + C t- Dif 2 ’ by where A = Mr ■ B = — — - ; C = 6 ; D = 2 y z My observations enable me to make at least a partial test of the applicability of this formula within time ranges which are beyond the 1908-9.] Note on a Study of Polarisation. 171 50 secs. 100 secs. 150 secs. 200 secs. 250 secs. 300 secs. Time 5 mins. 172 Proceedings of the Royal Society of Edinburgh. [Sess. limit of Bouty’s law. For this purpose I have, in the case of each of the curves in hg. 2, obtained values of the constants A, B, C, and D by selecting four points on the curves, reading off the corresponding values of p and t, substituting into the above expression, and solving the four equations thus obtained. The four points selected had to be on a part of the curve for which the values of t were, at the one end, large enough to give trustworthy observations of p, and, at the other end, small enough to be within the assumed time limit of the applicability of the formula. They had, consequently, to be taken from comparatively small portions of the curves. It is clear, however, that according to the expression under consideration we must have p = 0 for t = 0, and that the origin in thus necessarily a point on the curve. Tables I., II., and III. give the values of the polarisation calculated by the above formula, the values observed, and the differences between them. It will be seen that in all three tables (especially in the first and third ) the observed and calculated values of the polarisation show considerable 1908-9.] Note on a Study of Polarisation. 173 Table I. Curve for Anode No. 1. A=--803, B = *000090, C = '002202, D= - -000526. The constants were calculated from the values of the polarisation, as obtained from the curve, corresponding to the times 05, 1, 1*5, and 2 mins. . Time (in mins.). Polarisation. Observed. Calculated. Difference. JL 6 450 400 50 i 3 490 479 11 1 2 530 530 0 3 $ 587 589 - 2 1 638 640 - 2 2 790 790 0 3 900 895 5 4 969 974 - 5 5 1006 1034 -28 Table II. Curve for Anode No. 2. A= - '645, B= -000075, C = ‘00244, D= - -000428. The constants were calculated as above from the values of the polarisation at the times 05, 1, 2, and 3 mins. Time (in mins.). Polarisation. Observed. Calculated. Difference. i 6 365 374 - 9 i 435 433 2 1 2 465 469 - 4 l 565 558 i 2 686 687 - 1 3 783 783 0 4 864 858 6 5 923 920 3 6 959 9 i 0 - 11 174 Proceedings of the Royal Society of Edinburgh. [Sess. Table III. Curve for Cathode No. 3. A= - 8-461, B = ’00005, C = -0100, D= - -02962. The constants were calculated as above from the values of the polarisation at the times 0‘3, 0’4, 0-5, and 06 mins. Time Polarisation. T (in mins.). Observed. Calculated. Difference. 1 1 *2 155 131 24 i r, 200 158 42 l 3 205 191 14 1 9 210 210 0 2 7? 220 223 -3 5 6 230 232 -2 l 240 239 1 ii 258 251 i disagreement for large and for small values of the time. For the larger values of the time the disagreement is of no moment, for they are beyond the limit within which the formula was assumed to hold. In the case of the small values of the time large differences were to be o expected, because time was observed by means of an ordinary watch, and also because the curves are exceedingly steep for these values of the time. Comparatively small errors in determining the time of starting the current would produce large differences of uniform sign (see Tables I. and III.), while small errors in determining1 the times of the observation of the earlier stages of polarisation would give rise to differences of variable sign (see Table II.). Throughout the range which can fairly be tested by these experiments the agreement is fairly good. In the original form of Wiedeburg’s formula there are only three constants, whereas I have used four. These must therefore be con- nected by some relation, which can readily be shown to be AC = D, by using the values of A, B, C, and D obtained on page 170. In none of my three sets of constants does this relation hold ; the product of AC being in all cases just about three times as great as D. This seems to indicate that the points used for the determination of these constants have been taken too far along the curve, i.e. at places where Wiedeburg’s formula may no longer be applicable. It would be possible by repeated trials to find a range of points which would furnish such values of the constants as to satisfy the condition AC = D, but as these observations are merely 175 1908-9.] Note on a Study of Polarisation. preliminary ones I have not thought it advisable to do so. I hope before long to repeat the experiments with more satisfactory precautions against the sources of error referred to above. The expenses of the above experiments were defrayed in part from the Tait Memorial Fund. (Issued separately April 12, 1909.) 176 Proceedings of the Royal Society of Edinburgh. [Sess. XI. — A Special Form of Photographic Camera for Recording the Readings of the Scales of Scientific Instruments. By James Robert Milne, D.Sc. (MS. received February 23, 1909. Read December 21, 1908.) Some years ago, when employed in work that involved the use of a polarimeter, there was brought forcibly to my notice the great loss of time which the frequent reading of the Nicol dial necessitates. To avoid this, I had a special form of camera made for the purpose of recording the readings automatically. This method proved successful from the first, but it is only latety that the mechanism of the camera attained its final form ; for it has required several years of experiment and alteration to evolve a form of camera which should be wholly automatic and yet reasonably simple. It will be readily understood that the function of the camera is to make a series of photographs of the scale-and-vernier of the polarimeter or other instrument, which, on subsequent examination, will show the relative position of the scale-and-vernier at the time of each exposure. When in use, the camera is so placed that its lens is focussed on the scale-and-vernier, and the latter is lit up by an incandescent gas burner with a piece of ground-glass interposed to diffuse the light evenly, or by an incandescent electric lamp having a “ frosted ” bulb. The scale-and- vernier must be so arranged that it is the scale, and not the vernier, which moves. The camera can be placed at any reasonable distance from the polarimeter according to the focal length of the lens employed, and of course it is not attached to the polarimeter in any way. Nor need the camera be placed directly at right angles with the scale-and-vernier to be photographed, as I find that a mirror can be used to deflect the rays of light, which allows of the camera’s being placed on one side. The mirror need not be silvered on the front surface, as the reflection from the glass is not sufficiently bright to give rise to a double image on the negative, hence a piece of ordinary plate mirror-glass answers very well. If it be desired to keep the room dark, it is not a difficult matter to arrange some form of covering for the path of the light on its way to the camera. The exposure required with the ordinary silvered brass scale is only a fraction of a second. A single plate is sufficient for many records, as only the vernier and the 177 1908-9.] A Special Form of Photographic Camera. part of the scale adjacent to it at the time require to be shown in each of the records. In the camera about to be described, 60 photographs in 6 rows of 10 each are obtained on a 5 x 4-inch plate. A general idea of the appearance of the camera may be gained from fig. 1, which for the sake of greater clearness is diagrammatic only , as are all the subsequent figures. A is a wooden upright, in the front of which is fixed the tube B carrying the lens. Behind A comes the “ carriage ” C, which rolls backwards and forwards by means of two wheels running on the top of A. To the back of C is attached a light metal frame F, which moves up and down C on guides, and in which is inserted the dark slide. It will be noticed that the upright A is slightly tilted ; this causes C, when free, to roll down DE to the lower end E. Similarly, when free, F falls down the guides on C. A horizontal slot is cut in C, so that the light from the lens tube B may pass to the plate behind. In order to exclude the entrance of extraneous light between A and C, a short camera bellows is attached to the front of C, and its plush-coated front edge rubs lightly against the back of A. A similar bellows is attached to F, and rubs against C. The mechanism of the camera is shown in fig. 2. The part of it which actuates the shutter is like an “ Atwood’s machine ” ; A with its weighted arms being the wheel, and B and C respectively the weights. C is a long strip of metal which moves up and down through the lens tube. A long- shaped opening is cut in the middle of it, and during each movement there is a brief interval when light can pass along the lens tube and reach the plate behind. The arms of the axle A increase its inertia, so that at the completion of each revolution it operates the lever D without fail. Below the weight B there is hung a weighted lever R, pivoted at P, which is shown drawn up by the cord attached to the pin of the disc F. As B is somewhat lighter than C, no movement will take place until the experimenter gives VOL. xxix. 12 178 Proceedings of the Royal Society of Edinburgh. [Sess. the knob G at the end of the axle H a half -turn, thus releasing R, and adding its weight to B. B and R together then overcome C and fall ; C rises, and the axle A with its arms revolves. After one revolution the motion is stopped because the pin projecting from the ball K (the ball Q has no pin) now comes in contact with the lower side of the lever D. When the experimenter gives another half -turn to the knob G, R is again raised, B is then overweighted by C, and the ball K revolves back to its original position, where it is arrested by the pin’s coming in contact with the upper side of D. Thus every time the experimenter gives the knob G a half- turn an exposure is made. It remains to be explained how the plate is moved after each exposure. The parts D and E may be compared to the “ escapement of a clock. Each time D is pushed from one side to the other by the pin of the ball K, a tooth on the wheel E is freed, because the teeth are spaced alternately nearer to and farther from the centre of the wheel, and E revolves under the action of the weight L* until it is stopped by the engagement of the next tooth with D. In this way the cord M wound round a small wheel on the axle of the wheel E is made to draw the carriage N one step along, at the conclusion of each exposure. This small wheel (S, fig. 3) is not fixed to the axle of the wheel E, and is only carried round with it because of its ratchet P, which is drawn forward by the arm Q attached to * The weight L requires to be removed each time a fresh plate is inserted. 179 1908-9. | A Special Form of Photographic Camera. the axle O. On completing a revolution the projecting end of P comes in contact with a fixed stop R, and is depressed, which raises the other end free from Q, thus releasing the small wheel from the axle, so that the carriage can run back to its starting-point, the small wheel turning back- wards freely on the axle until its ratchet once more on the completion of a revolution re-engages with Q. The return of the carriage C (fig. 1) brings about also the vertical move- ment of the plate. It will be noticed that the frame F containing the dark slide is furnished with a row of 6 catches T, T, . . . , each of which in turn engages with a stop V fixed to the carriage C. When C runs back along DE, the stop W fixed to A strikes against the catch which is in action for the time being, and pushes it clear of V, thus permitting of the descent of the frame F until the catch next above in its turn engages with Y. Fig. 4 shows a full-size reproduction of a negative, from which it will be seen that the record made by the camera is a very legible one. Fig. 3. — M is the cord to the carriage, which is wound round the grooved circumference of the wheel S. In order that the observer may be able to identify individual photo- graphs, or to indicate the commencement of a new series of records, a means is provided whereby he can produce at will on the photographs either a single or a double wedge-shaped mark. Two small levers are pivoted so that either may be swung in front of the scale into the field of view of the camera by a touch of the observer’s finger, their ends being respectively in the shape of a single and of a double wedge. In my own work I do not, as a rule, require to use these marks, as 1 always take the average of ten readings, and the record of each experiment occupies just one line on the plate. In order to relieve the observer from having to count the exposures, I have arranged an electric bell which rings at each return of the carriage when the ten exposures have been made. The observer is thus able to give his undivided attention to the work of adjusting the polarimeter, and the speed at which the readings can be made is greatly 180 Proceedings of the Royal Society of Edinburgh. [Sess. increased, for the eye of the observer need never leave the telescope of the polarimeter, nor is he required to remove his hand from the screw actuating the Nicol dial. I am accustomed to use a “ backed ordinary ” plate, and a hydroquinone developer, but any of the usual plates and developers may be employed. Fig. 4. No special care need be taken with the development of the plate, because all that it is necessary to obtain is a negative which is legible, and this can be secured without any difficulty. “ Prints ” of the negatives need not be made, as it is so easy to store the latter. The strip of blank space which appears at the foot of each negative is convenient for the purpose of writing particulars upon relating to the experiment whose readings it records. 181 1908-9.] A Special Form of Photographic Camera. The advantages of this method of making photographic records of the readings of an instrument are — (1) The saving of labour and strain to the eye of the observer, which is left in a better condition for its principal work. (2) The elimination of the possibility of errors of reading on the part of the observer. (3) The great saving of time which is effected. (4) The elimination of all personal bias due to a knowledge of the results that are being obtained. (5) The securing of a permanent record of the readings. (6) The entire separation of the recording apparatus from the polari- meter or other instrument, whose mechanism is not added to or interfered with in any way. I have to express my great obligation to the Carnegie Trustees for granting me the funds necessary to defray the expenses of the construction of the apparatus. Department op Physics, Edinburgh University. (Issued separately April 17, 1909.) 182 Proceedings of the Royal Society of Edinburgh. [Sess. XII. — On an Improved Form of Magnetometer and Accessories for the Testing of Magnetic Materials at Different Temperatures. By James G. Gray, B.Sc., Lecturer on Physics in the University of Glasgow, and Alexander D. Ross, M.A., B.Sc., Assistant to the Professor of Natural Philosophy in the University of Glasgow. Communicated by Professor A. Gray, F.R.S. (MS. received January 29, 1909. Read February 1, 1909.) In the usual form of magnetometer the magnetising solenoid is placed with its axis in the magnetic east and west line passing through the magnetometer needle. The effect of the current is balanced at the needle by means of a compensating coil connected up in the circuit. This latter coil has its axis coincident, or nearly so, with that of the solenoid. When a feebly magnetic specimen is under examination the solenoid, and con- sequently the compensating coil, must of necessity be brought up close to the needle. If large magnetising currents are employed, any small shift of the coils from their correct positions may be sufficient to seriously impair the balance. In consequence of this the operation of adjusting the position of the compensating coil (the solenoid is usually clamped once for all in a convenient position) is a difficult one, especially as the slight inevitable movement of the coil which results from clamping it in position generally results in the balance being interfered with. Even if this adjustment be accomplished with the requisite accuracy for the undisturbed position of the magnetometer needle, it does not necessarily follow that the compensation is complete for the needle in its deflected position. In practice the axes of the solenoid and compensating coils are in general slightly inclined to one another and to the east and west line passing through the needle. The effect of this is to increase the directive force on the needle for one direction of the current and to diminish it for the other. That this is the case will be seen from fig. 1, in which the want of alignment of the coil and solenoid has been greatly exaggerated. The magnetometer needle is situated at the point P, and it has been assumed that the solenoid and coil are so placed that they produce fields at P in the directions P S and P C respectively. If the intensity of the field due to the solenoid be denoted by Fs, and that due to the coil by Fc, then since the coils balance for the undisturbed position of the needle it follows that Fs cos (h = Fc cos 6 2- There are left, however, the components of the intensities 183 1908-9.| An Improved Form of Magnetometer. in the north and south direction, and it is evident from the figure that if H is the horizontal component of the earth’s magnetic field at P, the total directive force at the needle is H + (Fs sin + Fc sin 02). If the current is reversed in the circuit the directions of Fs and Fc change, and the directive force at the needle becomes H - (Fs sin d1 + Fc sin 02). The presence of the effect referred to may be made apparent by placing a permanent magnet close to the magnetometer, and thus deflecting the needle. On reversing a current in the circuit a change in the deflection will in general be observed. The magnitude of the errors introduced may be determined in this way for various parts of the scale and allowed for in the results, or the coils may be rotated until the effect disappears. If the former method is adopted, the labour of computing the results is much increased, and, further, it is difficult to make a proper correction, since the allowance to be made is a function both of the angle of deflection and the strength of the current. The second method can only be used if the coils are capable of being rotated on their stands, and the adjustments would be difficult and troublesome to carry out. The necessity for attending to this source of inaccuracy was first pointed out by Erhard,* who investigated the magnitude of the errors which were involved by neglecting it. In the case of a magnetometer of the usual type examined by him, it was found that with a magnetising field of 128'3 C.G.S. units in the solenoid there was a change of 6*8 per cent, in the directive force on the needle on reversal of the current. Erhard advised that the magnitudes of the errors introduced should be determined for various parts of the scale and allowed for in the results. While carrying out a research on certain feebly magnetic alloys the authors found that the elimination of the aforementioned sources of error caused very considerable delay in the progress of the work. An attempt * “ Eine Fehlerquelle bei magnetometrisclien Messungen,” Ann. der Phys ., 1902, p. 724. 184 Proceedings of the Koyal Society of Edinburgh. [Sess. was therefore made to design a form of magnetometer which would over- come these disadvantages which are common to instruments of the usual type. In planning the apparatus the following requirements were kept constantly in view : (1) the magnetometer must be capable of accurate and rapid adjustment, (2) there must be no resultant Erhard effect, (3) the instrument must be suited for testing specimens at all temperatures from that of liquid hydrogen to the critical temperature, (4) it must be alike efficient for testing strongly magnetic and feebly magnetic specimens, (5) the magnetising solenoid must be capable of furnishing fields up to at least 400 C.G.S. units, (6) the instrument must be rigid, all parts being fitted on one bed-plate, and the coils must be capable of being clamped without danger of destroying the compensation in so doing. The general principle of the instrument which has been evolved will be seen from fig. 2. n s represents the magnetometer needle provided with a L * n I s C, H s C3 Fig. 2. concave mirror, by means of which and a source of light L, its movements are observed on the scale S S. H is the magnetising solenoid placed due east or west of the magnetometer needle and clamped in a convenient position. C1 and C2 are compensating coils placed with their axes approxi- mately in coincidence with that of the solenoid. In adjusting the apparatus the effect of the current in H on the needle ns is first approximately annulled by means of Cj , which is then clamped in position. The final adjustment of the compensation, so far as the undisturbed position of the needle is concerned, is carried out by means of C2 , which on account of its great distance from the needle contributes only a small fraction of the balancing field, and thus provides an adjustment of great refinement. The position of C2 necessary for balance having been obtained, it is clamped in position ; obviously, since the distance of C2 from the needle is great, any slight movement caused by doing so produces no perceptible effect on the compensation. 185 1908-9.] An Improved Form of Magnetometer. If the axes of Cx , H, and C2 were coincident and passed through the magnetometer needle, the adjustment would now be complete. If, however, the needle ns is deflected by means of a permanent magnet, and a large current is reversed in the circuit, in general an alteration in the scale reading on S S will be observed. A coil C3 , placed with its axis in the magnetic north and south line passing through the needle, is now included in the circuit. By properly adjusting the direction of the current in C3 , and altering the distance of C3 from the needle, the compensation can be made perfect for all positions of n s* In a magnetometer where n s, Cl5 H, and C2 are all carried on stands moving in one channel in the bed-plate there should be little departure of the axes of the coils from coincidence. Accordingly the resultant magnetic field, due to the coils and solenoid, in the north and south direction will be small. The coil C3 is therefore made of little power, and a small change in its position brings about only a very slight alteration in its effect upon the needle. It can therefore be clamped without any risk of upsetting the balance. The manner of making the adjustments will be fully explained later. The instrument with its compensating coils and other fittings is shown in plan in fig. 3. The bed-plate is in the form of a cross, and is built of well- seasoned mahogany planks 22 cm. broad and 2*5 cm. thick. The length over all is 350 cm., and the breadth from end to end of the arms 135 cm. The cross-piece is at a distance of 100 cm. from one end of the main length. Like the main portion of the bed-plate, it is formed from one piece of wood, the two lengths being set accurately at right angles and half checked into one another. The junction is made rigid by means of glue and brass screws. A channel 11 5 cm. broad is formed over the entire length of the cross-piece by means of two mahogany strips which are square in section and fixed parallel to the edges of the arms. A similar channel runs down the main length of the bed-plate, being discontinued where it is crossed by the channel already mentioned. The wooden strips forming these channels are permanently fixed by glueing and by brass screws driven in from the under side of the base-board. After they have been constructed they are made of perfectly uniform width by sand-papering, the width being tested from time to time during the process by means of a wooden gauge. A is a mahogany box consisting of bottom, sides, and top, the ends which face east and west being left open. In the bottom is a slot running parallel to the cross-piece of the bed-plate. A brass screw projecting upwards from the base-board of the magnetometer passes through this slot and is provided * A side coil lias been used by Dr G. E. Allan in liis magnetometric work for giving compensation throughout the scale, but it does not permit of the adjustment here described. 186 Proceedings of the Royal Society of Edinburgh. [Sess. with a brass washer and locking-nut. By this means the box can be moved through a small distance in the north and south direction, and securely clamped in position. On the upper surface of the box is fastened a plate of glass on which stands the magnetometer proper. This part of the instru- ment is also constructed of mahogany. A wooden pillar 20 cm. in height has a narrow hole drilled longitudinally down through it. This hole terminates in a small cell with a glass window in front. The cell is just large enough to contain the mirror of the magnetometer — a concave mirror, 1 cm. in diameter, having a focal length of 50 cm. The mirror has attached to its back a small piece of magnetised watch-spring about 8 mm. in length. The needle and mirror are suspended by a tine quartz fibre from a screw at Fig. 3. — Plan of the Magnetometer. the top of the upright pillar of the magnetometer. By means of this screw, the axis of which is vertical, all torsion can be removed from the fibre when the needle is hanging in its equilibrium position ; and by giving the screw an observed number of complete turns a determination of the torsional rigidity of the fibre can be made. The pillar of the magnetometer is attached to a circular base provided with three small brass levelling-screws. The position of these feet on the glass top of the box-stand is defined by the hole, slot, and plane method. A A (fig. 6) is the magnetising solenoid. Two brass tubes 45 cm. in length are connected at their ends by brass rings so as to form a water- jacket B B measuring 4 cm. in internal and 6 cm. in external diameter. On the outside of this is wound 868 turns of No. 15 s.w.g. copper wire in four layers (only one layer is shown in the figure). The wire is double silk-covered, and each layer is varnished over after winding. The terminals 1908-9.] An Improved Form of Magnetometer. 187 of the coil are mounted on an ebonite block at one end of the solenoid. D and C are the inlet and outlet tubes of the water-jacket. Although the water-jacket is somewhat narrow it is found to be effective in keeping the helix of wire cool, even though the interior is raised to a temperature of over 1000° C. by means of an electric furnace. The water-jacket is made small in capacity in order to keep down the mean radius of the solenoid, and lienee maintain the end effect of the solenoid small. The field at the centre of a coil of length 2 1 and radius a is less than that given by O’^irnC in the ratio (l2 — 2a2)/l2, where n is the number of turns in the coil per unit length and C is the magnetising current in amperes. In the case of the solenoid now described the reduction in the field from the value 0'47mC due to the finite length of the coil is only 1T4 per cent. The solenoid is carried on a mahogany base-board provided with two vertical supports terminating in V-shaped grooves to receive the coil. The position of the solenoid carrier in the channel of the magnetometer board may be fixed by means of a brass clamp (shown in fig. 3). This friction clamp is furnished with two screws which press mahogany blocks against the outer surfaces of the wooden strips forming the channel of the magnetometer bed-plate. Cj_ and C2 (figs. 2 and 3) are circular coils of 15 cm. radius erected on wooden stands provided with brass clamps as in the case of the solenoid. Each coil is wound in three sections, the terminals of which are screwed into the base of the stand. The sections in the case of Cx contain 5, 7, and 9 turns of wire respectively, and in the case of C2 6, 8, and 10 turns. These sections may be used singly or in combination, and accordingly there is a wide range of variability in the powers of the coils. C3 is a coil of similar construction, but has a radius of only 6 cm., and is built in two sections of 1 and 3 turns of wire respectively. D is a coil having a radius of 12 cm., and its function is to prevent loss of time due to the needle vibrating about its position of equilibrium. It is connected up in series with a single cell and a reversing key ; and by properly tapping the key a series of impulses is communicated to the needle, which is thus quickly brought to rest. L is a further sliding stand carrying the object screen. This consists of a vertical wire placed in front of a window of obscured glass fitted in a metal box containing an incandescent lamp. By altering the position of this stand, the image of the cross-wire formed by the mirror of the magneto- meter can be produced at any distance from 110 cm. upwards. From 150 cm. to 200 cm. is in most cases a suitable value. At this distance it is received on an engine-divided glass scale of the usual type. E is a deflector stand on which a small permanent magnet may be L 8 8 Proceedings of the Royal Society of Edinburgh. [Sess. mounted in the “ B ” position of Gauss. The construction of the stand is similar to that of the stand which carries the magnetometer proper. On the top of it is fixed a rectangular block of wood provided with a groove for receiving the magnet. The bed-plate of the magnetometer is mounted on six pairs of mahogany feet, which are fastened to a rigid table by means of brass screws. The process of setting up the apparatus is as follows. The centre of the magnetometer needle has first to be placed on the axis of the solenoid. To accomplish this, coil C1 (fig. 3) is removed, and the solenoid H is moved along the bed-plate towards A until its inner end is almost in contact with the back of the magnetometer casing. The stand A is then moved in its channel until the needle is brought exactly on to the axis of the helix, and is then permanently fastened in this position by means of the clamping screw already mentioned. The table carrying the magnetometer is now placed so that the long channel of the bed-plate lies due east and west, the adjust- ments being carried out and tested by means of the well-known method described in Gray’s Absolute Measurements in Electricity and Magnetism. The method is as follows : — A wire is stretched out vertically beneath the needle, and accurately parallel to the short channel of the bench. On passing a current through this wire a deflection of the needle is produced. If the current is reversed in direction the deflection will have the same numerical value as before, provided that the wire lies exactly magnetic north and south. The table is so placed that this condition is fulfilled, and its feet are then clamped to the floor by means of L -shaped brass brackets. The scale is erected on a separate table in order that the movements of the observer may not set up oscillations of the needle. The coils C15 H, and C2 are now con- nected up in series with the storage battery, ammeter, and variable resist- ances, etc., care being taken that the direction of the current in Cx and C2 is opposite to that in H. The permanent adjustments of the instrument are now complete. When a specimen has to be tested the solenoid H is moved to a convenient distance from the magnetometer needle and firmly clamped. The coil C2 is placed at the far end of the magnetometer table, and a current two or three times greater than the maximum to be used in the subsequent test is sent through the complete circuit. Coil Cx is then moved until it just falls short of balancing the effect of the solenoid on the needle. It is then securely clamped. Coil C2 is next slowly moved up towards the magnetometer needle until the deflection of the latter is brought exactly to zero ; C2 is now clamped, and the accuracy of the compensation verified by suddenly reversing the current in the coils. No measurable change in the scale reading should 189 1908-9.] An Improved Form of Magnetometer. result. The current having been interrupted, a small permanent magnet is next placed east and west on the stand E, and the stand moved along the cross channel in the magnetometer bed-plate until the spot rests near one extremity of the scale. The current is again made and reversed, and if any appreciable deflection of the spot on the scale is observed coil C3 is in- cluded in the circuit, the current being so directed through it that the de- viations of the needle from its equilibrium position are diminished. The coil is gradually moved closer to the magnetometer until the Erhard effect is completely wiped out, and is then clamped in position. The compensation now holds for all parts of the scale, and the apparatus is ready for carrying out magnetic tests. The several sections in which the three compensating coils are built allow the adjustment to be completely made with the coils in several different positions. This is a great advantage, as it always affords a means of escape from any arrangements of the coils which might prove awkward when specimens are in the solenoid. With reference to the adjustment of the coils described above, it should be noted (1) that the method is systematic, and that there is no possibility of failure to secure a balance — all the adjustments are carried out in a perfectly definite manner ; (2) that the method is delicate ; for, owing to the great dis- tance of coil C2 from the magnetometer needle, it may generally be moved several millimetres without causing any appreciable error in the compensa- tion ; (3) that the method is capable of furnishing a high degree of accuracy ; with the near end of the solenoid at a distance of only 12 cm. from the magnetometer needle it is quite possible to arrange that the change in the scale reading brought about by reversing a current of 15 amperes in the circuit is only a fraction of 1 mm. with the scale at a distance of 175 cm. from the needle ; (4) that the operations can be carried out with great rapidity ; unless the solenoid is very close up to the magnet- ometer, the changing over of the apparatus from one degree of sensibility to another can be carried out within the space of two minutes. The magnitude of the directive force at the needle is easily determined by passing a measured current through one of the balancing coils and noting the deflection of the magnetometer needle produced. The value of the directive force is then easily calculated. Fig. 4 is a photograph of the apparatus when adjusted for the examina- tion of a strongly magnetic specimen ; fig. 5 shows the arrangement when a feebly magnetic specimen is being dealt with. When the solenoid has to be placed very close to the magnetometer needle to allow of a very feebly magnetic specimen being examined, the coil C1 is placed on the opposite side 190 Proceedings of the Royal Society of Edinburgh. [Sess. of the needle to the solenoid. For general use, however, it is convenient to have the solenoid and coil on the same side. It is worthy of remark, in passing, that even if is placed as close up as possible to the end of the Fig. 4. solenoid, it can alter the field at the centre of the specimen by not so much as \ per cent. When used for testing specimens at temperatures higher than that of the room, an electric furnace of a type similar to that devised by Dr G. E. Allan,* is placed within the helix. In fig. 6 it is shown in position. A Fig. 5. tube E of unglazed porcelain of about the same length as the solenoid, having an internal diameter of 23*5 mm. and a thickness of about 2 mm., is wound non-inductively with fine platinum wire ; the ends of this wire are brought out to two terminals mounted on a slate frame at F. The tube * Phil. Mag., 1904, p. 46. 1908-9.] An Improved Form of Magnetometer. 191 is enclosed in a tube G of Jena glass, which fits as a cartridge within the magnetising solenoid. The space H H between the glass and porcelain tubes is packed with dry kaolin clay, which performs the double duty of supporting the furnace and preventing the coils of the platinum wire from changing their positions when expanded by heat. A cylinder of electrolytic D sheet-copper is placed within the tube E, and assists in maintaining a very uniform temperature over the space occupied by the specimens. In the figure the platinum wire is shown equally spaced over the porcelain tube. In reality this is far from being the case. The proper winding of the tube is an exceedingly troublesome operation, and can only be accom- plished by repeated trial. I m Fig. 7. 0 c The temperature of the furnace is measured b}^ means of the ordinary thermo-element or a platinum resistance thermometer. The two wooden stands used for the pyrometer are shown in position in figs. 4 and 5. As will be seen at once, the several slots in the horizontal carrier for fitting on the tops of the stands permit of these latter being placed clear of the sliding bases of the compensating coils. For tests at the temperature of liquid air the arrangement shown in fig. 7 is employed. The specimen A is enclosed in a glass tube BCD, of which the end B is closed and the end D is open and bent up. Cork bungs 192 Proceedings of the Royal Society of Edinburgh. [Sess. F, F, are fitted on the tube so as to bring the axis of the specimen into coincidence with that of the solenoid. A third bung F or a pad of cotton- wool is used to prevent access of warm air into the interior of the solenoid, and a covering of cotton-wool on the portion C D prevents it from warming up and conducting heat to the specimen. Instead of closing the glass tube at B, a cork may be used to stop up the opening, The cork, however, if dry, is liable to loosen and permit the liquid air to leak out, or if it is at all damp it expands and fractures the tube. Where tests have to be made as the specimen slowly warms up from the temperature of liquid air a Dewar tube is used, with its mouth closed by a cork which has two bent tubes passed through it — one for pouring in the liquid air, and the other for the bringing out of the leads from one or more thermo-elements in contact with the specimen. The dimensions given above for the internal diameter of the solenoid will be found sufficient for receiving a double vacuum Dewar tube for tests at — 252° C. on specimens immersed in liquid hydrogen. A slightly modified form of the stand supporting the solenoid permits of the latter being carried in an east and west position on one of the arms of the cross-piece of the magnetometer. The apparatus is therefore avail- able for use with specimens in either the “ A ” or “ B ” position of Gauss ; the methods described in Gray’s Absolute Measurements in Electricity and Magnetism for the determination of the effective lengths of the specimens thus become available. The considerable height of the magnetometer needle above the level of the magnetometer base-board (18 cm.) would also permit the apparatus to be readily adapted for testing by the “ one-pole ” method.* Several instruments of the above type have been built in the Physical Institute of the University of Glasgow, and are giving every satisfaction. * See Ewing’s Magnetic Induction in Iron and other Metals , p. 39. ( Issued separately April 17, 1909.) Ill the printer is not responsible, the expense of such proofs and corrections will be charged against the author. All proofs must, if possible, be returned within one week, addressed to The Secretary , Royal Society , Mound , Edinburgh, and not to the printer. To prevent delay, authors residing abroad should appoint some one residing in this country to correct their proofs. 4. Additions to a Paper after it has been finally handed in for publication, if accepted by the Council, will be treated and dated as separate communications, and may, or may not, be printed immediately after the original paper. 5. Brief Abstracts of Transactions Papers will be published in the Proceedings, provided they are sent along with the original paper. 6. Separate Issue of Reprints; Author’s Free and Additional Copies. — As soon as the final revise of a Transactions paper has been returned, or as soon as the sheet in which the last part of a Proceedings paper appears is ready for press, a certain number of separate copies or reprints, in covers bearing the title of the paper and the name of the author, are printed off and placed on sale. The date of such separate publication will be printed on each paper. The author receives fifty of these reprints free, and may have any reasonable number of additional copies at a fixed scale of prices which will be furnished by the printer, who will charge him with the cost. To prevent disappointment, especially if the paper contains plates, the author should, immediately after receiving his first proof, notify to the printer the number of additional copies required. 7. Index Slips. — In order to facilitate the compilation of Subject Indices, and to secure that due attention to the important points in a paper shall be given in General Catalogues of Scientific Literature and in Abstracts by Periodicals, every author is requested to return to the Secretary, along with his final proof, a brief index (on the model given below), of the points in it which he considers new or important. These indices will be edited by the Secretary, and incorporated in Separate Index Slips, to be issued with each part of the Proceedings and Transactions. MODEL INDEX. Schafer, E. A. — On the Existence within the Liver Cells of Channels which can be directly injected from the Blood-vessels. Proc. Roy. Soc. Edin., vol, 1902, pp. Cells, Liver, — Intra-cellular Canaliculi in. E. A. Schafer. Proc. Roy. Soc. Edin., vol. , 1902, pp. Liver, — Injection within Cells of. E. A. Schafer. Proc. Roy. Soc. Edin., vol. , 1902, pp. The Papers published in this Part of the Pkoceedings may be had separately, on application to the Publishers, at the follow- ing prices : — No. IX., No. X., No. XI., No. XII., Price Is. 8d. Sd. 6d. 8d. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SESSION 1908-9. Part IV.] VOL. XXIX. [Pp. 193-384. CONTENTS. NO. PAGE XIII. Life and Chemical Work of Archibald Scott Couper. By Richard Anschutz, Ph.D., LL.D., Professor of Chemistry in the University of Bonn. ( Translated and communi- cated by Emeritus- Professor A. Crum Brown, M.D., D.Sc., LL.D.) (With Two Plates), .... 193 (Issued separately April 30, 1909.) XIV. On the Magnetic Properties of certain Copper Alloys. By Alexander D. Ross, M.A., B.Sc., Assistant to the Pro- fessor of Natural Philosophy in the University of Glasgow, and Robert C. Gray, Thomson Experimental Scholar in the University of Glasgow, . . . . .274 (Issued separately May 3, 1909.) XV. Low Temperature Experiments in Magnetism. By James G. Gray, B.Sc., Lecturer on Physics in the University of Glasgow, and Hugh Higgins, M.A., Thomson Experi- mental Scholar in the University of Glasgow. ( Com- municated by Professor A. Gray, F.R.S.), . . . 287 (Issued separately May 11, 1909.) XVI. On the Discharge of Water from Circular Weirs and Orifices. By G. H. Gulliver, B.Sc., A.M.I.Mech.E., Lecturer in Engineering in the University of Edinburgh, . . 295* (Issued separately May 11, 1909.) [ Continued on page iv of Cover. EDINBURGH : Published by ROBERT GRANT & SON, 107 Princes Street, and WILLIAMS & NORGATE, 14 Henrietta Street, Covent Garden, London. MDdCCCIX. Price Eleven Shillings and Ninepence. REGULATION S REGARDING THE PUBLICATION OF PAPERS IN THE PROCEEDINGS AND TRANSACTIONS OF THE SOCIETY. The Council beg to direct the attention of authors of communications to the Society to the following Regulations, which have been drawn up in order to accelerate the publication of the Proceedings and Transactions, and to utilise as widely and as fairly as possible the funds which the Society devotes to the publication of Scientific and Literary Researches. 1. Manuscript of Papers. — As soon as any paper has been . passed for publication, either in its original or in any altered form, and has been made ready for publication by the author, it is sent to the printer, whether it lias been read or not. The ‘ copy ’ should be written on large sheets of paper, on one side only, and the pages should be clearly numbered. The MS. must be easily legible, preferably typewritten, and must be absolutely in its final form for printing; so that corrections in proof shall be as few as possible, and shall not cause overrunning in the lines or pages of the proof. All tables of contents, references to plates, or illustrations in the text, etc., must be in their proper places, with the page numbers left blank ; and spaces must be indicated for the insertion of illustrations that are to appear in the text. 2. Illustrations. — All illustrations must be drawn in a form im- mediately suitable for reproduction ; and such illustrations as can be reproduced by photographic processes should, so far as possible, be preferred. Drawings to be reproduced as line blocks should be made with Indian ink (deadened with yellow if of bluish tone), preferably on fine white bristol board, free from folds or creases ; smooth, clean lines, or sharp dots, but no washes or colours, should be used. If the drawings are done on a large scale, to be afterwards reduced by photography, any lettering or other legend must be on a corresponding scale. If an author finds it inconvenient to furnish such drawings, the Society will have the figures re-drawn at his expense ; but this will cause delay. When the illustrations -are to form plates, a scheme for the arrangement of the figures (in quarto plates for the Transactions, in octavo for the Proceedings) must be given, and numbering and lettering indicated. 3. Proofs. — In general, a first proof and a revise of each paper will be sent to the author, whose address should be indicated on the MS. If further proofs are required, owing to corrections or alterations for which [Continued on page iii of Cover. Proc. Roy. Socy. of Edin. ] [Vol. XXIX Frontispiece. 1908-9.] Life and Chemical Work of Archibald S. Couper. 193 XIII. — Life and Chemical Work of Archibald Scott Couper. By Richard Anschutz, Ph.D., LL.D., Professor of Chemistry in the University of Bonn. Translated and communicated by Emeritus- Professor A. Crum Brown, M.D., D.Sc., LL.D. (MS. received January 25, 1909.) Preface. Archibald Scott Couper is one of the most singular appearances in the history of the development of Organic Chemistry in the nineteenth century. He comes on the scene at the time — the end of the ’fifties — when the valency theory began its victorious entrance into our science. His two experimental investigations, “ On some Derivatives of Benzene,” and “ On Salicylic Acid,” as also his communication on “A New Chemical Theory,” were published within the limits of one year, and then with startling suddenness his scientific career comes to an end. Belonging to none of the then existing chemical schools, and furnished with an excellent philosophical training, Couper boldly attacked with sharp criticism the theories prevailing in chemistry at the time. No claim of priority can be made for his assumption of the concatenation of carbon atoms, but, as will be shown in this paper, his statement was quite independent of that published somewhat earlier by Kekule. Without any doubt, Couper deserves the credit of having introduced into constitutional formulae the lines indicating union of atoms, and of having thus produced what are now called structural formulae. The results of his work on salicylic acid, long doubted by all the chemists who had repeated his experiments, were at last shown by the present writer to be accurate. In my efforts to help to his historic rights a fellow-chemist as distin- guished as he was unfortunate, and to obtain information as to his origin and life, I have been assisted by my honoured colleagues Heinrich Debus, Greville Williams, Adolf Lieben, Albert Ladenburg, and Alexander Crum Brown. Above all, I have to thank the sympathetic zeal with which Alexander Crum Brown, at my request, gave himself to the discovery of biographical details of his countryman’s life. All of that, which I have been able to communicate, as also the translation of this paper into English, is his work. VOL. XXIX. 13 194 Proceedings of the Royal Society of Edinburgh. [Sess. Although in physical science there are no national frontiers, still we may expect that the life and achievements of a distinguished investigator will be of special interest to his countrymen. This consideration moved me to offer my paper on the life and chemical work of Archibald Scott Couper to the Royal Society of Edinburgh, and I had the pleasure of seeing it accepted. Couper ’s three short papers from the Comptes rendus de VAcademie des Sciences have been reprinted here. Couper published his paper on salicylic acid also in English in the Edinburgh New Philosophical Journal , adding his new structural formulae for the derivatives of salicylic acid prepared by him. He gave a full account of his new chemical theory in a paper in the London, Edinburgh, and Dublin Philosophical Magazine, and at the same time published a French translation of this paper, with some additions, in the Annales de chimie et de physique . I have thought it convenient to print the papers on salicylic acid and the two full accounts of the new chemical theory in both languages, on alternate pages, so as to facilitate reference. I am hopeful that this unambitious paper may conduce to place the memory of Archibald Scott Couper in its right place in the history of our science, and I thank the Royal Society of Edinburgh for the way in which it has met my endeavour to do this. Richard Anschutz. In the history of the development which organic chemistry (or the chemistry of the compounds of carbon) underwent in consequence of the introduction of the hypothesis of the quadrivalence of carbon and the concatenation of carbon atoms, we meet alongside of the conspicuous name of Friedrich August Kekule that of Archibald Scott Couper. But Couper had to submit to the hard fortune that his paper “ On a New Chemical Theory” was, owing to no fault of his, published too late. It is true that this paper is referred to in chemical history books, but Couper himself fell so completely out of memory that I have not been able to find his name in any of the dictionaries of scientific biography. As Couper’s three papers appeared for the first time, soon after one another, in the Comptes rendus Jtebdomadaires des seances de VAcademie des Sciences , many chemists seem to have taken him for a Frenchman, although his Christian name “ Archibald ” * points to Scotland, which is indeed his native land. * In the Comptes rendus the name is given as A. Couper ; in the Annales de chim. et de phys. as A. S. Conper. 1908-9.] Life and Chemical Work of Archibald S. Cooper. 195 Besides the theoretical paper, Couper published a communication “ On some Derivatives of Benzene,” and, somewhat later, a very excellent experimental work, “ Researches on Salicylic Acid.” But just as Couper, through no fault of his, came too late with his theoretical paper, so also with his work on salicylic acid, in which he investigated the action of phosphorus pentachloride on salicylic acid, he had the misfortune that two of the most distinguished German chemists, August Kekule and Hermann Kolbe, as well as some others, repeated his experiments, but were unable to confirm his results. Here Couper’s appearance in chemistry comes to an end. Although his gifts seemed eminently to qualify him for a brilliant scientific career, no further communication of his is to be found in any scientific journal. How did this come about ? What became of Archibald Scott Couper ? My interest in Couper was first awakened by his work on the action of phosphorus pentachloride on salicylic acid, a subject on which I also was specially engaged. My sympathy with Couper grew when, in the course of the studies required for the preparation of a complete biography of Kekule, I found it necessary to go very thoroughly into Couper’s paper “ On a New Chemical Theory.” This paper of Couper’s must indeed always take its place beside that of Kekule “ On the Constitution and Metamorphoses of Chemical Compounds and on the Chemical Nature of Carbon.” The first information I obtained as to Couper’s life was from a letter of Greville Williams, to whom my honoured friend Heinrich Debus applied in order to help me. Some time ago, with Debus’ permission, I appended this letter as a note to my paper “ On the Action of the Pentachloride and of the Trichloride of Phosphorus on Substituted o-Phenolcarboxylic Acids,” published in Liebig s Annalen * and I repeat it here : — “21 Bournevale Road, Streatham, S.W., 10th August 1903. “Dear Sir, — I grieve to say that I know nothing of the origin of poor Couper. I first became acquainted with him when I was assistant to Dr (afterwards Lord) Playfair in the University of Edinburgh, where Couper was a student in the laboratory, but he soon left. I only saw him once more, when he came up to me on the seashore at Dunoon on the Clyde, but he was then a complete wreck. I believe his trouble originated in sunstroke. I deeply regret being unable to give you more information about this great but unfortunate genius. — Yours very truly, “Greville Williams.” * cccxlvi. 291 (1906). 196 Proceedings of the Royal Society of Edinburgh. [Sess. At my request Debus now applied to Dr Alex. Crum Brown, Playfair’s successor in the Edinburgh Chair of Chemistry. Although the problem seemed hopeless, he attacked it with the greatest earnestness and un- common skill, and he succeeded. I am thus enabled to give the following notes of Couper’s life, and here thank my honoured friend and distinguished colleague for his kindness in placing in my hands the results of his successful efforts. The communica- tions which I have used in these biographical notes were obtained by Crum Brown in the first place from Couper’s cousins, Mrs Little and Miss Tait, Kirkintilloch, and Mr Dollar, the eminent veterinary surgeon, London, and from a university friend of Couper, Mr Berring, Coblenz. Archibald Scott Couper was born March 31st, 1831, at Townhead,* Kirkintilloch, Dumbartonshire, about six miles north-east of Glasgow. He was the only surviving son of Archibald Couper, proprietor of a large cotton-weaving establishment, employing from 600 to 700 weavers. His mother’s maiden name was Helen Dollar. Couper’s father inherited the business from his father, who was married to Janet Scott. Couper’s second name, “ Scott,” thus came to him from his paternal grandmother. There is not much to say about Couper’s early youth ; it is obvious that he had a good and careful education at home. In the summer or autumn of 1851 Couper went with his intimate friend, Alexander Hamilton, -f* to Germany. They had become acquainted in Glasgow, where a similarity of taste in literature and philosophy drew them together. The two young Scotsmen, in a family in Halle to which they had been recommended, applied themselves so diligently to the study of the German language (wdiich is said to be easier for Scotsmen than for Englishmen), that they were soon able to use it with ease. During the winter session 1851-52, Couper attended Latin and Greek classes in the University of Glasgow. In the summer of 1852 we again find Couper and Hamilton in Berlin, where Berring j made their acquaintance. Berring reports that at that time Couper followed no special line of study, but took a look at various fields of knowledge. In August 1852 Couper returned to Scotland, and exchanged the University of Glasgow for that of Edinburgh. From this continued * Tlie house, which is in the street, is now converted into shops, and the garden partly covered with buildings. t Alexander Hamilton, M.A. 1851, D.D. 1872 ; United Presbyterian minister, Kilmarnock 1855-1872, Brighton 1871-1896. Died at Brighton, 1902. X Afterwards Geheimrat, and director of the engineering works in connection with the navigation of the Rhine. 1908-9.] Life and Chemical Work of Archibald S. Couper. 197 university attendance we may conclude that Couper had decided not to follow his father’s business, and that his father was pleased to allow his talented son the choice of a learned career. In Edinburgh the study of philosophy took its place beside that of language. Couper attended the lectures of Sir William Hamilton on logic and on metaphysics, and of Professor MacDougal on moral philosophy. Still Couper does not seem to have taken to chemistry ; at least, we find no mention of scientific studies in his notebooks. Next summer, 1853, Couper and Hamilton returned to Germany and spent some weeks on a visit to Berring’s family in Minden, Westphalia. They then made a tour through South Germany, North Italy and the Tyrol, and returned to Scotland. In the autumn of 1854, or the spring of 1855, Couper came again to Berlin, which evidently had an attraction for him. His friendship with Berring, who was then studying engineering at the “ Bauakademie ” in Berlin, led the two to take rooms together in a small private hotel. 75 Dorotheenstrasse, where they lived together till Couper left Berlin for Paris in August 1856. In the meantime Couper had made up his mind for physical science in general and for chemistry in particular. We have no means of know- ing what influences or considerations led to this decision, but in any case the turn for chemistry was not present in his early youth, but must have gradually developed during the years of his university life. Berring cannot now with certainty give the name of Couper’s teacher of chemistry in Berlin, but he thinks he worked under Rammelsberg. However that may be, there is no doubt that he attended Sonnenschein’s lectures on analytical chemistry, and worked for two months in the summer of 1856 in his laboratory. In short, he used the three or four sessions he spent in Germany to perfect himself in analytical chemistry. While many of his countrymen went to Heidelberg or to Munich, to work under Bunsen or to hear Liebig’s lectures, Couper turned to Paris and found a place in Wurtz’s laboratory. In passing, it may be mentioned that in the same year Kekule began to lecture in Heidelberg, his chemical student days lay behind him when Couper’s hah just begun. With astonishing rapidity, after only three or four sessions of chemical study, Couper had acquired the knowledge and the skill necessary to enable him to carry out independently experimental chemical investigations. On Couper’s arrival in Paris, Wurtz had just published his brilliant 198 Proceedings of the Royal Society of Edinburgh. [Sess. discovery of glycol, by the treatment with caustic potash of the glycol diacetate obtained by the interaction of ethylene iodide and silver acetate. Couper’s first work, published in August 1857, is so closely connected with this discovery that one is led to surmise that Wurtz had suggested its subject to Couper — indeed, Couper’s paper, “ Recherclies sur la Benzine,” * immediately follows a paper by Wurtz, “Note sur la liqueur des Hollan- dais,” j- in the Gomptes reudus. Couper’s Investigations on Benzene. Couper started with the supposition that it is possible to convert benzene into the corresponding alcohol and the corresponding glycol. With this view, he treated boiling benzene with bromine vapour and thus discovered brombenzene (boiling point 150°), as well as the dibrombenzene fusing at 89° and boiling at 219°, our p dibrombenzene. He nitrated and sulphonised the monobrombenzene. He heated both the brombenzenes to 200° with silver acetate in sealed tubes. He ascertained that mono- brombenzene scarcely acts on silver acetate. With better hope of success he tried the action of silver acetate on dibrombenzene, but unfortunately lost his material by an explosion, and had to postpone the continuation of the experiment. In his communication Couper uses the small equivalents C = 6, 0 = 8, 4 as Wurtz also always did at that time, and wrote, for instance : — “ Bromobenzine C12H5Br Dibromobenzine C12H4Br2 ra2fj4 ) Phenylglycol diacetique /C4H3Q2^ } °4-” From this it will be seen that Couper was, at that time, by no means so much under the influence of Gerhardt’s type theory as Kekule was so early as April 1854 ; see his famous paper, “ On a New Series of Sulphurated Acids.” I He had not, like Kekule, had the opportunity of developing his scientific opinions by close scientific intercourse with Gerhardt in Paris, and then with Odling, and especially with Williamson in London. No doubt Couper uses for his expected “ phenylglycol diacetique ” a typical formula; but it is of a sort then generally used even in Germany, and derived from the multiple type of water H202, and not from the type H20 * Comptes rendus, xlv. 230-232. See Appendix to this paper, p. 235. t Ibid., xlv. 228-230. I Proceedings of the Royal Society of London, vii. 37-40. 1908-9.] Life and Chemical Work of Archibald S. Couper. 199 of Gerhardt and Williamson. I specially note this point, because Couper, in the new theory which he produced in the course of the next year, freed himself, at least partially, from these erroneous assumptions. Although Couper’s paper “ Sur une nouvelle theorie chimique ” * appeared somewhat later than his second and last experimental work, “ Recherches sur l’acide salicylique,” f I think it more convenient to con- sider Couper ’s theoretical views here. For it is not until the close of the paper “On a New Chemical Theory,” that Couper applies this theory to salicylic acid, whereas in the French paper on salicylic acid, as also in that on benzene, he uses almost exclusively empirical molecular formulae. In order to bring his work before his own countrymen, Couper published a full exposition of his new theory in the London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science H e translated this paper into French, and, with some additions, published it in the Annales de chimie et cle physique .§ He also translated the paper on salicylic acid into English, applying his new theory to the formulation of the derivatives of salicylic acid discussed in it. This translation was printed in the Edinburgh New Philosophical Journal , 1858. || On Couper’s New Chemical Theory. As soon as Kekule, at that time Privatdocent in Heidelberg, saw Couper’s paper in the Comp>tes rendus, he brought forward his claims to the two most important propositions contained in it. Already, in the report of the meeting of the French Acadeni}^ on the 30th August 1858, we find Ivekule’s communication, “ Remarques de M. A. Kekule a l’occasion dune note de M. Couper sur une nouvelle theorie chimique.’T We shall therefore most conveniently follow Couper’s statements along with Kekule’s remarks on them. In this connection there came to my mind a remark which Kekule introduced into his speech at the celebration of the twenty- fifth year of the benzene theory, held in Berlin on the lltli of March 1890 : ** “ Some ideas at some time lie in the air : if one does not give expression to them, another will soon do so.” Or, as I may add in expansion, different thinkers often come independently and about the same time to proclaim * Comptes rendus, xlvi. 1157-1160. See Appendix to this paper, p. 237. t Ibid., xlvi. 1107-1110. See App., p. 266. X xvi. 104-116. See App., p. 240. § [3], liii. 469-489. See App., p. 241. || viii. 213-217. See App., p. 267. "fT Comptes rendus, xlvii. 378-380. ** Ber. d. Deutsch. Chcm. Ges., xxiii. 1304. 200 Proceedings of the Royal Society of Edinburgh. [Sess. the same idea, when the hour of its birth has struck. For, in Couper’s paper, “ On a New Chemical Theory,” the hypothesis of the quadrivalence of carbon and of the concatenation of carbon atoms was developed shortly after the same had been done by Kekule, and it was — as I have already indicated — only by an accident fateful for Couper that his paper did not appear simultaneously with that of Kekule, “ fiber die Constitution und die Metamorphosen der chemischen Yerbindungen und die chemisclie Natur des Kohlenstoffs,” * which became so famous. No doubt Kekule had already set up the marsh-gas type in his paper on mercuric fulminate, and in a note to the paper, “ fiber die sogenannten gepaarten Verbindungen und die mehratomigen Radicale,” sent to the editors of Liebigs Anncilen on the 15th of August, 1857, expressed himself thus *f : — “ Der Kohlenstoff ist, wie sicli leicht zeigen lasst und worauf ich spater ausfuhrlicher eingehen werde, vierbasisch oder vieratomig d.h. 1 Atom Kohl enst off =■0 = 12 ist Equivalent 4 At. H.” In this the hypothesis of the concatenation of carbon atoms was also contained Implicitly. All the same, authentic communications which I have received from highly valued sources leave no doubt that Couper’s paper “ On a New Chemical Theory ” was in the hands of Adolphe Wurtz before the number of Liebig s Anncilen issued on the 19th of May, and containing Kekule’s paper, dated 16th March, was published. J In a letter dated 29th March 1906, Adolph Lieben writes to me : — “ Couper’s Arbeit ist ganz unabhangig von der Kekule’s, was Niemand besser Aveiss als ich. Couper, der damals, so wie ich, in Wurtz’s Laboratorium arbeitete, war gewohnt seine Entwiirfe und Ideen mit mir durchzusprechen und Iibergab mir auch, vor der Publication, seine spater in den Comjpt. rend. 1858 erschienene Abhandlung zur Priifung, dann iibergab er sie Wurtz. Mittlerweile erscliien das Ende Mai ausgegebene Heft der Annalen mit Kekule’s ahnlieher Arbeit und Couper war iiber dieses Zusammentreffen ausserst bestiirzt.” In a letter dated 12th May 1906, Albert Ladenburg gives the following from his recollection : — “Couper arbeitete bei Wurtz in Paris und bat dissen seine Abhandlung iiber die Vierwertigkeit des Kohlenstoffs der Akademie zu iiberreiclien. Wurtz, der damals selbst noch nicht Mitglied war, musste die Abhandlung an einen Anderen der Mitglied Avar (gewohnlich Balard) geben. Er verbummelte dies ein wenig und so erscliien Kekule’s Mitteilung, ehe die von Couper der Akademie vorgelegt Avar. Darob grosser Zorn von Couper, der Wurtz zur Rede stellte und ausfallig wurde. * Liebig’ s Annalen , cvi. 129-159. f Ibid. , cvi. 129-159. t Ibid., civ. 133, Anm. 1908-9.] Life and Chemical Work of Archibald S. Couper. 201 Wurtz liess sicli das niclit gefallen und vervvies ilm aus deni Laboratorium. Couper scheint sich dies sehr zu Herzen genommen zu liaben, und in Paris glaubte man den Anfang seiner Kranklieit daher zu datieren. Die Geschichte selbst ist authentisch, icli babe sie von Wurtz.” Now that it is thus settled that Couper ’s paper “On a New Chemical Theory,” presented by Dumas to the French Academy, was independent of the corresponding exposition published somewhat earlier by Kekule, I turn to its contents. It is the case that the line of thought, and so also the mode of expression of the two, have often a startling similarity, though there is no lack of individual peculiarities. Kekule points out that the opening sentences of Couper’s paper — “Je remonte aux elements eux- memes dont j’etudie les affinites reciproques. Cette etude suffit, selon moi, a l’explication de toutes les combinaisons chimiques ” — completely agree in meaning with the passage in his own German paper,* which he gives in French thus: — “ Je crois necessaire pour l’explication des proprietes des combinaisons chimiques de remonter jusqu’aux elements eux-memes qui les constituent.” A little further on Couper says of carbon : “ La puissance de combinaison la plus elevee que l’on connaisse pour le carbone est celle du second degre, c’est-a-dire 4.” To this comes as the second property of carbon : “ II entre en combinaison avec lui-meme. “ Ces deux proprietes suffisent a mon avis pour expliquer tout ce que la chimie organique offre de caracteristique. Je crois que la seconde est signalee ici pour la premiere fois. A mon avis, elle rend compte de ce fait important et encore inexplique de l’accumulation des molecules de carbone dans les combinaisons organiques. Dans les composes ou 2, 3, 4, 5, 6, etc., molecules de carbone sont liees ensemble, c’est le carbone qui sert de lien au carbone.” Kekule seems to have overlooked the fact that Couper does not claim for himself the hypothesis of the quadrivalence of carbon, but only that of the concatenation of the carbon atoms, for he remarks on the passage just quoted (from which he omits the words, “ Je crois que la seconde est signalee ici pour la premiere fois ” ) as follows : — “ Nous ne saurions lui accorder que ces proprietes soient signalees par lui pour la premiere fois. Deja dans mon premier Memoire [page 133, note] j’ai dit expressement que le carbone etait de nature quatriatomique, c’est-a-dire, que 1 atome de carbone (C = 12) est equivalent a 4 atonies d’hydrogene (H — 1), j’ai ajoute que, par con- sequent, les combinaisons les plus simples du carbone avec des elements du premier groupe (elements monatomiques) etaient CH4 , CC14 , etc. Dans * Liebig's Annalen , cvi. 13G. 202 Proceedings of the Royal Society of Edinburgh. [Sess. mon second Memoire j’ai donne, en outre, plus de developpement a cette idee [page 153] et j’en ai tire comrne corollaire [page 154] que dans les substances contenants plusieurs atonies de carbone, on ne peut expliquer cette accumulation que par l’hypothese que les atonies du carbone lui- meme soient lies entre eux, en neutralisant ainsi une partie de leur affinite generale. J’ai cru pouvoir fonder cette hypothese sur divers exemples trop prolixes pour les rappeler ici ; je me contenterai de faire remarquer que, moi aussi, j’ai donne une formule generale qui exprime, pour une certaine classe de combinaisons, le nombre d’atomes d’hydrogene combines avec n atomes de carbone, dans les termes suivants : p n * 4— 2)+2 ? tandis que M. Couper, de son cote, l’exprime de cette maniere : CnMn.4 - Mm 2 = «CM4 - mM2 oil m est 02 C H C\ H .O2 0 / / Ik c/ H C--' H )02 C- — O2 ... 0 ( 0— OH • 0 OH” C-. OH All these compounds belong, according to Couper, to the type ?iCM4. At the close of his paper in the Philosophical Magazine , Couper expresses his intention to discuss, in a later paper, the second type (nCM4 — mM2) and to apply his principles to the cyanogen compounds. His paper in the Annales de chimie et de physique closes with formulae for hydrocyanic acid, cyanic acid, and cyanuric acid : — H) Hydrocyanic acid > Az c I HO— 0 ) HO J Cyanic acid > Az or, with O = 16, >Az C I C H— 0—0— Az— 0— Az— 0— OH Cyanuric acid C— A: (c or, with 0 = 16, I 0— OH HO— Az— C— Az— OH I I C— Az— C OH Thus in cyanuric acid Couper assumed that the three carbon atoms and the three nitrogen atoms are combined alternately in ring form. By his method of writing formulae Couper took an important step forward. His formulae, in fact, enabled him, in a simple and clear way, to express his views as to the mutual combination of the atoms in the 1908-9.] Life and Chemical Work of Archibald S. Couper. 217 molecules of chemical compounds. Kekule still, at that time, made shift, if we may use the expression, with typical formulae. Although his ideas were no less clear than those of Couper, yet the formulae he used were still quite those of the type theory. He wrote glycollic acid : — O O deriving it from the double water type. Couper, as is clearly shown by his tartaric acid formula, would have written glycollic acid thus : — ••••(>• OH V 0“ A O' ‘•'OH • -H2 and from this we at once get our present structural formula for glycollic acid : — C " OH . 0 p " OH It was not until the spring of 1859 that Kekule, in the first part of his Lehrbuch , in remarks on the mutual union of atoms, gave his well- known graphic representation in which the basicity of the atoms is indicated by a difference in the size of their symbols — a difference in size which, as Kekule expressly says, is not intended to express any difference in the actual size of the atoms, but only the number of chemical units which an atom represents, that is, the number of hydrogen atoms to which it is equivalent. We have already become acquainted with Butlerow’s remarks on Couper’s new chemical theory. But before him, immediately after the appearance of Couper’s paper in the Annates de chimie et de physique, Wurtz expressed his views in reference both to Ivekule’s paper, “ Uber die Constitution und die Metamorphosen der chemischen Verbindungen und uber die chemische Natur des Kohlenstoffs,” * and to Couper’s “ Sur une nouvelle theorie chimique.”t His remarks were published in the Repertoire de chimie pure et appliquee , a journal he had just founded for notes on current chemical literature. The distinguished position of Wurtz, and his relation to Couper, make his criticism specially worthy of our consideration. * Rep. 20-24. t Rep. 49-52. Hi C2H20 j H 218 Proceedings of the Royal Society of Edinburgh. [Sess. After a short note of the contents of the paper, he combats Couper’s assumption of 0 = 8, and says : “ Cette theorie electrochimique d’un nouveau genre aurait besoin de s’appuyer sur quelques faits.” But there is not wanting a word of recognition by Wurtz : — “ Je dois faire remarquer encore que les idees enoncees par M. Couper et qui me paraissent ingenieuses et acceptables, si on les degage certaines hypotheses accessoires et de quelques nuages qui en enveloppent l’exposition, ne sont nullement en contradiction avec la doctrine des radicaux, et meme avec cette des types moleculaires contre lesquelles l’auteur a cru devoir rompre une lance.” Wurtz closes his notice with the following statement of opinion : — “ En general, je trouve les formules de M. Couper trop arbitraires, trop eloignees de l’experience. Par nos formules rationnelles nous n’avons pas la pretention de representer la constitution intime des combinaisons. Ces formules ne representent que les metamorphoses, c’est-a-dire des faits accessibles a l’experience et demontres par elle. Voila leur a vantage. Dans les formules de M. Couper, au contraire, la place de chaque atome se trouve marquee, non seulement par le pouvoir basique des elements, mais encore par je ne sais quelle attraction electrique ou polaire. C’est trop d’hypotheses, et l’on a tort de nous presenter toutes ces choses comme la loi et les prophetes. A cet egard, M. Kekule, qui me parait avoir mieux compris le sens et la portee des idees, qu’il a enoncees le premier, a dit sage- ment a la fin de son Memoire : ‘ Pour mon compte, je n attache qu’une importance secondaire a des considerations de cet ordre la.’ ” And here Wurtz should not have let the opportunity slip of putting it on record that Couper had given him the MS. of his paper for the Gomptes rendus before Kekule’s paper appeared in Liebig s Annalen. Further we may note how Wurtz expressed himself some years later as to formulse in which, exactly as had been first proposed by Couper, the mutual relations of the atoms forming a compound were represented by means of lines joining the symbols. In his work, La theorie atomique , Paris, 1879, livre ii., “ Atomicite, ou valence des atomes dans les com- binaisons,” Wurtz discusses very fully the distribution of the hydrogen atoms in ethane, and says (p. 156) : “ Telle est la signification de la formule : H H H3C — Cli3 = H— C— -C— H l H 1 H dans laquelle cet echange d’unites de saturation est marque par les traits qui separent les lettres.” To this he appends a note : — “ Cette notation generalement usitee aujourd’hui a ete employee pour la premiere fois dans 1908-9.] Life and Chemical Work of Archibald S. Couper. 219 les lec^ons que j’ai faites au College de France pendant l’ete de 1863, et qui ont ete publiees d’abord dans le Moniteur scientifique du Dr Quesneville, et plus tard sous le titre Lemons de philosophie chimique, Hachette, 1864. Je renvoie a cet egard aux pages 140, 143, 145, 158 et 182 de cet opuscule.” When Wurtz wrote these lines he had evidently forgotten the formulae in Couper ’s paper which he had condemned as too fantastic.* Butlerow, Couper’s other critic, returns to the question in 1868, f about ten years later, after organic chemistry had undergone so mighty a development under the influence of the valency theory, and now fully recognises Couper’s position. He says : — “ Dass ferner die von Couper (leider nur kurz) ausgesprochenen Ansichten, mit den jetzt fast allgemein anerkannten identisch sind, verneine ich nicht, und sicher sind die von Couper gegebenen Formeln rationelle Formeln im gegenwartigen Sinne des Wortes, d.h. Constitutionsformeln oder Formeln chemischer Structur.” 1 shall now sum up the results. It is quite certain that Kekule pro- claimed the hypothesis of the quadri valence of carbon and the concatena- tion of carbon atoms before Couper. In contrast to Kekule, Couper started the idea of affinity of degree in chemical elements, and illustrated it by the examples of carbonic oxide and carbonic acid. In the former he regarded carbon as bivalent, in the latter as quadrivalent, thus recognising a change of atomicity or valency. Albert Ladenburg, in his lectures On the Development of Chemistry during the last Hundred Years, published in 1869, refers as follows to Couper’s formul 96 ‘ Hier begegnen wir zum ersten Male Constitutions- formeln im heutigen Sinne des Worts, Symbolen, welche aus der Erkennt- niss der Atomio^keit der Elemente hervoro-eofancren sind ” ; and a little further on : — “ Diese beiden Abhandlungen von Kekule und Couper bilden die Grundlagen unserer Anschauungen liber den Aufbau der Yerbindungen.” Hermann Kopp, in his work, Die Entwickelung der Chemie in der neueren Zeit, gives a similar decision as to Couper’s formulas : — “ Die Formeln, durch welche Couper seine hierauf beztiglichen Vorstellungen ausdrtickte : — ( O— OH C <; z.B., fiir den Methyl — , ( H3 ( 0— OH C I H2 fiir den Aethylalkohol, c-h3 * Compare also Ernst von Meyer’s Geschichte der Chemie , Leipzig, 1889, S. 270, Anm. 3. + Liebig's Annctlen , cxlvi. 260 (Heft ii., issued on 6th May 1868). + S. 269. 220 Proceedings of the Royal Society of Edinburgh. [Sess. ( O— OH { Q2 fur die Essigsaure, u.s.w. : c-h3 sie waren bereits solche, wie sie als s.g. Structurformeln weiter zu ent- wickeln und fester zu begrtinden viele Chemiker nachher als eine der ihrer Wissenschaft vorzugsweise gestellten Aufgaben betrachteten, viele jetzt es thun.” * I close this section with an extract from Ernst von Meyer’s Geschichte der Chemie von den dltesten Zeiten bis zur Gegenwart, first published in 1889: — “Ferner legte Couper grossen Nachdruck auf die Fahigkeit der Kohlenstoffatome sich unter einander zu vereinigen und zwar so, dass ein Theil des ihnen eigenen Bindungsvermogens ausgeglichen wird. Diese Vereinigung von Atomen versinnlichte er durch Striche, welche zwischen den mit einander verbundenen Theilchen in den chemischen Symbolen angebracht wurden, er legte so den Grund zu den sogenannten Structur- formeln.” f Couper’s Investigations on Salicylic Acid. Couper’s second and last experimental investigation was laid before the French Academy of Sciences at the meeting of the 7th June 1858. + It was entitled “ Recherches sur l’acide salicylique.” He says that he under- took this work in order to throw some light on the disputed questions as to the constitution and basicity of salicylic acid. This subject had engaged Chiozza, who worked at it in Gerhardt’s laboratory, Gerhardt himself, and his pupil Drion. Unknown to Couper, Kekule and also Kolbe, along with Lautemann, were at the same time occupied with it. Following these investigations, which had then for their aim the clearing up of the question of the constitution of salicylic acid, we see Gerhardt, Kekule, Kolbe, and Couper writing formulae for salicylic acid, and we shall have no difficulty in deciding which of these four investigators made the boldest and most successful advance in this region. In 1852 Chiozza, probably on the suggestion of Gerhardt, examined the action of phosphorus pentachloride on gaultheria oil, § at that time the usual source of salicylic acid. He found that, on the distillation of the product of the reaction, a liquid was obtained which behaved like an acichloride, giving chlorobenzoic acid on treatment with water. * Page 829. t Page 270. I Cornptes rendus , xlvi. 1107-1110. § Ibid., xxxiv. 850-851, seance dn lundi, 31 May 1852. 1908-9.] Life and Chemical Work of Archibald S. Couper. 221 A succeeding paper by Gerhardfc * introduces us to the problem as it presented itself to chemists at that time, eleven years before the founda- tion of Kekule’s benzene theory. Gerhardt found two anomalies in the behaviour of the ethers of salicylic acid. First, that they give well-defined salts when treated with bases. Second, that treatment with chlorine or bromine does not lead to substitution in the alcohol radicals, but to the formation of ethers of chloro- or bromo-salicylic acid. At first Gerhardt gave “ salicylate de methyle (huile de gaultlieria) ” a formula similar to that of silver salicylate : — C7H502 ) C7H502 ) V o o. OH3 I Ag ) The first of the two anomalies — the only one that interests us here — led Gerhardt to regard the ethers of salicylic acid not “ coniine une molecule d’eau dont 2 atonies d’hydrogene etaient remplaces l’un par du salicyle et l’autre par du methyle ou d’ethyle,” but “ comme une molecule d’eau dont 1 atome d’hydrogene seulement etait remplace par le groupe methylsalicyle ou ethylsalicyle, c’est-a-dire par du salicyle contenant deja lui-meme du methyle ou de l’ethyle en substitution a de 1’hydrogene : — C7H4(CH3)02 j O Hydrate de methylsalicyle. H ) C7H4(C2H5)02 j H Correspondingly, he gives the potash salt of gaultlieria oil the formula and 0 Hydrate d’ethylsalicyle.” name “ C7H4(CH3)02 K 0 Oxyde de potasse et methylsalicyle.” He adds: — “ L’experience a pleinement justifie mes presomptions. Rien n’est plus facile, en effet, que d’etherifier les ethers salicyliques, comme on etherifie l’alcool ou l’esprit-de-bois.” For, by treatment with benzoyl chloride, the salicylic ethers give the corresponding benzoyl derivatives. “ C7H4(CH3)02 j C7H50 ) C7H4(C2H5)02 ) 0 C7H30 ) In order to obtain the “chlorure de methylsalicyle,” Gerhardt sub- * Comptes rendus , xxxviii. 32-34, seance du lundi, 9 Jan. 1854. 0 Benzoate de methylsalicyle, ou oxyde de benzoile et de methylsalicyle. Benzoate d’ethylsalicyle ou oxyde de benzoile et d’ethyl- salicyle.” 222 Proceedings of the Royal Society of Edinburgh. [Sess. jected gaultheria oil to the action of phosphorus pentachloride ; but, to his surprise, he obtained, after a vigorous action, both from the methyl and from the ethyl ether, a new chloride, “ chlorure de salicyle,” Cl ( ' ^ is obvious that Gerhardt did not distil the product as Chiozza had done, but drew his conclusion as to its nature only from the action on it of methyl and ethyl alcohol, by which it is retransformed into ethers of salicylic acid. Gerhardt does not quote Chiozza’s paper, nor does he discuss its contents. Gerhardt’s pupil, Drion, further extended Gerhardt’s experiments on sali- cylic ethers.* His observations are of interest to us here, as he describes the preparation of salicyl chloride somewhat more in detail than Gerhardt had done : — “ Le chlorure de salicyle que j’einploie pour la preparation du salicylate d’amyle a ete obtenu, pour la premiere fois, par M. Gerhardt, en faisant agir le perchlorure de phosphore sur l’huile de gaultheria. Dans cette reaction remarquable, il ne se forme que des traces d’oxychlorure de phosphore ; mais il se degage beaucoup d’acide chlorhydrique, et j ai constate egalement la production abondante de chlorure de methyle. Le chlorure de salicyle peut etre chauffe j usque vers 200 degres sans se decomposer, mais on ne peut le distiller. “ Dans le but de l’obtenir pur j’ai cherche a le distiller sous une pression moindre que celle de l’atmosphere. Bientot d’abondantes fumees d’acide chlorhydrique sont sorties de la poinpe et m’ont contraint de renoncer a l’emploi de cet appareil. J’ai continue la distillation sous la pression atmospherique, et j’ai recueilli dans le recipient un liquide fumant, pre- sentant tous les caracteres des chlorures organiques.” Treated with water, the distillate yielded a mixture of salicylic and chlorobenzoic acids, from which Drion concluded that the “ chlorure de chlorobenzoile, C7H4C10, Cl,” was formed by the decomposition of the “chlorure de salicyle.” “ Il avait ete obtenu deja par M. Chiozza en faisant agir le perchlorure de phosphore sur Tacide salicylique.” I sum up the collection of observations made in Gerhardt’s laboratory by Chiozza, Gerhardt, and Drion on the action of phosphorus pentachloride on gaultheria oil. The violent reaction of the two substances takes place with the evolution of hydrochloric acid and methyl chloride : only traces of phosphorus oxychloride are produced. The undistilled product of the reaction, when treated with methyl alcohol, gives methyl salicylate, and was therefore pronounced to be salicyl chloride, the acichloride of salicylic acid. But the supposed salicyl chloride cannot be distilled unchanged, either under ordinary or under reduced pressure. The product obtained * Comptes rendus , xxxix. 122-125, seance du lundi, 10 juillet 1854. 1908-9.] Life and Chemical Work of Archibald S. Oouper. 223 by distilling under ordinary pressure gives, with water, salicylic acid and monochlorobenzoic acid, and was therefore regarded as a mixture of the acichlorides of these acids. The puzzling thing was, what had become of the phosphorus oxy- chloride which must have been formed by the reaction of the hydroxyl of the salicylic acid with the phosphorus pentachloride ? The production of chlorbenzoyl chloride from the supposed salicyl chloride was also unin- telligible. Besides, most of the conclusions lacked the support of analysis. The problem had, therefore, attractiveness enough to lead a sharp- sighted investigator like Couper to attack it again. I use, for reference in the meantime, only Couper ’s first paper, that in the Gomptes rendus * in which he contented himself with the use of empirical molecular formulae, as we should now call them, using the atomic weights C = 6 and 0 = 8. He describes his method and the course of the reaction thus :■ — He added gaultheria oil in small quantities at a time to the phosphorus pentachloride, in the proportion of one equivalent of the former to two of the latter. After the reaction (which ran exactly the same course when salicylic acid was used) was finished, he distilled the product under ordinary pressure. When the trace of phosphorus oxy- chloride and the excess of the pentachloride had been driven off, there passed over, between 285° and 295°, a colourless liquid, which he named “ trichlorophosphate de salicyle, C14H4Cl3Ph06,” formed according to the equations : C16H806 + PhCl5 = HC1 + 02H3C1 + C14H4Cl3Ph06 ; gaultheria oil C14H606 + PhCl5 = 2HC1 + C14H4Cl3Pli06.” salicylic acid The “ trichlorophosphate de salicyle ” is instantly decomposed by hot water, giving hydrochloric, phosphoric, and salicylic acids ; according to the equation : C14H4Cl3Pli06 + 8HO = PhH308 + 3HC1 + C14H606. If the “trichlorophosphate de salicyle” is quickly distilled, it partially decomposes with abundant evolution of hydrochloric acid. Above 300° there passes over a liquid which, when sealed up in a glass tube, deposits large crystals of “ monochlorophosphate de salicyle, C14H408ClPh.” Both the trichlorophosphate and the monochlorophosphate take up moisture from the air and give rise to a new acid, “ acide phosphosalicylique, C14H7Ph012.” This is formed in accordance with the equations : C14H4Cl3Ph06 + 6HO = 3HC1 + C14H7Ph012 ; C14H4C1PH08 + 4H0 = HC1 + C14H7Ph012. * xlvi. 1107-1110. 224 Proceedings of the Royal Society of Edinburgh. [Sess. The “acide phosphosalicylique ’ is tribasic, and Couper regarded it “comme une combinaison conjugee d acide phosphorique et d ’acide salicylique, PhH308 + C14H606 = C14H7Ph012 + 2HO.” These results, says Couper, do not, in all points, agree with the observa- tions published by Gerhardt, Chiozza, and Drion, and raise a doubt as to the existence of the salicyl chloride described by Gerhardt, a product that has never been analysed. Couper then points out that the formation of salicyl chloride from salicylic acid or from gaultheria oil could not take place without the production of phosphorus oxychloride, whereas he had observed only traces of this substance. Whether these contradictions were the result of some accident or of special conditions under which the various observers worked, could only be decided by new investigations. The formulae of the three new compounds containing phosphorus, which he had obtained from salicylic acid, were substantiated by Couper by means of a series of analyses. He used empirical molecular formulae and the small equivalent weights C = 6 and 0 = 8. A week after the publication of this paper on salicylic acid, there appeared, in the Comptes rendus , Couper s first communication on a new chemical theory. He applies his new theory to the derivation of constitu- tional formulae for salicylic acid and for his “ trich loroph ospl iat e de salicyle,” assuming C = 12, but retaining 0 = 8. In the somewhat later paper, published in the Edinburgh New Philosophical Journal , he gives constitutional formulae, not only for these, but also for the “ monochloropliosphate de salicyle ” and the “ acide phos- phosalicylique.” These formulae are given below as Ia, IIft, IIIa, and IVa, and beside them I have given, as Ib, IIb, III&, and IV&, the formulae obtained by doubling the atomic weight of oxygen : Salicylic Acid. R. I, (0 = 16). ( C" H2 (C H2 C c ( C - TI ( C • H (' C 11 ( C - H c c (c -0 -OH ( C OH : (O2 ! ( o C c< (O-OH ( —OH From this formula (I*) for salicylic acid Couper derives the following formula for the “ terchloropliosphate of salicyle ” : — 1908-9]. Life and Chemical Work of Archibald S. Couper. 225 C na. i C- H2 ( C-H | C H C • i (; • !>•• ii. 11,(0 = 16). Monochlorophosphate of Salicyle. Ill, C< c h2 I C H j C-H | C- 0 •() 02 1 0-0 c c c j 02 ) Cl III, (0 = 16). c h2 c- -H j C H I C 0 0 c ••••o 1° j Cl Phosphosalicylic Acid. IV,. c c j C H2 \ C H | C-H ( C O -op : ( 02 C) ( O -OH 02 O --OH 0 - OH c c IV, (0 = 16). C-H2 C H C -H fO } C - OP OH C jO ! OH ) OH These formulae, Ia, IIa, IIIa, and IVa, are structural formulae, in our present meaning of the term. They strike us as still more modern when, in them, we use 0 = 16, that is, divide the number of oxygen atoms by 2 (or write O for Couper ’s O2 or — 0 — O — ), as is shown in the formulae X6, II6, III,, IV,. The formulae XIa and II, show us what has become of the phosphorus pentachloride, the residue of which replaces the hydrogen of the hydroxyl and of the carboxyl in the salicylic acid. We see that Couper supposed the hydroxyl and the carboxyl to be attached to the same carbon atom. VOL. XXIX. 15 226 Proceedings of the Royal Society of Edinburgh. [Sess. Thus, so early as seven years before the establishment of Kekule’s benzene theory, Couper endeavoured to take account of the mode of union of the seven carbon atoms of salicylic acid. As I have pointed out in the preceding section, Couper, in his fuller paper in the Philosophical Magazine , “ On a New Chemical Theory,” everywhere replaces the brackets of his structural formulae by lines indicating the union of the atoms. If we carry this out in the case of the eight formulae given above, and represent, as has been done in later times, the double union by two parallel lines, we obtain the following eight forms, lc, IIC, IIIC, IVC, and I„ II„ XIXd, IV, : — I, I’d (O = 16). C H2 Ci- VC H V C H C C 0 OH i o2 Cr:" o OH IXC. C H2 c •;:C H ,.C -11 c c o-o. o2 PCI, C o--o .-■6C H2 5ce: \4c h .-•3C H .,0 OH j O C'-; OH II, (0 = 16). , C H2 C ■ C H , C H C C 0. : PCI, C;>" 0 IIIc C H2 c : C H III, (O = 16). C H2 C ' C H C H c O' C 0 0 o2 C H C C 0 0 02 p 0 P c- HI C': O' -Cl 0 0 1908-9.] Life and Chemical Work of Archibald S. Couper. IV. 1 T c • . C H2 227 IV, (O = 16). C H2 C 'C- C C ' c- II H •o- O2 o2 OP 0 -O H 0....0 ...H c- •o OH c c- c c c- 0 c- H H 0 OP’ ..Oil OH •OH As I said some time ago, in discussing these formulae * : — “ If my recon- struction of Couper ’s formulae is justifiable, these formulae clearly show what Couper lacked for the discovery of the benzene theory. Four carbon atoms — I have numbered them in formula I, ; they are 2, 3, 4, and 5 — are represented by Couper in the same state of combination with one another as Kekule’s formula gave them at a later date.” Couper had only to take one step more, to unite the carbon atoms 6 and 1, and close the ring: this would have involved the transference of a hydrogen atom from 6 to 5, and of the hydroxyl from 1 to 2. And Couper had already arrived at the assumption of the union of multivalent atoms in ring form, as is shown by the formula, given in an earlier part of this paper (p. 216, and Appendix, p. 265), by which Couper expressed the constitution of cyanuric acid. “ Undoubtedly Archibald Couper was, at that time, August Kekule’s most dangerous rival.” Of the three chemists whose work was criticised in Couper ’s salicylic acid paper, Gerhardt was gone (having died August 19, 1856, in Strassburg, soon after his settlement there), Chiozza said nothing, and only Drion attempted to defend himself and Gerhardt. t He maintained that the existence of the salicyl chloride observed by Gerhardt, although not isolated in a pure state owing to its non volatility, was indubitably proved by the readiness with which it reproduced the ethers of salicylic acid when treated with alcohols. It will be seen that Drion makes his task too easy : he tries neither to refute Couper ’s description of the course of the reaction nor to explain what became of the phosphorus oxychloride, which must have been produced in the formation of salicyl chloride, but which neither he nor Couper had observed. It is remarkable that Couper and Kekule encountered one another not only in the theoretical but also in the experimental field. Kekule, in * Liebig’s Annalen , cccxlvi. 290. t Comptes rendus , xlvi. 1238, seance du lundi, 21 juin 1858. 228 Proceedings of the Royal Society of Edinburgh. [Sess. connection with the formation of glycollic acid from monochloracetic acid, tried to convert monochlorobenzoic acid into salicylic acid. He prepared the chlorobenzoic acid from its chloride, which he obtained, according to Chiozza’s directions, by distilling the product of the reaction of phosphorus pentachloride on salicylic acid. His attempts to pass from the sodium salt of chlorobenzoic acid to salicylic acid, as he * and Reinhold Hoffmann f had obtained glycollic acid from chloracetic acid, convinced Kekule of the small reactive power of the chlorine in chlorobenzoic acid. He could as little replace it by hydroxyl as Couper could the bromine in brom- benzene and dibrombenzene. This communication of Kekule, “ Bildung von Glykolsaure aus Essigsaure,” which closes with the experiments as to salicylic acid, was sent to the editors of Liebig s Annalen on the 25th December 1857. Couper’s paper on salicylic acid appeared in the first June number of the Comptes rendus,\ so that Kekule could not have known anything of this work of Couper. But, after the appearance of Couper’s paper, Kekule, who had in the meantime moved from Heidelberg to Ghent, applied himself with the greatest zeal to the continuation of his work on salicylic acid. In his communication laid before the Belgian Academy on the 4th August 1860,§ entitled, “Faits pour completer l’histoire de 1’acide salicylique et de l’acide benzoique,” which appeared in the number of Liebig s Annalen || published 4th February 1861, under the title, “ Beitrage zur Kenntniss der Salicylsaure und der Benzoesaure,” Kekule minutely discusses Couper’s work. Kekule gives salicylic acid the formula Hr The phosphorus compound, C7H4C13P03, described by Couper, is regarded by Kekule as an indirect combination of phosphorus oxychloride with the anhydride of salicylic acid, or as a compound of the radicals salicyl and phosphoryl, belonging to a mixed type, according to the formula H3CI3 H20 - H20 + 3HC1. He cannot confirm Couper’s statements as to the products of the action of phosphorus pentachloride on salicylic acid or on its methyl ether. He writes, in the Annalen : — “ Ich habe diesen Versuch mehr als 20mal * Liebig's Annalen , cv. 286-292 (Heft iii. issued 27th Maerz 1858). t Ibid., cii. 12. f xlvi. 1107-1110. § Bull. Acad. Roy. Belg. (2), x. 337-350. || cxvii. 145-164. 1908-9.] Life and Chemical Work of Archibald S. Conper. 229 wiederholt und dabei mehrmals betrachtliche Mengen der Materialien und in sehr wechselnden Mengen in Arbeit genommen. Ich habe niemals den von Couper beschriebenen Korper erhalten, der nach diesem Chemiker bei 285° bis 295° tiberdestilliert. Ich habe vielmehr stets beobachtet, dass, sobald die Temperatur der iiberdestilherenden Dampfe auf hochstens 280° gestiegen ist, der Rtickstand in der Retorte sich unter heftigem Aufblahen und mit Hinterlassung einer schwarzen blasigen Masse zersetzt. Ich habe mich ausserdein tiberzeugt, dass 1 Molectil Methylsalicylsaure ” [that is, gaul tlieria oil, the methyl ether of salicylic acid] “ nur 1 Molectil Phosphor- superchlorid zu zersetzen im Stande ist, und dass alles im Uberschuss zugesetzte Phosphorsuperchlorid bei der ersten Destination unverandert tiberdestilliert. Ich habe ferner gef unden, im Widerspruch mit den Angaben von Couper dass eine sehr betrachtliche Menge von Phosphor- oxychlorid gebildet wird.” “ Ich habe endlich gefunden, das der Rtickstand in der Retorte, man mag die Destination zu Ende ftihren oder in irgend einer Periode unterbrechen, bei Zersetzung mit Wasser oder Kali wessentlich Salicylsaiire liefert, die nur Spuren von Chlorbenzoesattre enthalt.” The key to Kekule’s want of success is to be found in the fact that he had kept the product of the reaction too long at a temperature of 180°-200 ', to expel the phosphorus oxychloride and the excess of phosphorus pentacliloride, before proceeding to distil, so that he obtained chlorbenzoyl chloride. This is shown with a probability bordering on certainty by the fact that Ivekule found, in the undistilled chloride, only 3 per cent, of phosphorus,* while Couper’s “ trichlorophosphate de salicyle ” contains 11 5 per cent. As Kekule was induced by his researches on glycollic acid to occupy himself with salicylic acid, so Hermann Kolbe was led to salicylic acid from the transformation of lactic acid into chloropropionic acid. His work, in which he was seconded by E. Lautemann, appeared under the title, “ Uber die Constitution und Basicitat der Salicylsaiire,” in the number of Liebig s Annalen issued 11th August, 1860. Kekule’s communication on salicylic and benzoic acids was presented to the Belgian Academy on the 4th of August of the same year, so that it was only in the German version of his paper in the number of the Annalen issued 4th February 1861, that he could take notice of Kolbe and Lautemann’s work ; but Kekule’s remarks in opposition to Kolbe have no reference to the action of phosphorus penta- chloride on salicylic acid, and therefore need not be referred to here. Kolbe and Lautemann make no reference to Couper’s salicylic acid * Compare Liebig's Annalen, cxvii. 148, Anm. t Ibid., cxv. 157-206. 230 Proceedings of the Royal Society of Edinburgh. [Sess. paper, which, indeed, they do not seem to have seen. They prepared the chloride of chlorobenzoic acid (called by them chlorosalylic acid) by Chiozza’s * method, as follows : — “ Wir brachten in eine tubulierte Retorte 3 Theile (2 Aeq.) gepulverten FtinfFach Chlorphosphor, den wir durch langeres Eintauchen des Retortenbauchs in Eiswasser stark erkalteten, nnd hierauf 1 Theil (1 Aeq.) trockene pulverige Salicylsaure. Beide wurden durch Umschutteln oder durch Umrtihren mit einem krummen Glasstab gut gemischt. “ Alsbald erfolgt eine heftige Reaction, wobei der Inhalt der Retorte sich unter Aufblahen verflussigt und Salzsaure in Strom en entweicht. Bei nachherigem Erhitzen geht der grosste Theil der fliissigen Masse ats farb- loses Liquidum liber. Der Rest blaht sich zuletzt stark auf und es hinter- bleibt schliesslich eine leichte schwammige Ivohle. Bei der Rectification des Destillates geht zuerst Phosphoroxychlorid liber, hernach steigt die Siedetemperatur ziemlich rasch bis 260° C. Als das Thermometer 240° C. anzeigte wurde die Vorlage gewechselt. Der grosste Theil der noch iibrigen Fllissigkeit geht dann zwischen 260° und 270° C. liber, erst ganz zuletzt steigt die Temperatur noch bis auf 300° C. Was liber 240° C. abdestilliert, besteht hauptsachlich aus Chlorsalylsaurechlorid. fiR) C12 < } [c2o2] , Cl ( Cl ) enthalt aber daneben noch Salicylsatirechlorid. j ) c12 - [C202] , Cl ( HO J wie die Bildung von Salicylsaure beim Zusammenbringen mit Wasser beweist, und ausserdem Chlorsalyltrichlorid. (H4, c,J Uc8cy,ci.” I ci ) Kolbe wrote, for salicylic acid itself, the following formula : — Salicylic Acid. I h4 , HO , C12 \ [C202] , O . ( ho2 I Obviously, Kolbe and Lautemann, in the distillation of the product of * Annales de chim. et de phys. (1852) [3], xxxvi. 102-107. 1908-9.] Life and Chemical Work of Archibald S. Couper. 231 the reaction, had obtained in the distillate some of Couper’s “ trichloro- phosphate de salicyle,” which had passed over undecomposed. But they regarded it as a mixture of salicyl chloride and chlorosalyl chloride, because with water they obtained salicylic and chlorosalylic (chloro- benzoic) acids. They did not test the distillate for phosphorus, and took no note of the possibility of the formation of a derivative of salicylic acid containing phosphorus. I now place together the formulae assigned to salicylic acid by Gerhardt, by Couper, by Kekule, and by Kolbe, appending to Couper’s formula (la, P- 224 of this paper) the formula I have deduced from it by putting 0 = 16, and replacing the brackets by lines representing bonds (Id, p. 226). according to Gerhardt : according to Couper : Salicylic Acid c7h5o, H 0; c j C R2 l C H j C H ( C -0 -•OIL ,02 C O OH; reconstructed with 0 = 16, and lines in place of brackets : W C H2 C \C H C H C :-C OH according to Kekule : according to Kolbe : 232 Proceedings of the Royal Society of Edinburgh. [Sess. Kekule himself, as will be seen, had not yet, in the year 1860, ventured to express an opinion as to the mode in which the seven atoms of carbon are united to one another, although he had already, in the first part (published in the spring of 1859) of his Lehrbuch der organischen Chemie , sought to represent the structure of simple inorganic and organic com- pounds by means of graphic formulae, which for lucidity leave nothing to be desired, as, for instance, the formula of acetic acid : * Involuntarily the thought arises — how would Archibald Scott Couper have supported his observations and his views in the face of the opposition of his fellow-chemists ? Would not organic chemistry have undergone a more rapid development if he had succeeded in fully working out his ideas as to the mode of constructing the formulae of carbon compounds ? Couper was just the man to do that. But what was this investigator like, who, so young and, after so short an acquaintance with chemistry and at the time of which we are speaking, ventured to pronounce on the mode of union of the atoms in such com- plicated compounds as salicylic acid, tartaric acid, mucic acid, grape sugar, cyanuric acid, etc. ? Mr Berring gives us from the treasury of his memory the following picture of his friend : — “ Couper was a very handsome man, tall and slender, of a distinguished, aristocratic aspect. His fine face, with its glowing colour, was animated by the almost miraculous brilliancy of his deep black eyes. He had no appearance of weakness, but yet his health was delicate, and I have heard Hamilton say that his mother was always anxious about him. The basis of his character, as is often the case with Scotsmen, was deeply religious. He was very fond of music — classical, serious, and lively — and seldom missed a good concert when he was in Berlin.” Mr Berring wrote to Crum Brown, on receiving from him a copy of the portrait prefixed to this biography : “ This is an excellent picture, and will let you see that Couper was the strikingly handsome man I described.” The original of the portrait is a hand-coloured photograph in the possession of Mr Dollar. It was taken in Paris in 1857, or in the beginning of 1858, and is therefore of the same date as Couper s scientific work. Couper ’s features betray an energetic will combined with a penetrating understand- ing. In his theoretic paper, his pleasure in the philosophical, critical * Compare Bd. i., Seite 164, Anm. 1908-9.] Life and Chemical Work of Archibald S. Couper. 233 treatment of the fundamental principles of chemistry is unmistakable. His mode of thought is quite his own, his statements of his observations, supported by excellent analyses, are clear and definite. Is it not strange that such an investigator should have made no answer to the criticisms of his theoretical views by Kekule, Wurtz, and Butlerow; that he made no attempt to refute the doubts of Drion and of Kekule as to the accuracy of his work on salicylic acid ? But no further writing came from Couper’s pen. As a scientific man he had disappeared, and twenty-seven years had to elapse before the correctness of his statements as to the action of pentacliloride of phosphorus on salicylic acid was demonstrated by another. In the meantime, quite a number of chemists had busied themselves with the supposed salicyl chloride, mostly in order to study its action on other substances. Carius,* with the view of obtaining thiosalicylic acid, brought the undistilled product of the action of phosphorous pentacliloride on salicylic acid into reaction with an aqueous solution of excess of potassium sulphide. In Kolbe’s laboratory Glutz, f in 1867, showed that, by continued heating with a reflux condenser, for a day, of gaultheria oil with two equivalents of phosphorus pentacliloride, the latter ultimately completely disappears, and a better yield of chlorsalyl chloride is obtained. He states that, on distilling, after the phosphorus oxychloride has been driven off, the temperature quickly rises to 230°-260°, and that below 240° the distillate consists half of chlorsalyl chloride and half of salicyl chloride. Pierre Miquel J prepared “ salicyl carbimide ” by the action of undistilled “ salicyl chloride ” on metallic thiocyanates, and remarks : “ Le chlorure de salicyle s’obtient difficilement dans un etat de purete satisfaisant, il ren- ferme toujours des composes visqueux et retient avec beaucoup d energie de - Foxy chlorure de phosphore.” OH Otto Fischer, § in the same year, by heating “ the chloride C6H4qqqj , freed as much as possible from phosphorus compounds,” to 180° with dimethyl aniline and zinc dust in a current of carbonic anhydride, obtained the salicein of dimethyl aniline. Schreib, |j in 1880, states that in the action of phosphorus pentacliloride on salicylic acid only one molecule of the pentacliloride enters into reaction ; a second molecule is without effect and is recovered unchanged on heating to about 110°. He goes on to say : “ Bei weiterem Erhitzen geht * Liebig's Annalen , cxxix. 11 (Heft i., issued 8th Jan. 1864). t Ibid., cxliii. 194 (Heft ii., issued 20tli July 1867). J Annales de chim. et de phys. (1877) [5], xi. 304. § Berl. Ber. (1877), x. 954. || Ibid . (1880), xiii. 465. 234 Proceedings of the Royal Society of Edinburgh. [Sess. z u erst ein grosser Theil des gebildeten Phosphor oxy chloric! und spater Ortho- chlorbenzoylchlorid liber, bis sich, bei circa 260°- 270° der Retorteninhalt unter starkem Aufschanmen zersetzt.” From all these statements it will be seen that it is difficult to obtain Couper’s “ trichlorophosphate de salicyle ” from the product of the action of phosphorus pentachloride on salicylic acid by distilling under ordinary pressure. Contrary to Drion’s statement, the difficulties disappear, as I showed in the year 188 5 A when the distillation is conducted under diminished pressure. By working exactly according to Couper’s descrip- tion, with the materials he used, and distilling quickly, immediately after the reaction is finished, under ordinary pressure, “trichlorophosphate de salic3de ” is also obtained, although the yield is not so good. In the course of exhaustive investigations, carried out along with George Dunning Moore, we were able also to confirm Couper’s statements as to the “ mono- chlorophosphate de salicyle ” and the “ acide phosphosalicylique.” And thus, certainly late enough, there came a brilliant justification of Couper’s work on salicylic acid, work which chemists had gradually come to look on as so certainly inaccurate that no notice was taken of it in any of the treatises on organic chemistry. How often since then have I longed to know what became of Couper ! No doubt, there have been cases of English chemists who, after a meteor flash of one brilliant piece of scientific work, taken up by other engagements, have for many years been absent from the purely scientific field ; still, they have always attained a position which could not allow their names to be overlooked, not to say to be forgotten. It was otherwise with Archibald Scott Couper. He disappeared so suddenly and so completely from the scientific arena that there was not time for his name to gain entrance into the English, German, or French books of scientific biography. This enigma was completely solved by the investigations of his country- man, Alexander Crum Brown. It was not his disappointment that, by no fault of his, his paper, “ Sur une nouvelle theorie chimique,” was not pre- sented to the French Academy of Sciences until after the publication of Kekule’s famous paper, “ Tiber die Constitution und die Metamorphosen der chemischem Verbindungen und die chemische Natur des Kohlenstofls,” that broke Couper down, but a severe attack of illness. Having returned, late in the autumn of 1858, from France to Scotland, he obtained, in the end of December, the post of second laboratory assistant to the distinguished Professor Lyon Playfair, Edinburgh. * Liebig's Annalen, ccxxviii. 308-321 (Heft, iii., issued 18tli May 1885). Proc. Roy. Socy. of Edin. ] [Vol. XXIX. Laurel Bank, Kirkintilloch. June 23, 1906. Entrance to Kirkintilloch Cemetery. June 23, 1906. To face 'page 235 1908-9.] Life and Chemical Work of Archibald S. Couper. 235 His future academic position seemed thus made secure. But soon after his entry on his new office, Couper suffered from a serious breakdown in health, and for two months was under special medical care. On his recovery he went on a fishing expedition, when over-exertion and long exposure to the sun caused a return of his illness, necessitating retirement and medical treatment for a longer time. Greville Williams was therefore quite right in his recollection of a sunstroke. He never completely recovered, and was incapable of undertaking any serious work, but lived in retirement, tenderly cared for by his mother — at first in the old home in the Townhead, and after 1880 in the comfortable house, Laurel Bank, Kirkintilloch, which she had built specially as a quiet home for him. His father died on the 30th December 1859, in his sixty-second year. Couper ’s health seems to have somewhat improved, and he was able to take a long walk every day, to converse occasionally with friends, and now and then write a letter. Every morning and evening he read aloud to the household a chapter of the New Testament, and went regularly to church on Sundays. He died, unmarried, at Laurel Bank, on the 11th March 1892, almost sixty-one years old. His mother had the sad satisfaction of nursing him to the end. She died at Laurel Bank, 15th April 1895, at the advanced age of ninety-three. The house, Laurel Bank, in which Couper lived for twelve years, and where he and His mother died, as also the picturesque entrance gate of the Kirkintilloch cemetery, where he and his ancestors are buried, are shown in the plates taken from photographs by Crum Brown. In the history of organic chemistry the sorely tried Archibald Scott Couper deserves a place of honour beside his more fortunate fellow-worker, Friedrich August Kekule. APPENDIX I. Recherches sur la benzine ; par M. A. Couper.* Supposant qu’il serait possible de transformer la benzine en alcool et en glycol phenyliques, j’ai ete conduit a faire avec ce carbure d’hydrogene les ex- periences suivantes. Lorsqu’on fait arriver dans un appareil convenable, de la vapeur de bronie dans de la benzine bouillante, il se degage de l’acide bronihydrique, et l’on obtient successivement deux composes bromes, la bromobenzine et la dibromobenzine. La bromobenzine (bromine de phenyle), C12H5Br, passe a 150 degres. C’est * Com'ptes rendus, t. xlv. pp. 230-232 (10 aout 1857). 236 Proceedings of the Royal Society of Edinburgh. [Sess. un liquide parfaitement incolore, doue d’une odeur analogue a celle de la benzine elle-meme. II ne se solidifie pas a — 20 degres. Sa densite de vapeur a ete trouvee egale a 5,631. La densite de vapeur theorique est de 5,4237. Elle a donne a 1’analyse : Experience. Theorie. Carbone . 45,40 45,86 Hydrogene . . 3,27 3,18 Brome . . 50,84 50,94 Elle possede a un degre remarquable la stabilite bien connue de la benzine. Elle reagit a peine sur l’acetate d’argent a la temperature de 200 degres. Chauffee avec de l’acide nitrique fumant, elle se transfornie en un compose cristallin fusible au-dessous de 90 degres et volatil sans decomposition. Ce compose renferme d’apres mes analyses C12H4(Az04)Br et se transformerait probablement en bromaniline sous l’influence des agents reducteurs. La bromobenzine se dissout dans l’acide sulfurique fumant ; la solution abandonnee a Pair laisse deposer, en absorbant l’humidite, des cristaux d’acide sulfobromobenzinique. Get acide est tres-deliquescent. Lorsqu’on ajoute de Lammoniaque a sa solution aqueuse, il se forme un sel ammoniacal qui est presque insoluble dans l’eau et qui cristallise immediatement. Ce sel renferme C12H5Br, S206,, AzH3, comme le prouvent les analyses suivantes : Experience. Theorie. Carbone . 27,86 28,34 Hydrogene . 3,47 3,14 Brome . . 31,35 31,48 Azote . . 5,67 5,51 Lorsqu’on laisse pendant longtemps la monobromobenzine en contact avec un exces de brome, de l’acide bromhydrique se forme et se degage continuellement, et un corps solide se depose en cristaux au fond du vase. Ce corps est la dibromo- benzine qu’on purifie facilement en le faisant cristalliser dans Tether. La dibromo- benzine renferme C12H4Br2, comme le prouve l’analyse suivante : Experience. Theorie. Carbone . 30,30 30,50 Hydrogene . 1,92 1,69 Brome . 67,81 100,00 Elle cristallise en magnifiques prismes obliques. Elle fond a 89 degres et distille sans alteration a 219 degres. Elle reagit sur l’acetate d’argent, mais tresdentement et en formant sans doute du phenylglycol diacetique C12H402 [ C4H303 \ C4H303 C12H4 (C4H302)2 O4. Cette experience ayant ete perdue par suite d’une explosion, je me reserve d’en faire le sujet d’une nouvelle etude. 1908-9.] Life and Chemical Work of Archibald S. Couper. 23 7 APPENDIX II. SUR UNE NOUVELLE THEORIE CHIMIQUE ; PAR M. A. CoUPER. (NOTE PRESENTEE par M. Dumas.) * J’ai l’lionneur d’exposer a l’Academie les traits principaux d’une nouvelle theorie chimique que je propose pour les combinaisons organiques. Je remonte aux elements eux-memes dont j’etudle les affinites reciproques. Cette etude suffit, selon moi, a l’explication de toutes les combinaisons chimiques, sans qu’on ait besoin de recourir a des principes inconnus et a des generalisations arbitraires. Je distingue deux especes d’affinite, savoir : 1°. L’affinite de degre; 2°. F affinite elective. J’entends par affinite de degre, l’affinite qu’un element exerce sur un autre avec lequel il se combine en plusieurs proportions definies. Je nomine affinite elective, celle que differents elements exercent les uns sur les autres, avec des intensites differentes. Prenant pour exemple le carbone, je trouve qu’il exerce son pouvoir de combinaison en deux degres. Ces degres sont representes par CO2 et CO4, c’est-a- dire par l’oxyde de carbone et Tackle carbonique, en adoptant pour les equivalents du carbone et de l’oxygene les nombres 12 et 8. En ce qui concerne ses affinites electives, le carbone s’eloigne des autres elements et montre, pour ainsi dire, une physionomie particuliere. Les traits qui caracterisent cette affinite elective du carbone sont les suivants : 1°. II se combine avec des nombres d’equivalents egaux d’hydrogene, de chlore, d’oxygene, de soufre, etc., qui peuvent se remplacer mutuellement pour satisfaire son pouvoir de combinaison. 2°. II entre en combinaison avec lui-meme. Ces deux proprietes suffisent a mon avis pour expliquer tout ce que la chimie organique offre de caracteristique. Je crois que la seconde est signalee ici pour la premiere fois. A mon avis, elle rend compte de ce fait important et encore inex- plique de Taccumulation des molecules de carbone dans les combinaisons organiques. Dans les composes oil 2, 3, 4, 5, 6, etc., molecules de carbone sont liees ensemble, c’est le carbone qui sert de lien au carbone. Ce n’est pas l’hydrogene qui peut lier ensemble les elements des corps organiques. Si, comme le carbone, il avait le pouvoir de se combiner a lui-meme, on devrait pouvoir former les composes H4C14, JDCl6, H8C18. En ce qui concerne Foxy gene, j’admets qu’un atome de ce corps en combinaison exerce une affinite puissante sur un second atome d’oxygene qui lui-meme est com- bine a un autre element. Cette affinite est modifiee par la position electrique des elements auxquels se sont respectivement attaches les atomes d’ox}^gene. Les developpements qui vont suivre feront comprendre cette pensee. La puissance de combinaison la plus elevee que l’on connaisse pour le carbone est celle du second degr£, c’est-a-dire 4. La puissance de combinaison de l’oxygene est representee par 2. Toutes les combinaisons du carbone peuvent etre ramenees a deux types. L’un d’eux est representee par le symbole nCM\ l’autre par le symbole wCM4 - mM2, * Comptes rendus, t. xlvi. pp. 1157-1160 (14 juin 1858). 238 Proceedings of the Poyal Society of Edinburgh. [Sess. oil m est < n, on bien ?zCM4 + mCM2, ou n peut devenir nul. On peut citer, comme exemple du premier type, les alcools, les acides gras, les glycols, etc. Les alcools methylique et ethylique seront representes par les formnles cJO OH c / °*"‘ OH [ II3, ; \ " H2 C'"‘H3 . On verra facilement que pour l’alcool methylique la limite de combinaison du carbone est egale a 4, le carbone y etant combine a 3 d’hydrogene et a 1 d’oxygene. Cet oxygene, dont le pouvoir de combinaison est egal a 2, est a son tour combine a un autre atome d’oxygene uni lui-meme a 1 d’hydrogene. Dans le cas de l’alcool ordinaire, chacun des deux atomes de carbone satisfait son pouvoir de combinaison d’un cote en s’unissant a 3 atonies d’hydrogene ou d’hydro- gene et d’oxygene, et de l’autre cote en s’unissant a l’autre atome de carbone. L’oxygene y est combine de la meme maniere que dans l’exemple precedent. Dans ces cas, on verra que le carbone appartient au premier type, chaque atome etant combine au second degre. Dans l’alcool propylique, ^ j O " OH ( : 1112 C • H2 C ” H3, la puissance de combinaison de l’atome de carbone qui est situe au milieu est reduite a 2 pour l’hydrogene, puisqu’il est combine chimiquement a chacun des deux autres atomes de carbone. Des formules analogues aux precedentes expriment la constitution des autres alcools. La constitution de Tether est representee par la formule L’acide formique est 1’acide acetique of0 °lc : I H2 H2J : C II3 H3 ' C . / O " OH C < O2 U C f 0 "OH ; \0* C • • H3. La constitution du glycol est representee par la formule fO-OH C\ : ( H2 I I H2 C to —OH, * This “ 0 ” is omitted in error in the original. 1908-9.] Life and Chemical Work of Archibald S. Couper. 239 celle de l’acide oxalique par la formule 0 OH O2 O2 .0— OH, ou, si l’on veut reunir l’oxygene negatif a Tun des poles de la molecule, par la formule C- C- / o2* c | u : I o2 c 0 • OH O -OH. Quoi qu’il en soit cependant, on peut voir d’apres cette theorie que, dans la constitution des acides organiques du premier type, la presence de 2 atonies d’oxygene combines ensemble de maniere que tous les deux sont attaches directement au carbone et situls pres de l’oxygene negatif, e’est-a-dire de l’oxygene qui entratne avec lui l’oxygene constitue dans un etat electropositif par sa combinaison avec 1 atome d’un element relativement electropositif, que la presence, dis-je, de ces atonies d’oxygene est necessaire pour que l’oxygene negatif se trouve dans cet etat electrique qui donne au corps les proprietes generalement designees par le nom d ’acides. Ceci est un cas particular d’une loi generate ; car on peut voir, d’apres cette theorie, comment la valeur electropositive ou electronegative des elements modifie et conditionne mutuellement la valeur electropositive ou electronegative des autres elements. Cette loi differe de l’hypothese electrique que les chimistes ont defendue autrefois, mais qui n’a jamais pu recevoir une application complete a leurs vues sur la chimie organique ; celle au contraire que j’enonce s’accorde parfaitement avec Impli- cation aux faits de la theorie que je propose. II ne me reste qu’a aj outer la maniere dont je formule 1’acide salicylique et le trichlorophosphate de salicyle que j’ai fait connaitre dans un travail soumis a 1’Academie dans sa derniere seance. Acide salicylique. C---H2 C ' H C—H C • 0 • OH C O2 0 - OH Trichlorophosphate de salicyle. f C""H2 (C'H fC H c\ (c • 0--0 j i | o2 [phci3 Clo-o J Ces formules suflisent, pour le moment, pour indiquer mes idees sur la constitu- tion des corps. * Misprinted “ C2” for “ 02” in the original. 240 Proceedings of the Royal Society of Edinburgh. [Sess. APPENDIX Ilia. On a New Chemical Theory. By Archibald S. Couper, Esq. (Communicated by the Author.*) The end of chemistry is its theory. The guide in chemical research is a theory. It is therefore of the greatest importance to ascertain whether the theories at present adopted by chemists are adequate to the explanation of chemical phenomena, or are, at least, based upon the true principles which ought to regulate scientific research. Among those which have lately been developed, there is one, on account of its apparently numerous merits, which particularly claims investigation, and respecting which we deem that it would not be unprofitable were either new proofs of its scientific value furnished, or, on the contrary, should considerations be adduced establishing not only its inadequacy to the explanation, but its ultimate detriment to the progress of science. I allude to the system of types as advocated by Gerhardt. This system, striking alike for the breadth of its conception, and the logical and consequent manner in which it has been developed, has been controverted from the point of view afforded by theories less far-reaching than the one under consideration, and even based upon a one-sided and restricted appreciation of certain chemical reactions. The consequence is that this opposition has not impaired the favour with which the unitary system has been received, but has rather tended to display it in a more advantageous light. Imposing as this theory is, it is nevertheless all the more necessary to submit it to a strict investigation ; for there is nothing so prejudicial in the search for truth as the blind spirit of conservation. A rational belief demands the test of a preliminary doubt. There are two conditions which every sound theory must fulfil : — ■ 1. It must be proved to be empirically true. 2. It must no less be philosophically true. I admit that this theory is for the most part empirically true ; that is to say, it is not contradicted by many of the facts of the science. Evidence that this condition is only partially fulfilled, is to be found — 1. In the circumstance that the peroxides, for instance, do not fit very satis- factorily into the types. 2. The principle of double decomposition cannot ivell be applied to the con- version of the anhydrous sulphuric acid into the hydrate of that acid by the action of one equivalent of water, the formulae of these bodies being, according to Gerhardt, in their free state O.SO2 and H20. Combined, they become simply SH204. The same remark applies in like manner to carbonic acid. In these instances the wonted consequence of Gerhardt is missed. The fact of the density of the vapour of these bodies being the same in the free as in the combined states, may have prevented him from doubling the formulae of these anhydrous acids. The types of this theory being essentially types of double decomposition , this instance of a simple * Phil. Mag., vol. xvi. , 4th series (1358), pp. 104-116. 1 908-9. J Life and Chemical Work of Archibald S. Con per. 241 APPENDIX III b. SUR UNE NOUVELLE THEORIE CHTMIQUE j PAR M. A. S. COUPER.* L’etude de la chimie doit avoir pour but l’etablissement de la theorie de cette science ; une theorie elle-meme est un guide qui nous conduit dans les recherches chimiques. II est done de la plus grande importance de s’assurer si les theories actuellement admises par les chimistes suffisent pour l’explication des phenomenes chimiques, ou si elles sont au moins basees sur les vrais principes auxquels doivent se soumettre les recherches scientifiques. Parmi les theories recemment developpees, il en est une qui, en raison des nombreux avantages qu’elle parait offrir, merite une etude particulierement appro- fondie ; il nous a semble d’ailleurs que la science ne pourrait qu’y gagner, soit que cet examen vienne apporter de nouvelles preuves en faveur de cette theorie, soit au contraire qu’il etablisse son insuffisance et les dangers qu’elle presente pour les progres de la science. Je veux parler de la theorie des types, telle qu’elle a ete defendue par Gerhardt. Ce systeme, remarquable en meme temps par la largeur de sa conception et par le developpement logique qu’il a re§u, a ete combattu au point de vue de theories beaucoup moins satisfaisantes, basees sur une appreciation incomplete de certaines reactions chimiques. Il en est resulte que cette opposition, loin de diminuer la faveur avec laquelle le systeme unitaire avait ete regu, a plutot contribue a le montrer sous un jour plus avantageux. Quelque imposante que soit cette theorie, il n’en est que plus necessaire de la soumettre a un severe examen ; car rien n’est nuisible, dans la recherche de la verite, comme l’aveugle attachement aux idees regues. Une croyance rationelle exige l’epreuve preliminaire du doute. Toute bonne theorie doit remplir deux conditions : 1°. Il faut qu’elle s’accorde avec l’experience ; 2°. Il n’est pas moins necessaire qu’elle soit philosophiquement vraie. J’admets que la theorie unitarienne s’accorde pour la plupart des cas avec l’ex- perience ou plutot qu’elle n’est pas contredite par beaucoup des faits de la science. Cependant les remarques suivantes feront voir que cette condition n’est remplie qu’en partie : 1°. Les peroxydes ne rentrent pas d’une maniere bien satisfaisante dans les types ; 2°. Le principe de double decomposition ne peut pas bien s’appliquer a la trans- formation de 1’acide sulfurique anhydre en hydrate par l’action de 1 Equivalent d’eau : la formule de ces deux corps etant, d’apres Gerhardt, a l’etat libre, OSO2 et H20, combines ils deviennent simplement, SH204. La meme remarque s’applique d’une maniere semblable a l’acide carbonique. Dans l’explication de ces faits, on ne retrouve plus la consequence habituelle de Gerhardt. La densite de vapeur des acides anhydres de ces corps, etant la meme a l’etat de liberte et a l’etat de combinaison, aurait du l’empecher d’en doubler la formule. Les types de Gerhardt etant essentiellement des types de double decom- Annales de chimie et de physique, [3], t. liii. (1858), pp. 469-489. VOL. XXIX. 16 242 Proceedings of the Royal Society of Edinburgh. [Sess. combination diminishes somewhat the value of the otherwise great logical merit of this system. Having taken notice of such exceptions, the empirical truth of the theory may be otherwise admitted. The philosophical test demands that a theory be competent to explain the greatest number of facts in the simplest possible manner. In applying this test, three aspects of it require to be taken into consideration : — 1. As to the extension of the theory. 2. The explanation it affords of the facts. 3. The manner of this explanation. As to the first : this theory indeed brings every chemical combinate under a certain comparative point of view with every other. Herein apparently is its merit. Nevertheless, should our test be applied to its full extent, it will be found that it is fatal to this system, in other respects so imposing. The comparative point of view which it adopts is fundamentally false. As to the second: it does not explain the facts at all; consequently the most essential point of the test is unfulfilled. 3. This condition of the test is in like manner unfulfilled from the fact of the second not being complied with. Why is it that Gerhardt’s theory so signally fails in these two essential requisites Because it is based upon an old but vicious principle, which has already retarded science for centuries. It begins with a generalization, and from this generalization deduces all the particular instances. But it does not come within the limits of a chemical paper to enter upon a discussion which is purely metaphysical. Nevertheless, the theory of Gerhardt can only be combated upon metaphysical grounds, because it is only in overturning a general principle of research that the theory can be proposed. Gerhardt’s generalization lacks, moreover, the merit of being represented by a type having a known existence. from which he derives every chemical combinate, being in itself indefinite, cannot of course be contained or be produced in any definite body. That, however, which may be demanded of the type is, that in itself it should afford at least an instance of that which it is meant to represent. Now the . TJ part “ n” of the type represents the notion of indefinite multiples of 0 . But not H H a single instance of a multiple of 0 has been proved to exist ; much less has it H been proved that there exists, or can exist, multiples of this body in an indefinite series. The perfection or imperfection of the type meant to represent the generalized notion is, however, a matter of comparatively inferior moment. It is the principle involved in this generalization which is essentially pernicious. Should the principle which is therein adopted be applied to the common events of life, it will be found that it is simply absurd. Suppose that some one were to 1908-9.] Life and Chemical Work of Archibald S. Couper. 243 position, cet exemple cle simple combinaison directe diminue en quelque degre la valeur logique de cette theorie, qui est d’ailleurs si grande. Cette exception line fois constatee, on peut admettre pour le reste la verite empirique du systeme. II reste a examiner si elle remplit la condition non moins importante de lie pas se trouver en disaccord avec les principes philosopliiques. Ces principes demandent que la theorie puisse expliquer le plus grande nombre possible de faits, de la maniere la plus simple. En soumettant une theorie a cette epreuve, il faut examiner : 1°. Son etendue ; 2°. L’explication qu’elle donne des faits ; 3°. La maniere dont elle donne cette explication. Quant au premier point, la thOorie unitaire met cliaque combinaison chimique dans certains rapports de comparaison avec tous les autres. C’est la que se trouve en apparence son merite. Cependant si nous approfondissons l’examen de cette theorie, nous trouverons que ce merite meme est fatal pour elle. Le point de vue qu’elle prend pour ses comparaisons, est un point de vue essen- tiellement pernicieux. Pour le second point, elle n’explique pas les faits du tout, de sorte que la condition la plus importante n’est pas remplie. La deuxieme condition n’etant pas remplie, la troisieme ne Test pas davan- tage. Comment se fait-il que la theorie de Gerhardt ne reponde pas, sur ces points essentiels, aux exigences de la philosophic h C’est parce qu’elle est basee sur un principe ancien mais vicieux, qui a autrefois retarde la science pendant des siecles. Elle prend pour point de depart une generalisation dont elle deduit ensuite tous les cas particuliers. Mais ce n’est pas dans un travail chimique qu’il est possible d’entreprendre une discussion purement metaphysique, quoique la theorie de Gerhardt ne puisse etre combattue efficacement que par des raisons metaphysiques, puisqu’elle ne peut etre mise en avant qu’en renversant un principe general des recherches scientifiques. La generalisation qui fait le fond du systeme de Gerhardt n’a pas meme le merite d’etre representee par un type ayant une existence connue. nO H H’ dont il derive tous les composes chimiques, etant lui-meme indefini, ne peut etre contenu dans aucun corps defini. Cependant on a le droit de demander a un type de fournir en lui-meme au moins un exemple de ce qu’il est cense representer. Or la portion n du type represente l’idee de multiples indefinis de 0 H H’ et non-seulement il n’existe pas de multiples de 0 H H en serie indefinie, mais on n’a pas meme prouve l’existence d’un seul de ces multiples. La perfection ou l’imperfection du type qui doit representer l’idee generale, est toutefois d’une importance relativement inferieure. C’est le principe meme de la generalisation qui est essentiellement pernicieux. Si ce principe etait applique a la vie ordinaire, on le trouverait tout simplement absurde. Supposez, par exemple, que quelqu’un veuille systematiser la reunion des 244 Proceedings of the Royal Society of Edinburgh. [Sess. systematize the formation of letters into words that formed the contents of a book. Were he to begin by saying that he had discovered a ce7'tain word which would serve as a type , and from which by substitution and double decomposition all the others are to be derived , — that he by this means not only could form new words, but new books, and books almost ad infinitum , — that this word also formed an admirable point of comparison with all the others, — that in all this there were only a few difficulties, but that these might be ingeniously overcome, — he would state certainly an empirical truth. At the same time, however, his method would, judged by the light of common sense, be an absurdity. But a principle which common sense brands with absurdity, is philosophically false and a scientific blunder. Suppose the book that had formed the basis of this system were a German one, where all the words were found to be composed at least of two letters, still even in this language the viewing and systematizing of words as a series of double decom- positions would be no less ridiculous. The sure and invincible method of arriving at every truth which the mind is capable of discovering is always one and the same. It is that, namely, of throwing away all generalization, of going back to first principles, and of letting the mind be guided by these alone. It is the same in common matters. It is the same in science. To reach the structure of words we must go back, seek out the unde- composable elements, viz., the letters, and study carefully their powers and bearing. Having ascertained these, the composition and structure of every possible word is revealed. It would be well to call to recollection the parallelism of chemical research with that of every other search after truth ; for it has been in overlooking this, that in chemistry false and vacillating theories have been advocated and a wrong route so often pursued. In mathematics the starting-point is not generaliza- tions, but axioms, ultimate principles. In metaphysics, Descartes led the way of progress by analysing till he thought he could reach some ultimate elements beyond which it was impossible for him to go, then studying their force and power, and proceeding synthetically. The recognition of this method wrought the regeneration of science and philosophy. On the other hand, look where Gerhardt’s generalization of Williamson’s generalization leads him, and legitimately too, — a fact which his logical spirit clearly discerned. He is led not to explain bodies according to their composition and inherent properties, but to think it necessary to restrict chemical science to the arrangement of bodies according to their decomposition, and to deny the possibility of our comprehending their molecular constitution. Can such a view tend to the advancement of science ? Would it not be only rational, in accepting this veto, to renounce chemical research altogether 'l These reflections naturally lead to the inquiry after another theory more adequate to satisfy the just demands which can be made upon it. There is one which, as it is still supported by many distinguished chemists, cannot be passed over altogether unnoticed. It is that of the theory of certain combinates in organic chemistry which are to be viewed as analogous to, “playing the part of,” inorganic elements. These are denominated radicals, and are supposed to be contained in all organic chemical products. In addition to this, and also in connexion with it, there is a doctrine describing many combinates to be copulated, conjugated, by addition. 1908-9.] Life and Chemical Work of Archibald S. Couper. 245 lettres en mots formant un livre. S’d commengait par dire qu’il a decouvert un certain mot pouvant servir de type, duquel tons les autres penvent se deriver par substitution et par double decomposition, que par ces moyens on peut former non- seulement des mots nouveaux, mais des livres en quantite presque infinie, que ce mot forme ainsi un admirable point de comparaison pour tous les autres, que dans tout cela il n’y a que quelques diflicultes peu nombreuses pouvant etre ingenieusement tournees, cet homme etablirait certainement une verite experimentale. Cependant, en meme temps, sa methode, jugee a la lumiere du sens commun, serait une absurdite. Or un principe condamne par le sens commun est philosophiquement faux et ne peut etre qu’une erreur scientifique. Supposez que le livre pris pour base du systeme dont nous venous de parler, soit un livre allemand, oil tous les mots sont composes au inoins de deux lettres; meme dans cette langue il serait ridicule de considerer les mots comme resultant de series de doubles decompositions. La methode sure et infaillible d’arriver a toute espece de verite est toujours la meme. Elle consiste en particulier a mettre de cote toute generalisation, a remonter aux premiers principes, et a prendre ceux-ci pour seuls guides de l’esprit. Ceci est vrai pour les affaires ordinaires, et tout autant pour la science. Pour etudier 1a. structure des mots, il faut remonter aux elements indecomposables des mots, aux lettres, et se rendre compte soigneusement de leurs proprietes. Celles-ci une fois etablies, la composition de tout mot possible est expliquee. Il serait utile de rappeler la necessite de suivre, en chemie, la meme marche que dans tout autre genre de recherche de la verite ; car c’est en oubliant cette necessite, qu’on a defendu, en cliimie, des theories fausses et vacillantes, et qu’on a tant de fois marche dans une mauvaise voie. En mathematiques, le point de depart ne se trouve pas dans des generalisations, mais dans des axiomes. En metaphysique, Descartes a montre le chemin du progres en continuant son analyse jusqu’a ce qu’il crut avoir atteint des elements derniers, au dela desquels il lui etait impossible d’aller, en etudiant ensuite leurs forces et leurs proprietes, et en procedant enfin par synthese. C’est le triomphe de cette methode qui a regenere la science et la philosophic. D’un autre cote, voyez oil Gerhardt est conduit par sa generalisation d’une premiere generalisation de Williamson : il arrive necessairement a. un fait que son esprit logique lui a clairement montre ; il renonce a expliquer la constitution des corps d’apres leur composition et leurs proprietes inherentes, et croit necessaire de restreindre la chirnie a un arrangement systematique des corps d’apres leurs decom- positions, niant meme la possibility de comprendre leur constitution moleculaire. Une semblable maniere de voir peut-elle tendre a ravancement de la science ? et ne serait-il pas raisonnable devant un pared veto , de renoncer completement aux etudes chimiques 1 Ces reflexions conduisent naturellement a rechercher une tlieorie repondant mieux aux justes exigences de la raison. Il en est une, appuyee encore par beaucoup de chimistes distingues, que nous ne pouvons pas passer sous silence. C’est cede qui regarde certains composes de la chirnie organique comme analogues aux corps simples de la chirnie minerale, et jouant le meme role qu’eux. Ces corps sont appeles radicciux , et on en admet l’existence dans tous les composes organiques. Il se lie a cette tlieorie une doctrine, qui regarde beaucoup de combinaisons comme copulees ou conjuguees par addition. 246 Proceedings of the Royal Society of Edinburgh. [Sess. It is impossible here to enter upon any extensive criticism of this theory. I can only remark that it is not merely an unprofitable figure of language, but is injurious to science, inasmuch as it tends to arrest scientific inquiry by adopting the notion that these quasi elements contain some unknown and ultimate power which it is impossible to explain. It stifles inquiry at the very point where an explanation is demanded, by putting the seal of elements, of ultimate powers, on bodies which are known to be anything but this. Science demands the strict adherence to a principle in direct contradiction to this view. That first principle, without which research cannot advance a step, dare not be ignored ; namely, that a whole is simply a derivative of its parts. As a con- sequence of this, it follows that it is absolutely necessary to scientific unity and research to consider these bodies as entirely derivative, and as containing no secret ultimate power whatever, and that the properties which these so-called quasi elements possess are a direct consequence of the properties of the individual ele- ments of which they are made up. Nor is the doctrine of bodies being “ conjugated by addition ” a whit in advance of that which I have just been considering. This doctrine adopts the simple expedient of dividing certain combinates, if possible, into two imaginary parts, of which one or both are bodies already known. Then it tells us that these two parts are found united in this body. But how they are united, or what force binds them together, it does not inquire. Is this explication arbitrary? Is it instructive? Is it science ? I may now be permitted to submit a few considerations relative to a more rational theory of chemical combination. As everything depends upon the method of research employed, it will in the first place be necessary to find one that may be relied upon. If the method is good, and conscientiously carried out, stable and satisfactory results may be expected. If, on the contrary, it is vicious, we can only expect a corresponding issue. A satis- factory method is, however, not difficult to find, nor is it difficult in its application. The principle which ought to guide all research is in every case the same. It is that of analysing till it is impossible to reach more simple elements, and of studying these elements in all their properties and powers. When all the properties and powers of the individual elements are known, then it will be possible to know the constitution of the combinates which their synthesis produces. It is necessary therefore in chemical research, in order to ascertain the various qualities and functions of the different elements, — 1. To consider the whole of chemistry as one. 2. To take into consideration every known combinate, and to study the character, functions, and properties displayed by each element for itself, in each of these com- binates in all their different conditions and aspects It is by a comparison of the different bodies among themselves that we are able to trace the part that is per- formed by each element separately. 3. To trace the general principles common to all the elements, noting the special properties of each. This method is essentially different from that where one class of bodies is 1908-9.] Life and Chemical Work of Archibald S. Couper. 247 II est impossible d’entrer ici dans line critique detaillee de cette theorie. Je dois me borner a faire remarquer qu’elle n’est pas seulement une maniere de parler inutile, mais qu’elle nuit encore a la science en tendant a arreter l’analyse scientifique par l’idee que ces quasi-elements renferment quelque force derniere inconnue, qu’il est impossible d’expliquer. En dormant le caractere d’elements, de forces dernieres a des corps qu’on sait n’etre rien moins que cela, elle arrete les recherches au point meme dont on demande l’explication. La science reclame une stricte fidelite a un principe directement oppose a cette maniere de voir. Ce principe, sans lequel les recherches scientifiques ne peuvent pas faire un pas, c’est qu’un tout est simplement un derive de ses parties. Comme consequence, il en resulte qu’il est absolument necessaire pour l’unite de la science et pour le progres des recherches de considerer ces corps qu’on a appele radicaux , comme derives et comme ne renfermant aucune force derniere cacliee, et d’admettre que leurs proprietes sont une consequence directe des proprietes in- dividuelles des elements qui les composent. La doctrine des corps conjugues par addition n’est pas un progres sur celle que nous venons de considerer. Cette doctrine adopte le simple expedient de diviser, lorsque c’est possible, certains composes en deux portions imaginaires, dont l’une ou bien toutes deux sont des corps deja connus. Elle declare ensuite que ces deux corps se trouvent unis dans le compose en question. Mais elle ne s’inquiete pas de savoir comment elles sont unies ou quelle force les lie. Cette explication n’est-elle pas arbitraire? Nous apprend-elle quelque chose1? Est-ce la de la science? II me sera permis maintenant de faire valoir quelques considerations relatives a une theorie plus rationelle des combinaisons chimiques. Comme tout depend de la methode de recherche employee, il est avant tout necessaire d’en trouver une dans laquelle nous puissions avoir confiance. Si la methode est bonne et si elle est appliquee consciencieusement, nous pouvons en attendre des resultats certains et satisfaisants. Si au contraire elle est vicieuse, nous ne pouvons attendre qu’un mauvais resultat. Heureusement, il n’est pas difficile de trouver une bonne methode, qui ne presente pas de difficultes dans son application. Le principe qui doit guider toutes les recherches est dans tous les cas le meme. C’est celui d’analyser jusqu’a ce qu’il soit impossible d’atteindre des elements plus simples, et d’etudier ces elements dans leurs proprietes et leurs forces. Les forces et les proprietes des elements etant toutes connues, il sera possible alors de connaitre la constitution des combinaisons produites par leur syn these. Il est done necessaire, dans les recherches chimiques, pour s’assurer des pro- prietes et des fonctions des differents elements : 1°. De considerer la chimie comme formant un ensemble unique. 2°. D’etudier tous les composes connus et de se rendre compte du caractere, des fonctions et des proprietes de chaque element, dans chaque compose, sous tous les points de vue et dans toutes les conditions differentes. C’est par la comparaison des dilffirents corps entre eux que nous pouvons recon- naitre le role que joue chaque element separement. 3°. De rechercher les principes generaux eommuns a tous les elements, en prenant note des proprietes speciales de chacun d’eux. Cette methode est essentiellement difffirente de celle oil une classe de corps est 248 Proceedings of the Royal Society of Edinburgh. [Sess. chosen as a point for the restriction of our views of the properties of the others — where only the qualities found in the first are to he measured out to the rest. I shall now proceed to inquire how its more thorough application tends to the development of a rational chemical theory. It has been found that there is one leading feature, one inherent property, common to all the elements. It has been denominated chemical affinity. It is discovered under two aspects : — (1) affinity of kind ; (2) affinity of degree. Affinity of kind is the special affinities manifested among the elements, the one for the other, etc., as carbon for oxygen, for chlorine, for hydrogen, etc. Affinity of degree is the grades, or also limits of combination, which the elements display. For instance, C202 and C204 are the degrees of affinity of carbon for oxygen. C202 may he called the first degree, and C204 may he termed the second degree, and, as a higher degree than this is not known for carbon, its ultimate affinity or combining limit. Affinity of degree in an element may have only one grade. It may have, however, and generally has more than one. Here then is an inherent property common to all elements, by the removal of which the chemical character of an element will be destroyed, and by virtue of which an element finds its place marked out in a complex body. It is such a property that is required to form the base of a system. Nor would its suitableness for this purpose be affected by the discovery that the elements are themselves composite bodies, which view the chemist is perhaps not unwarranted to adopt. For, in such a case, the necessity would doubtless still be found to exist of adopting the principle of affinity, or something at least equivalent to it, as the basis of the explanation of chemical combinates. In applying this method, I propose at present to consider the single element carbon. This body is found to have two highly distinguishing characteristics : — 1. It combines with equal numbers of hydrogen, chlorine, oxygen, sulphur, etc. 2. It enters into chemical union with itself. These two properties, in my opinion, explain all that is characteristic of organic chemistry. This will be rendered apparent as I advance. This second property is, so far as I am aware, here signalized for the first time. Evidence as to its being a property of carbon may therefore be required. It will be found in the following : — What is the link which binds together bodies composed of 4, 6, 8, 10, 12, etc., equivalents of carbon, and as many equivalents of hydrogen, oxygen, etc. ? In these you may remove perhaps all the hydrogen or oxygen, and substitute so many equivalents of chlorine, etc. It is then the carbon that is united to carbon. Further, that it is not the hydrogen that is the binding element in these combinates is evident ; thus — 1908-9.] Life and Chemical AVork of Archibald S. Couper. 249 ehoisie pour restreindre nos idees sur les proprietes des autres corps, et oil celles seulement reconnues dans les premiers sont accordees aux derniers. Je vais maintenant chercher comment l’application plus complete de cette methode conduit au developpement d’une theorie rationnelle de la chimie. On a trouve qu’il existe un trait saillant, une propriete commune a tous les elements. On a appele cette propriete affinite chimique. Elle se presente de deux manieres differentes : 1°. Elle peut s’exercer comme affinite elective ; 2°. Elle peut s’exercer comme affinite de degre. L’affinite elective est l’affinite que les elements montrent les uns pour les autres : ainsi le carbone pour l’oxygene, pour le clilor, pour l’hydrogene, etc. L’affinite de degre est l’affinite qui s’exerce entre deux elements en proportions multiples ; ce sont des limites de combinaison. Par exemple C202 et C204 sont les degres de l’affinite du carbone pour l’oxygene.* On peut appeler, C202 premier degre, et C204 second degre, et comme on lie connait pas, pour le carbone, de degre plus eleve, affinite derniere ou limite de combinaison. L’affinite de degre, pour un element, peut n’avoir qu’un degre. Cependant elle peut en avoir et en a generale- ment plus d’un. C’est done la une propriete inherente aux elements, qui leur est commune a tous, et dont la suppression entrainerait la destruction du caractere cliimique de l’element ; elle marque a chaque element sa place dans un corps compose. II faut une propriete de ce genre pour former la base d’un systeme ; elle resterait encore suffisante pour cela, quand bien meme on decouvrirait, ce que les cliimistes n’ont pas le droit de regarder comme impossible, que les elements eux-memes sont des corps composes ; car dans ce cas, sans aucun doute, on se trouverait encore dans la necessite d’adopter le principe de l’affinite ou de moins quelque chose d’equivalent, comme base de l’explication des combinaisons chimiques. Pour le moment toutefois, il est impossible de remonter a des elements plus simples. II est done necessaire provisoirement de partir des affinites et des proprietes deeouvertes dans les elements, pour arriver a la theorie de leurs com- binaisons. Comme application de cette methode, considerons maintenant le seul element carbone. Ce corps possede deux caracteres qui le distinguent particulerement : 1°. II entre en combinaison avec des nombres egaux d’equivalents d’hydrogene, de clilor, d’ox}rgene, de soufre, etc. 2°. II entre en combination avec lui-meme. Dans mon opinion, ces deux proprietes suffisent pour expliquer tout ce que la chimie organique presente de caracteristique ; c’est que je demontrerai plus loin. La seconde de ces proprietes est, je crois, signalee ici pour la premiere fois. On peut demander de prouver que ce soit la une propriete du carbone. Ce qui suit va le demon trer. Quel est le lien qui tient ensemble les composes de 4, 6, 8, 10, 12, etc., molecules de carbone et d’un pared nombre d’equivalents d’hydrogene, d’oxygene, etc. ? On peut enlever de ces composes tout l’liydrogene et tout l’oxygene peut-etre, et le remplacer par autant d’equivalents de clilor, etc. C’est done le carbone qui est uni au carbone. De plus, il est evident que ce n’est pas l’hydrogene qui sert de lien dans les combinaisons, car on a * Misprinted “l’hydrogene” in the original. See the English paper. 250 Proceedings of the Royal Society of Edinburgh. [Sess. H 0 i Cl O2 H ° H p2 0 j ^ 0 ) and C2 qJ H o f Cl Here the whole four of hydrogen are not bound by a mutual affinity ; for each element of hydrogen can be substituted for one of chlorine in regular series, beginning with the first and ending with the last. The atoms of oxygen are, on the contrary, united in pairs (which will be more fully developed hereafter), and only for two atoms of oxygen two of chlorine can be substituted ; thus — 01 p2 0 j O O { 0 1 C2 Cl Cl 0 0 C2 Cl Cl Cl Cl In the same manner, with bodies that contain multiples of C2 united to hydrogen, etc. Take the inverse of this. If the four atoms of hydrogen were bound together, we could evidently expect to form such bodies as Cl Br Br Br PI H4 11 Cl H4 Cl Cl H4 11 Cl and H4 !]'' Br Cl Cl Cl Cl or for bodies like C4H4, C6H6, C8H8, one would naturally expect to find the carbon Cl2 substituted for chlorine, and find bodies like H4 0„, H6C16, II8C18, etc. These bodies are not only unknown, but the whole history of hydrogen might be investigated and not a single instance be found to favour the opinion that it has any affinity for itself when in union with another element. How, on the other hand, carbon remains chemically united to carbon, while perhaps 8 equivalents of hydrogen are exchanged for 8 equivalents of chlorine, as in naphthaline. Analogous to this is the conversion of alcohol, C4°5 and the hydrocarbide C4H° into C4C16. All the countless instances of substitution of chlorine, etc., tend in the same direction. They prove beyond doubt that carbon enters into chemical union with carbon, and that in the most stable manner. This affinity, one of the strongest that carbon displays, is perhaps only inferior to that which it possesses for oxygen. Another feature in the affinity of carbon is, that it combines by degrees of two; thus, C202 and C204, C4H4 and C4H6, C6H8 and C6H8, C8H8 and C8H10, etc. : from these last it is especially evident that two is the combining grade of carbon. It becomes still more apparent when we compare the bodies C4H4 and C1 1 C4H5C1, that is, C4H I etc. Many such proofs might be added, while, on the H4 * Misprinted “ C2 ” in the original. See the French paper. 1908-9]. Life and Chemical Work of Archibald S. Couper. 251 Ici les 4 molecules d’hydrogene ne sont pas liees ensemble par une affinite mutuelle, car chaque element, d’hydrogene peut etre remplace par un element de chlore, en commen^ant par le premier et finissant par le dernier. Les atomes d’oxygene sont, au contraire, unis par paires (c’est ce qui sera plus completement developpe plus bas), et on ne peut remplacer que 2 molecules d’oxygene par 2 de chlore. Ainsi J8|. 8}- CS Cl Cl Cl I Cl J }■ II en est de meme pour les corps qui renferment des multiples de C2 unis avec de l’hydrogene, etc. Prenons l’inverse de ce raisonnement. Si les 4 atomes d’hydrogene etaient unis ensemble, nous aurions le droit d’attendre la formation de corps tels que rcn fBrl fBrl fBrl H4- Cl Cl H.. Cl Cl H4] r ’ 1 ci H4- Br Br " [cij ici (cij l ci J ou bien pour des corps tels que C4H4, C6H°, C8H8, on s’attendrait naturellement a voir le carbone remplace par du chlor et a trouver des corps tels que H4C14, H6C16, H8C18, etc. Non-seulement ces corps sont inconnus, mais on pourrait encore etudier toute l’histoire de l’hydrogene sans trouver un seul exemple en faveur de l’opinion qu’il aurait quelque affinite pour lui-meme, lorsqu’il est combine avec un autre element. On peut remarquer aussi que le carbone reste chimiquement combine avec lui- meme, pendant que peut-etre huit atomes d’hydrogene sont remplaces par huit atomes de chlore, comme dans la naphtaline. La transformation de l’alcool C4^ et du carbure d’hydrogene C4H6 en chlorure de carbone C4C16, sont des faits analogues. Ainsi que tous les nombreux exemples de substitution de chlore, les faits precedents prouvent, sans qu’il soit possible de conserver aucun doute, que le carbone s’unit chimiquement avec le carbone, et cela de la maniere la plus stable. Cette affinite, l’une des plus energiques parmi celles que montre le carbone n’est peut-etre inferieure qu’a celle qu’il a pour l’oxygene. Un autre trait saillant de l’affinit6 du carbone est le suivant : il se combine par degres pairs. Ainsi on a C202 et C204,— C4H4 et C4H6, — C6H6 et C6H8, — C8HS et C8H10, etc. Ces derniers composes, en particulier, prouvent evidemment que le carbone se combine avec des nombres pairs d'atomes. Cette propriete devient encore plus evidente lorsque nous comparons les corps (01 ) C4H4 et C4H5C1, ou C4 < H V , etc. I H4) 252 Proceedings of the Royal Society of Edinburgh. [Sess. other hand, there are no instances contradictory of this point. Hence the circum- stance that it must ever remain impossible to isolate a combinate of the form C2H3 or C4H5, etc. Carbon having only two grades of combination of two atoms each, a fact which is easily traced throughout all organic chemistry, this inherent property of the element may legitimately furnish two grand types for all its combinates. The first type will be nC2M4. The second type will be nC2M4 — mM2T As examples belonging to the first type, may be mentioned the alcohols of the sethylic form, their aethers, the fatty acids, etc. Thus methylic alcohol has the formula C2 ... o • 0H H3 5 and eethylic alcohol, "O ""OH ; IT2 02-.-H3 In these instances it will lie observed, that for each double atom of carbon the combining power is (4) four, which is the ultimate limit of combination for carbon in all bodies yet produced. In the latter instance it is apparent, inasmuch as if the combining limit of two C2s be each reduced by 3 in hydrogen or oxygen, there still remains a combining power of one to each of the two C2s which each expends in uniting with the other ; C2 -h3 therefore : , or, C2 • H3 what is the same thing. ™ ••()••• on C •• h2 belongs to the type nC2M4. C2 • H3 Again, the inherent properties of the elements may be viewed as dividing bodies into primary, secondary, tertiary, and so on, combinates. These may be termed so many orders of complicity. Thus C4H6 is a primary combinate, or it belongs to the first order of complicity ; but C4....^5 is a secondary combinate, or belongs to the second order of complicity. C202 and C204 are primary, while C204, 20H and C204, 20Ka are secondary. A primary combinate is then nC2 united to nM4 or to nM4 — mM2 in such a * Misprinted “ mM ” in the original. 1908-9.] Life and Chemical Work of Archibald S. Couper. 253 On pourrait ajouter bien d’autres preuves en sa faveur, tandis qu’il n’y a point de faits en contradiction avec elle. II resulte de la qu’il doit etre impossible d’isoler un compose de la forme C2H3 on C4H5, etc. Le carbone ne se combinant qu’en deux degres differents et chaque fois par deux atonies (fait que l’on peut verifier aisement dans toute la chimie organique), cette propriety fondamentale de l’element peut legitimement fournir deux grands types pour toutes les combinaisons dans lequelles il entre. Le premier type sera ?^C2M4, et le second ?zC2M4 — mM2, oil m est un nombre moindre que n. Les alcools de la forme ethylique, leurs ethers, les acides gras, etc., rentrent dans le premier type. Ainsi l’esprit-de-bois a pour formule et l’alcool 0 — OH H3 C ,1 ( )— OH I H2 C2 — H3 . On remarquera que, dans ces exemples, la puissance de combinaison de chaque double atome de carbone est de 4 ; c’est la la derniere limite de combinaison du carbone dans tout les corps obtenus jusqu’a ce jour. Le dernier exemple montre dans le carbone un meme pouvoir de combinaison ; car, en deduisant du pouvoir de combinaison de chacun des doubles atonies de carbone trois forces employees par l’hydrogene et l’oxygene qui leur sont combines, il reste encore libre une force qui s’exerce dans l’union des doubles atonies l’un avec l’autre ; il en resulte que C2 — H3 C2— H3 , ou, ce qui revient au meme, C2— 0— OH ^H2 C2— H8, appartient au type ?iC2M4. On peut considerer les proprietes inherentes des elements comme divisant les corps en primaires, secondaires, tertiaires, etc. ; c’est ce qu’on peut appeler les divers degres de complication. Ainsi C4H6 est un compose primaire, c’est-a-dire qu’il appartient au premier degre de complication. Mais C4 ()— OH H5 est un compose secondaire ou appartient au second degre de complication. C202 et C204 sont primaires, tandis que C204 — 02II2 et C204 — 02K2 sont secondaires. Une combinaison primaire est done composee de nC2 uni a ^M4 ou a %M4 — mM2, 254 Proceedings of the Royal Society of Edinburgh. [Sess. manner that the combining energy of the complement (nM4, etc.) either potentially or actually does not extend beyond nC2. A secondary combinate is one in which the combining energy of the complement is not all expended upon nC2, but is extended further to one or more elements. On the same principle there are tertiary combinates, etc. These orders of complicity ought in reality to be subdivided. This, however, I do not think it necessary for the present to enter upon. It will now be understood why an alcohol belongs to the type nC2M4, and on the same principle why a free aether belongs to the same type, thus (02 0 *5 p2 *, while they are at the same C2 • H3 H3 C2 time secondary combinates. A secondary combinate, that is to say, a body belonging to the second order of complicity, is, as will be understood from the principle which forms the ground of the rational theory, a direct consequence of an inherent property of one or more of the elements which form the complement to the carbon. In the instance before us, it is a certain property of the oxygen which is the cause of the secondary combinate. This property is the affinity which one atom of oxygen in combination always exerts towards another atom of oxygen likewise in combination. This affinity is modified by the electric position of the element to which the respective atoms of oxygen are bound. From this property results the fact, that in organic combinates the atoms of oxygen are always found double. For instance, the combining limit of oxygen being two, when two molecules of r;2""0"" ^ — H2 are set at liberty, the free affinities of the oxygen instantly produce the C2"H3 union of these molecules. The cause of the union of two molecules of C2H3 has been already remarked. In the two cases, the causes of the union of the respective molecules are in so far different, that the one is the result of a property of the carbon, while the other is the result of a property of the oxygen. The view here adopted of the nature of oxygen is, I am convinced, alone in conformity with the reactions where the properties of this body develope themselves. The vapour of anhydrous sulphuric acid, for instance, is conducted into anhydrous 0> aether. The following will then be the reaction : — S2 ■ • O2 O2 cation with C4 SL C4, the two atoms of the oxygen of the sulphuric acid '■■‘11° TP**’* entering into communi- * The vertical dotted line between these two “ C2’s ” is omitted in the original. 1908-9.] Life and Chemical Work of Archibald S. Couper. 255 de telle sorte que le pouvoir de combinaison du complement (wM4), soit virtuelle- inent, soit actuellement, ne depasse pas celui de n C2. Les combinaisons secondaires sont celles oil le pouvoir de combinaison du com- plement, au lieu de se porter entierement sur ^C2, s’etend encore sur un ou plusieurs autres elements II existe de meme des combinaisons tertiares, etc. Ces degres de complication devraient a la rigueur etre subdivises. Toutefois je ne crois pas necessaire, pour le moment, d’entrer dans ces details. On comprendra maintenant comment un alcool appartient au type ?zC2M4, ainsi qu’un ether libre ; par exemple, j 0 0 ) C2— - C2 I H2 H2 ) C2- -H3 H3- -C2 et que tous deux sont des composes secondaires. Les combinaisons secondaires, c’est-a-dire les corps appartenant au second degre de complication, prennent naissance (on le comprendra en partant du principe qui forme la base de la theorie rationelle), en vertu d’une propriete appartenant a un ou plusieurs des elements combines avec le carbone. Dans les exemples precedents, c’est une certaine propriete de i’oxygene qui est cause de la complication du corps. Cette propriete consiste dans l’affinite qu’une molecule d’oxygene en combinaison excerce tou; jours sur une seconde molecule d’oxygene elle-meme combinee. Cette affinite est modifiee par l’etat (electrique ?) des elements auxquels les deux atomes sont lies. II resulte de la que, dans les composes organiques, les atomes d’oxygene vont toujours par deux. Par exemple, le pouvoir de combinaison de l’oxygene etant 2, quand 2 molecules 1° H2 sont mises en liberte, l’affinite non satisfaite de l’oxygene produit imme- C2< de C2- -H3 diatement l’union de ces molecules. On a deja vu la cause de l’union de deux molecules de C2H3. Dans ce dernier cas, l’union des molecules est due a une pro- priety du carbone, et dans le premier a une propriete de l’oxygene. Les vues emises ici sur la nature et les fonctions de l’oxygene sont, j’en suis convaincu, seules conformes aux reactions dans lesquelles les proprietes de ce corps sont en jeu. Par exemple, on fait arriver la vapeur d’acide sulfurique anhydre dans de (op l’etlier anliydre. Yoici quelle sera la reaction : S2< etant mis en presence de ( O2 C4, les deux atomes d’oxygene de l’acide sulfurique et les deux atomes * The two upper “ O’s ” have been omitted in the original. See the English paper. 256 Proceedings of the Royal Society of Edinburgh. [Sess. and the two atoms of the oxygen of the sether (now in presence of each other) being in different (perhaps different electric) conditions, mutually loosen their former affinities and reunite themselves to the (electrically?) different atoms of oxygen of these respective combinates. The same principle may naturally be expected to display itself with regard to acids and bases. The oxygen of an acid unites itself to the (electrically ? ) different oxygen of water. The oxygen of a base on the same principle has an affinity for the electrically different oxygen of water. It will be observed — 1. That the oxygen of the water of an acid can only be expelled by that of a base and vice versa. 2. It is to be remarked that it is not the metal of a base which exchanges places with the hydrogen of the hydrate of an acid ; for if that were the case, the affinity of the oxygen of the metal, and also of the acid, would be greater for the oxygen of the water than the affinity of the hydrogen for that same oxygen. But this is not so. The very opposite is the truth. If one atom of hydrogen be withdrawn from the hydrate of an acid or from the hydrate of an oxide , it is universally accompanied by an atom of oxygen. It is evident, then, that the affinity between the positive and negative atoms of oxygen is less than that which attaches these atoms to the element with which they form a primary combinate. A consequence of this truth is, that it is impossible to double the equivalent of oxygen, if the chemical equivalents are to be understood as not being in direct contradiction to any chemical truth or essential feature in the properties of an element. Carbon differs entirely in this respect from oxygen. There is no reaction found where it is known that C2 is divided into two parts. It is only consequent therefore to write, with Gerhard t, C2 simply as C, it being then understood that the equivalent of carbon is (12) twelve. This value of the atom will be adopted in the following part of this paper. Sulphur, selenium, etc., being bodies displaying properties similar, not to carbon, but to oxygen, it will be necessary to retain the equivalent value that has generally been assigned to them. I have now shown how ordinary alcohol, C2H602 common sether, and the hydro- carbide, C2H6, belong to the type nCM4. The phenomena which necessitate this view of the constitution of these bodies have a like consequence in regard to the other alcohols, glycols, acids, and sethers of this series. p--0 -OH : ••• H2 Propyle alcohol is (V..qq2 > where it wrill be seen that the atom of carbon C ■ H3 situated between the two others, on account of being chemically united to these, is reduced to the combining power of two for hydrogen, oxygen, etc. One combining power is given up to the carbon upon the one side, and a second to the carbon upon the other. It will be observed also that the primary combinates ought in rigour to be them- selves enumerated in an inverse order. The type nCM4 becomes then in reality the 1908-9.] Life and Chemical Work of Archibald S. Couper. 257 d’oxygene de Tether se trouvant dans nn etat (peut-etre electrique) different, les affinites mutnelles des atonies d’oxygene d’un meme corps s’affaiblissent, et ils s’unissent aux atomes (electriquement 1) differents d’oxygene de l’autre compose. La meme chose se passe naturellement entre les acides et les bases. L’oxygene d’un acide s’unit avec Toxygene (electriquement ?) different de l’eau. L’oxygene de la base, en vertu du meme principe, s’unit avec Toxygene (electriquement'?) different de l'eau. On remarquera : 1° que l’oxygene de l’eau contenue dans un acide ne pourra etre chasse que par celui d’une base ; 2°. Que ce n’est pas le metal de la base qui prend la place de Thydrogene de l’acide hydrate; car si cela avait lieu, l’affinite de Toxygene combine au metal, ainsi que celle de Toxygene de l’acide, serait plus grande pour Toxygene de l’eau que l’affinite de Thydrogene pour ce meme oxygene. Mais il n’en est pas ainsi ; bien au contraire, si un atome d’hydrogene est enleve a l’acide hydrate ou a une base hydratee, il est universe! lement accompagne d’un atome d’oxygene. II est done evident que Tafhnite entre les atomes d’oxygene positif et negatif est moindre que celle qu’ils ont pour l’element qui forme avec eux un compose primaire. Il resulte de tout ceci, qu’il est impossible de doubler l’equivalent de Toxygene, si Ton veut que les equivalents chimiques ne se trouve en contradiction avec aucune verite chimique, avec aucun trait essentiel de la physionomie propre d’un Element. Le carbone differe completement sous ce rapport de Toxygene. On ne connait pas de reaction oil C2 soit devise en deux parties. Il faut done, pour etre conse- quent, ecrire avec Gerhardt C2 simplement C, en portant a 12 l’equivalent du carbone. C’est cette valeur du poids atomique que nous admettrons dans le reste de ce travail. Le soufre, le selenium, etc., etant des corps qui offrent des proprietes semblables a celles de Toxygene et non a celles du carbone, il sera necessaire de conserver les equivalents general ement admis. J’ai montre maintenant comment l’alcool C2H602, Tether et le carbure d’hydrogene C2H6, appartiennent au type wCM4. Les phenomenes qui conduisent a cette maniere de voir sur la constitution de ces corps ont une consequence semblable pour les autres alcools, les glycols, les acides, les ethers de cette serie. L’alcool propylique * est | 0— OH ] c I H- > . C— H2 C — H3 On remarquera que l’atome de carbone situe entre deux autres, etant cbimiquement combine avec chacun d’eux, son pouvoir de combinaison est reduit a 2 pour Thydrogene, Toxygene, etc. Une des forces de combinaison s’exerce sur un element de carbone d’un cote, et une seconde sur un element de carbone de l’autre. Les composes primaires devraient etre a la rigueur eux-memes enumeres dans un ordre progressif de complication. YOL. XXIX. * Misprinted “ Le propylglycol ” in the original. 17 258 Proceedings of the Royal Society of Edinburgh. [Sess. type CM4. This enumeration, however, does not appear to possess any great practical utility, and it is perhaps preferable simply to denote it in an indefinite manner by adding “n ” to the true type CM4 C - 0 -OH : "H2 C — H2 In like manner the butyle alcohol is to be viewed as , and so on C H2 C " H3 throughout all the series of these alcohols. The constitution of the aethers will be evident : C'" 0 °" "C :""H2 H2 * C H H C represen£s the mixed butylic-ethylic aether. C—H2 C—H8 .0- OH Formic acid is represented by the form Cv O2 ; acetic acid in like manner, H C " 0 OH ;-02 C -H3 C— 0 OH O2 Propionic acid is g C " H3 The constitution of glycol may be represented as follows : — q "O'" OH : H2 6"-h2 O—OH * The vertical dotted lines between the two “ C’s ” is omitted in the original. 1908-9.] Life and Chemical Work of Archibald S. Conper. 259 Le type wCM4 devient alors en realite le type CM4. Mais cette enumeration ne paralt pas avoir une grande utilite pratique, et il est peut-etre preferable de designer le type d’une maniere indeterminee en ajoutant n au vrai type CM4. L’alcool butylique est de meme represente par ( 0— OH c ( 31- C— H2 C— H2 0— H3 et ainsi de suite en parcourant toute la serie de ces alcools. La constitution des ethers n’est pas moins evidente. C f 0- ■°\ c ! H2 H2 j C — H2 H3— C C— H2 C— H3 representera Tether mixte butylethylique j O-OH j L’acide formique sera . . C ■ O2 > ; H | L’acide acetique . L’aeide propionique j 0— OH) n J " I o- 0— H2 C— H3 On peut ecrire le glycol ainsi j O— 0H\ c] [ H2 j H2 C / | 0— OH 260 Proceedings of the Royal Society of Edinburgh. [Sess. In like manner as to the acids of these glycols ; oxalic acid, for instance, may be C'-'O-OH : •••O2 represented as C ' " o2 • ■ 0 • " OH Respecting these acids, it may perhaps be allowable to suggest the possibility of the molecule having two poles, and that especially the atom of oxygen situated at one or perhaps both, and near to two atoms of oxygen bound together, and forming no secondary combinate, may be in a state presenting great affinity for basic oxygen. Analogy with electric poles may perhaps demand the opinion that all the negative oxygen be situated upon one side of the molecule. It will in that case be preferable C”"02 : —O2 to represent the oxalic acid as C . 0 OH Be that as it may, however, the rational 0 OH method of investigation proves it to be a law, that in acids of the type nCM4 the presence of two atoms of oxygen bound together so as to form only a primary part of the same molecule, and situated close to the negative oxygen, is necessary to the calling forth or production of this negative state. This is a particular instance, but it moreover shores generally how the electro- positive or the electro-negative value of the elements mutually modify and condition the electropositive or electronegative value of each other when in combination. This law is different from the electric hypothesis which chemists have formerly defended, but which never could be traced throughout a thoroughgoing application of their views to organic chemistry. The law here distinctly enounced coincides exactly with, and is rendered apparent by the application of the theory of chemical combination which I support. 1908-9.] Life and Chemical Work of Archibald S. Conper. 261 et l’acide oxalique ci°-0H I O2 ) o2 ( 0 — OH, C Relativement aux acides, il sera peut-etre permis d’emettre la supposition que les molecules possedent deux poles, et que la molecule d’oxygene situee aupres de l’un des poles (ou peut-etre des deux) et dans le voisinage des deux molecules d’oxygene liees ensemble et ne donnant pas lieu a la formation d’un compose secondaire, que cet oxygene, dis-je, se trouve dans un etat tel, qu’il possede une grande affinite pour l’oxygene basique. L’analogie avec les poles electriques exige peut-etre que tout l’oxygene soit place d’un cote de la molecule. II vaudrait rnieux, dans ce cas, representer l’acide oxalique par t O2 A C I O2 1 j G J 0- ( -OH 0— OH Quoi qu’il en soit, la methode rationelle d’analyse prouve que c’est une loi que, dans les acides du type ?iCM4 la presence de deux atonies d’oxygene lies ensemble de maniere a former une partie primaire de la meme molecule, et situes dans le voisin- age de l’oxygene negat.if, est necessaire pour produire dans cet oxygene l’etat negatif oil il se trouve. Ceci n’est qu’un cas particulier d’un fait plus general, car il resulte de ce qu’en general l’etat electropositif ou electronegatif des elements modifie ou entraine l’etat electropositif ou electronegatif des elements combines avec eux, et reciproquement. Cette loi dilfere de l’hypothese electrique que les cbimistes ont defendue autre- fois, mais qui n’a jamais pu recevoir une application complete a leur vues sur la chimie organique. Celle au contraire que j’enonce ici s’accorde parfaitement avec la theorie que je defends, et s’en deduit d’une maniere simple. Misprinted in the original. See p. 260 and also p. 239. C 0— OH 262 [Sess. Proceedings of the Royal Society of Edinburgh. But to return. Glycerine is 0 OH H C • 0 OH o O •' OH H , and glyceric acid : O' " OH c •• H2 C " H2 c. H2 "O'' OH G-O2 C--Q- OH Glucose has been perhaps too little investigated to afford data sufficient to determine definitely its formula. Taking, however, mucic and saccharic acids as starting-points, these bodies may be meanwhile represented as : — H \ C O OH H C 0 OH H (V 0 OH l the acids. H C. c. c 0 OH* O2 O2 0 • OH 0 OH Glucose. ( G C. C: C C:' H 0 OH H 0 OH H 0 OH H 0 OH H O ' OH H 0 OH C H V 0 OH It will thus be seen that these combinates all belong to type nCM4. * This “ OH ” is omitted in the original, f The oblique dotted line here is omitted in the original. X The vertical dotted line between the “ C’s” is omitted in the original. 1908-9.] Life and Chemical Work of Archibald S. Couper. 263 Mais revenons aux formules des combinaisons les plus importantes. La glycerine est representee par ( 0 — OH C 0— OH H > C et l’acide glycerique par C H2 H2 0— OH ] rll c -! 0— OH 0— OH C H2 c j O2 | 0— OH La glycose est peut-etre trop mal etudiee pour qu’on puisse determiner definitive- ment sa formule. Mais en prenant 1’acide mucique et l’acide saccharique comme points de depart, ces trois corps peuvent etre provisoirement represents par rK C J c c H 0— OH H j 0— OH H ( 0— OH (h >0 — OH* c - c\ I >02 c\ \02 1 0 — OH I 0— OH Les acides. La glycose. ( C c c c c 0— OH H j 0— OH )h j 0— OH ! H j 0— OH !h j 0— OH (h r 0— OH f 0— OH H II en resulte que ces composes appartiennent au type wCM4. This “ OH ” is omitted in the original. + Misprinted “ H ” for “ 0 — OH ” in the original. 264 Proceedings of the Royal Society of Edinburgh. [Sess. Many others might be added. For instance, tartaric acid : — C "0 " OH "I ....0o c H O OH > C 0 -OH " "H* And the bibasic acid produced from it by the action of heat will be perhaps C'O- OH : O2 c; c: • H :::o2 • H tartrelic acid. C ••• o2 -o - Oil OH It is my intention to consider, in a future communication, the second type, and to apply my views to the cyanogen combinates, etc. * A horizontal dotted line is erroneously printed here in the original. 1908-9.] Life and Chemical Work of Archibald S. Couper. 265 On pourrait ajouter beaucoup d’autres corps, par exemple Facide tartrique : ' 0— OH ^ 02 0 fH c J { 0 — OH OH C 0 0 H O2 0— OH V. J et Facide bibasique derive de 1’acide tartrique par Faction de la chaleur sera peut-etre 0— OH^ O2 H C- Dans un autre Memoire je me propose de m’occuper du second type. En attendant, j’ajouterai seulement la maniere dont je considere la constitution des principaux composes cyaniques. Des raisons entierement semblables a celles qui me font admettre 4 pour limite du pouvoir de combinaison du carbone, me conduisent a assigner 5 comme limite de combinaison a Fazote. Le premier degrE de combinaison de cet element se rencontre dans l’ammoniaque et equivaut A3. Le second, qui est egal a 5, se trouve, entre autres composes chimiques, dans le chlorure et dans l’oxyde d’ammonium ainsi que dans l’acide azotique. II rEsulte de la que le carbone et Fazote combines, de maniere a atteindre tous deux les limites de leur pouvoir de combinaison, formeront un corps dont l’affinite fibre s’exercera en fixant un Equivalent d’hydrogene ou d’un autre element. Ainsi la formule de l’acide cyanhydrique sera H | Az. Cj L’acide cyanique sera HO— 0 Facide cyanurique 1 cf Az ; HO— 0— Az— C— AzO— OH C' c Az i f 0 — OH Dans cette derniere formule, les atonies de carbone et d’azote sont lies par 2 unites d’affinite et non par 4, comme dans les deux premiers exemples. 266 Proceedings of the Royal Society of Edinburgh. [Sess. APPENDIX IV a. Recherches sur l’acide salicylique ; PAR M. Couper.* Les recherch.es que j’ai honneur de soummettre a l’Academie ont pour objet 1’action du perclilorure de phosphore sur le salicylate de methyle. Je les ai entre- prises dans le but de jeter quelque lumiere sur une question controversee : la constitution et la basicite de 1’acide salicylique. Une violente reaction se manifeste au contact de l’huile de gaultheria et du perclilorure de phosphore. 11 est necessaire, pour la maitriser, d’aj outer par petites portions l’huile essentielle au perclilorure dans le rapport de 1 equivalent du premier corps a 2 equivalents du second. De l’acide chlorhydrique et du chlorure de methyle se degagent pendant tout le cours de l’operation. Le produit obtenu est sounds a la distillation fractionnee. Une trace seulement de chloroxyde passe d’abord, un exces assez considerable de perclilorure de phosphore distille ensuite, et lorsque la temperature a atteint 160 degres, le residu constitue un liquide noir. Si l’on continue la distillation, la temperature s’eleve rapidement a 285 degres. La plus grande portion du produit passe entre 285 et 295 degres, sous la forme d’un liquide incolore ou legerement colore en jaune. On le recueille separement. 11 reste une masse noire qui se solidifie par le refroidissement. Le liquide recueilli vers 290 degres a donne a l’analyse les resultats suivants : Experiences. Theorie. Carbone 30,86 29,4 29,9 30,65 Hydrogene . l,58t 1,59 1,51 1,46 Chlore 41,01 41,05 38,86 Phosphore 12,2 ... ... 11,5 * Comptes rendus, xlvi., 1107-1110, seance du lundi, 7 juin 1858. t Misprinted in original “ 1,38 ” for “ 1,58 ”. Compare the English text. 1908-9.] Life and Chemical Work of Archibald S. Couper. 267 APPENDIX IV b. Researches on Salicylic Acid. By Archibald S. Couper.* Conflicting opinions being entertained among chemists respecting the constitution and basicity of salicylic acid, in order, if possible, to throw some additional light upon this question, I have been induced to undertake the investigation of the action of two equivalents of pentachloride of phosphorus upon the salicylate of methyl. When these two bodies are brought into contact, the reaction which ensues is exceedingly violent, and it is necessary to add very gradually the one equivalent of oil of gaultheria to the two equivalents of perchloride of phosphorus. Vapour of hydrochloric acid, mingled with that of the chloride of methyl, is disengaged during the whole course of the operation. The residue of this reaction is submitted to distillation. A trace of oxychloride passes over, and is followed by something approaching to an equivalent of the perchloride of phosphorus. The temperature having now risen to about 160°, the residue has darkened in colour. Submitted to a further distillation, a colourless or slightly yellow liquid passes over, while the temperature rises rapidly to about 285° and 295° Cent. The portion passing between these temperatures is collected apart. It constitutes the larger part of the product of distillation. There remains a pitchy residue, which solidifies on cooling. The liquid collected, as described, on being submitted to analysis, furnished the following results : — 1. 0*41 grms. of substance gave 0*464 grms. of carbonic acid, and 0*0585 grms. of water. 2. 049 grms. of substance gave 0*528 grms. of carbonic acid, and 0*0705 grms. of water. 3. 0*515 grms. of substance gave 0*565 grms. carbonic acid, and 0*071 grms. of water. 1. 0*438 grms. of substance gave 0*7595 grms. of chloride of silver. 2. 0*34 grms. of substance gave 0*563 grms. of chloride of silver. 1. 0*651 grms. of substance gave 0*283 grms. of the pyrophosphate of magnesia. These analyses lead to the crude formula, — C7H4C13P06. Found. Calculated. I. II. III. Carbon . 30*86 29*4 29*9 30*65 Hydrogen 1*58 1*59 1*51 1*46 Chlorine 41*01 41*05 38*86 Phosphorus . 12*2 11*5 Edinburgh New Philosophical Journal . New series, vol. viii., July to October 1858, 213-217. 268 Proceedings of the Royal Society of Edinburgh. [Sess. La composition de ce corps est representee par la formule C14H4Cl3Ph06. II se forme, en vertu de la reaction suivante : C16H806 + PhCl5 = HC1 + C2H3C1 + C14H4Cl3Ph06 Essence de gaulth^ria. Chlorure Trichloropliosphate de m^thyle. de salicyle. Je me suis assure que le trichloropliosphate de salicyle prend aussi naissance par Faction du perchlorure de phosphore sur l’acide salicylique C14H606 + PhCl5 - 2HC1 + C14H4Cl8Ph06. < r * v ^ Acide salicylique. Trichloropliosphate de salicyle. Entre ces deux corps solides, la reaction est moins violente qu’avec Fessence. 11 se degage de Facide chlorhydrique, et lorsque Faction est terminee, le residu est le meme que celui qu’on obtient avec Fhuile de gaultheria. Les deux produits distillent exactement de la meme maniere et a la meme temperature, et les liquides obtenus possedent la meme composition et les memes proprietes. Le trichloropliosphate de salicyle obtenu par Fun ou l’autre de ces precedes se decompose bientot au contact de Feau froide et immediatement lorsqu’on le chauffe avec ce liquide. Les produits de cette reaction sont Facide chlorhydrique, Facide phosphorique et Facide salicylique. C14H4Cl3PhO(i + 8HO = PliH308 + 3HC1 + C14H606, Trichlorophosphate Ac. phosphorique. Ac. salicylique. de salicyle. 1908-9.] Life and Chemical Work of Archibald S. Couper. 269 According to the rational theory which I seek to develop in another paper,* * * § the constitution of this body may he represented as : — ( C- H2 (C • H ( C II C I ( C O Oh i (O2 Ip-’-ci3 c ' I j 0""0j It is a tertiary derivative ; the secondary deri- vative, salicylic acid, being ( C H2 C ( C H ( C H C • ! C O OH c ( O2 1 0 OH The reaction, of which this body is the result, is represented by the following equation f : — C7H606 + PCI5 - 2HC1 = C7H4C13P06. This is the same body which, unpurified, Gerhardt calls the chloride of salicyl, 1 and Chiozza the chloride of chlorobenzoil,§ or the hydrochlorate of monochloro- benzoic acid. In order to determine rigorously whether the body produced by Chiozza from salicylic acid was really the same as that which Gerhardt and I have obtained from the oil of gaultheria, I investigated the action of the perchloride of phosphorus upon the pure acid. The reaction which takes place between the two solid bodies is less violent than when the oil was employed. Nevertheless, in this instance also the action is prompt. After the vapour of hydrochloric acid has passed off, the residue in the flask is identical with that which remains when the oil of gaultheria is employed. These two products distil in identically the same manner, with the same physical appearances, while the products of distillation produce exactly the same results upon analysis. These products display also entirely the same results in all their reactions. The terchlorophosphate of salicyl obtained by either process is very soon decom- posed by water in the cold, and immediately, upon the application of heat, the products being hydrochloric, phosphoric, and salicylic acids. Chiozza’s monochlorobenzoic acid, which he believes to be produced along with hydrochloric acid in the decomposition of this body, is only salicylic acid || rendered impure by hydrochloric and phosphoric acids. Chiozza did not succeed in producing the reaction for salicylic acid by the perchloride of iron. Nor is it to be observed till the liquid containing the phos- * Phil. Mag., August 1858. t Couper gives here the equation representing the action of PC15 on salicylic acid (of which he speaks a few lines further on) instead of that for the action on gaultheria oil. X Comptes rendus, xxxviii. 34. § Annates cle chim. et de phys. [3], xxxvi. 102. || Couper is mistaken in this. Chiozza certainly had in his hands cldorobenzoyl chloride and chlorobenzoic acid. 270 Proceedings of the Royal Society of Edinburgh. [Sess. Je me suis assure, par Fanalyse, qu’il se forme veritablement dans cette reaction, de Facide salicylique et pas de Facide monochlorobenzo'ique. Lorsque le trichloro- phosphate de salicyle est rapidement distill e, il se decompose en partie en emettant d’abondantes vapeurs d’acide chlorhydrique. Au-dessus de 300 degres il passe un corps liquide, qui, lorsqu’on le conserve pendant quelques jours dans un tube ferine, depose de volumineux cristaux qui renferment : Tlieorie. Carbone . 40,2 39,16 38,44 Hydrogene 2,3 1,96 1,83 Chlore . 17,07 ... 16,25 Cette analyse, le mode de formation de ces cristaux et surtout leur dedouble ment par Feau que je vais indiquer plus loin me portent a leur attribuer la composi tion representee par la formule suivante : C14H408ClPli. Comme cette substance, que je nomme monochlorophosphate de salicyle, se decompose a Fair dont il attire l’humidite et qu’elle est formee d’ailleurs par un liquide bouillant a une temperature tres-elevee, je ne me suis pas arrete a la pensee de l’obtenir sous une forme plus pure, et j’ai du me contenter de Fanalyse precedente. 1908-9.] Life and Chemical Work of Archibald S. Couper. 271 phoric acid is separated from the crystals of salicylic acid, but as soon as this is done, the application of the test gives the intense and characteristic colour produced by the acid in question. An analysis which I have made confirms this result. 0*301 grms. of these crystals, expressed between folds of bibulous paper, re-crystallised from water, and dried, upon combustion, gave 0*668 grms. of carbonic acid, and 0*116 grms. of water. Found. Calculated. Carbon 60*52 60*86 Hydrogen 4*27 4*34 In another analysis 0*2205 grms. of substance gave 0*4885 grms. of carbonic acid, and 0*0875 grms. of water, which, calculated, gives — 60*42 % for carbon, and 4*4 % for hydrogen. This acid agrees also in all its physical aspects with the salicylic acid. It is evident, then, that those three bodies, — namely, the chloride of salicyl of Gerhardt, the chloride of chlorobenzoil, and the chlorobenzoilic acid of Chiozza, are not yet known. When the terchlorophosphate of salicyl is quickly distilled, hydrochloric acid is given off in considerable quantity, while the body, at the same time, acquires a dark colour. The last portion of the product of this distillation, which passes at a temperature above 300° Cent., being allowed to stand for a day or two in a closed tube, deposits large crystals, which, having been pressed between folds of bibulous paper, and submitted to analysis, gave the following results : — 1°. 0*3565 grms. of substance gave 0-5255 carbonic acid, and 0*074 grms. water. 2°. 0*57 grms. of substance gave 0*826 grms. carbonic acid, and 0*101 grms. of water. 1°. 0*255 grms. of substance gave 0*176 grms. of chloride of silver. Compared with the crude formula C7H408C1P, these results will be : — Carbon . Hydrogen Chlorine Found. I. II. 40*2 39*16 2*3 1*96 17-07 The rational formula is — C c c • H2 c H c- H c ■ *0 • O' C o2 ( O2 -P ■ J \ c< lo- •0. I Cl Calculated. 38-44 1*83 16*25 The monochlorophosphate of salicyl being a body which is quickly decomposed by exposure to the air, and only to be obtained from a liquid passing at an exceed- ingly high temperature, I did not think it easily possible to obtain a purer body, and have contented myself with the above analysis. Although these analyses might in themselves leave some doubt as to the composition of the body, still, when taken in 272 Proceedings of the Poyal Society of Edinburgh. [Sess. L’aetion lente que Phumidite exerce sur les produits a la fois clilores et phos- phores que je viens de decrire confirme la composition que je leur attribue. Lorsqu’on les expose a Pair, ils en attirent peu a peu la vapeur d’eau ; le chlore qu’ils renferment se combine a l’hydrogene, et est remplace par de l’oxygene. II se forme ainsi un acide nouveau, que je nomme acuie phosphosalicylique , et dont la composi- tion est exprimee par la formule C14H7Ph012. Ce produit, qui est solide, a donne a Panalyse les resultats suivants : Experiences. Theorie. Carbone .... 38,05 38,53 Hydrogene . . . . 3,39 3,21 Phosphore . . . . 14,48 14,22 II prend naissance en vertu des reactions suivantes : C14H4Cl3Ph06 + 6HO = 3HC1 + C14H7PH012 V v , Trichlorophosphate Ac. phosphosalicylic. de salicyle. C14H4ClPh08 + 4HO = C1H + C14H7Ph012. V ^ Monochlorophosphate de salicyle. L’ acide phosphosalicylique est un acide tribasique. On peut l’envisager comme une combinaison conjugee d’ acide phosphorique et cPacide salicylique PhH308 + C14H606 - C14H7Pli012 + 2HO. Les experiences que je viens de decrire sommairement ne s’accordent pas en tons points avec les observations qui ont ete publiees sur le meme sujet par MM. Gerhardt,* Chiozza,f et Drion.J Elies semblent en particulier jeter quelques doutes sur l’existence du chlorure de salicyle de M. Gerhardt, produit qui n’a jamais ete analyse. Nous ferons remarquer d’ailleurs que la formation de ce produit par Paction du perchlorure de phosphore sur P acide salicylique ou sur l’huile de gaultheria devrait etre accompagnee de celle du chloroxyde de phosphore. Or, dans les reactions dont il s’agit il ne se forme que des traces de cette substance, comme l’indiquent d’ailleurs les auteurs que nous venons de citer. Les divergences que nous signalons tiennent-elles a quelque circonstance fortuite ou a des conditions particulieres dans lesquelles se sont places les observateurs, c’est ce que de nouvelles experiences devront decider. * Comptes rendus} t. xxxviii. p. 34. f Annales de Chimie et de Physique (3e serie), t. xxxvi. p. 102. X Comptes renduSy t. xxxix 1908-9.] Life and Chemical Work of Archibald S. Couper. 273 connection with a combinate which I am about to describe, and which is produced from the monochlorophosphate of salicyl, as well as from the terchlorophosphate, I think I may be warranted in ascribing definitely to it the above formula. This compound is produced by the exposure to the atmosphere of the bodies just mentioned. The chlorine contained in them decomposes the water of the atmosphere combining with an equivalent of hydrogen, while the oxygen is taken up by the bodies in question in replacement of the chlorine. This new oxygen, however, enters into the state in which it is found in acids, and has a great affinity for the oxygen of water and bases. It therefore attracts the water of the atmosphere, and the combinate becomes an hydrated acid. This body being submitted to analysis, gave results according with the rational formula — ( C""H2 cl C”H C— H Q2 ■■ o o o Hd o o : { O2 0 OH C- | ( 0 -OH J C7HT012P * 1°. 0-2845 grms. of substance gave 0397 grms. of carbonic acid, and 0086 grnis. of water. 0T785 grms. of substance gave 0 103 grms, of the pyrophosphate of magnesia. Carbon . Hydrogen Phosphorus . Found . Calculated 38-05 38-53 3-39 3-21 14-48 14-22 This phosphosalicyclic acid is a tribasic acid, and forms insoluble salts with baryta, lead, and silver, containing three equivalents of these metals. I propose taking into consideration more fully the constitution of salicylic acid in a subsequent communication. The formula here given of that body may be in the meanwhile suggestive. * Couper has here for phosphorus the symbol “Ph” as throughout the French paper. Elsewhere in English he uses “ P”. (. Issued separately April 30, 1909.) VOL. XXIX. 18 274 Proceedings of the Royal Society of Edinburgh. [Sess. XIV. — On the Magnetic Properties of certain Copper Alloys. By Alexander D. Ross, M.A., B.Sc., Assistant to the Professor of Natural Philosophy in the University of Glasgow, and Robert 0. Gray, Thomson Experimental Scholar in the University of Glasgow. (MS. received February 5, 1909. Read February 15, 1909.) In May 1907 a paper was read before this Society by one of us on the magnetic properties of the Heusler alloy.* After that date the investiga- tion was extended to two other copper-manganese-aluminium alloys, and latterly the scope of the research has been further extended by a series of tests carried out by the present authors conjointly on simple aluminium and manganese bronzes, and on the constituent metallic elements in the pure form, while additional tests have been made on the manganese-aluminium bronze. Some of the more interesting results obtained since the 1907 paper are given in the present communication. Specimens. — The specimens referred to in this paper were cast by Gray and Caldwell, Paisley, and Steven and Struthers, Glasgow, and had the following compositions : — (1) Casting B. — 62 per cent, copper, 25 per cent, manganese, 125 per cent, aluminium, and a trace of lead. (2) Casting D. — 76 per cent, copper, 16 per cent, manganese, and 8 per cent, aluminium. (3) Casting E. — 55 per cent, copper, 30 per cent, manganese, and 15 per cent, aluminium. (4) 5 per cent, aluminium-bronze (that is, 5 per cent, aluminium, 95 per cent copper). (5) 10 per cent, aluminium-bronze. (6) 60 per cent, aluminium-bronze. (7) 70 per cent, aluminium-bronze. (8) 30 per cent, manganese-bronze. (9) Pure aluminium. (10) Pure manganese. It will be observed that B is the ordinary Heusler alloy, and that in D and E the same relative proportions (viz., those of the atomic weights) of manganese and aluminium have been maintained, while the amount of * A. D. Ross, “ Heusler’s Magnetic Alloy,” Proc. Roy. Soc. Edin., xxvii. part 2, p. 88. 1908-9.] Magnetic Properties of certain Copper Alloys. 275 copper has been varied. This scheme was adopted because the effect of variation of the ratio of manganese to aluminium had already been investigated by Heusler, Starck, and Haupt,* and also because certain considerations seemed to indicate that copper played a not unimportant part in the magnetism of the Heusler alloy. f The specimens from castings B, D, and E were of uniform size, viz., cylinders of length 20 cm. and diameter about 1 cm. They were tested in the condition as cast, except that the ends were cut off square. No further dressing was given as that process would probably have altered the magnetic properties slightly owing to the heat evolved in the operation. The materials included under (4)-(10) in the above list were too feebly magnetic to lend themselves to testing in the usual magnetometric method. The specimens were accordingly cast in the form of small cylinders 8 cm. in length and 6 mm. in diameter, and were magnetised by means of a powerful electromagnet. Apparatus. — For testing the castings B, I), and E the Gray- Boss magnetometer j was used. Alloys D and E exhibited only feeble magnetic properties, and the obtaining of a hysteresis cycle with the material in the quenched condition was a matter of very considerable difficulty. Such tests had to be carried out in the early morning hours, when the slight disturbance of the magnetometer zero due to electric earth-currents was at a minimum. The magnetisation of the specimens included under (4)-(I0) in the above list was carried out with the large electromagnet belonging to the Physical Laboratory of Glasgow University. The magnet is of cast steel with a permeability almost coincident with that of wrought-iron. It is rectangular in shape, measuring about 100 cm. in length and 40 cm. in height. In addition to the coils on the poles, the whole length of the yoke is wound. During the experiments the pole-pieces were kept 11 cm. apart in order to freely admit the specimens when enclosed in vessels for holding liquid air. With this separation a field of 4400 C.G.S. units was obtained on exciting the magnet with the current from a 110- volt storage battery. The permanent magnetism so induced in the specimens was measured by a delicate magnet- ometer, the motion of whose needle and mirror was observed by means of a scale placed more than two metres distant. Quenching and Liquid Air Tests. — In the previous paper an account has * “ Magnetisch-cliemische Stnclien,” Per. cl. Deutsch. Pliys. Gesell., 1903, S. 220. t See article by J. G. Gray and A. D. Ross, Pliys. Zeit ., x., No. 2, S. 59. J. G. Gray and A. D. Ross, “ On an Improved Form of Magnetometer, etc.,” Pror. Roy. Soc. Edin., 1908-9. 276 Proceedings of the Poyal Society of Edinburgh. [Sess. been given of the effects of liquid air on alloy B both in the cast and in the quenched condition. Similar tests were now made with alloy D. As it had been found that quenching of such bronzes at temperatures exceeding 600 C. produced cracking of the material, the quenching was carried out at Fig. l. 450° C. Fig. 1 exhibits the results obtained. While the most important point here is the percentage changes produced by the varying treatment, the absolute values of the intensity of magnetisation (I) and the strength of the magnetising field (H) are also given for facilitating comparison with other materials. In calculating H, allowance has been made for the end effect of the magnetising solenoid, and Du Bois’s factors * are employed in * Du Bois, Magnetische Kreise in Theorie und Praxis , Berlin, 1894. 277 1908-9.] Magnetic Properties of certain Copper Alloys. deriving the true field from that due to the current in the helix. The values of I are obtained on the assumption that the polar distance of the cylindrical specimens is their total length — an assumption which has been justified by comparison of such specimens with others turned down into ellipsoids of revolution. The curve A A shows the magnetic condition of the alloy in its original state. On re-testing with the specimen at the temperature of — 190° C. the dotted line curve A A' was obtained. The effect of cooling to liquid air temperature has been to increase the permeability O 80 jq 120 Fig. 2. and raise the saturation-point. The coercive force has been augmented but to a very slight degree, while the residual magnetism has increased about 30 per cent. After being quenched at 450° C. the specimen was almost non-magnetic as indicated by QQ. On cooling, however, to — 190° C. there was a marked increase in permeability and hysteresis as shown by the curve Q'Q'. Another specimen which had been very rapidly cooled in the process of casting gave P and P' respectively for the highest points on the 15° C. and the — 190° C. magnetisation cycles. It exhibits a large liquid air effect, and therein resembles the quenched material. Fig. 2 shows similar tests on alloy E — an alloy much poorer in copper. A is the magnetisation curve for the initial condition ; and A' the curve obtained when the specimen has been cooled down to — 190° C. The ascend- ing and descending limbs of the hysteresis cycle have been omitted, as the 278 Proceedings of the Boyal Society of Edinburgh. [Sess. cycle does not differ much from that obtained at room temperature. Q and Q' are the magnetisation curves obtained at 15° C. and — 190° C. respectively. The hysteresis is now almost inappreciable, and it will be observed that the liquid air effect has been reversed in direction. A chilled casting tested without further thermal treatment gave the curves P and P', which closely resemble those for the quenched material. Effect of Baking the Alloys. — The effect of baking the alloys D and E at various temperatures was now investigated, it being thought possible that such treatment would result in an improvement of the magnetic quality. Various temperatures up to 500° C. were employed, but all resulted in a lowering of the magnetisation curve. Fig. 3 exhibits the nature of the results obtained. In the upper diagram is shown the effect of maintaining alloy D at a temperature of 260° C. The ordinates of the graph are the intensities of magnetisation for the fields mentioned, while the abscissae give the duration of the baking in hours. The continuous lines show the changes in the intensity of magnetisation for fields of 125 and 30 C.G.S. units respectively, the tests being made with the specimens cooled down to room temperature after the baking process. The dotted curves are obtained with the specimen cooled to —190° C. after the baking. The result of this thermal treatment has therefore been (i) to lower the saturation intensity continuously towards a limiting value, (ii) to cause at first a slight increase in the susceptibility for low fields, (iii) to reduce the susceptibility for all fields towards a definite limiting value, (iv) to reverse the liquid air effect in specimens baked for more than 8 hours. The hysteresis was also found to increase with time towards a maximum value. The lower part of fig. 3 similarly exhibits the effect of baking alloy E at 210° C. The results are shown only for H = 125, as they are of the same nature for all fields. The alloy undergoes a steady and rapid deterioration in quality, and after 10 hours’ baking has almost acquired an equilibrium condition. The liquid air effect in this alloy is reversed after 2 hours’ baking at 210° C., but it will be noticed that its direction was originally opposite to that in alloy D. The effect of baking alloy B has also been investigated by the authors. It has been found that the best magnetic condition of the alloy is obtained by exposing the material for a period of 6 to 8 hours at a temperature of 170° C. This results in an increase of over 10 per cent, in the saturation value of I,* while the short duration of the baking process does not produce any marked increase in the hysteresis loss in taking the material through * Baking, however, always reduces the values of I corresponding to small fields. 1908-9.] Magnetic Properties of certain Copper Alloys. 279 a magnetic cycle. Prolonged heating at the same temperature slightly reduces the susceptibility, and greatly augments the coercive force and“the hysteresis loss. I 20 10 % . V N \ \ V" V H=125 S. ' * — — H=30 V _J O 10 20 30 hrs. I 9 6 3 O 10 20 3( 3 hrs. Fig. 3. Fig. 4 shows the results of exposing the alloy B to steadily increasing temperatures. In each case the alloy was placed in a furnace at the required temperature, kept there for 3 hours, and then the furnace was shut off* and the alloy allowed to cool in position and tested cold. The tests were made for a series of temperatures from 50° to 480° C., each 280 Proceedings of the Royal Society of Edinburgh. [Sess. temperature employed exceeding the previous one by about 30°. The ordinates in the diagram are the intensities of magnetisation, while the abscissae are the temperatures of baking. The continuous lines are ob- tained by testing the baked specimen at room temperature in fields of 8, 16, and 110 C.G.S. units respectively. The dotted lines give the results of Fig. 4. similar tests made with the baked alloy cooled to — 190° C. The curves show the improvement of the material for high fields with baking at temperatures in the neighbourhood of 170° C. They also exhibit a marked deterioration in the magnetic quality after baking of the specimen about 250° C., and a subsequent recovery prior to the rapid deterioration after 330° C. This dip in the curves is very remarkable, and points to some extensive change in constitution of the material. It is noteworthy, too, 281 1908-9.] Magnetic Properties of certain Copper Alloys. that the growth of hysteresis is specially rapid in the case of specimens exposed to temperatures between 200° and 250° C., and the maximum limit attained is greater than in specimens which have been subjected to prolonged heating at about 320° C. Indeed, a specimen which has been baked for some time at say 250° C., and thus gives a hysteresis cycle of large area, can have its hysteresis loss much reduced by a subsequent short heating at, say, 330° C. The variation in the liquid air effect shown in fig. 4 is also interesting. With the material in the condition as cast, cooling to — 190° C. improves the quality for all fields. In the case of' specimens which have been baked at temperatures in the neighbourhood of 250° C. the effect is reversed in sign for fields below 30 C.G.S. units, and it is much reduced in magnitude for high fields. The quality of specimens baked at 330° C. is much the same as in the unbaked condition, both as regards tests at room temperature and at that of liquid air. In specimens exposed to still higher temperatures the susceptibility once more falls off, and this is again accompanied by a lessening and final reversal of the liquid air effect. Critical Temperatures. — In a paper * read before this Society by Mr J. G. Gray, of Glasgow University, results are given for the change in susceptibility produced by heating and cooling an alloy of similar composi- tion to B while a constant applied field is maintained. An interesting- contrast is also made with the results obtained by Hopkinson j* for nickel - steels. Similar tests have been carried out with alloys D and E, and the results are set forth in fig. 5. The ordinates are the intensities of magnetisa- tion, while the abscissa are the temperatures of the electric furnace within the magnetising solenoid as registered by a platinum, platinum-iridium pyrometer. The continuous lines indicate the values of I corresponding to an applied field of 125 units, and the dotted lines those for 11 = 30, while the arrow-heads distinguish the heating from the cooling curves. It will be observed that in the case of alloy D (shown in the upper diagram) the susceptibility falls off continuously with increasing temperature, as in the results given by Gray for alloy B. The critical temperature is, however, much lower, being approximately 280° C. instead of 500° C., and the deteriora- tion of the specimen due to the temperature cycle is more marked. In the case of alloy E there is a pronounced increase in susceptibility with increas- ing temperature to nearly 200° C., and then a rapid falling off as the critical temperature (345° C.) is approached. A similar maximum of susceptibility * “Experiments with Heusler’s Magnetic Alloy,” Proc. Roy. Soc. Edin., vol. xxviii., part 5, p. 403. t Proc. Roy. Soc., December 12, 1889 ; January 23, 1890 ; May 1, 1890. 282 Proceedings of the Royal Society of Edinburgh. [Sess. is attained during the process of cooling; but the resultant effect of the complete temperature cycle is to produce a great deterioration in the magnetic quality of the material. Fig. 5. A series of such successive heatings and coolings carried out with each of the alloys D and E resulted in a gradual, but lessening, deterioration in quality. It was not found possible to restore the quality to such a marked degree as effected by Mr B. Y. Hill in the case of an alloy having 283 1 908—9. ] Magnetic Properties of certain Copper Alloys. the composition copper 60 per cent., manganese 25 per cent., aluminium 15 per cent.* Simple Bronzes, Manganese, and Aluminium. — With a view to throw- ing some light on the magnetic properties of the Heusler alloy, tests were carried out on the alloys (4)-(8) already mentioned, and on pure manganese and aluminium. These materials were magnetised with a field of 4400 C.G.S. units, and their permanent magnetism was subsequently measured. Tests were also made with the specimens surrounded with liquid air and thus cooled to —190° C., and the whole procedure was thereafter repeated with the material quenched at 500°-600° C. In the accompanying table the results are given and compared. The results obtained with similar specimens were Intensity of Magnetisation. Percentage Composition of Cast Material. Quenched Material. No. Material. Magnetised at Magnetised at Cu. Mn. Al. Ox 0 O - 190° C. h- » Cn o p - 190° C. 4 95 5 ■010 091 029 •no 5 90 10 •184 •228 •145 175 6 40 60 2 2 2 2 7 30 70 2 2 •021 •027 8 70 30 •057 •072 •096 •118 9 ... 100 2 2 2 2 10 ... 100 4-76 4-68 3 74 3-70 1 indicates that the value of I is less than 0‘Q1. in excellent agreement, and hence the percentage changes occurring between the separate tests on any specimen are thoroughly reliable. At the same time, owing to the uncertainty as to the exact dimensions of the specimens, their polar separation, and their distance from the magnetometer needle, the absolute values tabulated for I are only approximate. They are given as indicating the order of the intensity of magnetisation, and as affording a convenient method of comparing the properties of the different materials. In the “ Eighth Report of the Alloys Research Committee ” are given the equilibrium curves of the copper-aluminium alloys.-]- It will there be found that (a) the 5 per cent, aluminium-bronze is a solid solution of aluminium in copper, ( b ) the 10 per cent, aluminium-bronze is a mixture of Cu4Al and * Physical Review , vol. xxi. p. 335. t Proc. Inst. Mech. Eng., 1907, p. 204. 284 Proceedings of the Royal Society of Edinburgh. [Sess. Cu3A1, (c) the 60 per cent, bronze consists of CuA12 and a eutectic alloy, (d) the 70 per cent, bronze is chiefly eutectic with the addition of a solid solution of copper in aluminium. Accordingly, the two aluminium alloys which show a specially marked improvement in magnetic quality when cooled to liquid air temperature are the two bronzes which contain free copper. The same two (viz., the 5 per cent, and 70 per cent, bronzes) also show an increased retentivity in the quenched state. This again agrees with the results obtained for metallic copper.* The 10 per cent, aluminium- bronze does not contain free copper, and does not improve on quenching. It shows, however, an increased retentivity at liquid air temperature. Accord- ingly, one or both of the compounds Cu4A1 + and Cu3A1 is magnetic. The 60 per cent, aluminium-bronze, which consists of CuA19 and eutectic, is practically non-magnetic. Turning now to the 30 per cent, manganese-bronze, we have another alloy containing free copper. It exhibits the same peculiar properties as the two aluminium-bronzes which had free copper, in so far as its retentivity is greater at liquid air temperature than at 15° C., and is greater in the quenched than in the cast condition. The manganese which is a constituent of this bronze is, comparatively speaking, strongly magnetic,! but it will be seen that the effects of liquid air and quenching are the reverse of those found in the manganese-bronze. In a paper shortly to be laid before this Society by Mr J. G. Gray and one of us, it will be shown that manganese -steel does not give an increased residual magnetism after quenching, as does manganese-bronze, and further that when in the normal condition its quality degenerates slightly when the material is cooled to —190° C. Manganese-steel is therefore somewhat similar to pure manganese in its magnetic properties, and gives effects altogether unlike those found in the purest copper. Accordingly, as manganese-bronze resembles copper in its magnetic properties and is essentially different from manganese and manganese-steel, it seems natural * J. G. Gray and A. D. Ross, “ fiber die Herstellung permanenter Magnete aus Proben nahezu remen Kupfers,” Phys. ZeiL, x., No. 2, S. 59. t The existence of tlie compound Cu4A1 mentioned by Carpenter and Edwards in the report, loc. cit ., has been questioned by other experimenters. See in this connection the investigations of Gulliver, Proc. Inst. Mech. Png., 1907, p. 345 ; Curry, Journ. Phys. Chem ., 1907, p. 425 ; Gwyer, Zeit. Anorg. Chem. , 57, S. 125, 1908 ; Guillet, Revue de metallurgie , 5, p. 413. The occurrence of Cu3A1 is generally accepted, and the existence or non-existence of a compound Cu4A1 does not materially affect the present discussion. | The manganese used in this test was a specially purified sample supplied by E. de Haen of Seelze. That its magnetism was not due to iron impurity was shown by chemical analysis. The amount of iron present was probably less than one part in 10,000, and certainly did not exceed one part in 5000. Taking the upper limit, it follows that the iron present was less than Aq of that which would be required to account for the residual magnetism. 285 1908-9.] Magnetic Properties of certain Copper Alloys. that its magnetism may be due in great measure to the free copper contained, and not to a manganese-copper constituent. Lastly, the tests given in the table indicate that pure aluminium (such as had been used in making the aluminium-bronzes and the Heusler alloys) is not susceptible of retaining any measurable trace of permanent magnetism. The result of the tests on the materials (4)-(10) is therefore to show that specimens containing free copper undergo a marked improvement in magnetic quality on cooling from 15° C. to — 190° C., and that quenching is likewise accompanied by an increase of residual magnetism — except, of course, in so far as these effects may be masked to a greater or less extent by those due to the presence of other magnetic materials. The Magnetism of the Heusler Alloy. — These results have an important bearing on the magnetism of the Heusler alloy. A characteristic feature of these bronzes is that their retentivity at the temperature of liquid air is greater than at room temperature. This holds even in the case of baked specimens of alloy B or D, where the cooling diminishes the saturation value of I. Such an effect is of the same kind as that given by free copper. It is also similar to that found in the 10 per cent, aluminium-bronze, but its great magnitude in such cases as the quenched castings D is more suggestive of the free copper than of the copper-aluminium compounds. Hitherto the magnetism of the Heusler alloy has been often ascribed to the manganese alone, whose transformation temperature it has been conjectured — though neither proof nor evidence can be adduced in support — is lowered by its solution in the other constituents. The one point always referred to in this connection is the list of several elements arranged by S. Meyer * in descend- ing order of atomic susceptibility (that quantity being defined as the mean susceptibility of a space containing one gram atom of the substance per litre). The series is as follows : — Ho, Er, Gd, Mn, Fe, Sa, Co, Yt, Nd, Ni, Pr. This list is of course based to a very large extent on the magnetic properties exhibited by salts of the elements. Manganese therefore comes before iron. For although in general the magnetism of pure iron is incom- parably greater than that of manganese, yet the susceptibility of many manganous salts exceeds that of the corresponding ferrous and ferric compounds, j* The experiments described in the present paper have, how- ever, a more immediate bearing on the subject. The authors do not claim that the investigations afford an explanation of the magnetic phenomena of the Heusler alloy, but they consider that the magnetic properties of the alloy show a suggestive similarity to those of Cu3A1, and that the presence * Ann. d. Phys., 1889, lxix., S. 236. t Per. d. Dentsch. Chem. Gesell 1900, xxxiii. S. 448. 286 Proceedings of the Royal Society of Edinburgh. [Sess. of free copper in the alloy may at least play a not unimportant part in determining the magnetic behaviour of the bronze. That manganese is also an important factor is unquestionable, as its omission destroys the remarkable properties of the bronze just as the exclusion of the copper would do. It should be noticed, in support of the view here adduced, that the liquid air effect in the Heusler alloy increases in magnitude with increasing copper content, and hence probably with increasing amount of free copper. The investigations described in this paper have been carried out in the Physical Laboratory of the University of Glasgow, and the authors desire to express their thanks to Professor Gray for the facilities he gave for the carrying out of the work. Summary. 1. Manganese-aluminium bronzes exhibit less hysteresis, but are also less magnetic, after quenching. 2. Such alloys, if rich in copper, are more magnetic at — 190° C. than at 15° C. 3. Continued baking at steady temperatures reduces the susceptibility and increases the hysteresis towards definite limits. 4. These effects are not simply related to the temperature of baking. 5. The liquid air effect in baked specimens is often (especially for low fields) of opposite sign to that in the virgin alloy. 6. In Heusler alloys containing 76, 62, and 55 per cent, copper respectively, and the remainder manganese and aluminium in atomic proportions, the critical temperatures are 280°, 500°, and 345° C. 7. The quenching and liquid air effects in the Heusler alloys are very similar to those in Cu3A1 modified by effects due to the presence of free copper and free manganese. (Issued separately May 3, 1909.) 1908-9.] Low Temperature Experiments in Magnetism. 287 XV. — Low Temperature Experiments in Magnetism. By James G. Gray, B.Sc., Lecturer on Physics in the University of Glasgow, and Hugh Higgins, M.A., Thomson Experimental Scholar in the University of Glasgow. Communicated by Professor A. Gray, F.R.S. (MS. received February 15, 1908. Read same date.) The alterations brought about in the magnetic moments of magnets, composed of various metals and alloys, by alternate cooling and warming between ordinary room temperature and that of liquid air have been very fully investigated by Dewar and Fleming.* It was found by these experimenters that in the case of most of the metals examined the effect of the first cooling upon the magnet — which had previously been magnetised to saturation in the field of an electromagnet — was to bring about a very considerable reduction in its magnetic moment. On allowing the magnet to warm to room temperature its magnetic moment still further diminished. On cooling once more to the liquid air temperature the magnetic moment increased, and from and after this stage it was found that the magnetic moment of the magnet when cold exceeded that of the magnet when at room temperature by a definite amount. The changes brought about by the treatment were found to be much greater in the annealed than in the quenched condition of the material. In a few cases, notably that of the chromium steels, the effect of the first cooling was to increase the magnetic moment ; in other cases the treatment caused very little alteration in the magnetic moments of the specimens. In the experiments of Dewar and Fleming the specimens were magnetised initially at room temperature. It occurred to one of the authors of the present paper to repeat the procedure, starting with a specimen magnetised to saturation when at the temperature of liquid air. On carrying out such an experiment it was found that the changes produced by the treatment differed in many respects from, and were even more remarkable than, those observed by the aforementioned investigators. The method of experimenting was as follows : — A short bar of the metal to be examined was placed within a glass tube bent up at one end to admit liquid air. The end of the tube through which the specimen entered was closed by means of a cork, and the tube thoroughly wrapped up in cotton- * Proc . Roy. Soc., vol. 60, p. 57. 288 Proceedings of the Royal Society of Edinburgh. [Sess. wool. The tube, containing the specimen, was then placed between the conical pole-pieces of a very powerful electromagnet. On exciting this magnet the specimen was exposed to a magnetising field of 4400 C.G.S. units. The tube was next withdrawn and mounted on a special stand so that the specimen lay at a considerable distance from a magnetometer needle, and with its axis lying along the magnetic east and west line passing through the needle. By means of the magnetometer the magnetic moment of the specimen was measured under the following conditions : (1) at room temperature immediately after being magnetised, (2) after cooling the specimen to -190° C., (3) after the specimen had regained room temperature, (4) on re-cooling to —190° C., and so on. This is the procedure of Dewar and Fleming. The tube was now withdrawn and placed in position between the poles of the electromagnet and the specimen brought to the temperature of liquid air. The magnet was then excited and the tube withdrawn and placed once more in position on the magnetometer. The magnetic moment of the magnet was observed (1) at — 190° C. following on the magnetisation of the specimen, (2) after the specimen had warmed to room temperature, (3) on cooling once more to — 190° C., and so on. The results obtained differ from those observed by Dewar and Fleming in that the reversible condition described above is arrived at after the first warming up of the specimen from — 190° C. to room temperature, and the per- centage change in magnetic moment then brought about by cooling from room temperature to that of liquid air is much greater than is the case for a specimen which has been magnetised initially at room temperature. The following table gives the dimensions and chemical compositions of the specimens employed in the experiments : — Dimensions and Chemical Composition of Specimens Employed. Description of Material. Length of Speci- men in Cms. Dia- meter of Speci- men in Cms. Mass in Grins. Percentage Composition. Car- bon. Man- ganese. Sili- con. Sul- phur. Phos- phorus. Steel wire 7-7 0-27 3-36 0-755 0-660 0-066 0-017 0-027 Special hard steel . 7-2 0-96 40-0 1-321 0-339 0-143 0-023 2-745 Manganese steel 7-0 0-96 39-0 0-71 6-00 ... ii ii 7-0 0-96 39-0 0-60 12-00 1908-9.] Low Temperature Experiments in Magnetism. 289 Results for Steel Wire Specimen. Specimen as Received. — The results obtained on testing the specimen in this condition are exhibited in fig. 1. After being magnetised at room tem- perature the effect of the first cooling was to bring about a diminution in its magnetic moment of 45 per cent. On warming it to room temperature the magnetic moment still further diminished by about 11 per cent. On cooling the specimen once more the magnetic moment increased by about 9 per cent., after which stage the effect of the cooling always resulted in an increase in the magnetic moment of about this amount. In the figures the firm lines give the magnetic moments of the speci- i Steel Wire fas supplied) Fig. 1. mens at room temperatures, and the dotted lines the magnetic moments at -190° C. Starting with the specimen magnetised when at —190° C., the effect of the first warming was to bring about a diminution in the magnetic moment of about 44 per cent. After this stage had been reached, cooling to — 190° C. caused an increase in the magnetic moment of nearly 125 per cent. Specimen in Annealed Condition. — (1) Magnetised at room tempera- ture.— The effect of the first cooling was to reduce the magnetic moment by about 40 per cent. On warming to room temperature the magnetic moment further diminised by 20 per cent., after which stage the effect of cooling the specimen was to increase the moment by about 5 per cent. (2) Specimen magnetised at — 190° C. — The effect of the first warming was to diminish the magnetic moment by about 65 per cent., after which VOL. xxix. 19 290 Proceedings of tlie Royal Society of Edinburgh. [Sess. each cooling resulted in an increase in the magnetic moment of nearly 40 per cent. The results obtained for the material in the annealed condition are shown in fig. 2. I 1 ~ ■ 1 1 1 1 ____ 1 1 1 1 1 1 1 1 1 1 i i i i i i i i i i j i i i 1 1 I 1 1 1 1 1 1 1 1 1 1 r i i i i i i i i i L i i i : J ‘ i 1 ! I I l 1 1 1 1 t — — — 1 1 1 i Specimen Magnetised at 15° C. Specimen Magnetised at -190° C. Steel Wire (Annealed) Fig. 2. Specimen in Quenched Condition. — (1) Specimen magnetised at room temperature. — The effect of the first cooling was to diminish the magnetic moment by about 2*5 per cent., and on warming to room temperature a Steel Wire (Quenched) Fig. 3. further reduction of 3-5 per cent, took place. Further cooling always resulted in an increase in the magnetic moment of nearly 1 per cent. (2) Specimen magnetised at —190° C. — The effect of allowing the speci- 291 1908-9.] Low Temperature Experiments in Magnetism. men to warm to room temperature was to diminish its magnetic moment by 16 per cent. The magnet was now in a condition in which its magnetic moment at — 190° C. exceeded its magnetic moment at room temperature by about 15 per cent. The results for the steel wire in the quenched condition are exhibited in fig. 3. Results for Special Hard Steel. The results obtained on testing a specimen of this variety of steel are shown in figs. 4, 5, and 6. They resemble the results obtained for the steel Special Hard Steel (Forged) Fig. 4. wire. It will be seen that after the reversible state has been arrived at the magnitudes of the changes brought about by the cooling are much more marked in the case of the specimen when magnetised at —190° C. than when magnetised at room temperature. Results for Manganese Steel (6 per Cent. Mn). The results obtained for this steel in the annealed condition are shown in fig. 7, and are very remarkable. On magnetising the specimen at the temperature of the room its magnetic moment was found to be 250 C.G.S. units. On cooling the specimen to -190° C. its magnetic moment diminished to 93 C.G.S. units ; and on allowing it to warm to room temperature the magnetic moment fell to 59 C.G.S. units. From and 292 Proceedings of the Royal Society of Edinburgh. [Sess. after this time the effect of cooling the specimen to —190° C. was to bring about an increase in the magnetic moment of about 9 per cent. Special Hard Steel (Annealed) Fig. 5. Starting with the specimen magnetised when at the temperature of liquid air, the initial magnetic moment was 590 C.G.S. units. On warming i i i Special Hard Steel (Quenched) Fig. 6. to room temperature, the magnetic moment fell to 387 C.G.S. units ; and the effect of cooling once more to — 190° C. was to bring about an increase in the magnetic moment of about 13 per cent. The specimen was now remagnetised at room temperature, and the 293 1908-9.] Low Temperature Experiments in Magnetism. procedure repeated. It will be seen that the results obtained differ very greatly from those yielded by the freshly annealed specimen. The initial magnetic moment was now 557 C.G.S. units. On cooling the specimen to — 190° C. its magnetic moment diminished to 416 C.G.S. units. Warming to room temperature resulted in the magnetic moment still further diminish- ing to 406 C.G.S. units, and after this stage any subsequent cooling resulted in a small increase taking place in the magnetic moment. 560 520 480 440 400 360 320 280 240 200 160 120 80 40 I 1 1 t 1 1 1 1 1 1 1 1 j ! ! ' J | I i i i i ; ! 1 « i 1 i 1 1 1 I i i 1 1 1 i i i i i o 1 I . 1 1 i 1 1 I 1 i i i 1 1 1 1 1 1 i I 1 1 I 1 1 1 1 1 1 1 l i i i 1 I 1 1 1 1 1 i 1 1 1 i 1 n~ i i i i 1 1 4 - 1 i i i 1 1 1 | 1 1 — j — i i 1 1 1 I ! ! 1 i 1 ! ! I 1 1 (__ 1 1 I 1 j ) i i i I 1 1 1 1 i 1 1 i 1 1 i ! i i i i i ~T~ I 1 * i 1 1 1 1 1 1 1 1 1 i I 1 l 1 i l t l 1 I J _ ! 1 1 1 1 t 1 1 i~ 1 I 1 i ! 1 i i i i 1 l i - i 1 1 ! 1 1 i i 1 1 1 I 1 1 j— ! _L_ i 1 1 ! 1 i 1 Magnetised at Room Temperature Magnetised in Liquid Air Manganese Steel (6 Mn.) Annealed Fig. 7. Magnetised at Room Temperature after Cooling Quenching produces very little change in the properties of this steel, and for this reason the results obtained with the specimen after quenching are not included. The properties of this steel for low and moderate fields have been in- vestigated by A. D. Ross and one of the Authors. The results obtained will be communicated shortly to this Society. In the annealed condition the material is, comparatively speaking, feebly magnetic. Cooling to the temperature of liquid air results in the permeability being greatly in- creased, and on warming to room temperature a further large improvement in magnetic quality is brought about. 294 Proceedings of the Royal Society of Edinburgh. [Sess. Results for Manganese Steel (12 per Cent. Mn). On placing a specimen of this variety of steel in the field of the electro- magnet a weak magnet was obtained. No appreciable change in its magnetic moment or in the magnetic quality of the material was brought about by the cooling in liquid air. The experiments described in the present paper were carried out in the Natural Philosophy Institute of the University of Glasgow, and the authors desire to express their thanks to Professor Gray for the facilities granted them for the carrying out of the work. ( Issued separately May 11, 1909.) 1908-9.] Discharge of Water from Circular Weirs. 295 XVI. — On the Discharge of Water from Circular Weirs and Orifices. By G. H. Gulliver, B.Sc., A.M.I.Mech.E., Lecturer in Engineering in the University of Edinburgh. [(MS. received October 9, 1908. Read November 2, 1908.) Many investigators have measured the flow of water through orifices, and over weirs of various shapes and sizes. The discharge through a vertical circular orifice, situated at distances below the water surface much greater, relatively, than the diameter of the aperture, has been made the subject of study on several occasions, but the case of a circular weir, or notch — that is, a circular hole discharging across only a portion of its area — has been neglected hitherto. The author has had occasion recently to investi- gate the discharge of such a circular weir, more especially with regard to its suitability for measuring the flow of streams, a purpose for which weirs of rectangular shape are used almost exclusively at present. The problem forms an interesting example of the utility of graphical methods in cases for which solutions would be unobtainable by purely mathematical means. 1. Circular Weir, or orifice partly drowned. Fig. 1 represents an orifice of radius K. Let AB be the water surface, which is situated at a height H from the lowest point of the orifice. Let CD be ail elementary strip of vertical thickness dh, and at a mean depth h below the water surface. The area of the strip, CD, is 2CF.cZ/i. But (CF)2 4- (OF)2 = (OC)2 = R2, and OF = OK + KF = (R - H) + 7*; therefore (CF)2 = R2 - (R - H + ft)2 = 2R(H - ft) - (H - ft,)2 = (H - ft){D - (H - ft)}, where D, the diameter of the orifice, is written instead of 2R. The area of the elementary strip, CD, is 2 iS/(H-ft){D-(H -h)}.dh. The discharge of water across this area, neglecting losses due to friction and contraction of the jet, is 2 J(R - ft,){D - (H - ft,)} .dli. J2gh cubic feet per second. 296 Proceedings of the Royal Society of Edinburgh. [Sessi The total discharge of water from the oritice is 2 J2g j Jh{ H - h){ I) - (H - h)\ . dh cubic feet per second, = 12 '05 1 Jh{ H - h){ D — (H — /&)} . dh gallons per minute, if D, H, and h, in the last expression, are measured in inches ; these are the units most commonly used in practice. In fig. 1 the water surface, AB, lias been taken between the centre and the bottom of the hole, but the form of the expression for the discharge remains the same whatever the position of this surface. The integral is elliptic, and does not admit of a direct solution, but the result may be obtained by a graphical method, as follows. A definite value of H, in terms of D, is taken, and numerical solutions of the expression Jh(K-h)\D-(K-h)} are found by giving to h various values between zero and H, again in terms 297 1908-9.] Discharge of Water from Circular Weirs. of D. Thus the discharge is calculated for a number of layers between the water surface and the bottom of the orifice, each result being in the form of a product of D3/2 and a number. The values of these elementary dis- charges are then plotted as abscissae, with the corresponding values of li as ordinates, and a curve is obtained which shows the variation in the dis- charge from the bottom of the aperture to the water surface. The area under this curve, divided by the scale of the drawing, gives the value of the integral for the particular head chosen, in the form of a product of D5/2 and a number. The values of H actually taken were OTD, 0*2D, and so on by tenths of D up to TOD. To obtain the total discharge for each definite head of water, the elementary discharges were calculated for layers at depths of 005D, 0T0D, etc., from the water surface — that is, at every twentieth part of the diameter between the water surface and the bottom of the orifice. The curves obtained in this manner are shown in fig. 2. The area under each curve gives the total discharge of the weir for the corre- sponding head of water. For the original drawing the horizontal scale is : — 1 inch — 005 D3/2, and the vertical scale is: — 1 inch = OTD, so that 1 square inch represents 0005 D5/2. By multiplying each area by 0’005D5/2, and then by the constant 1205, the corresponding discharge is obtained, as given in the second column of Table I. The discharge for any size of orifice can be 298 Proceedings of the .Royal Society of Edinburgh. [Sess. calculated from these figures ; if D is measured in inches the results are in gallons per minute. The figures entered in the third column of Table I are the discharges calculated for an orifice 2^ inches in diameter. Table I. Head = H. Theoretical Discharge. Height of Layer of Maximum Discharge. Orifice of any Diameter. Gallons per minute. Orifice of 2^ inches Diameter. Gallons per minute. OTD 0'0434D5/2 0-428 •053D 0-2 0T711 1-689 •102 0-3 0-3808 3-758 •145 0-4 0-6652 6-563 •183 0-5 1-004 9-904 •217 0-6 1-398 13-79 •247 0-7 1-831 18-07 •274 0-8 2-290 22-59 •298 0-9 2-747 27-11 •319 1-0 3-169 31-27 •337 IT 3-519 34-72 •353 1-2 3-820 37-69 •366 1-3 4-109 40-55 •377 1-4 4-362 43-04 •386 1-5 4-615 45-54 •395 1*6 4-832 47-68 •403 1*7 5-061 49-94 •409 1*8 5-278 52-08 •414 T9 5-471 53-98 •418 2-0 5-675 56-00 •422 If the areas under the curves of fig. 2 are taken as abscissae, and the corresponding values of the head as ordinates, a curve is obtained which shows the total discharge of the weir for any head ; this curve is given in fig. 3. The discharge for the orifice, under a head of water equal to some fraction of the diameter of the hole, can be obtained by multiplying the abscissa of fig. 3, measured at the corresponding head, by D5i2, D being taken in inches. The curves, of course, are applicable to any circular orifice, since all circles are similar. The results obtained until now refer to what is generally known as “ theoretical discharge ” — that is, the quantity of water which would escape from the orifice if there were no friction, and no contraction of the jet. The actual discharge is considerably less than the theoretical, chiefly on account of the fact that the free jet is smaller than the area through which it has emerged. The ratio of the actual to the theoretical discharge is usually called the “ coefficient of discharge.” 299 1908-9.] Discharge of Water from Circular Weirs. Some experiments were carried out in order to find the actual quantity of water passing over a circular weir under various heads, and to ascertain the value of the coefficient of discharge. The diameter of the orifice employed was 2J inches, and the aperture had the usual sharp edges, so as to leave the jet free to contract. The head of water was measured in the ordinary way, by means of a hook gauge. The results of the experiments Table II. Head. Inches. Actual Discharge by Experiment. Gallons per minute. Theoretical Discharge from Curve. Gallons per minute. Coefficient of Discharge. 1-23 5-66 9-62 •588 1 -31 6-69 10-80 •619 1-42 7-80 12-50 •624 1-50 8-73 13-79 •633 1-56 9-23 14-66 •630 1-58 9-49 15-05 •631 1-70 10-68 17-03 •627 1-75 11-40 18-07 •631 1-83 12-15 19-40 •626 1-96 13-59 21-72 •625 2-02 14-51 22-85 •635 2*08 14-82 23-92 •620 2T0 15-02 24-32 •618 2T9 16-06 25-90 •620 2 *22 16-75 26-50 •632 2-30 17-32 27-90 •621 2-45 19-17 30-50 •629 2-52 20-21 31-50 •642 2-59 20-53 32-60 •630 2-69 21-39 34-00 •629 2-74 22-11 34-70 •637 2-85 22-72 36-10 •629 2-99 23-68 37-80 •626 313 24-78 39-25 •631 3-28 25-81 40-80 •633 3-40 26-59 42-00 •633 3-59 27-63 44-00 •628 3-76 28-66 45-65 •628 3-90 29-63 46-90 •632 4-03 30-35 48-20 •630 4T8 30-87 49-40 •625 4*35 31-91 50-80 •628 4-49 32-74 52-00 •630 are given in Table II., and are plotted in fig. 3. A scale of discharge in gallons per minute for the orifice employed is appended to the horizontal axis of the diagram, and the values of the theoretical discharge, given in the third column of Table II., were obtained by multiplying the lengths of the abscissae of the theoretical curve by this scale. The fourth column of the table gives the coefficient of discharge — that is, the ratio of actual dis- 300 Proceedings of the Royal Society of Edinburgh. [Sess. charge to theoretical discharge. The numerical value of this coefficient varies somewhat irregularly, but not more so than could be expected with the somewhat imperfect apparatus used in the experiments. For all heads less than D (2*5 inches), excluding the first reading, the average coefficient is 0626. No measurements could be made for heads below T23 inches, as the water began to run down the face of the apparatus, and there was imperfect contraction of the jet. This head is roughly equal to one-half the diameter of the hole, but the effect occurs when the velocity of the jet is insufficient to prevent the adhesion of the water to the metal, and thus depends upon the absolute head, and not upon the ratio of head to diameter ; with a larger orifice the experiments could have been carried down to a relatively lower water surface. The most striking result, from a practical point of view, is that the curve of discharge is very nearly a straight line for values of the head between D and D/2. In fig. 3 the line through the points found experi- mentally has been drawn straight, and it represents, very closely, the results of the observations. The theoretical curve is straight between D and 0’7D, but is curved between 07D and 05D, though the departure from the straight line is not great. Thus there would be a considerable simpli- fication in working out results if such a weir were adopted for gauging streams. The corresponding curve of discharge for a rectangular weir is of parabolic form, and only approximates to a straight line with relatively high heads of water. The circular weir has the disadvantage that it cannot be used for shallow streams, unless a deeper pool is excavated behind it. This is not always practicable, though it would be of great use in eliminating, to a considerable extent, the uncertainty in measuring the flow of the stream due to the “ velocity of approach ” of the water before it reaches the weir. The equation to the straight line, which represents approximately the discharge for any head between the centre and the top of the orifice, is easily obtained as Q = c(4*46 D3/2.H - T29 D5/2), where Q is the actual discharge, in gallons per minute ; H is the head of water, measured in inches from the bottom of the orifice ; D is the diameter of the orifice, in inches ; and c is the coefficient of discharge, which may be taken as 0'625. For any particular size of aperture this simplifies to the form Q = aH - b, where a and b are numerical constants. The equation for the orifice used in the above experiments is Q = 11H - 8 gallons per minute (very nearly). 301 1908-9.] Discharge of Water from Circular Weirs. 2. Circular Orifice, completely drowned. It seemed profitable to continue the investigations and experiments with the orifice completely drowned. An approximation to the theoretical dis- charge of a circular orifice is obtained easily, if the area of the hole is multiplied by the velocity corresponding with a head measured from the water surface to the centre of the aperture ; or the discharge Q = Jig h7 ,7tD2/4 cubic feet per second = 4'731 D2H'1/2 gallons per minute, if D and £T are measured in inches for the last expression, H'|being the Fig. 4. distance from the water surface to the centre of the orifice. This result is very nearly accurate when the head is large compared with D, but for relatively low values of H' it becomes less so. The true theoretical dis- charge was therefore investigated up to a head equal to 3D/2 above the centre of the orifice — that is, to a height above the top of the hole equal to the diameter. The expression for the discharge found on page 2 applies here also, and the method of solution adopted was the same. Fig. 4 shows curves similar to those of fig. 2, except that now the value of H begins at D, and is in- creased by steps of OTD up to 2D. The outermost curve of fig. 2 and the 302 Proceedings of the Poyal Society of Edinburgh. [Sess. innermost one of hg. 4 are for the same head D. The areas under this second series of curves are given in the lower part of Table I., and have been plotted in fig. 5 as a curve of discharge for the orifice ; this curve lias been prolonged downwards by adding that of fig. 3. The change in curvature when the orifice is just completely filled is very noticeable. A curve of actual discharges for an aperture 2J inches in diameter, correspond- ing with the experimental results given in Table II., is shown also on fig. 5. DISCHARGE Fig. 5. The head could not be carried above 4*49 inches because this represents the full supply of water to the apparatus. When the water level is in the neighbourhood of the top of the orifice there is some irregularity in the flow ; sometimes the hole runs full, and at other times there is a small air-space at the top, the surface conditions being unstable. It may be well to point out here, though the effect is of most importance when the orifice is not completely drowned, that the height of the water at the vertical plane of the aperture itself is always less than the “ still water head ” measured at some distance away from the point of dis- 303 1908-9.] Discharge of Water from Circular Weirs. charge. Thus the conditions of actual discharge are not exactly the same as those assumed in calculating the theoretical flow. The coefficients of discharge for the drowned orifice are given also in Table II. ; the average value of the coefficient for heads above the top of the orifice is 0‘ 631. The dotted line in fffi. 5 shows the theoretical discharge as calculated from the approximate formula given above. The difference between the results obtained from the accurate expression and those from the approximate one is not great ; it amounts to about 6 per cent, when the water is just level with the top of the hole, and diminishes to 2J per cent, at the highest head taken. The results obtained graphically from the accurate expression may be in error to the extent of about 1 per cent., due partly to drawing and partly to the planimeter. It is of interest to note the position of the layer of maximum discharge for any height of the water surface. This is marked upon each of the curves of figs. 2 and 4, and dotted lines are drawn through the points. The heights of the points were measured, and are given in the last column of Table I., in terms of D. The height of the plane of maximum discharge gradually rises and approaches D/2 as the head is increased, a result which was to be expected. Summary. The discharge of water through a vertical circular orifice is represented by an expression which does not admit of a direct mathematical solution, but from which results have been obtained by graphical means. The shape of the curve of actual discharge is similar to that found for the theoretical discharge ; both curves are sensibly straight lines for positions of the water surface between the centre and the top of the orifice. The value of the coefficient of discharge probably lies between 0625 and Q’630 for low heads. {Issued separately May 11, 1909.) C 304 Proceedings of the Royal Society of Edinburgh. [Sess. XVII. — The Electromotive Force of Iodine Concentration Cells with One Electrode saturated with Iodine. By A. P. Laurie, D.Sc., M.A. Cantab. (MS. received January 16, 1909. Read February 15, 1909.) This investigation was undertaken with the view of determining the number of free iodine ions present in saturated solutions of iodine in potassium iodide of varying strengths. The Nernst equation for iodine concentration cells can be written as follows : — E = *02955( og V °(I) — — log 2 * (iy) (i); where I2 and I'2 are the concentrations of free iodine, and I and I' are the number of iodine ions present at the two electrodes. To consider first the neighbourhood of the electrode surrounded by the dilute solution of iodine : The distribution between potassium iodide and iodine is conditioned by the mass equation KIxL KL -£ = If (2); or, if we call a the total number of potassium iodide molecules added, and b the total number of iodine molecules added, and x the total number of free iodine molecules present, then we have (a — b + x)x b - x h On expanding the quadratic we get for the first term kb — x (3). a - b + k which, within the limits of the solutions actually used, can be utilised for determining the value of x. The mean value of k, taken from Jakowkin’s first four tables, is '00138.* Applying equation (4), we can calculate the number of free iodine molecules present — that is, the value of P2. Further, if the, amount of iodine added is very small as compared with the total amount of potassium iodide, we may assume that the number of iodide ions present can be calculated from the known ionisation constants for potassium iodide of the strength used. We thus get the total value of the expression log r2 (IT If we now consider the solution saturated with iodine surrounding the other electrode, and if we assume that the solubility of iodine in water is * Zeits. Phys. Ghem xx. 36. 1908-9.] Electromotive Force of Iodine Concentration Cells. 305 not affected by the presence of KI, except in so far as they enter into com- bination, then we get for the value of I2 the solubility of iodine in water at 25° C. — that is, '00134 molecules in 1000 c.c. If we could neglect the contact electromotive force between the solutions we could therefore calculate the number of iodine ions present in the saturated solution by simply putting the known values into equation (1) and measuring the E.M.F. of the cell. As far as potassium iodide is concerned, there is so little difference in the velocity of the potassium and iodide ions that this must be very small, but we have also the presence of I3 ions to consider. Where the number of I3 ions is very small compared with the number of iodide ions, this electromotive force is no doubt negligible, and in former measurements of the electromotive force of such iodine cells I showed that when the total amount of iodine present is small as compared with the potassium iodide, the experimental results showed that the contact E.M.F.’s may be neglected. In these experiments, however, we have a very considerable concentra- tion of iodine in proportion to the total potassium iodide round one electrode, and a very small concentration round the other electrode. We can therefore no longer neglect this possible source of error in the calcula- tion of the number of iodine ions present. With the view of determining the amount of this contact electromotive force I used the method devised by Cumming.* Having first measured the electromotive force of the cell, with potassium iodide solution between the respective solutions of iodine in potassium iodide, I replaced the potassium iodide by 10 normal ammonium nitrate solution, and remeasured the electromotive force. In the subsequent tables the electromotive force in potassium iodide is given, and also the correction obtained by replacing the potassium iodide by ammonium nitrate as the connecting liquid. Before giving the experimental results it is necessary to consider a little more closely the mass equation investigated by Jakowkin. It is evident that in the form in which it is written above no consideration is taken of the relative amount of ionised and un-ionised potassium iodide, and potassium tri-iodide present. Dawson f shows that it is necessary in this connection to consider separately the three mass equations KI ^±K + 1 KI3^±K + r3 I2 + I * A. C. Gumming, Trans. Faraday Society , vol. ii. part 3. + Chem. Soc. Trans., vol. lxxix. p. 239. VOL. XXIX. 20 306 Proceedings of the Royal Society of Edinburgh. [Sess. in order to completely investigate Jakowkin’s equation. Dawson’s investi- gation is made on the assumption that KIa is the only polyiodide present. The presence of higher polyiodides would evidently complicate the matter still further, but it has been proved by Jakowkin and Dawson’s results that such higher poly iodides can at most be present in very small quantities in dilute solutions. If we then consider a dilute solution of potassium iodide saturated with iodine, and if we determine the total amount of iodine present, then this amount less the solubility of iodine in water (’00134) will give us the total amount of combined iodine, which in a dilute solution may be regarded as wholly present as ionised or unionised KI3. The number of iodide ions present having been determined as described above, we can evidently determine the total number of uncombined KI molecules by applying the ionisation factor for that strength of potassium iodide. Further, if our methods of investigation are correct, the total amount of uncombined KI molecules (determined from the measurement of the number of iodide ions by means of the E.M.F.) added to the total number of combined KI molecules (determined by the titration of the saturated iodine solution) should equal the total number of KI molecules added to the solution, as long as we are justified in assuming that the only polyiodide present in appreciable quantity is KIS. If, however, an appreci- able amount of polyiodides higher than KIS are present, this would no longer be true ; for the number of combined KI molecules present, as determined by the E.M.F. , would be less than the total number of combined iodine molecules determined by titration. The actual measurements of the E.M.F. of the iodine concentration cells were made with a Dolazelek electrometer, the solutions being enclosed in the small stoppered electrodes which are figured in the paper above referred to.* The correction for the contact E.M.F. was found by transferring the stoppered electrodes from the potassium iodide solution in which they were immersed to the ammonium nitrate solution of the same temperature, and taking readings after the electrodes had had an hour or two to settle down. The results obtained were a little irregular, but I consider the error as probably not more than a millivolt in any single case. The iodine saturation -point was determined as follows. A solution of potassium iodide of the required strength, and containing the small quantity of iodine required for the one electrode, was first prepared. This electrode was then filled with this solution and stoppered, and the same solution ■* Laurie, Proc. Roy. Soc. Edin ., vol. xxviii. (1908), pt. 5, p. 382 ; Zeit. Phys. Chem ., lxiv. 5. 1908-9.] Electromotive Force of Iodine Concentration Cells. 307 poured into the bottle in which the stoppered electrodes were to be immersed. The other electrode was then filled up with coarsely powdered iodine, and some more of the same solution was run in among the powdered iodine by means of a fine pipette till the electrode was full. It was then stoppered, and finally immersed in the bottle along with the other electrode. The whole cell was then sealed with paraffin-wax and placed in the thermostat. The electromotive force usually rose rapidly, reaching its maximum in E.M.Fs. of saturated solution. •12 Graph 1. about twenty-four hours and then remaining constant for some days. Readings taken after a week showed usually a slow dropping of E.M.F., probably due to the gradual diffusion of the iodine from the strong electrode, through the solution and into the weak electrode. The iodine and potassium iodide used were Merks’s pure preparations. As a check, a preparation of specially pure iodine was made by dissolving Merks’s pure iodine in strong potassium iodide, precipitating by dilution with water, washing, drying over calcium nitrate, and finally subliming. This iodine introduced into the electrode instead of the iodine formerly used did not cause any appreciable change in the E.M.F. Although all the values given are not the result of more than one measure- 308 Proceedings of the Royal Society of Edinburgh. [Sess. ment, the more important values were determined more than once with freshly prepared solutions, and found to agree very closely (in dilute solutions, usually within ‘0003 of a volt). The intermediate values when plotted give a perfectly smooth curve, graph 1. In strong solutions the saturation-point cannot be determined quite so sharply, but an error of a millivolt is the outside limit. The following table contains (1) the number of molecules of potassium iodide present, (2) the number of molecules of iodine present in the dilute iodine electrode, (3) the E.M.F. with potassium iodide of the same strength connecting the stoppered electrodes, (4) the correction in E.M.F. obtained by immersing the stoppered electrodes in ammonium nitrate, (5) the number of iodine ions present calculated from the corrected E.M.F., and (6) the total amount of uncombined KI present. All the ammonium nitrate corrections given were experimentally deter- mined except the one for *7 KI, which was obtained by interpolation. Table T. — E.M.F. for Saturated Iodine against ’0005 Iodine Molecules. No. of KI Molecules. No. of Iodine Molecules. E.M.F. NH4N03 Correction. No. of Iodine Ions. Total Free KI. •025 •0005 •0640 + -0030 •0117 •0127 •05 •0005 •0728 + -0034 •0226 •025 T15 •0005 •0830 + -0039 •05 •056 •344 •0005 •0987 -b "0044 T35 T57 •5 •0005 T040 + -0046 T84 •22 •7 •0005 •1099 + -0055 •23 •273 •85 •0005 T136 + -0064 •256 •307 1-0 •0005 T172 + -0008 •264 •317* * This does not agree with the value calculated by Maitland (Z. /. Eletrocli., 1906, 265), hut his calculation involves Crotogino’s E.M.F. for a normal KI sat. iodine cell, which probably requires a considerable correction for contact E.M.F. due to I3 ions. In order to determine the amount of combined iodine present the amount was calculated for the dilute solutions by interpolation from the results of Noyes and Seidenstecker.* As the solutions used by me do not differ greatly from theirs in the amount of KI present, this can be done safely. At the same time independent determinations were made for these dilute solutions and found to agree so closely with the figures obtained by interpolation that they were taken. For solutions above T normal KI, fresh determinations of the satu- ration-points were made in the following manner. The potassium iodide solution with excess of solid iodine was introduced into a closely stoppered bottle sealed outside with paraffin-wax and placed in a thermostat at 25° C. After being kept rotating in the thermostat for more than a week, the * Zeits. Phys. Cliem ., xxvii. 357. 1908-9.] Electromotive Force of Iodine Concentration Cells. 309 solution was allowed to settle in the thermostat for some hours, a little quickly withdrawn in a graduated pipette through a plug of glass-wool, introduced into a flask containing some potassium iodide solution and titrated. The bottle was then closed, rotated for several more days, and a fresh sample removed and titrated. The second titration was found to agree very closely with the first, as the following figures show : — Table II.- — Iodine Saturations. No. of KI Molecules. No. of Iodine Molecules. •025 •05 T15 •Q95 + -00134 > fnterpMated nom Noyes s •0575 + -00134 ) results- 1st Determination. 2 nd Determination. Mean. •344 T89 T90 T895 •5 •295 •297 •296 •7 •440 •442 •441 •85 •579 •578 •5785 1-0 •712 •711 •7115 These values will be found to be a little higher than those obtained by Bruner,* but they have been taken as correct for the purposes of this paper. From these values, less the solubility of iodine in water, we obtain the total number of molecules of iodine in combination with the potassium iodide. The following table embodies the results obtained. Column I. gives the total number of potassium iodide molecules present ; column II., the total amount of uncombined KI as calculated from the E.M.F. ; column III., the total amount of combined iodine as obtained from the titration ; and column IV., the sum of the values in columns II. and III. Table III. I. No. of KI Molecules. 11. Total Free KI. III. Total Com- bined Iodine. IV. Sum of 1 1. + III. •025 •0127 0125 •0252 •05 •025 •025 •05 •115 •056 •0575 •1135 •344 T57 T89 •346 •5 •22 •295 •515 •7 •273 •440 •713 •85 •307 •578 •885 1-0 ■317 •711 1-028 * Zeits. Phys. Chem. xxvi. 150. 310 Proceedings of the Royal Society of Edinburgh. [Sess. This table shows that the total uncombined KI molecules added to the total combined iodine molecules equals the total number of KI molecules present in dilute solutions, while in the stronger solutions up to normal KI the iodine is in slight excess, indicating the presence in small quantities of higher poly iodides. For the dilute solutions, the results justify the method, as the total amount of the uncombined KI agrees very closely with the results obtained by Jakowkin and Noyes. As the potassium iodide solutions grow stronger and the solubility of the iodine increases, the Graph 2. amount of uncombined potassium iodide diminishes. The results are more clearly shown in graph 2. The total numbers of potassium iodide molecules present are taken as ordinates — for curve (a) the total number of combined iodine molecules, and for curve (b) the total number of free potassium iodide molecules, are taken respectively as abscissae. The straight line (c) shows the relation which exists between combined iodine and uncombined KI in dilute solutions. These results show clearly that up to normal KI there is very little polyiodide present higher than KI3, if we assume the method to be reliable for solutions up to this strength. While the application of the Nernst equation is more and more likely 1908-9.] Electromotive Force of Iodine Concentration Cells. 311 to yield erroneous results as the solutions get stronger, yet it seemed of some interest to measure the E.M.F. of a cell containing thrice normal KI., as this solution dissolves a number of molecules of iodine equal to the number of molecules of potassium iodide, so that it might be regarded as containing KL only. The results were as follows : — EMF= T01 ; NH4K03 correction = *02 ; number of iodine ions= '23. Total uncombined KI = ’275. It will be noted that while the total uncombined KI has not diminished much, it now represents a very small percentage of the total KI present, so that even this solution contains very little polyiodide higher than KI3. The amount, however, is now quite perceptible, and doubtless from this point onwards rapidly increases. It seemed also of interest to investigate the number of iodine ions present in a series of solutions consisting of normal KI, with successive additions of iodine up to saturation-point. Jakowkin has shown that in such solu- tions the value of k is ‘001365 where little iodine is present, but pro- gressively diminishes with addition of more iodine. In my former paper I determined the E.M.F. of a series of cells containing *0139 molecules of 312 j*1 **&&■*»* iodine in normal KI at one electrode (the value of k being for this solution *001365), and the series of strengths of iodine given in Jakowkin s table at the other electrode, up to and including *508 of iodine. These values were measured at 20*4° C., but have been corrected for 25° C. and included in Table IV. Additional measurements have also been made for stronger solu- tions up to and including the saturation-point. These E.M.F.’s are also given in Table IV., as well as the correction for contact E.M.F. as determined for certain of the solutions. Graph 3 shows the E.M.F.’s plotted against the 7 * - 6 E o c C '5 V) _a> 3 O -4. o 2 a) c -a '3 o o t. _ a) '2 -O E 3 z 1 Volts -001 002 -003 004 005 006 007 008 10 normal Ammonium Nitrate corrections for Iodine in normal KI Graph 4. iodine concentrations. Graph 4 shows the corrections plotted against the iodine concentrations. These results can also be used to calculate the number of iodine ions in the strong solutions. For, in the dilute solution of iodine we can calculate the amount of free iodine present from the value given by Jakowkin for K for this solution, namely *001365, and we can without serious error assume the number of iodide ions present to be given by the ionisation ratio for normal KI. On the other hand, the amount of free iodine at the strong iodine electrode can be calculated by using the value of k as determined by Jakowkin for that particular strength of solution. It is true that Jakowkin has not determined the value of k for strength Proceedings of the Royal Society of Edinburgh. [Sess. 1908-9.] Electromotive Force of Iodine Concentration Cells. 313 beyond *508 of iodine ; but if the changing values of k , subtracted from '001365, be plotted against the iodine concentrations, it will be found that the graph is very nearly a straight line. If this straight line be produced until it passes through the value for saturation with iodine ('71), and if the value for k so obtained be used to calculate the amount of free iodine present in a saturated solution, then the value obtained is very nearly '00134. It is therefore justifiable to use this graph to determine the values of k between '508 and '71 of iodine. The following table contains the number of iodine ions calculated, as above described, from the E.M.F.’s as measured. Table IV. — E.M.F.’s of Jodine Solutions in Normal KI with -00139 I., in the Dilute Electrode. No. of Iodine Molecules. E.M.F. nh4no3 Correction. No. of Free Iodine Ions. •0322 •0110 •0003 •758 •056 •0187 0005 •738 T09 •0277 •0010 •708 •209 •0382 •0020 •636 '279 •0441 •0026 •566 •362 •0498 •0033 •522 *508 •0597 •0051 •402 •57 •0644 •006 •353 •61 •0672 •0065 •325 •65 •0701 •0071 •299 •70 •0734 •0078 •274 •712 •0745 •008 •262 It will be noted that the number of iodide ions present in the saturated solution with '0139 molecules of iodine in the weak electrode agrees very closely with the number as determined from the solution containing '0005 of iodine. (If k — '00138 is used instead of k — '00136 in making the calculation, this number is slightly altered.) When it is remembered that in the one case the concentration of the iodine was '0005 and in the other case it was '0138, the agreement between these numbers is very satisfactory. At the other end of the table is to be found the number of iodide ions for a solution containing '03 of iodine. If the number of I3 ions correspond- ing to this amount of iodine be added to the number of iodide ions as measured from the E.M.F., then the total number of iodide ions agrees with that derived from the conductivity of a normal solution of KI. A very interesting graph (5) can be constructed in the following manner from these results. Take the number of iodine ions as ordinates, and the respective strengths of iodine as abscissae. Mark on the base line the number of iodide ions present in a normal KI solution, and opposite '71 of 314 Proceedings of the Royal Society of Edinburgh. [Sess. iodine mark the number of iodide ions present in the saturated solution, and join these two points by a straight line. The intermediate values will be found to lie along this line, not departing from it more than can be accounted for by the experimental error. Dawson has shown that the ionisation of KI3 is the same as the ionisa- tion of KI, so that if we consider the ratio of combined to uncombined K ions, it is evident that the un-ionised K ions will remain constant, and will be represented in the diagram by a perpendicular line ab, drawn from *79 Iodine Ions against total Iodine in normal KI Graph 5. on the base line, while the distribution of the K ions between I and I., ions is given by the line a c for any given amount of iodine in solution. It appears further, from a consideration of this graph, that KI3 is practically the only complex present. For if we consider the solution containing *5 molecules of iodine, we find that the number of free iodine ions present is '41, which means that the amount of free KI present is just about *5, thus leaving ‘5 of KI molecules combined with the 5 iodine molecules as KL. If, on adding more iodine to this solution higher com- plexes were formed, the graph would not continue as a straight line. If we consider again the table in Jakowkin’s paper for normal KI, it 1908-9.] Electromotive Force of Iodine Concentration Cells. 315 is evident that in a normal KI solution containing very little iodine the dissociation constant for I.,±^I0 + I is the same as in dilute solutions. But as the amount of iodine in the solution is increased this dissocia- tion constant alters, the X3 molecules becoming more stable. In dilute solutions the amount of iodine can be varied without affecting this constant, but in presence of a very strong iodine solution, such as that present in normal KI, the tendency of the Ivl3 to dissociate diminishes. It is for this reason that it is possible to dissolve more iodine in these solutions. For the total amount of iodine which can be dissolved is controlled by the solubility of iodine in water and by the value of k. If k is smaller, then, considering the equation — -- — MyC _ ^ p. -g evident that the ratio of total iodine dissolved to total KI present can be pushed further, till the limiting value of x is reached, namely -00134. a While, therefore, the increased solubility of the iodine is accounted for up to a certain strength of KI by the alteration of the dissociation constant of I3 ions, the formation of still higher polyiodides in still stronger solutions is no doubt due to the fact that it is only under the influence of very high concentrations that they are stable, and therefore begin to be present in considerable quantities. In conclusion, I have to thank Mr King for his assistance, and the Carnegie Trust for the grant which enabled me to carry out these experiments. ( Issued separately May 11, 1909.) 316 Proceedings of the Royal Society of Edinburgh. [Sess. XVIII. — Cynomacrurus Piriei, Poisson abyssal nouveau recueilli par FExpedition Antarctique Nationale Ecossaise. Note prelimi- naire, par Louis Dollo, Sc.D. (Cantab.), For.Mem.G.S., C.M.Z.S., a Bruxelles (Musee). Presentee par M. R. H. Traquair, M.D., F.R.S., V.P.R.S.E. (MS. received March 12, 1909. Read same date.) I. Introduction. 1. — 1. L’existence des Macruridce a Finterieur du Cercle Polaire Arctique est connue depuis longtemps. C’est Sven Loven qui en rapporta le premier exemplaire ( Macrurus berglax), de Hannnerfest (Finmark), lors de la premiere Expedition suedoise au Spitzberg, sur F Enigheten, en 1837.* 2. Par contre, ce n’est que depuis dix ans (1899) que la presence des Macruridce a ete constatee a Finterieur du Cercle Polaire Antarctique, par FExpedition de la Belgica (1897-1899), avec le Nematonurus Lecointei,\ a une latitude presqu’identique : 1. Enigheten. — Arctique: 70° 39' 15" N. 2. Belgica. — Antarctique: 70° 40' 00" S. II. — 1. Jusque maintenant, une seule espece de Macruridce a ete recueillie a Finterieur du Cercle Polaire Arctique. \ * C. J. Sundevall, “Om de tva Nordiska arterna af fiskslagtet Macrourus (Lepidoleprus Risso) och badas forekommande vid Norrige,” Kongliga Vetenskaps-Academiens Handlingar , for dr 1840, p. 1, Stockholm, 1842. R. Collett, “ Meddelelser om Norges Fiske i Aarene 1884-1901 (3die Hoved-Supple- ment til ‘Norges Fiske’), it,” Forhandlinger i Videnskabs-Selskabet i Christiania , Aar 1903, No. 9, p. 76, Christiania, 1904 : “ I Finmarken liar den vseret kjendt siden 1837, da Loven bragte det fprste europseiske Exiil. fra Hammerfest til Riks-Mnseum i Stockholm.” Je remercie MM. les Professeurs R. Collett, Directeur du Mnsee zoologique de Christi- ania, et E. Lonnberg, Conservateur au Musee royal d’Histoire naturelle de Stockholm, des renseignements qu’ils ont bien voulu me fournir sur les Macrurides arctiques. t L. Dollo, “ Poissons de FExpedition Antarctique Beige,” Re'sidtats du Voyage du S.Y. “ Belgica ” en 1897, 1898, 1899, sous le commandement de A. de Gerlache de Gomery,~p. 44, Anvers, 1904. X A. Brauer, “ Die Tiefsee-Fische (I. Systematischer Teil),” Wissenschaftliche Ergebnisse der deutsclien Tief see- Expedition auf dem Damp>fer “ Valdivia ” 1898-1899, pi. xvii., Iena, 1906. 317 1908-9.] Dr Louis Dolio on Cynomacrurus Piriei. 2. Renversant l’ordre du progres des connaissances dans ce domaine, il etait reserve a l’Expedition Antarctique Rationale Ecossaise de decouvrir une deuxieme espece de Macruridce a l’interieur du Cercle Polaire Antarctique , et, en meme temps, le Macruride le plus antarctique actuellement capture : 1. Scotia. — Antarctique: 71 "50' S. 2. Belgica. — Antarctique: 70 40' S. III. — L’Expedition de la Scotia (1902-1904) est, d’ailleurs, la seule Expedition Antarctique, depuis la Belgica , qui ait ramene des Macruridce de Yinterieur du Cercle Polaire, car les autres : 1. Southern Gross * * * § (1898-1900), 4. Antarctic^ 1901-1903), 2. Discovery f (1901-1904), 5. Francais || (1903-1905), 3. Gauss l (1901-1903), n’en mentionnent pas, ou n’ont pas meme penetre a l’interieur du Cercle en question. IV. — Le Macruride pris par la Scotia a l’interieur du Cercle Polaire Antarctique est nouveau et nettement caracterise, notamment par sa dentition: je l’appellerai Cynomacrurus Piriei, en l’honneur du Docteur J. H. Harvey Pirie, medecin et geoiogue de l’Expedition, dont Fimportante decouverte de Graptolites aux Orcades du Sud est encore presente a la memoire de tous. U" II. Malacocephalus et Cynomacrurus. I. — Qu’on se serve de la Cle donnee par M. A. Gtinther, Conservateur honoraire au British Museum, dans sa monographie des Poissons abyssaux * G. A. Boulenger, “ Pisces,” Report on the Collections of Natural History made in the Antarctic Regions during the Voyage of the “ Southern Cross f p. 174, Londres, 1902. t G. A. Boulenger, “Fishes,” National Antarctic Expedition (1901-1904), Natural History , vol. ii. {Zoology), Vertebrata (iv.), Londres, 1907. J E. von Drygalski, “ Zum Kontinent des eisigen Siidens,” Deutsche Siidpolar expedition : Fahrten und Forschungen des “ Gauss ” (1901-1903), p. 478, Berlin, 1904. § E. Lonnberg, “ The Fishes of the Swedish South Polar Expedition,” W issenschaftliche Ergebnisse der schwedischen Siidpolar -Expedition 1901-1903, vol. v., No. 6, pp. 9 et 51, Stockholm, 1905. L’Expedition Antarcticpie Suedoise signale deux Macrurid.es, mais l’un provient du Canal du Beagle et l’autre du Detroit de Bransfield, done peclies en dehors du Cercle Polaire. || L. Vaillant, “Poissons,” Expedition Antarctique Frangaise (1903-1905), p. 12, Paris, 1906. IT J. H. Harvey Pirie, “ On the Graptolite-bearing Bocks of the South Orkneys,” Proceedings of the Royal Society of Edinburgh, vol. xxv. p. 463, Edimbourg, 1905. 318 Proceedings of the Royal Society of Edinburgh. [Sess. du Challenger * * * § — ou de celle que j’ai publiee dans mon memoire snr les Poissons de la Belgica ,f — par : 1. Ses dents premaxillaires snr denx rangs, 2. Ses dents mandibulaires snr un rang, 3. Sa deuxieme epine dorsale lisse, 4. Ses deux dorsales separees par une distance plus grande que la base de la premiere, le Macruride recueilli par la Scotia a l’interieur du Cercle Polaire Antarc- tique semble venir se classer dans le genre Malacocephalus. \ II. — Comparons done le Poisson de l’Expedition Antaretique Nationale Ecossaise au tyrpe du genre Malacocephalus, qui est le Malacocephalus Icevis, Lowe, 1843 : § Malacocephalus, Gunther, 1862. 1. Pas de croc premaxillaire. 2. Pas de grands crocs mandibulaires. 3. Ecailles , tres petites : plus de 16, en serie transversale, entre l’epine de la premiere dorsale et la ligne laterale. 4. Anus, entre les ventrales, et pres de la base de celles-ci. 5. Ventouse larvaire, || representee par des espaces nus au voisinage de l’anus. 6. Barbillon, bien developpe. 7. CEil, grand (orbite = J tete, en- viron), sans membrane orbitaire. 8. Cavite buccale, blanclie. Cynomacrurus, Dollo, 1909. 1. Ei\ croc premaxillaire. 2. Des grands crocs mandibulaires . 3. Ecailles : 8, en serie transversale, entre Pepine de la premiere dorsale et la ligne laterale. 4. Anus , immediatement au devan t de Panale. 5. Espaces nus, manquant complete- ment. 6. Barbillon, absent. 7. CEil, petit (orbite = y tete, environ), avec large membrane orbitaire. 8. Cavite buccale, noire. * A. Gunther, “Report on the Deep-Sea Fishes,” Voyage of H.M.S. “ Challenger ” during the years 1873-1876, Zoology , vol. xxii. p. 124, Edimbourg, 1887. t L. Dollo, Poissons de V Expedition Antaretique Beige , etc., p. 38. X Depuis la publication de mon memoire sur les Poissons de la Belgica , M. D. S. Jordan, President de la Lelancl Stanford Junior University, a Palo Alto (Californie), a cree le genre Nezumia, pour un Macruride du Japon, mais cet ichthyologiste semble avoir perdu de vue que Chalinurus Murrayi (A. Gunther, Deep-Sea Fishes, etc., p. 146) a douze rayons a chaque ventrale. D ’autre part, Dolloa a les dorsales presque contigues, et non separees par une distance plus grande que la base de la premiere. Quoiqu’il en soit, Cynomacrurus se distingue aisement de Nezumia, par l’absence de dents villiformes et par sa deuxieme epine dorsale lisse. D. S. Jordan and E. C. Starks. “List of Fishes dredged by the Steamer ‘Albatross’ off the Coast of Japan in the Summer of 1900, with Descriptions of New Species and a Review of the Japanese Macrouridse,” Bulletin of the United States Fish Commission, vol. xxii. (1902), pp. 602 et 620, Washington, 1904. § A. Gunther, Deep-Sea Fishes, etc., p. 148. || F. A. Smitt, A History of Scandinavian Fishes, Part II p. 582, Stockholm, 1895. 319 1908-9.] Dr Louis Dollo on Cynomacrurus Piriei. III. — Le Macruride de la Scotia est, par consequent, un tout autre Poisson que le Malacocephalus Icevis, et il ne pent rentrer dans le meme genre, au sens donne actuellement a ce mot dans la famille a laquelle il appartient : d’ou le nom de Cynomacrurus, destine a rappeler, en outre, les crocs caracteristiques de ranimal. III. Diagnose du Cynomacrurus Piriei. I. Sous - Famille : Macrurince. — Par sa premiere fente branchiale reduite, notre Macruride se range dans la sous-famille des Macrurince. Yoici, d’ailleurs, la description de son appareil branchial : 1. Ou'ies , largement ouvertes. 2. Membranes branchiosteges, soudees seulement a la partie tout a fait anterieure de risthme et unies entre elles sur une faible etendue. 3. Branchies, au nombre de 4, avec lamelles bien developpees. 4. Fentes brancliiales : I. Reduite, mais beaucoup plus grande que la cinquieme. II. Largement ouverte. III. Largement ouverte. IV. Largement ouverte. V. Simple boutonniere. 5. Brancliiospines : Arc I. En avant, reduites, non epineuses. En arriere, claviformes, robustes, espacees, a extremite libre epineuse, un peu plus courtes que les lamelles branchiales, alternant avec les branchiospines anterieures de Tare suivant. Arcs II et III. En avant et en arriere, comme en arriere de l’arc precedent. Arc IV. En avant, comme les deux arcs precedents. En arriere, absentes. Arc Y. Absentes. 6. Pseudobranchies , absentes. II. Genre: Cynomacrurus, Dollo, 1909. — Dans ce qui va suivre, j’in- diquerai en italiques les caracteres differentiels de Cynomacrurus et de Malacocephalus, qui sont les deux genres de Macrurides les plus voisins, d’apres]les cles en usage aujourd’hui : 1. Dents premaxillaires, sur deux rangs. Rang interne : petites dents, assez serrees et regulierement espacees d’un bout a l’autre de la serie. Rang externe : en arriere, comme le rang interne ; vers l’avant, plus espacees ; au tournant de la face laterale et de la face anterieure, un croc bien marque ■; sur le devant, petites dents, de nouveau, mais un peu plus grandes que les dents laterales, et prehensiles. 320 Proceedings of the Royal Society of Edinburgh. [Sess. 2. Dents mandibulaires , sur un rang. Grands crocs irreguliers , espaces, dont les plus grands, enormes, depassent en longueur le croc premaxillaire. 3. Deuxieme epine dor sale, lisse. Filamenteuse , s’enroulant a Fextremite libre. 4. Distance des dorsales , plus grande que la base de la premiere. 5. Barbillon , completement absent. 6. Anus , immediatement au devant de Yartale. 7. Espaces nus, entierement absents au voisinage de l’anus. III. Espece : Cynomacrurus Piriei, Polio , 1909. — -Enfin, nous avons, pour la diagnose speciftque : B. 6. D1. 10. P. 21. V. 12. 1. Museau (region de la tete en avant du bord anterieur des orbites), court (ne mesurant guere plus de 1*5 fois le diametre de Forbite, qui est petite), tronque en avant. 2. Rostre (region de la tete en avant de la limite anterieure de la bouche), tout petit, obtus, sans tubercule median, termine en avant par les preorbitaires, qui debordent.* 3. Bouche , large, laterale, depassant le bord posterieur de l’orbite du quart du diametre de celle-ci. 4. Narines , situees immediatement au devant de Forbite, bien developpees, contigues. Prenarine, tubuleuse, a contour etrangle en son milieu et a grand diametre horizontal. Postnarine, simple ouverture mytiliforme, mais beaucoup plus grande que la prenarine, et a grand diametre vertical. 5. CEil, petit, entoure d’une large membrane orbitaire, qui forme une bordure egale au tiers du diametre de Fceil. Orbite, contenue un peu moins de 7 fois dans la longueur de la tete. CEil, contenu 1 1 fois dans la longueur de la tete. Espace interorbitaire, plat, large, egal a 2 fois le diametre de Forbite. 6. Preopercule , a angle se projetant en arriere en un lobe arrondi, dentele et ecailleux. 7. Cavites mucipares, tres developpees et deboucliant a la surface de la tete par d’enormes ouvertures, particulierement derriere Forbite. 8. Anus, dont la distance a Fist Mil e est moindre que les | de la longueur de la tete. Yerticale de Fanus passant en arriere de la premiere dorsale et en avant de la deuxieme, et aussi en avant du milieu de la distance qui separe les deux dor- sales (dans le premier ^ de cette distance, en arriere de la premiere dorsale). * Nous avons done, chez les Macruridce, deux sortes de rostres : 1. Avec terminaison ethmoidale . . . Gcelorhynchus. 2. Avec terminaison preorbitaire . . . Cynomacrurus. Ce dernier etant, en tout petit, ce dont Peristedion nous montre Fextreme exageration, chez les Triglidce, par un phenomene de Convergence. 321 1 908— 9.]^ Dr Louis Dollo on Cynomacrurus Piriei. 9. Ecailles , caduques, presque toutes tombees. Sur la tete, epineuses, avec 3, 4, ou 5 rangees d’epines. Sur le dos, des deux cotes de la deuxieme dorsale, epineuses aussi, avec 1, 2, ou 3 rangees d’epines plus fortes. Sur le ventre, inermes, mais avec des plis marquant les rangees d’epines disparues, montrant done que ce sont des ecailles epineuses degenerees.* Nombre d’ecailles entre la ligne laterale et la deuxieme epine dorsale : 8. 10. Premiere dorsale , avec une base contenue a peu pres 3 5 fois dans la longueur de la tete. 11. Deuxieme dorsale , comme^ant a une distance de la premiere plus grande que la base de celle-ci (pas beaucoup moindre que le double de cette base) et sensiblement egale a la moitie de la longueur de la tete. 12. Queue , gephyrocerque (homocerque) filamenteuse.f 13. Pectorales, mutilees, faibles, dont l’extremite libre n’atteignait certainement pas la verticale de l’anus,! et, par consequent, beaucoup plus courtes que la region post-orbitaire de la tete. 14. Ventrales, mutilees, avec rayon externe prolonge en un filament atteignant l’anus, quoiqu’il soit plus court que la moitie de la longueur de la tete (t4t seulement). 15. Coloration : les ecailles etant presque toutes tombees, le poisson a une teinte generale violacee. Par contre, la prenarine, le bord de la postnarine, les regions nues de la tete, le rayon externe des ventrales, la cavite buccale et la cavite branebiale sont noirs. 16. Longueur totale : 0m,31 environ. IV. Type du Cynomacrurus Piriei. — Le type du genre et de Fespece est conserve an Scottish Oceanographical Laboratory, a Edimbourg (Ecosse). IV. Bignomie du Cynomacrurus Piriei. I. Biogeographie. Habitat: 71° 50' S. et 23° 30' W. Mer de Weddell. Ocean Antarctique. Quadrant Americain. Station 414. Scotia. * G’est-a-dire cycloides secondaires, ou Pseudocycloides (L. Dollo, Poissons de V Expedition Antarctique Beige , etc., p. 140). Les traces de l’indestructible passe ( Irreversibilite de V Evolution) sont, ici, les plis, derniers vestiges des rangees d’epines disparues (L. Dollo, “Les Lois de l’E volution,” Bulletin de la Societe beige de Geologie, vol. vii. p. 165, Bruxelles, i893). t L. Dollo, “ Sur la Phylogenie des Dipneustes,” Bulletin de la Societe beige de Geologie , vol. ix. p. 96, Bruxelles, 1895. L. Dollo, Poissons de V Expedition Antarctique Beige, etc., p. 235. X Chez Malacocephalus, inserees en arriere de la verticale de l’anus ! (A. Gunther, Deep- Sea Fishes, etc., pi. xxxix., fig. B). VOL. XXIX. 21 322 Proceedings of the Royal Society of Edinburgh. [Sess. IL Ethologie. 1. Profondeur. — 2102 fathoms. 2. Nature du Fond. — Vase bleue. 3. Temperature du Fond. — 3 1 ° *5 F. 4. Temperature de la Surface. — 29° *1 F. 5. Densite de VEau ( Fond ). — 1 '02555. 6. Densite de VEau (Surface).—!' 02520. 7. Mode de Capture. — -Filet vertical de 2m'50 d’ouverture, entre 0 et 1000 fathoms. 8. Date de Capture.— lb Mars 1904. 9. Heure de Capture. — -Entre 9 heures du matin et 8 heures du soir. 10. Nombre d’Individus captures. — Un seul. 11. Compagnons de Peciie. — 5 especes de Poissons, parmi lesquels le Prymno- tlionus Hookeri , et 15 especes d’autres animaux. V. Cynomacrurus Piriei et Nematonurus Lecointei. I. Comparaison. — II serait, maintenant, interessant de comparer, entre eux, les deux seuls Macrurides actuellement connus a l’interieur du Cercle Polaire Antarctique : * Nematonurus Lecointei, Polio, 1900. 1. Dents premax illaires, sur deux rangs, mais sans croc. 2. Dents mandibulaires, sur un rang, mais sans grands crocs. 3. Deuxieme epine dor sale, barbelee. 4. Distance des dorsales, plus grande que la base de la premiere (plus de 3 fois). 5. Rostre, a extremite ethmoidale. 6. Bouche , dont la fente n’atteint pas la verticale du centre de l’ceil. 7. Bar billon, present. 8. CEil, contenu 5J fois dans la lon- gueur de la tete, avec large membrane orbitai re. 9. Orbite, contenue 4 fois dans la longueur de la tete. 10. Espace inter orbit air e , moindre que le diametre de l’orbite. Cynomacrurus Piriei, Polio, 1909. 1. Dents premaxillaires , sur deux rangs, avec un croc bien marque. 2. Dents mandibulaires, sur un rang, avec grands crocs irreguliers. 3. Deuxieme epine dor sale, lisse et filamenteuse. 4. Distance des dorsales, plus grande que la base de la premiere (moins de 2 fois). 5. Rostre, a extremite preorbitaire. 6. Bouche, depassant le bord posterieur de Torbite du quart du diametre de celle-ci. 7. Barbillon, absent. 8. OEil, contenu 11 fois dans la lon- gueur de la tete, avec large membrane orbitaire. 9. Orbite, contenue presque 7 fois dans la longueur de la tete. 10. Espace inter orbitaire, egal a deux fois le diametre de l’orbite. * L. Dollo, Poissons de V Expedition Antarctique Beige, etc., p. 44. 323 1908-9.] Dr Louis Dollo on Cynomacrurus Piriei. 11. Anus , presque contre Fanale, mais avec verticale passant, entre les dorsales, en arriere du milieu de la distance de celles-ci. 12. Longueur totale : 0m'43 environ. 1. Habitat : 70° 40' S. et 102° 15' W. Mer de Bellingshausen. Ocean Antarctique. Quadrant Pacifique. Belgica. 2. Profondeur: 1531 fathoms. 11. Anus, iminediatement au devant de Fanale, mais avec verticale passant, entre les dorsales, dans le premier hui- tieme de la distance de celles-ci, en arriere de la premiere dorsale. 12. Longueur totale ; 0m,31 environ. 1. Habitat: 71° 50' S. et 23° 30' W. Mer de Weddell. Ocean Antarctique. Quadrant Americain. Scotia. 2. Profondeur : 2102 fathoms. II. Conclusion .■ — II resulte de ce qui precede que les deux Macrurides de Finterieur du Cercle Polaire Antarctique sont bien distincts et appartiennent certainement a deux genres differents. L’un habite, d’ailleurs, le prolongement de FAtlantique ( Cynomacrurus Piriei) ; 1’autre, le prolongement du Pacifique (Nematonurus Lecointei ). VI. Cynomacrurus Piriei et Macrurus berglax. I. Comparaison. — Comparons, a present, les Macrurides de Finterieur du Cercle Polaire Antarctique au seul Macruride connu de Finterieur du Cercle Polaire Arctique, en remarquant qu’il suffit de s’occuper, ici, de Cynomacrurus Piriei et de Macrurus bergla.x, puisque Nematonurus Lecointei a ete etudie en detail dans mon memoire sur les Poissons de la Belgica :* Macrurus berglax, Lacepede, 1800. 1. Dents premaxillaires , constituant une bande villiforme. 2. Dents mandibulaires, constituant egalement une bande villiforme. 3. Deuxieme epine dorsale, barbelee. 4. Distance des dorsales, moindre que la base de la premiere. 5. Rostre, a extremite ethmo'idale. 6. Bouclie , dont la fente n’atteint pas la verticale du centre de Foeil. Cynomacrurus Piriei, Dollo, 1909. 1. Dents 'premaxillaires, sur deux rangs, avec un croc bien marque. 2. De?its mandibidaires, sur un rang, avec grands crocs irreguliers. 3. Deuxieme epine dorsale, lisse et filamenteuse. 4. Distance des dorsales , plus grande que la base de la premiere (presque le double). 5. Rostre, a extremite preorbitaire. 6. Bouclie, depassant le bord posterieur de Forbite du quart du diametre de celle-ci. * F. A. Smitt, Scandinavian Fishes, etc., p. 587. 324 Proceedings of the Boyal Society of Edinburgh. [Sess. 7. Barbillon, present. 8. C Eil , contenu 4 fois dans la longueur de la tete, avec large mem- brane orbitaire. 9. Orbite , contenue moins de 3 fois dans la longueur de la tete. 10. Espace interorbitaire, beaucoup moindre que le diametre de l’orbite (la moitie environ). 11. Anus, presque contre l’anale, mais avec verticale en arriere de l’origine de la deuxieme dorsale. 12. Longueur totale : lm,00 environ. 1. Habitat: 70° 39' 15" N. Finmark. Ocean Arctique. Quadrant Europeen. Eniglieten. 2. Profondeur : 100 a 300 fathoms. 7. Barbillon , absent. 8. (Eil, contenu 11 fois dans la longueur de la tete, avec large membrane orbitaire. 9. Orbite , contenue presque 7 fois dans la longueur de la tete. 10. Espace interorbitaire, egal a deux fois le diametre de l’orbite. 11. Anus, immediatement au devant de l’anale, mais avec verticale passant, entre les dorsales, presque contre la premiere de celles-ci. 12. Longueur totale : 0m’31 environ. 1. Habitat: 71° 50' 00" S. Mer de Weddell. Ocean Antarctique. Quadrant Americain. Scotia. 2. Profondeur: 2102 fathoms. II. Conclusion. — II resulte clone, egalement, de ce qui precede que le Macruride de l’interieur du Cercle Polaire Arctique est bien distinct de ceux de l’interieur du Cercle Polaire Antarctique et qu’il appartient certainement aussi a un genre different. Circonstance encore defavorable a la Theorie de la Bipolarite. Mais je revienclrai prochainement la-dessus. VII. Morphologie des Barbillons inframandibulaires. I. Macrurince. — La longueur du barbillon est fort variable dans cette sous-famille : * 1. Hymenocephalus longibarbis 2. Cetonurus crassiceps C § de la longueur de la tete. 1 Ficlji, 315 fathoms. de la longueur de la tete. Kermadec, 520 fathoms. { Cependant, sa presence est tres constante, car je ne connais que deux cas, sur plus de 125 especes, ou il manque tout a fait : 1. Hymenocephalus lethonemus Japon, 120 a 265 fathoms. j* 2. Cynomacrurus Piriei Mer de Weddell, 2102 fathoms.} * A. Gunther, Deep-Sea Fishes, etc., pi. xviii., fig. C et pi. xxxvii. t D. S. Jordan and E. C. Starks, List of Fishes, etc., p. 615. 1 Bien que le Cynomacrurus Piriei ait ete peche entre 0 et 1000 fathoms, je prends ici, comme plus haut, la profondeur maximum au point de capture, puisque les Macrurides sont adaptes a la Vie Benthique, vu leur Queue Gephyrocerque : ce sont done des Poissons de Fond. 325 1908-9.] Dr Louis Dollo on Cynomacrurus Piriei . II. Morphologie. — Les recherches comparatives faites a cette occasion m’ont fourni le petit tableau suivant sur la Morphologie cles Barbillons inframandibulaires : 1. Cutane 2. Rayons branchiosteges 3. Rayons pectoraux 4. Rayons ventraux Macrurus * Mullus.f Rhodichthys.\ Ophidium.% VIII. La Membrane orbitaire. I. Macrurides polaires. — Les Macrurides de Tinterieur des Cercles Polaires : 1. Macrurus berglax, Lacepede, 1800 — Arctique, 2. Nematonurus Lecointei, Dollo, 1900 — Antarctique, 3. Cynomacrurus Piriei , Dollo, 1909 — Antarctique, ont l’ceil entoure d’une large Membrane orbitaire. II. Repartition. — Examinons si on peut trouver dans la Biogeographie, dans la Bathymetrie, ou dans la Grosseur de FCEil, une cause a cette structure : [| 1. Biogeographie 2. Bathymetrie 3. Gros Yeux 4. Petits Yeux J Cynomacrurus Piriei : Antarctique. I Coryphcenoides altipinnis : M. du Japon. C Cynomacrurus Piriei : 2102 fathoms. I Macrurus berglax : 100 a 300 fathoms. C Ccelorhynchus fasciatus : Orb. = § tete. ( Macrurus berglax : Orb. > I tete. ( Chalinurus liocephalus : Orb. — J tete. 1 Cynomacrurus Piriei : Orb. < J tete. M. orb. large. „ absente. „ large. „ absente. „ large. Nous avons done, d’une part, une large Membrane orbitaire a Tinterieur et en dehors des Cercles Polaires, puis a de faibles et a de grandes Profondeurs. Et, d’autre part, nous avons de Gros Yeux et de Petits Yeux avec ou sans Membrane orbitaire. * F. A. Smitt, Scandinavian Fishes , etc., p. 587. t S. Lo Bianco, “ L’origine dei barbigli tattili nel genere Mullus,” Atti della Reale Accademia dei Lincei, vol. xvi. p. 577, Rome, 1907. J A. S. Jensen, “On Fish-Otoliths in the Bottom-Deposits of the Sea (I. Otoliths of the Gadus-Species deposited in the Polar Deep),2’ Meddelelser fra Kommissionen for Hav- unders(/>gelser ( Fiskeri ), vol. i. (No. 7), pp. 5 et 6, Copenhague, 1905. § G. A. Boulenger, “ Teleostei (Systematic Part),” Cambridge Natural History ( Fishes , etc.), vol. vii. p. 713, Londres, 1904. || A. Gunther, Deep-Sea Fishes, etc., pp. 138, 139 et 145. 326 Proceedings of the Poyal Society of Edinburgh. [Sess. Ce nest, par consequent, ni par la Biogeographie, ni par la Bathymetrie, ni par la Grosseur de PCEil, que nous arriverons a eclaircir l’origine de cette disposition. III. Signification. — Mais la signification nous en sera, sans doute, donnee par l’observation suivante : * “ In all fishes the general integument of the head passes over the eye, and becomes transparent where it enters the orbit; sometimes it simply passes over the orbit, sometimes it forms a circular fold. The anterior and posterior portions may be especially broad and the seat of an adipose deposit (adipose eyelids), as in Scomber , Caranx, Mugil, etc. In many of these fishes the extent of these eyelids varies with the seasons ; during the spawning season they are so much loaded with fat as nearly to hide the whole eye.” D’autant plus que, si le specimen de Malacocephalus loevis figure par M. Gunther : *f* Pernambouc (Bresil), 10 Septembre 1873, 350 fathoms, ne montre pas la moindre trace de membrane orbitaire, celui represente par Smitt : l Lysekil (Gothebourg, Suede), 10 Novembre 1852. rivage, permet de constater 1’existence d’une Membrane orbitaire deja fort accentuee. II s’agit, des lors, tres probablement, d line disposition saisonniere, et vraisemblablement en rapport avec 1’epoque de la reproduction. * A. Gtintlier, An Introduction to the Study of Fishes, p. 112, Edimbourg, 1880. A. Gtintlier, “ Fische der Siidsee,” Journal des Museum Godeffroy, vol. ii. pi. 84, 85, 86 et 120, Hambourg, 1873-75. + A. Gtintlier, Deep-Sea Fishes , etc., pi. xxxix. fig. B. X F. A. Smitt, Scandinavian Fishes , etc., p. 594. {Issued separately May 13, 1909.) 1908-9.] On Lagrange’s Equations of Motion. 327 XIX. — On Lagrange’s Equations of Motion, and on Elementary Solutions of G-yrostatic Problems. By Professor Andrew Gray, F.R.S. (MS. received January 12, 1909. Read February 15, 1909.) 1. It is now well known that Lagrange’s equations of motion for a system of connected particles are not applicable to certain cases of motion — for example, to a rigid sphere rolling without sliding on a given surface. In his Principien der Mechanik, Hertz has referred at considerable length to this subject, and has applied the adjective “ holonomous ” to those systems to which the equations are applicable, and has called all others “non- holonomous.” These adjectives correspond to distinct characteristics of the systems as regards the constraints to which they are subject. Holonomous systems are those in which the constraints are expressed, or can be expressed, by finite equations ; in non-holonomous systems, on the other hand, these conditions, or some of them at least, are expressed by differential relations, which do not fulfil the conditions of integrability. 2. Long before Hertz’s book appeared, attention had been called to the subject; for instance, Ferrers pointed out in the Quarterly Journal of Mathematics , vol. xii. (1871-73), that in the case of a hoop rolling on a horizontal plane, while the equation for the inclination of the hoop to the vertical could be obtained from the expressions for the kinetic and potential energies by Lagrange’s method, that method failed to give the equations corresponding to the other co-ordinates. Erroneous solutions of the hoop problem have, however, since that time been published by more than one writer who had not perceived the fact noticed by Ferrers. An oversight of this kind in a solution of this problem given by another mathematician seems to have led Appell to his theorem ( Comptes Rendus , 1899) by which the equations of motion for holonomous and non-holonomous systems alike are obtained by what has since been called the “ kinetic energy of the accelerations of the system.” 3. When Lagrange’s equations are deduced from the principle of least action, or by means of Hamilton’s characteristic function, the effect of the nature of the connections of the system is left more or less obscure. Some observations were made by Hertz on the subject, but these were far from conclusive, and it was first shown in 1896 by Holder ( Gott . Nadir., 1896), 328 Proceedings of the Royal Society of Edinburgh. [Sess. by an examination of the logic of the process of deduction, that the varied motion was not in all cases what it was tacitly assumed to be, in itself a possible motion — that is, one consistent with the kinematical conditions of the system. What we are entitled to assume is only that if the motion be slightly varied from a configuration C in the actual succession of configura- tions to a corresponding configuration C' in a neighbouring succession, the variation from C to C' must be consistent with the conditions of the system. Holder examined the cases for which, as Hertz pointed out, the method of least action seemed to give erroneous results, and showed how, by a stricter logical process than that usually employed, they could be brought likewise under the scope of the principle. 4. To make clear how the method fails, I shall consider the process of derivation of Lagrange’s equations from the equations of motion of a free particle — a process first employed, so far as I am aware, by Lord Kelvin. Exact equations of the kind first indicated by Ferrers, applicable to all cases of motion in which the co-ordinates are such as to explicitly define the configuration at any instant, will be obtained ; and then I shall inquire how the method of ignoration of co-ordinates, and the gy rostatic equations, first given by Lord Kelvin, are to be modified when this is done. This inquiry is the principal object of the present paper, and it will be seen leads to a simple result. Solutions will be added of a few problems illustrative of the methods arrived at, and of the sources of errors that may easily arise in their application. 5. The relations between the x, y , 0 co-ordinates of a representative particle and the independent parameters qv q2, ... , qk may be written in the form Sx = alSql -f a2Sq2 + ....+ akSqk \ + •••■ + hh* • • ( i ) Sz = c^qx + c2Sq2 + .... + ck8qk ‘ for a displacement possible at time t. In the case of finite equations of condition the coefficients av a2, ... , bv b2, ... , cv c2, . . . . are partial differential coefficients of functions of the co-ordinates qv q2, . . . , qk : in every case they are functions of the co-ordinates. The real displacements for an interval of time dt are dx = aldq1 + a2dq2 + ....+ akdqk + adt j dy — b1dq1 + b2dq2+ . . . . + bkdqk+ bdt . . . (2), dz = cldql + c2dq2 + ....+ ckdqk + cdt " where a, b, c are zero if the constraints do not depend on the time. It is supposed that the coefficients are so chosen that equations of condition ex- 329 1908-9.] On Lagrange’s Equations of Motion. pressing variations Sqk+1, . . . Sqk+m of m other parameters connected by m kinematical equations with the variations of the parameters qv q2, . . . , qk are taken account of. We shall also suppose for the present that the kine- matical equations do not involve the time t explicitly. 6. From (2) the values of x, y , z can be found, and from these again the values of x, y, z. The latter include, besides terms in qv q2, ... , qk) also terms involving the time-rates of variation of the a, b, c coefficients. If, then, we substitute in the expression -JS{m(x2 + y2 + £2)}, we get a transformed expression of which part, which we may call S, is an explicit function of qv q2, . . . , qk. If then we write 2KX + bi Y + c,-Z) = Q*, the generalised force according to the usual specification, we obtain P|-Qi, P = Q2. (3), a^i dq2 which are Appell’s equations. 7. Consider now the equations of motion mx = X, my = Y , mz = Z . . . (4), of a free particle, and from the equations of this form for the particles of the system construct S{m(a1aj + byj + c-^z)} = + IqY + cY Z)] 2 {m(a2x + b2y + c2z) } = %(a2X + b2 Y + c2Z) l . . . (5). The quantities on the right-hand sides in (5) are the generalised forces Qp Q2, .... of the Lagrangian equations. It will be observed that since any Q is the coefficient of Sq in the expression Q Sq for the work done in a possible variation of the parameter q, Q does not include any of what may be called the non-active forces — that is, forces such as those due to guides and constraints which are invariable. We have then to consider the equation 1{m(ax + bij + cz)} = Q ..... (6). Lord Kelvin’s process was as follows : — Writing dx/dq, dy/dq, dz/dq instead of a, b, c, for the system was tacitly supposed to be holonomous, he obtained (in a slightly different notation) .me d ( .dx\ . d dx dq dt\ dqj dt dq and then proved that dx dx d dx dx dq dq ’ dt dq dq ’ 330 Proceedings of the Royal Society of Edinburgh. [Sess. so that ..dx d ( ,dx\ . doc dq dt\ dq) dq Hence we obtain at once, putting T = + & + &)}, and supposing x, y, z, replaced by their values from (2), the typical Lagrangian equation of motion d 0T _ 0T dt dq dq That d dx dx dt dq dq follows from the equation d dx d dx . d dx d dx . d dx _ dt dq dq1 dq dqr, dq dqk dq k dt dq ’ Q (7). for here dx/dq is supposed to be the partial derivative with respect to q of an explicit function of qv q2, . . qk, t, and therefore d dx 0 dx 0 dx 0 dx dq i dq dq dql 1 dq2 dq dq dq2 ’ (8). 8. But if the system is non-holonomous this process is no longer ap- plicable, and another must be sought. In discussing this question I shall no longer refer to the Cartesian co-ordinates of the particles composing the system, As a rule, we are given only equations connecting the quantities by which the kinetic (and potential) energy is primarily ex- pressed with the generalised co-ordinates, and there must be as many such equations as are required to express the configuration of the system at any instant in terms of these co-ordinates. Let the kinetic energy be primarily expressed by the time-rates of change u, v, w, . . . , of quantities u, v, w, . . . , which fulfil equations. Su = a1Sq1 + a2dq2 + . , . . . + ct^qi + + 60^2 ’ • • • + efisj j Sv = 4- b2$q2 -f . . • • + diSqi +/10-S1 +f2ds2 + . . • • +fjh For a rigid body u, v, , may be taken as the product of the square roots J M, J N, . . . , of inertia coefficients M, N, . . . , into velocity com- ponents of the centroid, or the products of angular velocities of the body about given axes by the square roots of the proper inertia coefficients for this case ; and so for other systems. Thus if T be the kinetic energy we shall have T = \ (id1 + v2 + w2 + . . . . ) (10). 331 1908-9.] On Lagrange’s Equations of Motion. The parameters are divided in (9) into two sets — the q s and the s s — for a purpose which will appear later in connection with ignoration of co-ordinates. By (9), u = a1ql + a2q2 + ....+ + elsx + e2s2 +....+ qs,- v = b1q1 + b2q2 + .... + biqi+fls1+f2s2 + .... +fjSj - . (11), if we suppose, as we do for the present, that t does not appear in the kinematical equations. 9. Also we have, by the signification of it, v, ... , equations of motion ii = U, v = Y , and therefore obtain a series of equations of the form ciqil + bqv + ....= rq U + bfi + . . . . = ctqii -}- bqv -f- . . . . — ct^XJ -1- bi\ r . . . . = Q2 _ (12), where Qp Q2, . . . , are generalised forces according to the meanings of u, v, ... . These are i+j such equations, since there are now supposed to be i+j independent parameters qv q2, ... , sv s2, ... . By (10) and (11) we have d 0T , . . 4 . v n ] ' ' ' ' )_Ql d 0T / . . 9 . \ _ n " • • • (13). — — — (a2u + b9v +•...) — Qo at dq2 ' ■ , These are equivalent to the equations which, as Ferrers showed, must be substituted for the ordinary Lagrangian equations as typified by (6). They are applicable in all cases, whether the system is holonomous or not, provided always that the co-ordinates chosen are capable of expressing the configuration of the system, or position of the body at any instant. 10. It must, however, be remembered that different modes of breaking up the kinetic energy into a sum of squares according to (10) are in general not equivalent, but involve different sets of forces. For example, the term JA(02+ sin2 0 . f2), which occurs in the expression for the kinetic energy of a gyrostatic pendulum, or of any kinetically symmetrical body rotating with one point fixed, and which is already a sum of two squares, may also be written in the form JA (6 cos (p + f sin 0 sin ^>)2 + JA(dsin f —

2 1 = -f- b^v -4- . . . . \ <£2T = d2u + b2v + .... . . . . (20). If the form of T be modified in any way, for example, by the sub- stitution of the values of sv s2, ... . in terms of the momenta dT/dslt 0T/0s2, . . . . , and the other velocities qv q2, .... , then if T' be the modified form of T, < p XT', cp2 T', .... will be understood to denote the operations indicated in (20), but performed with the new values which are then given to the coefficients of qv q2, .... , qk. 14. It follows from what has been stated that, as has already been pointed out, the operations indicated in (20) cannot be performed without reference to the fundamental equations from which that expression has been derived. For example, two terms in T might be A Ad2-f- JBi/A These might be derived either from ii= JA.6, v= JByjs, or from u = J A sin 6.6+ VL cos 6 .\js, v= JA cos 6.6— ^JB sin 6 . \[r. The former mode of derivation would satisfy the conditions of integrability so far as these terms are concerned, the second would not. It is possible, in fact, to specify two distinct cases of motion which have precisely the same expressions for the kinetic and potential energies, but which have not the 334 Proceedings of the Royal Society of Edinburgh. [Sess. same equations of motion. An example will be given at the end of the present paper. 15. Let now the form of T be modified by the substitutions indicated above. Our object is to inquire what modification is required in the process of “ ignoration of co-ordinates ” by the non-integrability of the relations between the generalised co-ordinates and the functions of these co-ordinates and their velocities from which the kinetic energy is derived. We shall sup- pose, therefore, that the co-ordinates sv s9, . . . . , are absent from the kinetic energy, and from the function V of the co-ordinates from which the forces are derived, if that function exists. Writing them for a moment r1 = dT/dsv r2 — dT/ds2, . . . , we see that if the fundamental relations were integrable rv r2, , would be constants, since then we should have 7 = 0, 7 = 0, .. 0,q ds2 on the supposition that either 7 = 0, 7|o, . . 0sx ds2 or no generalised forces corresponding to sv s2, tions of motion are now, however, — —-X tT= o'1 dt ds± M d 8T rV n ^aT,=X2T=0 where J — 6-^u + yjr + . . • ■ | ........ r . . , exist. The equa- • (21), • (22); so that x2> ■ • • • > are the operators for the s co-ordinates that l 2 (23) ; 335 1908-9.] On Lagrange’s Equations of Motion. where cv c2, ... . are constants. These conditions are fulfilled in a large number of problems regarding rotating fly-wheels in which the co-ordinates qv q2, . . . . determining the positions of the axes of rotation have no influence on the momenta 0T ldsv .... When the system is holonomous the constancy of these momenta is secured by the fact that the differential equations (22') become dT/ds1 = 0, .... Equations (23) extended are + .... )ql + +/i^2 "t • • • • )$2 • • • ■ + (ei“ "h/p + • • • • )$\ + ( 6i)> (^2’ ^2)’ • • • > (sv si )’ (sv %)> • • • • Lu ^2)5 (^2’ ^2)’ • • • j (Sl> ^2)’ (s2> ^ 2 )’ ' • * • we can write equations (24) as follows : — (VSi)«i + («2» Sl)6'2+ • • • • = Cl~( Sl)4l-( ?2» Sl)?2~ • • • •] (•sl> ^2)^1 (c S2)% • ' • • = C2 ~ Ll> ^'2)^1 ~ (?2» ^2)^2 * (25). From these sp s2, . . . . , can be determined in terms of cv c2, . . . . , and qv q2, ... . These values then substituted in the expression for T convert it into a function of qv q2, ... , cv c2, . . . , so that all trace of the variables sv s2, .... is now removed. We have to inquire what form the equations of motion take when this substitution is made. First we form expressions for sv s2, ... . Let (cv cx), (cv c2), . ... , denote the ratios of the consecutive first minors of the determinant of equations (25) to that determinant, and put Then K = i{(cv . 9K s, = — 1 0Cj . _aK dc2 Cl)Cl2 + 2(ci) C2)clc2Jr • • • •} ~ (4lM + ^2^1 + . ... ) ~ (^1^2 ^2^2 +••••) (26). (27); ^i = (cn Gi)(1 = (cp Cj)(^2, sx) + (c-p r2)(g,2, s2) + . . . , B2 = (c2, c i)(^2 , Sj) > • + (C2, C2)fe» S2) + • • • • J (28). where 336 Proceedings of the Poyal Society of Edinburgh. [Sess. 17. Let now T' denote the expression for the kinetic energy when sv s2, ... . have been expressed as in (27), and T denote the former expression. Since qv q2, .... , appear in T' exactly as they did before the substitutions, and now appear besides in consequence of the substitu- tions, we have 0T 0T 0*, — = — + c-,-1 + c d9l 0£ 0^ where for sv s2 , ... . inserted. Thus 0T 0S, — + cl. 1 + c*! + (29); ai+ dJL 2dq2 ‘ dq2 dq2 ' ^ ' ~*dq2 , their values from (27) are supposed to have been d 0T = d_ 0T + d I \ = _ ^(dA\ dt dql dt dqY dt\ \ dqj / dt dql \ dt / by (27), so that — 0T- + ^c— V — — ^ dt dqY \ dt ) dt dq^ _£ 0T' dt dq2 \ dt) dt dq9 j Now from the original expression for T we have £ ^ dt 0g1 do T dt dq2 - <^T - Q1 - 2 T = Q2 J (30). (31). But if we substitute in d\ T, for example, the values of sv s2, .... , from (27) we obtain after reduction _irr =-—{«!- - 2(eA)}^ + {«2 - ^(eB)}^2+ . . . . ] -^{&i-S(/A)}[{61-2aA)}tf1 + {61-S(^B)}*+ ] (33). Collecting on the right of this expression the coefficients of qv q2, .... , we see by (32) that -*r~-*T + ^ + A*)* + S fdA + Adf dt dt \v + . . 1908-9.] On Lagrange’s Equations of Motion. 337 Now / . , . aT dA, dA-. • (34). Also by (22) and therefore ** + «$+ =0; dt dt -^r=-^T+2(cf), or But by (30) and (31) this gives d dT T, n X di^*1 Ql d aX , T|V r\ '■ . . . . diWA*2 =Q2 . (35). • • ; Hence we have the very simple rule : modify the expression for T by substituting for sv s2, .... , their values from (27), and then proceed as if no velocities of co-ordinates sv s2, .... , had ever entered into the expression for the kinetic energy. The equations of motion obtained are of course applicable also to holonomous systems. 18. To verify the results obtained, we write the first of (35) in the form ddT ar /,T,_a x\_n dt^~Wi~vl (36), and consider what it becomes when the system is made holonomous. We have = -(d1u + .... ) + %(c^j . . . (37); and since we have also now u= {a, - 2(eA)}g, + {a9 - 2(eB)}ff9 + . . . . v= {b1-^(fA)}q1 + {b2-^(fB)jq2 + we obtain 0T ddi = u + V + 'a b dq . (38). 22 VOL. XXIX. 338 Proceedings of the Royal Society of Edinburgh. [Sess. If now dajdql — dajdq2, .... db2/dq1 = dbl/dq2, .... , (37) becomes (0 0 u.ii + b-,v + . ... —u\ ffi- — 2(eA) -I- q*- — S(6l>) + . { dq1 dq1 ■-! by (22')- Hence finally d 8T 0T' . / /0A 0B\ dt dqY dq1 ( \dq2 dqj Qi (39) (40); and, similarly, for the other equations. The terms in qv q2, . . . . are called gyrostatic terms. The coefficient of qx in the first equation, of q2 in the second, and so on, is zero. This simple modification of the expression for the kinetic energy by which the equations of motion are obtained when certain co-ordinates are ignored, may be compared with the modification given by Routh for the case of holonomous systems {Stability of Motion, p. 60). If T and Tr have the meanings assigned above, we have now and obtain 0T_0T 2/ ds_ d dT 0T# dt £3T_0T= Q | dcjj dq1 1 \dt dqY dqj i dt cq 1 dqx |> (41). But, as has been shown above, § 17, 0s \ = — *Z\ C I . Z.I c dt dqf d ds\ dA\ 2(^^=_a (c-), (42), so that (41) becomes A- A - ^ + 4,2 < c(A _ A) l + 4 5 1 ,(A _ A) dt dqx dqY I \0g1 dqj ) ^ | \dq2 dqj + -Qi| (43). Equations (41) show that if we modify the expression T to T' by substituting in it the values of sv s2, ... . given by (27) and then write rnV rrv 1 JL ^1^1 ^0^2 . * • • we can use T " to obtain the equations of motion for the co-ordinates qv q2, .... , qk for a holonomous system by the ordinary process. Equa- tions (43) show that the so-called gyrostatic terms flow from the added expression — c1s1 — c2s2 — . In equations (35) these added terms are dispensed with, and the equations are applicable to all kinds of systems. 339 1908-9.] On Lagrange’s Equations of Motion. 19. As a first and very simple example, we take the motion of a particle of mass m in a plane curve. If at time t the radius- vector drawn from a fixed point be of length r, and make an angle d with an axis of x drawn from the same origin, the co-ordinates of the particle are x = r cos 0 , y = r sin 6. Hence for the kinetic energy T we have 2T = m{(r cos 0 - rd sin d)2 + (r sin d 4- rd cos d)2) . . (41), or 2T = m(r2 + r2d2) ..... (45). In applying (13) to the problem of finding the r, 6, equations of motion of the particle, we have to take the first expression for the kinetic energy. We obtain d 3T By (13) we have to subtract from this m(r cos d — rd sin 0)— (cos 6) + m(f sin 6 -\-r0 cos 0)-^(sin 0) ; dt dt d that is, mrd2. The same result would, of course, be obtained by calculating 0T /dr. Hence the r-equation of motion is m{r — r6 2) = K ; where It is the applied force in the outward direction along r. For the d-equation we have d 0T dt dd + 2 rfd). By (13) we have to subtract from this d • d - m(r cos d - rd sin 6) — {r sin 6) + m(r sin 6 + rd cos d)~(r cos 6) v 'dt dV or zero, thus the d-equation of motion is m(r2d -1- 2 rfd) — © ; where 0 is the applied force perpendicular to the radius- vector. This method, if it had been applied to the value of T in (45), would have failed. T is here a sum of squares referred to a set of axes so specialised that in the formation of T the quantities cos d, sin d have taken the special values 1 and 0 ; and unless we go back to the fundamental expressions, for the velocities along the unspecialised axes Ox, O y, it is not apparent how the process is to be carried out. It will be observed that from (44) we have 3 / n\ 3 / —(cos 6) = - — (r sin 00v ’ dr -L(sin d) = ^-(r cos d) dd ’ dr ' 340 Proceedings of the Royal Society of Edinburgh. [Sess. so that the integrability conditions are fulfilled. Thus it is possible to proceed in the ordinary way by calculating dT/dr and subtracting it from mr. The function of r involved in (44) and (45) is the same, and so in the latter case the ordinary process remains applicable, though then, appar- ently, the integrability conditions seem unfulfilled. This explains why in many cases, e.g. in the next example, when specialised axes are taken, the ordinary method is applicable, while the other, set forth in § 9 above, is not. The latter can only be applied when the values of u, v, . . . . are perfectly general. 20. As a first example we take the gyrostatic pendulum problem referred to above. The pendulum as ordinarily made is a rigid body symmetrical about a longitudinal axis, and containing a fiy- wheel with its axis of rotation along the axis of symmetry. The suspension is by a Hookes joint, or by means of a piece of steel wire so short that it may be taken as untwistable, while yielding equally freely to bending forces in all vertical planes containing the wire. Let 6 be the inclination of the axis of symmetry to the vertical, (p the angle which the vertical plane through this axis makes with a fixed plane through the vertical containing the point of support, \js the angle which a plane containing the axis of the fly-wheel, and fixed in the wheel, makes with an axial plane fixed in the pendulum. We shall not suppose in the first instance that the pendulum, apart from the fly-wheel, is symmetrical, but take C as its moment of inertia about the axis of the wheel, which we shall suppose to be a principal axis of moment of inertia, and A and B as the other two principal axes for the point of support. We shall also denote the moment of inertia of the fly-wheel about its axis by C', and its moment of inertia about any axis at right angles to this through the point of sup- port by A'. It is easy to show that the angular velocity of the pendulum (apart from the fly-wheel) about the axis of symmetry is — <^>(l-cos0). That of the fly-wheel about the same axis is \js — ^)}] + \™{y{py - qx) + y(py+py - qx))] + similar expressions for fly-wheel .... (48) From this we have to subtract, according to (13) above, 3[m{ - z(rx - pz) + y(py - qx)) J + S[m'{ z(r'x -pz')+y(py' 342 Proceedings of the Poyal Society of Edinburgh. [Sess. With the substitutions y =rx—pz, z = rpy — qx, y — rx' —pzf, z =pyr — qx', B q = ^Z{m(xz — zx)} , A'q = 2 { m(x'z — zx) } , the result becomes (A + A ')p - (?> - C + A' - C')qr + C q(r' - r). This is to be equated to the moment L of external forces round the axis of A. Hence we get (A + A')p-(B + A' -C-C’)qr + C'q(r -r) = L . . (49). If now we suppose the angle

(1 — cos0) for r, \[s — <£(1 — cos 0) for f, we get the 0-equation of motion. Similarly the other equations can be obtained. If we suppose the pendulum to be symmetrical about the axis of the fly-wheel, (49) becomes, with the above substitutions, AO - {(C + C,)(l - cos 0) sin 0 + A sin 0 cos 0}4>2 + C' sin 6if/

Sx1 = - ySx, Syx = y cot . Sx. (2) Due to the alteration of 0 we have Sx2 — - a sin 0 cos . SO, Sy2 = - a sin 0 sin cf> . SO, Sz — a cos 6S6 . 344 Proceedings of the Royal Society of Edinburgh. [Sess. Combining these, we get x— — a(\j/ + cos 0) sin . 0 \ y = a(ij/ + cos 0) cos cf) - a sin 0 sin . 0 f . . . (53), z = a cos 0.0 / which are the kineftiatical conditions. The kinetic energy of the motion of the centroid is Tc = \ m(x 2 + y2 + z2) = sin 0 cos . 6 + cos 0 sin + sin . \j/)2 + ( - sin 0 sin <£ . 6 + cos 0 cos . cj> + cos c j> . if/)2 + cos2 0 . #2] (54). This reduces to Tc = fyna2(62 + cos2 0 . 2 + ^2 + 2 cos 0 . 2 sin2 0) + C(xf/ + cos 0)2} . . . (55); where C is the moment of inertia of the body about its axis of symmetry, and A that about any other axis at right angles to the axis of symmetry and passing through the centroid. Then T = T(. + Tr (56). 27. It will be seen from an examination of the expression for Tc above, that the integrability conditions are fulfilled as between 0 and cp, and 6 and \fs. As regards Tr the relative co-ordinates are integral functions of 6, cp, \fr ; and the ordinary methods apply. Hence the 0-equation for the hoop or disk can be found in the ordinary way by the equation d 0T 0T 0V — — T - — . . . . . (57) : dtdO dO dO where V ( = mga sin 0) is the potential energy. The

) - 2/^(cos o cos cf)) } =0 at c

\ , • d, , x I A dtU+ma\xdt{sm^+yjfcos^ } since dTr/d\Js — 0. The last two equations may be written out in full by the reader. The ^-equation reduces to d 0T o • a a I a r - ma - sm 6 . 6

2 sin 0 cos 0 + (C + wa2)^ sin 6 = - mga cos 0 (59). 345 1908-9.] On Lagrange’s Equations of Motion. 28. The last equation is written down for the sake of the comparison of the Lagrangian method, modified or not, with the following elementary, and I think instructive, method of solving gyrostatic and other rotational problems. It depends on the single principle, which can be demonstrated in a moment, that if a directed quantity L be associated with an axis, OA say, which is turning towards a second axis, OB say, at right angles to the first, with angular velocity w, there is, as a consequence, a rate of growth of the quantity in the direction OB of amount Lw. If there is already associated with this second direction, at the instant considered, a component of the same quantity M, which is changing at rate M, the total rate of growth of the vector associated with the instantaneous direction of OB is M + Lco. [It is to be understood that M is taken following the direction OB as that revolves keeping itself at right angles to OA.] This, of course, is a particular case of the proposition that if Lx = Lx cos Q1 + L2 cos 02 + L3 cos d3, then 1bx — Lj cos 01 + L2 cos 02 + L3 cos 03 — L sin dj . 6X — . . . . But it forms by itself a simple rule, immediately evident, and applicable to all kinds of rotational problems. The simplest possible example of this is a particle of mass m moving in a circle of radius r with speed v. At a point P on the circle the particle has momentum mv in the forward direction along the tangent. But the tangential direction of motion of the particle is turning towards the radius at P with angular velocity v/r. Hence the rate of growth of momentum in the direction from P to the centre is mvv/r = mv2/r. If, as there may be, there are two different directions OA, perpendicular to one another and to OB, with which are associated directed quantities of the same kind L, L', and these are turning towards OB with angular velocities <*/, there will exist in consequence a rate of growth of the quantity along OB of amount Lco + LV in addition to M. 29. Now apply this principle to the problem of the hoop. Take axes through the point of contact P with the horizontal plane on 346 Proceedings of the Koyal Society of Edinburgh. [Sess. which the hoop rolls — one parallel to the axis of figure, one tangential to the hoop in the plane of rolling, and one at right angles to these through the centroid. These axes are represented by PC', PD', PE in the figure (p. 345). About PC' the angular velocity is \js + (p cos 0, and the angular momentum is (C + m sin 0 about PE there is a rate of growth (C A ma2)(\js (p cos 0)(p sin 0 of angular momentum about the instantaneous position of PD'. Again, in consequence of the turning with angular velocity cos 6 about PC' the axis PE is moving away from PD', and angular momentum about PD' is growing from this cause at rate — A2 sin 6 cos 6 + (C + ma2)(fxj/ sin 0 ; and this is equal to the moment of applied forces — mga cos 0, so that we get the same equation of motion as before [(59) above]. In the same manner the

+ C '{0 - 0(1 - cos $)}] sin 0 . Again, the axis OE is moving away from the instantaneous position of OD with angular velocity 0 cos d, and there is associated with OE, in this position, angular momentum A 0 sin d. Hence angular momentum about the instantaneous direction of OD is growing from this cause at rate — A 02 sin d cos d. From all these causes combined, the rate of growth of angular momentum about the fixed direction with which OD coincides at the instant is AO - { A cos 0 + (C + C')( 1 - cos 0) } sin 0 . 2 + C '00 sin 0 ; and this equated to L, the moment of the applied forces about OD, gives the d-equation of motion. It will be seen that this result agrees with (50) above. In precisely the same manner the other equations of motion of the pendulum could be obtained. It will be noticed that the terms which (apart from Ad) are obtained in these two examples from the motion of the axes are those contributed in the Lagrangian method by the term — dT/dO. This affords an interpretation of the term in question, and of corresponding terms in the equations of motion in other cases. [See also § 19.] 31. I may notice here the fact, which I have pointed out elsewhere, that this simple principle enables Euler’s equations of motion for a rigid body turning about a fixed point to be established intuitively and without analysis. Refer to principal axes passing through the fixed point and turning with the body. Let A, B, C, be the moments of inertia, and <*)]_, ft>2, O3, the angular velocities about these axes. Angular momentum is growing about the first axis at rate A d>1, in consequence of the rate of change of wr But as the body moves the third axis, about which the angular momentum is C co3, is turning towards the instantaneous position of the first with angular velocity w2 about the second, and hence angular momentum is growing about the first direction at rate Co )2a>3. Also the second axis, about which the angular momentum is B a>2, is turning away from the instantaneous position of the first owing to the turning with angular velocity o)3 about the third, and hence angular momentum is 348 Proceedings of the Royal Society of Edinburgh. [Sess. growing about the first direction at rate — Beoo(*)3. Thus, equating the total rate of growth of angular momentum about the first axis arising from these causes to the moment L of applied forces, we get Ao1 — (B — C)a>2 y1 = y + r1 sin 6 sin z1 = z + i\ cos 6 x2 = x + r2 sin 0 cos y2 = y + r2 sin 6 sin cf> z2 = z + r2 cos 6 , where miri = - m2r2 > L = m1 + m2 ’ - m1 r m2 + m2 ‘ 0 and (j) are the angular co-ordinates of the straight line AB. x1 = x + rl sin 0 cos + rl cos 0 cos cf)0 - r1 sin 6 sin , ij\ — V + L sin 0 sin + cos ^ siR ^ + 7\ sin 0 cos , z1=z + ?\ cos 0 -rl sin 00. x2, y2, and z2 are obtained similarly. 1908-9.] On Energy Accelerations and Partition of Energy. 351 The kinetic energy T = V\ 2 + y 2 + where = £(mi + m2)(^2 + y 2 + &) + ^"’2 + r 2^2 + 7’2 sin2 1 2 = + m2)(x 2 + ;?/2 + if2) + ^M(r2 + r202 + r2 sin2 Oft2) , M = mx + m2 The Force Function is specified as follows: — Let the interior force of the system be an attractive force between the masses, and let f(r) be the corresponding potential energy. The exterior forces are supposed due to the action of other molecules or to external disturbances ; if Vv zo) +Ar) • Forming Lagrange’s equations, we have (m1 + m£)x — - / , \- ov (?»1 + m2)y= - — / , \- 0 v {m1 + m2)z= - — M < r - r(02 + sin2 0(f)2) 1 MM - — (r20) - r sin 6 cos 02) i r dt J M d /■ si n 0 dt (r2 sin2 0(f)) = - 0V dx 0Y av 0Y or 1 0Y r 00 1 0Y r sin 0 d (1). (4) Let the assumption be made that for any given position of either of the particles all directions of translation of the molecule are equally probable. The actual motion is unknown, and we will apply the theory of pro- bability to the probable motion. Let us suppose that the probability that a particle is moving with a given velocity ux is equal to the probability that it is moving with the reverse velocity ; in other words, that the probability of uY lying between ux and u1Jrdu1 is equal to the probability of its lying between - -Uj and — u± — dnY in any direction. 352 Proceedings of the Royal Society of Edinburgh. [Sess. We have assumed, therefore, that the probability that the motion is along Ox is the same as the probability that the motion is along any other axis, and that all transverse velocities of either particle perpendicular to AB are equally probable. Let and x2 + y2 + z2 = u 2 r2Q2 _j_ r2 gin2 0^2 _ g2 . then, using square brackets to denote mean values, we have O2] = |>2] = [i2] = J|>2] and [r2#2] = [r2 sin2 62] = h\q2 ] , where the mean values are formed according to the method laid down in Also we must clearly have L dt^x \ — 0, etc., and the mean values of the six momenta and the fifteen products of momenta taken two together all obviously vanish. The assumptions made, when interpreted physically, represent the property that the molecule under consideration is assumed to belong to an isotropic substance. Let similar assumptions be made with regard to the force. The functions T>1(a)1, yv sq) and $2(a32, Vv z%) are constantly changing owing to the motions of the molecules, and it will be necessary to finally express our results in terms of the mean values of the differential coefficients of these functions with respect to the ’co-ordinates of the points. Let us assume that our external field of force is an equally probable one ; in other words, that the probability that the force has a certain value is the same as the probability that it has the reverse value, and that the probable force in one direction is equal to the probable force in another direction ; so that = 0, and since the axes might be taken in any directions, 0 also 021" _0aq2J L dj/]2 02] " 3x^iyY_ but 022 . 0aq ’ dx2_ 4= 0 necessarily. 1908-9.] On Energy Accelerations and Partition of Energy. 353 Similar relations are, of course, true for d?2(a32, Vv zz)’ and fhe mean values of 1 1 and clearly vanish. dx1 dy1 ox 2 dy 2 Also but -0Y dr _ ~/0V\2" ~/0Y \2~ ~A> _w _ A dy) - A dzJ _ [02Y1 r 02y_ r02vi _ dx2 _ Ay1] Jdl1 J 02V~ _dxdy_ = 0, 02V _d0d(p 4=0 in general, although = 0, 02 V dxdO = 0 , etc., 0Y' -dx and the other mean force com- ponents vanish. (5) Let us form what Dr Bryan calls the accelerations of the energy components in the Arch. Neerlandaises to which I have referred. From Lagrange s equations we obtain jt\ b(nh + m2)x2 Differentiating again with respect to the time, we have £ { «•»! + { £ f ' - 4© ’ where ) represents the total change due to the motion of the particles and the variation of the field ; and thus d /0 Y\ dt\dx J 00.0 .0 .0 A 0 ■ AJ ^ \0Y — + x— +y + z — + r — + rtf — + r sin 0 — 7 — - — — , dt dx dy dz dr rdO r sm Odcfi/dx where — represents the part due to the variation of the field alone. As, dt however, we are considering a statistically stationary state, positive and negative values of g^(g-") are equally probable independently of the value of x, and consistently with our assumed conditions the mean value of this term is to be put equal to zero. Therefore, taking mean values, we have in accordance with our assumptions d2 i / \ . o jpU™l+m2)X 1 /0Y\2 - r £c2i -02V- ml 4 m0 i\dx ) J j _ dx1 _ ■ (2), and the corresponding equations in y and 0 will give the same result. vol. xxix. 23 354 Proceedings of the Royal Society of Edinburgh. Also, from Lagrange’s equations [Sess. i dt Mr2 } — Mrf(82 + sin2 62) .dV % Therefore ~2{hr2) = rr(0 2 + sin2 (92) + r2(02 + sin2 04> 2) + 2 rr(00 + sin2 + sin 0 cos 66(f>2) 10V.. f( 0 0V .02V . S2V . 02V M 0r JV1\0£ 0?’ 0r2 r000r rsm Odcfidr . 02V . 02V .02Y + x + y + 1 dxdr ' dydr 0z0r = { r(^'2 + sin'- } ^ - 3r2( ft + sin2 6ft) - £ + 2 . A 0V 2 . . 1 0V - —r u- — - —r smM — . . M r 06* M sin 6* d Taking mean values, we have v/2 M2 + [r2(02 -1- sin2 $cjj>2)2] - 3[r2(d2 + sin2 02)] - ^ •>■2 02 V dr2 _2 M r(62 + sin2 $2)— dr The Lagrangian equations referring to the angular co-ordinates will now be considered. We have M-(l sin2 6 ft) = - 2rf.P - M<£2— (r2 sin2 0). dr . d dr Therefore M Y (r2 sin2 <9<^2) = - 2/ dt drf> dt 2 Substituting in Lagrange’s equations for f, 0, and and simplifying, (d/2 . we obtain for M -^(r2 sin2 d<^2) the expression CLv d / 9-0 /1\0V 0 ; . ^ d( — — (r2 sim 61) -- - 2r sm 6* — — - 2 9 dt' dcf> r cftVrsi 0V r-1 site sin Odcf) 9 ( . .7 12 + A < — + M— (r2 sin2 0) > - 2r2 sin2 0M4 - 2r2 cos2 0M$22 Mr2 sm2 6 I 0<£ dt ) — 2Mr2— (r sin2 0) + 2 r2 sin 0 cos 0^ . dt dr dO 1908-9.] On Energy Accelerations and Partition of Energy. 355 Also we have — (r262) = - 2 rrO2 4- 2 r292 sin 0 cos 0- 2 - 2 AL , dV ’ MdO upon substituting for the accelerations from Lagrange’s equations, as before. Then ~(r2f?2) - - 2 r292 - 2rr0 2 - 4rr00 - 20‘I ~ dV ’ M dO M dt\dO + 2 sin 9 cos 64>2—(r29) + r2$(2 cos 2 $4>29 + 2 sin 204>cfi) . dr Substitute for r, etc., from Lagrange’s equations, as before, = 6™2 - 2^4 - *<«* e + + 2,^1 ^ + i i(5)2 8.,a0Y 1 4r . ^ /j,20Y ,0 .ajo ■ a n Q/jl d/dY\ 4 -r0— — - — sin 6 cos 9d>2 — - 12rrtf<£2 sin 6 cos 0 - 20— — ( — T i r dO M M ^ r0(9 Md/V067 - 4 cos 6^- + 2r2 sin2 6 cos2 . M Upon taking mean values, we have ‘ dt2 3[r2<92] — [?-2 A] — [(cos2 0 + 2 U2<92(/>2] + 1Y1. 1 /0Y\2' r2 V dOJ . and sin2 62) 1 M 1 |4] — [r2 cos2 $A2] — [r22 sin2 0] 4- M r2 sin2 0 0V' dr The three equations determining the mean accelerations of the energy components corresponding to r, , 0 are therefore W' dr " fJ2 _ /l;- dt 2 l M2 — ^ J 4- [r2(#2 + sin2 #2)2] — 3[r2($2 4- sin2 0 2)] 1_ M ' ,o02Y" rZ (J 2 a /j dt 2 (|r2 sin2 Ocfi2) 1_ M r2 sin2 6(j>2 — . 1 0 0Y r sin 6 d(ft\r sin 6dJ _ dr2 1 2_ M d df + M2 rdr 0 V \2 (3) + 3[r22 sin2 0] + 3[r2A cos2 #<£2] - [?’2 sin2 r sin <90<^> 2 df J rdr (U d2 dt 2 „(ir26»2) = 3[r2 A] — [r2 A] — [(cos2 0 4- 2)r2A2] 4- 1 1 + [r2 sin2 6 cos2 0<£4] M M2 orn 0 ( 0 V \ 1 0V\2' ,2(92 " Ll 4 rdOYrdOJ 2M T , df~ rdr (5). 356 Proceedings of the Boyal Society of Edinburgh. [Sess. (6) In accordance with the assumptions laid down, the last two equations must be exactly the same. Expressing this condition, we have 3[r2 cos2 002cj> 2] — [r2 sin2 #4] = [r2 sin2 0 cos2 (94 } - [(cos2 0 + 2 )r2#22] - [r2#4] In order to evaluate these mean values, let us put (6). Then Now q cos i(/ = rO q sin t f/ — r sin 6

2 sin2 <9] — 9. t- sin2 1 1/ cos^ if/ if* £ sin2 2i b 4r2 T 2n [sin2 2ifA = — / sin2 2i J/difr = \ . 2 7TJ (7). Likewise and [?‘26,22 sin2 ff\ = -g- r •v*2 [r2 sin4 #4] = | t’-2^4] = f T 2tt for these depend merely on the evaluation of j sin4 \Jsd\/s and j cos4 \fsd\js. By differentiating the equations (7), squaring and adding, and using the relation (6), we can obtain also the relations and \r202(f>'2] = Ty [r2 sin2 04> 41 _5_ 1 6 v \ r2 _r2 _ , (8) but these relations will not be required. Yd2 (7) Expressions such as — (rr&) -til and L^V2 sin when evaluated are found to all vanish identically in accordance with the hypotheses. Now let ds2 — r2d02-\-r2 sin2 0d(p2, so that ds is a small element of length perpendicular to the straight line AB ; and let us add together both sides of equations (4) and (5). 1903-9.] On Energy Accelerations and Partition of Energy. 357 We obtain J? \(r2d2 + r2 sin2 0&) + 1 M 2 M2 r*(P—( '0Y \ riO fo) ) -f r2 sin2 Of 0Y r sin 0dcf>\r sin 0dcf)/_ av _y avy v sin ' \rdO ) - [r2 sin4 0f~\ — [r2#4] + ^ + 3 2df rdr ;.2 —{f-Q2 + r2 sin2 622) - 2[r202(fi 2 sin2 #] or rj ^ i r ,a2v~ 1 r/0Y\2i (frl Upb M L2a?J + M2 LU)J + 3 ~ 9 L r J - 2[r202'2 sin2 0] - [r2 sin4 6^4] - [r2#4] + M q- or 2 M 02y- 0£2 + M2 + 3 ^2^.2 r ^2 1 + M < Z df rdr _ 2 df rdr Similarly we obtain ' d2 df (¥2) M* 70vy~ \0r7_ + T 2 -3 ^2^2 2 M 02Y~ 0r 2 2 M df rdr In accordance with our hypotheses we may suppose that x •2 0£2 . 0W “ 0r2 202Y r — 0S2 . = \x2~\ = m wi . 0X2 J ■0W" 0r2 _ -0W- _ 0S2 . , etc. (8) We liave thus obtained three equations which determine the mean energy acceleration components corresponding to translation, vibration, and rotation ; namely, d2 a 1 /0VY2 1 Tf2l ~02V (m1 + m2)2 _\dx) _ ml + ra2 _0X2_ 2 M2 1 M2 iypyi + cf -3 r r2 i %2 \0r / _r2 _ _r2 [©1 - “2' + 3 i i -s l s- to| to to 1 1 2 M ,902Y" i dr2 2 M T d£ rdr -k2l MLi J 0S2 + 1 M o df' r-y rdr (9)- The conditions for a stationary distribution require that the mean acceleration of energy shall vanish, just as in statics the conditions of equilibrium require that the accelerations of the bodies of the system shall vanish. 358 Proceedings of the Royal Society of Edinburgh. [Sess. The equations representing these conditions will be called equations of energy equilibrium, as in the Arch. Neerlandaises to which reference has been made. The equations of energy equilibrium are therefore /0V\2' Vc§ = (TOj + Wl2)[flS2] 02V dx2 /.2 -rAl *•2 1 M2 1 M djy dr) ' 202Y' 3 a? 1 " .<202V 2 " M . 0r2_ M [j 1 ~ (d\\2~ 1 " M2 _\ 0S / _ M _ df rdr _ 2 df rdr (10). j f)2\7- ;/2y 32y (9) In the case of a Newtonian field — 9 -f = 0, and therefore our assumptions would require that dx 2 dy2 dz 2 ~02Y~ 02V 02Y . 0a£_ M2- _ dz2 _ 0. The first of the equations of energy equilibrium shows that these assumptions ray- are impossible in this case, and likewise in the case where Adx2. is negative; so that we must exclude this latter case and that of a Newtonian external field of force. (10) It is next necessary to obtain expressions for We know that v = /VE(lj> V\> O + Vv %)+/W • Therefore, 0Y _ d% dx ^ldx ^2dx2 0Y 0$. 09 0Y 0$, 0<3>9 — Zfip, P'2 - CZ 0Z1 CZ2 ~02Y~ r/0V\2i _0a)2_ A 08/ - , etc. 0V __ df~ 0?" dr ni 1 ( ( 8$, 09\ . a , , , r,% ; osx 03>,\ , + ( m2/x1 — - ??? 1/x2 — ■ 4 j sin 61 sm 9 + ( m2ju,1 — ± - ??q/x0 — ^ ] cos 6 dyl S;/„/ 0^1 02f 0V _ rdO rn 1 { / 0$, 0<3>2\ , , , + m, H ‘"ay ^ , / 04>, 04>,\ a ■ , ( S'**, 0*>,\ ■ O + ( -1 - ) cos 0 sin - ( m.yy-— U - ) sin 61 ] 0Y 1 r sin Odcj) ml + ra. 0$, 0<$2\ • , + 1 mj + m2 0^1 0$9 , , m o/*,— J - m.Uo — * cos ‘ s2/i W 1908-9.] On Energy Accelerations and Partition of Energy. 359 02V „02$, S]4>o dx2 2 dx-^2 — = mijh J ( sin2 0 cos2 sin2 6 sin2 <£ 4- cos2 0 dr2 (mj + ro2)2 I S^2 fyj2 V g2^ _ _ j 4- terms of the type 2 h sin $ cos 0 sin > 023v 02<|»f m >2 j sin2 ?'l + m2)2 * ^22 + terms which vanish when the mean values are taken J- 4- m1>2 in2 e 2 ^ + ^ sin2 e sin2 ^ + — 2 C0S2 0 (>»! + m2)2 1 0*/ 02/22 3%2 d-f dr ( 8V ] = maVi J gin2 ^ + COg2 _ 2 sin cos ^Y?1- 1 r sin Od 02U> sin2 ch — | + cos2 <£- — | - 2 sin cos $ 0.r92 0i/92 0^*i02/i 02<1>.> dx2dy2 } r + thUll ) cos + sin sin 0(m1 4- m2) ( dx{ dy1 d% dV2 ixr,m, ( ,0$o , . . — - — X-2 -1- < cos <£— -? + sill 0 r sin + m2) ( cx2 Therefore Now, if sin 0 cos (p — l, sin 0 sin

] = [sin2 0 sin2 ] = [ sin2 «/>] = J. If we take the mean values, we have, in accordance with our assumptions, 0Y~ _ R/~ _0r _ Ldr_ _\dx1 + y2z Y^k2- \dx< + 2/X|/X9 "03>i 0

2Y1 2ft71m2/x1/x2 \drj _ (nzj 4- w2)2 _\0x1 / (mj 4- m2)2 _ \0fC2 / _ (mj 4- m9)2_ 0$x 0$,. dXn dx 2-J 2 m^fji^2 r py! 2m2[x2 r yyh 4 m1m2fjL1ix2 0$! 0$2 (m1 + m2)2 _ \0a;1 / _ (m1 + m2)2 _\dx2J (m1 + m2)2 _0X1 0d?2_ pi). r^ii r 02i 7?7i 2/X2 rs^i 0S2 _ (Wj 4- m2)2 _0X12 _ (Wj + n?9)2 — i Cl d CP| 360 Proceedings of the Royal Society of Edinburgh. [Sess. It is also necessary to determine the mean values of the differential coefficients of V with respect to xv x2, yv y2, zv z2, in terms of the mean values of the coefficients with respect to x, y, z, r, 0, sin 0 cos dx Xi Xn - r\ • , /) -I y n r\ ^1 <3r sin 6 sin = Vi — -1A , cos 6 = — = ???., and dr x-. — x9 . n , rdO n , — — , — = — = sin V cos

, dx} nij 4- m2 dx1 r dxl r sin $d dx1 = - sin y> , Let us differentiate with respect to x1 and x2, and we easily obtain, upon taking mean values, the relations A*1 H Atl/>c2 03qx 2“ _ V dx , m-, (% + ^2)5 2 avy 0j;/ (rax + ra2)s 0Y\2' dx) 0$1 0<&2 _ dxY 0^2_i mxm2 70 vy AW + 1 ^ 3 _ 1 3 0vy- W . 0Y\2- 0r / W)' + ± + ir (S’: n 0vy 03/ + i Y-T \dr) dr 7VY \drJ (12). K + %)5 If the second differential coefficients be written down and mean values be taken, we have A1! fx2 02$x ??q2 p2vi ”02V” +i 02 V 1 d2f _ 0^x2_ (rax + ??i2)2 _0X2 _ _0r2 _ _ 0S2 _ 3 \_dr2\ m92 '02V” +l ”02Y” +§ ■02V” 1 ~d2f~ 1 r L0^2J (mi + ™»)2 dx2 _ L 0r2 J _ 0S2 _ 3 _dr2 (13). A 1 • Also, since - — -V — () ox2ox1 0 = m yn9 "0‘2 V" -02y- dr2 (mx + m9)2[_0x2 From (12) we obtain the relation m9/xp + ~d2/~ dr2 -02y- 0ss fd® A2 /0\2 / \ r0, 03> 1 _\0aJ1) _ — m-yx.2 _\W _ _0£1 0X2_ = 0 (14). (15) when the masses are unequal ; and using the equations (11) we have 0V\2" dx) m, + m9 „ 1 m1 — m2 dl ni-i -H m9 9 >2 _ \ 02’1/ J ?/q - m2 /0vy _ ... m2W r wi + »iW \ 0s / _ m12 — m22 L\0^1/ J wij2 — m22 03y2 dx.-) 0$, 0£o (16), when m1 4= m2. Also /0Y\2- \ 0r / df\2' dr, + h Ivy '08/ 1908-9.] On Energy Accelerations and Partition of Energy. 861 Again, using the equations (13) and (14), we have m2/q a2^ — 7?q/x2 P2^.2i mAm2 “02V_ _0a?12_ _0a?o2_ 711 j + 7772 0a?2 _ 02V~ 06'2 = (?>i1 + m2) when m1 4= m2 ; so that we have the important relation (17), -I “02V~ (77?! + 7779 ) 2 “02V~ L0a?2_ 77717772 _ 0S2 _ Also, from the equations (9), 02V- d2f + " 02V~ _dr2 _ _dr2 _ _"0S2~_ (18). (19). (11) The three equations of energy equilibrium finally take the forms [Xs] = m. m,2 - ni 02 . 2 A^i Lwj/ J - /V 7».W \dx2J _ J— 1 a. _0a?12_ 3 r2 9 t ( 777 2 + 7772\2 1 ! 02 0a;2 0a?r 3 T (m1 + 7?72) m2 + m2 2 .o02$ m]m2 dA2 ir/ '024>2 _ to:/2 _ _ 2(?^ + ??i2) ??21m2 9 df m1 + vie Ah 777-, 0a?!2. /A | ( 7 77- j “t- 7?79) ] /q 771! m1m2 7.^7. a^2' 0a?! , 7 77 2 777 2 ,2^2/ /h 7?72 ^r2J 0$, 04>, I 0a?2 0a?9_ /h " 2 0^1 77?! + 777 2 777x 0a*1‘2_ 777-, 777 2 1 A r ^ yi Ah 0$! 0$2 1 777! _\0a?1 / _ m0 _0a?i 0a-2_ 2/X1(»W1 + 7779) ( /q 777 2 777 9 I 777 x and these forms can be used in the case when the masses are equal. / 362 Proceedings of the Royal Society of Edinburgh. [Sess. Maxwell’s Law of Equipartition. (12) Maxwell’s Law of Partition of Kinetic Energy requires that, if the kinetic energy of the system be expressed as a sum of squares, the mean values of these squares taken over a large number of systems distributed according to a certain permanent or stationary law shall be equal. In the case of this system, the kinetic energy is equal to Mm, + mv)(x2 + y2 + z 2) + /.;-2 + r2 Q2 + r2 sjn2 5)^2 \ _ “ 1 *ml + m2 Therefore, since [r‘2&2] = [r2 sin2 Of2] = pq2] , it is necessary that (m1 + m2)[x 2] = 7n'm<2 [r2] = J [q2] m1 + m2 J m2 + m2 or (ml + m2)2[a?2] = m1m9[r2] = pn^mpq2] , if Maxwell’s Law of Partition holds good. In this case, the equations of energy equilibrium show that M2 dp 9r dr, M w O 1 1 2 df _\drj M __ rdr_ (mi mf)" r,;,‘21 1 3/q j I1 1 Wl /q 0 \02?1 ) J m2 _02?j 02?2 _ _ J_ (TO! + m2)2U21 M m1m2 L J dff dr 2 Vi 0% + y^2)2m.2-| ?rq L' J m1m2 ~02<1>1' _0aq2 _ = 0 MjA2] 3/q j /q dr ) _ M I TOj 0^1 02?-, _ /*2 ■0$T 0A2i , r 0^1 0^2 0q)j+fti or vy dr) 3 /q/q jU., 0$1 0$ m2L02?i 02?, ^ 0$ L02?2 02? 03q 0$2"| ( f02$] 02?x2 _ 02~ _dxj dx2_ Therefore, since the square of a real quantity is necessarily positive, /V fSfiV L\ cxj J + /q /q ~01 02" _ 0./q dx2 __ is essentially positive ; so that, if Maxwell’s Law holds good, the condition for equipartition of energy which has been obtained shows that m _ \ drj 2_ 2 /x | ji.) 0<1>1 02 _ 0Z‘] dx0_ (Pf 2 (If _ dr 2 r dr_ must be positive, in the case when the denominator does not vanish. (13) In the general case, when the masses are unequal and when Maxwell’s Law may or may not hold good, our investigations give at once certain simple inequalities. It does not matter which is the greater of the two masses ; let us suppose that mx > m2. It has been shown that and 70YV A dx) 0vy ds) ml + m2 ml - m2 9 ° TlX-y fXtT) Ml' _\0X1 q2‘ 9_ \0£Cc m-^ — m^[_\dx2J 0 /q>“ /0^_y^ _ V dXn, o _\ds J L\0^/ J m2 _01 02" l_0,r1 dx2_i >0. >0 Stability in the General Case. (14) In discussing the stability of the energy equilibrium let us first consider the translational mean energy. Let [i*2] = T„ + « . where T0 is a third of the mean translational kinetic energy determined by the equation of energy equilibrium, and e is a small variation which may be due to initial disturbance. We thus obtain, by substituting in equations (9), e = — 02V ml + m2L0.r- For stability the variations in e must be periodic, and this condition is W satisfied if dx2_ is positive ; and this is precisely what has been assumed, in order that our hypotheses may allow energy equilibrium to be possible. The term involving [g4] in the equations of energy equilibrium makes it very difficult, at any rate, to deal with the question of stability in the general case, as far as the mean vibrational and rotational kinetic energies are concerned. Let us consider, however, the question of stability, when we suppose Maxwell’s Law to hold good. From the equations which give the average energy accelerations it is clear that ~i(g2+r2) M2 0Y\2 /0V\2' dr) +\ds) 1 7 1 M2 \dr) _ M a M 2 df ' rdr ' 9 02V , .,02V" a'aF + r a? + 2M2 1 M 1_ M df rdr dr 2 1908-9.] On Energy Accelerations and Partition of Energy. 365 If Maxwell’s Law holds good, we have 3 d2 r/1 2X1 1 2 dt2^2^ _ M2 df_ y dr) 2M '02Y IP] i M 2M fe2] ~d?f dr 2 E2] ~ d£ 3 -4- /0V\2 _rdr_ 2M2 i\ds) J (23). Let [J^2] = P + ^ j where T2 corresponds to energy equilibrium, and is a small variation in the rotational kinetic energy. Then V 2 df 3M + — + 0.s2 dr 2 7- dr For stability it is necessary that the average value of 3ajY + xy + 2 # 0s2 dr2 r dr should be positive. Now, since ~02Y_ ??q?7?2 02W Las2] (ml + ?a2)2 _0X2_ .0s2. must be positive; for our assumptions require that -02y- 0a:2 should be positive. The question of stability will be considered in particular examples. In the general case, suppose that we put JM = T1 + ^ ib2] = T2 + % and fc4] = fe4]„ + f > where [g4]0 is the value of [q4] corresponding to energy equilibrium, and t, = m0 ' tWk2J„ with the corresponding rotation. We have the equations and d2 iy.2 dt22 J 1 M2 i i ^ 1 to 1 1 + (f~ _r2_ - 3 r *9 9~ 1 r*qz 1 M Ao02V1 dr2 _ 2 M > df 1 A rdr_ d\ 2“ dgE. 1 “M2 ~/0Y\2 \0S / - X4 2*2 + 3 f2q2 7 ‘2 . 1 M r 202V~ i + M 2 df q 2 rdr Now [>¥] = [r2] [T2 11 P?2 M £w 0S2 + M^2 df_ 1 It is next necessary to evaluate We know that [g2] = 2 [r2#2] . Now r2#2 = {r202}o + e2 , suppose, where e2 is small, and {r2d2}0 denotes a value of r20'2 corresponding to energy equilibrium ; so that, if we take mean values, 7/2 = W* Squaring both sides of the above relation, we have r404 _ }0 + 2e2{r2#2}, and when we take mean values this becomes [r4#4] = [r4#4]0 + 2?72T2 or for we have proved that so that whence We thus have ' 1_L- 12T t[24] = tfe4]o + 2%T2. [»"b4] = lb4] ; b4] = b4lo + Tr>72T2 > £=-VVb . r, =ilT 71 3 x2 r- r- *• = -¥T2 % 1 V2 + ^2-12T2 r/2+ 12T2 1 _02V' 0r2 M (if 1 *?i %2 M 02y" 0S2 + %2 M rdr df rdr The energy equilibrium is stable, if the equation L2- 12 I 2 1 ^2 1 2T0 ~r ^2 2_ M W"| x 3r2 J ’ dr2 , i>2-¥'b 6 T> 3 L2 /y*Z 12 T, £ M rdr 1 + 12Tn 1" 0 -j 02V + 1 df ry* 2 1 y>2 M _ 0S2 _ M _rdr_ 0 . (24), treated as a quadratic in p2, lias positive roots. 1908-9.] On Energy Accelerations and Partition of Energy. 367 This requires two complicated conditions, namely, that 6Tf + 1 and M - 3T 5 2T 3 X 2 W W1 f {fTs ry*L J l fi rp \ 4 If - 6T, - 12Tj rl o*2 + M 4_ M W' . 0s2 _ ~d£ rdr 1 M 'j\2 + 0<^ 0$7 / 1 i - 'si 2 - _0Zj 0a?2 _ _\0.r1 y )2 _ 0£, S*2- 0aq 0^2 2 m 0^T _0iC|2 _ r2 < 4 m d£ dr - - M m 'ddf dr 2 m fe2] d£ rdr — lL [r2] m 02$! +24 i/3£1y + a$i »2" _0^]2 _ mA _\0.r1 / 0aq 0x2 _ — — [22] 023>T CU f :L 1 1 v + 3_5i ™s] - - [, 0ro 023q = fX /0<£>A2 0^ 0<3>2 -dy^zdf- _ _dx)2 _ _ \0x1 / 0aq 0£2 _ _dr 2 r dr _ (26). 368 Proceedings of the Royal Society of Edinburgh. [Sess. The Law of the Inverse Square. (16) The case will now be considered in which the law of force between the particles is that of the inverse square of the distance. Let f(r) = — — where X is a constant. /y* ' Then dj \ dr d?[_ ~dr 2 2A so that and r t7/i = A :i ~ ryyi = A2 _rdr_ _r3_ LW; _ _r4_ ri2/ = - 2A 1 _dr2_ — i CO 1 The equations of energy equilibrium become [U = /^i 7— Y2- _\0(T1 / _ + /x2 rd&, i _0^! dx2 _ (?/?! + m2) 02$1 _0iC12 _ \ r2 r rL T r2 X2 M2 r4 2Ar - m[2 ] + 2hM > (27) III n r vqp^1 I /q j Ah Lory J M ] wq 0<£p 2' _\0£C1 / _ /y ??2n 0^ 0$2 0aq 0cc2_, = ^T//2! 7/0 0-1 i_0aq2_, “ /xi ) Aq M I m. V 0xy _ Ah //io '0^ 0^ l_0Z12_J - I *[©' + /U 0^3 0^2 _0.r1 0x2_ t_zy 2 df dr 2 r dr Now, in this case a2^ d2f 2 #• —, + - — 0, a/,ij r ar and Lda;p simply cannot vanish ; so that the condition for equipartition becomes dfV dr J 3/X]^X2 01 0^>2 _dx1 dx2_ 1908-9.] On Energy Accelerations and Partition of Energy. 369 If ^1^2 good. d$j jm>2 ?Jx1 dx2. is negative, Maxwell’s Law cannot possibly hold In the special case when ju2 — — juv Maxwell’s Law cannot possibly hold good if 0dy2 _dx1 dx2_i cannot hold good if is positive; and in the case when the Law m1 m2 — - -v-‘ 1 is negative. -OX1 ox2 J In considering the question of stability in the case when Maxwell’s Law rp)2y- liolds good, we obtained a condition that 3 ds2 J + d2f 2 df 7> ' ~ should be positive ; this becomes a condition that condition is satisfied. -02 y L ds2 J dr2 r dr_ should be positive ; and this The Law of the Direct Distance. (17) Let the law of force between the particles be supposed now to be that of the direct distance. Let f(r) = b\r2. Then We obtain at once df d2f . 1 ( df\2 0 „ -4-=A> = and ( -f- ) =A2^2 rdr dr 1 \drJ whence 0V\2' ds) - [q2 + r2] '02V' 0^ -X[^ + 22] = o Also we must have A2[r2] + ? 'N u> [ ec co 1 _1 9“ M | A + ~02V~ 1 La*2 J 02] = ~(dV\ \dxj 2 ~ ifh + ™2) a2v _dx2_ These equations may be written in the forms [x-2] = and I1 1 ©)■] + A2 a$j a$2 _a.x] ax2 _ + w2) a2^ _a^2_ [ <1 2 + r2] = '04>A2 At W(S mi l1 2 ~d$>x aO m1 _\dx1J _ m2 _0aq dx2_ / (30). The condition that Maxwell’s Law should hold good becomes in this case A2[r2] - 3/q^2 01 02" . ?)Xl CX.2_ SV 0-Tj2 3A Pi \ox1/ J + /X2 0$! 0$2 _0aq dx2_ which may also be put in the form 02$ _ _ — 3ytq 0^y Lva^ 3fXr, '0$! 0^>2 dxl dx2_ ) A + 023> 0^x2 J J u o • (31). Now, it has been shown that if Maxwell’s Law holds good, it is necessary that i I ^ rS 2_ Splp2 0

2 _dxx dx2_ d\f 2 df __dr 2 r dr _ should be positive. In this case, therefore, A[r2] 0 1 1 i PP i ~d2Y~ L 062 J M rA , 02a~i ds2 _ AB 1 M 2M2 w (32), (33); it is much simpler to use these expressions than the corresponding ones for [ q 2] and [g4] . 3 r/0v\2' W\2’ ds) _ + A2 - ABM = 2 LV 06' ) + A2 - M2 0Y\2 ds) J + A2 - A i - A Y" a M/ My2\2 0V\2" ds) a ) and this is a positive quantity, if we suppose that A and a are of the same sign. 1908-9.] On Energy Accelerations and Partition of Energy. 373 1 It is necessary that AB should he greater than 2M 0V\2 ds) J in order that energy equilibrium may be possible, if the hypotheses are justifiable. Let us consider the question of stability. From the equations which we have obtained for the general case S^2+'2) 1_ M2 dr) 1_ M T ,df rdr + 1 M dr 2 1 _ _^2 + r2] 2M2 02Y" 0S2 avy ds) so that in this case la2 3 (d Y\2 J "2M2 _ V 0s / _ A;2 AB__A[- 2]_2[ 2] M2 M M au ] Mu J '02Y' ds2 Let [ A q2] = T0 + >7, where T0 is the value of [Jg2] corresponding to energy equilibrium, and is a small variation in it. Then "02 V IP , 2 f A , v + — < — + M I a = 0. must be positive. This condition is necessarily For stability — + a L . satisfied if we suppose that A and a are of the same sign. (19) The case where the external force follows the law of proportion of mass to weight. — In this case the equations of energy equilibrium are scarcely simplified, but we have the following relations, if we suppose that = P*=k:— m1 m2 m , _ \ dx^ / _ - Vic 70A2 + m dx. - m( 0$x 0^>2 _ dxY dx2 d% _dx1 dx2 0$] 0$2_ U0.r1 dx2_ 023»1 Jdxf _ _dx2_ and "a*v" dx2 _ ~02Y~ k(ml + m2) 02^ _dxf _ lcmgn2 r02$1 _ ds2 _ ml + m2 \_dxf_ (34). 374 Proceedings of the Royal Society of Edinburgh. [Sess. The following inequalities must hold good : — m n2 r pah > m J i — i 1 \dxj _ A _\dx2J and 03q dxY p, y < > d%V~ dx2/ _j d&j 0<£2 _dx1 dx2_ ran /0# ,\21 r00, where it is supposed, for convenience, that m1 is the greater of the two masses. Conclusions. (20) A purely dynamical problem has been considered, which may throw additional light on the theory of gas molecules. Equations have been obtained which should determine the law of partition of energy for a system composed of two attracting particles moving in any field of force, when certain hypotheses concerning the probable motion have been made ; these hypotheses require that the mean value of V2V should be positive, where V is the potential energy due to all the forces of the system ; so that the field has been assumed not to be a Newtonian field. There are three such equations, which I have called, for obvious reasons, the equations of translation, vibration, and rotation. From these equations I have, by equating to zero the three component mean energy accelerations, obtained three equations of energy equilibrium — in other words, equations which should determine the mean values of the squares of the velocities of the system corresponding to a stationary state ; but a term involving the mean value of the square of what I have called the rotational energy appears to be an unfortunate hindrance to the work in the general case. A condition has been obtained that Maxwell’s Law of Equipartition of energy should hold good, but there is apparently no reason why it should be satisfied. This condition is quite independent of the masses of the particles, and becomes a very simple one when the law of force between the particles is that of the inverse square of the distance. In none of the special cases considered is equipartition found to necessarily exist ; and in the particular case in which the attraction between the particles offers very great resistance to any variation of the distance between them the Law cannot possibly hold good. 1908-9.] On Energy Accelerations and Partition of Energy. 375 The stability of the energy equilibrium has been investigated. There should be three conditions for stability, corresponding to the three equations of translation, vibration, and rotation. The condition corresponding to the mean translational energy is very simply obtained, and is necessarily satisfied ; but the other two conditions are so complicated as to be apparently useless. In certain special cases, a second simple stability condition has been obtained, i.e. in the case in which Maxwell’s Law holds good ; when the law of force between the particles is that of the direct distance, this second condition is found to be necessarily satisfied if the hypotheses are justifiable. (. Issued separately May 15, 1909.) 376 Proceedings of the Poyal Society of Edinburgh. [Sess. XXI. — The Systematic Motions of the Stars. (Second Paper.) By Professor Dyson. (MS. received February 16, 1909. Head March 1, 1909.) 1. In a previous paper * the hypothesis propounded by Kapteyn that the stars are moving in two streams was examined by considering the proper motions of stars which were moving more than 20" a century. By a graphical method the directions of these two streams were found with results in fair agreement with those found by Kapteyn and Eddington by other methods and with different material. It was evident from that paper that it would be possible in a large percentage of cases to say with tolerable certainty to which stream individual stars of large proper motion belonged. The most satisfactory way of doing this seemed to be to compare P the direction of each star’s proper motion with the direction of the two streams already determined. Thus, in the diagram, if P be the north pole, S the position of any star, A the direction of Stream I, B that of Stream II, and ST the direction of a star’s proper motion, the nearness of ST to SA or SB furnishes a criterion as to whether the star belongs to Stream I or Stream II. The determination of the angles PSA and PSB was made with very great ease by Mr W. B. Blaikie’s beautiful device for solving spherical triangles. In each case SA and SB were also determined. Although Mr * Proc. Royal Soc. Edin ., vol. xxviii. pp. 231-238. 377 1908-9.] The Systematic Motions of the Stars. Blaikie’s “ spherical slide rule ” admits of more accuracy, these angles were only determined to the nearest degree. 2. The material used differs slightly from that of the former paper. The proper motions of Professor Porter’s Catalogues, Nos. 13 and 14 of the Cincinnati Observatory Publications, were substituted for those of No. 12. Additional proper motions were obtained from two papers by Dr Ristenpart in the Astronomische Nachrichten, Nos. 4245 and 4276, and from a list of proper motions of the stars observed by Carrington, determined at Green- wich, and published in the Monthly Notices of the Royal Astronomical Society , vol. lxviii. p. 48, and a few from other sources. To facilitate arrangement of the stars in different groups a card catalogue was made. 3. In order to show clearly the method pursued, a table is given of the stars whose proper motion equals or exceeds 100" a century. For each star the name, magnitude, type of spectrum, and approximate R.A. and Dec. for 1900 are given. The magnitudes are taken from the “ Revised Harvard Photometry ” (vol. 1., Harvard Annals), the “ Harvard Photometry ” (vol. xiv.), or the “ Harvard Photometric Durchmusterung ” (vol. xlv.), in the order given. The magnitudes of fainter stars are mainly derived from the Catalogues of the Astronomische Gesellschaft and the Cape Catalogue of Astrographic Reference Stars. The type of spectrum is obtained from the “ Revised Harvard Photometry ” or the “ Draper ” Catalogue. The amount and direction of the centennial proper motion are next given ; then the angle AST (positive when PSA > PST) and the angle SA under the headings A, a ; then the angles BST and SB. The assumed positions of A and B are — A . R.A. 90° Dec. - 10° ) B . . . 255° „ -60° i These agree closely with the mean of the positions determined by Kapteyn, Eddington, and myself, and quoted at the end of my previous paper. [Table. 378 Proceedings of the Royal Society of Edinburgh. [Sess Table showing Divergence of Stars of p.m. > 100" from the Directions of the two Streams. Type Approx. No. Name of Star. Mag. of Proper A. a. B. b. Spec- Motion. trum. R.A. Dec. 1 Groomb. 34 8-3 h 0 m 13 + 43°5 285 o 82 + o 18 o 95 + 140 134 A 2 C Toucani 4-3 ii 0 15 -65-5 208 55 + 36 79 + 168 34 A 3 13 Hydri 2-9 ii 0 21 -77-8 225 82 + 5 79 + 151 36 A 4 Lac. 147 5-7 ii 0 32 -25*3 139 90 + 6 78 + 118 79 A 5 Cordoba 617 5-8 ii 0 36 -60-0 100 64 + 23 76 + 152 50 A 6 1? Cassiop. 3-8 ii 0 43 + 57-3 121 113 — 9 92 + 125 148 A 7 Lai. 1299 5*9 ii 0 43 + 4-8 135 147 — 46 80 + 60 98 •8 •2 8 fi Cassiop. 5 '4 ii 1 2 + 54-4 376 115 - 7 90 + 121 148 A 9 t Ceti 3*7 ii 1 39 - 16-5 194 296 + 157 63 - 93 93 Neiilier 10 Lac. 661 6*3 ii 2 6 -51*3 227 73 — 3 63 + 129 63 A 11 W.B. II. 95 8-8 • • • 2 9 - 1-7 100 95 + 6 58 + 106 110 A 12 S Triang. 5T ii 2 11 + 33-8 116 101 + 17 70 + 112 142 A 13 Piazzi II. 123 5 ’9 ii 2 32 + 6-4 234 57 + 50 54 + 143 119 A I 14 Lai. 5490 7-0 • • • 2 56 + 61 *3 102 137 — 3 80 + 127 165 A 15 i Persei 4-2 ii 3 2 + 49-2 132 94 + 38 71 + 132 160 A 16 £ Reticuli 5 '5 ii 3 16 - 63-0 146 64 — 16 60 + 132 55 A 17 e Eridani 4-3 ii 3 16 - 43-5 315 76 — 17 49 + 117 74 A 18 Lai. 6888-9 8-4 ... 3 40 + 41-2 134 154 — 14 61 + 53 157 A 19 Lai. 7443 8-4 . . . 3 56 + 35 0 222 128 + 14 54 + 70 153 A 20 40 Eridani 4-7 II 4 11 - 7-8 405 212 -114 28 - 25 112 B 21 W.B. IY. 1189 6-5 II 4 56 - 5-9 124 152 — 47 16 + 29 114 •2 •8 22 C. Ast. 1734 8-7 5 8 -45-0 880 130 - 108 36 + 49 75 B 23 W.B. Y. 592 8-5 • • • 5 26 - 3 7 224 162 — 36 11 + 13 116 Bl 24 -n- Mensse 5-7 II 5 45 -80-5 112 11 — 7 70 + 160 39 A 25 Cordoba 6886 8-5 ... 5 46 -70-2 130 344 + 20 60 - 172 49 A 26 a Canis Maj. -1-3 I 6 41 -16-6 131 203 + 100 12 - 36 100 B 27 aCanis Min. 0-5 II 7 34 + 5 ’5 124 213 + 24 28 - 53 118 •6 •4 28 Lac. 2957 5-4 II 7 42 -34-0 172 353 — 43 34 + 178 80 A 29 Lai. 15290 8*5 e • • 7 47 + 30-9 150 152 + 65 48 + 7 140 B 30 Lai. 15565 7-0 • ■ • 7 54 + 29-5 117 188 + 30 48 - 39 138 •8 •2 31 Lai. 16304 6-0 II 8 14 — 12-3 101 194 + 76 33 - 36 98 B 32 Lac. 3386 6-5 II 8 29 - 31 -2 133 303 — 9 41 - 147 79 A 33 Lai. F. 1384 8-5 ... 8 46 + 7P2 141 256 — 34 86 -162 155 A 34 Lai. F. 1457 6-7 II 9 8 + 53T 170 249 — 21 75 - 122 147 A 35 6 Ursse Maj. 3-3 II 9 26 + 52T 109 239 — 6 76 -109 144 A 36 W.B. IX. 154 9 ... 9 46 -1P8 198 143 + 123 53 + 9 89 B 37 Groomb. 1618 6-5 II 10 5 + 50-0 144 250 — 9 80 -116 138 A 38 Lai. 21185 7'5 • • • 10 58 + 36*7 473 187 + 66 84 - 43 121 B 39 Lai. 21258 8*5 ... 11 1 + 44-0 450 282 — 30 86 -141 127 A 40 O.A. (N) 11677 9T ... 11 15 + 66*4 309 274 — 18 95 - 147 142 A 41 Brad. 1584 6T II 11 30 - 33 3 109 321 - 55 78 -176 59 A 42 Lac. 4887 5-0 II 11 42 -39-9 155 285 — 19 79 - 143 52 A 43 Groomb. 1830 6*5 II 11 47 + 38-4 701 145 + 115 94 + 2 117 B 44 Lac. 4955 7*0 ... 11 53 — 27T 128 242 + 20 84 - 95 60 A 45 Ltd. 23223 8-0 ... 12 20 - 3-7 134 261 — 1 95 -110 77 A 46 43 Comae 4*3 II 13 7 + 28-4 118 319 — 50 109 - 165 100 A 47 61 Yirginis 4-8 II 13 13 - 17-8 151 225 + 30 104 - 74 58 A 48 Berlin 4999 8-8 ... 13 40 + 18'4 190 172 + 96 117 - 15 88 B 49 Lai. 25372 8*5 ... 13 41 + 15-4 230 129 + 128 117 + 28 85 B 50 a Bootis 0*2 II 14 11 + 19-7 228 209 + 62 123 - 49 87 B 1908-9.] The Systematic Motions of the Stars. 379 Table showing Divergence of Stars — continued. No. Name of Star. Mag. Type of Spec- trum. Approx. Proper Motion. A. a. B. b. E.A. Dec. h m o // o o o o 51 Berlin B. 5072-3 9-0 • • . 14 21 + 24T 140 143 + 132 126 + 18 90 B 52 a2 Centauri 0-2 II 14 33 -60*4 374 281 — 49 99 — 176 18 A 53 Lai. 27026 7-5 • . • 14 46 - 23'9 101 243 — 3 122 — 87 43 A 54 Piazzi XIV. 212 5-8 II 14 52 -21*0 200 148 + 93 125 + 10 45 B 55 Lai. F. 2544 7*5 ... 14 53 + 54-1 110 297 + 5 122 — 134 63 A 56 O.A. (N) 14320-2 9-3 ... 15 5 - 15-9 368 195 + 49 130 — 33 49 •5 •5 57 O.A. (N) 14318-9 8-8 ... 15 5 -16-0 373 195 + 47 129 — 34 49 •5 •5 58 Lai. 27744 7-0 ... 15 9 - i-o 145 248 + 7 136 — 83 63 A 59 C. Ast. 5545 5*7 II 15 5 -47-9 164 260 — 35 111 — 121 19 A 60 Lai. 28607 7 3 ... 15 38 -10-6 118 255 — 14 139 — 88 52 A 61 7 Serpent. 3-9 II 15 52 + 16-0 132 167 + 110 150 + 4 77 B 62 Lai. 30044-5 7 5 ... 16 26 + 4-4 144 199 + 57 157 — 24 65 B 63 Lai. 30694 7-5 ... 16 48 + 0-2 160 207 + 34 160 — 29 60 B 64 W.B. XVI. 906 8-0 ... 16 50 - 8-2 129 226 — 2 155 — 47 52 •7 •3 65 Lai. 31055 7-5 ... 17 0 - 4-9 148 221 + 4 159 — 41 55 *7 •3 66 A Ophiuchi 4-9 II 17 9 -26*5 124 204 - 4 142 - 21 33 67 Brad. 2179 6-7 II 17 10 -26*4 124 203 — 3 142 — 20 33 O A 68 Lac. 7215 5-9 II 17 12 -34-9 116 97 + 89 134 + 87 26 Neither 69 72 Herculis 5*4 II 17 17 + 32*6 105 173 + 161 155 + 9 92 B 70 W.B. XVII. 322 7-5 ... 17 21 + 2*2 135 207 + 23 168 — 24 62 •2 •8 71 O.A. (N) 17415 9-9 ... 17 38 + 68'4 132 197 + 157 121 — 11 128 B 72 70 Ophiuchi 41 II 18 0 + 2-5 113 167 + 13 173 + 21 65 B 73 P.M. 2164 8-7 ... 18 42 + 59-5 225 330 + 44 130 — 136 121 A 74 Munich (I) 1810 9-0 ... 18 53 + 5-8 125 190 — 80 166 + 5 69 B 75 a Draconis 4-9 II 19 33 + 69-5 184 164 138 129 + 41 135 B 76 Lac. 8267 6-0 II 19 56 -67*6 130 121 + 30 98 + 152 20 A 77 S Pavonis 3-6 II 19 59 -66*4 162 134 + 16 100 + 132 21 A 78 Lai. 38383 7-5 . 20 0 + 231 140 229 L58 148 — 28 91 B 79 Lac. 8362 5 3 II 20 4 -36-4 163 163 — 21 125 + 53 38 A 80 Lac. 8381 5*7 II 20 9 -27-3 130 110 + 26 131 + 101 46 A 81 O.A. (N) 20452 8-5 ... 20 18 -21-7 122 155 — 25 134 + 64 52 A 82 Lac. 8620 6’5 ... 20 51 -44-5 110 209 — 77 113 + 16 37 B 83 C.P.D. -34°, 8843 8-5 ... 20 56 -34-5 130 173 — 44 119 + 44 46 •7 •3 84 61 Cygni 5T II 21 2 + 38-3 521 52 + 16 130 + 156 110 A 85 Lac. 8760 7-5 ... 21 11 -39-3 343 252 125 113 — 32 44 B 86 W.B. XXL 502 9T ... 21 24 - 12-9 104 115 — 3 124 + 95 67 A 87 c Indi 4-8 II 21 56 - 57*2 470 123 — 1 97 + 131 37 A 88 7 Indi 5-4 II 22 16 -72-7 147 121 + 3 88 + 130 31 A 89 Lac. 9352 7-5 ... 22 59 -36-4 693 80 + 27 96 + 136 59 A 90 Brad. 3077 5-6 II 23 8 + 566 218 82 + 3 106 + 142 137 A 91 W.B. XXIII. 175 8-0 ... 23 12 - 14-4 129 201 — 98 99 + 10 79 B 92 O.A. (N.) 25685 6*6 II 23 27 + 58-6 109 86 + 3 102 + 145 140 A 93 Lai. 46650 8-5 ... 23 44 + 1-9 136 135 — 35 94 + 75 97 A 94 85 Pegasi 6-0 II 23 57 + 26-6 130 139 — 40 95 + 75 120 A 95 Cordoba 32416 8-5 ... 23 59 -37-9 623 113 15 84 + 99 65 A 380 Proceedings of the Boyal Society of Edinburgh. [Sess. 4. Inspection of the above table shows very clearly the preference in the apparent motions of the stars for the directions of the two apices A and B, and the extent to which they diverge from these directions. For example, Nos. 1-6, which are all at a considerable distance from A (95°, 79°, etc.), are all moving in directions not far from the direction of A, and in directions far from that of B. Nos. 20, 22, 36, etc., are similarly moving approximately towards B. Nos. 9 and 66 do not fall in either stream. No. 23 is taken as belonging to the second stream (moving towards B), as its distance from A is only 11°. There are a number of doubtful cases, such as No. 27. In the first instance doubtful cases were omitted, and the following tables formed giving the numbers, at various distances from the two apices A and B belonging to the two streams, which diverged 0°-10°, 10° -20°, etc., from the directions of the two streams. Stream I. 60°-120° from A. Proper Motion. o 05 o o 10°-19°. 20°-29°. 30°-39\ 40°-49°. 50°-59°. > 100" 14 9 5 7 2 2 60"-99" 19 20 10 2 3 1 50 -59 17 12 5 6 1 0 40 -49 24 22 17 9 8 2 35 -39 26 15 14 6 8 1 30 -34 37 21 17 16 2 1 27 -29 26 16 14 10 4 1 24 -26 29 31 19 12 7 2 22 -23 27 21 13 12 6 1 20 -21 19 15 12 16 3 1 18 -19 10 11 7 6 1 1 40°-59° and 121°-140° from A. > 100" 6 4 2 0 1 1 60"-99" 6 4 4 1 6 0 50 -59 2 3 7 3 1 1 40 -49 9 4 6 3 3 2 35 -39 cr o 2 2 1 1 1 30 -34 10 12 3 1 1 1 27 -29 8 3 5 2 1 0 24 -26 9 5 5 4 1 0 22 -23 11 8 3 3 1 1 20 -21 6 5 5 3 1 0 18 -19 3 2 3 0 1 0 381 1908-9.] The Systematic Motions of the Stars. Stream II. 60°-120° from B. Proper Motion. 0°-9°. 10°-19°. 20°-29°. 30°-39°. 40°-49°. 50°-59°. > 100" 5 4 7 1 1 0 60"-99" 9 7 11 4 12 0 50 -59 8 8 10 0 0 3 40 -49 16 9 6 5 1 1 35 -39 9 5 1 11 1 1 30 -34 17 13 11 8 4 1 27 -29 10 11 13 6 2 0 24 -26 10 8 6 11 4 3 22 -23 25 19 9 11 7 2 20 -21 12 6 9 5 1 4 18 -19 14 9 13 3 3 2 40°-59° and 121°-140° from B. > 100" 1 2 1 1 1 0 60"-99" 2 3 0 4 2 0 50 -59 2 1 3 1 1 0 40 -49 11 5 5 0 0 0 35 -39 4 2 3 1 2 0 30 -34 7 4 2 3 0 0 27 -29 6 1 2 2 0 1 24 -26 5 4 1 2 1 0 22 -23 1 1 1 1 0 0 20 -21 1 2 1 3 2 0 18 -19 0 1 2 0 0 0 The numbers are not given separately for the different magnitudes of the stars whose distances from their apices are less than 40°, but the totals are given below with those of the preceding tables. Stream I. Distance from A. 0°-9°. 10°-19°. 20°-29°. 30°-39°. 40°-49°. 50°-59°. 60°-120° 248 193 133 102 45 13 40°-59° and 121°-140° 75 52 43 21 18 7 20°-39° and 141°-160° 30 11 8 13 15 6 Stream II. Distance from B. 0°-9°. 10°-19°. 20°-29°. 30°-39°. 40°-49°. 50°-59°. 60°-120° 135 99 96 65 26 17 40°-59° and 121°-140° 40 25 19 17 9 1 20°-39° and 141°-160° 4 7 7 2 1 2 382 Proceedings of the Royal Society of Edinburgh. [Sess. In this way the stars were provisionally divided as follows : — 110 moving in directions more than 60° from both apices. 1023 belonging to Stream I. 574 „ „ Stream II. 217 doubtful. 1924 Total. Kapteyn and Eddington, using stars of large and small proper motions, found an equal number in the two streams. The above result is not at variance with this, for if Stream I has a larger stream velocity, a greater proportion of stars belonging to Stream I will naturally be obtained by limiting the stars to those of large proper motion. 5. The number of stars at different distances from the two apices, moving in directions within 60° and 30° of the two apices, are as follows : — Distance from Apex. Fraction of Area of whole Sphere in- cluded. Number in Stream I within 60°. Number in Stream II within 60°. Number in Stream I within 30°. Number in Stream II within 30°. 60°-120° •508 736 440 574 330 40°-59° and 120°-140° •264 216 111 170 84 20°-39° and 141°-160° •171 71 23 49 18 The relative density of the stars of the two streams at different distances from the apices, moving within 60° and 30° of the directions of the streams, are therefore : — Distance from Apex. Within 60°. Within 30°. I. i — i hH I. II. 60°-120° 145 87 113 65 40°-59° and 121°-140° 82 42 64 32 20°-39° and 141°-160° 41 13 29 10 6. If the velocity of Stream I be v, then at a distance 0 from A the resolved part of this perpendicular to the line of sight is v sin 0. The mean value of this for stars between 60° and 120° from A (more accurately 59 and 120|°) is *92 v ; for stars from 40° to 60° and 1 20° to 140° from A is -82 v. 383 1908-9.] The Systematic Motions of the Stars. If the velocity of Stream II be v', then at a distance 0' from B the resolved part of this perpendicular to the line of sight is v sin O'. Assum- ing that the accidental distribution of velocities is the same in the two streams, the distribution of stars in the two streams should be the same when v sin 0 = v' sin O'. Using this argument, the agreement between the numbers 87 and 82 of the last table and between 65 and 64 leads to an equation *92 v = '82 v ; while the agreement between 42 and 41 and between 32 and 29 leads to •82 v — *52 v. 7. These results are very rough, and would be altered considerably if the stars whose proper motions are between 18" and 23" were omitted. The results suggest that, by a more careful division of the stars into the two streams and by better grouping, it will be possible to determine the relative velocities of the streams. Dividing the figures on p. 381 by *508, ‘264, and *1 71, we obtain Distance from Apex. 0°-9°. 10°-19°. 20°-29°. 30°-39°. 0 0 1 CO 0 50°-59°. ( 60°-120° 49 38 26 20 9 3 I { 40°-59° and 121°-140° 28 20 16 8 7 3 ( 20°-39° and 141°-160° 18 7 5 8 9 4 ( 60°-120° 27 20 19 13 5 3 II \ 40°-59° and 121°-140° 15 9 7 6 3 0 ( 20°-39° and 141°-160° 2 4 4 1 1 1 With this table as a guide the original assortment of the stars into the two streams was revised, and the doubtful cases decided. E.g., No. 56 in Table I. A = 49° a = 130°. B = 33° 6 = 49°. If belonging to Stream I this star will fall in the last group but one of the second line : interpolating with the number in the last column of the second line we get 6. If the star belongs to Stream II it will fall in the 4th column of line 5, and we again have the number 6. The star is equally likely to belong to either stream, and it is treated as if '5 belongs to Stream I and ’o to Stream II. After this revision a table like Table II. was again formed. The follow- ing changes were made, however. Stars of proper motion 18" and 19" were omitted. These stars were included originally before the proper motions in B.A. and Dec. were combined, so as to make sure of getting all the stars of p.m. > 20" 384 Proceedings of the Royal Society of Edinburgh. [Sess. The stars were also arranged according to the following distances and their supplements from the apices : — 65°-115°5 or siu (dist.) from '9 to TO 45°-64° „ ,, '7 to *9 30°-44° „ „ -5 to -7 18°-29° „ „ -3 to -5 12°-17 3 J •2 to "3. The results are shown in the following tables, the figures being given for stars of different proper motions. Stream I. 65°-115°. Proper Motion. 0°-9°. 10°-19°. 20°-29°. 30°-39°. 40°-49°. 50°-59°. > 100" 13 7 4 7 2-8 2 60"-99" 17 17 9 3 2 1-3 50 -59 15 10 5 5 1 0 40 -49 25 19 17 8 8 2-9 35 -39 23 13 14 3 9 3-5 30 -34 29 19 11 9 2-7 1 8 27 -29 21 16 11 9 4 1-3 24 -26 28 27 18 11 6 2*7 22 -23 25 24 8 9 4-8 32 20 -21 15 10 8 13 4-7 4'2 45°-64° and 135°-116°. >100" 5 5 3 0 2-2 1*5 60"-99" 7 5 6 0-9 5 0 50 -59 4 5 3 3-9 1 1-3 40 -49 8-9 6 7 4-7 5 2-2 35 -39 8-8 4 5*4 44 3 24 30 -34 16 14 10-9 8-6 3*7 0-3 27 -29 9 5 7 1 0 1-9 24 -26 8 9 7-7 2-7 1*5 0-5 22 -23 11 9 8 7-9 4 1 20 -21 10-8 11 8 4 2-8 0-6 30°-44° and 150°-136°. > 100" 2-8 1 0 0 1 0 60"-99" 3 2 1-7 3 2 0-3 50 -59 2'9 0 4 1 0 0-3 40 -49 2-6 5-4 1*4 1-7 1-7 2-7 35 -39 4 2-4 3 3 1 0-4 37 30 -34 5-4 4-6 2-7 0-6 4-0 2-2 27 -29 4-7 0 3-8 2-5 2-4 0-5 24 -26 5 3 2-9 5 3 0-5 22 -23 6 2-9 0-5 1 1 1 20 -21 5 37 3-4 1*4 1 0 iii the printer is not responsible, the expense of snch proofs and corrections will be charged against the author. All proofs must, if possible, be returned within one week, addressed to The Secretary, Royal Society, Mound, Edinburgh, and not to the printer. To prevent delay, authors residing abroad should appoint some one residing in this country to correct their proofs. 4. Additions to a Paper after it has been finally handed in for publication, if accepted by the Council, will be treated and dated as separate communications, and may, or may not, be printed immediately after the original paper. 5. Brief Abstracts of Transactions Papers will be published in the Proceedings, provided they are sent along with the original paper. 6. Separate Issue of Reprints; Author’s Free and Additional Copies. — As soon as the final revise of a Transactions paper has been returned, or as soon as the sheet in which the last part of a Proceedings paper appears is ready for press, a certain number of separate copies or reprints, in covers bearing the title of the paper and the name of the author, are printed off and placed on sale. The date of such separate publication will be printed on each paper. The author receives fifty of these reprints free, and may have any reasonable number of additional copies at a fixed scale of prices which will be furnished by the printer, who will charge him with the cost. To prevent disappointment, especially if the paper contains plates, the author should, immediately after receiving his first proof, notify to the printer the number of additional copies required. 7. Index Slips. — In order to facilitate the compilation of Subject Indices, and to secure that due attention to the important points in a paper shall be given in General Catalogues of Scientific Literature and in Abstracts by Periodicals, every author is requested to return to the Secretary, along with his final proof, a brief index (on the model given below), of the points in it which he considers new or important. These indices will be edited by the Secretary, and incorporated in Separate Index Slips, to be issued with each part of the Proceedings and Transactions. MODEL INDEX. Schafer, E. A. — On the Existence within the Liver Cells of Channels which can be directly injected from the Blood-vessels. Proc. Roy. Soc. Edin., vol, 1902, pp. Cells, Liver, — Intra-cellular Canaliculi in. E. A. Schafer. Proc. Roy. Soc. Edin., vol. , 1902, pp. Liver, — Injection within Cells of. E. A. Schafer. Proc. Roy. Soc. Edin., vol. , 1902, pp. IV CONTENTS. NO. XVII. The Electromotive Force of Iodine Concentration Cells with One Electrode saturated with Iodine. By A. P. Laurie, D.Sc, M.A. Cantab., ..... (Issued separately May 11, 1909.) XVIII. Cynomacrurws Piriei, Poisson abyssal nouveau recueilli par I Expedition Antarctique National e Ecossaise. Note pre- liminaire, par Louis Dollo, Sc.D. (Cantab.), For.Mem.G.S., C.M.Z.S., a Bruxelles (Musee). ( Presentee par M. R. H. Traquair, M.D, F.R.S, V.P.R.S.E.), . . . 316 (Issued separately May 13, 1909.) - o8 XIX. On Lagrange’s Equations of Motion, and on Elementary Solutions of Gyrostatic Problems. By Professor Andrew Gray, F.R.S., . . . . . 327 (Issued separately May 13, 1909.) XX. On Energy Accelerations and Partition of Energy. By C. W. Follett. (Communicated by Professor W. Peddie), 349 (Issued separately May 15, 1909.) XXI. The Systematic Motions of the Stars. (Second Paper.) By Professor Dyson, . . . . . .376 (Issued separately May 15, 1909.) PAGK 304 The Papers published in this Part of the Proceedings may be had separately, on application to the Publishers, at the follow- ing prices : — No. XIII., No. XIV, No. XV., No. XVI., No. XVII., No. XVIII., No. XIX., No. XX, No. XXL, Price 4s. 9d. ? ? 5 » J? y y lOd. 6d. 6d. 3d. 8d. Is. 4d. Is. 6d. Is. Od. PROCEEDINGS OP THE ROYAL SOCIETY OF EDINBURGH. SESSION 1908-9. Part V.] VOL. XXIX. [Pp. 385-480. CONTENTS. NO. PAGE XXII. Flexural Vibrations of Thin Rods. By George Green, M.A., B.Sc., Assistant to the Professor of Natural Philosophy in the University of Glasgow. (Communicated by Professor Gray), ...... 393 (Issued separately April 30, 1909.) XXIII. A Negative Attempt to detect Fluorescence Absorption. By Robert A. Houstoun, M.A., D.Sc., Ph.D., Lecturer on Physical Optics in the University of Glasgow. ( Com- municated by Professor A. Gray, F.R.S.), . . .401 (Issued separately July 8, 1909.) XXIV. Experiment with the Spark Gap of an Induction Coil. By Dr Dawson Turner, ..... 414 (Issued separately July 8, 1909.) XXV. Strophanthus sarmentosus : its Pharmacological Action and its Use as an Arrow Poison. By Sir Thomas R. Fraser, M.D., F.R.SS. L. & E., Professor of Materia Medica in the University of Edinburgh ; and Alxster T. Mackenzie, M.A., M.B., Ch.B., Carnegie Research Scholar, . . 415 (Issued separately July 9, 1909.) [Continued on page iy of Cover . EDINBURGH : Published by ROBERT GRANT & SON, 107 Princes Street, and WILLIAMS & NORGATE, 14 Henrietta Street, Coyent Garden, London. MDCCCCIX. * / 100" 4 3 6-8 1 2 0 60"-99" 7 6 8 4 2-7 1 50 -59 7 4 10 0 0 3 7 40 -49 15 8 5 6 1-8 1-5 35 -39 8 3 1 10 1 0-5 30 -34 15 10 9 7 3 5 1-6 27 -29 9 9 11 5 0-7 0-3 24 -26 10 8 5 11-3 3-8 3 22 -23 22 15 5 10 5-6 3-8 20 -21 11 5 8 3 1 5d 45°-64° and 135°-116°. > 100" 1 3 1-8 0-5 2-9 0-7 60"-99" 37 3 2-8 3-5 1 0 50 -59 3 5 2 2-4 2 0 40 -49 8-7 6-9 5 1-4 0-3 1-5 35 -39 4 4 1 2-4 1-5 0-4 30 -34 10-3 7 5-2 4-4 2 '4 0-8 27 -29 7-6 2 6-8 3-8 3 7 1-8 24 -26 4-6 7 2-2 2-7 2 03 22 -23 4 5 5-5 1-3 1*3 1-6 20 -21 3-5 3 36 0-5 3 0-5 30°_44° and 150°-136°. > 100" 1 1-5 1-2 0 0 0 60"-99" 0 1 0 2-3 1 0 50 -59 0 0 1 o-i 0 0 40 -49 2-8 3 3 1*4 0 1*0 0 35 -39 1 0 1 0 1 0 30 -34 4 2 0-3 0-3 0-2 0 27 -29 0-5 1 0-6 2-3. 0 1-5 24 -26 2 1-1 2 1-3 0 0 22 -23 o-i 0 2-6 1 0-5 0 3 20 -21 0-3 0 1-3 1 0 0-2 VOL. XXIX. 25 386 Proceedings of the Royal Society of Edinburgh. [Sess. 9. Taking the sums of the columns in the preceding table and giving the sums for the small groups which are not given in detail, we find — Stream 1. Limits of Dist. from Fraction of Area of Sphere. ; Number of Stars whose Directions diverge. Apex. 0°-9°. 10°-19°. 20°-29°. 30°-39o. 40°-49°. 50°-59°. 65°-115° . . . . •430 211 162 105 77 45 22-9 45°-64°, 116°-135° •283 88-5 73 66-3 37-8 28-2 11-1 30°-44°, 136°-150° •157 4L4 25 23-6 17-2 16-5 10-6 18°-29°, 151°-162° •084 10-5 5-8 4-1 7*0 63 2-5 12°-17°, 163°-168° •026 1-8 3-4 1 1-6 0-2 Stream II. 65°-] 15°. . . . •430 108 71 68-8 573 22-1 20-5 45°-64°, 116°-135° •283 50-4 45-9 35-9 27-4 20*1 7-6 30°-44°, 136°-150° 18°-29°, 151°-162° •157 11-7 9-9 11-4 8-3 3-7 2-0 •084 2-6 5-2 3-9 o-i 2d 1-2 Dividing by the areas, the proportional number of stars per unit area belonging to the different groups is obtained, the mean value of the sine of the angular distance from the apex being given in first column. Stream I. Sin (dist.). 0°-9°. 10°-19°. 20°-29°. 30°-39°. 40°-49°. 50°-59°. •957 49-1 27*7 24-4 17-9 10-5 5 3 •818 31-3 25-8 23-4 13-4 io-o 3-9 •606 26-4 16-0 15-1 11-0 10-5 6-8 •404 12-5 6-9 4-9 8-3 8-7 3-0 Stream II. « •957 25-1 16-5 16-0 133 5-2 4*8 •818 17-8 16-2 12-7 9-7 7-1 2-7 •606 7-5 6*3 7 3 5 3 2-4 1-3 •404 34 6*2 4-7 0-2 2-5 1-4 The above figures show that stars of Stream I whose mean distance from the apex of Stream I is sin-1 '606 are distributed similarly to the stars of Stream II at mean distance sin ~ *957 from their apex. 10. If the numbers of stars belonging to the two streams are equal, and 387 1908-9.] The Systematic Motions of the Stars. their random distribution similar, it follows that the stream velocities are in the ratio — *957 : ’G06 or 1 : ‘63. If the stars within 30° of the directions of the two apices are con- sidered, we find — 8in (dist.). I. II. •957 111*2 57-6 •818 80-5 46-7 •606 57-5 21*1 •404 24-3 14-0 And the number of stars of Stream I distant sin 1 *404 from A agrees o sufficiently well with the number of Stream II distant sin-1 ’606 from B to confirm this result, but the weight of this determination is small. The interest of this determination lies in the difference between this result of approximately 3:2 in the relative stream velocities with that of 3 or 4 : 1 found by Eddington using stars of all proper motions. 11. The value of the method here employed depends on the uniformity with which the stars are distributed. It is therefore of interest to examine whether the distribution of magnitude of proper motion varies with the distances from A and B in the two streams. Confining our attention to stars moving within 30° of the directions of A and B respectively, i.e. those stars whose velocities are largely determined by the stream velocities, we find between the distances 65° and 115° from A and B the following table for the number of stars whose proper motions are above certain limits : * — Proper Motion. I. II. >100" 24 14 > 60 67 35 > 50 97 56 o A 158 84 > 35 208 96 > 30 267 130 > 27 315 159 > 24 388 182 > 22 445 224 > 20 478 248 * As a p.m. of >994" is called 100", the limits 100", 60", etc. are more strictly 992", •59A, etc. 388 Proceedings of the Royal Society of Edinburgh. [Sess. Multiplying the numbers 111*2, 805, etc. of § 10 by 4'30, so that they may refer to the same fraction of the sphere as the numbers in the above table, we obtain for the density of stars whose proper motions are >19"*5 at different distances from the apices of the streams — 0. Sin 6. I. II. 73° •957 478 248 55 •818 346 201 37 •606 247 91 24 •404 104 60 Interpolation from the previous table shows that between the distances 65°-115° from A and B respectively there are belonging to the two streams — I. // II. 478 stars p.m. > 19-5 248 stars p.m. > 19-5 346 55 > 25*2 201 5 i > 22-4 247 55 > 31-0 91 55 > 36*6 104 5 5 > 00 60 55 > 47*5 Comparison of this table with the previous one shows that there are in Stream I as many stars per unit with p.m. >25//-2 at mean distance 73° from the apex, as there are at mean distance 55° with p.m. 19//,2, and so on. If the accidental velocity is small compared with the stream velocity and the stars are uniformly distributed, then at a distance 0 from A the number of stars per unit area whose p.m. >v will equal the number per unit area 90° from A, whose p.m. >v cosec 0. Multiplying by the corresponding values of sin 0 we obtain — I. II. 18*7 u 18*7 20'6 18-3 18-8 22*2 19-6 19-2 The accordance of these figures may be regarded as a check on the uniformity of the distribution of the stars. As there are 247 stars of Stream I between 65° and 115° from A with p.m. >3T/-0, and 248 of Stream II between 65° and 115° from B with p.m. >19//-5, the stream velocities are in the ratio of 31 : 195 or 3 : 2, confirming the previous result. 389 1908-9.] The Systematic Motions of the Stars. 1 2. When the stars are arranged according to their type of spectrum the following table is obtained : — Limits of Proper Motion. Stars of Type I. Stream I. Stream II. Stars of Type II. Stream Stream IN dlllol • Stars of unknown Spectra. Stream Stream ^e^per > 100" 0 1 33 9 10-1 2 25-6 15-4 0 60"-99" 3 0 35 0 15-0 8 51-9 34-1 3 50 -59 0 0 16-2 15-8 4 47-6 24-4 5 40 -49 4 0 39-2 17-8 4 93-8 54-2 4 35 -39 4 1 32-6 12-4 1 71-7 31-3 7 30 -34 4 2 44-7 24-3 3 102-1 56-9 11 27 -29 4 1 27T 13-9 5 75-9 53-1 4 24 -26 8 3 43-2 17-8 5 95-2 48-8 9 22 -23 6 2 39-8 16-2 7 82-6 70-4 10 21 -22 8 4 31-0 12-0 6 70-7 43-3 6 Total I 41 14 342-7 155-3 45 717-1 431-9 59 The stars whose type of spectrum is known are in nearly all cases of 6m,5 or greater. A large proportion of the remaining stars are between 8m 0 and 9m 0. In the above table it may be noticed — (i) That no stars of Type I are moving in directions diverging more than 60° from the directions of A and B. (ii) That the proportion of stars belonging to Stream I is large for Type I stars. This may be accidental, as there are few stars. Attention is drawn to it, as if it holds generally it will afford a partial explana- tion of the smaller ratios found for the stream velocities (3:2) here, as compared with the ratio (3:1) found by Eddington. (iii) The number of stars diverging more than 60° from A and B is smaller for the faint stars. (iv) A somewhat greater proportion of faint stars belong to Stream II. None of the differences referred to above are very striking. Generally speaking, the two streams consist of the same kind of stars. Incidentally, the relative number of stars of large proper motions belonging to the spectral types I and II is given in the above table. The numbers are as follows : — Proper Motion. Type I. Type II. >100" 1 46 50"-100" o a 94 30"-50" 15 179 20"-30" 36 224 390 Proceedings of the Royal Society of Edinburgh. [Sess. The small number of stars of large proper motions belonging to Type I is a well-known result. 13. In the following tables the stars of Type I belonging to the two streams are given. It will be seen that they diverge less from the general drift of the streams than the other stars. The most divergent stars appear to be such very bright stars as Sirius and /3 Centauri, etc. Stars of Type I arranged in order of Magnitude of Proper Motion. Stream I. Star’s Name. Mag. R.A. Dec. Proper Motion. A. a. Groomb. 884 7T h ni 4 44 + 45*7 // 68 + 13 o 58 a Aquilse .... 1-0 19 46 + 8-6 66 + 41 154 Lai. 4141 .... 6-9 2 10 + 23-8 60 + 7 65 iUrs. Maj. 31 8 52 + 48-4 49 -13 70 e Cephei .... 4-2 22 11 + 56-6 46 - 12 113 Groomb. 94 7-4 0 29 + 47-4 40 + 19 93 5 Capric. .... 3-0 21 42 -16-6 40 -27 119 i Centauri .... 2-9 13 15 - 36-2 37 - 4 99 Lai. 305 .... 6-5 0 14 - 8-6 36 - 1 85 a Lyrae .... OT 18 34 + 38-7 36 -20 150 a Piscis Aust. 1-4 22 52 - 30-2 36 -11 99 /3 Centauri 0-9 13 56 -59-9 33 + 56 95 7 Cor. Aust. 5*5 18 58 - 31 ’2 33 + 6 136 8 Cassiop. .... 2*8 1 19 + 59-7 31 + 17 89 Piazzi I. 131 6-4 1 33 - 9-9 31 + 25 65 67 Ursse Maj. . 5T 11 57 + 43-6 31 - 19 96 ^Yirginis .... 3-4 13 30 - 04 29 -19 112 Gr. 3042 .... 5-7 20 4 + 52-9 28 + 2 130 6 Pegasi .... 37 22 5 + 5-7 28 + 16 119 Piazzi I. 70 63 1 20 + 34-1 27 0 80 fx Ceti .... 4-4 2 40 + 9-7 26 + 14 53 aPictoris .... 3 3 6 47 -61*8 25 + 3 53 aCan. Yen. 2-9 12 51 + 38-9 25 - 12 106 a Pegasi .... 2-7 22 59 + 14-7 25 + 39 107 a Leonis .... 1-3 10 3 + 12-5 24 - 18 64 5 Corvi .... 3T 12 25 -16-0 24 + 29 93 t Centauri 4-0 12 32 -48-0 24 - 7 88 A Bootis .... 4-3 14 13 + 46-6 24 -21 120 Lai. 37403 5-5 19 38 -15-7 24 - 5 145 6 Cassiop. .... 4-6 1 5 + 54-6 23 + 13 89 | Cephei .... 4-4 22 1 + 64T 23 - 6 112 Groomb. 2296 . 5-0 15 55 + 55-0 23 + 17 129 Lai. 1344 .... 5-6 4 2 -27-9 22 - 4 33 7 r Sextant .... 5-9 9 47 + 2-9 22 -45 59 7 Pavonis .... 4-4 17 59 - 63-7 22 0 106 a Androm. 2-4 0 3 + 28-5 21 -37 94 Groomb. 706 7-4 3 29 + 42-6 21 + 6 63 X 1 Hydrse .... 5-7 11 1 -26-8 21 + 1 72 30 Draconis 5*2 17 47 + 50-8 21 + 6 139 a Gruis .... 2 '2 22 2 -47-5 21 -28 101 89 Leonis .... 5-8 11 29 + 3-6 20 + 20 83 7 Centauri 2-4 12 36 -48-4 20 - 7 89 Brad. 2792 5-6 21 22 + 46-3 20 - 5 124 1908-9.] The Systematic Motions of the Stars. 391 Stream II. Star’s Name. Mag. R.A. Dec. Proper Motion. B. b. a Canis Majoris . -1-3 li m 6 41 -16-6 // 131 - 36 100 9 Hydra .... 3-8 9 9 + 2-7 35 - 4 106 Piazzi VI. 59 6-0 6 13 - 22*7 34 + 29 96 80 Piscium 5-7 1 3 + 5-1 32 - 31 108 Lalaude 25818 . 6-4 13 59 + 11*3 32 - 3 80 6 Andromedse . 6-0 23 6 + 43-0 28 - 9 127 45 Bootis .... 5-0 15 3 + 25-3 26 + 27 89 Groombridge 2630 8-0 18 34 + 63-6 26 0 125 a Opliiuchi 2-1 17 30 + 12-6 25 + 31 73 y Ceti .... 3-8 2 38 + 2-8 22 -25 117 Groombridge 717 6-3 3 32 + 42-2 22 -27 158 23 Andromedse . 5-6 0 8 + 40-5 20 + 3 122 21 Eridani 6-3 3 34 - 6-0 21 + 3 112 5 Leonis .... 2-6 11 9 + 21-1 21 + 21 107 A Piscium .... 4-6 23 37 + P2 20 -16 96 The directions of the 110 stars which did not fall within 60° of the directions of either A or B were examined, but no evidence was found to indicate that they belonged to a third stream. The proper motions of the stars classified as belonging to Streams I and II were treated by Airy’s method of determining the solar apex. The following positions were found for A and B : — A. K. A. 93° Dec. -7°. B. R.A. 246° Dec. - 64°. The position of A agrees almost exactly with that found in my previous paper (R.A. 94° Dec. — 7°) ; that found for B lies between the position found there (R.A. 240° Dec. —72°) and the assumed position (R.A. 255° Dec. — 60°) of this paper. With the above positions of A and B and relative velocities of the two streams in the proportion 3 : 2, the apparent motion in two streams may be resolved into a motion of the solar system towards a point — (Apex) R.A. 283° Dec. + 44 ; and a motion of two streams in opposite directions in the direction — (Arertex) R.A. 268° Dec. -21°. Corresponding to the velocities 3 and 2 for the two streams, the velocity of the solar motion is T55, and the relative velocity of the two streams 404. If instead of using the positions of A and B found by Airy’s method, those found in my previous paper are used, the co-ordinates of the apex are found to be R.A. 281°, Dec. + 42°, and of the vertex R.A. 268°, Dec. — 24°. 392 Proceedings of the Royal Society of Edinburgh. [Sess. In the Astronomische Nachriclden , No. 4291, M. Beljawsky determines the apex and vertex according to the ellipsoidal hypothesis of the dis- tribution of proper motions which has been put forward and developed by Professor Schwarzschild in the Nachrichten der k. Gesellschaft der Wissen- schciften zu Gottingen, 1907 and 1908. As M. Beljawsky uses the proper motions given by Professor Porter (Cine. Publ. 12), the material he uses largely coincides with what I have used. He finds the following positions : — (Apex) R.A. 281° Dec. +36°. (Vertex) R.A. 266° Dec. - 24°. It is of interest to notice that the two-stream hypothesis of Kapteyn and Eddington agrees with the ellipsoidal hypothesis of Schwarzschild both when applied to the Groombridge stars and to the stars of large proper motion ; and that the differences found by using different stars are more than those found by using different methods. It is hardly possible to say which representation accords most closely with the facts. ( Issued separately May 15, 1909.) 1908-9.] Flexural Vibrations of Thin Rods. 393 XXII. — Flexural Vibrations of Thin Rods. By George Green, M.A., B.Sc., Assistant to the Professor of Natural Philosophy in the University of Glasgow. Communicated by Professor Gray. (MS. received December ]4, 1908. Read January 18, 1909.) § 1. The main object of this paper is to point out a method of applying hydrodynamic solutions already obtained to the solution of problems relating to flexural vibrations of thin elastic rods. The results found apply to rods not subjected to permanent tension, and vibrating so that one principal axis of each transverse section lies in the plane of vibration. The central line of the rod is assumed to remain unaltered in length ; and particles lying in a plane transverse section, when undisturbed, remain always in a plane normal to the central line. For convenience in what follows we may here derive the equation of motion of a rod subject to these conditions. Taking w as the area of each section, k2 co its moment of inertia, q as Young’s modulus, dx as the length of the central line of a small portion, R its radius of curvature, and N as the total tangential force acting on the cross-section at x, we obtain the equation of angular motion of the element 2 3 1 i \T 2 (/K“(jl> — — - + Al = pKA(Ji> dx R dxdt'2 (i), where y is the vertical displacement of the element and p is its density. The equation of vertical motion is 0X 02// dx PMdt2 As pointed out by Lord Rayleigh,* whose notation we have adopted, terms depending on the angular motions of the sections of the bar may be neglected in the above equations ; accordingly, by eliminating N from (1) and (2) we obtain finally the equation a2// , 272 diy 0 W + Khd^ = 0 (3), in which we have put for f and b2 for dx2 R p 2. Consider now frictionless liquid in a straight canal with vertical * Theory of Sound , vol. i. 394 Proceedings of the Royal Society of Edinburgh. [Sess. sides. Take the origin of co-ordinates at point O, at a distance h above the undisturbed level, and draw O X parallel to the canal and 0 Z vertically downwards. Let the motion be infinitesimal and let f, be the displace- ment components at any time t of any particle of water whose undisturbed position is x, z. If the motion of the water be started primarily from rest by pressure applied to the free surface, the hydrodynamical equations of motion take the well-known form : 0 0 i=2Z(x,z,t) ■ • • (4); from which we obtain by integration 0 (=si^x’z’ t); II iTl Cl) Ok • (5)- In virtue of the incompressibility of the fluid we have also the equation 0^ 0JU dx2 dz2 (6)> which shows that if

_ 1 040 'dz2 g2 ~dt^ at a free, or level, liquid surface. Equations (6) and (8) combined give us the relation dx2 g2 dt 4 ’ 1 and when we put y in place of <•/>, Kb in place of -, and interchange x and ty o this equation may be written in the form 279^ __n dP + K 1 3*4 0 (3), which is the equation already found for flexural vibrations of an elastic bar, when terms depending upon the angular motions of the sections of the bar may be neglected. Accordingly equation (9) proves that every Flexural Vibrations of Thin Rods. 395 1908-9.] hydrodynamical potential function, with x and t interchanged, is a solution of equation (3) above. (The converse is not always true.) In relation to the flexural waves problems £ is in general to be treated as a constant. § 4. It may be of some interest to note that, in all solutions for elastic bars obtained by applying the above result, the displacement y at each point of the bar may be regarded as derived from a single function Y(t, z, x) such that V 0Y dx (10). Further, it follows from the relationship established between such a function V and the hydrodynamic potential function, that every function derived from V by differentiations or integrations with respect to t, z , x, is a solu- tion of the differential equation (3). Thus any solution of (3) may be a displacement potential, or a displacement, or a velocity. If the function V represents displacement, we readily find from equation (7) that the curvature at each point x of the bar can be obtained by a single differentia- tion with respect to z, being given by the equation i _ i ay R kI) dz (II), from which the potential energy can easily be obtained. § 5. Solutions for vibrations of a rod of finite length l are derived directly from the hydrodynamic solutions for waves in a canal of length l by simple interchange of x and t ; and they are applicable to all cases, whether the rod has its ends free, or clamped, or “ supported.” In particular, the normal functions are easily obtained in this way. In the case of an infinite rod, all mathematical results relating to surface waves in a canal infinitely long and infinitely deep become immediately useful ; space-curves in the hydrodynamical waves problems becoming time-curves for the flexural waves, and vice versa. § 6. In this connection it may be useful at a later time to examine some of the numerous hydrodynamical solutions relating to surface waves and groups of waves. A number of curves are shown in papers on Water- Waves * by the late Lord Kelvin, illustrating results derived from particular hydrodynamic solutions comprehended in the following general expression, given in his last Waves paper : — dj+k+l l - ,°vl- x {RS}or{RD}^^^)e In this, {RS} denotes a realisation by taking half the sum of what follows * Proc. Poy. Soc. Edin vol. xxv., Feb. and June 1904 ; vol. xxvi., Oct. 1906. 396 Proceedings of the Royal Society of Edinburgh. [Sess. it with dt i ; { RD ] denotes a realisation by taking the difference of what follows it with ± i divided by 2 i. As an example of flexural waves in an infinite elastic rod, arising from a given initial displacement, we may take the solution y = { RS} l where + H) 1 / xH X2 e 4 Kb(z+it) -■'t“ (j A-2L'V“” T = J(z2 + t 2), and r = tan -i (t ■ (12)- In what follows, z is taken as 1 and *6 as -r- in order to allow us to use 4 Lord Kelvin’s hydrodynamical results in our present problem. § 7. Taking the origin of co-ordinates at the middle of the bar, the initial configuration is given by X- — c 4/c b y = e . (13). Almost immediately after the commencement of motion, an infinite number of waves are formed along the bar, with amplitudes diminishing according X 2 to the law e 4*&T2 and with the distances from zero to zero becoming shorter and shorter as we pass from the middle toward the ends of the bar. The zeros come into existence at the ends of the bar, and begin travelling inwards to the middle. The first zero formed comes almost instantaneously to the middle region, and the others follow it in their order of formation. The inward progress of the zeros soon ceases, the first zero never quite reaching the centre ; in a short time they begin to move in the opposite direction and continue to do so for ever, and the amplitudes at any point x ultimately fall off according to The middle point of the rod subsides to its undisturbed position nonvibrationally, while the distance from it to the first zero on either side continually increases after a certain time, being given by the equation x 2 = 3k&tt£. § 8. The seven curves given by Lord Kelvin, as space curves for water- waves, on page 191 of his paper, Proc. Roy. Soc. Edin., vol. xxv., Feb. 1904, show the condition of things in our present problem at seven different points near the middle of the bar, as t increases from 0 to oo , provided the curves be continued to meet the axis of t asymptotically at infinity (see fig. 1 and § 9 below). These curves show that points very near the origin never pass through their initial positions, but fall back nonvibrationally to them ; points farther from the middle rise slightly and then behave in the same Flexural Vibrations of Thin Rods. 397 1908-9.] way. At points along the bar more and more distant from its middle point the disturbance consists of a larger and larger number of waves which travel inwards past the point considered, before t== 1, and after that recross the point in the opposite direction one by one. When the first 398 Proceedings of the Royal Society of Edinburgh. [Sess. zero recrosses the point it subsides gradually to its original place of rest, only reaching it, however, after an infinite time. The successive maxima of displacement increase very slowly at first, then more quickly, and then diminish finally according to as already stated. t * Flexural Vibrations of Thin Rods. 399 1908-9.] § 9. The diagrams of figs. 1 and 2 are taken from Lord Kelvin’s paper referred to in § 8, and they are reproduced without change of the lettering applicable to them as water-wave diagrams. To make them correspond exactly to the flexural-waves problem solved by equation (12), we must reduce the ordinates in both figures in the ratio J 2 : 1 ; then in fig. 1 replace t by x on each of the seven curves, and take ordinates as represent- ing displacement and abscissas as representing time. As a water-waves diagram fig. 2 represents the vertical displacement of the water at point x — % from t — 0 to t = oo ; as a flexural-waves diagram it represents the shape of the right-hand half of the rod, x = 0 to x — oo , at time t = 2, corresponding to the initial configuration given by equation (13). These curves are useful chiefly as illustrations of the propagation of waves in dispersive media from a given initial disturbance confined in the main to the neighbourhood of the origin. They show clearly the distinctive features of wave-propagation in the two cases where the wave-velocity varies directly as the square root of the wave-length and inversely as the wave-length respectively, for an infinite succession of regular sinusoidal waves. It is interesting to observe that in both cases the wave-disturbance is ultimately spread throughout the entire medium, but that in the case of water-waves the wave-length of the disturbance at any time increases continuously, and in the case of flexural-waves it diminishes continuously, as we pass outwards from the middle point of the initial disturbance. In the case of water-waves also, Lord Kelvin’s investigations show that each individual wave lengthens and increases in speed as it advances, while in the case of flexural-waves each wave lengthens and diminishes in speed, as we shall see by equations (15) and (16) below for the solution we have chosen for illustration. § 10. At a moderate time after the motion has commenced, Tinay be put equal to — in equation (12), and the argument of the cosine varies then xH only with so that it is easy for us to trace the outward progress of any particular maximum or zero of displacement along the bar. Thus the position of any zero is determined by an equation of the form xH 4 n + 3 C — : r 7 r 4k6T2 4 and the velocity of the zero is given by (11), dx 8>Kbct — x 2. 2 Kbc dt 2 tx ' x ■ (15)- When t is large, so that we may put t_ rp 1 V equation (14) enables us to 400 Proceedings of the Royal Society of Edinburgh. [Sess. write (15) in the following approximate form, dx . x dt ' 2 1 • (15'). It of can easily be verified that when t is very small and x great the velocity any zero is given by dx m x dt='~2t, (16). In each case, what we obtain in these equations is also the wave-velocity for an infinite train of waves of wave-length equal to that maintaining in the immediate neighbourhood of the point x at time t. §11. To obtain the velocity of the group of waves of wave-lengths approximately equal to A — that maintaining in the neighbourhood of x at time t — we put xH (x - \)H _ 0 4/c6T2 “ 4k6T2 “ T (17), which enables us to write down the group-velocity thus : — dx 87 TKbt — Xx dt X t (18). When t is very small and x great, the right-hand side of (18) is approxi- mately equal to — If in (17) we take the wave-length A as small compared with x, we can obtain the following approximate expression for A when t is great : — A- 47 TKbt x (19). With this value for A, the right-hand side of (18) becomes ( x \ t Equations (15)-(19) show that in the two cases, when t is small and x great, and when t is great, the group-velocity is twice the wave-velocity ; which is in accordance with the theory of group- velocity given by Osborne Reynolds and extended by Lord Rayleigh. (. Issued separately May 15, 1909.) 1908-9.] Negative Attempt to detect Fluorescence Absorption. 401 XXIII.— A Negative Attempt to detect Fluorescence Absorption. By Robert A. Houstoun, M.A., D.Sc., Ph.D., Lecturer on Physical Optics in the University of Glasgow. Communicated by Professor A. Gray, F.R.S. (MS. received March 20, 1909. Read July 12, 1909.) According to Kirchhoffs law every body in a state of pure temperature radiation absorbs those rays which it emits, and the ratio of the coefficient of absorption to the coefficient of emission is constant for all bodies. In many cases which do not come under the category of temperature radiation — for example, a sodium flame — the wave-lengths emitted are also absorbed. It is thus possible that a fluorescing substance, in addition to its ordinary absorption, may absorb while fluorescing those wave - lengths that it fluoresces. From a photometric study of fluorescent uranium glass Burke stated he had discovered such an effect. A cube the edges of which measured 1 cm., transmitted while fluorescing only 57 per cent, of the light it transmitted when not fluorescing, the measurements being made, of course, on light of the wave-length emitted during fluorescence. Nichols and Merritt investigated the subject in detail, obtained a similar result for fluorescein, using a Lummer-Brodhun spectrophotometer, and found that the additional absorption produced during fluorescence — or, to give it its usual name, fluorescence absorption — possessed many strange properties ; for example, it did not follow the exponential law. Camichel repeated Burke’s work with two different experimental arrangements, and found no effect; he also obtained no effect with fluorescein. Miss Wick, using the same apparatus and working in the same laboratory as Nichols and Merritt, confirmed their results for resorufin. For a full description of the work of these observers and an account of the present state of the question, together with the necessary references, the fourth volume of Kayser’s Spectroscopie (1908), pp. 963-973, should be consulted. Since that volume was published an article has appeared by R. W. Wood * in which he gives an account of a new and ingenious method of observing the effect directly — without combining three separate * R. W. Wood, “ On a Method of showing Fluorescent Absorption directly if it exists,” Phil. Mag., Dec. 1908. VOL. XXIX. 26 402 Proceedings of the Royal Society of Edinburgh. [Bess. photometric measurements. He applied this method to fluorescein under various conditions, and his results were wholly negative. The object of the present article is to describe an attempt to detect fluorescence absorption in the case of fluorescein and uranium glass. Two different kinds of uranium glass were used. The method employed was in principle the same as the method of Nichols and Merritt, though the experimental arrangement was somewhat different. The results were wholly negative, and attention is directed to two causes of error which may not have received sufficient care, one of which produces a spurious effect, having one of the properties claimed for fluorescence absorption by Nichols and Merritt. It is true that the analogous reversal of a spectral line cannot be produced very easily ; but, making every allowance for the uncertain nature of the phenomenon studied, the author inclines to the belief that all cases of fluorescence absorption hitherto obtained have been due to systematic errors in the photometric arrangement. The spectrophotometer * used has already been described elsewhere, and proved admirably adapted for the purpose. It consists of a spectro- scope before the slit of which is fitted a polarising prism specially designed to divide the field into two halves which are polarised at right angles to one another, and which touch one another without overlapping. The fields are matched by means of a nicol eyepiece. Light enters the special prism by two apertures, one for the upper and one for the lower half of the field, and in obtaining the transmission curve of a piece of coloured glass it is put in turn before each aperture, both apertures being illumi- nated by a portion of an incandescent mantle 15 cms. away. When a self-luminous piece of glass is used close up to the aperture, if the light emitted by the glass is comparable in intensity with the light transmitted by it, it cannot be placed before either aperture, but must be placed before the lower beam e, f in fig. 2 in the article above referred to. If it is placed before the upper one, the light in the upper half of the field will not be quite plane polarised, for some of the rays diverge at too great an angle. The transmission curve of the substance investigated was first of all determined in the ordinary way, the substance being placed in turn before the two apertures, just as if it were an ordinary piece of glass. The fluorescent light can be neglected in comparison with the transmitted light. Then the arrangement shown in the diagram 1 was used, and the * R. A. Houstoun, “A New Spectrophotometer of the Hiifner Type,” Phil. Mag., Feb. 1908. 1908-9.] Negative Attempt to detect Fluorescence Absorption. 403 fluorescent substance kept before the lower aperture throughout the course of the experiment. An incandescent gas-lamp G was used for exciting the fluorescence. It was placed in a box to cut off all stray light, and its rays were focussed by a lens L on the fluorescing body U. The exciting rays not required were absorbed by a black screen not shown. The fluorescent light from the side of the body entered the instrument. As a comparison source an electric glow lamp was used. This was also placed in a box (not shown), and its intensity reduced to the right strength by placing fogged photographic plates of graded density in front of the opening in the box by which the light issued. S and K are two screens. When K is in position the exciting rays do not reach the substance, and it does not fluoresce. When S is in position the rays from the comparison source do not enter the substance and the lower aperture of the instrument. The passage from the comparison source to the upper aperture was always clear, and the upper half of the field was always illuminated by the comparison source alone. The first measurement made with this arrangement was to obtain the variation of the intensity of fluorescence with the wave-length for the substance. To do this, the screen S was placed in position, the screen K removed, and the comparison source adjusted to a suitable intensity. The lower half of the field was then illuminated solely by fluorescent light. The two halves were matched for different wave- lengths, the relative intensity of the comparison source and the fluorescent light obtained, and thus the shape of the fluorescence curve determined. This was repeated with a piece of cobalt glass in front of the exciting source in the position of K, in order to see whether the shape of the fluorescence curve varied with the nature of the exciting light. The shape did not, although the intensity did. When the transmission curve and the fluorescence curve of the sub- stance were known, a wave-length was taken on the fluorescence maximum 404 Proceedings of the Royal Society of Edinburgh. [Sess. and the experiment carried out as follows : — First of all the screen K was placed in position and the intensity T of the light transmitted by the substance when not fluorescing obtained. The intensity of the com- parison source was made so small that the transmitted light caused no appreciable fluorescence. Then the screen S was placed in position, the screen K removed, and the intensity F of the fluorescent light determined. Both screens were then removed and a determination was made of the light received from the substance when fluorescing and transmitting at the same time, C. If there is fluorescence absorption T + F > C. If a, /3, y be the angles made by the nicol with its zero position, I the intensity of the light received from the comparison source at the upper aperture of the instrument in the above three readings, and s, s' the transmission factors for the instrument for the two halves of the field, s, s' including everything but the effect of the eyepiece nicol, we have in the usual way Ts' = Is tan2a, Fs = Is tan 2/3, C s' = Is tan2y. Hence, instead of T, F, C, we may write the square of the tangent of the appropriate angle. The angles a, /3, y were determined by taking readings in two neighbouring quadrants and halving the difference. The result thus depends on three separate photometric measurements and is subject to three times the error of a single photometric measure- ment, and that not a very easy one. The space between the sources and the apertures of the instrument was built in so as to keep the room in absolute darkness. Observations were made in the order TFC, CFT so as to eliminate any error due to fluctuation in the relative intensity of the exciting and comparison sources. Instead of using an independent comparison source, light was reflected from the exciting source on to a square of white cardboard and the latter used as comparison source. The two would then vary together. This method was not found so satisfactory on account of greater difficulty in eliminating stray light. Scattered light from particles suspended in the glass or solution was expected and looked for, but did not prove to be an appreciable source of error. The measurements will now be described in order. Ukanium Glass — First Specimen. This was a pale yellow cube, of unknown manufacture, length of side 11 '4 mm., which fluoresced green. The following table gives the 1908-9.] Negative Attempt to detect Fluorescence Absorption. 405 fraction of the incident light transmitted by the glass for different wave- lengths : — A A 598 h/j. •906 467 ,14,11 •523 560 •829 452 •383 529 •781 438 •195 504 •630 425 •098 484 •570 As about 8 per cent, of the incident light is lost by reflection at the two faces, this fraction varying inappreciably with the colour, for A = 598 /ul/ul only 1 per cent, of the incident light is absorbed in the glass. The following table gives the intensity of the fluorescence for different wave-lengths, compared with an electric glow lamp, in arbitrary units, (1) when excited by an incandescent gas-mantle, (2) when the same source was used with a filter of cobalt glass : — A (1) (2) 606 up •147 •068 576 •599 •318 550 1-88 1-04 528 3-92 2-07 509 4-86 2-77 493 2-13 1-09 479 •455 ... This and the preceding table are plotted in the adjoining diagram 2. The fluorescence curves are, of course, not corrected for absorption in the glass, i.e. the intensity of the actual fluorescent light emitted by the glass is given, not the intensity we would obtain if none of it were absorbed in the glass in the way out. This latter, or the typical fluorescence curve, as Nichols and Merritt call it, would be more symmetrical. The fraction of the incident light transmitted by the cobalt glass filter for different wave-lengths is given in diagram 3. At first, on measuring T, F and C, T + F was always greater than C. A careful investigation, however, showed that this was due to diffuse light reflected from screen S. In diagram 4, H represents the aperture of the instrument. The exciting rays entered in the direction of the arrow, the corners at A and B being screened. The side BD of the cube had black paper gummed on it, to absorb the exciting rays. The green light from the exciting source was roughly one thousand times as strong as the fluorescence from the glass. If one-hundredth of the incident light were diffusely reflected from BD to S, and one-hundredth of that 406 Proceedings of the Royal Society of Edinburgh. [Sess. were reflected into the instrument, it would increase the value of F by one-tenth. Also some of the exciting rays might arrive at S through being scattered on entering the glass or through not being parallel to the Diagram 2. — Uranium Glass. First specimen. direction of the arrow. Hence T + F — C would be positive and propor- tional to F. The nature of this error is shown in an exaggerated form by the following table, which was obtained by replacing the black paper on S by one somewhat greyish : — 1908-9.] Negative Attempt to detect Fluorescence Absorption. 407 T F c T + F-C T + F-C T 27-86 1-00 28-51 •35 •013 1-45 1-00 2 37 •08 •06 •700 1-00 1-555 •145 •21 •392 1-00 1-178 •214 •55 •143 1-00 •967 T76 1-23 T + F-C T increases as T decreases. This is a property claimed for fluorescence absorption by Nichols and Merritt. The screen S was not kept in the same place during the above readings. If it had been, the column T + F — C would have been constant. In the similar tables given by Nichols and Merritt, and Miss Wick, T + F — C is constant within the error of observation. This source of error was removed by replacing the “ dead black ” paper 408 Proceedings of the Royal Society of Edinburgh. [Sess. by black velvet, the diffuse reflection from which is considerably less. The following table gives some results then obtained : — T F C T + F-C Probable Error. 752 3906 4714 -56 20 825 843 1654 + 14 12 910 23 952 -19 9 768 823 1552 + 39 12 832 623 1428 + 27 12 590 779 1376 — 7 3 857 260 1175 -58 8 Each of the above results is the mean of six determinations made at one sitting, which took about two hours. The error is in every case greater than the calculated probable error. F, though represented by different numbers, was approximately the same strength throughout. The S Exciting Rays Diagram 4. numbers are proportional to the squares of the tangents ; it was not thought necessary here to reduce them so as to represent F by the same number in each row. In the observations recorded in the sixth row, the cardboard square was used as a comparison source. A cadmium spark was tried as exciting source, but was not steady enough. The above determinations were made on the wave-length A = 554 fi /u. A strip of spectrum 38 jul/a wide was examined with an equally wide slit. For a given brightness of field, the light is purer when the slit and the strip of the spectrum examined are equally wide. Owing to using this wide slit, a slight difference of tint between the two halves of the field was at first visible in the F measurements. This difference of tint is referred to by Miss Wick and by Burke, who did not resolve his light spectrally at all. In order to test whether the difference of tint made an appreciable error, a piece of green glass was placed before the comparison source. This made the upper half of the field distinctly yellower. It had a distinct effect, giving a value of (T + F — C)/T = Tl, and on making the difference of tint more pronounced (T + F — C)/T was obtained = *22. The very slight difference of tint present originally was removed by 1908-9.] Negative Attempt to detect Fluorescence Absorption. 409 placing a cell with copper nitrate, of a suitable strength, as colour filter before the comparison source. In the measurements made on fluorescein and the other piece of uranium glass, which showed a stronger fluorescence, a narrower slit was worked with and this precaution was not necessary. In the article above referred to Wood has indicated a method of testing the method employed for systematic error. The test would be improved if a piece of coloured glass, instead of a piece of clear glass, were placed before the slit at an angle of 45° to the axis of the collimator. Fluorescein. A standard solution was prepared by dissolving as much fluorescein as possible in water at room temperature, the undissolved particles being removed by filtration. The following table gives the fraction of the incident light transmitted through 1 cm. of this solution : — A A 535 fx/x •918 484 ixjx •0117 515 •710 475 •0381 504 •168 466 •0725 496 •0305 452 •1441 489 •0070 438 •3514 The above table does not include the loss for reflection. Thus for A = 515 /a/* '290 of the light entering the solution would be absorbed in it. The next table gives the fluorescence curves not corrected for absorption in the solution. In (1) the exciting source had not, in (2) it had the cobalt glass filter. A solution 1 cm. thick and one quarter the strength of the standard solution was used. A (i) (2) 604 fifi '0187 /x/x • . • 574 •137 •038 549 •476 •175 527 1-37 •516 508 2-30 •881 492 1-08 •486 The curves are plotted in diagram 5. The results of two sets of readings made on A = 508 ju/u are given : — T F C T + F-C Probable Error. 906 290 1173 + 23 10 935 694 1593 + 3 20 410 Proceedings of the Royal Society of Edinburgh. [Sess. Uranium Glass — Second Specimen. This piece measured 2x1x1 cms. and was from Schott u. Gen., Jena, the trade name for it being F 3757. The fluorescence was decidedly stronger than in the case of the other specimen. The following table gives the fraction of the incident light transmitted through 1 cm. of the glass, the loss from reflection being included : — A A 600 •929 484 fi/i •321 562 •914 467 •277 530 •903 452 •131 504 •494 1908-9.] Negative Attempt to detect Fluorescence Absorption. 411 The next table gives the fluorescence curves as in the two former cases : — A (i) (2) 620 •089 ... 598 •356 •104 578 •946 •310 560 2-82 •875 544 4-86 1-761 529 8-24 2-928 516 9-82 3-202 504 613 2*444 494 2-02 •811 484 •194 ... The curves are plotted in diagram 6. It will be noticed that although the absorption of the two glasses is somewhat different, the fluorescence is the same according to the curves. However, when examined with the spectroscope and a narrow slit, the fluorescence maximum of the second glass is seen to consist of four bands, three of which are situated at 516, 535, and 563 fxjj., the fourth being in the yellow. The first glass did not show bands, although one seemed to be almost visible. The results of two sets of readings made on X = 529 /ul/ul are given : — T F C T + F-C Probable Error. 1821 1055 2810 66 11 766 1291 2016 41 18 In analogy with the anomalous dispersion produced by an absorption band, if fluorescence produces a change in absorption, it should also produce a change in the index of refraction. This was sought for with a Jamin polarisation interferometer.* The two interfering beams are in this instrument about 12 mm. apart. They were passed through the same solution or the same piece of uranium glass and the solution or glass in the path of the one beam made to fluoresce. No shift of the bands was detected. An arc lamp was used as exciting source, but its full intensity could not be utilised, as the fluorescence became so strong that the interference bands could not be seen. The bands were obtained from a sodium or lithium flame. According to theory, the change should have been too small to detect. For, if we represent the index of refraction in the neighbourhood of an absorption band in the usual way by a complex quantity n( 1 - zk), * Gom'ptes rendus , 67, 1868, p. 814. 412 Proceedings of the Royal Society of Edinburgh. [Sess. and regard this as a function of X, it may be shown, according to the theories of Drude, H. A. Lorentz, and others, that the maximum change in n is one-half the maximum value of tik, which of course deter- mines the absorption. If (T + F — C)/T were ‘20 then, in the case of the measurements on fluorescein with the interferometer, uk should alter by 4*4 10~7 and n by 2*2 10-7, a wholly inappreciable amount on a length of 2 cms. In conclusion, a very simple construction of the molecule may be suggested to explain fluorescence in such a case as that of fluorescein, where we have a fluorescence band of somewhat longer wave-length than a well-marked absorption band. When a body is fluorescing its molecules are supposed to be in two states. In the first state let us 1908-9.] Negative Attempt to detect Fluorescence Absorption. 413 suppose that a negative electron is moving in an ellipse inside a sphere of positive electricity of uniform density p. Its period is then e being the charge on the electron and m its mass. Let us suppose that the electron executes forced vibrations under the action of the incident light, the amplitude increasing until it flies out of the sphere. It will then move in an ellipse under the inverse square law, the period being 3i rm r 3 pe a? where r is the mean diameter of the path and a the radius of the sphere. The period is now longer. We shall suppose that in this state the electron loses kinetic energy by radiation and finally falls back into the sphere, and that the process is again repeated. We should have in addition to assume the existence of irregular impacts on the sphere due to collision with other spheres, otherwise the electron would remain on its surface. This model has the advantage of explaining why the fluorescent light has a longer wave-length. Unfortunately it does not give it a definite period. The research described in this article was carried out in the Physical Laboratory of the University of Glasgow. The spectrophotometer employed was the property of the Carnegie Trust for the Universities of Scotland. (Issued separately July 8, 1909.) 414 Proceedings of the Koyal Society of Edinburgh. [Sess. XXIV. — Experiment with the Spark Gap of an Induction Coil. By Dr Dawson Turner. If the electrodes of an induction coil be placed at such a distance that a spark will not pass easily, then the introduction of a dielectric between the poles will greatly facilitate the sparking, provided the dielectric be placed near or against the positive pole, but will not have this effect if placed against the negative pole. Experiments were made with mica, sulphur, glass, and ebonite, etc. ( Issued separately July 8, 1909.) 1908-9.] Stropliantlius sarmentosus : Pharmacological Action. 415 XXV. — Strophanthus sarmentosus : its Pharmacological Action and its Use as an Arrow Poison. By Sir Thomas R. Fraser, M.D., F.R.S.S. L. & E., Professor of Materia Medica in the University of Edinburgh ; and Alister T. Mackenzie, M.A., M.B., Ch.B., Carnegie Research Scholar. (Abstract.) An extract of the seeds of Strophanthus sarmentosus appears to be an important ingredient of the arrow-poison of Nigeria and other parts of West Africa. While some of the other ingredients of this arrow-poison may possess toxic power, others of them have little or no toxicity and are introduced into the arrow-poison with the object, apparently, of rendering it more viscous and adhesive or with a superstitious intention. The seeds contain a glucosidal active principle as well as a large quantity of inert oil and other substances soluble in ether. In order to determine the nature of the pharmacological action, an alcohol extract freed from substances soluble in ether was used. Its minimum-lethal dose by subcutaneous injection per kilogram of animal was found to be, for the frog, 0*0035 gram ; for the rat, 0*3 gram ; for the rabbit, 0*0015 gram ; and for the cat, 0*002 gram ; and, by intravenous injection, for the rabbit, 0*0012 gram. The minimum -lethal dose is, therefore, by subcutaneous injection, almost the same for rabbits and cats, and for frogs it is twice as large, and for rats 200 times as large as for rabbits. The predominating effects are those produced upon the heart and the skeletal muscles. Under the influence of S. sarmentosus , shortening of skeletal muscles is produced, and, later, fibrillary twitches become conspicuous. When these twitches have disappeared, the contraction of the muscle under stimulation is more gradual, the amount of contraction is less, and the relaxation of the muscle is slower than before ; stronger stimuli are needed to produce contraction ; and, soon, the strongest direct electrical stimulation fails to cause contraction of the muscle. At this time the muscle is pale, rigid and acid in reaction. The effects of the extract on the heart are the most important of those 416 Proceedings of the Royal Society of Edinburgh. [Sess. produced. Small doses tend to produce a diastolic type of change, and large doses a systolic type. This applies equally to application of 8. sarmentosus to the outer surface of the heart and to its administration through the blood-stream. With small quantities the rate of the heart’s contractions is slowed, and the size of the diastolic as well as of the systolic movements of the ventricles and auricles, and the strength of the systolic contractions of both, are increased. These changes are produced when a dilution of even 1 in 500,000 is perfused through the frog’s heart. The slowing of the heart’s rate is partly due to this increased range of movement, but lengthen- ing of the diastolic pause plays an important part in the retardation. With large quantities, the heart’s contractions may, at first, be modified in the same way as with small quantities, but the diastolic expansions of the ventricles afterwards become reduced, the quantity of blood entering them becomes lessened, and the ventricles finally cease to contract and remain motionless in extreme systole. Previously to the final standstill, the ventricular pulsations are usually limited to small portions of its wall. Paralysis of the vagus by atropine, after the cardiac effects have been developed, does not modify these effects, nor does paralysis of the vagus, before and during the administration of the extract, prevent the occur- rence of the changes in the heart which are characteristic of the action of Strophanthus. The cardio-inhibitory function of the vagus nerve is not increased or otherwise appreciably modified by 8. sarmentosus. On the blood-vessels, the action of the extract is slight, for very strong solutions cause only an unimportant degree of contraction. 8. sarmentosus does not appear to affect the blood-pressure, excepting through the changes produced in the heart’s contractions. No evidence was obtained of a haemolytic or a blood-clotting effect, in vivo. The lymph hearts of the frog are practically unaffected by this substance. The chief effects on the respiration are attributable to the action on the heart, though there may also be a direct action on respiration through its medullary centre. The spinal reflex disappears a considerable time after the administration of lethal doses of the extract, and only after the heart and respirations have been much affected. This disappearance is due not only to reduced blood- supply, but also to a direct action on the cord. When applied to the skin of frogs, the extract is capable of temporarily abolishing the function of sensory nerves in strong solutions, such as from 1908-9.] Strophanthus sarmentosus : Pharmacological Action. 417 1 in 1000 to 1 in 500. Slight dilatation of the pupil accompanies the ansesthesia produced by placing such solutions on the eyeball of warm- blooded animals. The function of motor nerves is slowly impaired, owing to the action of the extract on the nerve-ends, and, much later, it is abolished. Before abolition of function, fibrillary twitches occur in the muscles. The occur- rence of these twitches is prevented by paralysing the nerve-ends with curara. It would appear, accordingly, that the action of S. sarmentosus is very similar to that of S. hispidus. (Issued separately July 9, 1909.) 27 VOL. XXIX. 418 Proceedings of the Roval Society of Edinburgh. [Sess. XXVI. — On the Histological Changes in the Liver and Kidney after Chloroform administered by Different Channels. By G. Herbert Clark, M.B., D.P.H. (From the Physiological Laboratory of the University of Glasgow.) (With Three Plates.) (MS. received April 17, 1909. Read May 3, 1909.) In a paper published in the Proceedings of this Society in 1908, D. Noel Paton (1) showed that chloroform acts very differently upon the metabolism when administered by different channels : that, when given by the respira- tory tract, its effect generally is simply to increase the protein metabolism, but that when given by the mouth, it produces a marked disturbance in the distribution of the urinary nitrogen, which he considers to be due to the chloroform acting as an hepatic poison. The action of the drug when administered hypodermically was found to be in the same direction as when given by the mouth. Miss Lindsay in conjunction with D. Noel Paton (2) showed that the rate of elimination varies with the mode of administration, being most rapid when given by the respiratory passages, and slowest when given by the mouth. It was further shown that the chloroform is fixed in the liver to a greater extent when given by the mouth than when given by the respiratory passages. They also, in confirmation of the work of others, recorded the appearance of albumin and of cellular debris and tube casts in the urine, especially after administration by the mouth or hypodermically. It therefore seemed desirable to study how far the action of chloroform upon the tissues varies with the mode of administration. Previous Investigations. Already a very large amount of work upon the action of chloroform upon the tissues has been recorded. An excellent resume of the literature is given by Stiles and McDonald (3) in their paper on delayed chloroform poisoning, and only a general statement of the results of previous investiga- tions is necessary. It appears to be generally recognised that administration of chloroform is often followed by degenerative changes in various tissues, and the majority of writers consider the change to be of the nature of a fatty degeneration. According to some, droplets of oil are to be seen in the blood-vessels. 419 1908-9.] Changes in Liver and Kidney after Chlorofornn Fraenkel (4), Marthen (5), and Cohn (6) further describe the appearance of a yellow pigment in the kidneys and liver of patients who died apparently as a consequence of having been anaesthetised with chloroform administered through the respiratory passages. There is considerable difference of opinion as to the cause of the degenerative change; some authors (Junkers (7) and Strassmann (8)) con- sidering that it is due to the toxic action of the drug on the cells them- selves, others to a primary destructive action on the red corpuscles. (Nothnagel (9) and Ostertag (10) ). In the paper referred to above, Stiles and McDonald describe in detail the post-mortem appearance of tissues removed from a child who died four days after an operation under chloroform ansesthesia. The changes consisted in extensive degeneration of liver and kidney tissue. In the case of the liver, the cells throughout the organ were markedly changed and vacuolated, but the most complete degeneration appeared to have taken place in the centre of the lobules. The cells contained droplets of oil, which were clearly demonstrated by staining with Sudan iii. Droplets of oil were also found in the hepatic veins. The kidney showed intense fatty degeneration, which was almost universal throughout the organ. Stiles and M‘Donald then made a series of observations upon rabbits, and to obtain a full action of the drug upon the tissues the chloroform was injected subcutaneously. Here again they found marked fatty changes in the liver cells, most marked in the central and intermediate zones of the lobules. The cells were seen to be occupied by numerous minute droplets which showed no tendency to coalesce, and many in the centre of the lobules were completely disorganised. In the kidneys the changes were less marked, and varied from cloudy swelling in the cells of the convoluted tubules and ascending loops of Henle to well-marked fatty change in these tubules and the collecting tubules. No fat was observed in the vessels, and it was noted that the glomeruli showed no change. The authors then examined similar tissues obtained from animals which had inhaled chloroform vapour for varying times. They found the changes to be similar to those observed after injection of the drug, but somewhat less marked. Doyon (13) also describes the histological changes in the liver after chloroform had been administered experimentally by the mouth and hypodermically. In both instances he found necrosis of the liver cells. 420 Proceedings of the Royal Society of Edinburgh. [Sess. Present Investigation. In carrying out this research the tissues used were for the most part those obtained from the rabbits referred to in the papers by D. Noel Paton and Miss Lindsay. A. Changes in Vitro. Before considering the changes which occurred in the body, it was thought advisable to find what was the effect of chloroform upon the tissues when it acted upon them in saline solutions kept at the body tem- perature. This subject was touched upon by D. Noel Paton in 1894 (11). In the first instance, 0 75 per cent, sodium chloride solution was used, and a small quantity of pure chloroform was introduced into a bottle filled with the saline, and shaken up with it thoroughly for about five minutes. The solution was then set aside for some time, and the supernatant fluid decanted off. The tissue was removed from a newly killed healthy animal, and having been divided into portions of about 1 X 1 x J c.m., these were immersed for varying times in the solution. As controls, portions of the tissue were fixed immediately in 10 per cent, formol-saline solution, and other fragments of similar size placed in a 075 per cent, sodium chloride solution, and left for times similar to those during which the chloroform saline acted. The tissues were kept in an incubator at the constant temperature of 35° C. for periods of \ hour, h hour, 1 hour, 1 £ hour, etc., to 24 hours. As the time elapsed, the tissue was removed from the incubator and immediately immersed in a 10 per cent, formol-saline solution. After fixation and hardening, the fragments were cut in paraffin, stained with hsemalum and eosin, and examined. The tissues were also stained by osmic acid, Scharlach rot, and Sudan iii. for fat. It was found that even the fresh tissue fixed in formol-saline containing 0*75 per cent, of sodium chloride immediately after death shows a slight variation from the normal. The cells look swollen, and their borders are not sharp. It seemed probable, therefore, that the saline solution used was not isotonic with the tissue immersed in it. The solution suggested by Castaigne and Ratliery (12) (A = 0‘78), approximately 1*3 per cent, of sodium chloride, was then tried. Kidney. — In this solution the kidney retains a normal appearance for a considerable length of time, and even after two hours’ immersion at a temperature of 35° C. there is but little change in the appearance of the cells. In the later experiments the chloroform was added to this solution. It was found that necrobiotic changes set in at once in the tissue in 1908-9.] Changes in Liver and Kidney after Chloroform. 421 chloroform, but that they do not appear in the control tissue for some time. After five hours the change in the control tissue is quite as great as in the chloroform tissue, and from that time onwards the greatest changes are present in the control tissue. This is due to the action of micro-organisms. In the kidney the first change which was observed was that the cells of the convoluted tubules seem to lose their definiteness of outline and the protoplasm takes on an appearance like cloudy swelling. The cells appear to be markedly granular, and their free margins rapidly take on a fringed appearance. This is followed by a gradual loss of power of taking on basic stains on the part of the nucleus. The degenerative changes observed in the tubules, beginning in a cloudy swelling, become more marked as time progresses, until eventually it was difficult to make out the details of structure of the organ. The tubules become filled with granular debris, and little is left beyond the basement membrane mapping out the position which the tubules have occupied. The glomerular tuft is unaffected in the earlier stages ; and, in fact, it is not until after the tissue has been immersed in chloroform-saline solution for three hours that the first marked change appears. This change consists of a slight shrinking of the glomerular tuft away from the capsule of Bowman. In the earlier stages this shrinkage is slight, and leaves a gradually increasing space between the tuft and the capsule, which after longer immersion is found to be occupied by an exudate staining deeply with hsemalum. The same shrinking and exudation appears in the glomeruli of the specimens immersed in saline solution, but some hours later. This confirms in vitro the observations of Marthen (5) and Stiles and M‘Donald (3). Liver. — In the case of the liver the influence of the chloroform is well shown, for at an early stage the normally well-defined nucleated liver cells lose their clearness of outline. The finely granular protoplasm becomes coarsely granular, and later becomes broken up and vacuolated. The nuclei soon lose their power of taking on basic stains, and in course of time the cells become so far disintegrated that but little sign of their normal struc- ture persists. After many hours the sections show merely granular debris. The same changes take place in the tissue immersed in saline ; but, as in the case of the kidney, this appears after a much longer immersion. Comparing the whole series of specimens which were examined in these experiments it may be broadly stated that in vitro the tissues immersed in chloroform-saline solution show necrobiotic changes at a very much earlier stage than do similar tissues immersed in a similar amount of a pure saline solution of the same concentration. 422 Proceedings of the Royal Society of Edinburgh. [Sess. B. Changes in the Living Animal. In considering the influence of the drug upon the tissues in vivo , two different factors have to be dealt with — the method of administration and the duration of the action of the drug. Administration by the Respiratory Tract. In the tissues taken from animals which had chloroform administered through the lungs the amount of change in the liver and kidney was on the whole but small. In some cases, notably those examined some time after ansesthesia, no variation from the normal was observable. The greatest change was in the organs removed from a rabbit which died immediately after the administration. Here the cells lining the ascending and descending tubules of Henle and the convoluted tubules of the kidney showed marked degenerative changes. The liver was much less affected, the cells being in an early stage of albuminous degeneration. It is notable that at the time the animal died the blood contained as much as 77*3 mg. of chloroform per 100 c.c. of blood, and that respiration had stopped during the administration of the drug. The specimens showing the next greatest change were those obtained from an experiment where a small-sized rabbit was anaesthetised for a short time and killed soon after. The blood was found to contain 308 mg. chloroform per 100 c.c. The sections of both kidney and liver showed extensive degeneration. Administration by the Stomach. When chloroform was administered in oil by the stomach the mortality was very great, and in those animals that survived the administration extensive changes in the organs were found. The kidney tissue had under- gone marked degeneration, and in many cases this had gone as far as actual necrosis. The tubules were frequently found to be choked with albuminous debris. In many instances granules which stain bright red with Scharlach rot were observed in the cells and in the debris. The nuclei showed a varying degree of affinity for the basic stain, losing the power to take on the stain as degeneration advances. The glomeruli were in no instance in an advanced stage of degeneration, signs of congestion alone being present. This observation is in accordance with the results obtained by the experi- ments in vitro. The degree of change in the kidney varies greatly with the length of time after the chloroform is administered. In cases where the animal was 1908-9.] Changes in Liver and Kidney after Chloroform. 423 killed within a few hours of this administration, degeneration had not advanced very far. Three hours after the drug had been given the cells showed a considerable degree of cloudy swelling, and here and there there were signs of desquamation in the ascending and descending tubules of Henle. In a specimen taken at 5J hours the degeneration had advanced greatly, and the tubules contained a great deal of albuminous material. The cells were frequently found to be vacuolated, and the nuclei had taken on the hsemalum stain badly. When the animal recovered, the kidney tissues apparently began to repair after arriving at this point of degeneration. In specimens taken from animals which were killed two or three days later, apparently recovering from the effects of the drug, the changes were never found to be more marked than those described. On the other hand, when the animal died overnight after the administration or was killed when obviously dying, the kidney was found to be rapidly losing all signs of its original structure; the cells lining the tubules were frequently lost alto- gether, nothing being left but the basement membrane. Where the cells were still apparent, the nuclei were stained badly and the tubules were choked with debris. Here and there throughout the organ, particularly in one or two specimens, masses of blood were observed, apparently between the tubules and not in the vessels (figs. 1 and 2). Where this was observed, the cells lining the tubules adjacent to the blood were frequently found to contain small dark-coloured granules similar to those described by Fraenkel (4), Marthen (5), and Cohn (6). These were not observed in any other position in the kidney. In the liver the degree of change was also found to vary with the length of time after the administration of the drug, and also with the progress towards recovery of the animal. Examined three hours after administration, the cells at the periphery of the lobules showed but little change — at most a slight degree of cloudy swelling. The cells in the centre of the lobule, on the other hand, had undergone a granular change, and the nuclei had begun to lose their power of taking on the stain. After five hours this was still more marked ; and an hour and a half later some of the cells in the centre of the lobule had completely broken down, leaving granular debris in place of the cells. When the animal showed evidence of recovering from the effects of the drug, no further change in appearance of the tissues was observed. When the animal was found dead in the morning after the administration, or 424 Proceedings of the Koyal Society of Edinburgh. [Sess. showed signs of dying at an early date and was killed in consequence, the degree of change was very much greater. The centre of each lobule was found to be occupied by a granular mass showing neither nuclei nor any appearance of liver tissue. The intermediate zone was frequently also affected, and in the worst cases no sign of liver tissue was seen except a layer of two or three cells thick at the periphery of the lobules (fig. 3). In the granular debris a number of granules staining red with Scharlach rot were seen. The degenerative change in the liver in the animals where the chloroform was administered by the stomach is generally very great indeed, and in all cases appears much more complete than the change in the kidney. This is possibly due to the action of the chloroform “ anchoring ” itself to the liver cells. Administration Subcutaneously. When chloroform was given in the form of a subcutaneous injection, the mortality among the animals was very great, and a large proportion died during the night after the injection. On the other hand, the animals that recovered appeared to be quite active a day or two later. Histologically, the changes in the organs are very similar to those detailed above, the difference being one of degree. In the kidney, after four hours very little degeneration seems to occur, a slight degree of cloudy swelling being apparent. After five hours, some vacuolation was seen in one of the specimens examined. In one animal killed some hours later, and in a dying condition, the kidney showed an appearance comparable with that observed in some of the worst cases after administration by the stomach. The ascending and descending tubules, the convoluted tubules, and more markedly the collecting tubules showed little or no sign of cellular lining. They were choked and frequently distended with albuminous debris. In all the cases, however, the glomeruli retained an appearance approximating to the normal. In the animals which died, the appearance of the kidney was similar to those just described. Parts showed tubules denuded of their epithelium, and other parts showed cells in an advanced state of degeneration (fig. 4). Generally there was evidence of congestion of the organ, and occasionally dark granules were observed similar to those referred to above. In the case of the liver there was generally a slight necrosis in the centre of the lobule even a very few hours after the administration, and as 1908-9.] Changes in Liver and Kidney after Chloroform. 425 time advanced this increased in amount (fig. 5). In the worst cases, where the animal was found dead or was killed in a dying condition, the state of the organ was like that described under administration by the stomach, viz., the organ was a honeycomb of cheesy material showing very little sign of the original liver structure. Summary. 1. When kidney or liver tissue is immersed in a saline solution contain- ing chloroform, degenerative changes take place similar to the normal necrobiotic changes but very much more rapid. In the case of the kidney the glomeruli are not affected for a very considerable time. 2. When chloroform is administered through the respiratory passages a considerable degree of degeneration is only occasionally found in the kidney and liver cells. It is more marked in some cases than in others where a similar amount of chloroform was given to animals of a similar size. This may be associated with the very varying rate at which the drug is eliminated, as shown by Miss Lindsay ( loc . cit.). The degree of change in the liver was never great. In the kidney there is frequently cloudy swelling, and occasionally desquamation of the epithelium of the ascending and descending tubules. 3. Where the drug is given by the stomach the mortality is great and the changes observed in the organs are marked. In all cases there is evidence of the toxic action of the drug. In the animals most affected, the structure of the liver is almost entirely lost, nothing remaining of the lobules but a shell of liver cells enclosing a cheesy debris. In the kidney the drug acts in a similar way, the degree of degeneration being somewhat less than in the liver. The glomeruli are but little affected even in the worst cases. 4. When the drug is given hypodermically the changes are similar to those observed when the drug is given by the stomach. The liver is again more affected than the kidney. On the whole, however, chloroform does not appear to be quite so destructive to the liver tissue when administered in this form. 5. The marked action of the drug upon the liver, whether administered by the stomach or hypodermically, is probably accounted for by the “ anchoring” action referred to by D. Noel Paton (1). It would be interest- ing to know if there is evidence of a similar action on the part of the kidney cells to account for the extensive degenerative change frequently observed there. 426 Proceedings of the Royal Society of Edinburgh. [Sess. 6. The result of these observations helps to explain the different effects of chloroform on hepatic metabolism. When given by the respiratory passages it is rapidly eliminated, produces no marked histological changes, and the metabolic disturbances are slight ; but when given by the mouth and hypodermically it is more slowly eliminated, has more time to produce its toxic action, and the metabolic disturbances are pronounced. In a future paper the action of chloroform upon the blood corpuscles will be dealt with. A grant was received from the Carnegie Trust to defray the expenses of this research. REFERENCES. (1) D. Noel Paton, Proc. Roy. Soc. Edin., vol. xxviii., 1907-8, p. 472. (2) D. Noel Paton and Miss Lindsay, Proc. Roy. Soc. Edin., vol. xxviii., 1907-8, p. 497. (3) Stiles and McDonald, Scottish Medical and Surgical Journal , Aug. 1904, p. 97. (4) Fraenkel, Virchow's Archiv , Bd. cxxvii. S. 381, and Bd. cxxix. S. 254. (5) Marthen, Berlin ldin. Woch ., 1896, No. 10. (6) Cohn, Deutsche Zeitsch. f. Chir ., 1902, Bd. ixiv. (7) Junkers, Tiber fettige Entartung infolge von Chlorof. Inhalat., Bonn, 1883. (8) Strassmann, Virchow's Archiv , 1889. (9) Nothnagel, Berlin Min. Woch., 1866. (10) Ostertag, Virchow's Archiv , 1889, Bd. cxviii. S. 250. (11) D. Noel Paton, Phil. Trans. Roy. Soc., 1894, vol. clxxxv. p. 248. (12) Castaigne and Rathery, Arch, de med. exper. et d'anat. path., Sept. 1903. (13) Doyon, Compt. rend. Soc. de biol., vol. lviii. pp. 30, 108, 853. ( Issued separately July 9, 1909.) Proc. Roy. Soc. Edin. ] [Vol. XXIX. Fig. 1. — Kidney from rabbit, No. 9a of the series, which bad lcc of chloroform administered in oil by the stomach. To the right is seen a quantity of extra-vascular blood. The cells lining the tubules are in various states of degeneration. The nuclei, as a whole, are badly stained. x 150. Fig. 2. — High power view of the tubules adjacent to the extra-vascular blood. The granules referred to in the text are well shown. x 800. Dr G. Herbert Clark. [Plate I. Proc. Roy. Soc. Ed in . ] [Vol. XXIX. Fig. 3. — Liver from the same rabbit. To the left the centre of the lobule is seen to be completely broken down, while to the right the cells at the periphery appear almost normal. x 150. Fig 4, — Medulla of kidney from rabbit, No. 33, which received an injection of lcc of chloroform subcutaneously. A considerable degree of degeneration is observable, and the nuclei are losing the power of taking on the basic stain. x 150. Dr Gl. Herbert Clark. [Plate II. Proc. Hoy. Soc. Edin. ] [Vol. XXTX Fig. 5. — Liver from the same animal. The centre of the lobule shows cells considerably degenerated and even vacuolated. The periphery — to the right — shows cells which are almost normal in appearance. x 150. Dk G. Herbert Clark. [Plate III 1908-9.] Internal Friction in Cases of Compound Stress. 427 XXVII. — On the Effect of Internal Friction in Cases of Compound Stress. By G. H. Gulliver, B.Sc., A.M.I.Mech.E., Lecturer in Engineering in the University of Edinburgh. (MS. received January 19, 1909. Head July 12, 1909.) In a previous paper * certain results were deduced for bars supporting simple tensile or compressive loads, on the assumption that materials exhibit an internal resistance to deformation of the nature of a frictional resistance to the sliding of the particles along the cleavage surfaces. These results are easily extended to any system of stress in a solid body. Let pv p2, and Ps he the principal stresses, acting normally to the three pairs of faces of a small cubic element, px being the maximum tension or minimum compression, and p3 the minimum tension or maximum compres- sion. If tensions are taken as positive, Pi>p2>ps • Then it is a well- known result that the plane of maximum shear is parallel to the direction of p.v and inclined at 45° to both px and p3, and that the value of the maximum shearing stress is i(p1—pB)- In the same manner, but taking into consideration the effect of internal friction, as already explained, the plane of sliding is parallel to the direction of p2, and is inclined at a = (45° + (p/2) to pv and at /3 = (45u — 0/2) to pB. The minimum resistance to sliding is, ju,K ~Pi sin a cos a + pp1 sin2 a-p3 sin /3 cos /3 + pp3 sin2 {3 = sin a COS a(p1 —p3) + p(px sill2 a +p3 COS2 a) ~ 2 {(cos ^ M sin ){p{ -p3) + p(pl+p3)\ = h{Pi( Jl +p2 + p) ~P3( Jl+p2- p)} where K is the cohesion of the material as defined before, and p ( = tan 0) is the coefficient of internal friction. Few investigations of the effect of compound loading upon metal bars have been carried out. The most complete series of experiments are those of Guest ; some interesting results have been obtained also by Hancock, by Scoble, and by Goodman. It occurred to the writer that these exjDeriments might afford some evidence for or against the influence of internal friction. Guest’s experiments f were made with ductile materials — steel, copper, and brass — in the form of thin tubes. These tubes were subjected to tension, to torsion, and to internal pressure ; and also to tension combined with torsion, to tension combined with internal pressure, and to torsion combined with internal pressure. The loads were so regulated as to obtain * Proceedings , xxviii., 1908, 374. t Phil. Mag., 1., 1900, 69. 428 Proceedings of the Royal Society of Edinburgh. [Sess. a number of stresses lying between p, 0,—p, and p, O, p. Internal pressure causes the intermediate principal stress to have a small negative value (compression), but this is of no importance. The criterion of strength for the steel tubes was taken as the yield-point, and the results of the experi- ments are given in a series of tables attached to the paper. The conclusion was drawn that the strength of a material is determined by the maximum shearing stress, and not by the maximum principal stress, or by the maxi- mum principal strain. The writer, by taking Guest’s data for the principal stresses, and assuming /a = 0T4 for the steel tubes, found that the numerical values of the minimum resistance to sliding were sometimes less uniform, and some- times more uniform, than the values of the maximum shearing stress. The figures are not sufficiently interesting to reproduce, but the experiments could not be said to give results more in favour of the minimum resistance theory than of the maximum shear theory. Another point of interest was the determination of the values of jjl which would accord with the experimental results. The values of this coefficient, obtained from the simple tension and simple torsion results only, are given in the table below, from which the amount of variation can be judged. The variations found for each separate bar, under the different conditions of loading, were quite as great. It should be pointed out that small errors in measuring stresses lead to relatively large errors in the determination of /x. No measurements of the direction of sliding at the yield-point seem to have been made by Guest. These experiments, there- fore, do not permit one to assign any definite value to /u. Table. Form of Specimen. Diameter. Thickness. tu. Remarks. | Guest — I. Round tube . D316 0-029 - 0-242 II. „ . . 1-250 0-028 . « • Several different results. III. 0-499 0-025 -0-071 IV. „ . . 1-250 0-025 + 0-093 V. „ . . 1-250 0*025 ... No torsion test. VI. 1-250 0-025 + 0-015 VII. „ . . 1 *250 0-025 + 0-160 VIII. 1-250 0-025 + 0-090 IX. 1-250 0-025 + 0-144 Hancock — Round tube rooo 0-050 + 0-146 rooo 0-075 + 0-380 « * 1-000 0-250 + 0-204 Round bar 0-500 ... + 1-189 429 1908-9.] Internal Friction in Cases of Compound Stress. The experiments of Hancock * were performed upon steel tubes and solid round bars, these being submitted to tension and to torsion, both singly and combined in various proportions. Similar calculations, taking /u as 0T4, gave results appreciably more uniform than the maximum shear, especially in the case of the thinnest tube. The divergences in Hancock’s results become much greater as the thickness of the tube is increased. The values of fj., calculated from the simple tension and simple torsion experiments, are given also in the above table. The absurd result shown by the solid bar is probably connected with the variation in stress over the cross section, caused by torsion. Scoble j* subjected solid round steel bars to combined bending and torsion. The magnitude of the stress across a section of a bar in such conditions varies considerably, so that it is impossible to determine the yield-point with any degree of accuracy. Recognising this difficulty, Scoble made use of a purely arbitrary point, found by prolonging the plastic curve backwards to meet the elastic curve. This point is certainly not identical with the yield- point, and since it depends upon the individual judgment in extrapolating a curve, which is itself liable to considerable variations in character, the results cannot be considered of great value. As they stand, however, they would give no definite value for jm, as is pointed out by Scoble himself. Goodman’s experiments were confined to the application of combined bending and torsion to solid round bars of cast iron — a brittle material — instead of the ductile substance, steel. The two cases are very different, and the results must be considered in a somewhat different manner. There is a distinct dissimilarity between ductile and brittle bodies in their behaviour under stress. When broken by simple tension, a ductile substance shows a more or less perfect shearing fracture, but a brittle substance ruptures along a direction approximately perpendicular to the direction of the stress. On the other hand, under a compressive stress brittle bodies give shearing fractures, while ductile materials are simply flattened, but sometimes crack along planes parallel to the direction of the load. Thus the ratio of the tensile strength to the compressive strength for ductile materials is a somewhat indefinite quantity, if strength be defined as the stress necessary to cause rupture. The same ratio for brittle substances is usually small, the compressive strength being much greater than the tensile strength; the ratio is 1/4 to 1/7 for cast iron, and as small as 1/50 for some stones. When subjected to combined stresses, ductile and brittle pieces may be * Phil. Mag., xi., 1906, 276 ; xii., 1906, 418. + Ibid., xii., 1906, 533. 430 Proceedings of the Royal Society of Edinburgh. [Sess. expected, therefore, to differ in their behaviour. A round steel bar, broken by torsion, shears along a surface which approximates to a plane at 5° to the axis of the bar — that is, at 50° to the direction of principal tension, corre- sponding with the direction of sliding in simple tension. Under similar conditions, a bar of cast iron breaks along a helicoidal surface inclined at 45° to the axis of the bar — that is, perpendicular to the direction of principal tension, agreeing also with the result of the pure tension test. In torsion the principal tension and the principal compression are numerically equal, but in cases where the principal stresses have different values the form of fracture of a brittle body will depend upon the sign of the principal stress which is the immediate cause of breaking. If the principal tension is greater than a certain fraction of the principal compression, the broken surface will be normal to this tension ; if the tension bear a less ratio to the compression, the broken surface will be inclined to the direction of principal compression at the angle f3 (less than 45°), found from the crush- ing test. But the manner in which fracture occurs is also of importance. Thus, in a bar of cast iron broken by bending, although the stress upon the trans- verse section which is most severely loaded may vary from a pure com- pression to a pure tension, with all intermediate ratios between tension and compression, fracture usually occurs along such a transverse section — that is, in a direction normal both to the principal tension and to the principal compression. Observation shows that the metal begins to separate on the tension side of the bar, and as the crack progresses the stress suffers a redistribution, so that the direction of tension at the extremity of the crack remains approximately constant and normal to the original direction of the crack. Under combined bending and torsion, therefore, the fracture of cast iron may be expected to take place in a direction normal to the principal tension. In Goodman’s experiments * the fractures had a helicoidal form, and the helix due to the intersection of the broken surface with the exterior of each bar was found to be, within narrow limits, perpendicular to the calculated direction of the principal tension. With regard to the deter- mination of the breaking stress, the objections to the use of solid bars in experiments of this kind have been pointed out already, and Goodman’s figures for this stress are not of great value — a point which he recognises. Since the writers mentioned above are all concerned with what is usually called the “equivalent bending moment” for a shaft submitted to simultaneous bending and torsion, it may not be out of place to give the * Mechanics Applied to Engineering, Longmans, 4th ed., 1904, 492. 1908-9.] Internal Friction in Cases of Compound Stress. 431 expression obtained for this moment when internal friction is allowed for. Let M be the bending moment applied to the shaft, and T the simul- taneously applied twisting moment. Let M' be the bending moment which would have the same maximum effect upon the shaft as M and T together. Then, assuming that the strength of the shaft is determined by the maximum principal (tensile) stress, M' = i(M+ CM2 + T2). This is the rule given by Rankine, and in general use among engineers. It would appear to be true only for brittle materials. If, as according to Guest, the strength be considered as determined by the maximum shearing stress, the expression becomes, M'= This seems to represent, at least very closely, the conditions for ductile materials. Finally, if the effect of internal friction is considered, and the strength is supposed to be determined by the minimum resistance to sliding, M' = -=L-— • {fxM + V(1+^)(M2 + T2)}. I* i /!■ i And, taking /x = 0T4, as on previous occasions, M' = 0T2M + 0-88 X/M2 + T2. This last expression gives values for M' which are intermediate between those of Rankine and of Guest, though they cannot be said to represent actual conditions for ductile metals more accurately than those of Guest. Summary. The minimum resistance to deformation, and the inclination of the surfaces of sliding, are given for any system of stress in a body, supposing internal friction to be operative. The effect of internal friction in various cases of combined loading, and the value of the coefficient have been calculated from experimental data. The results do not allow of a definite value being assigned to p for steel. Certain differences in the behaviour of ductile and of brittle bodies, when loaded, are pointed out. An expression for the equivalent bending moment of a shaft submitted to simultaneous bending and twisting, when internal friction is allowed for, is given. {Issued separately July 9, 1909.) 432 Proceedings of the Royal Society of Edinburgh. [Sess. XXVIII. — On the Friction at the Extremities of a Short Bar subjected to a Crushing Load, and its Influence upon the Apparent Compressive Strength of the Material. By G. H. Gulliver, B.Sc., A.M.I.Mech.E., Lecturer in Engineering in the University of Edinburgh. (MS. received November 30, 1908. Read December 21, 1908.) 1. Crushing Strength. In making crushing tests of various constructional materials the usual form of test-piece employed is that of a small cylinder or prism, having a height of 1 to 2 diameters. The pressure is applied to the bases of the specimen by means of two plates of steel or of cast iron, which are somewhat harder — that is, less easily deformable — than the material under test. The friction between these plates and the ends of the specimen necessitates, for the deformation and rupture of the piece, a load somewhat greater than if the friction did not exist. So far as the writer is aware, no investigation of the effect of this end friction has been published hitherto, and the following is offered therefore as giving an approximate solution to the problem. The method employed is simple. In any bar, two portions about to experience a relative movement along their common plane of sliding are regarded as two rigid bodies in a condition of static equilibrium, and the sum of all the forces acting on each piece is accordingly equated to zero. Since the external forces are known, or can be determined, the internal resistance to sliding, under certain assumptions, may be calculated. The method is admittedly imperfect, and the degree of approximation of the calculated results to actual conditions is uncertain ; but these results are not un- interesting, and they show, if not grossly incorrect, the importance of the influence of the end friction upon the apparent crushing strength of a bar. The assumptions made with regard to internal friction in a previous paper(1) are made here also. The coefficient of friction is supposed to be independent of the load ; and a cohesive force, K, is assumed to act normally to the surface of each particle of the metal, giving rise to an internal frictional resistance to sliding, equal to //K. It is assumed, further, that the external frictional resistance to deformation at the loaded ends of the specimen can be regarded as equivalent to a force applied to the piece in a direction tangential to these surfaces. In all cases the bars are supposed to 433 1908-9.] Crushing Strength. be so short that any bending is negligible. The results apply only to the yield point, and not to the breaking stress of a substance. In the case of a ductile material, after the yield point is passed, the conditions change greatly, and the test-piece does not rupture by shearing. A brittle bar, however, does usually break by the sliding of some portion over the remainder. A brittle material is often defined as one in which the yield point and the breaking stress are coincident. This is hardly correct, since most brittle substances suffer some permanent deformation before rupture ; but it suggests that the calculations may not be very incorrect when FIG. i. applied to the breaking strength of brittle materials in compression. This point is examined more fully in sections 4 and 5. 2. End Friction Neglected. Let the length of the bar be such that the surface of sliding does not cut the extremities, and suppose first that there is no end friction (fig. 1). Let g be the compression yield point of the material — that is, the stress on a normal cross-section at the moment when sliding commences. Let f3 be the inclination of the surface of sliding to the axis of the bar, and let /m ( = tan ) be the coefficient of internal friction for the material. Then, as has been shown already, the shearing stress along a surface of sliding is c sin l3 cos /3, and the resistance to sliding along this surface is vol. xxix. 28 434 Proceedings of the Royal Society of Edinburgh. [Sess. i iuc sin2 /3 + yuK, where Iv is the normal cohesion between the particles. So long as sliding does not occur, c sin 0 cos 0 — fxc sin2 0 must be less than //K ; and since c sin 0 cos 0 is greater than /me sin2 00 the difference between these two quantities increases as c is increased. Sliding takes place as soon as this difference exceeds ,uK, and the inclination of the surface of sliding, therefore, is such that c sin 0 cos 0 — fie sin2 0 is a maximum. Hence tan 20 = 1 j m, or 0 = 45° — 0/2. 3. Effect of End Friction with Plates Harder than Material Crushed. Let fJL ( = tan + <£') ; that is, when, I3' = (i5° - 4,' 12. Since /a and K are, by assumption, constants for any particular material, the ratio of c to c is given by c sin (3 cos (3 — /x sin2 (3 c sin f3' cos (3' - /x sin2 (3' - /x^' sin (3 ' cos (3' - fj! sin2 f3’ |{cos (/> - /x( 1 - sin )} J[(l - /x/xr) cos ( + ') ~(fjL + /i'){l - sin (cf) + ')}] cos (f>'( 1 — sin (/>) 1 — sin (cf) + (f>') Or, more conveniently for purposes of calculation, c V f + /x2 — /x c v/(l + y2)( 1 + /A2) - (^ + /x') If the length of the bar is relatively less than in fig. 2, sliding takes place as in fig. 3 or fig. 5. The conditions for each portion are the same as in fig. 2, so that the inclination of the sliding surfaces should remain constant. If the relative length of the bar is much greater than in fig. 2, bending occurs, and the above results no longer hold good. 4. Cast Iron. For cast iron the value of as determined from Morin’s experiments on sliding friction, varies from 0T5 to 0T6. The corresponding values of (j> are 8° 32' and 9° 5'. Hence (3 varies from 40° 44' to 40° 28'. 436 Proceedings of the Royal Society of Edinburgh. [Sess. If a specimen of cast iron is crushed between cast-iron platens, fi and // are equal, or nearly so. In this case (3 = (45° -$) = 36° 28' to 35° 55'. If the platens are of steel, will be somewhat less than 016, and fi' con- sequently slightly greater than the above values. The inclination of the sliding surfaces, measured from broken specimens of cast iron, usually lies between 35° and 37°, and therefore agrees closely with the calculated value of fi'. Taking fi' = 36° as an average result, the ratio of c' to c is c c fi 1 + fi2 - /x 1 + /x2 — 2 fi T2 (nearly). In extending this result to the breaking stress of cast iron, it should be noted that bars of this material originally cylindrical or prismatic become FIG 3 more or less barrel-shaped towards the end of the test. On this account the direction of compressive stress is no longer constant, but varies slightly from point to point within the body. In this case the results are closely represented by saying that the inclination of the surface of sliding to the direction of the compressive stress at each point is constant, and has the same value as already found. The most important effect of the change of shape of the bar is the resulting curvature of the surface of sliding (fig. 4). It may be pointed out that the mere existence of this deformation is evidence that cast iron possesses a yield point lower than its breaking stress ; but this yield point, as is well known, cannot be located definitely. The minimum length of a cast iron specimen necessary to secure a clean shearing fracture is cZcot36° — that is, about T4 d, where d is the diameter of the bar. The length should not be less than this at the moment of 437 1908-9.] Crushing of Stones. crushing, and must therefore be greater in the original specimen, since the bar is appreciably shortened under the load. The general practice is to make the length from 1 J to 2 times the diameter. Shorter bars fracture as shown in fig. 3. 5. Stone, Brick, and Concrete. The coefficient of friction for these materials is extremely variable, and only rough results can be given. For stones, fx usually lies between 0*4 and 0'6, the lower value corresponding with the harder and finer stones ; for masonry and brickwork an average value of /ul is from 06 to 0 65. The value of ft, the coefficient of friction between stone and steel, or stone and cast iron, may be taken as varying from 025 to 05. With these extreme values the following results are obtained : — For [x = 04, and // = 025 ; = 22°, ' = 14°, = 34°, and /?' = 27°. For jx — 065, and fx = 0*5 ; C P = 33°, C j>' = 27°, /3 = 28J*, ft = 15°. The inclination of sheared surfaces measured from broken stone test- pieces is apt to vary considerably. This is to be expected if one considers the variability and heterogeneity of most kinds of stone, even when samples are taken close together from the same quarry. The bedding of the stone gives rise to surfaces of minimum resistance other than those considered here. A crushed stone is usually much disintegrated, and the angles may be altered by the removal of loose material. Only such surfaces 438 Proceedings of the Royal Society of Edinburgh. [Sess. 9 as show unmistakable signs of sliding should be used for measuring the inclination. The writer has, from time to time, determined roughly the inclination of surfaces of sliding in a number of specimens of stone, cement, and mortar, and these have been supplemented by measurements made from illustrations of broken specimens given by various authors. Average values of these inclinations are : — Sandstone . . . 25° to 28° Limestone . . . 20° to 25° Cement . . 20° to 30° Mortar . . 15° to 20° Angles greater than these are not infrequent, but are certainly due in many cases to disintegration, and also to irregularities in the material. On the other hand, cracks parallel, or nearly so, to the direction of the applied crushing load are often found. These would appear to be due to the inability of such materials to withstand much lateral extension ; they are not caused by any sliding action, but are the result of the low tensile strength of the substance. The two extreme ratios of c to c, calculated from the above values of fi and //, are 1*5 and 3*0 nearly, showing that the end friction has a very considerable effect, especially on the softer and coarser materials. No values of the yield points of stones are known. Whether these figures apply with any accuracy or not to the ultimate strength of such substances is impossible to say at present. In order to obtain a clean shear a length of 2 to 4 diameters is necessary. Specimens of stone and concrete required for crushing tests are usually made in the form of cubes, and fracture takes place as shown in fig. 5 ; bricks are usually 9 inches by 44 inches, and 3 inches high, but are often halved vertically, across the long edges, before testing, in order to bring them within the crushing capacity of the testing machine. 6. Wrought Iron and Mild Steel. These materials, when crushed, do not fracture by shearing, and they are not usually tested in compression except in the form of long columns, in which bending is of supreme importance. The determination of the yield point and the inclination of the lines of Liiders from short pieces, however, should give useful checks on the previous arguments. According to Morin, the value of /x for wrought iron and steel is 0T4. This corresponds with 0 = 8°, ^8 = 41°, nearly. If the crushing platens are End Friction with Soft Plates. 439 1908-9.] of steel, /3' = 37°. So small an inclination of the lines of Liiders on com- pression specimens of mild steel has been seldom found by the writer ; it lies more usually between 40° and 45°, and sometimes even above 45°. No attempt is made here to explain this difference between calculated and ex- perimental values. Taking fx = /x — 0T4, the ratio of the apparent compression yield point to the true yield point is IT 8. The ratio of the tension yield point to the compression yield point is 0'76.* Hence the value of this latter ratio, found FIG. 5. 17 from experiments, should be 0* 7 6/1 T 8— -that is, 0'64. This last figure is certainly much lower than any obtained hitherto. % 7. Effect of End Friction with Plates Softer than Material Crushed. In sections 3 to 6 the material forming the plates between which the specimens are crushed has been supposed harder than the substance under test. It was a common practice at one time, in making crushing tests of stone, to place a sheet of lead between each end of the specimen and the corresponding platen of the testing machine, with the object of securing a uniform distribution of load. Experiments soon revealed that the effect of the lead, instead of being beneficial, caused a great reduction in the ap- parent strength of the stone, amounting on an average to one-half of the strength obtained when the stone was in direct contact with the platens. The reason of this is not far to seek. As the load is applied the soft lead is deformed to a greater extent than the stone. When the compressive stress reaches a certain value — generally known as the pressure of fluidity, and estimated variously at f ton to 3 tons per square inch3, 4) — the lead * This ratio was given previously as 0-70,

") be the coefficient of friction between the stone and the lead (fig. 6). The total resistance to shearing in this case is n • 9 n?f . ~T7~ ,f rf • /V t rvf tt ft • o otr \ic sim p + [iK. — i ifi c sm p cos (3 - [i c sim p , and the angle is such that n • ofr Oft • 9 nff « ft n • ntt _ n't ft // • n c sm p cos p - 1 ic sue p + fi/u c sm p cos p + /n c sim p is a maximum. Hence tan 2/3 " = = cot ( - and j3" = 45° - J(^> - ") = (3 + " /2. As a rule, the stone does not rupture by shearing, but splits up in a different manner, discussed below. In the case of soft stones and concrete the pressure of fluidity of the lead may never be reached, and the inter- position of the metal may have no appreciable effect upon the strength of the specimen. On the other hand, for materials with crushing loads far End Friction with Soft Plates. 441 1908-9.] ffibove this pressure of fluidity, the whole of the lead is squeezed out long before rupture occurs, and the metal has again very little influence upon the maximum load carried by the piece. The value of the ratio c"/c, though of little use, is not uninteresting: — c" sin (3 cos (3 - /x sin2 (3 c ~ sin f3" cos f3 " - fj. sin2 (3" + /x/x" sin f3" cos /3" 4- /x" sin2 (3" cos <£" (1 - sin ) Jl+ /x2 - /x ~ I — sin (-") = V(1+/x2)(1+/?72)-(/x-/x'7) The numerical values of fj, for stone have been given already on page 437, but the coefficient of friction of lead upon stone does not seem to have been determined. In order to obtain some idea of the importance of the action of the lead, let /u" be taken as 0’5, corresponding with " = 27°, roughly. For /x = 04, and /x" = 05 ; (3" = 47^°, and c"/c = 052. For /x = 065, and fx' = 05 ; (3" = 42°, and c"/c — 046. Though no great accuracy is claimed for these results, on account of the uncertainty as to the value of fx" they show very clearly the weakening effect produced by the lateral flow of the lead ; this effect will be greater or less than the above according as the true value of /m" is greater or less than 05„ A few measurements made upon blocks of cement and of mortar which had been crushed between sheets of lead showed that the inclination of the sliding surfaces was very little greater than when no lead was interposed. The pieces, especially those of cement, failed chiefly by splitting vertically into small fragments, as described below ; but a few surfaces of shearing were unmistakable. As already mentioned, stone specimens crushed between sheets of lead or other soft and plastic material do not usually give way by shearing. The frictional drag of the moving lead gives rise to a tensile stress in a direction normal to the crushing load ; rupture seems to be caused chiefly by this tension, and the stone splits into a number of vertical prisms. A little consideration shows that the tensile stress is a maximum on two vertical planes passing through the axis of the block in directions parallel with the vertical faces, and that its value on these planes approximates to \fx'c" if the specimen is cubical. Experiments show that the initial cracks occur, as a rule, in the middle of the vertical sides of the piece, and that the cracks soon extend inwards to the centre (5). The stone does not give way immediately, but continues to break up into smaller and smaller prisms as the load is increased, until complete failure occurs. The breaking load averages only about one-half of the value obtained without lead, but what 442 Proceedings of the .Royal Society of Edinburgh. [Sess. determines the exact crushing stress is not clear. The ratio of c"jcf is smaller the harder the stone ; experimental values vary from 065, to 043 (6,7,8), c' having been measured for blocks in direct contact with the crushing platens,, or previously faced with thin layers of plaster of Paris, which are easily scraped flat and parallel, and behave as integral parts of the specimen. c c" . c" From the values of — and — already given, the calculated values of — are C 0 c found to lie between 035 and 0T5, so that the actual effect of the lead is less serious than it would be according to the assumed conditions. 8. Effect of Length of Specimen upon its Apparent Strength. From the results given in section 3 it would appear that the crushing strength of a material should not be altered by the length of the test-piece, provided that this is short enough for no bending to take place. Published experimental results indicate that a greater load is required to cause rupture as the length of the specimen is diminished. Thus Bauschinger found, from careful tests on a specially fine and uniform sandstone, that a cube is about 20 per cent, weaker than a piece of half the height, and about 7 per cent, stronger than a piece 14 times the height (9). Similarly Hodgkinson, in a series of tests of small cast-iron cylinders, found that with a height equal to 1J diameter the piece was 3 per cent, weaker than when the height was only 1 diameter, 19 per cent, weaker than with a height of \ diameter, and 30 per cent, weaker than a cylinder with a height equal to \ diameter (101. If crushing strength is calculated as the total crushing load divided by the original area of cross-section of the piece, it is undoubtedly increased by diminishing the length of the specimen ; but if, as is more rational, the increase in the area of the material under load is allowed for, the case is different. This increase in area is greater the shorter the specimen. One might expect that the friction of the platens, when the specimen is relatively long, would not have so great an effect in the middle of the length of the piece as when this is short. Thus the amount of lateral extension of the middle of the specimen, relatively to that of the ends, would be greater with longer specimens. In crushing cast iron it is noticeable that a piece 14 diameter long assumes a very distinct barrel shape towards the end of the test (fig. 4), while a piece only 4 diameter long, though its dimensions change, remains nearly cylindrical. The final maximum diameter is greater in short specimens than in longer ones. The following table gives numerical results, not previously published, obtained from six cast-iron bars tested some time ago for another purpose. 1908-9.] 443 End Friction in Crushing Tests. The strength, as calculated for the actual area at the middle of the bar, shows a decrease for the shorter specimens ; though the nominal strength, calculated for the original area, shows the usual increase. Original Ratio Length/Diameter or Length/Side. r> , • Original Area Ratl° Final Area ' Crushing Stress, Tons per Square Inch. Calculated on Original Area. Calculated on Final Area. Round Bars, originally 1 Inch Diameter. 1-44 1-24 40*5 32*7 U01 U39 38*9 28*0 0-51 1-47 44*2 30*1 Square Bars, originally 1 Inch Square. 1*56 1*13 37*8 33*5 1-01 U33 42*0 31*6 0-51 1*48 45*3 30*6 9. Practical Determination of Compressive Strength from Crushing Tests. It would appear from the foregoing discussion that, in order to obtain the true compressive strength of a material by means of a crushing test it is necessary to reduce the friction at the ends of the specimen to zero. This result could be obtained only if the surfaces in contact were deformed at the same rate in contiguous parts throughout their whole area. The application of lubricants to the surfaces, for the purpose of reducing the end friction and of obtaining a closer approximation to the true crushing strength, is not to be recommended. For with specimens of high crushing strength the lubricant is soon squeezed out, and if the lubricant is possessed of a sufficiently high viscosity to allow a soft material to be crushed, it exerts a weakening influence upon the specimen. Graphite, boric acid, and similar solids possessed of lubricating properties are possible exceptions to this statement, but the writer has not yet investigated the effects of these. Summary. The effect of the friction of the crushing plates upon the yield point of short compression specimens has been investigated. With plates harder than the material under test, the end friction causes an increase in the apparent yield point. This increase is calculated as 18 per cent, for wrought iron and mild steel, 20 per cent, for cast iron, and 444 Proceedings of the Royal Society of Edinburgh. [Sess. 50 to 200 per cent, for stones, bricks, and concrete. These figures, except the first, may apply almost equally well to the crushing strength, but they require experimental support. The corresponding inclinations of the surfaces of shearing are 37° for wrought iron and steel, 36° for cast iron, and 27° to 15° for stones, etc. The first value is seldom obtained, but the others agree fairly well with average experimental results. When the crushing plates are of material softer than that under test, the lateral flow of the former diminishes the apparent strength of the specimen. With stones crushed between lead plates the strength is calculated as 035 to 0T5 of that obtained when iron or steel plates are employed. Experiments give 065 to 043 as the value of this ratio, but the specimens do not rupture by shearing in the manner contemplated. The total crushing load of a short specimen of cast iron is increased by diminishing the length of the piece, but the crushing stress per unit of area is simultaneously decreased. REFERENCES. (1) Gulliver, Proc. Roy. Soc. Edin ., vol. xxviii., 1908, p. 374. (2) Ibid., p. 378. (3) Kick, Proc. Inst. Civ. Eng., vol. 1. 1877, p. 188. (4) Unwin, Testing of Materials of Construction (Longmans, 1899), p. 393. (5) Pace, Atti Coll. Ingeg. Archi., Palermo, 1880, iv. (6) Unwin, Brit. Assoc. Report, 1887, p. 879. (7) Beare, Proc. Inst. Civ. Eng., vol. cvii., 1891, sect. ii. p. 341. (8) Pace, Int. Assoc. Test. Materials, Brussels Congress, 1906, Paper B 10c, p. 7. (9) Bauschinger, Mitt. Tech. Hoch., Miinchen, 1876, vi. (10) See (4), p. 259. The values of y used throughout the paper are taken chiefly from Trautwine, Civil Engineer's Pocket-Book (Wiley, New York, 1900), p. 373. (. Issued separately July 16, 1909.) 1908-9.] On Group- Velocity and Propagation of Waves. 445 XXIX. — On Group- Velocity and on the Propagation of Waves in a Dispersive Medium. By George Green, M.A., B.Sc., Assistant to the Professor of Natural Philosophy in the University of Glasgow. Communicated by Professor A. Gray, F.R.S. (MS. received March 16, 1909. Read June 7, 1909.) § 1. The theory of group- velocity has been developed by Stokes, Osborne Reynolds, Lord Rayleigh, and later by Professor Lamb. The application of the theory to light- waves was made by Gouy and Lord Rayleigh, and its importance in this connection was emphasised by Professor Schuster in his paper “ On Interference Phenomena,” Phil. May., vol. xxxvii., 1894. The question of the velocity of a group of waves, as distinct from the velocity of a wave, arose from the well-known observation that when a large group of waves advances into smooth water, each separate crest travels through the group towards the front, where it gradually dies down and disappears, while similar crests meantime have in turn taken its place in the group, so that the main group moves forward at a velocity less than that of the separate waves. § 2. It seems that Stokes was the first to prove that the phenomenon was capable of being dealt with analytically, by showing that when two infinite trains of waves, of equal amplitudes and nearly equal wave- lengths are superposed, we obtain an infinite succession of wave-groups, each of which advances with the half -wave- velocity. None of the groups maintains its outline constant for any interval of time, however short ; but the whole disturbance periodically returns to the configuration it had at any particular instant if the periods of the superposed trains be com- mensurable, and the effect is the same as if each group had moved forward in the interval, without change of shape, at the half-wave-velocity. A most important contribution to the theory of group-velocity was made by Osborne Reynolds in Nature, Aug. 23, 1877, where he gave a dynamical explanation of the fact that the regular part of a large group of waves of equal wave-lengths advances with only half the velocity of the separate waves. He proved that the energy propagated across a plane, when a regular train of waves is passing, is just sufficient to feed a regular procession of waves, travelling with half the corresponding wave- velocity. § 3. Lord Rayleigh pointed out in his article “ On Progressive Waves ” ( Theory of Sound, vol. i., Appendix) that the theorem given by Osborne 446 Proceedings of the Royal Society of Edinburgh. [Sess. Reynolds for the case of a regular procession of water-waves could be ex- tended to apply to all kinds of waves. His result may be briefly stated as follows. When a large regular group of waves is advancing in any dis- persive medium, the energy propagated in one wave-period across a plane at right angles to the direction of the wave-motion is equal to the energy contained in one wave-length of the group multiplied by the ratio of group-velocity to wave-velocity. § 4. It may be here remarked that the above results all refer to a regular group of waves, or rather to the regular part of a group which is irregular at the front or rear, or to a regular procession of mutually sup- porting groups, as in the explanation of group-velocity according to inter- ference principles given by Stokes and Lord Rayleigh. The difficulty of the subject lies in the application of the theory to the case of a finite group of waves, or to any irregular disturbance, and doubt has arisen as to whether the theory of group-velocity can be useful in determining the circumstances existing at any time in the actual front of a finite or infinite group of initially regular waves invading undisturbed space. Lord Kelvin, after examining mathematically the front of a large procession of initially regular waves advancing into smooth water, remarks : * “ The whole in- vestigation shows how very far from finding any definite ‘ group-velocity ’ we are, in any initially given group of two, three, four, or any number, however great, of waves.” In his last paper on “ Deep Sea Waves,” Proc. R.S.E., 1906, he examined more particularly the case of a finite group of initially regular waves, and came to the same conclusion (on finding that the fronts of the groups extend forward indefinitely to greater and greater distances as time goes on). With reference to diagrams which he gives of the water surface at different stages (reproduced on page 466 below), he says : “ The perceptible fronts of these two groups extend rightwards and leftwards from the end of the initial single static group, far beyond the 4 hypothetical fronts,’ supposed to travel at half the wave-velocity, which (according to the dynamics of Osborne Reynolds and Rayleigh in their important and interesting consideration of the work required to feed a uniform procession of water-waves) would be the actual fronts if the free groups remained uniform. How far this if is from being realised is illus- trated by the diagrams of fig. 35, which show a great extension outwards in each direction far beyond distances travelled at half the wave- velocity.” § 5. From these investigations it seems clear that the dynamical inter- pretation of group-velocity cannot be effectively applied to the circum- stances of a finite or irregular group of waves. The kinematical interpre- * Lord Kelvin, Proc. Roy. Soc. Edin ., vol. xxv., 1904. 447 1908-9.] On Group- Velocity and Propagation of Waves tation of group- velocity given by Lord Rayleigh ( Scientific Papers, vol. i. p. 540) has been presented with greater generality by Professor Lamb, who gives an interesting application of the theory to the wave-system arising from an impulse applied at a single point of a water surface.* Three separate presentations of the kinematical group-velocity are given by Professor Lamb. The first is contained in the argument from the interference of two infinite trains of waves of equal amplitudes and nearly equal wave-lengths, referred to in § 2 above. Here the groups considered are mutually supporting, the shape and motion of each depending on the presence of the others, and we cannot regard this case of group-velocity as providing a satisfactory explana- tion suitable to all cases. The more general treatment of the matter given in the two later demonstrations entirely completes the investigation ana- lytically. The second and third presentations are, however, in a sense distinct, one giving a phase relation between the Fourier trains into which any group of waves can be analysed, the other referring to the actual wave- disturbance ; and the question arises as to whether the demonstrations cannot be correlated with each other in such a way as to show that the same fundamental idea underlies all three. In neither of the two later demon- strations is the “ group ” a regular procession of waves such as that required by Osborne Reynolds and Lord Rayleigh in their dynamical theorems, and in neither is it clear that a “ group ” of waves has any definite group-velocity ; that is, if we understand by “ group ” “ a long succession of waves in which the distance between successive crests and the amplitude vary very slightly.” j- The two accounts of the matter agree if we understand “ group-velocity ” to mean the velocity of a point which moves so as to always coincide with the point of the wave-system where a particular wave-length singled out for observation is to be found. This is indeed the definition of group- velocity adopted by Professor Lamb ; but fuller investigation seems to be necessary to make clear the fundamental relation between the arguments used by Stokes, Osborne Reynolds, and Lord Rayleigh, and those given by Professor Lamb. § 6. The object of this paper is to present the idea of group- velocity in the way in which it is used by Lord Kelvin in his paper of 1887, “ On the Waves produced by a Single Impulse in Water of any Depth, or in a Dispersive Medium,” J but with greater fulness, in order to show that Lord Kelvin’s paper provides the explanation that is required. The group- velocity of this paper is essentially the principle of “ stationary phase ” used * Lamb, Hydrodynamics , §§ 234-238. t Lamb, “On Group-Velocity,” Proc. Lond. Math. Soc., vol. i., 1903-4. I Sir William Thomson, Phil. Mag., March 1887. 448 Proceedings of the Poyal Society of Edinburgh. [Sess. by Professor Lamb in his investigation of Ship- Waves ( Hydrodynamics , § 253), but applied to the Fourier trains which constitute any wave- disturbance. When this view is accepted, the difficulties raised by Lord Kelvin are removed, as it is consistent with the dynamical theory given by Osborne Reynolds and Lord Rayleigh and with calculated results shown in Lord Kelvin’s diagrams, which are reproduced below for the sake of illus- tration. The whole investigation may be useful in drawing attention to the manner in which group-velocity is concerned in the modification of an initially regular group of waves, or of any disturbance initially confined to a finite portion of a dispersive medium ; and in showing thereby that the idea of group-velocity contains the explanation of the modus operandi of dispersion. § 7. Following Lord Kelvin’s paper above referred to, let us consider, as being fundamental, the case of an infinitely intense disturbance confined to a point of the dispersive medium which is taken as the origin of co- ordinates. Let V be the wave-velocity of an infinite train of waves of period 27 r/kV and wave-length X ; then we have k = 27 r/A, and, since the medium is such that the wave-velocity varies with the wave-length, we have also V =f(k). The period and the velocity corresponding to A are each functions of k ; and for convenience in what follows we refer to period F(&) simply as period k. According to Fourier’s theorem, the displace- ment f at point x and time t is given by the equation + oo £= — I dk cos k{x- W} . . . . (1). 27 rj -oo This means that the initial disturbance may be regarded as due to the superposition of the effects of an infinite number of trains of regular waves of equal amplitudes, all of which agree in phase at the origin. Not only is the total number of trains infinite, but the number of trains whose wave- periods lie between k and k + 3k is also infinite, no matter how small Sk may be. At the origin the displacement is sensible ; at all other points of the medium, on account of disagreement in phase, the various trains interfere and produce zero displacement. At any time after the commence- ment of motion, the effect at any point is got by summing the effects due to all the trains, supposing each to have travelled in the interval a distance corresponding to its wave-velocity. By applying this we can get an idea of the manner in which the initial disturbance is propagated, reasoning as follows. § 8. Since all the trains initially agree in phase at phase zero, and since each train moves with a velocity corresponding to its wave-length, it is 449 1908-9.] On Group- Velocity and Propagation of Waves. clear that we cannot again have agreement in phase of all the trains at any single point. But, on the other hand, it can be shown that if at any time we have an infinite number of trains agreeing in phase at any point, and these trains move at nearly the same velocity, there will always be a point at which an infinite number of these trains, though not the whole number, will continue to agree in phase at a different phase. For example, taking into consideration only trains whose wave-lengths and wave-velocities are nearly equal, the space separating points of equal phase on any two of the trains increases continuously as we pass away on either side from the point where all the trains are in agreement of phase. Con- sequently, on one side of the point of agreement of phase all points on the trains having any specified phase must be approaching each other, while on the other side all points of equal phase are moving more and more apart. This is illustrated in the accompanying diagram, which shows two trains T1T1 and T2T2 agreeing in phase at phase zero at point 0. Each train moves rightwards at its own wave-velocity. If the wave-velocity for the trains gradually increases with increasing wave-length, then all points of equal phase on the left-hand side of 0 come in turn into coincidence as time goes on ; and if the wave-velocity for the trains gradually diminishes with increasing wave-length, then all points of equal phase on the right- hand side of O come in turn into coincidence, and then continue to move farther and farther apart forever. It follows, therefore, that for the infinite number of trains which we are considering, all nearly of the same velocity and wave-length, there will always be a point at which an infinite number of them will agree in phase, provided one such point exists initially. In general, the phase at which the agreement occurs, and the point of the medium at which the agreement occurs, alter continuously with the time. § 9. Now when an infinite number of trains of nearly equal velocity are in agreement of phase at any point, the sum of their effects must determine very approximately the displacement of the medium at that point. For the remaining trains are infinite in number and of all possible phases, and we shall therefore assume for the present that their effects counterbalance each other, as is the case initially with all the trains at vol. xxix. 29 450 Proceedings of the Koyal Society of Edinburgh. [Sess. every point except the origin ; leaving our assumption to be tested after- wards by results. This is equivalent to saying that the main effect at any point is produced by a small portion of the total number of trains, whose wave-velocities are nearly equal and whose points of equal phase coincide with the point of the medium considered. Other trains, whose phases at the point considered are nearly equal to that of the trains whose phases coincide there, contribute effectively to the resultant disturbance ; but the effects of the remaining trains disappear by mutual interference. As we pass from point to point of the medium at any time, the mean period of the effective trains at each point, and the phase at which their main agreement occurs, vary continuously. We can therefore speak of a certain wave-period which is the mean period of all the trains whose coincidence of phase at a given point determines the displacement of the medium at that point, as the predominant period at that point ; and our problem is to determine at what point of the medium any specified wave-period will be the predominant period at any time. § 10. If k be the mean period of an infinite number of trains of waves whose velocities are nearly equal to the wave-velocity corresponding to k, we require to know at what point of the medium these trains will agree in phase at any time. The equation to any particular phase may be written in the form k{x - tf(k)} = c . ..... (2), where c is a constant ; and the distance Sx between a point of phase c on any of the neighbouring trains and the point x is given by the equation kBx+ [x-tf(k) — tkf(k))Sk = § . . . (3). From this we see that the distance Sx between points of equal phase is zero for all values of Sk less than a certain value, provided * - tf(k) - tkf(k) = 0 (4). This equation therefore determines the place at which k is the predominant period at time t ; and it may be written in the form x={f(k)+kf\k)}t=m .... (5), where U is the group- velocity corresponding to the wave-period k. We may define the group-velocity as a function of the wave-length X which determines the velocity of a point coinciding at each instant with the point of agreement of phase of the infinite number of trains of wave-lengths very slightly differing from X. The group-velocity for the mean wave-length of a very large number of trains of nearly equal wave-lengths might more accurately be termed the velocity of their coincident phase, or simply the 451 1908-9.] On Group-Velocity and Propagation of Waves. coincident-phase-velocity or the stationary-phase-velocity for that wave- length. § 11. At present we have established an equation relating to the Fourier trains effective at each point of the medium, but nothing definite regarding the resultant wave-form of £. Indeed, it is evident from the above discussion that the resultant wave-form may be something differing considerably in each part from the constituent wave-trains which predominate at different points along it. It is to the constituent Fourier trains that the idea of group-velocity primarily applies, and we cannot speak of a group-velocity with reference to an endless succession of regular periodic waves ; that is, to a single train. We may remark that, so far as the group-velocity relates to the resultant wave-system it refers essentially to each single point of the system and not to an extended succession of waves. Before we can arrive at the conditions under which several consecutive wave-lengths of the resultant disturbance have the same group-velocity, it is necessary to find the relation between the predominating wave-period and the displacement £ at each point of the medium. § 12. The above presentation of group- velocity is effective in showing the intimate relation existing between group-velocity and dispersion. Dis- persion is in fact the result of the gradual separation of the points of predominance of trains of nearly equal wave-length and wave-velocity. This is clearly illustrated in our problem of § 7. Initially, the points of predominance of all the trains coincide at the origin ; immediately after, the points of predominance of very quickly moving trains occupy the most distant points of the medium, each having travelled out at its own coincident- phase-velocity. The separation out of the closely packed predominant points from the neighbourhood of the origin becomes continuously more and more complete for the less quickly moving trains, and the same process of separation goes on in the front and rear of each predominant point as it moves uniformly forward at its coincident-phase-velocity. Returning to equation (4) above, we see that the points of predominance corresponding to the two wave-periods k and k + 8k are continually separating from each other at the rate v given by the equation V — OK dk (6), which shows that the points of predominance of wave-periods intermediate to k and k + Sk are being spread over an ever-increasing length of the medium. The extent of the medium occupied by these points at time t is given by vt = /~Sk . dk (7): 452 Proceedings of the Royal Society of Edinburgh. [Sess. an amount which becomes appreciable as time goes on, no matter how small dV dll Sk may be, provided -P is not zero. If -p- is zero, then all wave-periods whose points of predominance are initially in coincidence or almost in coincidence maintain the same relation to each other throughout all time, and there is consequently no dispersion. This will be illustrated later for media for which V = a + b/k, where a and b are constants. § 13. Now, according to the principle of stationary phase adopted in §§ 8-10 above, only trains whose points of predominance are in the immediate neighbourhood of a point x contribute effectively to the resultant displacement £ at x ; hence we arrive at the conclusion that when the process of dispersion just described is sufficiently far advanced we can obtain the resultant displacement at any point by considering only the effects of trains differing infinitely little in period from the predominant period at the point. In the early stages of dispersion, when points of pre- dominance of widely differing wave-periods are very near one another, the resultant wave-curve £ near any point x will in general only very roughly correspond in wave-length and wave-period to the wave-period of the Fourier trains effective in the neighbourhood. It will now be shown that the correspondence becomes more and more pronounced as time goes on ; and we shall arrive at an understanding as to how group-velocity is to be applied to the resultant wave-curve. We shall find that the process described in § 12 leads ultimately to the following result referred to by Professor Lamb : “In a medium such as we are considering, where the wave- velocity varies with the frequency, a limited initial disturbance gives rise in general to a wave-system in which the different wave-lengths, travelling with different [constant] velocities, are gradually sorted out,” * and arrive at any given point in the order corresponding to their group- velocities. Each separate crest or trough, however, moves with continually increasing or continually diminishing speed. § 14. Returning now to equation (1), we assume that the dispersion is so far advanced that the phases of the effective Fourier trains in the neighbourhood of a point x are determined with sufficient accuracy by two terms of a Taylor’s series. Thus, taking k0 as the predominant period at x at time t, we have by equation (4) « - W%) - tk0f(k0) = 0 (8) ; and by Taylor’s theorem we have k{x - tf(k)} = k^x - tf(kQ)} + {k- k^bLk{){x - tf(kQ)} + ^ ~ ^ -Jp k0{x - tf(k0)} (9). * Hydrodynamics , 3rd ed., § 234. 453 1908-9.] On Group-Velocity and Propagation of Waves. Using now equation (8) in this, we may write it in the form M*-W} = M*-W}+^{-2/W-V'(W • <10)- In general, for the evaluation of the integral in equation (1) according to the method used by Lord Kelvin in his paper of 1887 our assumption is that the dispersion is exceedingly far advanced, and t therefore so great that the term { 2/ (Jc0) + k0f"(k 0)}( is very large for the greatest and A least values of k considered. If the dispersive medium is such that equation (10) is satisfied for all values of k, it is unnecessary to assume t to be very large, as (k — k0) may be taken as large as we please positively and negatively. In either case, therefore, when we transform equation (1) by the substitution ■ • • • (ii), A where the sign taken is such as to make £2 positive, the limits of 0 are practically + co and — co , and the value of £ is given by + 00 2i I dz cos [kQ{x - tf(k0) } ± z2] t c= ~-oo (i2) " 2*fi[+{2 /'W + VW}f ’ By means of the integrals ^+oo ^+oo j dz cos z2 = j dz sin z2 = . . . . (13) -CO ”-00 the above equation ultimately reduces to cos [kQ{x - (/(A'o)}] + sin W\x ~ (/Go)] 2ttH\ + { 2f\kQ) + A’0/"(&0) }]' cos K{x - tf(k0)} ± 7 T 247T H\ + { 2 f\kQ) + /ro/'iAto)}]4 (11), which has been verified by Lord Kelvin for water-waves in his paper, and proved to be in agreement with Cauchy and Poisson’s result for t very great compared with x. It is easy to verify that the result holds for all values of t and x in the case of flexural waves in an elastic bar. § 15. In this result the terms depending upon k0 vary very slowly in the neighbourhood of x, and the £ curve is nearly a simple sine curve there. Equation (14) therefore proves that in the case which we are considering, where the dispersion is fairly well advanced, the resultant displacement curve near any point of the medium at any time is a curve of exactly the same 454 Proceedings of the Royal Society of Edinburgh. [Sess. wave-length and period as the effective Fourier trains which predominate in the neighbourhood. It is clear also, from our equation, or from the considera- tions of § 12, that the correspondence of wave-lengths referred to becomes more and more perceptible and the approach to a regular sine curve in each neighbourhood more and more close as time goes on ; for the predominant period of the Fourier trains varies more and more slowly as we pass along the £ curve at later and later times. In this case therefore the demonstra- tion of a coincident-phase-velocity for the constituent wave-trains carries with it a demonstration of group-velocity for each part of the resultant wave- curve where a definite wave-length is observed. If, following Professor Lamb, we understand by “ group ” in this connection “ a long succession of waves in which the distance between successive crests and the amplitude vary very slightly,” our result would mean that, whereas a certain wave- length X is observable in the group at place x at time t , this particular wave- length will be found at any later time t' at a place x' given by the equation x=x + V(£ - t) ..... (15), where U is the group- velocity corresponding to the wave-length X. In this sense we can speak of a group-velocity with reference to each small part of the original “ group,” each part having a slightly different group- velocity from contiguous parts ; but the “ group ” as a whole has not any definite “ group-velocity,” unless we define its group-velocity to be the mean value of the group- velocities of its parts. Such a “ group,” however, quickly loses definite marks by which it could be recognised on account of its con- tinual extension by the process of § 12. § 16. It is important to observe from equation (14) that each wave of the resultant displacement curve moves at each instant with the velocity corresponding to its length. Thus in his paper of 1887, referred to in § 6 above, Lord Kelvin remarks : “ The result of our work will showT us that the velocity of progress of a zero, or maximum, or minimum, in any part of a varying group of waves is equal to the velocity of progress of periodic waves of wave-length equal to a certain length, which may be defined as the wave-length in the neighbourhood of the particular point looked to in the group (a length which will generally be intermediate between the distances from the point considered to its next neighbour corresponding points on the preceding and following waves).” To illustrate this for any medium in which the group-velocity is positive, let us take V = A kn, where n may be positive or negative, but not less than — 1. Equation (8) becomes in this case x = (1 + n)A kQ t = \Jt . (16); 455 1908-9.] On Group- Velocity and Propagation of Waves. and when we eliminate k0 from the argument of the cosine in equation (14) by means of this equation, the argument 0 may be written in the form «+i 6 = B: x + - : B = n n+1 1_ ( 1 + n) An (17), where the negative sign is taken when n lies between 0 and —1. If we follow the crest of a wave whose equation is given by 6 = '2rTT ...... (18), we can find the velocity of this crest by differentiating (17). Thus we have y _clx _ 1 x \ dt n+1 t > . . . . . (19) ; = by (16)) Since the phase varies by 2 tt as we advance one wave-length along the £ curve, the length A of the wave whose crest we are following is given approximately at any time t by the equation n+ 1 n+ 1 = 2rr ■ (20). With A small compared with x, this gives finally by means of equation (18) n x n+\ (r + \) ■ (21)- These equations show that each wave lengthens as it proceeds, and that its velocity alters accordingly. If the wave-velocity increases with increasing wave-length, each wave is continually accelerated; if the wave-velocity diminishes with increasing wave-length, each wave-crest moves with con- stantly diminishing speed. The individual waves which at any time constitute the part of the disturbance which has a certain wave-length A immediately pass ahead of this part, if the medium is one in which the wave-velocity exceeds the group-velocity, or fall behind it if the group- velocity exceeds the wave-velocity for that wave-length. In the former case succeeding waves in turn become of length A ; in the latter case, pre- ceding waves in turn become of length A. A point which moves so as to coincide at each instant with the point of the wave-system at which the wave-length is A travels at the coincident-phase-velocity corresponding to that wave-length. § 17. At this stage it is interesting to examine the coincident-phase- velocity with reference to a disturbance which can be analysed into a limited number of wave-trains. The most interesting case is that of two 456 Proceedings of the Royal Society of Edinburgh. [Sess. interfering trains, which was dealt with first by Stokes, and afterwards by Lord Rayleigh in § 191 of his Theory of Sound, vol. i. In Lord Rayleigh’s notation the two interfering trains are represented by t x COS H77-I and COS 2 7 A/ \r where r, t are the wave-periods, and A, A' the wave-lengths of the trains. At the origin, which may be chosen at the point of maximum displacement of any one of the wave-groups which constitute the initial disturbance, the phases of the two trains are initially zero ; and the point at which agree- ment of phase occurs at any later time is given by the equation t db t 'JCf T A T X (22), which corresponds to equation (4) above. It may be written in the form (23), Krr from which we obtain the coincident-phase-velocity U, as 1 1 l A' (24). When the trains are of nearly the same wave-period and wave-length, this becomes which is the form given by Lord Rayleigh. § 18. With reference to this case, the view of the matter here adopted frees us from what is in general a misleading conception in connection with group- velocity, namely, the reappearance of the entire group of waves at regular intervals. Thus Professor Schuster, referring to an extended suc- cession of waves, in his article “ On Interference Phenomena,” remarks : “ We can speak of definite rate of propagation U of the group, because at definite intervals t the group takes up the same shape, displaced through a distance Ut.” Our investigation proves beyond doubt that the reappearance of the same shape at regular intervals in a dispersive medium is confined to the particular case of a disturbance represented by two interfering trains. The original shape of any disturbance may maintain itself unchanged, or may reappear at regular intervals, in a medium for which the coincident-phase- velocity is constant or zero for all wave-periods ; but, as we have found in §12, in such media there is no dispersion. This will be illustrated in a later paper. The process of separation of predominant points referred to 12 above essentially involves continuous non-periodic change in the in shape of any initially given group of waves. § 19. The case of three, four, or any finite number of interfering trains 457 1908-9.] On Group! Velocity and Propagation of Waves. follows easily from the case of two trains ; for the coincident-phase-velocity differs for each pair of trains, and, except for occasional agreement of phase of three or more trains, no new features occur. When the number of trains is exceedingly large, and their wave-lengths and wave-periods vary very slightly, as in the explanation of group-velocity given by Gouy and Lord Rayleigh,* each wave-train has its own particular point of predominance in the wave-system ; which point moves at its own coincident-phase- velocity. The argument is, in fact, exactly the same for a disturbance represented by £= 2C cos k{x- tf(k) + *} .... (25) as that given in §§ 8-10 above; the point of the medium at which the wave-period k predominates being again found from equation (4). Here the number of terms is exceedingly large, and C and k vary continuously. The general features of propagation of the disturbance are the same as in the case of a single initial impulse. The wave-system is continually being modified by the process of § 12, and the resultant curve ultimately takes a shape in each neighbourhood corresponding in wave-length to the component Fourier trains which predominate there. As time goes on, the rate of change of the wave-length as we pass along the resultant curve becomes more and more gradual, and the whole disturbance occupies an ever-increasing extent of the medium on account of the difference in the coincident-phase-velocities maintaining throughout the wave-system. § 20. The argument regarding group-velocity contained in §§ 7-14 above has been confined to the particular case of the wave-system arising from an infinitely intense disturbance at a single point of a dispersive medium, but it is evident throughout the later parts of the discussion that the results arrived at are of much more general application. Group-velocity has been shown to depend upon the principle of “ stationary phase,” which, it seems reasonable to assume (see § 9), can be applied to any infinite com- bination of Fourier trains. It is practically Huygens’ principle in optics. The agreement in wave-length between the effective Fourier trains and the result- ant displacement curve at any point of the medium, on which the applica- tion of the theory of group- velocity to the resultant curve depends (§§ 14, 15), requires only that the predominant wave-period should vary continuously in the neighbourhood of the point considered. The condition that t be very great is required in § 14 to enable us to completely evaluate the integral in equation (1), but is unnecessary to prove the correspondence of wave-lengths referred to, which follows at once from considerations of continuity by Taylor’s theorem. In general, at only a short interval after a disturbance the * Lamb’s Hydrodynamics , 3rd ed., § 234. 458 Proceedings of the Royal Society of Edinburgh. [Sess. separation of predominant points will be sufficiently advanced to allow us to recognise a distinct group-velocity in the various parts of the wave-system. This makes it possible to apply the theory of group-velocity to any wave-system, provided the word “ group ” is understood to mean any part of the whole disturbance which has a specified wave-length. In general, the “ group,” as here defined, is confined to the immediate neighbourhood of a single point, which moves uniformly forward ; but when the wave- length varies very slowly from point to point, the group may be taken in a modified sense to refer to an extended portion of the wave-system where the wave-length is nearly constant, provided we remember that such a group would be continually increasing in length as it proceeds, and that its recognition soon ceases to be useful. § 21. We can now obtain from the theory of group- velocity a useful general understanding of the way in which any disturbance initially con- fined to a small portion of a dispersive medium is propagated into regions initially undisturbed. We may arrive at the effect of any initial disturbance by summing the effects due to point displacements applied at each point of the disturbed region ; but it is more convenient from our present standpoint to regard any initial displacement of the medium as due to a certain distri- bution of predominant points. Since the initial disturbance is limited in extent, it is clear that the Fourier trains into which it can be analysed must be infinite in number and of all possible wave periods, and we suppose that their points of predominance are arranged irregularly but continuously within the disturbed part of the medium. At any very short time after motion has commenced, an effect will have been produced in the most distant parts of the medium by the very quickly moving trains whose points of predominance have moved out in the interval. Near the place of the original disturbance the slowly moving trains still agree in phase, but irregularities in amplitude and wave-length must occur owing to the pre- dominant points of the quicker trains overtaking and out-stripping those of the slower. Indeed, it seems certain that irregularities in amplitude will persist, according to the manner in which the energy is distributed initially among the effective Fourier trains.f But, as time advances, the various trains sort themselves out according to their coincident-phase-velocities, and the wave-length of the resultant curve ultimately varies regularly and continuously as we pass outwards on either side from the place of the initial disturbance. At this stage the continuity of the disturbance allows us to regard the distance between corresponding points on two consecutive half-waves as equal to a half-wave-length of the train which has its point t Burnside, Proc. Lond. Math. Soc., t. xx. p. 22, 1888. 459 1908-9.] On Group- Velocity and Propagation of Waves. of predominance somewhere between them. Thus if we call twice the distance between any two consecutive zeros of the resultant wave-system the perceptible wave-length in their neighbourhood, the perceptible wave- length will agree very closely with that of the wave-train which predomin- ates at the point of maximum displacement between the zeros observed ; and the further progress of the dispersion may be described as a gradual increase in the extent of the medium sensibly disturbed, accompanied by a continual diminution in the rate of change of the perceptible wave-length from point to point of the system, owing to the process indicated in § 12. This is exactly the result described by Professor Lamb, quoted in § 13 above. More detailed description would require a knowledge of the initial distribu- tion of energy and of the law of diffusion of energy throughout the medium. § 22. The case of an initial disturbance consisting of a large succession of equal, regular waves of wave-length X, with undisturbed space in front and rear, is interesting in connection with the dynamical interpretation of group-velocity given by Osborne Reynolds and Lord Rayleigh, and on account of its importance in relation to sequences of light-waves in dispersive media. The mathematical expression representing such a group of waves would again involve all possible wave-periods, and we may state our initial conditions by saying that the wave-length X predominates in the part of the medium initially occupied by the group. According to the theory of group- velocity presented above, at any time t after the commencement of motion there will be a succession of waves of wave- length X displaced on either side from the place of the original disturbance a distance U t, where U is the group- velocity corresponding to wave-length X ; but in front of the waves of length X there will have appeared a continuous wave-disturbance, of which the wave-length increases con- tinuously as we pass farther and farther ahead if the medium is such that the coincident-phase-velocity of the wave-trains increases with increasing wave-length, and of which the wave-length diminishes continuously if the coincident-phase-velocity diminishes with increasing wave-length. Behind the main group of waves of length X there will also have appeared a continuous wave-disturbance of which the wave-length either decreases or increases continuously as we pass farther and farther behind the group of waves of wave-length X, according as the wave-length in front increases or diminishes. Each perceptible wave-length in the front or rear of the main group is always to be found in the wave-system at any time in advance of the place where it was observed at an earlier time by a distance corre- sponding to the group-velocity for that wave-length. The history of the individual waves is again that given in § 16. The process according 460 Proceedings of the Royal Society of Edinburgh. [Sess. to which the disturbance is propagated throughout the medium is the process o£ separation of points of predominance of the constituent wave- trains, so that we can at once say that the disturbance which we are considering gives rise to a wave-system consisting of a succession of waves of all possible wave-lengths, each wave-length appearing in the succession according to the order of its group-velocity. The energy of the initial disturbance is ultimately diffused throughout the entire medium. The “ group,” defined as the part of the whole disturbance which has the same wave-length as the original group, moves along at the group-velocity corresponding to its wave-length, being distinct for a time owing to the energy it retains. But the regularity of its shape cannot be maintained as it proceeds, for it must supply the energy necessary to feed the ultimately infinite succession of waves of greater and less wave-lengths which constitute its front and rear. As time goes on, therefore, a falling off from sinusoidality, which proceeds inwards from the front and rear of the group, must become more and more evident as the front or rear increases in importance ; and the amplitude of the sensibly regular central part must in time diminish. Thus it would seem that we cannot expect perfect regularity to be maintained in any part of a finite group for any time, however short. It is to the part of the group which remains sensibly regular that the dynamical theorem given by Lord Rayleigh applies. The law of diffusion of energy towards the front or rear of the wave-system essentially involved in the process of dispersion described in § 12 does not seem to be easily derived from the dynamical theory of group-velocity as hitherto developed. LTnless we can arrive at the law of falling off from regularity of the main group in the front and rear, it seems impossible to follow the distribution of energy throughout the entire system. The kinematical group-velocity theory, however, accounts satisfactorily for the speed at which a group of waves of sensibly the same length advances, and explains in a general wTay the process by which any initial disturbance is modified in invading undisturbed space. § 23. The formation and development of the front and rear of a large initially regular procession of waves in deep water, in accordance with the theory of group-velocity given above, is illustrated by the diagrams of Lord Kelvin’s paper, Proc. Roy. Soc. Edin., vol. xxxv., 1904, figs. 9 and 10. For water-waves, the group-velocity ~x/ increases with increasing wave-length, so that at any time long wave-lengths appear in the front and short wave-lengths in the rear of the main group, which, in the case treated by Lord Kelvin, consists initially of a large procession of waves of 1908-9.] On Group- Velocity and Propagation of Waves. 461 Fig. 9 ; Head and front of rightward procession. 462 Proceedings of the Royal Society of Edinburgh. [Sess. Fig. 10 ; Tail and rear of leftward procession. 1908-9.] On Group- Velocity and Propagation of AVaves. 463 wave-length 2 and period J ir. Figs. 9 and 10 show the wave-system at time t = 2bjir. Fig. 9 shows the front of the wave-system which has formed while the original group of wave-length 2 has travelled from the origin to point 25 on the diagram, which is exactly the distance required by group-velocity theory, g being taken equal to 4 in Lord Kelvin’s calculations. As an example of the application of group-velocity theory to the front of the wave-system, we may take the case of wave-length 6. The place in the wave-system where this wave-length, initially near the origin, should be observable at time 25 J 7r is given by x = 25 J ir x J\/\X ^ =. 43*3, which agrees well with fig. 9. The individual waves forming the front initi- ally belonged to the main group, and their places in the group have been taken by other waves, so that somewhere in the rear of the whole system, not indicated in the diagrams, fresh waves must be continually forming and then advancing with increasing length and speed towards the extreme front of the system. The point F on the diagram marks the place where the regu- larity of the main group perceptibly begins to fail. As we should expect from the continual advance of the individual waves through the group, the perceptible front is much more extensive than the perceptible rear, which is shown in fig. 10. The irregularity of the main group in the rear con- sists in the main in a variation in amplitude, without any falling off in the wave-length till we reach the extreme perceptible rear at R, beyond which we have a large number of imperceptible waves of continually diminishing wave-length. From fig. 10 we see that the rearmost wave of wave-length 2 at the time of the diagram has just reached the point 25, starting from point 0, which is in accordance with group-velocity theory. The perceptible rear never extends far beyond the last wave-length of the main group of wave-length 2, but the number of the perceptible waves in the front increases with the time, and the increase in wave-length from the regular waves forward becomes more and more gradual owing to the gradual increase in the group-velocity as we go towards the extreme front of the wave-system. We hope to give the law of falling off from regularity, as time goes on, at the front of a large group of sinusoidal waves, in a later paper dealing with the wave-system arising from a given distribution of pressure moving steadily over the surface of infinitely deep water. § 24. The diagrams of figs. 34 and 35 are taken from Lord Kelvin’s last Waves paper, referred to in § 4 above. Fig. 34 deals with the case of a disturbance mainly confined to the neighbourhood of the origin ; and all the diagrams are outlines of the water surface at the times indicated below each, J 7 r being the period of an infinite train of waves of wave-length 2 464 Proceedings of the Royal Society of Edinburgh. [Sess. and velocity 2jjnr. The zeros are numbered in the order of their coming into existence, so that we can study the history of each perceptible wave, or of each group defined as the part of the whole disturbance which has a given wave-length. According to the argument of § § 20, 21 above, the wave-trains are initially in agreement of phase near the origin, and, as their points of predominance separate from each other, the wave-length of the resultant curve in this case increases continuously as we pass from the middle outwards. It is clear from the diagrams that we can take twice the perceptible half-wave between ^any two zeros as the wave-length pre- dominating somewhere near the point of maximum displacement between the zeros, this being a very close approximation when the wave-length does not vary quickly in the neighbourhood. The following table of numbers, calculated from the numerical results from which the diagrams were drawn wherever convenient, or taken direct from the diagrams themselves, shows that each perceptible wave-length of the disturbance appears at each time of observation at a distance from the place of the original disturbance corresponding to its group-velocity. Column 1 gives the diagram observed in each case ; column 2 gives the zeros twice whose distance apart is used as the wave-length ; column 3 gives the actual position of the maximum or minimum between the zeros, from the original calculations or from the diagrams ; and column 4 gives its position approximately by the group- velocity theory of § 10, i.e. column 4 gives group- velocity multiplied by the time. Diagram. Zeros. Position of Maximum. On the Diagram. By Group- Velocity. 2 1 and 2 1-3 1 3 1 „ 2 3 3-4 4 1 „ 2 5 7*3 4 2 „ 3 2 2*3 6 4 „ 5 19-8 19-9 6 5 „ 6 15-1 15-2 6 6 „ 7 12-2 12-2 6 7 „ 8 10-3 10-3 6 8 „ 9 8'8 8-8 6 9 „ 10 8-0 8*0 An examination of the curves makes it clear that the agreement is practi- cally perfect where the change of wave-length between the zeros is slight ; and when the change of wave-length is considerable, as in the foremost 1908-9.] On Group-Velocity and Propagation of Waves. 465 466 Proceedings of the Royal Society of Edinburgh. [Sess. Initial group of five elevations and four depressions emerging as two groups travelling in opposite directions. 1908-9.] On Group-Velocity and Propagation of Waves. 467 waves at each time, the perceptible wave-length predominates at a point slightly beyond the maximum, which is what is to be expected. The whole progress of the disturbance is in entire agreement with the process described in § 21. § 25. Fig. 35 shows the manner in which a finite group of equal waves in deep water is modified as it proceeds, owing to the different coincident-phase- velocities of the component Fourier trains. The group of waves of wave- length 2 comprising the main “ group ” in diagram 1 can be observed in the two later diagrams displaced from the central position by an amount corre- sponding exactly to its group-velocity ; while it is clear that the individual waves forming this group are continually passing forward to form the front. Each wave originates near the origin and moves through the whole system, lengthening as it proceeds, and carrying some of the energy of the original group forward to the front, which continually increases in importance relatively to the main group, and becomes perceptible at greater and greater distances beyond it. “ While there is this great extension of the fronts outward from the middle, we see that the two groups, after emergence from coincidence in the middle, travel with their rears leaving a widening space between them of water not perceptibly disturbed, but with very minute wavelets in ever augmenting number following slower and slower in the rear of each group.” * It is easy to verify from the diagrams that each per- ceptible wave-length appears in the wave-system at any time, displaced from the position at which it is observable at an earlier time by the distance corre- sponding to the group-velocity for that wave-length. As an example we may take the wave-length at the maximum point of the wave marked/ in diagram 2. The particular wave at f in diagram 2 has disappeared beyond the diagram limits at the time of diagram 3, but the new wave at /in diagram 3 is of only slightly shorter wave-length and will suit for comparison. From the diagrams, the distance between the maximum points is about 8’4 units of the scale shown. The value of U for the perceptible wave-length at / is given by U = = = which gives U(8 ^/tt-4 n/tt) = 8'7. Thus the wave-length at the maximum near / in diagram 2 corresponds to the wave-length appearing slightly beyond the maximum in diagram 3, as is to be expected from its slightly greater wave-length. § 26. The general features of all these water-wave disturbances are the gradual increase in wave-length of the disturbance as we pass outward from the place of the original disturbance, and the continually increasing importance of the front as compared with the rear. It seems certain that * Lord Kelvin, Proc. Roy. Soc. Edin ., 1906. 468 Proceedings of the Royal Society of Edinburgh. [Sess. similar features will appear in the case of any medium in which the wave- velocity is greater than the group-velocity for each wave-length and in- creases with increasing wave-length (V = Ak~n, n< 1). But it is shown in an earlier paper (see Proc. Roy. Soc. Edin., vol. xxix., 1909) that all the curves shown for water-waves may be used as illustrations of waves in an elastic rod, which is a medium in which the group-velocity exceeds the wave- velocity and the wave-velocity diminishes with increasing wave-length. Our diagrams therefore illustrate the process of dispersion for two distinct laws of dispersion, namely : Y = A-Jc~h, U = J AxAr* ; and V = A 2/c, U = 2A2&. For the first, each diagram shows the displacement at each point of the medium at a given time ; for the second, each diagram shows the displacement at a given point of the medium from t == 0 to t = co . It is sufficient to point out the distinguishing features of the second case illustrated by the diagrams, which may be taken as typical of any medium in which V = A hn, n> 0. These are : the continuous increase in wave-length of the disturbance at each point of the medium as time goes on, and the continuously increasing impor- tance of the rear of any disturbance as compared to the front, owing to the individual waves lagging behind the main group and retaining part of its energy. One interesting point of difference between the two cases illustrated lies in the manner of formation of additional waves. Thus in fig. 34 we see from the numbering of the zeros that they are continually being formed in pairs near the point x = 1 : the outer zero travels outwards with con- stantly increasing speed, and the inner zero travels inwards with constantly diminishing speed. From a? = 0 to cc = l we have an ever increasing number of waves, each moving inwards with diminishing length and therefore also diminishing speed, and from x — 1 to x=oo we have an equal number of waves moving outward with increasing length and speed; each wave in the entire system moving at each instant with the velocity corresponding to its length. Only at t = oo is the number of water-waves infinite. The illustra- tions when applied to waves in an elastic rod, however, show that each zero is formed at infinity ; and an infinite number are formed in quick succession at the commencement. For a short time the waves formed all move inwards from infinity towards the part of the medium initially disturbed, lengthening and slowing down as they come inwards. Very soon the inward motion ceases, and all continue for ever afterwards moving outwards with in- creasing length and diminishing speed. At all times the wave-length diminishes from the middle outwards, and at each point it increases continuously with the time : in both respects exactly the reverse occurs in the case of water- waves; In both cases the flow of energy is outwards from the place of the original disturbance at all times and places, even when the 1908-9.] On G-ronp- Velocity and Propagation of Waves. 409 individual waves and wave-groups travel inwards — an interesting result in connection with the dynamical theory of group-velocity. § 27. Lord Kelvin’s investigation of 1887 therefore shows that the mathematical theory of group-velocity explains the modus operandi of dispersion. In relation to sequences of light-waves, — perhaps one of the most important applications, — where we are entirely concerned with the wave-length, and not with the individual waves, the theory emphasises the importance of group-velocity in all cases of refraction. Lord Kelvin’s diagrams not only illustrate the manner in which group-velocity is con- cerned in the formation of a “ front ” and “ rear,” and in the propagation of an initially finite disturbance, but also show how the velocity of the individual waves, according as it exceeds or falls short of the corresponding group-velocity, influences the distribution of the energy of the initial disturbance among the various wave-lengths of the disturbance throughout the medium. This is of importance whether we are concerned with the maintenance of distinct marks by which a group of waves may for a time be recognised, or merely with the energy contained in the part of a dis- turbance having a particular wave-length, which is of interest in connection with the theory of radiation. The extreme smallness of the amount of energy contained in the very short waves is a feature of all the diagrams. Thus in fig. 34 the energy of the initial disturbance would need to be very great if we are to regard the energy of even the largest imperceptible wave in diagram 6 as sensible. § 28. It is not intended in this paper to enter into a discussion of particular applications of the theory of group-velocity presented above, but it may be useful to point out in conclusion one application of importance in the theory of radiation, which is suggested by § 27. This is to the case of a black body, say a plate of metal, which is slowly heated on one side. At first only long heat-waves are observed, but shorter and shorter heat- waves are emitted as the temperature rises. At about temperature 525° C. the first visible rays appear, and the plate becomes red, owing to the long light-waves it sends out. As the temperature is further raised, shorter and shorter wave-lengths appear in appreciable amount, and the colour of the plate changes from red to yellow, and finally to white. The points of importance in relation to the diagrams are that the various wave-lengths are emitted in the order corresponding to their group- velocities, and that the energy of the disturbance required to make each wave-length perceptible is greater the shorter the wave-length; exactly as in the continuous water-spectra exhibited in the diagrams of fig. 34. It is interesting to find the idea underlying this application expressed in the 470 Proceedings of the Koyal Society of Edinburgh. [Sess. following passage, quoted from Professor Schuster’s article “ On Interfer- ence Phenomena ” referred to above: — “We cannot help speculating as to the ultimate cause which renders the regularity of vibration a function of the temperature only, and independent of the natural periods of the molecules. Perhaps the solution of the difficulty will be found in the fact that our observations tell us nothing directly as to the vibrations of the atoms or molecules. What we observe is the disturbance of the medium ; and the distribution of energy in the spectrum of an incandescent black body which is in thermal equilibrium may indicate a property of the medium rather than that of matter. That is t6 say, the motion of vibration in the molecule may be perfectly irregular, but the medium may take up and propagate some vibrations quicker than others.” § 29. In a later paper I hope to illustrate further the process of dis- persion by showing the wave - systems arising from the same initial disturbance in several media having different dispersive qualities. ( Issued separately July 16, 1909.) 1908-9.] A Simple Radioscope and a Radiometer. 471 XXX. — On a Simple Radioscope and a Radiometer for showing and measuring Radioactivity. By Dr John Aitken, F.R.S. (MS. received May 1, 1909. Read May 17, 1909.) While working at another subject I evolved a very simple piece of apparatus which on trial was found to be very sensitive to the penetrating rays of radioactive substances, so I have recently diverted my work from its original direction to study and improve this piece of apparatus. The principle of the action of the instrument is not new, as it depends on the fact discovered by Professor C. T. R. Wilson,* that ions in air super- saturated with water vapour become centres of condensation when the supersaturation is sufficiently great. Before going further it may be as well that a few remarks be made on the condensation of water in supersaturated air. If ordinary air saturated with water vapour be cooled by expansion, the vapour, it is well known, condenses on the dust particles in the air and a fog is formed. This fog is the denser the more numerous the dust particles, and if the particles be few only a rainlike condensation results on expansion ; and if no dust particles be present, then no condensation takes place, unless the expansion be great. In my early experiments on this subject it was shown j* that only a very slight expansion was necessary to make all the dust particles active as centres of condensation, an expansion of being sufficient to cause condensation to take place on even the smallest of them. It was further shown that higher expansions than might be made without any condensation taking place, but if the expansion was great, and caused to take place very rapidly, then condensation took place in dustless air ; but the subject was not further investigated. Here the matter rested till 1897, when C. T. R. Wilson took up the investigation and by means of most ingenious apparatus, in which the air was very rapidly expanded, he showed that there were always nuclei in moist air that became active centres of condensation when the supersaturation was great enough. If v1 be the initial volume of the air and V2 the final volume after expansion, he showed that condensation began in dustless air when vjv1 = 1*250. When the expansion is that amount the condensation is slight ; that is, only a few cloud particles are seen falling as a fine rain, and that as the * Trans. Roy. Soc ., Series A, 1897. t Trans. Roy. Soc. Edin., vol. xxxv. part i., 1888. 472 Proceedings of the Royal Society of Edinburgh. [Sess expansion is increased the number of drops increases slightly. This increase goes on slowly till a certain degree of expansion is reached, when the appearance of the condensation changes somewhat suddenly, the rainy condensation changing to dense fog ; that is, with the lower expansions the particles are few, large, and fall quickly, while in the second stage they are extremely numerous, very small, and fall very slowly. This sudden change in the nature of the condensation takes place when vjv1 = l‘ 38. With still higher expansions the number of particles becomes greater ; that is, the fog gets denser. In Wilson’s apparatus, as the expansion is extremely rapid, the degree of expansion may be taken as a measure of the supersaturation, and as the different instruments used by him give almost the same values for vjvv we may take it that they are correct. In the instruments here to be described the values of vjv1 are different from Wilson’s, and they differ with each other owing to the conditions not being so simple as in Wilson’s. But any difficulties one may feel about this will disappear if we will keep in mind that it is the degree of supersaturation and not the amount of expansion which determines the result. Supersaturation appears to depend greatly on the quickness of the expansion. A very slight slowing of the velocity of expansion, even though to the eye there may seem to be no change, requires a decided increase in the expansion. Part of this is due to heat exchanges between the air and the walls of the vessel and to radiation ; but in these experiments with high supersaturations a greater part is due to the manner in which the nuclei relieve the vapour tension. If the expan- sion be not instantaneous, then some of the nuclei, being better centres of condensation than others, come into action before the others : even in these infinitesimally small particles there seems, as elsewhere, to be no equality. The result of this is that the best nuclei begin condensing before the others, and if there is time given they rob the surrounding air of its vapour owing to the high supersaturation, so that if the other nuclei are to come into action time must not be given for this condensation to take place. We see from this that the quicker the expansion the greater the number of nuclei that will become active, while with a slow expansion an odd nucleus here and there will be able to relieve the tension. This suggests that the gradual increase in the number of drops observed with increase of expansion during both rainy and foggy stages may be as much due to increase in rapidity of expansion as to increase in its amount. These experiments on condensation in supersaturated air refer to the condensation which takes place on nuclei always present in saturated air. When X-rays and radioactive bodies acted on the air in Wilson’s 473 1908-9.] A Simple Radioscope and a Radiometer. apparatus so as to produce ions in the moist air, he showed that these ions became active centres of condensation ; and he also showed that the super- saturation necessary to make them centres of condensation was the same as that required for the nuclei always present in the air. He further showed that these ions were electrically charged, some with positive and some with negative electricity, and that they could be removed by an electric field, but, so far as his experiments went, there was no evidence to show that the nuclei always in the air carried any charge. Turning now to the new instruments, fig. 1 shows the arrangement of the radioscope which will be described first. A is a U-shaped glass tube about 2 cm. internal diameter, in which the air undergoes the compression and expansion necessary for causing condensation in the dustless air. The U tube is partly filled with water, and the upper part B is the expansion chamber in which the observations are made. The other side of the U tube is connected by means of the india-rubber tube C with the india-rubber ball D. This ball can easily be obtained in any chemist’s ; its fittings are removed, and the short piece of metal tube E put in their place. The tube E is fixed to the board F, so as to keep the ball in its place in the centre of the hollow cut out in the surface of F. The lever G turns on the hinges H. When G is pressed down it compresses the air in D and in the chamber B of the U tube. K is a strip of spring brass bent into a segment of a circle. On K slides the stop J, which can be fixed at any point on K by means of the pinching screw I. On the outer end of the lever G is fixed a small piece of metal L, and when the lever G is pressed down to com- press the air in the ball D it engages with the stop J and keeps the ball compressed until it is desired to expand the air in the test chamber B, when the spring K is drawn back, and the lever G being disengaged the ball at once expands and relieves the pressure in B. M is an india-rubber cord for preventing the lever G being forced too far over. This arrangement of compressing and allowing the air to expand is not the usual one in experiments of this kind, as it is customary to expand the air by means of a pump or similar arrangement. The method shown, however, has some advantages over the pump. There is no leakage in the working parts, and the simple act of pressing down the lever G is all that is required, while the catch J keeps the pressure on till the temperature and vapour pressures in the expansion chamber have adjusted themselves. It has, however, one defect due to the heat developed by the compression. On the first compression being made the air in the ball and tube gets heated, and some of this heat escapes before expansion is made, and unless con- siderable time is given before the next compression, it will be made at a 474 Proceedings of the Royal Society of Edinburgh. [Sess. O | size. 475 1908-9.] A Simple Radioscope and a Radiometer. slightly lower temperature, and therefore not so great as the first ; but this does not seem appreciably to affect the results. After a few compressions and expansions things get to a uniform condition, especially if the com- pressions and expansions are made at equal intervals of time. For illuminating the test chamber B the lantern N is used. A common gas-jet aided with a lens is required for some experiments, but for most cases an incandescent gas light may be employed and the lens omitted, as without it one gets a more uniform illumination. These experiments are best made in a dark room, and only as much light allowed to come from the lantern as is necessary. A vertical adjustable slit placed in front of the lantern works well. This slit should only be opened about 1 cm. for tubes of 2 cm. diameter, as the narrow strip of light prevents the dis- agreeable and distracting reflections from the glass surfaces. When well arranged with black background the tube should show nearly black. A magnifying lens held in an adjustable support will be found useful. The lens should be set so as to look rather downwards, to avoid the reflections from the surface of the tube, and across but rather towards the light. The method of operating with the apparatus is as follows : — The U tube A, after being thoroughly cleaned, is filled with water to about the amount shown in fig. 1. For this purpose a fine india-rubber tube, small enough to pass through the opening in the U tube, will be found useful ; by sucking out the air it is quickly filled with water, and by blowing in air it is rapidly emptied. The tube, after washing and filling, is connected by means of the tube C with the compressor D. The light is then adjusted to show the interior of the tube, and as little light reflected by the glass as possible. The lever G is now pressed down for a short time and released ; and on now examining the test chamber B it will be found to be full of fog formed by the vapour condensing on the dust in the air. The magnifying lens should now be adjusted so as to show each fog particle clearly. A number of compressions and expansions are next made by pressing and releasing the lever G. This must be done till no fog particles appear in B ; the last of them will be seen falling like small rain-drops. After all con- densation ceases on slow expansion, the screw I is loosened and the stop J slipped up to a point which will require a little compression for the catch L to engage with the stop J. The lever is then pressed down till L engages with J. After a short time the spring K is drawn back and the catch L released, when the lever at once springs up and the air in B is suddenly expanded. The air in B should be watched while this is taking place. If no drops appear, then the expansion has not been enough to give the supersaturation necessary to cause condensation on the nuclei present. If 476 Proceedings of the Royal Society of Edinburgh. [S'ess. this be so, then I is unscrewed and the stop J lowered to give a greater compression. When this is done it will be found that at a certain compression a few drops appear in B. If we go on pushing J down by stages so as gradually to increase the compression, it will be found that the number of drops increases. These drops are formed on some nuclei which Wilson has shown are always present in moist air. These nuclei for convenience we will call natural nuclei. If we go on increasing the compression it will be found that when it exceeds a certain amount that the condensation somewhat suddenly changes its appearance from the rainy form to the foggy, and this fog becomes denser with further increase in the compression. In the apparatus shown in fig. 1 we cannot tell without trial what amount of compression will be necessary to give the supersaturation required to cause condensation on the natural nuclei, as the action of the instrument is complicated. Part of the expansion in that form of apparatus is due to the compression of the ball D, but part is also due to this expansion being carried on by the impetus given by the expanding air to the water in the tube. That is, some of the energy put into the water at the beginning of the expansion is given out by it at the end. The result of this is that the compression necessary for this form of apparatus is less than that which Wilson found to be necessary with his apparatus for causing condensation in the absence of dust. As has been stated, Wilson found that when the expansion was as great as vjvx — 1*250 that condensation took place in dustless air, and for all his instruments this figure was fairly constant, but in the instrument above described this is far from being the case. Any slight alteration is the arrangement of the apparatus alters the degree of compression required. For instance, any change in the amount of water in the U tube alters the compression necessary, and any alteration in the tube connecting the U tube with the compression ball has a like effect. In Wilson’s apparatus a compression corresponding to a column of about 19 cm. of mercury would, when expanded, give the necessary supersaturation, but with the U tube a pressure of only from 14 to 16 cm. is required according to the conditions. In Wilson’s apparatus the foggy stage of the condensa- tion is arrived at when the compression is about equal to 28 ’8 cm., while the U tube requires only from 19 to 20’5 cm. It is impossible to give these pressures with greater definiteness, as they vary in all the instruments here described with but slight alterations in their arrangement, but the pressures remain constant while the conditions are constant. Other forms of the compression chamber were tried. The one shown at P, fig. 1, for instance, requires much greater compression to cause condensation 477 1908-9.] A Simple Radioscope and a Radiometer. than A, because it entirely depends on the expansion of the air. As this form of instrument requires to he frequently removed from its stand and turned upside down for the purpose of wetting the interior walls, and possesses no advantages, its use was abandoned. This form of compression chamber required a pressure of 20 cm. to give the first or rainy stage of condensation, and 30 cm. to give the foggy stage. The reason for it requiring a greater compression than Wilson’s, is due to the resistance offered to free expansion by the tube C and the ball D. The arrangement shown at R, fig. 1, was also tried. In this case the tube is similar to A, but the expansion is stopped when the air has expanded to its original volume ; that is, the movement of the water is stopped before expanding its energy in expanding the air. This was done by the arrange- ment shown in R. A floating valve rose and fell with the water in the right arm of the U tube, so that, after compression and release, when the water rose to its original level the valve suddenly closed the outlet. As no advantage was observed in its action, it was not further experimented with. The reason for making this instrument was that, theoretically, the best conditions of the expansions in these condensation experiments would appear to be that the expansion be done as quickly as possible. During the first part of the expansion quickness does not matter so much, because no condensation is taking place on the nuclei, but the quicker the expansion is made after a certain stage is reached the more nuclei will become active. Now, the arrangement shown at A, one would imagine, would rather tend to make the expansion slow towards the end, and it was thought that by stopping it when at its maximum rate that an advantage might be derived — giving it, of course, the same amount of expansion as before ; but, so far as the purpose for which the instrument is intended, no advantage was observed. This instrument required a compression of 21 '5 cm. to give the rainy stage and 32 cm. to give the foggy condition, but the pressure required was variable according to the setting. If the valve did not float just at the level of its seat — that is, floated slightly below it — then, as might be expected, the pres- sure required was less, as the moving water is allowed to do a little expansion. When working with the expansion chamber as shown at A, fig. 1, the water after expansion rushes back into the chamber B and by splashing develops a few nuclei, but these are so few they can hardly be said to interfere with the results ; and this splashing has the great practical advantage of keeping the inside walls of the tube wet. Returning now to the apparatus shown in fig. 1, suppose the com- pression is adjusted so as to give only an odd drop or two falling in the chamber B. If while in this condition any radioactive substance is brought 478 Proceedings of the .Royal Society of Edinburgh. [Sess. close to B, an increase in the number of drops will take place, it may amount to a slight shower or a dense shower or a fog, according to the strength of the radioactivity. These new drops are condensed on the ions formed by the radioactive body. Wilson finds that the nuclei always present in moist air, and these ions formed by the radioactive substance, require the same expansion to cause them to become nuclei. My experience, however, does not fully confirm this. This difference in our conclusions may be due to the difference in our apparatus. There, how- ever, may be a different explanation. It has been observed that if the apparatus here described be left for some time, that on making the first expansion after the rest that the number of drops on the natural nuclei is greater than that given before stopping work, and greater than that obtained on subsequent expansions ; but as the degree of expansion with this apparatus may alter with time, the conclusion is not certain. In Wilson’s experiments it is probable there were longer intervals between the expansions, and this would bring the expansion required by the natural nuclei near to that required by the ions. If this explanation be correct, then it looks as if these natural nuclei became larger or at least better centres of condensation with time. With the apparatus shown in fig. 1 it is found that if the compression is reduced till there is hardly a drop visible, that the instrument is quite as sensitive to radioactive substances as with higher compressions. Of course, there are not so many drops formed, because with higher expansions the drops produced on the natural nuclei are added to those produced by the radioactivity. But, making allowance for these natural nuclei, there does not seem to be more due to the ions than when the lower compression was given. The question might be asked here, Does the radioactivity act on the natural nuclei and increase their condensing power and cause them to become active with lower supersaturations ? It is evident that the whole of the nuclei due to radioactivity are not produced in this way, because, with comparatively feeble radiation, the number of drops far exceeds the densest shower given by the natural nuclei. The action of the radioactivity is to produce ions in the air in the chamber B, and these ions become centres of condensation on supersatura- tion. The ions produced by the radiations have a very short life. If we remove the radioactive substance before the expansion is made the density of the condensation is greatly reduced. If we allow two seconds to pass before the expansion is made, only a slight effect remains. After five seconds all the ions are gone, having combined with each other. The continued action of the radioactive substance does not make the ions 479 1908-9.] A Simple Eadioscope and a Radiometer. larger, or, at least, not better nuclei to any perceptible extent. We can understand why this should be so : the life of an ion being so short, there is no time for any cumulative action of the rays. An interesting point, however, was observed. If after forming a dense, cloudy, or a foggy con- densation we leave it alone to settle for a short time, and if while there are still a good number of particles present we compress the air and cause the particles to evaporate, on again expanding the air slowly it will be found that many of the cloud particles have left a dust - like nucleus, as a slow and slight expansion makes them active and a shower results. But, on the other hand, if we compress and evaporate the particles immedi- ately after they are formed, it will be found that hardly any of the dust- like nuclei are present, only an odd drop appearing on slow expansion. Under the first conditions the cloud particles had time to differentiate in size, some growing larger, and it is probable that these larger cloud particles do not thoroughly evaporate but leave a nucleus large enough to be active with but slight supersaturation. To give an idea of the sensitiveness of this apparatus to radioactivity, it may be mentioned that any of the following substances, when held near the tube, give considerable increase in the condensation : pitchblende, radioactive mud, uranium, and, of course, any feeble radioactive salts or very minute quantities of them. For instance, the radium on a Crookes Spintariscope gives quite a dense shower. To get more decided effects with weak radioactive substances, an aluminium window in the tube B has been occasionally used. A number of gases and vapours were mixed with the air in the test chamber to see if any of them would improve its action. Amongst the substances tried were sulphurous acid, peroxide of hydrogen, sulphuric, nitric, and hydrochloric acids, and chlorine gas. None of these seemed to improve the action of the instrument as a detector of radioactivity. The most interesting of these tests were made with chlorine mixed with more or less air which acted differently from the others. With chlorine, after the tube had been freshly filled, there was always a great difficulty in getting the air cleared of the dust-like nuclei, and the action of the radio- activity was to manufacture great numbers of these dust-like nuclei, as it took a great number of slow expansions to clear out the nuclei after a test had been made with some radioactive substance. If while there was chlorine in the test chamber it was exposed to the light of burning magnesium, it gave dense condensation if expanded while the light was still burning, but all effect was gone if allowed to stand half a minute before expanding. On the other hand, an incandescent gas flame seems to 480 Proceedings of the Royal Society of Edinburgh. [Sess. cause the nuclei to grow to dust size, as a less expansion gives condensation with incandescent light than with gas flame ; and if the air was exposed to the incandescent light for fifteen minutes, it gave condensation on very slight expansion, just like dust, while the strongest radium salt I possessed gave no indication of being able to increase the size of the nuclei. Some tests were also made with methylated alcohol in the U tube, but beyond the lower expansions required to cause condensation on the ions, no advantage was observed. Another form of instrument was tried which seems to have some advantages over the U tube owing to the expansion being quicker and more suddenly stopped. In this instrument the compression chamber is a short length of an ordinary test tube, connected directly with a pear-shaped india-rubber compression ball. The test tube was connected with the ball by means of an ordinary f-inch brass union joint, one end of the union joint being cemented into the neck of the ball while the test tube was cemented into the other end. This joint is necessary for cleaning the tube and filling it with water. The compressing apparatus had to be modified to meet the new conditions. The compressor shown in fig. 1 is turned upside down, and has an opening made in the base-board large enough for the passage of the test tube and union joint, while the hinged board in this case presses on the bottom of the compression ball. By this arrangement the compression chamber projects upwards through the compressor, and the compressions and expansions are made in the same manner as in the other instrument. The Radiometer. The principal defect of the radioscope above described is that it only gives a rough indication of the strengths of the radioactive substances brought near it. It, however, seemed possible, if we were to adopt the principle already in use in the dust-counter, to make an instrument that would give numerical values of the strengths of the different radioactive substances, as by this arrangement we would be able to count the number of drops formed in the test chamber, and thus obtain definite figures of the strengths. To carry out this idea, the instrument shown in fig. 2 was constructed. B is the condensation chamber, in which the air is compressed and expanded. This chamber is made of brass, and has an opening E in the top and another opening F in the bottom. These openings are closed with glass plates, the upper opening being covered with clear glass, and the lower one with a glass micrometer ruled with cross lines 1 mm. apart. The chamber B is connected with the compression apparatus shown in Ill the printer is not responsible, the expense of such proofs and corrections will be charged against the author. All proofs must, if possible, be returned within one week, addressed to The Secretary , Royal Society , Mound, Edinburgh, and not to the printer. To prevent delay, authors residing abroad should appoint some one residing in this country to correct their proofs. 4. Additions to a Paper after it has been finally handed in for publication, if accepted by the Council, will be treated and dated as separate communications, and may, or may not, be printed immediately after the original paper. 5. Brief Abstracts of Transactions Papers will be published in the Proceedings, provided they are sent along with the original paper. 6. Separate Issue of Reprints; Author’s Free and Additional Copies. — As soon as the final revise of a Transactions paper has been returned, or as soon as the sheet in which the last part of a Proceedings paper appears is ready for press, a certain number of separate copies or reprints, in covers bearing the title of the paper and the name of the author, are printed off and placed on sale. The date of such separate publication will be printed on each paper. The author receives fifty of these reprints free, and may have any reasonable number of additional copies at a fixed scale of prices which will be furnished by the printer, who will charge him with the cost. To prevent disappointment, especially if the paper contains plates, the author should, immediately after receiving his first proof, notify to the printer the number of additional copies required. 7. Index Slips.' — In order to facilitate the compilation of Subject Indices, and to secure that due attention to the important points in a paper shall be given in General Catalogues of Scientific Literature and in Abstracts by Periodicals, every author is requested to return to the Secretary, along with his final proof, a brief index (on the model given below), of the points in it which he considers new or important. These indices will be edited by the Secretary, and incorporated in Separate Index Slips, to be issued with each part of the Proceedings and Transactions. MODEL INDEX. Schafer, E. A. — On the Existence within the Liver Cells of Channels which can he directly injected from the Blood-vessels. Proc. Roy. Soc. Edin., vol, 1902, pp. Cells, Liver, — Intra-cellular Canaliculi in. E. A. Schafer. Proc. Roy. Soc. Edin., vol. , 1902, pp. Liver, — Injection within Cells of. E. A. Schafer. Proc. Roy. Soc. Edin., vol. , 1902, pp. IV CONTENTS. NO. PAGE XXYI. On the Histological Changes in the Liver and Kidney after Chloroform administered by Different Channels. By G. Herbert Clark, M.B., D.P.H. (From the Physio- logical Laboratory of the University of Glasgow.) (With Three Plates), . . . . . .418 {Issued separately July 9, 1909.) XX VII. On the Effect of Internal Friction in Cases of Compound Stress. By G. H. Gulliver, B. Sc., A. M. I. Mech. E., Lecturer in Engineering in the University of Edinburgh, . 427 {Issued separately July 9, 1909.) XXVIXI. On the Friction at the Extremities of a Short Bar sub- jected to a Crushing Load, and its Influence upon the Apparent Compressive Strength of the Material. By G. H. Gulliver, B. Sc., A. M. I. Mech. E., Lecturer in Engineering in the University of Edinburgh, . . 432 {Issued separately July 16, 1909.) XXIX. On Group-Velocity and on the Propagation of Waves in a Dispersive Medium. By George Green, M.A., B.Sc., Assistant to the Professor of Natural Philosophy in the University of Glasgow. ( Communicated by Professor A. Gray, F.R.S.), ...... 445 {Issued separately July 16, 1909.) XXX. On a Simple Radioscope and a Radiometer for showing and measuring Radioactivity. By Dr John Aitken, F.R.S., . 471 {Issued separately 1909.) The Papers published in this Part of the Proceedings may be had separately, on application to the Publishers, at the follow- ing prices: — No. XXII., . . Price 6d. No. XXIII., . • 55 lOd. No. XXV., . • 55 6d. No. XXVI., . • 55 Is. 3d. No. XXVII., • 55 6d. No. XXVIII., • 55 lOd. No. XXIX., • 55 Is. 6d. No. XXX., . • • 55 Is. Od. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SESSION 1908-9. Part VI ] VOL. XXIX. [Pp. 481-608. CONTENTS. NO. XXXI. Nematonurus Lecointei, Poisson abyssal de la “Belgica” retrouve par Y Expedition Antarctique Nationale Ecossaise. Note preliminaire, par Louis Dollo, Sc.D. (Cantab.), Ph.D. (Giessen), Min. et Geol. D. (Utrecht), a Bruxelles (Musee). Presentee par M. R. H. Traquair, M.D., LL.D., F.R.S., V.P.R.S.E., ( Issued separately August 5, 1909.) PAGE 488 XXXII. The Theory of Jacobians in the Historical Order of Develop- ment up to 1860. By Thomas Muir, LL.D., ( Issued separately August 6, 1909.) 499 XXXIII. Motion of Neptune’s Satellite. By David Gibb, M.A., B.Sc. (Communicated by Professor Dyson), . . .517 {Issued separately August 23, 1909.) XXXIY. The Pathogenesis of Micrococcus melitensis. By J. Eyre, M.D., Bacteriologist to Guy’s Hospital, Member Advisory Board of Mediterranean Fever Commission, and Chairman of the 1906 Working Party in Malta, . . • 537 (Issued separately September 7, 1909.) [ Continued on page iv of Cover . EDINBURGH: Published by ROBERT GRANT & SON, 107 Princes Street, and WILLIAMS & NORGATE, 14 Henrietta Street, Covent Garden, London. MDCCCCIX. Price Nine Shillings and Threepence. REGULATIONS REGARDING THE PUBLICATION OF PAPERS IN THE PROCEEDINGS AND TRANSACTIONS OF THE SOCIETY. The Council beg to direct the attention of authors of communications to the Society to the following Regulations, which have been drawn up in order to accelerate the publication of the Proceedings and Transactions, and to utilise as widely and as fairly as possible the funds which the Society devotes to the publication of Scientific and Literary Researches. 1. Manuscript of Papers. — As soon as any paper has been passed for publication, either in its original or in any altered form, and has been made ready for publication by the author, it is sent to the printer, whether it has been read or not. The ‘ copy 5 should be written on large sheets of paper, on one side only, and the pages should be clearly numbered. The MS. must be easily legible, preferably typewritten, and must be absolutely in its final form for printing ; so that corrections in proof shall be as few as possible, and shall not cause overrunning in the lines or pages of the proof. All tables of contents, references to plates, or illustrations in the text, etc., must be in their proper places, with the page numbers left blank ; and spaces must be indicated for the insertion of illustrations that are to appear in the text. 2. Illustrations. — All illustrations must be drawn in a form im- mediately suitable for reproduction ; and such illustrations as can be reproduced by photographic processes should, so far as possible, be preferred. Drawings to be reproduced as line blocks should be made with Indian ink (deadened with yellow if of bluish tone), preferably on fine white bristol board, free from folds or creases; smooth, clean lines, or sharp dots, but no washes or colours, should be used. If the drawings are done on a large scale, to be afterwards reduced by photography, any lettering or other legend must be on a corresponding scale. If an author finds it inconvenient to furnish such drawings, the Society will have the figures re-drawn at his expense ; but this will cause delay. When the illustrations are to form plates, a scheme for the arrangement of the figures (in quarto plates for the Transactions, in octavo for the Proceedings) must be given, and numbering and lettering indicated. 3. Proofs. — In general, a first proof and a revise of each paper will be sent to the author, whose address should be indicated on the MS. If further proofs are required, owing to corrections or alterations for which [Continued on page iii of Cover. 481 1908-9.] A Simple Radioscope and a Radiometer. fig. 1 by means of the tube C. The inside of the chamber, where possible, is covered with blotting-paper, which is kept wet for the purpose of saturating the air. The tube C is attached to the compression chamber B by means of the union joint D. This opening is required for the purpose of cleaning the cover glass and the micrometer, and also for wetting the interior of B. After the air has been compressed and expanded the drops fall on the micrometer and are counted with the aid of the lens L, while the illumination is effected by means of the spot-mirror M, either daylight L or artificial light being used. As the thick walls of the chamber B offer considerable obstruction to the rays from the radioactive substances, a window A is cut out on one side of the chamber and covered with aluminium 025 mm. thick. Fig. 3 shows the arrangement of the apparatus when fitted together. The part R, however, may be omitted, as it is for a special purpose, and will be described later. Between the compressor and the chamber B is intro- duced a pressure gauge P. This gauge is, however, not necessary, but is con- venient, as it shows whether all the joints are air-tight or not and the com- pression keeping constant. The gauge is not necessary for setting the amount of compression required, as that is obtained by trial. After the glass surfaces in B have been cleaned and the sides wetted and all con- vol. xxix. 31 482 Proceedings of the Royal Society of Edinburgh. [Sess. nected up, the first thing to be done is to get rid of the dust particles in B. This is done by pressing the lever G and releasing it, when a fog will be seen slowly settling in B : time is given for it to settle, then another compression and expansion is made, when more cloud particles appear. This process of compression and expansion is continued till all condensation ceases in B with slight compression. The stop J on the compressor is now fixed at any point on K and the lever G pressed down till L engages with the stop J. The compression is left on for a time, and then the trigger K is pulled back, the lever L released, and the air in B expanded. While the air is expanding the eye of the observer should be watching the micrometer through the lens. If no drops appear, then the expansion has not been enough to produce condensation in dustless air : the stop J must therefore be pushed further down and another trial made, and so on till some drops appear on the micrometer. Suppose, on the other hand, that on first trial there should appear a number of drops, then the compression must be reduced. It will be found that the best degree of compression for these experiments is that which gives just an odd drop or two visible over the whole field. In that condition, though the expansion is not enough to bring down all of what we have called the natural nuclei in the air, yet it seems to be enough to bring down all the ions formed by the radioactivity. It will, of course, only bring down the negative ions, as Wilson has shown that while negatively charged ions become active nuclei when the expan- sion is represented by V2/V1 = 1*250, while the expansion must be as great as V2/Y1 = l*31 to bring down the positive ions. If the expansion is in- 483 1908-9.] A Simple Radioscope and a Radiometer. creased beyond what is just necessary to bring down a few of the natural nuclei, then we get more drops on the micrometer with the same radioactivity, but there does not seem to be more due to the radioactivity ; the increase seems to be due to the greater number of the natural nuclei brought down. The method generally adopted was to make the compression necessary to give the odd drops, and then bring to a fixed point some radioactive substance which is kept as a standard test and note the number of drops. Repeat the test with slightly varying compressions, but always with the standard radioactive body, and note results. It will be found that the most satisfactory tests are made when the number of drops on the natural nuclei is small, and in that condition practically all the drops are due to the radioactivity. If higher compressions are used, we have to deduct from the total number of drops those due to the natural nuclei. If at any time there is any suspicion that the test is not correct owing to some imperfec- tion in the apparatus, all we have to do is to present the standard radio- active substance and see if we get the correct number of drops. For the measurement of strong radioactive substances we must either interpose screens or put them at a distance from the instrument, because the number of drops given by them is far too great to be counted. Reference has already been made to the importance of the quickness of the expansion in these condensation experiments, and the question naturally arose, Was the arrangement used the best for the purpose ? or would some other form of release not give better results ? Some experi- ments were accordingly made with other forms of release which promised to make the expansion quicker. The apparatus shown in fig. 4 was tried ; this was interposed between the compression chamber and the compressor, taking the place of R, fig. 3. V is a tube open at both ends and provided with a branch tube on which is a stopcock. The end of the tube Cr is connected with C, fig. 2, by means of a small piece of india-rubber tube, while the branch tube C" is connected with the compressor. S is a thick piece of sheet india-rubber which closes the end of the tube Y, the india- rubber being fixed on the lever T, which is hinged at its lower end, and held at its upper end by the catch U. The lever requires considerable force to compress the india-rubber and engage with U. The object of this is to make the india-rubber act as a spring as well as an air-tight valve to the end of the tube Y, so that when the lever is released from the catch U it will be forced rapidly away, so opening the end of Y quickly, and thus giving the air in the compression chamber a free outlet. After the compression has been made, the stopcock on the tube C" is closed, and 484 Proceedings of the Royal Society of Edinburgh. [Sess. the expansion is made by releasing the lever T, when the rubber valve springs from its seat and has considerable velocity before the air begins to escape, thus ensuring a quick and full opening of the outlet. Another method of release was also tried. As has been already stated. the ideal form of expansion is the quickest that can be accomplished, but the final part of the expansion is the more important, a slight slowing of the initial part not being likely to have any bad effect. Accordingly, the apparatus shown in fig. 5 was made to meet these conditions. As before, the tube Y is connected at C' with the expansion chamber B, fig. 2, and at C" with the compressor. The release valve in this case consists of a plunger W, which is very accurately ground into the end of the pipe Y. This plunger, though fitting quite easily, is air-tight with the aid of a little glycerine or oil. U is a catch for preventing the plunger from being blown out by the pressure of the air. The action of this release valve is as 485 1908— y.] A Simple Radioscope and a Radiometer. follows : — When the catch U is lifted the air in the expansion chamber at once begins to expand, but it is slightly retarded by the resistance of the plunger ; but by the time the plunger clears the end of the tube it is shot out with considerable velocity, being in fact a very quickly opening valve, and in this way a very free passage is given for the latter part of the expansion. The catch U is in the form of a nut screwed on to the end of the lever. The object of this was to enable tests to be made of the effects of different lengths of stroke of the plunger. With a long stroke the first part of the expansion will be retarded most, but the plunger will acquire a greater velocity, opening the pipe quicker, and the latter part of the expansion be more rapid. A short stroke of the plunger, while quickening the first part, will slightly retard the latter, as it does not open so quickly. After a number of tests neither of these additions seemed to improve the working of the instrument to an extent sufficient to make up for the greater trouble given by their use. Both the radioscope and the radiometer have the defect that they only test the more penetrating rays— -that is, the /3- and y-rays ; while the a-rays, which have most of the energy of the radiation, are stopped by the walls of the expansion chamber. It was thought, therefore, that if the radio- active body could be introduced into the expansion chamber, it would be capable of measuring much smaller degrees of radioactivity. When working with the apparatus shown in figs. 4 and 5, it was found to be possible to open one end of the expansion chamber and allow dusty air to enter that end without it in any way interfering with the action of the instrument, the reason for this being that the dusty air only penetrates a short distance into the tube, and the compressions and expansions make the dust particles into cloud particles and deposit them before they penetrate into the expansion chamber. Taking advantage of this, it seemed quite easy to introduce the radioactive body into the expansion chamber. The apparatus shown at R, fig. 3, was therefore constructed. V is the connecting tube as in figs. 4 and 5, and C" is the branch pipe to the com- pressor. In this case the branch pipe is connected at a small angle to the tube Y to allow as free a passage as possible for the expanding air. The open end of the tube V is fitted with a union joint U and a stuffing box S, through which passes the fine steel wire W. The end of the wire inside the tube is provided with a screw on which may be fitted a small pair of forceps, or other arrangement that may be suitable for the particular experiment. When we wish to introduce a small piece of any substance into the chamber B the union joint U is unscrewed and the forceps or other 486 Proceedings of the Koyal Society of Edinburgh. [Sess. arrangement screwed on to the wire W. The substance being firmly secured, the union joint is replaced and screwed up, then a few compressions and expansions are made to throw down any dust clinging to the sample, after which the wire is pushed forward into the apparatus till the forceps is just visible on the edge of the field seen through the lens. Compression and expansion are now made and result noted. It may be mentioned that a piece of pitchblende about the size of a pin-head gives copious showers under these conditions. Its action, however, does not seem to be constant, as the shower may sometimes permit of counting the drops, while the next shower will be so dense it is impossible to do so. Salts of radium, however, seem to give showers of constant density. For instance, a small disc of brass about 2 mm. diameter was wetted with a very weak solution of a radium salt and allowed to dry. The solution used for this purpose was very weak, being made of a small speck of a very weak salt dissolved in, half an ounce of water. On testing this small quantity of radium inside the chamber it gave very dense showers about 50 drops per sq. mm., while through the aluminium window it only gave about 1 per mm. It may be mentioned that this disc did not give a scintillation of action when tested with the phosphorescent screen. A similar disc of brass was put into a bottle in which was a weak radium salt to test the effects of the emanations from the radium. After the disc had been in the bottle five hours to collect radium A — the active deposit of the emanations — it was put inside the expansion chamber and gave at first about 30 drops per sq. mm. Another disc put in the same bottle with radium for one hour gave nearly the same number. In both cases the number remained high for some time, but in a few hours both ceased to act. As the experiments were made simply for testing the radiometer, no notes were taken of the rates of decay. In collecting the radioactive deposit care was taken that the disc did not touch the bottle containing the radium. The disc was fitted to a new cork which had been fitted to the bottle, and so arranged that the cork supported the disc in the middle of the space over the radium, and all metal parts connected with the disc were further cleaned with emery cloth to remove any chance of contamination. In using this method of working great care has to be exercised that the body introduced into the expansion chamber does not interfere with the expansion of the air. As already pointed out, any alteration in the tube between the expansion chamber and the compressor alters the results. In making these experiments it was found necessary to test the forceps to see if their introduction did not interfere with the results, when it was found 487 1908-9.] A Simple Radioscope and a Radiometer. that if the forceps were at a distance from the chamber — that is, in the tube — they did interfere with the expansion, but that if they were in the expand- ing part of the chamber they did not. Again, when testing the radium salt on disc, another similar disc was made but kept free from all radio- active matter and its action on the expansion tested before the disc with the radium was tried. It is possible that some other method of introducing the substance to be tested into the expansion chamber might be devised which would give less trouble, but as yet none has been tried. When the substance to be tested is introduced into the expansion chamber it is evident there are risks of the instrument becoming con- taminated either by some of the substance tested escaping from the forceps with the rush of air during expansion, or by the emanations given off by the bodies tested. Care has therefore to be taken that the bodies tested are firmly secured, and the tests quickly made, so that as short a time as possible may be given for the emanations to collect. (. Issued separately July 21, 1909.) 488 Proceedings of the Royal Society of Edinburgh. [Seas. XXXI. — Nematonurus Lecointei, Poisson abyssal de la “Belgica” retrouve par PExpedition Antarctique Nationale Ecossaise. Note preliminaire, par Louis Dollo, Sc.D. (Cantab.), Ph.D. (Giessen), Min. et Geol. D. (Utrecht), a Bruxelles (Musee). Presentee par M. R H. Traquair, M.D., LL.D., F.R.S., Y.P.RS.E. (MS. received June 7, 1909. Read June 7, 1909.) I. Introduction. I. — Nous avons vu, recennnent, que les Macruridce, dans l’etat actuel de nos connaissances, sont represented par une espece a l’interieur du Cercle Polaire Arctique et par deux especes a l’interieur du Cercle Polaire Antarctique * II. —Maintenant, si nous considerons la Zone situee entre 60° N. et le Cercle Polaire Arctique , nous constatons que les Macruridce n’y figurent pas pour moins de 8 especes, appartenant a 6 genres et a 2 sous-familles.*|* Toutes ces especes sont groupees dans le bassin de l’Atlantique, — et on comprend l’absence de Macrurides, poissons essentiellement abyssaux, dans la region correspondante du Pacifique, car la Mer de Behring atteint rarement 100 fathoms entre 60° et le Cercle Polaire, — tandis que les profondeurs de 100 fathoms et moins occupent un espace tres restreint dans l’Atlantique entre 60° N. et le Cercle Polaire Arctique. III. — Passant, ensuite, a la Zone situee entre 60° S. et le Cercle Polaire Antarctique, nous remar quons que, jusqu’aujourd’hui, pas un seul Macruridce n’y etait signaled En effet, il n’y a que trois Expeditions Antarctiques, en dehors de la Scotia (1902-1904), qui aient publie des Macrurides: 1. Erebus and Terror (1839-1843). — Provenance : Cotes de l’Australie Meridionale, par consequent bien au Nord de 60° S. § * L. Dollo, “ Cynomacrurus Piriei, Poisson abyssal nouveau recueilli par l’Expedition Antarctique Nationale Ecossaise,” Proceedings of the Royal Society of Edinburgh, vol. xxix. p. 316, Eclimbourg, 1909. t Voir, plus loin, remuneration detaillee. I A. Brauer, “Die Tiefsee-Fische (I. Systematischer Teil),” Wissenschaftliche Ergebnisse der deutschen Tief see- Expedition auf dem JJampfer “ Valdivia ” 1898-1899, vol. xv., pi. xvii., Iena, 1906. § J. Richardson, “Fishes,” Zoology of H.M.S. “ Erebus ” and “ Terror ,” imder the com- mand of Captain Sir James Clark Ross, R.N., F.R.S., during the years 1839 to 18f3, p. 53 Londres, 1846. 489 1908-9.] Dr Louis Dollo on Nematonurus Lecointei. 2. Belgica (1897-1899). — Provenance: Interieur dn Cercle Polaire Antarctique, par consequent au dela de la Zone qui nous interesse ici.* 3. Antarctic (1901-1903). — Provenance : Detroit de Bransfleld, par consequent, cette fois, entre 60° S. et le Cercle Polaire Antarctique, mais le poisson perit avant d’avoir pu etre determine d’une maniere precise, dans le desastre, a jamais deplorable, qui engloutit le navire.f Quant aux Expeditions Oceaniques qui ont recueilli des Macrurides et qui ont penetre entre 60° S. et le Cercle Polaire Antarctique, — c’est-a-dire celles du Challenger (1873-1876) et du Valdivia (1898-1899), — elles n’en ont pris qu’au Nord de 60° S. J Ce qui est d’autant plus etonnant que les profondeurs considerables abondent dans la Zone limitee par 60° S. et par le Cercle Polaire Antarctique. IV. — II etait done encore reserve a 1’ Expedition Antarctique Rationale Ecossaise de rapporter le premier Macruridce de la Zone situee entre 60° S. et le Cercle Polaire Antarctique. Ce Macruride, comme je vais le montrer, n’est autre que le Nematonurus Lecointei , decouvert par la Belgica a l’interieur du Cercle Polaire Antarctique. Rien de trop surprenant a cela, d’ailleurs, puisque le Macrurus berglax se trouve, a la fois, a l’interieur du Cercle Polaire Arctique et dans la Zone situee entre 60° N. et ce Cercle Polaire. § II. Identification du Specimen de la “ Scotia.” 1. Concordances. — 1. Sous-Famille. — Par sa premiere fente branchiale reduite, le Macruride subantarctique de la Beotia appartient a la sous- famille des Macrurince. 2. Genre. — Par ses dents premaxillaires sur deux rangs, ses dents mandibulaires sur un seul, sa deuxieme epine dorsale barbelee et ses nageoires dorsales largement separees, notre poisson vient se ranger dans le q'enre Nematonurus. o * L. Dollo, “Poissons de l’Expedition Antarctique Beige/’ Resultats du Voijage du S.Y. “ Belgica ” en 1897 , 1898, 1899, sous le commandernent de A. de Gerlache de Gomery, p. 44, Anvers, 1904. t E. Lonnberg, “ The Fishes of the Swedish South Polar Expedition,” Wissenschaftliche Ergebnisse der schwedischen Siidpolar -Expedition 1901-1903 unter Leitung von Dr. Otto Nordenskjold, p. 50, Stockholm, 1905. I A. Gunther, “Report on the Deep-Sea Fishes,” Voyage of H.M.S. “ Challenger ” during the years 1873-76 : Zoology, vol. xxii. p. 122, Edimbourg, 1887. A. Brauer, Die Tiefsee-Fische, etc., p. 256. § A. Brauer, Die Tiefsee-Fische, etc., pi. xvii. 490 Proceedings of the Royal Society of Edinburgh. [Sess. 3. Espece. — Par les ecailles du corps inermes et caduques, les ecailles de la tete armees de cinq rangees d’epines, la distance des dorsales plus grande que les trois quarts de la longueur de la tete, la verticale de l’anus passant en arriere du milieu de cette distance et les ventrales avec dix rayons dont l’externe plus grand que la moitie de la longueur de la tete n’atteint pas l’anus, Fanimal consider e s’identifie avec le Nematonurus Lecointei * II. Discordances. — A part de minimes differences dans les dimensions de la fente buccale, dans le diametre de l’orbite, dans la largeur de l’espace interorbitaire, dans la longueur du museau, ou d’autres semblables qu’on pourrait trouver, et qui n’ont pas, pour moi, de valeur specifique, je ne mentionnerai, ici, que trois discordances a expliquer : 1. Premiere Dor sale. — Elle a 10 rayons, au lieu de 9 : mais nous rencontrons un cas analogue de variation, 13 a 14 rayons, dans la premiere dorsale du Malacocephalus Icevis.f 2. Distance des Dorsales. — Au lieu d’etre presqu’egale a 3J fois la base de la premiere dorsale, elle n’atteint pas 2 J fois cette base : mais, coniine la distance en question est, quand meme, plus grande que les § de la longueur de la tete, on voit que c’est la base de la premiere dorsale qui est plus developpee que d’ordinaire, ce qui est en rapport avec le rayon supple- mentaire, et non la distance des dorsales qui est reduite. 3. Pectorales. — Elies ont 20 rayons, au lieu de 21 : variation individuelle de meme ordre chez Macrurus berglax (18 a 19) et de plus forte amplitude chez Nematonurus armatus (18 a 20)4 III. Conclusion.- — II convient de regarder le Macruride subantarctique de la Scotia comme un nouvel exemplaire de Nematonurus Lecointei , Dollo, 1900. III. Bionomie du Nematonurus Lecointei. I. Donnees. — Comparons, maintenant, au point de vue bionomique, le Nematonurus Lecointei de la Belgica et celui de la Scotia : § “ Belgica.” “ Scotia.” I. Biogeographie. I. Biogeographie. Habitat: 70° 40' S. et 102° 15' W. Habitat: 62° 10' S. et 41° 20' W. Mer de Bellingshausen. S.E. Orcades du Sud. Ocean Antarctique. Ocean Atlantique. Quadrant Pacifique. Quadrant Americain. Numero 873. Station 313. * L. Dollo, Poissons de V Expedition Antcirctique Beige , etc., p. 44. + A. Gunther, Deep-Sea Fishes , etc., p. 148. I Ibid., pp. 130 et 150. § L. Dollo, Poissons de V Expedition Antarctique Beige, etc., p. 45. 1908-9.] Dr Louis Dollo on Nematonurus Lecointei. 491 II. Ethologie. 1. Profondeur. — 1531 fathoms. 2. Nature du Fond. — Vase et roclies erratiques. 3. Temperature du Fond. — 33° F. 4. Temperature de la Surface. — 28° ‘2 F. 5. Densite de VEau (Fond). — Inconnue. 6. Densite de VEau (Surface). — In- connue. 7. Mode de Capture. — Chalut a etrier de cinq pieds. 8. Date de Capture. — 14 mars 1899. 9. Heure de Capture. — Entre 5^ et 6 heures du soir. 10. N ombre d’lndividus captures. — Deux, pris ensemble. 11. Compagnons de Peclie. — Alcyonaires, Asterides, Ophiurides, Bryozoaires, Lamellibranches. II. Discussion. — 1. Latitude. — D’ nurus Lecointei se rencontrerait a l’ir et dans la Zone situee entre 60° S. et < Belgica ..... Scotia ..... Difference II. Ethologie. 1. Profondeur. — 1775 fathoms. 2. Nature du Fond. — Vase bleue et blocs de plus d’un quintal. 3. Temperature du Fond. — 31° F. 4. Temperature de la Surface. — 29° ‘6 F. 5. Densite de VEau (Fond). — 1 ‘02560. 6. Densite deV Eau (Surface). — 1*02477. 7. Mode de Capture. — Chalut. 8. Date de Capture. — 18 mars 1903. 9. Heure de Capture. — Entre 8 heures du matin et 8 heures du soir. 10. N ombre d’lndividus captures.— Un seul. 11. Compagnons de Peclie.— Crinoides, etc. Dres notre determination, le Nemato- erieur dn Cercle Polaire Antarctique, ! Cercle Polaire : 70° 40' S. Antarctique. 62° 10' S. Atlantique. 8° 30,_ Mais le Macrurus berglax, de l’interieur dn Cercle Polaire Arctique, se rencontre egalement dans la Zone situee entre 60° N. et ce Cercle Polaire, — ■ et meme bien plus au Sud, jusqu a la Nouvelle-Angleterre, done avec une difference de latitude beaucoup plus considerable : Olga . . . . .74° 56' N. Spitzberg.* Albatross . . . .41° 47' N. Massachusetts.]- Difference . . 33° 09' * E. Ehrenbaum, “ Die Fische der ‘ Olga ’-Expedition,” Wissenschaftliche Meeresunter- suchungen , herausgegeben von der Kommission zur Untersuchung der deutschen Meere in Kiel und der biologischen Anstalt auf Helgoland , vol. vii. p. 62, Oldenbourg, 1905. t G. B. Goode and T. H. Bean, “ Oceanic Ichthyology,” Smithsonian Contributions to Knowledge , vol. xxx. p. 391, Washington, 1895. 492 Proceedings of the Royal Society of Edinburgh. [Sess. D’autre part, le Nematonurus armatus nous offre une variation de latitude encore plus forte : Challenger .... 36° 10' N. Pacifique central.* Challenger .... 53° 55r S. Indique austral.f Total . .. . 90° 05'" — Parallelement, nous avons : 2. Longitude. Belgica . Scotia Difference pour le N ematonurus Lecointei. Puis : Enigheten Albatross Total . pour le Macrurus berglax. Et : Challenger Challenger Total . 102° 15' W. Antarctique. 41° 20' W. Atlantique. 60° 55~ 23° 40' 00" E. Finmark.J 65° 37' 30" W. Massachusetts. 89° 17' 30" 45° 31' E. Indique austral. || 151° 34' W. Pacifique central.1I 197° 05', ~ ou 162° 55' pour le A ematonurus armatus. 3. Bathymetrie. — Enfin, nous noterons les chiffres suivants : Scotia 1775 fathoms. Atlantique. Belgica 1531 „ Antarctique. Difference . . 244 „ pour le Nematonurus Lecointei. * J. Murray, “Summary of Results,” Voyage of H.M.S. “ Challenger ” during the years 1873-76, p. 961, Edimbourg, 1895. + Ibid., p. 505. t R. Collett, “ Meddelelser om Norges Fiske i Aarene 1884-1901 (3die Hoved -Supple- ment til ‘Norges Fiske’), II.,” Forhandlinger i Videnskabs-Selskabet i Christiania , Aar 1903, No. 9, p. 76, Christiania, 1904. § G. B. Goode and T. H. Bean, Oceanic Ichthyology , etc., p. 391. || J. Murray, Summary of Results, etc., p. 443. IT Ibid., p. 1034. 493 1908-9.] Dr Louis Dollo on Nematonurus Lecointei. Puis : Ingolf . Olga Difference pour le Macrurus berglax. Et : Challenger Challenger Difference 1931 fathoms. Greenland.* * * § 218 „ Spitzberg.f ms 2425 fathoms. 400 2025 v> Pacifique central. J N. Zelande.§ pour le Nematonurus armatus. 4. Conclusion. — Notre determination est, des lors, justifiee aussi bio- nomiquement. IV. LeS MACRURIDiE ET LA BlPOLARITE. I. Bipolarite. — II reste toujours utile de s’occuper de cette theorie, a laquelle nous avons declare, plusieurs fois, ne pouvoir nous rallier, ni en principe, ni en fait. 1 1 Car, il y a quelques mois a peine (1909), M. E. Vanhoffen, Conservateur au Musee royal d’Histoire naturelle de Berlin, ecrivait encore : “ In der dritten Arbeit wies ich auf die ausgesprochene Bipolaritat der Lucernariden hin.” 1 [ Puis, a propos des Radiolaires : “ Eine ganze Anzahl von Arten zeigte auch auffallende Uebereinstim- mung mit nordischen Formen und vier von ihnen werden als Beispiele fur Bipolaritat besonders hervorgehoben, da sie im nordlichen und siidlichen Kaltwassergebiet haufig anzutreffen sind, wahrend sie im ganzen Warm- * C. Liitken, “The Ichthyological Results,” The Banish “ Ingolf "-Expedition, vol. in p. 24, Copenhague, 1899. t E. Ehrenbaum, Die Fische der “ Olga ” - Expedition , etc., p. 62. J J. Murray, Summary of Results , etc., p. 1034. § A. Gunther, Deep-Sea Fishes, etc., p. 150. || L. Dollo, Poissons de V Expedition Antarctique Beige , etc., pp. 191-207. L. Dollo, “Notolepis Coatsi, Poisson pelagique nouveau recueilli par l’Expedition Antarcticjue Rationale Ecossaise,” Proceedings of the Royal Society of Edinburgh , vol. xxviii. p. 61, Edimbourg, 1908. IF E. Vanhoffen, “Vorwort,” Deutsche Siidpolar- Expedition 1901-1903, vol. x. p. v, Berlin, 1909. 494 Proceedings of the Royal Society of Edinburgh. [Sess. wassergebiet nach den bisherigen Forschungen fehlen und es ausgeschlossen erscheint, dass diese grossen und charakteristischen Arten liber sehen wurden.” * * * § II. Macruridce. — 1. Donnees. — Or, nous avons, ici : 1. — A l’interieur du Cercle Polaire : f j' Arctique 1 Antarctique Macrurus berglax. j' Cynomacrurus Piriei. { Nematonurus Lecointei. Oceans :% A. A. P. 2. — Entre 60° de Latitude et le Cercle Polaire : l j Arctique I Antarctique Chalinura Simula. § Coelorhynchus ccelorhynchus.\\ Coryphcenoides rupestris. IF cequalis ** berglax.-\-\ Ingolfi .§ Nematonurus Goodei.§ ' Trachyrhynchus Murray i .** Nematonurus Lecointei.\\ Macrurus A. A. A. A. A. A. A. A. A. * E. Vanhoffen, Vorwort , etc., p. vi. t L. Dollo, Cynomacrurus Piriei , etc., p. 316. j A = Atlantique, I = Indique, P = Pacifique, ou leurs prolongements a l’interieur des Cercles Polaires. § 0. Liitken, Ichthyological Results, etc., pp. 24, 26, 27, 28. | R. Collett, “Norges Fiske,” Forhandlinger i Videnskabs-Selskabet i Christiania, Aar 1874 (Tillsegsh.), p. 129, Christiania, 1875. IT J. E. Gunnerus, “ Efterretning om Berglaxen, en rar norsk Fisk, som knnde kaldes Coryphcenoides rupestris,” Trondhjemske Selskabs Skrifter, vol. iii. p. 50, Copen- liague, 1765. ** R. Collett, “Fiske indsamlede under ‘Michael Sars’ s Togter i Nordhavet 1900- 1902,” Report on Norwegian Fishery and Marine- Investigations, vol. ii., No. 3, pp. 55, 56, 58, 62, Bergen, 1905. tt R. Collett, Meddelelser, etc., p. 75. Voir, plus haut, p. 490. 1908-9.] Dr Louis Dollo on Nematonurus Lecointei. 495 3. — Entre 50° et 60° de Latitude Nord Sud l Albatrossia pect oralis.* Bogoslovius Clarki* „ firmisquamis * Chalinura serrula * „ simula.f „ fdifera.\ Codorhynchus codorhynchus. \ „ Talismani. || Coryphcenoides rupestris.§ Macrurus acrolepis * \ „ cequalis .§ „ berglax „ cinereus * „ Gunther i.\\ „ lepturus ** * * §§ Malacocephalus lcevis.§ Nematonurus cyclolepis.% „ Goodei: f „ suborbitalisr |*f \ Tracliyrhynchus Murray i.\\ (Codorhynchus fasciatus.§§ Lionurus jilicauda. § § Macruronus novce-zelandice. § 1 Nematonurus armatus. § § P. P. P. P. A. P. A. A. A. P. A. A. P. A. P. A. P. A. P. A. P. I. P. I. * B. W. Evermann and E. L. Goldsborough, “ The Fishes of Alaska,” Bulletin of the Bureau of Fisheries, vol. xxvi. pp. 224, 349, Washington, 1907. t G. B. Goode and T. H. Bean, Oceanic Ichthyology , etc., pp. 407, 412. I C. H. Gilbert, “The Ichthyological Collections of the steamer ‘Albatross’ during the years 1890 and 1891,” United States Commission of Fish and Fisheries ( Commissioner’s Report , 1893), p. 458, Washington, 1895. § E. W. L. Holt and W. L. Calderwood, “ Survey of Fishing- Grounds, West Coast of Ireland, 1890-1891 : Report on the Rarer Fishes,” Scientific Transactions of the Royal Dublin Society, vol. v. pp. 451, 455, 463, 472, Dublin, 1895. || R. Collett, “Fiske indsamlede under ‘Michael Sars’ s Togter i Nordhavet 1900- 1902,” Report on Norwegian Fishery and Marine Investigations, vol. ii., No. 3, pp. 55, 56, 58, 62, Bergen, 1905. IF C. Liitken, Ichthyological Results, etc., pp. 24, 26, 27, 28. ** D. S. Jordan and C. H. Gilbert, “ The Fishes of Bering Sea,” The Fur Seals and Fur- Seal Islands of the North Pacific Ocean, part 3, p. 487, Washington, 1899. ft T. Gill and C. H. Townsend, “Diagnoses of New Species of Fishes found in Bering Sea,” uProceedings of the Biological Society of Washington, vol. xi. p. 234, Washington, 1897. | i. A. Gunther, Deep-Sea Fishes, etc., p. 153. T. H. Tizard and J. Murray, “ Exploration of the Faroe Channel, during the summer of 1880, in H.M.’s hired ship ‘Knight Errant,”’ Proceedings of the Royal Society of Edinburgh, vol. xi. p. 660, Edimbourg, 1 882. §§ A. Gunther, Deep-Sea Fishes, etc., pp. 129, 141, 150, 157. II est impossible, pour le moment, de savoir exactement ce qu’est le Macruride du Canal 496 Proceedings of the Royal Society of Edinburgh. [Sess. 2. Resultats. — Condensant et comparant, nous obtenons : S. Families. En tout : | Arctique : [ Antarctique : En commun, au Nord et au Sud : Genres dominants A l’interieur du Cercle Polaire : Entre 60° Lat. et J Arctique : le Cercle Polaire : ( Antarctique : Entre 50° et 60° JNord: de Latitude : Sud : 1 1 2 1 2 2 Genres. 1 2 6 1 9 4 Especes. 1 2 8 1 20 4 Especes : Genres : * A l’interieur du Cercle Polaire . -{ Entre 60° Lat. et le Cercle Polaire Entre 50° Lat. et 60° Lat. . f A l’interieur du Cercle Polaire . Entre 60 Lat. et le Cercle Polaire Entre 50° Lat. et 60° Lat. . ( f l 0 0 0 0 1 6 o ft Au Nord : Macrurus : c Arctique ..... x Atlantique ..... x Pacilique ..... x Indique ..... x ■ Antarctique .... 0 f Arctique ..... 0 Atlantique ..... x Pacifique ..... x Indique ..... x Antarctique x III. Conclusions. — 1. Macruridce. — II resulte de ce qui precede que les Macrurides, comme les autres Poissons, f ou meme comme les autres Au Sud : Nematonurus : \ du Beagle (Terre de Feu) recueilli par l’Expedition Antarctique Suedoise (E. Lonnberg, Fishes of the Swedish South Polar Expedition, etc., p. 9). Quant au Macruronus magellanicus (E. Lonnberg, “ Fisclie,” Ergebnisse der Haw, burger Magalhaensischen Sammelreise , p. 15, Hambourg, 1907), je ne vois pas de raisons suffisantes pour le separer du M. novce-zelandice. Ce que confirme, biogeographiquement, la distribution de Coelorhynchus fasciatus, Genyp- terus blacodes, Macruronus novce-zelandice et Neophrynichthys latus (L. Dollo, Poissons de V Expedition Antarctique Beige , etc., pp. 214, 215 ; A. R. McCulloch, “Fishes and Crustaceans from Eight Hundred Fathoms, The Expedition of the ‘Woy Woy,’ The Results of Deep- Sea Investigation in the Tasman Sea,’5 Records of the Australian Museum, vol. vi. p. 348, Sydney, 1907). * Les deux genres communs au Nord et au Sud, Ccelorhynchus et Nematonurus, sont d’ailleurs, cosmopolites. t L. Dollo, Poissons de V Expedition Antarctique Beige, etc., pp. 199, 205. L. Dollo, Notolepis Goatsi, etc., p. 61. 497 1908-9.] Dr Louis Dollo on Nematonurus Lecointei. Vertebres,* sont defavorables a la theorie cle la Bipolarite, — puisqu’il n’en existe pas une Espece commune aux deux Zones situees entre 50° de Latitude et le Pole correspondant, ni non plus un Genre commun a Finterieur des deux Cercles Polaires. 2. Meduses. — Comment, des lors, expliquer les cas cites par M. Van- hoffen ? Mais, en ce qui concerne les Meduses, ce Zoologiste ne retient comme polaires que les especes suivantes : f Arctiques : 1. Halicyatlius lagena, 2. Lucernaria quadricornis , 3. Nausithoe polaris, 4. Cyanea arctica, 5. Aurelia limbata, 0 0 0 0 AnTARCTIQUES : 0 0 0 0 0 1. Lucernaria australis , 2. Lucernaria sp., 3. Desmonema Chierchiana, 4. Ulmaropsis Drygalskii, et il n’y a pas une seule Espece commune au Nord et an Sud dans sa liste entiere, qui en comprend cependant 31. 3. Radiolaires. — Quant aux Badiolaires, M. le Docteur A. Popofsky, de Magdebourg, interprete les 4 Especes communes au Nord et au Sud par la Continuity en Profondeur.% Ce serait done du Cosmopolitisme. 4. Bipolarite. — Or, comme je l’ai deja dit,§ — en dehors des constatations de fait, a condition qu’elles soient etablies d’une maniere indiscutable, — -je ne me refuse pas a admettre, theoriquement, la possibility d’Especes * L. Dollo, Poissons de V Expedition Antarctique Beige , etc., pp. 199, 205. L. Dollo, Notolepis Goatsi, etc., p. 61. t E. Vanhoffen, “ Die Lucernariden und Skypliomedusen,” Deutsche Sildpolar -Expedi- tion, 1901-1903 , vol. x. pp. 48, 49, Berlin, 1908. J A. Popofsky, “ Die Radiolarien der Antarktis,” Deutsche Sildpolar -Expedition, 1901- 1903 , vol. x. pp. 197, 198, Berlin, 1908. § L. Dollo, Poissons de V Expedition Antarctique Beige, etc., p. 207. M. G. Enderlein, Conservateur du Musee de Stettin, a traite, recemment, en detail, la question de la Bipolarite et celle de l’Antarctide (G. Enderlein, “ Die biologische Bedeutung der Antarktis,” Deutsche Sildpolar -Expedition, 1901-1903 , vol. x. p. 352, Berlin, 1909), en s’appuyant principalement sur les Insectes, mais, — bien que je me sois occupe des memes sujets, d’une manitre approfondie, et bien que le Zoologiste allemand fasse aussi usage des Poissons pour ses deductions, — mon memoire de la Belgica lui est reste completement inconnu, — quoiqu’il ait paru dans un recueil uniquement consacre aux problemes antarctiques. VOL. XXIX. 32 498 Proceedings of the Poyal Society of Edinburgh. [Sess. bipolaires sporadiques, meme avec Aires de Dispersion discontinues, a cause des Migrations en Profondeur. Ce que je ne puis accepter, c’est que les Pannes polaires soient des Reliquats a peine modifies de la Faune universelle de la St talloiv- Water (G. Pfefier) ou de la Mud-Line (J. Murray).* J’ai donne mes raisons jadis, et les faits nouveaux qui sont venus depuis a ma connaissance, notamment sur les Macruridce, non plus que ceux releves par M. Vanhoffen, ne sont pas de nature a modifier mon opinion. Je garde done vis-a-vis de la Bipolarite la meme attitude qu’en 1904.* * L. Dollo, Poissons de V Expedition Antarctique Beige , etc., p. 207. ( Issued separately August 5, 1909.) 1908-9.] Dr Muir on the Theory of Jacobians. 499 XXXII. — The Theory of Jacobians in the Historical Order of Development up to 1860. By Thomas Muir, LL.I). (MS. received March 22, 1909. Read June 7, 1909.) My last communication in reference to the history of Jacobians dealt with the period 1815-1841 ( Proc . Roy. Soc. JEdin ., xxiv. pp. 151-195). The present paper continues the history up to 1860. Jacobi, C. G. J. (1844-1845). [Theoria novi multiplicatoris systemati sequationum differentialium vulgarium applicandi. Crelles Journ., xxvii. pp. 199-268 ; xxix. pp. 218-279,333-376: or Math. Werke (1846), i. pp. 47-226 : or Gesammelte Werke, iv. pp. 317-509.] The portion of this long memoir which is of interest to us in the present connection is the first section (pp. 201-209) of the first chapter, the heading being “ Lemma fundamental eiusque varii usus : de determinantibus functionalibus partialibus.” Passing over the treatment of the first two cases of the lemma we come upon the general enunciation of it, which is — If A , A, , A2 , . . . , A„ be the cofactors of K dx. V dxn in the ox„ determinant ■■■<"), then 'dxdxfdxf ' dx. BA 9A, 3A0 - — + — — - + — — ^ + dx dx dXn + 0A, dx„ = 0 '1 w^2 Preparatory for the proof it is pointed out that since f A+yAl+ . . . +Aa„ I ..M dx OX} 0Xn \ OX OX} OXnJ an alternative form of the lemma is 0(/A) 0(/A1)+ _ _ + 0(/Ab) = y(±hfdj\ _ _ _ 0A\ dx dx-} dxn \ dx dx v dxnJ Then calling the given determinant R, and noting that A , A x , . . . , An are themselves functional determinants, A* being the determinant of f \ , f2, ... , fn with respect to x, xx, ... , x{_x, xx+l, . . . , xn, Jacobi seeks to prove the lemma true in the case of R from assuming it true in the case of A< . To be able to formulate it in the latter case he takes each element of the first 500 Proceedings of the Poyal Society of Edinburgh. [Sess. row of R along with each element of the second row, thus forming (n + 1)2 products whose cofactors in the determinant he denotes by (00) (01) (02) . . . (On) (10) (11) (12) . . . (In) (20) (21) (22) . . . (2 n) (nO) (nl) (?z2) . . . (nn) — that is to say, he puts (lk) for the cofactor of a notation which necessitates d in R dx{ dxk 5 (Hi) = - (Id) and (it) = 0 . It follows on this that the cofactors of dj\ dj\ dj\_ df_ dx ’ dXj ’ ’ 0xi_1 ’ dxi+1 in are (i, 0) , (i, 1) , . . . , (i, n) , and takes the form 3ft, 0) | 3(t,i) + . . . dx dx-, or |{|o)/l, 3{(»,l)/x} + dx dxl thus the assumption above made ■ 8P» = 0 dxn d{(i,n)fA) = A dxn Since, however, (i , k)f\ = — (k, %)fx and = 0, we can apply to the latter the general proposition that if aik be any quantities whatever such that aik — — aki , aH = 0 , and Ef stand for then dfljo , 90*1 + | in ox dx1 dxn 0H 0H, 0H„ “f* — — 1 + . . . + 0x dXj dxn as desired. There only then remains to show that the lemma holds in the case of two variables, and this is unnecessary because it is then identical with the familiar proposition = ffi_ m dx dy dy dx In addition to this gradational proof Jacobi gives one of a different 00^i* dxf- dxi dx, dxk * The reason for this, of course, is that + = 0. 501 1908-9.] Dr Muir on the Theory of Jacobians. kind. Since A* , he says, does not involve differential-coefficients with 0A- 0A- respect to xi , it follows that and cann°t involve differential- coefficients taken twice with respect to any one variable. Further, second differential-coefficients taken with respect to different variables x,L , xk can- not occur anywhere save in* dAj + 9A/C dXr; dXr. d2f w J rr All we have got to show therefore is that the cofactor of ~ & ox, ox, m k 0A- 0A . . . x — 1 + x— * vanishes. To do this we express A, in terms of the elements of OXi oxk 1 one column and their cofactors, say A Stl A, = a, V-+ + dx, dxi. + + a, ¥n 1 dx, . and thus know as above that A Vi 3/a Ak = - 0-1^— - ~ • • dx. dx, a. ¥n ' dx , where oq , a2 , • • • involve no differential-coefficients taken with respect to xi or with respect to xk. The observation made in the course of the first proof that A , A 1: . . . , An are themselves functional determinants leads Jacobi to the conception of “ partial functional determinants ” on the analogy of partial differential quotients. The fundamental lemma then becomes viewable as the analogue of 0^i dy dx dy dx = 0, or, in Jacobi’s words, “ gravissimam manifestat analogiam determinantium functionalium et quotientium differentialium partialium.” Apparently this recalls to Jacobi another analogy of the same kind, which he had omitted to draw attention to in his paper of 1830, when the first two cases of the lemma had been originally enunciated by him. The proposition involving the said analogy he now generalises thus : — If f , f \ , f o , . . . , f n be expressible as series the terms of which involve only powers of the variables x , xx , x2 , . . . , xn , the functional determinant does not * It would have been well to make clear here that every term of the final expansion of 20 A ■ — 1 contains one and only one second differential-coefficient. 000% 502 Proceedings of the Royal Society of Edinburgh. [Sess. involve a term in x_1 xx 1 x2 1 . . . . xn \ In support of it he has only to point out that the functional determinant is equal to S(/A) + 8(/A1)+ _ _ _ + 9(/An) dx dx1 dxn ’ and that the development of the kth term of this expansion cannot contain a term in . After referring to a possible application of the lemma in connection with definite multiple integrals, Jacobi concludes § 2 by returning to the lemma itself and throwing it into a third form originally announced in 1841 ( Be determ, funct. § 9). Viewing x , xx, x2, . . . , xn as functions of }f , . . . , fn he obtains of course {Be determ, funct. § 8) dx A dx. A, dxn A„ d/~n’ d/~n’ ‘ ’ W ~ r’ so that by substitution the lemma becomes or 0 = dx, d — - f 09 Xn v + R ^ + . . . + K-i , r J dxn 11 y idx + K) 9/ ! > '71 J dx. + J 7 dx,. where firstly R and the as’s have to be viewed as functions of the /’s and all differentiated with respect to /, and secondly the differential-coefficients thus obtained have to be expressed in terms of the cc’s preparatory to performing the final set of differentiations. Here the consideration of functional determinants would have come to an end in the present memoir, had it not been that a theorem on the subject which had been given incorrectly in 1841 (Be determ, funct. § 14) was now wanted in § 3 for use. Two and a half pages (pp. 215-217) of matter are consequently intercalated in order to enunciate the theorem 503 1908-9.] Dr Muir on the Theory of Jacobians. correctly, to prove it, and to elucidate it by a commentary. The enuncia- tion is — If f1 = a1, f|=a2, . . . . , fn = a„, where the as are constants , the functional determinant + ¥i ¥2 d'Xj dx2 hfn dx„ will not be altered in value if before performing the differentiations every function 1] be transformed in any way whatever by means of the equations fi+1 = ai+1, fi+2 — ai+2 fn = an . On looking back it will be seen that Jacobi had previously not excluded the use of the first i— 1 equations in making transformation of f . His proof now depends on taking the a’s to the same side as the f s ; denoting the resulting equations by (p1 = 0 , , 0c j>< 0a„, da[ 0ao and then showing that the denominator of this is ( — 1)' closes by assuming as allowable that 4>i = hy fl + a iff 2 + . . . + hf fn , and having thus obtained His commentary 2 ± di d 2 0$/-^ 0^2 dfn dx„ 2 • ■ • V)- 2( m dx ! dx9 ¥ dx , he concludes that the condition for the equality of the two functional determinants is that the determinant of the As shall be equal to 1. Hesse (1844). [Ueber die Elimination der Variabeln aus drei algebraischen Gleich ungen voin zweiten Grade mit zwei Variabeln. Crelles Journ., xxviii. pp. 68-96: or Werke, pp. 89-122.] Having demonstrated that for the elimination of tfy-j. y C) y from the three quadrics fx , /2 , f?> it was important to discover a function of the third degree possessing certain properties, Hesse proceeds (§ 11) to show how such a function may be obtained. From a well-known theorem regarding the differentiation of homogeneous functions he has, on putting u(A) for , oxk 504 Proceedings of the Poyal Society of Edinburgh. [Sess. xfif + x2uf] + x3 u[3) = 2/i , XxU(f + X2U{f + Xzuf = 2/2 , XxU[f + x2uf + x3 uf = 2/3, and, 0 being Jacobi’s determinant of /x , /2 , /3 with respect to a;1 , cc2 , &3 , there thus follows (a) Xx(f> = 2/l(42)43) - U‘f)u3)) + 2/2(ttjM3) - wf <>) + 2/3«>i43) - «43)«42)) , with similar expressions for x2f , x3ff ; so that any set of values of which makes /x , f2, /3 vanish will make vanish also. The formal enunciation of this result is then given, and it is pointed out that the like theorem holds when there are n homogeneous functions all of n variables and of the rth degree. From (a) by differentiation there is next obtained dd> x ^ + + = 2 <(«> - wifW,21) + 2a?'(af af - af af3) + 2<«>m!?> - + 2/\ 4 («?“? - alaf) + 2/2-— (afaf1 - afaf21) + 2/s -^(afa!,31 - afa!? ) , da?-, ^ “ dx. 'dxy and thence ~4> 02 y = 2/,— (wf?43) - 4MC + 2/2 — (XX ~ XX) + 2/3 — «}z43) - XX ) , OXy OXy OXy so that any set of values of which makes the ternary quadrics j\ , f2 , /3 vanish, will make the first differential quotients of the determinant of fy , f2 , /3 vanish also, — a second theorem which is asserted to hold when the number of homogeneous functions is n, the number of variables n, and each function of the rth degree in the said variables. Combining the two results, and using later phraseology, we may say that When n n-ary 11 -tides vanish , their Jacobian and each of its first differential-quotients will vanish also. The connection of this with the problem of elimination can be indicated in a few words. Jacobi’s determinant being of the third degree in x1,x2, x3, its first differential-quotients are like fi, f2, /3 linear in Xy , Xy , x3 , x2x3 , x3Xy , XyX2 ; and consequently the resultant is at once obtained as a six-line determinant. 1908-9.] Dr Muir on the Theory of Jacobians. 505 Cayley, A. (1847, February). [On the differential equations which occur in dynamical problems. Cambridge and Dub. Math. Journ., ii. pp. 210-219 : or Collected Math. Papers, i. pp. 276-284.] This is a short exposition of Jacobi’s elaborate memoir of 1844 with considerable variation in the details. The portion (§ 1) which concerns us is of course that referring to the “ fundamental lemma.” This is o established in its third form, the proof, like that originally given by Jacobi, being dependent on the theorem 0R ^ SXr dxk but differing in appearance, mainly because of the use of differentials. Bertrand, J. (1851, February). [Memoire sur le determinant d’un systeme de fonctions. Journ. (de Liouville) de Math., xvi. pp. 212-227 : abstract in Comptes Renclus .... Acad. des. Sci. (Paris), xxxii. pp. 134-135.] Recalling how Jacobi had insisted on the marked analogy between a functional-determinant and a differential-coefficient, Bertrand at once intimates the adoption of a new definition of the former which in his opinion makes the analogy still more striking, and from which the properties of the determinant are deducible like mere corollaries. Save that A and S are used where Bertrand without distinction uses d, the following is the definition: — If f \ , f2 , . . . , fn be functions of xlyx2, . . . , xn , and the latter receive n distinct sets of increments ^jJi .... Ag&i AgX., .... Aq.X-,^ A rP^\ A,,.^ 2 .... A nXn with the result that the corresponding increments of the functions are 1 • • • • A1_/ n ^2/l ^2/2 • • • • ^2 ‘bn ^nf\ “At f 9 .... A nf n , 506 Proceedings of the Boyal Society of Edinburgh. [Sess. then the limiting value of the ratio of the determinant of the second array to the determinant of the first array as the elements of the latter array are indefinitely diminished is called the determinant of the n functions. Since in the circumstances mentioned dx-x A kfi — Z~^kxi + ~ + dA BXr dfi . + ~ — &kXn OX„ for all values of h and i not greater than n, it follows from the multiplica- tion-theorem that the aforesaid limiting value is equal to dfl S/i dxx dx2 dxn Vs V, d/2 dx1 dx2 dxn ¥n 3/» Vn dxx cx2 dxn and, this determinant being independent of the increments given to the independent variables, it is held that the definition is legitimised. It might have been added that the name assigned to the limiting value is also thereby justified. The more important of Jacobi s results, eight or nine in number, are then re-established, precedence being given to those regarding the vanishing of the determinant. Supposing, first, that the functions are independent of one another, he asserts that x1 , x2 , . . . , xn may be conceived as expressed in terms of fx , f2, ... , fn ; and, the latter being viewed as independent variables, the determinant of their increments can be con- sidered as completely arbitrary and can thus have a value different from zero. Further, in respect to this determinant the determinant of the increments of y } * * * ? IX cannot be infinitely great, because the terms of both determinants have the same number of infinitesimal factors of the first order. It thus follows that their quotient — that is, the functional determinant — is not zero. Next, supposing that the functions are not all independent of one another, but that fp+1 , fp+2 are functions of /i , /2 , . . . , fp , and that the latter alone are mutually independent, Bertrand asserts that we may suppose \fi = 6 , Aj/g = 0 , . . . . , A Jp = 0 , this in fact being possible in an infinite number of ways, because only p relations are thereby established between the increments Aptq , , Axxn. It will then result that the increments of fp+1,fp+ 2, . . . , fn being 507 1908-9.] Dr Muir on the Theory of Jacobian s. sums of multiples of the increments of f\ , f2 , . . . , fp will also be zero ; and thus the whole of the first row Al/l Al/2 \fn will be composed of zeros, and the determinant to which it belongs will vanish. On the other hand the determinant of the increments of the x’s can at the same time be made different from zero, the increments in the first row being not necessarily all zero and those in the other rows being what we please. The ratio of the two determinants therefore vanishes. Following this are given the theorem regarding the relation of y/+|i ¥2 ¥n\ to y/ + ^i^>ii . ^ V “ dx1 dx2 dxj \ ~ 0/j 0/2 ' ' ' c/J ' the theorem for finding the functional determinant when the f s are given mediately as functions of the x’s, that is to say, as functions of lD 1 , £»2 > • • • » Xn)> X2> ■ ■ ’ Xn) ; • • • • , 4>p(Xl >X2’ • ■ • > Xn) ' ai1 d the corresponding theorem when the functions are only implicitly given, that is to say, by means of connecting equations FiA'i , x, 2 5 X, , fi , /a , ■ • • > fn) = 9 , Xc 2 5 Xn j ,t \ 5 f 2 5 • ■ • j fn) — 9 • The mode of treatment will be readily guessed from what has gone before. The same cannot, however, be confidently affirmed in connection with the theorem which expresses the functional determinant as a single product. This is found grouped under the heading “ Diverses formes que l’on peut donner a un determinant ” (fonctionnel), the said forms being obtainable on varying the systems of increments assigned to the variables. In the first example, the array of increments of the x’s is taken to be aA 0 0 0 A.2x2 . . . , 0 0 0 . . . . Anxn ; other array to be dx1 1 1 dxL d.fnA ' ’ dxl r 1 1 4 x Sx,22 * 3x„ 2 2 ' ' x ■ ■ dx2 2 2 x oxn |-2A„x„ . . fan ■ • |^A„x„ fan 508 Proceedings of the Royal Society of Edinburgh. [Sess. and the ratio of the determinants of the arrays to be y* / + AAk ty_i _ ty'n\ ' ^ V ~ dx1 dx.2 dxj To this there is added “ C’est l’expression donnee comme definition par M. Jacobi,” — a remark, however, equally applicable when, as at the outset, the increments of the afs were taken in their most general form. Pre- paratory to the next example it is pointed out that any n of the variables x 2 ’ XK fi , A 9 5 ,fn may have arbitrary values, the other n being then determinable ; and that therefore if n— 1 of them be taken to be invariable, the ratios of the increments of the others may be considered known. We thus see that the two arrays i-H rH <1 \x2 AjflJg . . . \xn Vi 0 0 0 0 ^2^2 ^2^3 • ' \2xn a2/, ^2 / 2 0 0 0 0 A3^3 ^3/l ^3/2 ^3/3 • • 0 0 0 0 ■ • Anctn ^nj 2 Al/3 • • . *nfn of the second example are simultaneously possible, the n indepmdent variables in the case of the first row being xx , f2 , /3 , . . . , fn , in the ( -se of the second row x1,x2,fs,. . . , fn, and so on: and we copsquently^ 'arn that the functional determinant may be written in the fori}1 (W) (W) . . . (dA\ \0.r1/ \dx2J \d xj on the understanding that the brackets enclosing jdxr imply that fr is there viewed as a function of x, , x„ , . . . , xr , fr , , , / f . A third i ' z 7 7 r ? j 7 -f- 1 * r+‘2 ? * * * 7 J 71 pair of possible arrays is A \xi 0 0 0 ^l^TO+1 .... A yln 0 A 2^2 0 0 A^.'m+i ^2*^j®+2 ' .... A2 xn 0 0 A3X3 . . 0 ^3Xm+\ ^3^171+3 .... 0 0 0 • • ^rrpC'rn A„i^rrt+i ^m^'m+2 .... AmXn 0 0 0 0 Am+i^m+i 0 . : . . 0 0 0 0 0 0 ^m+2^'m+2 0 0 0 0 0 0 0 .... Anxn Dr Muir on the Theory of Jacobians. 509 1908-9 and \A ^1/3 • • • ^\fm 0 9 9 Ao/l Ao/ 3 (M <] 9 9 9 A3/ 2 A3/3 * ' ■ • • A3/m 0 0 9 ±mfl Aw,/3 • • • Am/m 9 9 9 A m+l.f 1 A m+l.f 2 • • * m A 77l-|-l./" ; 777-}- 1 Ar/7-fl./7n-|-2 • • ■ Attj-I-I f n A771+2./ 1 ^m+2 J2 A771+2/3 • • • A m+’Z.fm A777-)-2ym-}-l A777-1-2 J777+2 • • • • ^m+2.f n &nfl A n.t 2 An/3 • • • Any m A njm+l A71./ 777 -f-2 • • ■ ■ A „/„ from which the functional determinant is obtained in the form + ¥m+ 1 Of m.+ 2 0-^m+l ^'^m+2 ¥n) dxnJ where, from looking as before at corresponding rows of the two arrays, we see that in the first determinant fx , /2 , . . . , fm are to be viewed as functions of xx , x2 , . . . , xm , fm+1 , /m+2 and in the second determinant /m+1 , /m+2 , • • • , fm are t° be viewed as functions of 00- ^ ? * * * ? * The next section is still more interesting, as it concerns the proposition which Jacobi stated incorrectly in his original memoir of 1841 and returned to in 1844. The data according to Bertrand are the usual n functions 5 fn each dependent on 00 ? t^2 y • • • y ? with the addition that the said functions when expressed in terms of x±, x2, ... , xn, f1, f2, . . . ,fn become 0X , 02 . . . . , n: and the problem he sets himself is to find the relation between V (±¥l ... S4\ and y(±^ ^ “<-*J \ dxx dx2 dxn ) ^ \ dXj dx2 dxn J the differentiations in the latter determinant being performed on the understanding that the /’ s there occurring in the c p’s are to be viewed as constants. The equations <^>1 f y 9 , 0 2 ./ 2 9 , . . . , l 07 2 ± dA ¥? dxY dx0 Vr dxnJ ) « (-i) dxx dx2 dxrj 0^1 _ 1 00L 001 a/i a/2 ¥n 002 002 _ ^ 002 9/i 3/2 0/4 ' 'lJ u ‘ n S/j 3/2 d(t>n , ‘ ' 0A; 510 Proceedings of the Royal Society of Edinburgh. [Sess. which is the relation desired. If fn) ' ’ • • • ) ^n) Further, he views the numerator and denominator here as standing for the determinants of Bertrand’s arrays of differences, remarking pointedly that the fraction indicated “is a real fraction, provided its numerator and denominator be interpreted in a manner exactly analogous to that in which the numerator and denominator of an ordinary total or partial differential -coefficient are interpreted.” Having thus explained his notation he proceeds to generalise the proposition that of r ?)Xy ^ 3/ r d%2 _j_ kf?l j ^ q dxj dfs dx2 dfs ‘ ' dxn dfs according as r and s are equal or unequal. He recalls Jacobi’s theorem (Be determin. fund. §11) that if ux, u2, . . . , um be functions of yliy2, . . . , yn,n being greater than m, and the y’s be functions of xx , x2 , . . . , xn , then d(uaiua9. . . . uam) _ | 9(? y / + df_ dj\ df^\ = , dfnJ " \~ dx dx1 ’ dxj or, say, SR = 1 . Further, he notes that as a consequence of these two theorems there results ~df[ dx. fdxk_ L0/J = fa*.?/* Of: dx{ which he might well have generalised by changing the i , k of the second factor of both sides into r , s. In dealing with the “ fundamental lemma ” his order of procedure is the reverse of Jacobi’s, that is to say, he deduces the form of 1844 from the original form of 1841. Thus, using the latter in regard to S, he has whence, because of R being the reciprocal of S, he obtains so that on substituting there results which on further substituting for becomes the form desired. ojk 515 1908-9.] Dr Muir on the Theory of Jacobians. The next fresh paragraph (p. 91) appears, although unnecessarily, as an addendum to Jacobi’s solution of a set of simultaneous linear equations whose determinant is a functional determinant (Be determ. fund. § 8). If the square of R be obtained by row-by-row multiplication, and the square of S by column-by-column multiplication it is easily verified that (hth row of S2) x (7t,tb column of R) = °— , dh i.e. = (k , 7i)th element of S , thus incidentally giving S2R = S as it should do. From this it is deduced that (hth row of S'2) x (&th row of R2) = 1 or 0 according as h and k are equal or unequal, * and that therefore R2 and S2 as just defined are in the matter of their primary minors related as R and S have been shown to be. In the remaining fourteen pages (pp. 92-106) the only matter calling for attention concerns Jacobi’s theorem where d/n+m\ 7)np / B=y ( ^ \ dx dx1 dfn dx. n — 1 and bW 2 dx dx-. ¥n- 1 of n +i dxn- 1 dxn+T. From this Brioschi, by taking the /’ s to be linear functions of the x’&, obtains Sylvester’s theorem of March 1851 regarding a compound de- terminant. Bellavitis, G. (1857, June). [Sposizione elementare della teorica dei determinant!. Memorie . . . . Istituto Veneto .... vii. pp. 67-144.] To the subject of a “ Determinante formato colle derivate-prime di alquante funzioni di altrettanti variabili ” Bellavitis devotes nine and a half pages (pp. 52-61, §§65-78), that is to say, about the same as Spottis- woode, though his selection of theorems is not quite the same. In substance he gives nothing fresh. His symbolism for the determinant of u , v , . . . with respect to x , y , . . . resembles Cauchy’s of 1841, being | D xu , Dyv , . . . | ; other changes made by him in notation are less satisfactory. * Viewing R and S as matrices of which the conjugates are R and S we have as an equivalent of this SS-RR-SqSR-R = SR=RS = 1. 516 Proceedings of the Royal Society of Edinburgh. [Sess. Baltzer, R. (1857). [Theorie und Anwendung der Determinanten, .... vi + 129 pp., Leipzig. French translation by J. Honel, xii + 235 pp., Paris, 1861.] “Die Functionaldeterminante ” is the heading of Baltzer ’s thirteenth chapter or section (§ 13, pp. 61-72). Though the exposition is neither so full nor so fresh as Brioschi’s, it has the advantage in arrangement, concision and clearness. Jacobi’s last theorem ( De determ. fund. § 18), expressing the determinant as a single product, m /%\ m . . . /ma XdxJ Kdxf \dxj \dxnJ ’ Baltzer makes his first, the proof being readily altered to suit. This change enables him to deal very effectively with the proposition regarding the vanishing of the determinant. For then he can assert that as the determinant vanishes, one of the factors of the said product must vanish ; and thence step-by-step can infer the vanishing of the succeeding factors including the last,— a conclusion which entails fn being expressible in terms of the other /’s. A footnote recalls the fact, which we should have noted before this, that Mobius had given in Crelles Journ., xii. p. 116, in the year 1834, the equation (txuy - tyux)(vtwu - vuwt)(xvyw - xwyv) - 1 where tx stands for dt/dx. Salmon, G. (1859). [Lessons Introductory to the Modern Higher Algebra. xii + 147 pp., Dublin.] Salmon gives little, and certainly nothing fresh, on the subject; but his unreserved adoption of Sylvester’s word “Jacobian” (§§ 53, 54; p. 37) doubtless helped greatly to spread the usage. LIST OF AUTHORS whose writings are herein dealt with. 1844. Jacobi . 499 1844. Hesse . 503 1847. Cayley . 505 1851. Bertrand . 505 1851. Spottiswoode . . 510 1856. Sylvester . 510 1854. Donkin 510 1854. Donkin 512 1854. Brioschi 513 1857. Bellavitis .... 515 1857. Baltzer 516 1859. Salmon 516 (. Issued separately August 6, 1909.) 1908-9.] Motion of Neptune’s Satellite. 517 XXXIII. — Motion of Neptune’s Satellite. By David Gibb, M.A., B.Sc. Communicated by Prof. Dyson. (MS. received 10th June 1909. Read 12th July 1909.) 1. Neptune’s satellite was discovered by Mr Lassel of Liverpool in 1846. This satellite differs from the other planets and satellites, except those of Uranus, in the direction of its motion, which is from east to west. After the satellite had been observed for a few years, it was pointed out by Mr Marth that the node and the inclination of its orbit were slowly changing. These changes were explained by Tisserand and Newcomb as arising from the spheroidal shape of Neptune. The observations prior to 1892 have been discussed by Dr Struve in the Memoir es de V Academie Imperials des Sciences de St Petersbourg, viie serie, tome xlii. No. 4. Since then a large number of valuable observations have been made at American observatories, especially by Prof. Barnard, and at Greenwich Observatory. The former were obtained visually with a position micrometer, the latter from photographs. Some of the American observations have already been discussed by Mr Hall (A.J., xii. 22, xix. 65), Mr Brown (A.J., xx. 134), and Prof. See ( A.N. , 153), and the Greenwich observations are discussed in the Monthly Notices (vols. lxv. and lxviii.) by Prof. Dyson and Mr Edney. In this paper I propose to discuss some of the visual observations made since 1892. Since 1899 the Connaissance des Temps has given tables which facilitate the calculation of the ephemeris of the satellite. These tables are based on the elements of Dr Struve. As no such tables are published previous to the above date, I have formed them from 1892 to 1898 inclusive, using the same elements. 2. The elements given by Dr Struve are :-= - Epoch 1890*0. a = 1 6" *27 1 u = 234°*42 n= 61°-25748 N = 185°T5 + 0°T48(£ - 1890) 1= 1 19° ‘35 — 0°T65 t - 1890), where a is the distance of the satellite from the planet for the mean distance of the planet from the Earth. n = mean daily motion u = longitude of satellite X = longitude of node I = inclination of orbit referred to the Earth’s equator and the equinox of date. 518 Proceedings of the Royal Society of Edinburgh. [Sess. The small eccentricity found by Dr Struve is neglected. From these elements the auxiliary quantities B, P, and U are found by means of the equations : cos B sin P = — cos (a - N) sin I cos B cos P — sin 8 sin (a - 1ST) sin I 4- cos 8 cos I sin B = cos 8 sin (a - N) sin I - sin 8 cos I cos B sin U = — cos 8 sin (a - 1ST) cos I - sin 8 sin I cos B cos U = cos 8 cos (a - N), where P = position angle of the pole of the orbit of the satellite B = planetocentric latitude of the Earth with reference to the orbit of the satellite 180— U = planetocentric longitude of the Earth with reference to the orbit of the satellite. With these auxiliary quantities the distance 8 and the position angle p are found from the equations : 8 sin (p - P) = r sin (u 4- U) s cos (p — P )=r sin B cos (u + U), where r — a(p)/p P =(/>)(! + a cos B cos (u + U) sin 1") and (p) is the mean distance of Neptune from the Earth. The formulae employed in obtaining the corrections to the elements are those deduced by Mr Marth, viz. : s sin dp = r sin r sin du 4- (?’ sin r cos I + r cos r cos u sin I) sin dls — r cos t sin u sin dl - r sin r cos u . 2e sin Q + r sin r sin u . 2e cos Q ds = r cos cr cos r sin du 4- r cos cr sin p cos 8 sin cZN + r cos or sin t sin u sin dl 2e sin Q — r cos cr cos t cos u + - sin u 2 + (r cos a cos r sin u — -- cos . 2e cos Q + , V 2 ) a where e = eccentricity Q = longitude of periastron measured from the node of the satellite’s orbit on the Earth’s equator sin r = - sin B s V • ~T‘ cos r = - cos B sin {u + TJ) S COS O' = cos B cos (u 4- U). 519 1908-9.] Motion of Neptune’s Satellite. 3. The following table gives a list of places where most of the observa- tions made since 1892 may be found : — Observatory. Epoch. Source. Yol. Page. Observatory. Epoch. Source. Yol. Page. Lick 1892-3 A J. XIII 10 1905-6 A.J. XXV 100 1893-4 XIV 9 Washington *1897-8 XX 134 1894-5 XV 26, 42 *1899-1900 A.N. 153 257 1895-6 XVII 62 1902-3 A.J. XXIII 144 1896 XVII 62 ** 1 904-5 XXIV 188 1897 XVIII 168 **1905-6 XXV 93 1898 XX 71 Lowell 1896-7 XVII 132 1898-9 A.N. 149 374 1898 XX 30 Y erkes *1897-8 A.J. XIX 27,65 Greenwich *1902 M.N. LXII 624 1898-9 XX 41 *1902-3 LX1II 504 1899-1900 XXII 27 *1903-4 LX IV 835 1900-1 XXIi 29 *1904-5 LXVI 10 1901-2 XXIII 105 *1905-6 LXVII 92 1902-3 XXIII 107 *1906-7 LXVIII 33 1903-4 XXV 41 *1907-8 LXVIII 586 1904 XXV 42 A. J. — Astronomical J ournal. A.N. = Astronomische Nachrichten. M.N .= Monthly Notices of the Royal Astronomical Society. * Elements are deduced from these measures. ** Measures are compared with the ephemeris, but the corrections to the elements are not deduced. 4. In the next table are given, for each series, the observer, the mean date, the times of observation, and the values of cl s and s dp in the sense Tabular — Observed, obtained by differencing the observed distances and angles with those I have computed from Dr Struve’s elements : — Lick Observatory — Prof. Barnard. 1893-0. Paris Mean Time. d s. s dp. Paris Mean Time. d s. s dp. 1892 H. M. s. // // 1892 H. M. S. // // Nov. 13, 15 8 2 -0-25 + 0-08 Dec. 16, 12 23 44 - 0-07 + 0-02 18, 18 32 58 + 0-01 -0-14 1893 20, 17 41 21 + 0-37 -0-07 Jan. 8, 15 8 30 -0-27 + 0-37 Dec. 9, 14 49 2 + 0-03 -0-11 13, 15 20 32 + 0-05 + 0-18 20, 12 24 6 -0-17 + 0-10 Lick Observatory — Prof. Barnard. 1894-0. 1893 H. M. s. 1894 H. M. s. Nov. 12, 18 45 25 -0-05 -0-08 Jan. 10, 13 10 19 + 0-02 - 0-20 13, 18 33 42 + 0-32 -0-21 21, 14 34 l“7 i -0-08 - 0-02 Dec. 3, 14 8 45 + 0-30 + 0-46 22 12 42 19 -0-11 4-0-07 10, 14 47 9 -0-21 -o-oi 28, 11 32 29 + 0-06 -0-02 1894 Feb. 26, 11 53 43 + 0-02 4-0-10 Jan. 7, 14 49 38 - 0-30 -0-07 520 Proceedings of the Koyal Society of Edinburgh. [Sess. Lick Observatory — Prof. Barnard. 1895-0. Paris Mean Time. d s. s dp. Paris Mean Time. d s. s dp. 1894 H. M. s. // 1895 H. M. s. // Nov. 18, 19 32 12 + 0-21 -0-12 Feb. 5, 11 31 5 + 0-08 + 0-27 19, 18 53 16 + 0-05 + 0-12 17, 12 43 41 - 0-07 + 0-21 Dec. 23, 13 45 19 -0-04 o-oo 18, 13 32 48 + 0-01 -0-51 31, 15 0 39 o-oo + 0-04 24, 12 3 28 -0-05 -0-43 1895 25, 11 19 9 o-oo + 0T7 Jan. 6, 13 14 5 -0-05 + 0-07 Mar. 3, 11 45 22 -0-27 -0-11 28, 13 31 34 + 0-25 + 0-09 4, 11 41 1 -0-16 -0-07 Feb. 4, 11 10 43 + 0T4 -0-24 Lick Observatory — Prof. Schaeberle. 1895-0. 1 1894 H. m. s. 1895 H. M. s. Dec. 13, 12 33 37 + 0-30 + 0-07 Jan. 30, 11 55 16 + 0-09 + 0-17 1895 31, 12 51 50 + 0-36 + 0-08 Jan. 10, 11 56 47 -o-io -0-13 Feb. 2, 12 17 7 -0-21 + 0-02 25, 14 30 39 + 0-04 + 0-27 3, 12 It / 4 + 0-05 - 0-09 26, 13 49 6 -0-04 -0-06 6, 11 53 32 + 0T4 + 0-17 29, 14 19 2 -0-17 + 0-07 Lick Observatory — Prof. Schaeberle. 1896-0. 1895 H. M. s. 1895 H. M. s. Oct. 27, 15 54 28 -0-06 -0-07 Dec. 7, 13 41 12 -o-oi + 0-25 28, 15 46 28 + 0-03 + 0-16 9, 13 23 28 -0T2 + 0-12 29, 15 56 53 -0-08 + 0-20 31, 12 24 6 + 0T2 + 0-25 Nov. 9, 15 46 51 -0-01 + 0T1 1896 20, 14 25 3 -0-09 + 0-23 Jan. 2, 13 7 59 + 0-20 -0-02 Feb. 21, 11 59 42 + 0-15 + 0-14 Lick Observatory — Prof. Schaeberle. 1896-8. 1896 H. M. s. 1896 H. M. s. Oct. 16, 17 5 54 + 0-37 + 0-07 Oct. 29, 15 34 57 -0-15 + 0-02 17, 17 4 18 -0-20 + 0-19 30, 17 8 17 + 0-31 -0-26 27, 16 7 9 + 0-22 -o-oi Nov. 6, 17 33 31 -0-18 + 0-35 28, 15 34 35 + 0-11 + 0-03 Lick Observatory — Prof. Schaeberle. 1897-8. 1897 H. M. s. 1897 H. M. s. Sept. 1 3, 19 2 43 - 0-35 + 0-33 Nov. 15, 15 14 20 -0-17 -0-02 18, 19 41 56 + 0-05 + 0-10 27, 15 49 34 + 0-15 -0-07 Oct. 16, 16 43 59 + 0-00 + 0-15 29, 14 43 59 -0-04 + 0-25 18, 16 39 21 -o-io + 0-22 Dec. 3. 15 47 10 -0-12 + 0-11 29, 16 53 28 - 0-03 + 0-10 11, 12 50 18 -0-23 + 0-32 30, 15 40 39 - 043 + 0-14 24, 12 26 22 + 0-17 -0*03 Nov. 1, 16 5 30 -o-io + 0-10 25, 14 50 2 + 0-03 -0-07 12, 15 47 5 -0-18 + 0-20 27, 12 21 4 -0-29 + 0-13 1908-9.] 521 Motion of Neptune’s Satellite. Lick Observatory— Mr Aitken. 1899-0. Paris Mean Time. d s. s dp. Paris Mean Time. d s. s dp. 1898 H. M. s. 1898 H. M. s. Oct. 14, 19 36 32 -0-08 -0-20 Nov. 20, 15 25 20 + 0-44 + 0-15 16, 18 22 21 + 0-10 4- 0-03 Dec. 2, 14 45 39 + 0-23 + 0-06 23, 17 31 21 + 0-45 -0-25 3, 15 18 45 + 0-45 -0-20 Nov. 5, 17 41 47 - o-io + 0-52 9, 14 56 42 + 0-25 -o-ii 11, 14 49 7 -0-21 + 0-47 11, 14 21 59 -0-26 + 0-34 12, 17 21 45 -0-49 -047 1899 15, 17 38 29 + 0 15 -0-12 Feb. 11, 16 25 18 + 0-22 -0-05 Lick Observatory — Mr Hussey. 1899-0. 1898 H. M. s. 1898 H. M. s. Oct. 27, 17 38 22 + 0-03 -0-17 Dec. 23, 13 17 14 - 0-27 + 0-39 28, 17 32 26 — 0 09 -0-08 1899 Nov. 17, 16 34 34 + 0-13 + 0-21 Jan. 5, 12 14 19 + 0-26 + 0-21 Dec. v, 12 11 47 + 0-46 + 0-11 12, 12 20 21 -0-37 + 0T2 15, 19 54 30 — 0-23 + 0-40 20, 12 38 59 -0-16 -0-06 16, 12 49 55 — 0-53 -0-02 Feb. 10, 15 16 12 + 0-09 + 0-02 16, 14 35 14 -0-19 + 0-00 Yerkes Observatory — Prof. Barnard. 1899-0. 1898 H. M. s. 1899 H. M. s. Aug. 29, 17 32 28 -0-24 + 0-21 Jan. 18, 10 33 0 4-001 4-0-06 30, 17 14 57 -043 + 0-15 24, 10 10 52 -0-09 4-0-02 31, 17 15 11 + 0-02 -0-03 30, 12 15 9 4-0-39 -0-24 Sept. 1, 16 37 10 + 0-50 -0-08 31, 12 47 11 - 0-03 4-0-03 2, 16 34 47 + 0-06 -o-oi Feb. 6, 9 34 43 4-0-39 - 0-30 3, 16 57 3 -0-11 + 0-03 7, 10 54 26 -o-io 4-0-03 14, 15 59 56 + 0-17 + 0-09 9, 12 1 43 4-0-28 -o-oi 20, 16 34 4 + 0-08 -0-16 10, 9 27 33 -o-oi 4-0-17 22, 19 9 40 -0-04 -0-13 11, 10 48 35 4-0-29 - 0-13 26, 16 21 55 + 0-02 -0*07 12, 10 40 43 4-0-23 -0-12 27, 16 22 39 + 0-00 + 0-30 13, 9 7 33 4-0-20 -o-io Oct. 10, 15 17 17 -o-io + 0T1 20, 11 22 9 + 0-13 + 0'14 11, 17 4 41 -0-14 -0-23 28, 9 58 11 -0’18 4-0-12 Nov. 7, 14 26 46 -0-28 + 0-04 Mar. 13, 11 11 12 -0-20 - 0-23 14, 20 18 21 + 0-24 -0-38 18, 9 35 0 4-0-17 -0-06 15, 12 50 25 -0-06 -0-06 19, 9 53 44 4-0-11 -0-02 22, 17 51 50 + 0-19 -0-15 28, 10 14 44 -0-05 4-0-03 24, 11 44 48 + 0-08 + 0-05 29, 9 39 59 4-0-18 4-0-08 26, 11 57 6 -0-02 4-0 26 30, 10 20 42 + 0-43 -0-04 29, 14 46 38 + 0-24 -0-19 Apr. 3, 10 21 53 -0-21 4-0-20 Dec. 3, 12 20 32 + 0T2 -0-16 4, 9 46 44 4-0-14 4-0-03 6, 15 56 54 + 0-04 + 0-02 7, 10 17 35 -0-04 4-0-23 10, 11 45 11 + 0-48 -0T6 17, 9 45 12 4-0-03 -0-16 11, 11 11 42 + 0-04 4-0-14 18, 9 44 55 -0-07 4-0-28 12, 11 35 30 -0-02 4-0-11 19, 9 42 36 -0-14 4-0-15 13, 11 18 17 -0 54 4-0-06 522 Proceedings of the Royal Society of Edinburgh. [Sess. Yerkes Observatory — Prof. Barnard. 1900’0. Paris Mean Time. d s. s dp. Paris Mean Time. d s. * s d‘p. 1899 H. M. s. 1899 H. M. s. Aug. 13, 17 54 33 + 0-11 -0T6 Oct. 23, 15 0 54 + 0-24 -005 14, 17 53 33 + 0-30 -0-03 28, 16 14 44 + 0-12 + 0-05 15, 17 59 42 + 0-02 -0-07 29, 14 14 48 -0-02 + 0-05 18, 17 48 48 + 0-02 + 0-25 30, 15 45 11 + 0-01 -0-03 19, 17 32 13 + 0-19 + 0-18 Nov. 4, 14 22 31 + 0-34 + 0-10 20, 17 48 32 -0-12 -0-06 5, 15 54 48 + 0-06 + 0T0 21, 17 50 22 + 0-21 + 0-18 6, 14 2 34 + 0-08 + 0-20 22, 17 28 25 -0-15 -0-06 11, 13 27 6 + 0-06 + 0-01 26, 17 29 7 + 0-23 -0-14 12, 15 52 25 -o-io -o-oi 27, 17 51 53 + 0T4 + 0-18 18, 14 10 13 -0-19 + 0-10 28, 17 43 7 -0-08 + 0-39 19, 14 11 23 + 0'03 + 0T7 29, 17 40 0 -0T3 + 1-15 25, 12 39 39 -0-20 + 0-29 Sept. 3, 17 53 52 - 0-31 + 0-14 26, 12 53 25 + 0-09 + 0-06 4, 17 28 h t ( -0-37 + 0-40 27, 13 2 0 + 0-22 -0-05 6, 16 57 53 + 0-54 -0-69 Dec. 4, 12 0 46 -0-43 -0-08 8, 17 54 50 + 0-13 + 0-05 1900 10, 17 58 36 + 0-05 + 0*18 Mar. 30, 10 23 14 -0-03 + 0-01 ii, 17 48 43 + 0-14 + 001 31, 9 46 18 -o-io + 0-21 12, 17 47 28 + 0-25 + 0-09 April 2, 9 58 54 -o-io + 0T9 18, 16 51 38 + 0-03 -0-29 3, 9 45 55 -0-09 + 0-11 24, 16 0 27 + 0-02 + 0-16 4, 10 16 7 + 0-06 + 0-10 25, 16 58 26 -0-20 -0-11 6, 9 31 12 + 0-08 + 0-28 26, 16 40 3 -0-09 + 0-27 h- O 9 35 50 -0-18 + 0-27 30, 16 49 9 -o-ii -0T0 9, 9 29 56 -0-42 -0-02 Oct. 1, 16 28 51 + 0-09 -0-07 10, 9 35 23 + 0-15 -o-oi 2, 17 0 11 -o-ii + 0-31 18, 9 54 43 + 0-20 + 0’3 / v, 16 21 45 + 0-02 + 0-01 19, 10 40 46 -0-51 -0-29 8, 17 1 32 -0-07 + 0*28 22, 10 8 41 + 0T4 -0-72 9, 17 25 30 + 0-14 + 0-05 24, 9 51 35 + 0-28 + 0T3 14, 18 0 3 - 0-23 + 0-31 26, 9 50 9 -0-04 + 0-04 15, 14 27 39 + 0T4 + 0-59 27, 9 48 27 -0-34 -0-13 17, 15 44 53 + 0-13 + 0-00 30, 9 53 2 -0-08 -0-02 21, 17 22 18 + 0-26 + 0-06 May 4, 9 56 5 + 0-35 -0-24 Yerkes Observatory — Prof. Barnard. 1900-9. 1900 H. M. s. 1900 IT. M. s. Sept. 6, 17 5 55 -0-08 -0-40 Oct. 17, 13 46 54 -o-ii + 0-51 10, 17 30 51 - 0-22 -0-07 18, 16 37 4 + 0-24 -0-08 11, 17 43 56 -0-31 -o-oi 25, 14 25 14 -0-34 - o-oi 13, 17 43 8 + 0-16 + 0-09 26, 14 48 7 + 0-02 + 000 19, 16 53 1 + 0-28 -0-05 27, 16 15 29 -0-15 -0-22 24, 15 45 50 + 0T5 -0-34 30, 16 46 15 + 0-08 + 0-25 25, 16 3 20 + 0-23 + 0T9 Nov. 1, 18 1 39 -0-03 + 0-02 Oct. 2, 16 20 40 -0-28 + 0-32 2, 18 9 13 + 0-11 -0-19 3, 16 24 53 -Oil + 0T9 3, 14 30 24 + 0-21 + 0-06 4, 16 3 10 - 0-39 -0-21 4, 13 35 41 + 0-10 -0-05 5, 17 21 13 + 0T3 + 0-03 5, 14 59 31 + 0-31 + 0-10 8, 17 5 6 -0-08 + 0T6 8, 17 58 24 + 0-18 -0-27 9, 17 4 27 + 0-10 + 0-04 13, 14 36 43 -0-33 + 0-00 10, 16 11 55 + 0-07 -0-14 22, 11 25 50 + 0-24 -0-38 11, 17 18 11 + 0-18 -0*40 26, 11 59 37 -0*45 - 0-43 16, 15 28 25 +o-oo -o-io Dec. 8, 13 27 20 -o-ii -0-05 1908-9.] 523 Motion of Neptune’s Satellite. Yerk.es Observatory — Prof. Barnard. 1900-9 — continued. Paris Mean Time. d s. s dp. Paris Mean Time. d s. s dp. 1900 H. M. s. 1901 H. M. s. Dec. 11, 11 20 30 + 0-06 + 0-06 Jan. 14. 15 15 54 + 0-01 -0-06 18, 11 40 25 + 0-04 + 0T5 16, 11 4 18 -0-18 + 0-16 19, 14 35 30 4-OT7 -0-06 19, 10 19 19 + 0-24 + 0-00 28, 15 13 42 - 0-43 -0-09 21, 13 39 51 + 0-01 4-0*14 29, 12 40 27 -0-04 + 0-20 25, 11 14 21 + 0-17 4-0-00 31, 17 6 22 -0-23 -0T2 28, 10 44 30 -0T6 +o-oi 1901 Feb. 5, 10 52 48 + 0-11 -0-20 Jan. 1, 10 33 8 + 0-46 -0-48 Yerkes Observatory — Prof. Barnard. 1902-0. 1901 H. M. s. 1902 H. M. s. Aug. 27, 18 3 35 -0-12 + 0-32 Jan. 10, 11 48 58 -0-16 4-0-05 Sept. 3, 17 48 51 -0-15 + 0-18 12, 10 38 12 + 0-42 4-0-00 16, 17 33 29 + 0-27 -0-13 13, 10 17 40 - 0-02 -0-03 22, 17 42 50 4- 0-43 - 0-13 18, 10 5 40 + 0-17 4-0-09 23, 17 44 30 + 0-17 + 0-03 24, 13 56 39 - 0-09 4-0-20 24, 17 16 45 + 0-26 +o-oo 27, 10 0 1 -0-45 4-0-03 Oct. 1, 17 25 35 -0-46 + 0-33 31, 9 45 49 + 0-21 4-0-18 20, 18 47 58 - 0-39 -0-26 Feb. 2,* 9 42 54 -0-26 + 0-06 21, 15 50 34 + 0‘05 + 0-15 7, 9 28 2 -o-oi 4-0-09 29, 15 31 9 + 0-16 -016 8, 9 3 7 - 0-30 + 0-20 Nov. 12, 18 33 21 -0-32 + 0-02 15, 9 12 16 -0-24 -0-02 18, 16 58 30 + 0-14 + 0-03 17, 8 56 41 + 0-06 + 0-20 19, 13 12 16 + 0-09 -0 03 24, 9 0 7 + 0-07 4-0-13 26, 17 37 2 -015 -f 0'48 25, 8 54 52 4-0-02 - 0-03 Dec. 10, 13 43 58 + 0-27 + 0-26 Mar. 17, 10 42 45 + 037 - 0-39 15, 12 0 46 + 0-04 - 0-25 18, 10 27 52 4-0-01 4-0-19 16, 13 42 41 -0-29 + 0-12 24, 9 51 34 -0-03 + 0-11 17, 12 26 10 -0-24 + 0-10 25, 10 5 23 -0-36 4-0-10 22, 10 31 8 + 0-20 + 0-44 April 6, 9 47 43 -0-45 -0-12 23, 11 50 30 + 0-00 - 002 8, 10 0 10 -0-06 + 0-05 29, 12 11 23 -0-26 + 0-16 13, 9 56 4 - 0-38 -0-10 30, 10 36 50 -0-30 + 0-22 14, 9 41 18 -0-15 4-0-13 1902 15, 9 49 2 + 0-10 -0*25 Jan. 2, 10 28 35 + 0-24 + 0-27 5, 11 58 25 + 0-04 -0-21 Yerkes Observatory — Prof. Barnard. 1903-0. 1902 H. M. s. 1902 H. M. s. Aug. 25, 18 12 6 4-0-25 4-0-14 Dec. 1, 17 I"7 7 45 4-0-13 + 0-23 Sept. 1, 17 27 14 -0-39 4- 0"35 30. 11 40 10 - 0-35 - 0-30 8, 18 30 37 - 0-31 + 0-14 1903 9, 17 29 28 4-0-05 -0-12 Jan. 12, 12 10 49 + 0T3 4-0-05 15, 17 30 23 -0-24 - 0*24 19, 11 44 34 4-0-25 4-0-04 16, 17 19 36 4-0-21 -0-15 20. 10 5 21 + 0-24 + 0-17 18, 17 49 35 4-0-00 4-0-09 F eb. 9, 11 41 38 4-0-12 -o-io Oct. 6, 17 47 33 -0-30 4-0-28 16, 11 1 46 4-0-32 4-0-33 7, 15 29 33 -0-15 + 0-36 17, 10 46 41 4-0-23 4-0-08 13, 17 14 9 -0-40 4-0-25 23, 10 55 10 4-0-04 4-0-07 14, 16 59 58 -0*44 -0-15 24, 11 52 1 + 0-02 -0-11 27, 19 19 37 - 0-38 4-0-28 Mar. 2, 10 28 18 -0-17 -005 Nov. 24, 13 17 57 -0-08 -o-io 25, 10 29 27 -0-07 4-0-00 30, 12 7 41 -0-06 4-0-06 524 Proceedings of the ftoyal Society of Edinburgh. [Sess. Yerkes Observatory — Prof. Barnard. 1904 0. Paris Mean Time. d s. s dp. Paris Mean Time. d s. s dp. 1903 H. M. s. 1903 H. M. s. Aug. 31, 18 41 40 -0-38 + 0-39 Dec. 21, 13 53 39 -0*25 + 0-27 Sept. 21, 17 13 3 + 0-02 + 0-05 22, 11 50 43 -0-51 - 0T3 28, 16 47 54 + 0-25 -0-11 1904 Oct. 13, 15 31 21 -0-04 + 0-00 Jan. 3, 16 4 17 -0-13 + 0-63 19, 16 54 30 -0-19 + 0T8 26, 14 4 47 - 0-35 + 0-08 20, 13 49 9 -o-oi -033 F eb. 2, 11 11 28 -0-13 - 0-12 26, 17 4 5 + 0T3 -0-04 15, 13 48 56 + 0-12 + 0-33 27, 15 49 23 + 0-17 -0-08 16, 13 49 26 -0-16 + 0-31 Nov. 9, 15 1 4 + 0-00 + 0-28 April 4, 10 5 55 -0-19 + 0-03 21, 16 25 15 -0-13 + 0-02 18, 10 54 4 -o-ii + 0.06 24, 14 43 54 -0-25 -0-20 19, 11 24 59 + 0-36 -0.42 Dec. 14, 12 50 45 + 0-41 + 0*19 Yerkes Observatory — Prof. Barnard. 1904-9. 1904 H. M. S. 1904 H. M. s. Oct. 15, 16 12 23 -0-12 + 0-23 Nov. 21, 14 3 0 -0-27 + 0-02 22, 18 45 43 - 0-32 + 0-22 26, 14 1 56 + 0-04 -0-39 29, 15 13 3 -0-05 -0-02 28, 15 30 44 -0-13 + 0-08 31, 15 42 22 + 0-17 + 0-02 Dec. 5, 13 24 30 + 0-23 + 0-20 Nov. 5, 13 35 43 + 0-12 +o-oo 10, 13 47 2 -0-22 + 0-08 12, 15 34 25 -0-02 - 0 32 12, 14 38 15 -0-22 -0-03 14j 15 55 57 -0-49 + 0-18 31, 11 35 41 -0-42 + 0-20 Yerkes Observatory — Prof. Barnard. 1906-1. 1905 H. M. s. 1906 H M. s. Dec. 9, 19 0 22 + 000 -0-29 Jan. 23, 13 42 48 -0-61 -0-17 19, 13 31 23 -0*54 + 0-36 Feb. 6, 14 22 28 + 0-14 -0-02 23, 17 37 24 -0-49 -0-24 27, 12 1 9 -0-22 -0-25 26, 13 17 44 - 0-38 -o-oi Mar. 20, 11 21 5 + 0-22 -0-27 30, 16 1 56 + 0-15 -o-oi April 17, 9 30 55 + 0-09 - 0-06 Mr Lowell’s Observatory — Messrs Drew AND CoGSHALL. 1897’0. 1896 h. M. s. „ 1897 H. M. s. Oct. 16, 16 43 57 + 0-42 + 0-54 Feb. 21, 13 1 7 + 0-09 + 0-37 29, 16 14 0 + 0-01 -0'41 22, 13 37 30 -0-15 -0-47 30, 16 10 51 + 0-09 -0-33 23, 12 53 5 -0-09 + 0-24 Nov. 4' 16 48 12 + 0-23 + 0-17 24, 12 40 27 -0-06 + 0-11 6, 16 26 23 + 0-69 - 0-03 25, 11 30 48 + 0-30 + 0-12 r r ^ 5 16 29 41 -0-17 -0-31 27, 13 4 1 -0-18 + 0-00 1897 28, 11 56 23 + 0-13 -0-36 Jan. 9, 15 17 49 + 0-54 + 0-06 Mar. 1, 12 2 44 -0-34 -0'13 14, 14 46 54 + 0-16 + 0-14 2, 11 56 51 -0-49 + 0-10 18, 14 50 13 + 0-56 -0-20 4, 10 32 34 + 0-37 -0-03 28, 15 17 49 +o-oo + 0-43 6, 10 36 56 + 0-07 -0-36 30, 14 41 11 - 0-30 + 0’09 7, 10 43 49 + 0-47 -0-56 Feb. 6, 13 3 51 -0-17 -0-37 8, 10 36 57 -0-39 + 0-17 8, 14 36 5 + 0"34 + 0-42 10, 10 25 57 + 0'05 -0-47 13, 14 30 9 -0-07 -0-17 lb 10 23 10 -0-17 -0-28 18, 13 44 15 -0-47 - 0 33 12, 10 29 30 -0-42 - 0-33 19, 13 56 25 + 0-59 -0-15 19, 9 55 42 -0-55 -0-76 20, 13 48 53 + 0-68 + 0-10 26, 10 16 44 + 0-01 -0-13 1908-9.] Motion of Neptune’s Satellite. 525 Mr Lowell’s Observatory — Messrs Drew and Cogshall. 1898-8. Paris Mean Time. d s. s dp. Paris Mean Time. d s. s dp. 1898 H. M. s. // 1898 H. M. s. Sept. 9, 18 53 28 + 0-07 + 0-08 Sept. 27, 18 34 40 -0-15 + 0-34 12, 18 41 53 -0-24 - 0-05 29, 18 15 2 + 0 09 + 0-33 14, 18 23 3 -0-62 + 0-06 Oct. 17, 18 13 56 - 0-36 + 0-14 18, 18 25 37 -0-30 + 048 21, 18 12 38 - 0-03 + 0-10 19, 18 36 45 -0-18 + 0-18 Nov. 9, 19 13 15 + 0-44 - 0-09 22, 18 1 10 -0-16 + 0-27 Dec. 7, 16 33 40 -0-33 + 0-50 Washington Observatory — Mr Dinwiddie. 1903-0. 1902 H. m. s. 1903 H. M. s. Oct. 24, 17 41 57 -0-27 -0-50 Jan. 6, 12 25 59 + 0-41 + 0-73 28, 17 27 56 -0-18 -0-04 Feb. 22, 9 42 52 -0-15 + 0-48 29, 17 54 49 + 0-00 -0-50 25, 9 50 49 - 0-38 + 0T2 30, 17 30 11 + 0-35 -0-26 26, 9 19 12 + 0-13 + 0-20 31. 17 57 48 + 0-02 - 0-23 Mar. 3, 8 47 16 -0-24 + 0-12 Nov. 1, 17 16 55 -0-37 + 0-46 12, 8 39 4 + 0-42 + 0-20 2, 17 18 32 + 002 + 0-21 17, 8 42 48 + 0-22 + 0*38 21, 16 0 53 + 0-06 +o-oo 18, 9 2 13 -0-30 + 032 Dec. 5, 15 33 0 + 0-03 -0-27 26, 8 50 54 -0-07 -0-38 7, 14 51 51 -0-32 + 0-67 Washington Observatory — Messrs Hammond AND Rice. 1905-0. 1904 H. M. s. 1905 H. M. s. Nov. 21, 16 52 53 + 0-14 + 0-08 Jan. 16, 10 48 34 - 0-34 + 0-34 30, 15 52 4 -0-16 + 0-46 27, 10 41 46 - 0-50 + 0-03 Dec. 14, 12 33 1 + 0-67 + 0-27 Feb. 7, 9 47 4 -0-18 - 0-06 16, 12 4 31 -0-24 + 0-01 10, 9 35 24 - 0-30 + 0-22 18, 12 38 25 -0-13 + 0-34 24, 9 35 1 + 0-03 - 0-05 19, 11 47 31 -0-22 -0-03 Mar. 10, 10 14 14 -0-21 + 0-49 29, 11 0 9 -0-51 + 0-05 13, 8 54 18 + 0-11 + 0-24 1905 25, 9 30 11 -0-07 -o-u Jan. 1, 10 39 24 + 0-05 + 0-35 31, 9 59 58 + 0-42 -0T7 Washington Observatory — Mr Hammond. 1906’0. 1905 H. M. s. 1906 H. M. s. Oct. 29, 14 47 16 -0-02 -0*16 Feb. 13, 8 25 32 -0-28 + 0-18 30, 14 36 7 -0-22 + 0-18 13, 11 41 47 -0-04 + 033 Nov. 1, 13 54 45 - 0-16 + 0-40 16, 8 54 21 + 0-37 + 0-43 1906 16, 10 43 8 -0-07 + 0-43 Jan. 5, 13 6 29 + 0-40 + 0-11 17, 8 47 39 + 0-12 + 0-34 6, 11 32 41 + 0-22 + 0-20 19, 8 53 49 + 0 00 + 0-46 16, 10 48 40 + 0-25 + 0-27 23, 8 38 26 -o-oi + 0-48 18, 12 52 55 + 0-35 + 0-29 23, 11 7 46 -0-20 + 0-19 24, 9 48 17 + 0-23 + 0*28 Feb. 24, 11 3 3 + 0-13 + 0-28 24, 11 56 44 + 0-19 + 0-40 25, 8 33 36 - 0-28 + 0-42 28, 11 58 7 + 0-13 -0-13 25, 10 46 24 + 0-43 4-0-28 29, 9 38 58 -0*06 + 0-44 Mar. 6, 9 24 12 +o-oo + 0-33 29, 12 46 48 +o-n + 0-20 10, 9 25 52 + 0-02 + 0-08 31, 9 46 54 -0-37 + 0-08 20, 17 26 33 -0-19 + 0-24 31, 12 0 32 -0-28 + 0-28 23, 17 51 19 + 0-33 -0-02 Feb. 11, 8 26 23 + 0-19 + 0-36 526 Proceedings of the Eoyal Society of Edinburgh. [Sess. 5. The equations of condition were then formed by using MartlTs formulae on page 518. The following, derived from the 1892 observations of Prof. Barnard, will serve as an example of these — Position-Angle. Date. Sin du. Sin dN. Sin dl. 2e sin Q. 2e cos Q. s sin dp. 1892 Nov. 13. - 9-55 54)0 + 7*05 + 8*23 - 4*84 = + 0*08 18. -11-7 4*51 3-01 + 11*3 + 2*94 = -0*14 20. -15-9 +9-11 + 5*77 - 4*32 - 15-3 = -0*07 Dec. 9. - 10'4 6*72 + 0*549 - 10-4 + 0*426 = -0*11 16. -10-6 +0-27 +1D9 - 4-48 + 9*60 = + 0*02 1893 Jan. 8. - 9-48 4-62 + 9-10 - 7*17 + 6*21 = + 0*37 13. -1D6 4*91 2*62 -11*3 + 2*47 = + 0*18 20. - 9-59 3*25 +10-3 - 6*29 + 7-24 = + 0*10 Distance. Date. Sin du. Sin dN. Sin dl. 2e sin Q. 2e cos Q. da/a. ds. 1892 Nov. 13. + 0-014 -0*016 + 0*005 - 4*29 - 7*27 + 16‘9 = - 0*25 18. + 7-03 -9-26 - 1*72 - 5*08 -8*41 , + 13*7 = + 0*01 20. -4-78 -0-711 - 12*2 -6*22 -2*21 + 10*2 = + 0*37 Dec. 9. + 5-37 -6-25 + 0*171 + 5*69 + 7*54 + 15*5 = + 0*03 16. -5-97 +4-71 - 4*38 + 4*30 + 8*62 + 15*1 = -0*07 1893 Jan. 8. -1-74 +1-63 - 0*776 + 4*17 + 7-46 + 16*7 = - 0*27 13. + 7-17 -9-21 + 1*44 + 5*55 + 8*19 + 13-6 - + 0*05 20. -3-25 +2-87 - 1*72 + 4*02 + 7*78 + 16*3 -0*17 6. Next the normal equations were formed for each series : — NORMAL EQUATIONS. Lick Observatory — Prof. Barnard. 1893*0. Sin du. Sin dN. Sin dl. 2e sin Q. 2e cos Q. da [a. Sin du +1220 - 39 -321 + 291 - 46 + 56 = - 1*86 Sin dN + 483 - 54 + 41 - 155 - 211 = -4*91 Sin dl + 607 - 95 + 106 - 232 + 1*05 2e sin Q + 759 + 168 + 158 = -7*82 2e cos Q + 899 + 349 = + 1*50 daja + 1776 — -7*51 Lick Observatory — Prof. Barnard. 1894*0. Sin du. Sin dN. Sin dl. 2e sin Q. 2e cos Q. da/ a. Sin du +1360 +173 -444 -536 - 140 + 78 = -2*23 Sin dN + 495 -145 - 120 + 194 - 207 — + 1*32 Sin 6.1 + 613 + 90 - 71 - 158 — + 0-08 2e sin Q + 916 + 178 - 178 — -8*45 2e cos Q + 1037 - 316 = + 1*31 daja + 2360 = + 0*09 1908-9.] Motion of Neptune’s Satellite. 527 Lick Observatory — Prof. Barnard. 1895*0. Sin du. Sin dN. Sin dl. 2e sin Q. 2e cos Q. da fa. Sin du + 2509 - 398 - 416 + 167 + 416 + 64 = + 8*35 Sin dN + 901 + 152 - 18 - 153 - 408 = - 9*07 Sin dl 4 1171 + 170 - 117 - 724 = - 4*02 2e sin Q + 1250 + 556 + 2 = - 8*62 2e cos Q + 1900 - 47 = - 5*12 daja + 2694 = + 0*92 Lick Observatory — Prof. Schaeberle. 1895*0. Sin du. Sin dl si. Sin dl. 2e sin Q. 2e cos Q. daja. Sin du + 1923 - 511 - 392 + 89 - 167 - 180 = -10*19 Sin dN + 613 + 155 - 16 + 109 - 115 = + 2*29 Sin dl + 1113 + 2 + 53 - 694 = - 2*13 2e sin Q + 749 + 326 II OC 05 + - 1*23 2e cos Q + 16*21 - 78 = + 14*38 daja + 1789 = + 4*77 Lick Observatory — Prof. Schaeberle. 1896*0. Sin du. Sin dN. Sin dl. 2e sin Q. 2e cos Q. da/a. Sin du + 1837 - 322 - 183 + 214 - 921 + 127 = -15*78 Sin dN + 679 + 156 + 312 + 306 - 396 = - 3*12 Sin dl + 776 - 341 + 213 - 567 = + 3*92 2e sin Q + 893 + 479 + 386 = - 7*19 2e cos Q + 1428 + 625 = + 8*67 daja * + 1918 = + 1*80 Lick Observatory — Prof. Schaeberle. 1896*8. Sin du. Sin dN. Sin dl. 2e sin Q. 2e cos Q. da/ a. Sin du + 1287 - 158 - 104 - 300 + 65 + 91 = + 1*74 Sin dN + 440 + 70 - 64 + 49 - 244 - - 13*13 Sin dl + 509 + 72 - 76 - 382 = - 4*29 2e sin Q + 637 + 239 - 107 = - 0*35 2e cos Q + 1010 - 375 = + 1*21 daja + 1420 - + 1*94 Lick Observatory — Prof. Schaeberle. 1897*8. Sin du. Sin dN. Sin dl. 2e sin Q. 2e cos Q. da/a. Sin du + 3222 - 717 - 382 + 420 + 1016 - 109 - 25*47 Sin dN + 981 + 72 - 26 - 491 - 94 = - 2*59 Sin dl + 1540 + 318 - 130 -1140 = + 7*17 2e sin Q + 1264 + 376 + 4 = -16*24 2e cos Q + 2733 + 459 = -13*01 daja + 3018 = - 19*25 528 Proceedings of the Poyal Society of Edinburgh. [Sess. Lick Observatory — Mr Aitken. 1899-0. Sin du. Sin dN. Sin dl. 2e sin Q. 2e cos Q. da/a. Sin du + 2842 - 840 - 455 4 + 947 - 344 = + 2-78 Sin dN + 740 + 39 + 132 - 424 + 152 = -18-45 Sin dl + 1530 + 234 - 91 - 1119 = + 0-35 2e sin Q + 861 - 67 - 122 = - 20-63 2e cos Q + 2359 + 289 — + 10-86 da/a + 2300 = + 12-61 Lick Observatory- —Mr Hussey. 1899-0. Sin du. Sin dN. Sin dl. 2e sin Q. 2e cos Q. da/a. Sin du + 1887 + 105 - 268 - 160 + 169 + 87 — -11-64 Sin dN + 608 - 25 - 136 + 6 - 223 = - 2-68 Sin dl + 609 + 127 4 - 387 = + 4-66 2e sin Q + 1143 + 162 - 88 = - 7-60 2e cos Q - + 1446 - 273 = - 5-67 da/a + 2804 = - 13-14 Yerkes Observatory— -Prof. Barnard. 1899*0. Sin du. Sin dN. Sin dl. 2e sin Q. 2e cos Q. da/a. Sin du + 9823 - 1887 - 943 - 545 + 705 - 310 = - 3-15 Sin dN + 2659 + 386 - 178 - 61 - 399 = - 2-94 Sin dl + 4386 + 393 - 58 -3319 = -12-79 2e sin Q + 3805 + 985 - 266 + 14-05 2e cos Q + 8311 - 600 - : + 50-02 da/a + 9557 = + 42-81 Yerkes Observatory— -Prof. Barnard. 1900-0. Sin du. Sin dN. Sin dl. 2e sin Q. 2e cos Q. da/a. Sin du + 11641 - 1051 - 892 + 267 -1432 + 176 = -56-53 Sin dN + 3296 + 422 + 429 + 922 - 929 = - 16-22 Sin dl + 4732 - 285 - 26 - 3439 = - 0-68 2e sin Q + 5230 + 1119 + 463 = + 46-47 2e cos Q + 9643 + 574 ■ + 44-62 da/a + 12774 = + 16-14 Yerkes Observatory— -Prof. Barnard. 1900-9. Sin du. Sin dN. Sin dl. 2e sin Q. 2e cos Q. da/a. Sin du + 9241 -1674 - 301 + 576 + 779 + 291 = + 22-20 Sin dN + 2472 + 420 + 149 - 333 - 860 = - 2-37 Sin dl + 3928 + 368 + 214 -3260 — - 4-36 2e sin Q + 3540 + 930 - 39 = + 47-64 2e cos Q + 7885 + 543 = + 52-73 da/a + 8748 = + 0-90 1908-9.] Motion of Neptune’s Satellite. 529 Yerkes Observatory— -Prof. Barnard. 1902'0. Sin du. Sin dN. Sin dl. 2e sin Q. 2e cos Q. daja. Sin da +8833 - 1019 - 510 - 505 - 241 + 69 = -25-68 Sin dN + 2310 + 139 - 198 + 188 - 232 = + 1-63 Sin dl + 3505 + 2 - 10 - 2905 = -11-59 2e sin Q + 3822 + 501 + 71 = + 16-45 2e cos Q + 7631 - 665 = + 69-36 da/a + 9508 = -32-73 Yerkes Observatory— -Prof. Barnard. 1903*0. Sin du. Sin dN. Sin dl. 2e sin Q. 2e cos Q. da/ a. Sin da +5348 - 1130 + 14 + 89 - 377 + 166 = - 15-12 Sin dN + 1316 + 197 + 117 - 19 - 202 - -13-16 Sin dl + 2332 - 160 + 35 - 1990 - + 9-42 2e sin Q + 1882 + 419 + 57 = + 15-66 2e cos Q + 4692 + 209 = + 36-18 da/a + 4751 = - 18-08 Yerkes Observatory— Prof. Barnard. 1904-0. Sin du. Sin dN. Sin dl. 2e sin Q. 2e cos Q. da/ a. Sin du + 4535 - 893 - 114 + 24 + 458 - 61 = - 18-14 Sin dN + 1089 + 7 + 21 - 148 + 26 = - 3-02 Sin dl + 1992 + 208 - 35 - 1682 = + 9-26 2e sin Q + 1592 + 30 - 41 = + 14-19 2e cos Q + 3957 + 19 = + 39-77 da /a + 4101 = -21-12 Yerkes Observatory — Prof. Barnard. 1904-9. Sin du. Sin dN. Sin dl. 2e sin Q. 2e cos Q. da/a. Sin du + 2850 - 459 + 187 + 74 + 65 - 14 = - 11-73 Sin dN + 899 + 126 - 235 + 27 + 30 = + 7-67 Sin dl + 1012 + 8 - 15 - 895 = + 5 33 2e sin Q + 1315 + 45 - 248 = + 1-15 2e cos Q + 2263 - 51 = + 15-04 da/ a + 2913 = -23-19 Yerkes Observatory — Prof. Barnard. 1906-1. Sin du. Sin dN. Sin dl. 2e sin Q. 2e cos Q. da/a. Sin du + 2141 - 466 + 199 - 283 + 215 + 206 = + 15-36 Sin dN + 493 + 81 - 114 - 130 - 224 = - 5-22 Sin dl + 951 - 96 - 53 - 826 = - 3-35 2e sin Q + 724 + 185 + 49 = + 4-70 2e cos Q + 1885 - 359 = + 13-72 da /a + 1858 = - 26-43 34 VOL. XXIX. 530 Proceedings of tlie Royal Society of Edinburgh. [Sess. Mr Lowell’s Observatory — Messrs Drew and Cogshall. 1897-0. Sin du. Sin dN. Sin dl. 2e sin Q. 2e cos Q. d i/a. Sin du + 6568 - 1230 - 962 - 229 + 1002 - 129 = + 66-88 Sin dN + 2080 + 324 - 112 - 399 - 587 = -32-28 Sin dl + 3136 + 289 - 242 -2166 = - 7-24 2e sin Q + 2827 + 1059 - 383 = - 15-60 2e cos Q -1-5342 - 974 = + 29-75 da/a + 6572 - + 25-87 Mr Lowell’s Observatory — Messrs Drew and Cogshall. 1898-8. Sin du. Sin dN. Sin dl. 2e sin Q. 2e cos Q. da/a. Sin du + 2226 - 352 - 103 + 29 + 529 + 237 = -27-51 Sin d'N + 673 + 133 - 208 - 137 - 452 = + 0-76 Sin dl + 1021 + 155 - 147 - 720 = + 8-36 2e sin Q + 1071 + 428 • 230 = + 2-98 2e cos Q + 1803 - 112 = - 12-57 da/a + 2229 = -25*09 Washington < Observatory — Mr Dinwiddie. 1903-0. Sin du. Sin dN. Sin dl. 2e sin Q. 2e cos Q. da/a. Sin du + 3174 + 120 - 105 + 92 + 65 + 107 = -21-84 Sin dN + 887 + 16 + 35 - 25 - 185 = - 5-89 Sin dl + 975 + 23 + 2 - 820 = + 8-75 2e sin Q + 1780 + 125 + 14 = -45-28 2e cos Q + 2475 + 94 = -20-11 da/a + 4286 = + 2*30 Washington Observatory — Messrs Hammond and Bice. 1905-0. Sin du. Sin dN. Sin dl. 2e sin Q. 2e cos Q. da/a. Sin du + 3332 - 405 - 321 - 17 + 370 - 362 = - 33-79 Sin dN + 821 - 174 + 14 - 163 + 432 = - 321 Sin dl + 1300 + 97 - 26 -1126 = + 18*48 2e sin Q + 1407 - 297 - 73 = - 8-73 2e cos Q + 2796 - 44 = - 44-66 da/a + 3472 = - 20-33 Washington Observatory — Mr Hammond. Sin du. Sin dN. Sin dl. 2e sin Q. 2e cos Q. da/a. Sin du + 5537 - 253 + 74 - 756 + 625 + 90 = - 96-84 Sin dN + 1445 - 53 - 133 - 294 + 69 = -15-33 Sin dl + 1875 + 277 - 126 -1641 = + 2-15 2e sin Q + 2724 + 35 - 23 = + 25-87 2e cos Q + 4432 - 802 = - 32-06 da/a + 6434 = + 22-05 1908-9.] Motion of Neptune’s Satellite. 531 7. In the next table are given the solutions of these equations. To these are added the solutions of those series marked with an asterisk on page 519. Lick Observatory — 36 -inch Refractor. Epoch. No. of Obsns. du. t 703 70YS 1 ' r r \ \ zo 1050 39 \ • / t m \ / ? x \ % # / / f \ Vi f ...MJ J. 101 i i / A / ■r 10 1000 36 V 4 r / a b r 100 99 37 N u 96 97 36 Intravenous Inoculation. Animal . Weight . Sex Dose Duration of infection . rabbit 1200 grams male entire agar culture . 11 days observed in the experimental animal are few and slight. For the first twenty-four hours after injection the animal may refuse food ; subsequently it appears normal in this respect. The temperature is usually but only 548 Proceedings of the Royal Society of Edinburgh. [Sess. slightly raised, and but very rarely goes above 40° C. The weight does not fall with that astonishing rapidity which is noted after intracerebral and intravenous injections, and death takes place suddenly and without premonitory symptoms in from three to five days. Post-mortem, the mesentery is found to be rolled up on itself, and appears quite red from dilatation of its vessels and from the presence of numerous haemorrhagic areas. The intestinal walls are markedly injected and are sticky, have lost their shining lustre, and the coils of the intestines are matted together by the peritoneal exudate, which is for the most part pink in colour and 1908-9.] The Pathogenesis of Micrococcus melitensis. 549 glutinous, and not present in very large amount ; while numerous yellow flakes consisting of polymorphonuclear leucocytes and micrococci are scattered all through the peritoneal cavity. In the case of the male animal the epididymis and vasa at first sight appear like clots of blood, from the excessive engorgement of their vessels. The testis itself is swollen and red, and on incising the organ the tunica vaginalis is found to be adherent to the body of the testis, bound down by sticky gelatinous pus, the interstices between the adhesions being occupied by a thin sero-pus containing flakes of fibrin. In the inspissated pus or in the sero-purulent fluid M. melitensis is particularly abundant. The spleen is large, generally of a dark red colour ; the Malpighian corpuscles are very prominent ; the organ itself is firm and tense owing to the pressure within the capsule, but on incising the organ the spleen pulp is frequently almost fluid. Cultures from all the organs yield copious growth of M. melitensis, the heart blood is full of cocci, and occasionally the urine contains a few, which have probably gained access through the peritoneum covering the walls of the ureter and the bladder. The temperature, weight, and agglutination curves of such an infection are shown in chart 5. 2. Chronic. — The course of a chronic intraperitoneal infection does not differ in any material respect from that of the chronic intravenous infection (see chart 6) beyond the length of time that usually elapses between inocula- tion and death. In the former case this period may extend to six or seven months ; in one of my cases thirteen months intervened. Post-mortem, no macroscopical lesions are present, the peritoneal cavity and the abdominal viscera are normal in appearance, and as a rule cultures of M. melitensis can only be obtained from the centrifugalised deposit of the bladder con- tents, or from the kidney tissue if large pieces of that organ are planted in broth. Occasionally all cultivations remain sterile, and the presence of specific agglutinins in the blood and changes in the histological structure of the blood and bone marrow form the only evidence of infection. D. Subcutaneous Inoculation. — 1. Acute. — No amount of experimental exaltation of the virulence of M. melitensis has yet enabled me to produce an acute infection of the rodent as the result of subcutaneous inoculation — the infection, so far as relates to the fatal termination, is always and extremely chronic. Again, unless the organism has been previously exalted in virulence by means of passages through animals of the same species, pus formation is the exception rather than the rule, and it is often difficult to obtain any evidence of successful infection, other than the presence of specific agglutinins in the blood-serum, if the process is allowed to pursue its natural course. 550 Proceedings of the Royal Society of Edinburgh. [Sess. o 2. Chronic . — The small swelling at the site of inoculation which marks the introduction of the emulsion of M. melitensis into the subcutaneous CHART 5. DAYS 77frre Weight, grms. °c. / 3 3 4 5 6 7 °F. 70 o 600 575 550 5Z5 4Z 47 707 706 40 ,05 104 30 \ A t 3 S) 703 70Z 707 700 F 38 Pvj m \ -S L_ 1 ri \ y V \ b 37 \ L \ f / \ SO 08 -< l \ \ u 36 \ 1 / * o . 1 ■sg r 07 Intraperitoneal Inoculation. Animal Weight Sex . Dose . Duration of infection . rabbit 560 grams male 0’3 agar culture 5 days tissues rapidly disappears, and a few hours after injection the animal appears quite normal. Twenty-four to forty-eight hours later, the seat of inoculation is marked by a large, hard, circumscribed tumour. The animal 551 1908-9.] The Pathogenesis of Micrococcus melitensis. appears distressed, and the temperature rises to nearly 40° C. During the next few days the local lesion becomes soft, and fluctuation can be obtained. A few days later necrosis of the skin covering the tumour takes place, a slough separates, and thick creamy pus crowded with M. melitensis exudes from the abscess cavity, leaving an extensive ulcerating cavity. After a week or two, during which the exudation gradually becomes less in amount, healthy-looking granulations spring up, cicatrisation proceeds, and in about three weeks the animal appears perfectly normal as to temperature, and may even put on weight ; but in the course of the following weeks or 552 Proceedings of the Koyal Society of Edinburgh. [Sess. months a decrease in weight may again be noted, and finally the animal dies (see chart 7). Post-mortem, beyond the cicatricial tissue at the seat of inocula- z o H «3 £> o o SC CO p O w z «3 H P O « 02 to O S '_l $ o CO cS CM oo w o Q T3 CL> O O s xn s *2 •s X <1 m the urine, and in the female from the milk ; also by the presence of specific agglutinins, often in large amount, in the blood serum. If the animal is destroyed later on, the micro-organism can be recovered from the various organs — in numbers and from a variety of situations, decreasing directly 557 1908-9.] The Pathogenesis of Micrococcus melitensis. with the length of time that has elapsed from the inoculation. The tempera- ture chart and serum reactions of some typical infections are here inserted (charts 8, 9, 10). UNGULATA. Horse , Mule, Cow, Goat, Sheep. A considerable amount of evidence was collected by the Mediterranean Fever Commission during 1905 and 1906, proving that various members of 558 Proceedings of the Royal Society of Edinburgh. [Sess. this family were the subjects of M. melitensis infection naturally acquired. Thus the horse and mule, by reason of the presence of often large amounts of specific agglutinin in the blood serum, were considered to be subject to natural infection, though the specific organism was never recovered from the tissues. The cow, goat, and sheep yielded stronger evidence, as the micro- organism was successfully isolated from the milk of some of the females in each species. The number of cows upon the island was too few to give any reliable information as to the percentage incidence of M. melitensis septicsemia; but in the case of the goat, which in Malta is the commonest quadruped, and numbers some 20,000 head, this point was studied by means of a careful examination of a large number of individuals, and from the results obtained it is estimated that nearly 30 per cent, are or have been the subject of M. melitensis septicaemia naturally acquired, while fully 10 per cent, yield absolute proof of present, though chronic, infection by the presence of the micrococcus in their milk. Having had no personal experience of the infection of mules, cows, or sheep by laboratory methods, I shall confine my remarks to the experimental inoculation of the horse and of the goat. Horse. — The horse I have infected by means of intravenous injections in the course of some immunising experiments whilst attempting to prepare an anti-serum. The clinical phenomena observed after inoculation of this animal — a chestnut mare — were remarkably few. The temperature rose within a few hours, but rarely more than T5° C. to 2° C., and the mare was u off her feed ” for perhaps twenty-four to thirty-six hours. The tempera- ture rapidly returned to normal, the coat remained smooth and glossy, and the animal appeared to be perfectly normal. Examination of the blood, however, showed the presence of specific agglutinins, and the cocci were present in the general circulation for between three and four weeks after each injection (chart 11). The goat , so far as my observation carries me, is never the subject of an acute infection, though it is true I have never employed the intracranial method of inoculation of this animal. The animal is susceptible to infection as the result of intravenous (see chart 12), intraperitoneal, subcutaneous, and cutaneous injection of M. melitensis, and also by feeding methods. By whatever method the infective material is introduced into the tissues, the clinical phenomena are similar. The animal rarely appears to be adversely affected. Its appetite is as vigorous as ever, and beyond a few days’ pyrexia, during which the coat may or may not lose a little of its sheen, nothing can be detected by the ordinary clinical methods of observation. Examination of the blood from time to time shows the presence in the serum of specific agglutinins, first demonstrable in from seven to twenty-one 559 1908-9.] The Pathogenesis of Micrococcus melitensis. days after infection ; while examination of the blood in the early stages of infection, of the urine later on, and later still, in the case of milch goats, of the milk, yields absolute evidence of the reality of infection, by the isolation CHART 11. Animal ...... horse Sex ...... female Dose . . . . . .25 milligrammes agar culture of the specific micro-organism. None of the experimental animals died as the direct result of the artificial inoculation. Consequently, I shall refer in detail only to some subcutaneous and cutaneous experiments which are of particular interest. Subcutaneous Infection. — Four normal healthy half -grown goats were 560 Proceedings of the Royal Society of Edinburgh. [Sess. selected, and injected subcutaneously, each with a different-sized dose of in- fective material. Thus one loopful of the growth from a forty-eight-hours agar culture was emulsified in 10 c.c. of sterile saline solution, and the four goats were inoculated subcutaneously at the root of the left ear with 1 c.c., 0T c.c., 001 c.c., and O’OOl c.c. respectively of the emulsion. Portions of the remainder of the emulsion, after suitable dilution, were plated out and incubated. Enumeration of the resulting colonies showed that the emulsion contained 10 million cocci per cubic centimetre. 1908-9.] The Pathogenesis of Micrococcus melitensis. 561 Consequent upon these injections, all four goats became infected, as shown by the appearance of specific agglutinins in the blood serum, hut from the clinical point of view there was little to record. At no time during the course of the experiment did either of the goats appear to be ill : their coats were in good condition, and the animals fed well, as usual. The temperature after an immediate but transitory rise was somewhat irregular, but not markedly so (see chart 13). All the animals were killed vol. xxix. 36 562 Proceedings of the Royal Society of Edinburgh. [Sess. at the end of six weeks, and at the post-mortem inspection ample evidence of M. melitensis infection was available in the recovery of the organism from the spleen in all four goats, and in three of them from other organs as well ; but the point of interest to be noted in this experiment is the relationship that exists between the size of the dose of infective material to the date of onset of signs of infection. Thus the first two goats, which received 10 and 1 million cocci respectively, gave evidence of reaction to the infection by the appearance of specific agglutinins in the blood within a week of inoculation, and a full ten days earlier than the other two goats, which had each received less than a million cocci. No. of Goat. No. of Cocci Injected. Serum Reaction. Titre of Serum at 44 days. Day of First Appearance. Titre. No. 10 10,000,000 7 1 : 20 1 : 200 „ 9 1,000,000 7 1 : 20 1 : 100 „ 5 100,000 17 1 : 20 1 : 20 „ 4 10,000 17 1 : 10 1 : 20 Cutaneous Infection. — The suspicion that had been aroused in my mind with reference to the probability of infection being carried from goat to goat by way of the goatherds’ hands when soiled with infective milk was strengthened by the knowledge that such a comparatively small amount of infective material as that just mentioned injected subcutaneously was sufficient to produce infection. The technique adopted by the Maltese goatherd closely resembles that of his English confrere, and consists in lubricating his own hands and the outside of the goat’s udder with some of the foremilk. When a number of goats have to be milked in rapid succession, the lubricant obtained from the first goat will serve for perhaps some half-dozen goats ; with the seventh goat a fresh supply of milk is taken for the same purpose, and so on. Now given that goat No. 1 or goat No. 7 is passing M. melitensis in its milk, it is obvious that at any rate goat No. 2 or goat No. 8 stands a very good chance of becoming infected by a process of subcutaneous inocula- tion ; I therefore investigated the possibility of this occurrence in the following manner. A healthy female goat, nearly full grown, was selected, cast on an operating table, and securely held by assistants. A fairly large area of skin over the left mammary gland was shaved somewhat roughly, in such 563 1908-9.] The Pathogenesis of Micrococcus melitensis. a manner as to remove in many places the superficial layer of epithelium as well as the hair, but care was taken to avoid drawing blood. Thus the shaved area replaced the scratches, abrasions, and small ulcers that are so frequently seen on the udder and teats of the milch goat. Next, the hands of the operator being protected by a pair of sterilised indiarubber gloves, four drops of freshly drawn milk (amounting in total bulk to 0'2 c.c.) from a goat known to be excreting M. melitensis were delivered into the palm of the right hand from a sterile capillary pipette, and then thoroughly rubbed into the shaved area with movements similar to those practised by goatherds as a preliminary to milking. The quantity of the milk used was so small that the skin surface rapidly dried, and the goat was then isolated in a stall, apart from the other animals. Immediately after the experiment was concluded, a sample of the milk that had been used was carefully plated out (after suitable dilution) and found to contain 24,800 M. melitensis per cubic centimetre ; the approximate number of cocci therefore that came into contact with the prepared area of skin amounted to 5600. Samples of blood were taken from a vein in the ear of this animal, and examined from day to day for the presence of specific agglutinins, which first made their appearance on the fifteenth day (dilutions 1 in 10 and 1 in 20). Three weeks after inoculation the goat was killed and a careful post-mortem examination carried out, with the result that the specific organism was recovered from the spleen and inguinal glands. The post-mortem observations upon animals killed after periods of observation varying in duration from three to at least fifty-three weeks are extremely interesting as showing that within a very few weeks of infection the micrococcus disappears from the general circulation, though still present in the spleen to about the end of nine months. Later still, the coccus cannot usually be recovered from this organ, but may be found in the mesenteric glands and the inguinal glands. In one animal where the organism was recovered from the tissues of the mammary glands it could not be detected in any other situation in the body ; in another successful recovery from the gland substance the coccus was also detected in the neighbouring inguinal glands and nowhere else. These results are more readily appreciated when arranged in tabular form : — [Tables. 564 Proceedings of the Royal Society of Edinburgh. [Sess. Results of Post-mortem Examinations of Goats Experimentally Infected. No. Sex. Remarks. ^ Duration of Infec- % tion or Period of Sf Observation. ^ Presence of M. melitensis noted U During Life. Titre of Serum. Post-mortem Findings. M. melitensis present in Heart Blood. s’ O) a> r—H Ph m Kidney. Glands. CD D Inguinal. Mesenteric. 1 E Cutaneous inoculation 3 1 : 100 + + 0 2 M Subcutaneous inoculation . 6 — 1 : 200 — + — + — — 3 M 55 55 6 — 1 : 100 — + — + + — 4 F 5? 55 6 ... 1 : 20 — + — — — 0 5 F 5 5 5 5 6 — 1 : 20 — + — — - 0 6 F 5 5 55 21 — 1 : 1500 — + — — + 0 7 F Feeding .... 26 — 1 : 100 - + - + - 0 8 F 55 .... 37 At 7 weeks 1 : 20 — — — - — 9 F Subcutaneous i noculation . 39 — 1 : 20 — + — — — 0 10 F Feeding .... 41 — 1 : 10 — — — — — 0 11 F 55 .... 42 — ? — + — — — 0 12 F 55 .... 45 At 13 weeks 1 : 10 — - — — — 0 13 F 55 .... 45 At 20 „ 1 : 150 — — — + — + 14 F 55 .... 49 At 20 „ 1 : 20 — — — — — + 15 F 55 .... 49 — 1 : 50 — — — — — — 16 F 55 .... 53 At 43 weeks 1 : 160 — — — — — 0 till killed. - =M. melitensis not recovered. + =M. melitensis recovered. 0 = Not examined. Post-mortem Examination of 5 Naturally Infected Milch Goats. Period of Observation. Weeks. M. melitensis recovered During Life from M. melitensis recovered Post-mortem from Urine. Milk. Titre of Serum. Heart Blood. Spleen. Glands. Udder. Mes- enteric. Inguinal. 19 1 : 20 + 0 19 - + 1 : 20 — — — — + 19 - + 1 : 10 — — — + 0 43 — + 1 : 160 — — — + + 56 + + 1 : 20 — — — — 0 - =M. melitensis not recovered, -f- =M. melitensis recovered. O = not examined. The point of greatest practical importance that emerges from the study of laboratory infections of the goat is the appearance of M. melitensis in the milk. When the fluid has been systematically examined in experi- mental milch goats the appearance of the coccus has invariably been a late phenomenon. One goat, for instance, commenced to pass the micrococcus in 565 1908-9.] The Pathogenesis of Micrococcus melitensis. its milk seven weeks after infection, another three months after infection. A third showed no signs of the coccus up to four months after inoculation, when it ran “ dry ” ; six months later still — that is, ten months after experi- mental inoculation — this goat dropped two kids, and three days later the coccus was first detected in the milk. A series of daily observations during the summer of 1906 showed that although the excretion of M. melitensis in the milk during some stages of the infection of the milch goat is persistent, it is by no means constant or even consistent ; nor was it possible to detect any correlation between the atmospheric temperature curve and the number of cocci excreted in the milk. So that for the moment the only explanation that can be offered of the day-to-day variations in the number of cocci present in the milk is that the micro-organism, lodged in a suitable soil and richly supplied with a medium of high nutritive value, multiplies rapidly in the interstices between and upon the surface of the gland-epithelium cells. This multiplication proceeds up to a certain point, when, owing perhaps to the mechanical irritation set up by the mere presence of the coccus, a flushing process is carried out by the milk itself, which removes the excess of cocci and leaves behind in the gland tissue only those cocci which are in intimate relationship with the gland cells. A certain interval is then necessary for further multiplication of those cocci left behind, when the process is repeated again and again. PRIMATES. Monkey, Man. Both the Rhesus and Bonnet monkeys resemble man in that they are susceptible to all the methods of experimental inoculation already enumerated, and in addition to infection through apparently intact mucous membranes. In these animals, as in man, the infection is usually of the subacute or chronic type, though occasionally acute infections of a rapidly fatal course are observed. In fact, the introduction of living cultures into the tissues of the monkey, or the administration of infective food, is followed by an attack of fever strictly comparable in general symptomat- ology, and in the course of the temperature curve, to one or other of the various types of the disease clinically distinguished in man. The multi- plication of the organism in the peripheral circulation and the production of specific agglutinins in the serum are similarly demonstrable, although the disease usually runs a shorter course, and in the majority of the experi- mental infections would end in complete recovery. 566 Proceedings of the Royal Society of Edinburgh. [Sess. Intracerebral inoculations generally produce a more acute and more fatal infection than that immediately to be described (see chart 14), while intracerebral passages result in a very marked exaltation in the virulence of M. melitensis for the monkey. i — i EH tn o P-i c n O >> O cS 13 9 O t-H CO £ o H < t=> o o £ I — i < p3 pp w pH w o Ph H & o .CD tl— I «t-H o • fH o • rH (D c3 m r-» O 2 p n C/2 £ c/2 CD s P • i—f o a o ® c3 CC f-t o P q a m a> rP © M P rS O C3 s s c3 •s « <5 02 rises, that it is sufficient to glance at its cage to realise when the hour of noon approaches. The pyrexia lasts usually from five to ten days' diarrhoea and loss of weight being, apart from the pyrexia, the most noticeable feature of the infection. A short period of slight pyrexia, normal or even subnormal temperature, may be succeeded by a second attack of high fever 568 Proceedings of the Royal Society of Edinburgh. [Sess. ?'b!C9 (see chart 15) ; but this is quite the exception. Usually it is directly followed by a period of intermittent pyrexia of slight range and short duration, the temperature gradually returning to normal and complete recovery taking place, although death may occur without warning at almost any period of the infection. Post-mortem, M. melitensis can be isolated from all the tissues and organs, though the spleen, which is hypertrophied and hard and dark in colour, and the lymphatic glands, which are enlarged and often present soft, almost dif- fluent areas in their interior, are the only organs of abnormal appearance. 569 1908-9.] The Pathogenesis of Micrococcus melitensis. In some cases of extreme chronicity, where the infection has pursued a very protracted course, and the temperature, though very irregular, has rarely risen above 40° C., the specific organism can often be recovered only from the lymphatic glands and urine (see chart 16). Infection by Feeding. — In a series of experimental feedings with infective goats’ milk in the summer of 1905, 93 per cent, of the monkeys were successfully infected, which sufficiently demonstrates their suscepti- bility to this form of infection. On the clinical aspect of the infection produced by feeding experiments it is unnecessary to dwell at length, hut a few points of interest may be briefly mentioned : — Temperature. — Speaking generally, the infection appears to be mild, as judged by the course of the experimental animals’ temperature and supported by their general appearance and behaviour during the six or seven weeks some were under observation, but opinions based upon clinical symptoms were rudely contradicted by the result of the post-mortem examinations. Again, speaking generally, the temperature chart of the Rhesus infected with M. melitensis, except in the case of very severe infections such as follow intracranial and intravenous injections of the micrococcus, shows but one period of pyrexia, followed by an intermittent temperature of slight range and short duration. A second period of pyrexia, or “ wave ” as it is colloquially termed, is quite the exception. The remittent type of pyrexia does, however, occur in the monkey ; also this animal sometimes exhibits a type of temperature absolutely comparable to the one obtaining in man when the subject of what Shaw has designated the “ ambulatory ” type of M. melitensis septicaemia. All these three types are met with in the course of experimental feed- ings, as will be seen in the three accompanying charts (17, 18, and 19), which I have selected from the many in my possession. In these three animals the severity of the infection must have been of nearly equal intensity in these cases, judging by the results of the bacterioscopic examination, which showed that the blood and all the organs of each of these animals were literally teeming with the M. melitensis. Agglutination Reaction. — The repeated examinations that were made of blood from each of the infected monkeys showed that for a day or two, or even several days, before a definite reaction was obtainable a 1 : 10 dilution of the serum produced microscopically what is regarded as an “ incomplete ” reaction — that is, the micrococci ceased to exhibit active vibratory move- ment and adhered together in small bunches ; but large clumps and masses were not formed, and the general field was made up of discrete cocci. Then 570 Proceedings of the Royal Society of Edinburgh. [Sess. a good reaction, large clumps in a perfectly clear fluid, readily visible with the two-thirds lens or, indeed, the unaided eye, would be produced by a low dilution of the serum — 1 : 10 or 1 : 20. Very often, even at this stage, the macroscopical reaction in the sedimentation tube was absent. Next, the microscopical reaction would often disappear for a day or two, or even longer ; finally, it would become firmly established, and obtainable in the majority of cases in considerably higher dilutions, and the micro- and macroscopical reactions would control and confirm each other with absolute precision. The exigencies of experiment, necessitating the destruction of 571 1908-9.] The Pathogenesis of Micrococcus melitensis. animals early in the course of the disease, are responsible for the fact that but few examples of the development of a very high agglutinative power in the serum were noted. Man. — Man is susceptible to infection by subcutaneous inoculation, to infection through apparently intact mucous membranes, and the administra- tion of infective food. Laboratory inoculations in which man has served as the experimental animal, though not intentional, are sufficiently numerous to enable us to say that the type of infection which results compares ab- solutely with that naturally acquired within endemic areas, and also enable us to fix within fairly narrow limits the period of incubation for sub- cutaneous infections. Thus of eight cases of laboratory infection where 572 Proceedings of the Royal Society of Edinburgh. [Sess. the exact date of inoculation could be fixed, the shortest period of incubation was 5 days, the longest 16 days, the average being just over 8 days (the exact duration being 5, 5, 5, 6, 8, 15, 15, and 16 days respectively). In those cases where the incubation period extended to 15 days, the accident which caused the infection was noted at the time, and strenuous efforts, by the liberal application of antiseptics, were made to reduce the probability of an attack of M. melitensis septicaemia. The lengthy incuba- tion period (16 days) in one case previously treated with M. melitensis vaccine would appear to indicate that some protection — although obviously inadequate — had been conferred as a result of the treatment. 573 1908-9.] The Pathogenesis of Micrococcus melitensis. Cases of M. melitensis septicaemia in man present different features with almost every individual attacked, but may be grouped under one or other of the headings acute, subacute, and ambulatory, and may be briefly described as follows : — (1) Acute Form. — This type is extremely acute from the onset, and is initiated in the previously healthy by rigors, accompanied by a temperature of 38*5°, 40°, or 4T5° C. ; severe headache, often limited to the back of the CHART 20. DA fXS Titre Weight grms. °c. 7 z 3 6 5 6 7 8 9 70 // /z 73. 77 73 76 // 78 79 ZO Z7 zz Z3 c> F. too 80 60 60 20 0 6Z 67 707 706 60 705 706 / • 3© / \ K A 4 703 102 \T r 4 V • 7 pfi M A f tin f V t I 38 [V L / M S 107 100 99 98 V •4 Mae § 3T 36 \ 97 ? Food Infection in Man. Type of infection ..... acute Result ....... death 23rd day of illness eyeball ; indefinite pains about the trunk and limbs, particularly in the back ; and general malaise. The face is flushed, the dorsum of the tongue is thickly coated with white fur, but pink and moist at the sides and tip, or more rarely dry, brown, glazed and cracked, and the breath offensive. Diarrhoea is not infrequently present during the first few days of the attack, but soon gives place to constipation. The pulse is strong and increased in frequency, though not usually in proportion to the temperature. The urine is diminished in amount, high in colour, and contains large quantities of uric acid and urates. This type of fever sometimes passes into the “typhoid ” 574 Proceedings of the Royal Society of Edinburgh. [Sess. state, and death results from cardiac failure (see chart 20), or, more rarely, hyperpyrexia supervenes. Sometimes a crisis occurs and recovery takes place, but usually the temperature gradually falls to or near normal, and the case assumes the subacute type. (2) The subacute form, on the other hand, is often slow and gradual in onset. For some days slight headache, thirst, constipation and gastric disturbances, pains in the back, neck, and limbs, usually described as “ rheumatic,” accompanied by insomnia, mental anxiety, and general depression, combine to produce a marked, but at the same time indefinite, feeling of ill-health. Next follows a steady and gradually increasing rise of evening temperature, with morning remission, until 39*5° to 41'5° C. is reached, followed by a similar and almost equally gradual fall until the morning temperature becomes practically normal. The remissions of temperature are almost invariably accompanied by profuse perspirations. The duration of the initial pyrexial attack varies in different cases from one to five weeks ; then, after an apyrexial interval lasting from five to ten days or a fortnight, during which the temperature remains at or about normal, a relapse sets in, similar in all respects to the first attack, but often distinctly shorter and less severe. This sequence of events is repeated again and again, the duration of the disease varying from six weeks to six or nine months (see charts 21 and 22). I have seen several cases where the duration of the disease has exceeded two years, and one where the fever had existed with typical pyrexial attacks at irregular intervals for three years. (3) Ambulatory Form. — Finally, mention must be made of the ambul- atory type of case described by Shaw, in which symptoms are entirely absent, or are limited to a few days’ fever (37*5° C.), and the only proof of the existence of the disease is the presence of agglutinins in the blood, and occasionally of the M. melitensis itself also ; while in the urine (although normal in appearance) the specific organism is often present in enormous numbers (22,000 per c.c.) and in a highly virulent condition. Marston in 1863, it should be noted, was also familiar with this ambulatory type of case, for he says upon the other [hand], so mild may the symptoms appear, that the patient may never be confined to bed, and be all the while supposed to be labouring under a peculiar form of dyspepsia.” Immunisation and Antibodies. The immunisation of rodents is a matter of considerable difficulty, and the amount of immunity attained is totally inadequate to the length of time and the labour involved — in fact, one is almost led to the conclusion 575 1908-9.] The Pathogenesis of Micrococcus melitensis. that in rodentia at any rate an active immunity to M. melitensis is never acquired. Full-grown rabbits and guinea-pigs occasionally appear resistant to small doses of the micrococcus or doses of cocci of low virulence ; but this immunity is apparent rather than real, and a larger dose, or a similar-sized dose of a more virulent strain, or inoculation by some other channel, will always produce a successful infection. Hence the observed absence of bactericidal substances from the serum of healthy or infected rodents is not 576 Proceedings of the Royal Society of Edinburgh. [Sess. a matter for surprise, and affords a ready explanation of the fact that after most careful treatment of an experimental animal by any of the approved methods of immunisation, the administration of a suitable quantum of M. melitensis culture is invariably followed by infection. These remarks hold good in the case of adult animals of all other orders of mammals, in- cluding monkeys — despite Shaw’s opinion to the contrary, which was based upon experiments made whilst he was still unaware of the fact that a type of infection could be produced in the monkey resembling the ambulatory 5 77 1908-9.] The Pathogenesis of Micrococcus melitensis. form of M. melitensis septicaemia in man, in which, though the blood and tissues contain the micrococcus, no pyrexia is produced — and probably man. But although specific bacteriolysin is absent from the serum of the inoculated animal, specific agglutinin is readily formed, and this aspect of resistance to the M. melitensis and its products has been exhaustively studied by many observers, particularly by Durham and myself. Agglutination React ion. — Since the “ serum reaction ” test of Gruber and Durham was applied to the diagnosis of M. melitensis septicaemia by Wright in 1897 this method has been extensively employed ; and it has been shown that the specific agglutinin may be present in the blood of infected animals, including man, from the fifth day onwards (Aldridge, Bassett-Smith, Gilmour) — exceptionally it is present on the first day, sometimes its appear- ance is delayed until weeks after the disease is well established. Usually it is present in large amount, giving to the serum a titre of 1 : 100 or 1 : 1000 even during the first week of the disease, whilst subsequently sera reacting in much higher dilutions, even up to 1 : 500,000, have been observed. Moreover, it must be noted that in man the agglutinins persist in the blood long after recovery, and the serum may react in dilutions of 1:50 and 1 : 100 for from three to seven or even ten years after naturally acquired infection. Finally, sera from healthy animals and from those suffering from infections other than those due to micrococcus melitensis never yield a complete reaction when tested in dilutions of 1 : 10 (Birt and Lamb), or a partial reaction when tested in dilutions of 1 : 20. Specific agglutinins are elaborated in response to injections of the dead bodies of M. melitensis as well as to living cultivations. Experiments have so far failed to confer active immunity upon any of the ordinary laboratory animals. After long-continued treatment of rodents by repeatedly injecting suitable doses of killed cultures in the attempt to produce some degree of immunity and the establishment and maintenance of a high agglutinin content of the blood serum, the introduction of even comparatively small amounts of living virulent cultures almost invariably caused the death of the animal. Animal. Weight in Grams. Period of Treatment. Titre of Serum. Dose of Living Cultivation. Method of Inoculation. Result. Rabbit 8 3000 7 months 1 : 1500 1 loop Intracerebral t in 10 days Rabbit 25 2500 7 „ 1 : 5000 o-oi „ t in 60 „ Rabbit 73 2800 7 „ 1 : 4000 o-oooi Subcutaneous Recovery Guinea-pig 50 600 4 „ 1 : 5000 1-0 Intracerebral t in 3 days vol. xxix. 37 578 Proceedings of the Royal Society of Edinburgh. [Sess. Passive acquired immunity is likewise conferred to a very slight degree only, for the serum of treated rodents, even when it possesses a very high agglutination titre, fails to protect normal rabbits and guinea- pigs against infection, or even to modify the course of such infection. Agglutinating serum from larger animals appears to be no more potent. On the other hand, a certain degree of immunity is undoubtedly trans- mitted from the infected maternal parent to her offspring, for in both the infected dog and goat, although the micrococcus melitensis, minute though it is, does not traverse the placenta and so no actual infection occurs, an appreciable amount of specific agglutinin is transmitted to the pups and kids. But beyond a doubt other antibodies are also carried over, for although these animals are readily susceptible to infection with M. melitensis via the alimentary tract, and although the infected parent is secreting milk teeming with the micrococcus, which is taken by the suckling young, infection does not result during the period of suckling. The inference is therefore justified that the young are supplied with other antibodies besides the specific agglutinins which protect them from infection during the period of suckling. These statements are based, it is true, upon a limited number of observations, but at my suggestion Professor Zammit is continuing these experiments, with results which go far to support my conclusions. Animal. Examination of Parent. Examination of Offspring. Titre of Serum. M. melitensis in Milk. Length of Life. Titre of Serum. Recovery of M. melitensis from Tissues. Dog 8 1 : 200 Yes Pup a . • • • • • 1 day 1 : 10 nil. „ ' b • . o 1 day 1 : 10 55 „ c • • • . . • 14 days 1 : 10 55 55 ^ . . . . . • 14 days 1 : 20 55 Dog 28 1 : 20 Yes Pup • • • • . • 5 days. 1 : 10 nil. 55 / • • . • . . 5 „ 1 : 10 55 55 9 ... ... 5 ,5 1 : 5 55 Goat 3 1 : 100 Yes Kiel a ... • • • 17 days. 1 : 50 nil. ,5 b ... ... 17 days. 1 : 20 55 This immunity, however, is only partial and temporary, being limited to protection against infection via the alimentary tract ; and to the period of suckling, for Jdie young are still susceptible to subcutaneous, intravenous, 579 1908-9.] The Pathogenesis of Micrococcus melitensis. or intraperitoneal infection during the suckling period, and at a later period of life to infection by feeding methods also. Morbid Anatomy. For the study of the morbid anatomy and morbid histology of M. melitensis infections, laboratory animals of course afford ample material, but the case mortality of M. melitensis septicaemia in man is extremely low. Writing in 1903, Hayat (38) could only collect details of 76 autopsies, derived from Malta (67), Palermo (5), Netley (2), Naples (1), and Padua (1), for study. In Malta, during 1904, four, and in 1905 nine, fatal cases were carefully investigated by the Mediterranean Fever Commission. Personally, whilst in Malta in 1906 I only had the opportunity of assisting at the post-mortem examination of one case of M. melitensis septicaemia that died in the Military Hospital, Valletta, and of being present at some twenty autopsies at the Civil Hospital, Floriana. The pathological apjeearances produced by M. melitensis septicaemia in fatal infections, based upon observations upon post-mortem examinations of lower animals and of man, I have already described elsewhere ( Lancet , June 20, 1908). Morbid Histology. Observations upon the morbid histology of M. melitensis septicaemia do not appear to have been numerous — chiefly, I imagine, because the changes that take place in the various organs and tissues are few, generally insignificant, and in no way to be distinguished from those noted in septicaemia due to any other micro-organism. This obtains no matter whether the material is collected from acute cases killed shortly after infection or from chronic cases where long intervals have elapsed between infection and death, or whether in lower animals or in man. I have carefully studied a large number of sections during the past seven or eight years, collected from many different mammals, and I must confess that up to the present I have been unable to demonstrate any extensive deviations from the normal — except in those cases where a laboratory inoculation has been planned to produce suppurative lesions such as subcutaneous abscess, suppurative peritonitis, or suppuration within the tunica vaginalis. Such lesions as have been observed are best considered in the order of the various organs, etc., adopted for the morbid anatomy. Heart, — Haemorrhages between the muscle fibres is the only noticeable feature : the myocardium itself appears norma]. 580 Proceedings of the Royal Society of Edinburgh. [Sess. Lungs. — Here and there at the bases, foci of congestion show desquama- tion of the alveolar epithelium and collections of extravasated red cells and fibrin filaments within the alveoli. Alimentary Canal. — In some situations, particularly in the duodenum, extravasations of red cells are to be found, limited to the mucous membrane immediately below the glandular layer, and to the submucosa ; in other spots, denudation of the surface epithelium and small - celled infiltra- tion at the base of the ulcer formed by the destruction of the mucous cells. In still other areas, marked proliferation of the cellular elements may be observed. Liver. — The capillaries are dilated with red cells, very few polymorpho- nuclear leucocytes being visible ; and small - celled infiltrations may occasionally be noted around the perihepatic vein. Numerous intracellular capillaries are obvious throughout the sections. No changes are apparent in the hepatic cells themselves, though occasionally the hepatic trabeculae seem to be attenuated. Spleen. — Arteries, capillaries, and venous sinuses are dilated and filled with red- blood cells. In acute cases the splenic pulp is crowded with red cells, but in cases of long duration there is considerable increase of lymphoid tissue and of Malpighian corpuscles. The elastic fibres and reticulum are normal. Kidney. — Hyperaemia is the chief change noted in this organ : the loops of the glomeruli are distended with blood ; the interlobular arteries and vasa erecta are also dilated. No thickening of the capsule and no change in the epithelium of either tubules or glomeruli can be made out. Mesenteric glands are enlarged, not so much by reason of hyperplasia of the follicles and trabeculae, as by hyperaemia, as is shown by the dilatation of the sinuses, which are filled with blood cells. The follicles are not, as a rule, particularly rich in lymphocytes. Bone-marrow. — In chronic infections this tissue shows marked altera- tions from the normal in its constitution. Nucleated red cells and lymphoid cells, that is, giant cells, mononuclear cells, and lymphocytes, are markedly increased in number ; granular cells, i.e. myelocytes and polymorphonuclear leucocytes, are considerably diminished : the whole forming a typical lympho- erythroblastic bone-marrow, and is in marked contrast to the leucoblastic marrows associated with, for instance, pneumococcic infections. Blood. — During the early stages of M. melitensis infection the micro- coccus can be detected in the peripheral blood by cultural methods, but microscopical examination of the blood direct usually, except in the very acute and severe infections, fails to demonstrate its presence. In man the 581 1908-9.] The Pathogenesis of Micrococcus melitensis. coccus has been isolated (by cultural methods) from the second to the three- hundredth day of the disease, and in numbers varying from less than one per cubic centimetre to over 10,000, by various observers. The histological structure of the blood in the first few days of infection is characterised by a relative polymorphonuclear leucocytosis. This, how- ever, soon gives place to a relative or an absolute leucocytosis, chiefly affecting the non - granular cells — the lymphocytes and mononuclear leucocytes. Brain . — No abnormal appearances can usually be observed. A human brain from a fatal case of M. melitensis septicaemia, which had during life shown unmistakable symptoms of cerebral irritation, I submitted to Dr F. W. Mott ; but he informed me that, apart from obviously post-mortem changes, the microscopical appearances of this organ were perfectly normal. In two monkeys injected intracerebrally with small doses of M. melitensis, of a strain that had not been exalted in virulence for this animal, abscess formation was observed localised to the cortex at the spot entered by the syringe needle. But in the majority of the intracerebral inoculations I have performed there has been no attempt at localisation of the micrococcus to the cerebral tissues. Some of the Italian observers — Caracciolo, Carbone, and Trambusti — record much more definite changes in the organs removed from M. melitensis septicaemia cases. Most of these I am rather inclined to attribute to post- mortem influences, which in Italy and Sicily so rapidly produce marked alterations in tissue cells. But one point on which all are agreed as being the most striking feature of sections not only of spleen but also of liver and kidney, is the presence of numerous cells which they term globuliferous cells, derived from the endothelium lining blood sinuses, and containing in their interior from one to fifteen or twenty red-blood discs. In the spleen of a case examined by Carbone, he says they were absolutely innumerable ; those containing a few blood cells only were rare, those containing from eight to ten were common, and some were seen containing very many more. These observations I have not been able to confirm. ( Issued separately, September 7, 1909.) 582 Proceedings of the Royal Society of Edinburgh. [Sess. XXXV. — The Development of the Auditory Ossicles in the Horse, with a Note on their possible Homologues in the Lower Vertebrata. By Ray F. Coyle, B.S. (From the Zoological Department of the University of Edinburgh.) Communicated by Professor J. C. Ewart, M.D., F.R.S. (With Six Plates.) (MS. received May 25, 1909. Read July 5, 1909.) I. The discussion as to the homologies existing between the sound-conduct- ing apparatus of the mammalia and certain elements of the lower jaw and branchial skeleton of fishes has occupied the attention of numerous authors. In fact the question may be considered as a classic, dating as it does to at least 1778, when Geoffry published his Dissertations sur Vorgane de Vouie de I’homme, des reptiles, et des poissons. From that time until 1898 — from Geoffry to Gaupp — the contributions to the literature upon this subject constituted an enormous amount. Inasmuch as Gaupp has given a detailed and masterly review of the literature up to the time of his work (1898), and since Fuchs thoroughly covered the ground seven years later, I shall not undertake that task in the present communication. Moreover, as this paper is in the nature of a preliminary report upon the entire developmental history of the skull in the horse, I shall not here review in detail the con- tributions to the literature since the time of Fuchs’ account (1905). A specialised apparatus for the conduction of sound to the auditory organ first makes its appearance as the stapedial plate (operculum) and columella auris of urodele amphibians. Amongst many Anura the spira- cular cleft, which disappears entirely during the development of the Urodela and Gymnophiona, becomes “ modified to form a Eustachian tube, opening into the pharynx and leading into a tympanic cavity. The latter is closed externally by a tympanic membrane supported by a cartilaginous ring (annulus tympanicus), and to it the distal end of the columella is attached ” (Wiedersheim). In the Mammalia the sound-conducting apparatus consists of an osseous malleus, articulated with the tooth-like incus. The incus articulates by its long arm (crus longum incudis) with the stapes (fig. 5). Many investigators have assigned the stapedial plate and accessory cartilages of the amphibia to the second visceral arch, making it thus possibly homologous to the hyomandibula of the fishes. Fuchs, however, has clearly shown that the stapedial plate is developed from the auditory 1908-9.] Development of Auditory Ossicles in the Horse. 583 capsule itself, which hence makes that theory untenable. Fuchs would go further, and, since he conceived it to be plainly established that the mammalian stapes could have no relationship with the hyoid arch, derive the mammalian stapes also from the auditory capsule, and thus a homologue of the amphibian operculum and stylus. Our problem is, then, to determine the process of development of the mammalian sound-conducting apparatus, and to compare the relationships of its various components with the relationships existing between those ' parts having a similar function or a similar position in the lower vertebrates, in order to determine, if possible, the exact homologies. Before, however, discussing the actual development it is fitting to define an exact position with regard to one or two points. Fuchs has rightly emphasised Reichert’s distinction between the terms visceral arch (Visceralbogen) and visceral bar (Yisceralstreifen). A visceral arch consists of an axis of mesenchyme with an epithelial covering, which is endodermal on the inner side and ectodermal on the outer. Each visceral arch lies between a pair of visceral clefts, and in the arch is developed the visceral bar. Each visceral arch may give rise to one or more visceral cartilages, i.e. in general the first arch gives rise to Meckel’s cartilage and the quadrate ; the second arch gives rise to the hyoid or Reichert’s cartilage (often composed of various elements) and the hyomandibula. I have used the term “ visceral bar ” to refer only to Meckel’s or the mandibular cartilage, Reichert’s or the hyoid ean cartilage and the remaining branchial cartilages. Thus it will be seen that there is a distinction between the quadrate and the first visceral bar and between the hyomandibula and the second visceral bar. Further, it is clear that the visceral arch is an embrvonic structure in which certain skeletal elements later develop, while in the lower vertebrates the visceral bar is a permanent skeletal element. I shall try to show that, contrary to Salensky and some other authors, the only part of the ossicular auditory apparatus to have any connection with a visceral bar is the malleus. The term visceral cleft comprises two distinct kinds of structures, one invaginated from the exterior, the other from the pharynx. The former will be known as gill furrows, the latter as pharyngeal pouches. The first pharyngeal pouch persists as the Eustachian tube, and the first gill furrow as the external auditory meatus.* * It lias again been recently asserted that the Eustachian tube is not the lirst visceral cleft but the second (M. T. Sudler, “ The Development of the Nose and the Pharynx and its Derivation in Man f Amer. Jour, of Anat., i. 1901-1902). However, as the designation of the Eustachian tube as first or second pharyngeal pouch does not affect its actual relations as a structure lying between and separating the Meckelian and Reichertian cartilages, a de- tailed examination of that point is foreign to the present discussion. 584 Proceedings of the Royal Society of Edinburgh. [Sess. II. My investigations were carried out upon a series of horse embryos which Professor Ewart kindly allowed me to study. The series comprised individuals from three weeks until twelve weeks, at weekly intervals, and then various stages up to full term. Of these one, aged four weeks, length 12 mm., was already sectioned and mounted. Models were made of the auditory region of the five- weeks embryo and of a seven-weeks embryo. The three-weeks embryo was found to be so young, showing no skeletal development other than the chorda, as to be of no concern in the present discussion. The four- weeks embryo is important as showing the primitive condition of the visceral clefts. Fig. 6 shows a drawing of a section of the head of this individual passing through the region of the first and second visceral clefts. The first pharyngeal pouch (I. P.P.) is seen to extend latterly and to almost open into the first gill furrow, always, however, with a separating membrane between. From this point the first pharyngeal pouch is seen to be re-bent and to extend medially and dor sally. The second pharyngeal pouch (II. P.P.) extends caudo-laterally until it almost meets the second gill furrow (not shown in figure), being also separated from the latter by a membrane. The ideal condition of the pharyngeal pouches I have shown in a diagram, substantially the same as that employed by Fuchs (text fig. 1, A). The conditions met with in this embryo are different only in that there is an extension of the first pharyngeal pouch medially (marked with an asterisk in figures). This re-bent portion plays an important part in later topographical relationships, for the stapes is developed medial and dorsal to it. The mesenchyme is arranged in dense masses both cranial and caudal to the first pharyngeal pouch, representing the first two visceral arches , and cranial nerves are found running through the mesenchyme. Fuchs has contended that the mandibular arch is lateral to the first pharyngeal pouch. This statement is indefinite, because the first pharyngeal pouch has become extended in one portion while retaining primitive rela- tionships in others. In the ideal condition it is enough to state that a structure lies cranial or caudal to the first pharyngeal pouch to immediately define its position with regard to the visceral arches. But in the four-weeks stage there has already arisen a new complication, and we must give the relative position of a structure with regard not only to the pharyngeal pouch, but also to the prominent flexure of the pouch. Thus it will be seen that in the present stage the mandibular arch lies lateral to the re-bent portion of the first pharyngeal pouch, and also cranial to the point of 1908-9.] Development of Auditory Ossicles in the Horse. 585 flexure. Thus to define the mandibular arch region as being separated from the region of the hyoid arch by a line passing from the extreme distal end of the first pharyngeal pouch to the first gill furrow is obviously a mistake. The plane of separation in this case passes through the prominent point of flexure of the first pharyngeal pouch and through the first gill furrow. Although this embryo shows no skeletal elements which may be definitely identified as such, it is important to further note the condition of the future auditory capsule. In fig. 7 a section is shown through the auditory sac. This appears as a hollow subspherical mass of ectodermal tissue, lying in the mesenchyme between the seventh and ninth nerves. The fifth and eleventh nerves are seen cranially and caudally respectively. Around the auditory sac the mesenchyme is seen to he in a condensed condition, which is an indication of future cartilage formation. Thus we have here the anlage of the auditory capsule, in a very primitive condition. In view of the contention of Fuchs that the stapes is developed from the wall of the auditory capsule, the position of the capsule as it here appears is very important. The seventh nerve runs latero-caudally from the ganglion shown in fig. 7, and crosses the vena capitis lateralis (not shown in the figures) and comes to lie between the latter structure and the outer surface of the head. It then runs caudally and ventrally, coming to lie in the position shown in fig. 6. The vena capitis lateralis shows at this stage the same relations as in the later embryos, that is, it runs dorsal and lateral to the auditory region, being crossed by the seventh nerve, until it reaches the region of the ganglion of the fifth nerve, where it bifurcates and loses its importance in this discussion. Figs. 1, 2 and 3 show three drawings of a model of the auditory region of a five-weeks horse embryo, length 15‘5 mm. The skull shows no sign of cartilage formation except in the posterior cranial portion (chorda and trabeculae) and in the first two visceral bars. The cartilage in these latter structures extends as far dorsal as to the area to be described as the anlage of the malleus, and is shown coloured blue in fig. 8. It is here scarcely yet in the condition of true cartilage, but it is in a very advanced stage of pro- cartilage. More dorsal to the point figured in fig. 8, cartilage disappears entirely except for a small area in the anlagen of the malleus and incus, to be described later. It will thus be seen that the dorsal (proximal) portions of the first two visceral bars are less advanced than their ventral (distal) ends towards cartilage formation. Lateral and somewhat dorsal to the first 586 Proceedings of the Royal Society of Edinburgh. [Sess. third of the first pharyngeal cleft, the mesenchymic area known as the first visceral arch thickens medio-laterally. Moreover, it begins to extend slightly cranially and strongly caudally, enclosing the chorda tympani, until it almost merges with . the hyoid arch. Now the more cranial portion extends in two directions, one dorso-laterally, the other dorso-medially. We have here the first anlage of the incus, with its crus longum and crus breve. The long cranio-caudal area of mesenchyme is the anlage of the malleus. At this time the mesenchymic mass encloses both structures , although their later forms are to be distinguished by certain cell differentia- tions. This distinction is important, and it is on this basis that I have modelled this embryo. The model does not show cartilage and pro-cartilage as distinct from the surrounding mesenchyme — but rather the whole mesen- chymal extent has been modelled. Kastchenko, together with some other investigators, has declared that the external auditory meatus has nothing to do with the spiracular or first visceral cleft. But inasmuch as the present discussion depends little upon whether the external auditory meatus be the first gill furrow or not, it is of no good to enter into that discussion here, except merely to state that the view of Kolliker, Gaupp, and others, that the external auditory meatus is derived from the first gill furrow, seems to have vastly more weight than the contrary hypothesis. The first pharyngeal pouch of the five- weeks embryo will be seen to arise somewhat caudal from the first gill furrow and to extend cranio- laterally for two-thirds of its length. Then it bends sharply, and for the remainder of its length extends medio-cranially. This medio-cranial flexure has apparently escaped Fuchs’ notice. It is marked in the diagram with an asterisk. Now it is evident that in the ideal condition, to speak of a structure as cranial to the first pharyngeal pouch would throw it at once into the territory of the mandibular arch. But as Fuchs rightly points out, to say that a structure is cranial to the first pharyngeal pouch when the relations are those of this stage, does not of necessity make it lie in man- dibular territory, for the mandibular arch in this case lies lateral to the first pharyngeal pouch. Moreover, the first pharyngeal pouch is inclined somewhat dorsally, as is shown in fig. 1, and consequently it is conceivable that a structure ( i.e . stapes anlage in diagrams) might have become so dis- placed by pressure and unequal growth as to lie medial and dorsal to the first pharyngeal pouch and still retain its ontogenetic relation with the first visceral arch. Reference to text fig. 1, B, and to figs. 1 to 3, will show that the mesenchyme has grown between and separated the first pharyngeal pouch 1908-9.] Development of Auditory Ossicles in the Horse. 587 from the first gill furrow by a space of considerable extent. We have here a condition similar to that found in the four-weeks embryo, except that the first pharyngeal pouch is thus separated from the first gill furrow. Moreover, the mesenchyme in extending down between the two structures might he conceived to have carried with it structures derived either from the mandibular or hyoidean arch. But it will be possible to determine from which arch these structures come, provided that they retain some close con- nection with their respective arches. If a structure lies both cranial to the flexure of the first pharyngeal pouch and lateral to the re-bent portion, that Fig. 1. — V. A., visceral arch ; G.F., gill furrow ; P.P., pharyngeal pouch ; S. , anlage of the stapes. structure is clearly in the region which is without question mandibular and which is, in fact, the same region which we have defined as the mandibular arch in the four- weeks embryo. It is in this position that the anlage of the incus lies, and about the ontogenetic relations of the incus there can be then no question. It is clearly developed from the first visceral arch. Medial to the incus anlage a spherical mass of mesenchyme arises, perforated by a minute branch of the carotis interna. This, the anlage of the stapes, lies medial and dorsal to the first pharyngeal pouch and cranial to the prominent point of flexure. F uchs states, in contradiction to Broman (who stated that the stapes arises caudal to the first visceral pouch), that the stapes lies medial to the first pharyngeal pouch, and with this view I have, in an earlier portion, concurred. But this is not entirely exact. The 588 Proceedings of the Royal Society of Edinburgh. [Sess. stapes anlage lies medial and dorsal to the first pharyngeal pouch. The stapes mesenchyme, moreover, extends to the crus longum incudis, and there is no point at which the incus and stapes may be said to be distinct * This relation is shown in fig. 10. The stapes anlage at one point lies very close to the auditory capsule, so close, in fact, as to be almost indistinguishable from it, but always we may find a line of demarcation, whereas the connec- tion between stapes and incus is exceedingly close, the mesenchyme having at all points an equal density. Moreover, the crus longum and the stapes show no signs of differentiation into cartilage. The hyoid bar as cartilage or pro-cartilage extends somewhat farther dorsal than the mandibular cartilage. It then contracts and sends a more or less broad band of mesenchyme to meet the stapes anlage. This is the hyostapedial ligament of Huxley and others, shown in the figures marked with a double asterisk. It is important to note that the entire auditory ossicular apparatus is at this time represented by a more or less homo- geneous mass of mesenchyme. It is impossible to distinguish sharply between the proximal ends of the hyoid cartilage, Meckel’s cartilage, the malleus, incus and stapes. Moreover, it is extremely difficult to draw a line sharply between the stapes and the auditory capsule — although apparently the stapes is much less intimately connected with the latter than with the other elements. I have spoken of the mesenchyme anlagen of the auditory ossicles as being more or less homogeneous. There are, however, within the area certain differentiations which it is important to notice. Fig. 8 (M) shows the Meckelian cartilage beginning to elongate cranio- caudally. This is the first indication of the malleus. The mandibular bar is carried up and into the malleus by a region of advanced pro-cartilage. The malleus is scarcely yet in the condition of pro-cartilage, but its outlines are fairly easy to distinguish by a somewhat denser arrangement of the mesenchyme. Proximal to the malleus, indications of pro-cartilage are observed to occupy a somewhat different position. Fig. 9 is a higher power view of a section distal to fig. 8, and shows the indication of an articulation between the malleus and incus. It will be seen, then, that pro-cartilage is found in the articular portion of the incus and in the distal end of the malleus ; that pro-cartilage indications are found in the malleus, and pro- cartilage is present in the connecting rod between the malleus and the * I found in examining sections of rabbit of seventeen days (length 13*5 mm.) and a mole (length 10'5 mm.) which Dr Beard kindly allowed me to use, that this connection between stapes and incus was less marked in the mole than in the horse, and lacking entirely in the rabbit. However, both individuals (mole and rabbit) were further developed than the four-weeks horse. 1908-9.] Development of Auditory Ossicles in the Horse. 589 cartilaginous portion of Meckel’s cartilage — and in no other 'portion of the auditory apparatus. Inasmuch as there is, even in this early condition, an evidence of a separate development of the incus and malleus, the former can have no possible connection with the first visceral bar. For the first visceral bar is essentially a cartilaginous element and the incus is at all times a separate and distinct element. But, on the other hand, the incus is a structure derived from the first visceral arch — a condition shown by its position, and by its relations with other structures. The incus lies lateral to the first visceral pouch and cranial to the point of flexure, in the territory peculiar to the first visceral arch. It lies also between the seventh and fifth nerves, the course and position of which I will describe later. Moreover, the articulation with the malleus is at this time a simple hinge articulation — of exactly the type that would he expected in a primitive jaw articulation. It is therefore evident that the malleus may he a product of the upper end of the Meckelian bar but that the incus is not. Fuchs has attempted to show that the connection between malleus and the mandibular bar is secondary, finding the mandibular articulation distal to the malleus. This would tend to corroborate the view of Bardeleben and some others that the mammalian lower jaw is a complete homologue of the lower jaw of lower forms. That the connection between Meckel’s cartilage and the malleus is not secondary and that the malleus is indeed developed from the proximal end of the first visceral bar, I shall now attempt to show. I have already called attention to the fact that the connection between Meckel’s cartilage and the malleus anlage was more advanced toward true cartilage than any more proximal portions of the products of the first visceral arch. Fuchs, in a diagram on page 152 of Arch, fur Anatomic und Physiologic, Jahrgang 1905, Supplement-Band, has figured this Meckelian- malleus connection as in an earlier condition of development toward cartilage than either the malleus-incus anlage or Meckel’s cartilage. My investigations do not afford evidence of anything approaching a similar condition. It is true that this connection is in an earlier stage than the more distal portion of the Meckelian bar, but it is more advanced than the malleus-incus portion or than the stapes. Now if the connection between the Meckelian bar and the malleus be fully formed in pro-cartilage before the malleus has reached a similar stage in its development, it seems im- possible to consider that connection as secondarily acquired. Moreover, Fuchs has figured in the same diagram an anlage of the true mandibular 590 Proceedings of the Royal Society of Edinburgh. [Sess. articulation distal to the malleus. I have failed to find this structure in any one of the four earlier embryos — the oldest of which shows the ossi- cular apparatus formed of true cartilage. Now if the mallear-incus articu- lation appears as the only mandibular articulation even at the time when the structures are formed of true cartilage, it follows that the later mandi- bular articulation must be both phylogenetically and ontogenetically acquired very much more recently. Therefore it seems clear that we must accept the reasoning of Gaupp and consider the quadrato-mandibular articulation as represented in the mammalia by the inco-mallear articula- tion. Further, the older view of Salensky, which Hertwig has followed, that both incus and malleus are split off, as it were, from the Meckelian bar, must be given up. The incus appears as a separate and distinct skeletal element developed from the proximal portion of the first visceral arch. The malleus appears at first, and continues to a very late period to be, a dependent portion of the first visceral bar. Before considering the relations of the stapes it appears advantageous to give a brief account of the courses of the main branches of those cranial nerves pertinent to our discussion, leaving, however, the elucidation of the facts rather largely to an examination of the figures. There are, of course, three nerves which bear an important relation to the auditory ossicles — the trigeminus, facial, and the vagus group, indi- cated in the figures by the numerals V., VII., and IX. The facial nerve exhibits the most important relations. The first branch (large superficial petrosal) is given off soon after the nerve leaves the ganglion. This branch runs medially and ventrally, and is of small moment here. The main trunk then bends slightly dorsal, along with the vena capitis lateralis, and runs almost directly caudal till it reaches the dorsal end of the hyoid bar. It is, moreover, dorsal to the tympanic cavity, so that all of the auditory ossicles must be ventral to it. At the proximal end of the hyoid it curves sharply latero-ventrally, sending off a small twig to the external ear and a larger branch — the chorda tympani. The chorda tympani skirts the hyoid bar and plunges into the mesenchymic mass surrounding the malleus and incus at the latero-caudal end, thence it runs cranio-medio-ventrally to emerge from the mesenchyme at the medio-caudal side of Meckel’s cartilage. Beyond the juncture of the main trunk and the chorda tympani the main nerve runs latero-ventrally and becomes un- important in the present discussion. Thus it will be seen that the auditory ossicles come to lie in a flexure of the seventh nerve — but that, nevertheless, they also lie in a position between the fifth and seventh nerves. It has been shown that the stapes arises medial and dorsal to the first 1908-9.] Development of Auditory Ossicles in the Horse. 591 pharyngeal pouch. Fuchs has nowhere figured or modelled the exact shape of this pouch as I have found it in the horse. The cranial reflexed portion which I have marked with an asterisk does not appear in his work. But the stapes anlage is in a very important position with regard to this portion of the first pharyngeal pouch. This position I have attempted to show in text fig. 4. It will be recalled that the stapes is related through mesenchyme to two distinct structures, the hyoid cartilage and the incus. This connec- tion between the hyoid and stapes represents the hyostapedial ligament of Huxley. Fig. 4 shows a model of the auditory ossicles of an embryo of seven weeks. It will be here seen that there is no such connection (marked ** in figures). In the stage represented in fig. 4 the entire auditory apparatus was cartilaginous. In an embryo of six weeks the same parts are of very young cartilage, and no hyostapedial connection is evident. It therefore seems plain that this connection never reaches the state of cartilage. Moreover, as Fuchs has shown, the distal end of the hyoid cartilage, as shown in figs. 1, 2, and 3, is not the true distal end, but the cartilage grows somewhat more dorsal than that point. The connection between hyoid and stapes, then, is to be considered as never attaining the dignity of a skeletal element. Moreover, a study of the drawings of the model and of fig. 11 will show that the stapes lies between the seventh and fifth nerves, while the hyoid arch lies between the seventh and ninth. The trigeminus ganglion has been omitted from the drawings of the models for the sake of simplicity, but it is shown clearly in fig. 11. In other words, the connection between stapes and the hyoid bar crosses the seventh nerve. This is shown in figs. 1 and 3. But that being true, there is no other possibility than to regard, with Fuchs, the hyostapedial ligament as a structure whose relation to the auditory ossicles must be purely secondary. It appears the more evident when certain histological characters are considered. An examination of the figures will show that the area marked in the figures ** is histologically different from the surrounding mesenchyme. This point has been amply dealt with by Fuchs. From the foregoing it is evident that the stapes has nothing at all to do with the second visceral bar. It is now pertinent to examine it with regard to its relations with the second visceral arch. We have seen that in its topographical relations the stapes shows characteristics which would seem to preclude the possibility of its being a product of the second arch — in that it lies medio-dorsal to the first visceral pouch, and between the seventh and fifth nerves. 592 Proceedings of the Royal Society of Edinburgh. [Sess. Hertwig, following Rabl, has given as his main reason for considering the stapes to be in part a derivation of the hyoid that the innervation of the M. stapedialis is from the seventh nerve. Moreover, the stapes is perforated by a branch of the carotis interna. Kingsley has stated that the malleus and incus are obtruded into the tympanic cavity from in front, i.e. are pre-spiracular, while he leaves one to infer that the stapes is obtruded from the back. Disregarding the lack of accuracy involved in such a statement, it appears that in the position of the stapes and in its relationship with the visceral arches we have to deal with a problem which is complicated by an enormous amount of shifting of position that has occurred during the growth of the embryo, and that such a statement is not an answer to our question. F uchs has come to the conclusion that the stapes is derived from the wall of the auditory capsule. With that view, which was the earlier view of Parker, Gaupp agreed in his earlier papers. More recently he has come to doubt the strength of that position. Hertwig concludes that the stapes is in part derived from the auditory capsule, and in part from the hyoid arch. Opposed to the arguments derived from the position of the stapes are the arguments of Rabl as to the nerves, and the argument drawn from the position of the arteria stapedialis. Miss Platt has stated clearly that muscles are phylogenetically older than the skeletal elements. The primitive con- dition, then, shows the muscles inserted into the integument, at which points cartilaginous bars were later developed. Now, in none of the embryos of from four to seven weeks is there any indication of a stapedius muscle. The first appearance that I have found of this muscle is in an embryo of about three months (fig. 12). I have studied no individuals of ages between seven weeks and three months, so that I do not know the exact time when the muscle appears. But inasmuch as the muscle appears very much later than the skeletal elements, and since even at four weeks the muscles of the neck are indicated, it would seem that as a diagnostic character the muscle is of small value — at least, not to be compared with arguments from relative position. Inasmuch, then, as the stapedialis muscle is innervated from the seventh nerve, and since the whole argument hinges on this point, I believe that, unless we have stronger corroboration, the fact that the stapes and N. facialis are related in this way must be regarded in the light of secondary evidence. The internal carotid may be seen in figs. 1, 2 and 3, just skirting the auditory capsule, running cranio-caudally between the capsule and the first pharyngeal pouch, ventral to the latter. Just as it is about to pass the 1908-9.] Development of Auditory Ossicles in the Horse. 598 cranial border of the first pharyngeal pouch, a minute branch is given oft" which runs cranio-laterally and perforates the stapes anlage, thence pro- ceeding cranio-laterally between the vena capitis lateralis and the anlage of the malleus and incus. Now, were the arteria stapedialis clearly the second aortic arch, one would be justified in considering that the perforation of the stapes by it was strong evidence in support of the claim that the stapes anlage were closely related to the second visceral arch. Tandler has shown that in the case of the rat and of man the arteria stapedialis is derived from three different structures. From the point at which it arises from the aorta dorsalis up to the stapes, it is the dorsal portion of the second aortic arch. From that point on the artery with its rami consists of structures which are either developed secondarily or from the first aortic arch. Thus the portion which actually perforates the stapes anlage is not developed from the second aortic arch. Moreover, the stapes of monotremes and of certain marsupials is not perforated by an artery. So then, if the stapes is developed similarly throughout the mammalia, the relations between it and the arteria stapedialis cannot be regarded as indications of its derivation. Thus it is seen that there is at present no evidence weighty enough to overbalance that drawn from considerations of relative position, and we must therefore conclude that the stapes is related neither to the second visceral bar nor to the second visceral arch. Fuchs arrived at this same conclusion, but went further and declared the stapes to be derived from the auditory capsule. We have seen that there is difficulty in visually separating the stapes from the auditory capsule at all points. Now let us agree that the stapes is developed from the mesenchyme of the capsule, and with that in mind examine some more fully developed stages. Text fig. 2 shows a section through the stapes and incus of an embryo of six weeks. The stapes and incus are just between a condition of pro- cartilage and true cartilage, and the cochlear portion of the auditory capsule is in the same developmental stage. The fenestra ovalis is clearly to be seen closed by a mesenchymous membranous indication. The vesti- bular portion of the capsule is still undifferentiated mesenchyme. The stapes is seen to be impinged against the closing membrane of the fenestra. Text fig. 3 shows a section through the same region of a seven-weeks embryo. Unfortunately the sections are not upon exactly the same plane, so that the one shows the incus, the other the vestibular portion of the capsule. However, the relations between fenestra ovalis and stapes are similarly shown. All the parts are now cartilaginous. The stapes is vol. xxix. 38 594 Proceedings of the Royal Society of Edinburgh. [Sess. obtruded into the fenestra ovalis. By referring to fig. 11 one sees the obtrusion of the stapes into the fenestra carried a step farther, and the portion enclosed in the fenestra is expanding to form a plate. Contrary to Hertwig, the plate and ring portion of the stapes are not developed separately. Moreover, we have a gradual shifting of the relative posi- Figs. 2 and 3. — S., stapes; A.Cx., auditory capsule, cochlear portion; A.Cn., idem-vestibular portion; VII, facial nerve; I. P.P., first pharyngeal pouch ; I., incus ; H., hyoid. tions of stapes and capsule, the direction of movement being toward the latter. If Fuchs is right the stapes must first be separated off from the auditory capsule and then afterwards push its way back into the fenestra. Consider again that in the early anlage of the auditory capsule there is no indication of a fenestra. The inference is that the capsule in chondri- fying simply leaves a space closed by mesenchyme, which later becomes the fenestra ovalis. There are a few sections which might indicate, as Fuchs 1908-9.] Development of Auditory Ossicles in the Horse. 595 has shown diagrammatically, that the stapes is cut off from a protuberance of the capsule, but in the model this slight swelling is seen to form the caudal boundary of the fenestra ovalis and to continue beyond the point of contact of the stapes. Moreover in the four- weeks embryo the vena capitis lateralis lies between the external surface of the head and the auditory capsule, and at this stage the auditory capsule shows no indication of any mesenchymic differentiation. In the five- weeks embryo the auditory capsule is quite distinct from the stapes, except for a very limited area. And the stapes at this stage is seen to lie not medial to the vena capitis lateralis, but dorsal to it. It will be recalled that in the four- weeks embryo the auditory capsule anlage lay between the seventh and ninth nerves. As development has proceeded, it is evident that the seventh and fifth nerves have come to lie more closely together, with a resultant shifting of the position of the capsule. But, as has been shown, the stapes arises in the area between the seventh and fifth nerves. I regret my inability to examine additional stages between those represented by the two embryos whose ages are four weeks and five weeks, but it is highly improbable that there would have been any great relative changes in the position of the various anlagen. To derive the stapes from the second arch would involve carrying it around the first visceral pouch. To derive it from the auditory capsule would imply a complicated process which would have certainly resulted in some more definite indication than we have in my second (five- weeks) stage. It is not at all surpising that the mesenchyme seemingly connects the capsule with the stapes, inasmuch as whenever two structures are developed closely together, the mesenchyme of their anlagen tends to become very difficult of visual separation. Moreover, if the auditory capsule and the stapes were from the same anlage, the stages of their development towards cartilage and later bone ought to bear a certain amount of relation one to the other. But this is not borne out by the facts. I have therefore come to the conclusion that the stapes cannot be developed from the auditory capsule. But if it is developed from neither the auditory capsule nor the second visceral arch, the question arises — Whence does it come ? The fact that the stapes lies medial and cranial to the first pharyngeal pouch, while it excludes the second arch, does not exclude the first arch from the formation of the stapes. For the stapes lies also dorsal to the first pharyngeal pouch, and cranial to the point of flexure. Fig. 1 shows also that the incus, which is undoubtedly derived from the 596 Proceedings of the Royal Society of Edinburgh. [Sess. first arch, also lies slightly dorsal to the first pharyngeal pouch. Again,, the stapes is clearly in the area between the fifth and seventh nerves. It would appear from the model that the stapes were between the large superficial petrosal branch of the seventh and the main trunk which bends around the hyoid. But by reference to fig. 11 the stapes will be seen to lie between the facial nerve and the trigeminal ganglion just as truly as does the incus. Moreover, the stapes is connected to the incus very closely > as is shown in fig. 10. In view of the evidence submitted I consider it to be clear that — 1. The whole ossicular chain is developed from the first visceral arch. s> C.L Fig. 4. — A.C. , auditory capsule ; C.L., crus longum incudis ; G.I., gill furrow; C.B. , crus breve incudis; H., hyoid; M., Meckel’s cartilage ; Ma., malleus ; P.P., pharyngeal pouch. 2. That the malleus alone is related to the first visceral bar. These relations are shown in text fig*. 4. III. There remains to discuss the possible homologies of the auditory ossicles. Reichert’s view that the malleus is the liomologue of the articulare and the incus of the quadrate, so admirably fills all the conditions of an exact homology that one is tempted to let the discussion end there. But clearly the articulare can be but a portion of the malleus, owing to the fact that the former is a covering bone and the latter is not so entirely. With this view the majority of authors substantially agree, as Parker (II.), Gradenigo, Gengenbaur, Salensky, Hertwig, Kingsley, Wiedersheim, Dollo, 1908-9.] Development of Auditory Ossicles in the Horse. 597 Rabl, Gaupp, and many others. As we have seen, the malleus and incus are derivatives of the first arch ; their articulation satisfies the proper conditions ; they are so similarly related to the chorda tympani and to the seventh nerve that I feel it unnecessary to argue at great length that they are homologous with the articulare and quadrate. Moreover, Gaupp’s discussion of that question is admirable, and may be considered final. The hypothesis held by Gadow, Albrecht, in part by Fraser and some others, that either one of these two elements is a derivative of the second arch, will not bear close analysis. Parker, followed by Gaupp’s first position, and Fuchs, together with many other investigators, have believed the stapes to be derived from the auditory capsule either wholly or in part, thus making it homologous with the sauropsidan stapedial apparatus. Others, as Gadow, Albrecht, Wieder- sheim, and many more, have believed the stapes to be homologous with the hyomandibular of fishes. As to the conditions met with in the Amphibia, I know them only through the literature. Miss Platt gives for necturus the fact that the operculum arises independently of the auditory capsule, and Killian for axolotl, whilst Stohr for triton and siredon derives the operculum from the anterior boundary of the fenestra. For the Anura he derives the operculum from a different portion of the auditory capsule. Fuchs, however, has I think clearly shown that the amphibian stapes is derived from the auditory capsule and the extra-collumella from the hyoid arch. The conclusion is at once drawn that the mammalian stapes is on no account homologous with the sauropsidan operculum plus the accessory parts. Peter has shown in the development of the skull of Ichthyophis glutinosis that the stapes is closely connected to the quadrate. But the stapes-quadrate connection is in the vicinity of the quadrato-mandibular articulation, whilst the mammalian stapedo-quadrate connection is at an entirely different region. Unless it can be shown, then, that the Amphibia develop two types of accessory auditory apparatus, it is impossible to consider the mammalian stapes as a representation of any structure found in the Amphibia and reptiles. And inasmuch as the hyomandibula of fishes is a derivative of the second arch, it is impossible to conclude that the mammalian stapes is homologous with it ; and the stapes cannot be a portion of the quadrate, because it is chondrified from a separate centre. Moreover, there are no other possible homologues, and therefore one is forced to conclude that the mammalian stapes has no homologue in the lower Vertebrata. 598 Proceedings of the Royal Society of Edinburgh. [Sess. IY. A brief summary of the principal conclusions to which I think my preparations lead is as follows : — 1. (a) The malleus, stapes, and incus are derivatives of the first visceral arch. In the case of the malleus and incus, this is evident from their position and relations with other structures. In the case of the stapes, the exact correlation of parts is more obscure, but it has been shown that, owing to twisting and compression, the stapes anlage has become shifted so that it lies dorsal and medial to the re-bent portion of the first pharyngeal pouch, but that it lies also cranial to the point of flexure. Inasmuch as in an early stage this point of flexure is a cardinal point in the topography of the region, the position of the stapes with regard to it, in addition to the relationship shown by the stapes with other structures, precludes the possibility of the stapes having been derived from the hyoid arch. But there is nothing in the position of the stapes nor in its other relation- ships to preclude the possibility of its having been derived from the first arch. And as the stapes has been shown to be independent of the auditory capsule, it is evident that it must be a derivative of the mandibular arch. (6) The stapes and incus are at all times structures distinct from the Meckelian bar, being chondrified independently. The malleus, on the other hand, is continuous with the proximal end of Meckel’s cartilage, and the connection between them is of a jDrimary nature. 2. The stapes cannot be homologous with any structure found in the lower Vertebrata, for it is derived from the first arch, whilst the amphibian and reptilian stapes is either derived from the auditory capsule or from the second arch, and the hyomandibula of fishes is also derived from the second arch. Thus the mammalian stapes must be regarded as a structure peculiar to that group. The malleus and incus are, however, homologous with the articulare (in part) and the quadrate of the lower groups. My thanks are due to Professor Cossar Ewart for the material for these investigations, and for many helpful suggestions, and it is from his laboratory that this communication is offered. It is a great pleasure to acknowledge my indebtedness to him and to Drs Beard and Ashworth of the Edinburgh University Zoological Department. A grant towards the expenses of the investigation has been made from the Earl of Moray Endowment Fund of the University of Edinburgh. 1908-9.] Development of Auditory Ossicles in the Horse. 599 LITERATURE. 1883. Albrecht, P., Sur la valeur morphologique de V articulation mandibulaire du cartilage de Meckel et des Osselets de Vouie , Bruxelles. 1905. Bardeleben, v. K., “Der Unterkiefer der Saiigetiere, besonders des Menschen,” Anat. Anzeiger , vol. xxvi. 1905. Bardeleben, v. K., “Die Homologie des Unterkiefers in der Wirbeltier- reiche,” Anat. Anzeiger Ergeb. 1907. Bardeleben. v. K., “Zur vergleichenden Anatomie besonders Palaon- tologie des Unterkiefers der Wirbeltiere,” idem , 1907. 1905. Fuchs, Hugo, “ Bemerkungen ueber die Herkunft und Entwickelung der Gehorknockelchen bei Kaninchen-Embryonen, etc.,” Archiv fur Anat. und Physi- ologic, Anat. Abthlg. (Supplement). 1906. Fuchs, Hugo, “ Nachtrag zu meiner Arbeit. Bemerkung fiber die Herkunft, etc.,” idem. 1907. Fuchs, Hugo, “Ueber die Entwickelung des Operculums der Urodelen, und des Distalidimus (Columella auris) einiger Reptilien,” Anat. Anz. Ergeb., 1907, p. 8, 34. 1888. Gadow, “ On the Modifications of the First and Second Visceral Arches, etc,,” Phil. Trans., 1888, vol. clxxix., B. 1898. Gaupp, E., “Ontogenese und Phylogenese des schall-leitenden Apparates bei den Wirbeltieren,” Merkle und Bonnet's Ergebnisse, p. 990. 1905. Gaupp, E., “Die Nicht-Homologie des Unterkiefers in der Wirbelthier- reiche,” Anat . Anz. Ergeb. 1907. Gaupp, E. (Discussion of Fuchs’ paper in 1907), idem. 1872. Gegenbaur, Das Kopfskelet der Selachier , etc., Leipzig, 1872. 1898. Goppert, E., “Der Kehlkopf der Amphibien und Reptilien,” Morphology Jahrbuch. 1887. Gradenigo, G., “Die Embryonale Anlagens des Mittelohres ; die mor- phologische Bedenkung der Gehorknockelchen,” Mitth. a. d. Embry ol. Inst. d. Unin . Wien, Heft 1887. 1869. Huxley, “On the Representations of the Malleus and Incus of the Mammalia in the other Vertebrate,” Proceed. Zool. Soc., 1869. 1905. IIertwig, O., Embryology of Alan and Mammals , translated from the third German edition by E. L. Mark. London, Swan Sonnenschein & Co., 1905. 1880. His, Anatomie Mensclier Embry onen, Leipzig, 1880. 1890. Killian, G., “Die Olirmuskeln des Krokodils, nebst vorlaufigen Bemer- kungen ueber die Homologie des Musculus stapedius und des Stapes,” Jenaische Zeitschrift filr naturwissenschaften, Bd. xxiv., N.F.B. xvii., 1890. 1890. Killian, G., “Zur vergleichenden Anatomie und Entwicklungsgeschichten der Olirmuskeln,” Anat. Anz., Bd. v. • 1904-05. Kingsley, J. S., “The Mammalian Lower Jaw,” Proceed. American Soc. Anatomists, 1904-05 (in outline, Amer. Journ. Anat., vol. iv.). 1906. Kingsley, J. S., Vertebrate Zoology. New York, Henry Holt & Co. 600 Proceedings of the Koyal Society of Edinburgh. [Sess. 1871-85. Parker, W. K., Various papers in Phil. Trans.,' in Trans. Linn. Society, vol. ii., and in Trans. Zool. Soc., vol. ii. 1898. Platt, Julia B., “The Development of the Cartilaginous Skull and of the Branchial and Hypoglossal Musculature in Necturus,” Morph. Jahr. 1898. Peter, K., “ Die Entwickelung und funktionelle Gestaltung des Schiidels von Ichthyophis glutinosis,” Morph. Jahr. 1837. Peichert, C., “Ueber die Visceralbogen der Wirbelthiere in Allgemeinen und deren Metamorphose bei den Vogeln und Saugethieren,” Arcliiv fur Anat. u. Physiol, und Wissenschaftliche Medicin, 1837. 1887. Babl, K., “Ueber das Gebiet des Nervus facialis,” Anat. Anz., 1887, Abt. 2. 1879. Stohr, Ph., “ Zur Entwickelungsgeschichte des Urodelenschadels,” Zeitschrift f. Wissen. Zool., Bd. xxxiii. 1881. Stohr, Ph., “Zur Entwickelungsgeschichte des Anurenschadels,” idem, Bd. xxxvi. 1880. Salensky, W., “Beitrage zur Entwicklungsgeschichte der knorpeligen Gehbrknbckelchen bei Saugethieren,” Morph. Jahr., Bd. vi. 1902. Taudler, J., “Zur Entwicklung-geschichte der Kopfartieren bei den Mammalia,” Morph. Jahr., Bd. xxx. 1877. Wjedersheim, R., “ Das Kopfskelett den Urodelen,” Morph. Jahr., Bd. iii. 1907. Wtedersheim, R., Comparative Anatomy of Vertebrates, trans. by W. N. Parker. 3rd edition, founded on the 6th German edition. London, Macmillan & Co. Ltd., 1907. EXPLANATION OF FIGURES. A.C. Auditory capsule. 1, cochlear, and 2, vestibular portion. A.S. Arteria stapedialis. Br. Barin. C.B. Crus breve incudis. C.I. Carotis interna. C.L. Crus longum incudis. Cli. T. Chorda tympani. E.A. External auditory meatus. G.F. Gill furrow. H. Hyoid cartilage. I. Incus. Ma. Malleus. M. Meckel’s cartilage. Ph. Pharynx. P.G. Processus gracilis. P.P. Pharyngeal pouch. S. Stapes. V.C.L. Vena capitis lateralis. Y. Eye. A. Auditory pit. Figs. 1, 2, and 3. Model of the auditory region of a five-weeks horse embryo (length 15 ’5 mm.), magnified 41 diameters. The auditory capsule and the ventral portion of the firs pharyngeal pouch are left incomplete. This model shows the mesenchyme areas, and not pro-cartilage or cartilage. Fig. 4. Model of the auditory ossicles of a horse embryo of seven weeks’ development (length 21 mm.), magnified 30 diameters. In this model the auditory ossicles only are shown complete. Proc. Roy. Socy. of Edin.] [Vol. XXIX. DORSAL A.S. m □ > r VENTRAL Fig. 1. CRANIAL Ma. V.C.L. Mr Hay F. Coylk. [Plate L MEDIAL MEDIAL Froc. Boy. Socy. of Edin. ] CRANIAL [Vol. XXIX. A.C. * VII S. V.C.L. A.S. C.B. Ma. M. Ch.T. CAUDAL Fig. 3. Mr Ray F. Coyle. Fig. 4, [Plate IL Proc. Roy. Socy. of Eclin. ] [Vol. XXIX. Fig. 8. I. Fig. 9. Me Ray F. Ooylf. [Plate III, Proc. Roy. Socy , of Edin. ] [Vol. XX3X Mr Ray F. Coyle, [Plate IV P-roc: Roy. Socy. of Edin. j [Vol. XXIX. Fig. 5. Ph. v. i: • :y ■' .-.‘V-'i/'-V/:-" '■ ■’ ■ ' ■*£;*>■ ■ : V- . - ' • ■ . : - *-r:’ ’• * ' *• . • * * *‘'-V '* V .^V* - Ev\ ?. - Fig. 7. Fig. 6. Mr Ray F. Coyle [Plate V Proc. Roy. Socy. of Ed An. ] [Yol. XXIX, A.S. Fig. 10. VII G.V. A.C. A.S. C.l. IX Fig. 11. Mr Ray F. Coyle. [Plate VI. 1908-9.] Development of Auditory Ossicles in the Horse. 601 Fig. 5. Auditory ossicles of a horse at term (the hones are here fully ossified), magnified three diameters. Fig. 6. Section through the first and second pharyngeal pouches and the first gill furrow of an embryo aged five weeks (length 12 mm.). x 32 diam. Fig. 7. Section through the auditory sac of the same embryo. x 54 diam. Fig. 8. Section through the proximal end of Meckel’s cartilage and the anlage of the malleus of a horse embryo aged five weeks. Blue represents pro- cartilage. x 66 diam. Fig. 9. Section through the maleo-incus articulation of the same embryo, x 208 diam. Fig. 10. Section through the stapes and incus anlagen of the same embryo, x 42 diam. Fig. 11. Section dorsal to fig. 10 through the stapes anlage of the same embryo, showing the arteria stapedialis. x 36 diam. Fig. 12. Section through the stapes and incus (crus longum) of an embryo aged about three months. The cartilage is shown blue. The stapes, incus, and vestibular portion of the auditory capsule show the beginnings of ossification. x 42 diam. (Issued separately September 9, 1909.) 602 Proceedings of the Royal Society of Edinburgh. [Sess. XXXVI. — Dr O. Pettersson’s Observations on Deep Water Oscilla- tions. By E. M. Wedderburn, W.S. (With a Plate.) (MS. received July 5, 1909. Read July 5, 1909.) Dr Pettersson has recently published a paper on “ Gezeitenaehnliche Bewegungen des Tiefenwassers ” ( Publications de Gir Constance , No. 47), in which he describes certain movements in the deep waters of the Skagerak observed in January, February, and March 1909 at the Swedish station Borno, in the Gullmarfjord, lat. 58° 24' N., long. 11° 33' E. The observations were taken daily at 12.30 p.m. by means of soundings made through the ice. The diagram accompanying this paper is a reproduction of a diagram prepared by Dr Pettersson, and shows the observed variations in the position of the isotherms and isohalines. No observations appear to have been made on 7th, 8th, 10th, and 11th February, nor from 15th to 18th March, so that there are large interpolations on the diagram. Fig. 1 is a map of the Skagerak, the point of observation being marked by a cross. There is a marked discontinuity in the density of the water of the Skagerak at this time of year at a depth which averages about 20 metres. The presence of this discontinuity is shown in all the observations. The following set of observations for 10th March is an example : — Depth, Metres. Temp. Celsius. Density. 0 •05 1-00212 10 '42 1-02315 20 •85 1-02387 25 3-98 1-02675 30 5-41 1-02670 40 5-88 1 02701 49-5 5-95 1-02701 The observations show an oscillation in the level of the discontinuity with a period of about fourteen days, which Dr Pettersson seeks to explain as a long-period tide in the lower dense layer, and states that the moon seems to have a tendency to accumulate the deep water of the Skagerak against the eastern coast whenever it attains a high northerly or southerly declination, and suggests that a yearly oscillation may, in the same way, be produced by the influence of the sun. He justly adds, however, “ It is difficult to imagine how this attraction can act in a different manner upon 603 1908-9.] Observations on Deep Water Oscillations. two water-layers (the surface water and the deep water) in the same part of the ocean. Likewise, the idea of tidal waves of so long periodicity as those described in the annexed diagram existing in such a limited part of the ocean as Skagerak presents almost insurmountable difficulties, whether they are assumed to have the character of forced or free waves. On the contrary Fig. l. The contours show depths every 50 fathoms. the whole character of the phenomenon bears out the idea that it is essenti- ally an oscillation in the deep water of the ocean, the origin of which must be left to future investigation to discover.” The observations of the Scottish Lake Survey have shown the presence of oscillations in the lower water of deep lakes during the autumn of the year, when there is a layer of warm water of uniform temperature super- imposed on the colder abysmal waters. When the boundary between the 604 Proceedings of the Poyal Society of Edinburgh. [Sess. upper and lower layers is sufficiently distinct, an internal (or temperature) seiche takes place in the lower layer, the period of which can be approximately calculated from the formula t= 2 l j g(p - p) h ii where p and p , h and h' are respectively the densities and depths of the upper and lower layers, and l the length of the lake.* In Loch Ness the period of this internal seiche was about three days, in Loch Garry about twelve hours. We also know from the elaborate observations on secondary undulations of oceanic tides carried out for the Earthquake Investigation Committee of Japan by K. Honda and others ( Journal of the College of Science, Tokyo, vol. xxiv., 1908), that in deep bays secondary undulations or seiches are of frequent occurrence, with a period given by the formula t = the node of the seiche being at the mouth of the bay, and the ]oop being at the end of the bay. It was suggested to me by Sir John Murray that the oscillations observed by Pettersson might be analogous to those observed by the Lake Survey, and it is not a very large stretch of imagination to suppose that Pettersson’s observations really show the presence, not of a long-period tide, but of a temperature seiche, having its node at the mouth of the Skagerak and its loop at the point of observation. A glance at the map will show that the basin is deep and well-defined, and that all the conditions favour an oscilla- tion of the lower dense layer of water. The period of such an oscillation should be given by the formula t = jk fi(p ~ p) t+i h K The line drawn on the map shows what may be taken as the mouth of the Skagerak, and the length of the basin is about 200 km. The Japanese observers found that a mouth correction had to be applied in calculating the period of a seiche in a bay ; and in the case of a basin of the breadth of the * Cp. Geogr. Journal , vol. xxiv. p. 430 ; Trans. Roy. Soc. Edin vol. xlv. p. 420 ; Proc. Roy. Soc. Edin., vol. xxviii. p. 1 ; ibid., vol. xxix. p. 98. 605 1908-9.] Observations on Deep Water Oscillations. Skagerak this correction is about 25 per cent, of the length,* making the effective length of the basin 250 km. In calculating the period of a temperature seiche in the Skagerak by the above formula, I assumed as the depth of the upper layer 20 metres and as its density h023. For the depth of the lower layer, I took first a depth of 100 metres and then a depth of 200 metres. The mean depth of the basin, calculated by taking the square of the mean of the square roots of the depths marked on the chart, was about 180 metres, which gives for the depth of the lower layer 160 metres. It is therefore thought that the true period for the basin should lie between the two calculated periods. These were respectively 14*2 days and 13‘9 days. This period is in very close agreement with the period observed by Dr Pettersson, and to my mind there is little doubt that the oscillations are not tidal, but are analogous to the oscillations observed in Loch Ness and Loch Garry, and also in the AVolfgangsee by Dr Exner. Dr Pettersson also gives a few observations made at Revsnoes, in the Great Belt, in July 1908, which indicate an oscillation of the deeper water with a period of about a day. They are too few to state the period of the oscillation with any certainty, but a calculation similar to the above shows that in a basin about 25 km. long there might be an oscillation with a 24- hour period. The basin of the Great Belt is very irregular, and it is difficult to know what may be the length of the basin in which an oscillation would take place. It seems likely, however, that the July observations also record the presence of an internal or temperature seiche. On several occasions the observations made by Sir John Murray in the sea-lochs of the West of Scotland showed oscillations in the bottom dense layer of water; and although the observations were not continued for a sufficient length of time to show whether the oscillations were periodic or aperiodic, it is quite likely that they, too, were due to an internal seiche.f Pettersson ’s observations were discussed at a meeting of the “ Challenger” Society held on 30th June 1909, and those present were practically unanimous in considering the tidal effect as a minor element. Dr Everdingen, however, pointed out that if there was a great interchange of water with the diurnal tides, similar curves would result from the fact that all the observations were made at the same hour each day, and thus at a later phase of the tide which would recur in about fourteen days. It is most unlikely, however, that the daily tides could produce anything like a range of 100 metres in the level of the lower layer of water ; and the feeling of the meeting was that * Op. cit p. 60. t E.g. see observations in Locli Etive in 1888, Proc. Roy. Soc. Eclin ., vol. xviii. p. 158. 606 Proceedings of the Royal Society of Edinburgh. [Sess. the suggestion of an internal seiche, communicated by Sir John Murray, was the correct one.* It is, of course, possible that the oscillations may be to some degree forced by tidal influences, and there is nothing new in the idea of a forced seiche, as Dr Pettersson seems to think, j- Pettersson adds, that whatever may be the main cause of the phenomena, there can be no doubt of their influence upon the fish-life and the fisheries of our seas. In 1877, G. Ekman discovered that herring shoals vanisiied suddenly from the Swedish fjords and from the coast bank whenever the ice-cold Baltic water accumulated there. In 1909, the greatest fish catches were made from 1st to 6th February and from 20th to 23rd February, when the warm and salt deep water had its periods of flow. In the ebb periods the fishery was almost nil, and ceased altogether about 27th February. It may be some satisfaction to people who think that scientific work should not be undertaken without a practical end in view, to know that the temperature observations made by the Scottish Lake Survey may bear fruit in a better understanding of the movements of herring shoals. * I am indebted to Dr H. R. Mill for a report of this meeting. t See Chrystal, “ Hydroclynamical Theory of Seiches/’ Trans. Roy. Soc. Edin ., vol. xli., part iii., p. 608, 1905 ; also ibid., vol. xlvi., part iii., p. 514. ( Issued separately August 14, 1909.) Proe. Roy. Socy. oj Ertin.] [Vol. XXIX. Mr E. M. Wedderburk, 1908-9.] Mendelian Action on Differentiated Sex. 607 XXXVII. — Mendelian Action on Differentiated Sex. By D. Berry Hart, M.D., F.R.C.P.E., Lecturer on Midwifery, Surgeons’ Hall, Edinburgh; Carnegie Research Fellow. (From the Laboratory of the Royal College of Physicians.) (Abstract.) It has long been known that the male and the female human genital tract contain not only organs characteristic of their sex proper, but also certain parts of the opposite sex in a less developed but yet perfectly definite form. Thus the female genital tract is made up of, not only its characteristic organs, the ovaries, tubes, uterus, etc., but also the epoophoron (parovarium) and its duct, the equivalent of the epididymis and ductus epididymis of the testis. In the same way, the human male has his characteristic sexual organs and also the appendix testis and prostatic utricle, the representatives of the fimbriated end of the Fallopian tube and of the lower end of the vaginal tract (hymen mainly, but varying). The significance of these facts has not been hitherto definitely investi- gated, and it occurred to me, in the course of a study of Mendelism in relation to the nature of sex, that the genital elements already defined might be considered as potent and non-potent, or as dominant and recessive in Mendel’s terminology, and as elements on which Mendelian action took place and could thus be studied. Mendel showed in his variation experiments with the eating-pea, that if peas with each one contrasted character,* such as tallness and dwarfness, the other characters being common, were crossed, all the plants were tall in F1, while in the subsequent selfed. generations the tall- ness and dwarf ness segregated in the ratio of D : DR : R as 1 : 2 : 1. This means that of the plants one quarter bred true to tallness (D), one quarter to dwarfness (R), while one half (DR) gave always DR : R as 3 : 1. It was found in the crossing experiments that it made no difference in the results which plant, tall or dwarf, was used for pollination. Mendel described the tallness as a dominant unit-character, D ; the dwarf- ness as recessive, R ; while the tall plant giving tails and dwarfs 3:1 is termed an impure dominant, DR. * Menclel chose seven characters, of which I select the one given above for illustration. 608 Proceedings of the Royal Society of Edinburgh. [Sess. The results can therefore be tabulated as follows : — If D be the term for dominant, R that for recessive, DR that for impure dominant, P for the first crossing plants, and F^F" for the subsequent generations, we have D X R P tall || d warf DR impure D F1 1 D* DR Rt F2 1 : 9 : 1 3 : 1 Mendel established, therefore, that the qualities which make up a plant may be considered as unit-characters, and that the ones selected for study, whether single or coupled, were autonomous, that is, did not blend, and ultimately segregated into D : DR : R as 1:2:1. DR always gives D : R as 3:1. Thus in the tall-dwarf crossing, the plants in the subsequent generations were not intermediate in height between tallness and dwarfness, but segregated the parental selected unit-characters practically unaltered. To explain this, Mendel advanced his theory of gametic segregation. He supposed that his unit - characters of tallness and dwarfness were segregated pure in the gametes of the tall and the dwarf plant respectively. He stated his theory in the simplest case as follows. If A be the dominant character, a the recessive, and Aa the impure dominant (Mendel’s hybrid), then A + 2Aa>-\-a gives the terms in the series for the progeny of the impure dominants of two differentiating characters. (A +5 2s. 6d. No. XXXVI., • 11 9d. No. XXXVII., )) 8d. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SESSION 1908-9. Part VII .] VOL. XXIX. [PP. 609-720. CONTENTS. NO. PAGE XXXVIII. Observations with a Current Meter in Loch Ness. By E. M. Wedderburn, W.S., and W. Watson, M.A., B.Sc., . 61G {Issued separately October 1, 1909.) XXXIX. Hydrolysis of Salts of Amphoteric Electrolytes. By Miss Heather Henderson Beveridge, B.Sc., Carnegie Research Scholar. ( Communicated by Professor James Walker), . 648 ( Issued separately October 14, 1909.) XL. The Superadjugate Determinant and Skew Determinants having a Univarial Diagonal. By Thomas Muir, LL.D., , 668 {Issued separately October 15, 1909.) XLI. The Skeleton of a Sowerby’s Whale, Mesoplodon bidens , stranded at St Andrews, and the Morphology of the Manus in Mesoplodon, Hyperoodon and the Delphinidse. By Sir Wm. Turner, K.C.B., D.C.L., F.R.S., President of the Society, . . . . . . 68 T {Issued separately October 14, 1909.) EDINBURGH : Published by ROBERT GRANT & SON, 107 Princes Street, and WILLIAMS & NORGATE, 14 Henrietta Street, Coyent Garden, London, MDCCCCIX. Price Six Shillings ^ftsonian ln$t% REGULATIONS REGARDING THE PUBLICATION OF PAPERS IN THE PROCEEDINGS AND TRANSACTIONS OF THE SOCIETY. The Council beg to direct the attention of authors of communications to the Society to the following Regulations, which have been drawn up in order to accelerate the publication of the Proceedings and Transactions, and to utilise as widely and as fairly as possible the funds which the Society devotes to the publication of Scientific and Literary Researches. 1. Manuscript of Papers. — As soon as any paper has been passed for publication, either in its original or in any altered form, and has been made ready for publication by the author, it is sent to the printer, whether it has been read or not. The ‘ cop^y ’ should be written on large sheets of paper, on one side only, and the pages should be clearly numbered. The MS. must be easily legible, preferably typewritten, and must be absolutely in its final form for printing ; so that corrections in proof shall be as few as possible, and shall not cause overrunning in the lines or pages of the proof. All tables of contents, references to plates, or illustrations in the text, etc., must be in their proper places, with the page numbers left blank; and spaces must be indicated for the insertion of illustrations that are to appear in the text. 2. Illustrations. — All illustrations must be drawn in a form im- mediately suitable for reproduction ; and such illustrations as can be reproduced by photographic processes should, so far as possible, be preferred. Drawings to be reproduced as line blocks should be made with Indian ink (deadened with yellow if of bluish tone), preferably on fine white bristol board, free from folds or creases; smooth, clean lines, or sharp dots, but no washes or colours, should be used. If the drawings are done on a large scale, to be afterwards reduced by photography, any lettering or other legend must be on a corresponding scale. If an author finds it inconvenient to furnish such drawings, the Society will have the figures re-drawn at his expense ; but this will cause delay. When the illustrations are to form plates, a scheme for the arrangement of the figures (in quarto plates for the Transactions, in octavo for the Proceedings) must be given, and numbering and lettering indicated. 3. Proofs. — In general, a first proof and a revise of each paper will be sent to the author, whose address should be indicated on the MS. If further proofs are required, owing to corrections or alterations for which [i Continued on page m of Cover. 609 1908-9.] Mendelian Action on Differentiated Sex. as fertilisation is completed, I speak of a male zygote and a female zygote. The proof for each of these statements will come up presently. I further employ Weismann’s terminology and views to a certain extent. Weismann has shown that the development - results in the adult (its determinates) are represented causally in the gametes and zygote by “ determinants,” and that there is continuity of the germ plasma. His term “ id ” for the group of determinants necessary in the gametes or zygote to produce a holophyte I also find convenient. Mendel’s and Weismann’s terminologies enable us to state and discuss this question — a most important point — and the terminology must be considered as analogous to an algebraic one. In the human race sex has differentiated. The zygote necessarily contains the determinants for the dominant (potent) and recessive (non- potent) sexual determinants, and this makes it an impure dominant, as in F1, i.e. it contains D and It determinants combined, and never normally segregated, I hold, in subsequent development. The human zygote being an impure dominant and produced by the union of male and female gametes, we have to consider the number and natures of the gametes producing such a zygote. For long it has been considered that one gamete from each parent was necessary, but the existence of dimorphic male and female gametes has shaken this belief. Many of the animals lower in the scale than man have two kinds of male gametes, one of them having in insects an extra chromo- some (McClung), and some have dimorphic female gametes. In man there are dimorphic spermatozoa, but it is disputed as to whether the ova are dimorphic (Russo, Heape). It has also long been held that sex was not determined at fertilisation, but later in the development of the embryo. This, however, is erroneous, and there is no evidence that the human zygote is hermaphrodite or indifferent in sex at any early stage. It has been urged by some able observers (Beard, Castle, and many others) that there are male and female eggs : this, however, makes an organism hermaphrodite, and the male gamete contain no sexual determinants, and is incompatible with the true view as to the origin of the gametes. For reasons that will presently appear, I consider there is the highest probability that in human fertilisation a sex and non-sex male gamete, and a sex and non-sex ovum are concerned : that for the formation of the male zygote a sex male gamete and non-sex female gamete have united ; for the formation of the female zygote a sex female gamete and non-sex male gamete. This makes sex determined at fertilisation, and necessarily gives the 50 per cent, of the two sexes. VOL. XXIX. 39 610 Proceedings of the Royal Society of Edinburgh. [Sess. The question of the origin of the gametes has now to be considered. This has been most studied as to the origin of the female gamete, the ovum. The opinion currently held is that it originates from a germ epithelial cell. One admits, of course, that this view has done good service as a stop-gap, but there is really no fact in its favour. It makes a gamete originate from a somatic cell whose fellows, not so transformed, become ordinary protective epithelium. No satisfactory intermediate stages have been noted, and in view of the great fact that each gamete contains a certain proportion of heredity determinants, it is at present impossible to see how a gamete, the most highly organised cell in the body as to function, could arise from a germ epithelial cell. This view of its origin, further, gives no clue to the understanding of how a gamete becomes so specially endowed. A more promising view of the origin of the gametes is that they are ultimately derived from the primitive germ-cell mass from which the primitive germ cells are first formed. These primitive germ cells become reduced to gametes — spermatogenesis and oogenesis. The P.G.C. mass is set aside from the zygote at its very earliest period. The zygote is thus divided into a somatic portion containing one id, and the P.G.C. mass, necessarily containing thousands of ids. The former is thus the somatic portion of the zygote, giving rise to the individual, while the latter is the propagative part, the stirp in Galton’s phrase. The holophyte is thus merely the trustee of the propagative part. In the stages of zygotic development subsequent to the formation of the P.G.C. mass, the P.G.C.’s travel back into the somatic part via the body-stalk (yolk-stalk) and blastoderm before the embryo is differentiated as such, and mobilise on the Wolffian ridges, thus ultimately forming in each case the sexual gland, ovary or testis. Much detail on this point has yet to be worked out. Most important deductions can be made from this view : 1. The P.G.C. mass is really an unreduced part of the zygote, and is thus zygotic. 2. Each P.G.C. is potentially a zygote. 3. The gamete is a reduced P.G.C., and this reduction normally prevents zygotic development of the P.G.C. 4. To regain the power of zygotic development, gametes of separate adults must unite, the male gametes with the female gametes ; and thus fertilisation is gametic variation. 5. The gametes contain certain of the heredity determinants, because they are derived directly and by reduction from an unreduced part of the zygote, the P.G.C. mass. 6. The male zygote in all likelihood also gives off a primitive sperm-cell 611 1908-9.] Mendelian Action on Differentiated Sex. mass, just as the female zygote gives off the primitive germ-cell mass ; and from these, as stated in 3, the gametes arise. The history of the development of this view of the zygotic origin of the gametes and its long neglect are of great interest. O C5 c5 Owen in 1849 made a remarkable observation. In his well-known paper on parthenogenesis he stated that “ not all the progeny of the primary impregnated germ cells are required for the formation of the body of all animals : certain of the derivative germ cells may remain unchanged and become included in the body which has been composed of their meta- morphosed and diversely combined or confluent brethren : so included, any derivative germ cell or the nucleus of such may commence to repeat the same process of growth.” This was a striking observation, and it is the irony of investigation that this epoch-making observation should have been neglected for more than half a century while his contribution to parthenogenesis, still an obscure and doubtful theory, should alone have attracted great attention and been constantly quoted. It was only in 1891 that Eigenmann inde- pendently described the same phenomenon in Cymatogaster segregatus and thus confirmed Owen’s work. Since then observations have been fairly numerous and important. Balbiani, Boveri, Beard, F. A. Woods, Ingalls, and others have substantiated and extended Owen’s discovery in their views of the continuity of the germ cells. Ingalls’s observation is of importance, as the primitive germ cells in a 4’9 mm. human embryo were found, not on the Wolffian ridges, but en route for them and arrested at the root of the mesentery beneath the coelomic epithelium. Beard especially has demon- strated and fought for this view. This origin of the germ ceils first shown by Owen may be combined with Weismann’s great generalisation of the continuity of the germ plasma under the term of the Owen-Weismann law, or continuity of the germ cells. This means that the gametes are a reduced part of the primitive germ cells, these arising from the primitive germ -cell mass, a non-reduced portion of the original zygote. The gametes are thus directly zygotic in their origin, are not derived from somatic cells, and they thus carry on the race pure and not influenced by the “ soma ” proper. This being the nature of the gametes, we have now to consider if we can in any way find out how the determinants of heredity, using this term in a general sense, are allotted to the dimorphic gametes. What contribu- tion does each gamete bring to the zygote it helps to form ? For this purpose a source of information is present which has been ignored by almost all observers with the exception of Wilms and Beard, viz. ovarian and testicular dermoids and the dermoids found elsewhere in 612 Proceedings of the Koyal Society of Edinburgh. [Sess. the body. I take up this question in regard to ovarian dermoids with which I am familiar, but shall add some remarks in regard to the less common testicular dermoids. The ovarian dermoid is a quite common and familiar tumour. It is usually cystic, and contains a creamy fluid often like salad dressing, and may have hair, teeth, brain, brain tissue, alimentary canal — in fact, samples, as it were, of all the germ layers, and not mainly of the ectoderm, as is usually urged. There is occasionally a more or less solid form, the teratoma ; and this, as Wilms pointed out, is usually an imperfect anterior part of an embryo. Wilms and others have shown that the tissues are normal in structure. A very important teratoma removed by operation by Culling- worth and examined by Shattock is a most remarkable specimen. It is preserved in the Hunterian Museum, London, and is well worth a visit. Two limbs are present, and a peritoneal cavity with a blind coil of intestine. There is a short rudimentary spinal column with a pelvic girdle, and in each of the lower limbs there is an osseous element filled with fatty marrow. Between the limbs are two distinct labia, between these a distinct depression, and behind them a perineal raphe. I must next draw attention to a very important fact as to all dermoids, viz., they contain no evident genital organs proper, and, so far as any observer has as yet noted, no microscopical elements pointing to their distinct existence. There is no doubt as to such teratomata not being the product of immediate fertilisation, as they are found in virgin women, and I have, like other operators, removed them from children before puberty. How, then, do we get such remarkable productions ? I have already stated that the primitive germ cell is a zygote owing to its origin, and must contain an id : the gamete is a reduced primitive germ cell. A primitive germ cell can therefore form an embryo, but never does so, owing to its apparently constant reduction to a gamete and its loss of the power of zygotic develop- ment. If, however, a gamete has a certain number of determinants and is imperfectly reduced, it may retain the power of zygotic development and thus form part of an embryo. Now in the ova I have suggested that we have two kinds, a sex ovum and a non-sex ovum ; and for the reasons already given we may consider a teratoma as a non-sex ovum which by an imperfect reduction has retained the power of zygotic development not normally possessed by a gamete. The teratoma never contains all the parts of the anterior part of an embryo; and this is significant, as we shall see. The same applies to testicular teratoma. In a recent paper Okhubo analyses the cases in the Prag collection, 11 in number, and also 107 1908-9.] Mendelian Action on Differentiated Sex. 613 other cases in literature, and to his valuable paper I must refer those interested. Before stating an explanation of dermoids, I may mention that chorio- epitheliomata, the malignant tumours associated with the hydatid mole, have been found in teratomata by Schlagenhaufer, Ritchie, and others. Many views have been brought forward as to the origin of teratomata, and the one I advise as a working theory is that it is derived from a non- sex male or female gamete which has retained its power of zygotic develop- ment. The facts already stated as to the primitive germ cells passing after their formation from the P.G.C. mass by the yolk-sac and blastoderm into the embryo and their occasional arrest en route , helps one to understand their rare position outside the ovary and testis. If thus a teratoma like Shattock’s is the anterior part of an embryo, i.e., in the main somatopleuric, and if it arises from a non-sex ovum, this makes the non-sex ovum contain the determinants of the somatopleuric part and the sex ovum the determinants of the genital organs and other parts of the splanchnopleure. This supports the popular belief that boys get brain and body from and through the mother, their sex and splanchnopleure through the father. The converse holds good for girls. A teratoma is only fart of the anterior part of an embryo ; but this is not inconsistent with the above supposition, and indeed boys do not follow the mother and girls the father fully in the respects defined above. This means that the father also contri- butes in part to the boy’s somatopleuric element, the mother to the girl’s. I think this line of inquiry as to teratomata very promising, and that a particularly full examination should be made of all suitable specimens. The human zygote, male and female, contains the determinants, inter alia, for the potent and non-potent organs. Thus, sex has differentiated from a hermaphrodite condition away far back in the invertebrata. Mendelism acts on differentiated sex, and is evident owing to the difference between the potent and non-potent organs. The potent and non-potent determinants are, however, combined and inseparable in the human zygote, and thus in twinning of one zygote we always get an equal division of sex determinants. It is different in some animals, and in black cattle we get male twins, one potent and the other sterile — the free-martin. In the potent twins the potent sex determinants have been segregated ; in the free-martin, the non- potent ones. Thus we may arrange the relations of sex differentiation to the Mendelian scheme as follows : — 614 Proceedings of the Royal Society of Edinburgh. [Sess. DxR Parent |j (gametes). DR* F1 Df DR Ri 1 2 1 I am accumulating facts showing that Menclelism acts in producing sex in bees. How extraordinary current explanations are in this question of bee sex may be understood when I state that the drone, a perfect male, is supposed to arise from an unfertilised egg of the queen — and this in view of the fact that in crossing with a black (English) queen and an Italian drone (yellow-striped) some of the progeny show yellow stripes. The view of the origin of the drone from an unfertilised egg is neither a fact nor a theory, but a reductio ad absurdum. The following are the main conclusions of this inquiry : — 1. The human zygote is an impure dominant of F1 in Mendel’s scheme. 2. Two varieties of gamete — male and female, sex and non-sex — are required to produce it. 3. The dominant and recessive determinants of sex are united in the sex gamete, and do not segregate normally. 4. It is probable that the somatopleuric determinants are in the main present in the non-sex gamete ; the sexual and splanchno- pleuric ones in the sex gamete. 5. A teratoma most probably arises from an imperfectly reduced non-sex gamete. 6. The free-martin is not a sterile cow when the potent twin is a bull, but a sterile bull with the recessive sexual determinants segregated in it. It is an extracted recessive. 7. Dominance of a character probably means that it is expressed in the soma, while at the same time the recessive character is secluded in the propagative part of the same plant, but is not expressed in the soma. It appears in the soma in a later generation ; and when the plant breeds true, the recessive or dominant character is present pure both in the propagative and somatic part. 8. The theory of gametic segregation is doubtful. 9. The gametes are derived, not from the germ or sperm epithelium, * The equivalent of the human zygote. t The equivalent of the potent twin in black cattle (extracted dominant). I The equivalent of the free-martin (extracted recessive). 1908-9.] Mendelian Action on Differentiated Sex. 615 but from the primitive germ-cell mass — a part of the zygote, and zygotic therefore. Thus the P.G.C.’s are also zygotes, and the gametes reduced P.G.C.’s. This generalisation I call the Owen- Weismann law. I finrerchfellhuncL 2 Urachu ZXar'nblase Itnke l/rntere 17 lillerscher (fang 16 l/rruerenvanc 15 'ierenanlaae 14 rHarnleiter 13 Leitband/ahaeschnLtten) 1Z 4 /Sinus unopenilalLs 6 (feschlecKtynmlsl 6 (jtschlQchlshockt, 7 ^tschlechlsfaH en. (fesMzditsftitxhe, 8 Fig. 1. — Diagram 1. Diaphragmatic ligament. 2. Urachus. 3. Bladder. 4. Urinogenital sinus. 5. Prepuce. 6. Sexual eminence. f urogenital system in type con 7. Sexual folds. 8. Sexual furrow. 9. Cloaca. 10. Genital cord. 11. Rectum. 12. Gubernaculum (cut). to both sexes (Bonnet). 13. Ureter. 14. Kidney rudiment. 15. Wolffian duct. 16. Muller’s duct. 17. Left Wolffian body with sexual gland. 1 Appendix veticularis 2 Ostium tubae 3 Fimbria ovarica Ovarium — 4 Ligamentum ovarii prophum 5 Uterut 6 Vagina Epoophoron Paroophoron 1 1 Ligamentum uteri rotundum IQ Gartner'scher Gang 9 Leietenring 8 -* W. bulb 3 and s.u.g. 7 Fig. 2. — Diagram of female urogenital organs, showing ovary, tube, uterus, vagina, ovarium, and round ligaments, Dominant : epoophoron and paroophoron, Recessive and on male type (modified from Bonnet). 1. Hydatid. 3. Ovarian fimbria. 8. Internal ring. 2. Ostium tubse. 4. Ovarian ligament. 616 Proceedings of the Royal Society of Edinburgh. [Sess. Fig. 3. — Diagram of male urogenital organs, showing testis, caudal liga- ment, gubernaculum, prostate, Dominant : appendix testis (Muller’s duct), and prostatic utricle, Recessive and on female type (Bonnet). 6. Vas deferens. In 2 and 3 the differentiated sexual organs are shown, arising from '•a hypothetical common type in fig. 1. LITERATURE. Adami, J. G., “The Principles of Pathology,” Oxford Medical Publications. 1909, Oxford, Henry Frowde. Adami remarks, apropos of the Differentiation of Sex : “ The existence in the normal male or female of useless rudiments of parts characteristic of the opposite sex, must not be taken as an indication that man is descended from an originally her- maphrodite ancestry. . . . Rather such rudiments are, in Mendelian terminology, recessive features, due to the origin of the fertilised ovum from both male and female germ-plasma” (pp. 257-8). Ahlfeld, Die Missbildungen des Menschen, I. Abschnitt, Leipzig, Gronow, 1880. Ballantyne, J. W., Antenatal Pathology and Hygiene , the Foetus and. Embryo , A Manual of , Edinburgh, Green & Sons, 1902 and 1904. Two vols. Bateson, W., Mendel’s Principles of Heredity , Cambridge, University Press, 1909. Bateson, Materials for the Study of Variation , London, Macmillan & Co., 1894. Bateson, The Methods and Scope of Genetics , Cambridge, 1908. In discussing Doncaster’s results as to the crossing of varieties of the currant- moth, Professor Bateson remarks : “If we are right, as I am strongly inclined to believe, we get a glimpse of the significance of the popular idea that in certain respects daughters are apt to resemble their fathers, and sons their mothers — a phenomenon which is certainly sometimes to be observed” (p. 44, Genetics , etc.). Beard, “The Germ-cells,” Parti., Raja Batis, Part I. contd., Journ. of Anat. and Phys ., 1904, pp. 82 and 341. Boveri, “ Befruchtung,” Merkel und Bonnet’s Ergebnisse, vol. i., 385-585. Carey, “Report of Two Testicular Teratomata, with a Review of the Recent Literature,” Johns Hopkins Hosp. Bull., vol. xiii., ATo. 140, 1902. 617 1908-9.] Mendelian Action on Differentiated Sex. Castle, W. E., “The Heredity of Sex,” Bull. Mus. Comp. Zool. Harvard , vol. xl., Ho. 4, 1903. Cunningham, J. T., “ The Heredity of Secondary Sexual Characters in relation to Hormones : A Theory of the Heredity of Somatogenic Characters, Arch, fiir Entivickelungsmechanik der Organismen (Roux’), Bd. xxvi., Heft 3. Castle’s theory is considered and discussed. Darbishire, “Mendelism,” Science Progress , No. 7, January 1908. Castle’s theory is explained and discussed. Darwin, C., Origin of Species and Variation of Animals and Plants under Domestication , London, Murray. Doncaster, “ Sex Inheritance in the Moth Abraxas grossulariata and its var. lacticolor ,” Pep. Evol. Comm ., iv. p. 41, 1908. Durham and Marryat, D. C. E., “ Inheritance of Sex in Canaries,” Rep. Evol. Comm ., iv., 1908. Eimer, Organic Evolution , London, Macmillan & Co., 1890, J. T. Cunningham’s translation. Eigenmann, “ The Precocious Segregation of the Sex-cells Cymatogaster aggregatus,” Journ. of Morph., vol. v. pp. 481-492. Galton, Natural Inheritance , London, Macmillan & Co., 1889. Geddes and Thomson, Evolution of Sex , London, Scott, 1901. Hart, D. Berry, “Nature and Cause of Descent of Testes,” Journ. of Anat. and Phys., 1909; also “Morphology of the Human Urinogenital Tract,” Journ. of Anat. and Phys. and E.O.S. Trans., 1900-1901. Hartung, Ueber einem Fall von Mamma accessoria, Erlangen, 1875, Druck der Univ. Buch Druckerei, E. Th. Jacob. Ingalls, “ Beschreibung eines menschlichen Embryos von 4*9 mm.,” Arch, fur Nuk. v. Anat., Bd. lxx. Kempe, v., Schwalbe's J ahresbericht , xxi. p. 632, for a short summary. Leichtenstern, Virch. Arch. f. Anat. und Path., 1878, p. 222. Lock, Recent Progress in the Study of Variation , Heredity, and Evolution, London, Murray, 1906. Lotsy, J. P., Vorlesungen iiber Descendenztheorien, Jena, Fischer, 1906. This is a most comprehensive and valuable work. M‘Clung, “The Accessory Chromosome-Sex Determinant?” Biol. Bull., iii., 1902, p. 43. Mitchell-Bruce, Journ. of Anat. and Pliys., 1879, xiii. p. 425. Mendel, “Versiiche liber Pflanzen Hybriden verb, naturf. Verein in Briinn ” (English translation by Bateson in Jour. Roy. Hort. Soc., xxvi., 1901). Ohkubo, Sakaye, “ Zur Kenntniss der Embryome des Hodens,” Roux ’ Archiv f. Entivickelungsmechanik der Organism., Bd. xxvi. Heft. 4. Owen, On Parthenogenesis, London, Van Voorst, 1849. Przibram, Experimental Zoology, Part I., “ Embry ogeny,” Cambridge, University Press, 1908. A most valuable monograph. Punnett, Mendelism, Cambridge, Bowes & Bowes, 1907. Quain, Anatomy, vol. i., Bryce on “Embryology,” London, 1908. Ritchie, J., “A Case of Embryoma occurring in the Mediastinum,” Jour, of Obst. and Oyncec. of the British Empire, iv. p. 65. 618 Proceedings of the Royal Society of Edinburgh. [Sess. Sabin, Amer. Jour, of Anat., vol. i. Schlagenhaufer, Wien. Min. Woch., 1902, Nos. 22 and 23. Shattock, E. G., “Ovarian Teratoma,” Erasmus Wilson Lecture, 1908, Lancet , i., 1908, p. 479. Sutton, J. Bland, Evolution and Disease , London, Walter Scott, 1890. Thomson, J. Arthur, Heredity , London, John Murray, 1908. A great store- house of facts. Weismann, The Evolution Theory (J. A. Thomson’s trans.), London, Arnold, 1904. Whetham, The Recent Development of Physiological Science , London, Murray, 1904. W iedersheim, Vergleichende Anat. der Wirhelthiere , Sechste Auflage, Jena, 1906. Wood Jones, “The Nature of the Malformations of the Rectum and Urogenital Passages,” Brit. Med. Journal , Dec. 17, 1904. Woods, F. A., “Origin and Migration of the Germ-cells in Acanthias,” Amer. Jour, of Anat., i. 307. His conclusion is “that the germ-cells in the dog-fish are not developed from somewhat specialised cells of the body, but that a few undifferentiated cells of the earliest type are taken out and passed on until the new individual is formed ” (p. 318). ( Issued separately September 29, 1909.) 1908-9.] Observations with a Current Meter in Loch Ness. 619 XXXVIII. — Observations with a Current Meter in Loch Ness. By E. M. Wedderburn, W.S., and W. Watson, M.A., B.Sc.* (MS. received July 5, 1909. Read July 5, 1909.) One of the authors having made an experimental investigation on the currents produced in a trough of water by a blast of air driven along the surface of the water, j* it was desired to test the correctness of his deductions by actual observations in a large lake. Loch Ness was chosen on account of its length and uniformity of basin, as it was thought that the length and narrowness of the loch would lead to clearly defined currents being set up in the lake. The sequel showed, as in the case of observations on seiches, that it would have been better to confine attention to a smaller lake, for a two- fold reason, (1) because in a large lake the difficulties of observations are much greater than in a small lake during stormy weather, and in very deep lakes the difficulties in the way of obtaining a fixed point from which to use the current meter are formidable, and (2) because it would seem from a few observations made in Loch Garry (Ness Basin) that currents are more defined and more regular in small than in great lakes. Various current meters have been designed, and after inquiry it was decided that the one best suited for observation in lakes was the instrument designed by Dr Ekman and described by him in Publications de Circonstance No. 24, and the choice was justified by the satisfactory way in which the instrument worked under adverse conditions. Fig. 1 gives a photograph of the instrument. The current is measured by the number of revolutions of a very light screw propeller, which is kept directed against the current by a vane set at right angles to the propeller. By an ingenious arrangement, at every thirty-three revolutions of the propeller a small metal ball is allowed to drop into a cup in the centre of a compass needle, after which the ball runs down a groove on the north leg of the needle into the compass box, which is rigidly attached to the meter. The compass box is divided into 36 divisions, * The cost of the current meter and the necessary gear with which the observations described were carried out was partly defrayed by a grant from the Moray Bequest of the University of Edinburgh. The cost of carrying on the observations was partly borne by a grant from the Carnegie Trustees. We have also to acknowledge indebtedness to Professor D’Arcy Thompson for advice, and for supplying a small but strong sounding machine for use with the current meter, and to Mr J. Davidson, Superintendent of the Caledonian Canal, for the use of a buoy and anchor and for assistance in preparing the necessary gear. t E. M. Wedderburn, “An Experimental Investigation of the Temperature Changes occurring in Fresh-water Lochs,” Proc. Roy. Soc. Edin ., xxviii. p. 2. 620 Proceedings of the Royal Society of Edinburgh. [Sess. each division corresponding to 10 degrees of the compass. The division into which a ball falls, therefore, shows the direction in which the vane is pointing Fig. 1. when the ball is allowed to fall, and in this way the direction of the current is determined. When an observation is to be made a small receptacle in the 1908-9.] Observations with a Current Meter in Loch Ness. 621 instrument is filled with the balls or shot which are to indicate the direction of the current, and the meter is lowered to the desired depth by means of a sounding line. One messenger is then sent down which releases the pro- peller, and the time at which the messenger reaches the meter is the time at which the observation begins. When it is desired to end the observation a second messenger is sent down which stops the propeller. The meter is then brought to the surface and the number of revolutions which the pro- peller has made read on the dials of the meter, the direction of the current being ascertained by the position of the balls in the compass box. The meter was constructed by the Central Laboratory for the International Study of the Sea, Christiania, under the superintendence of Dr Ekman, and was carefully calibrated before being sent out, the rate of the current in centimeter seconds being given by the formula v — *8 + ‘424 n, where n is the number of revolutions of the propeller per minute. The instrument was not supposed to be accurate for currents which produced fewer than 5 revs, per minute, but in our observations great accuracy was not aimed at and only qualitative results were desired. Owing to the conditions under which the observations were carried out the instrument could not always be kept in perfect adjustment, and for this reason, at least for the slower currents which were measured, the above formula is probably not correct. As will be seen in the sequel, most of the currents which were measured in Loch Ness were slower than 5 revs, per minute ; but as the meter very easily took up the direction of the current, the directions were measured with much greater accuracy than the velocities of the current. It was the exception rather than the rule that the compass balls indicated a steady current. The changes of direction were often very great during the time occupied by a single observation, and for this reason it would have been of great advantage had the balls been distinguishable from one another by numbers or otherwise, as then some idea could have been obtained of the manner in which the direction of the current varied. Such an arrangement was suggested by Dr Ekman, and also by our boat- man, Mr Wm. Macdonald, of Fort Augustus. It is, of course, necessary to have a fixed point from which to suspend the current meter during the observations. The method adopted was that used by Helland-Hansen in his current measurements in Norwegian fiords in 1906 (. Bergens Museums Aarbog, 1907, No. 15). A buoy was moored at the point of observation by two grapnels, to each of which was attached a line of a length about twice the depth of water in which the buoy was to be moored. The grapnels were put as far apart as the length of the line would allow in the direction of the axis of the lake. The lines were then 622 Proceedings of the Royal Society of Edinburgh. [Sess. tightened as much as possible, so that the buoy was moored under a con- siderable strain, and any variation in its position while so fixed was very small. At first the buoy was moored at a depth of nearly 700 feet about a mile to the north-east of Invermoriston by hemp ropes, but owing to the exposed position in the lake in which the buoy was fixed, little but disaster attended the observations which were made in that position. Even in a moderate breeze the waves in Loch Ness are of considerable size, and in a small rowing boat it was found very difficult and not a little dangerous to observe in the centre of the lake. The observations were put a stop to for a time by the loss, in some unexplained manner, of the compass box ; and during the interval which occurred before the lost box could be replaced the buoy broke from its moorings and took a journey of some sixteen miles, leaving about 2000 feet of rope at the bottom of Loch Ness. It was then decided to moor the buoy in a less exposed position in the lake, and in a less depth. Such a position was found in about 300 feet of water 300 yards off Invermoriston pier. At first the buoy was moored as before with ropes, and latterly with ordinary galvanised fencing wire, which was found more satisfactory and much cheaper. Mr J. Murray Grant of Glen- moriston kindly granted the use of his boathouse for housing the boats and apparatus, and thus gave material aid to the work. One or two observations were also made near Fort Augustus in the position where the Lake Survey yacht “ Rhoda ” was formerly anchored {Trans. Roy. Soc. Edin., vol. xlv. p. 410), and also at a point about 400 yards off' Glendoe pier. (See Sketch Map, fig. 2, for positions.) For the observations of short duration the meter was lowered from a rowing boat attached to the moored buoy. Even when all precautions were taken it was found that in strong winds the boat swayed a little with the wind, especially if the wind blew broadside on to the boat, and to a certain extent the observations are vitiated by this ; but the swaying of the boat was slight and slow, and may be neglected in view of the complexity of the observations. The variations in direction and strength of the currents which were observed were much greater than could be explained by the swaying of the boat. Observations were also frequently made by attaching the meter directly to the buoy and leaving it overnight ; and in such observations, as the buoy did not present a large surface to the wind, the effect of swaying with the wind was much reduced. The earlier observations were made by Mr E. M. Wedderburn, including a few observa- tions in Loch Garry ( Proc . Roy. Soc. Eclin., vol. xxix. p. 98), and those in August and September by Mr W. Watson. During the succeeding winter a number of observations were made by Mr Wm. Macdonald, who acted as boatman throughout, and whose inventive faculty overcame many difficulties. 1908-9.] Observations with a Current Meter in Loch Ness. 623 The observations in Loch Garry were so satisfactory, and showed so clearly the existence of a return current to supply the place of water carried along at the surface by the wind, that the Loch Ness observations were looked forward to with confidence. But the Loch Ness observations have proved so complicated that the authors do not pretend to understand them fully, and in what follows they have endeavoured to select from the observa- 87654-3210 I — i — i — i — I — -t — r— i — r o MILE SCALE “i 1 r 7 2 3 Fig. 2. 4 MILES tions such as they think they are able to explain. Most of the observations are tabulated in the Appendix to this paper, as they will be of interest for comparison in the event of current measurements being made in other lakes. Numerous temperature observations were also made in Loch Ness to correlate with the current observations. These also are given in the Appendix. The Invermoriston temperature observations for every fifty feet are shown graphically in fig. 3. The temperature changes at the surface and 50 feet are evidently chiefly due to the changes of wind ; but the observations at 624 Proceedings of the Royal Society of Edinburgh. [Sess. 100, 150, and 200 feet show a well-marked, if somewhat irregular, tempera- ture seiche. The rapidity of the change of temperature from 2nd to 3rd September is especially notable, and will be referred to later. Before proceeding to discuss the current observations it is necessary to point out that very considerable currents must accompany the temperature seiche, apart from the currents and return currents produced by winds. A AUGUST 1908 SEPTEMBER INVERNORISTON - LOCH NESS Fig. 3. rough calculation of the magnitude of these currents has been made as follows : — The mean depth of Loch Ness is about 138 metres (450 feet), and it was assumed that for the purposes of calculation the lake could be replaced by a rectangular basin of this depth and with a length of 36 km. (22J miles). It was further assumed that there was a sharply defined discontinuity at a depth of 46 metres (150 feet). Then for a seiche with an amplitude of 46 metres the quantity of water both in the upper and in the lower layer trans- 1908-9.] Observations with a Current Meter in Loch Ness. 625 f erred from one side of a node to the other is (as the node is at the centre of the lake) 1800000 x 2300 x 6 = 4145 x 107 cub. cm., where 6 is the breadth of the lake. All this water must pass through the nodal section, and it was assumed that in the upper and lower layers respectively this transference was accomplished by a current uniformly spread over the nodal section whose area in the upper layer is 466 x 102 sq. cm. and in the lower layer 926 x 102 sq. cm. The transference takes place in half the period of the seiche, which for purposes of computation was taken as forty hours. The average rate of the current at the node on the foregoing assumptions is, then, in the upper layer 414 xlO7 46 x 102 x 40 x 3600 cm. sec., or approximately 6 cm. sec., and similarly in the lower layer 3 cm. sec. The currents in the two layers are of course in opposite directions. If it is further assumed that the motion of the water particles is harmonic, the maximum velocities of these currents are found to be about 10 cm. sea and 5 cm. sec. respectively. A current of 10 cm. sec. would produce over 20 revs, per minute of the propeller of the current meter. In the tables of observations in the Appendix, the first entry gives the rate of the current in centimetres per second calculated according to the formula supplied with the instrument. The second entry shows the directions of the current. The prefix gives the number of balls which have fallen into the compass box, and the suffix the variation of the directions in degrees. The centre figure gives the number of degrees east or west of north or south which denote the mean direction for the current. The third entry gives the time of commencing and sending the observation in hours (numbered from 1 to 24) and minutes. A bar over the time of ending the observation indicates that the observation was not ended until the next day, and that the hour refers to the following day. At the top of each column appears the date on which the observation was commenced, and at the left hand the depth at which the observations were made are shown. Thus the entry for 150 feet on 12th August: T212N7E1S017*32 — 10’28, means that the average velocity for the currents for the period of observa- tion was 12 cm. secs. ; that there were twelve indications of direction, that the average direction was 7° east of north, that the variation in the direction of the current was 180°; that the observation started at 17 hours (5 p.m.) 32 minutes on the 12th and ended at 10 hours 28 minutes on 13th August. All temperatures are measured in degrees Fahrenheit, and all depths are given in feet. Wind force is estimated on the scale 1 to 10. A glance at the tabulated observations will show the great complexity of the results and will give some idea of the difficulty of correlating them. VOL. xxix. 40 626 Proceedings of the Royal Society of Edinburgh. [Sess. In their discussion we have dealt separately with the results obtained at Station B, Invermoriston (see Sketch Map), and at Station C, Fort Augustus. Preliminary Observations. A few observations were made at Station A (Invermoriston) in April and May when the water was of practically uniform temperature, about 42° F. On only one occasion was a current rate of over 5 cm. secs, observed, and at a depth of only 24 feet. Currents were indicated at both 500 and 600 feet on the two occasions on which observations were obtained at these depths, although the winds during the period of observation were not very strong. The winds were also variable, so that no importance can be attached to the direction of the currents. For the observation at 500 feet the meter was left immersed for a week and the current directions varied from N. 30 W. to S. 40 E. When the meter was brought to the surface at the close of the 600-feet observation it was found that the compass box had disappeared, so that the directions were not recorded. Invermoriston Observations. During the period from 30th July to 5th September the observations show currents with a velocity over 5 cm. sec. in a direction opposite to that of the wind on seven occasions, viz. : Date. Velocity. Cm. sec. Depth. Feet. Direc Of Current. Don Of Wind. Aug. 7 8-4 6 N. 51 E. S.W. „ 7 74 15 N. 59 E. 5? „ 10 5T 2 N. 30 E. 5? „ 27 7-4 15 N. 45 E. „ 28 11-2 15 N. 80 E. 95 „ 28 12-3 30 N. 60 E. 9? Sept. 3 6-8 15 S. 10 W. N.E. On all these occasions it is seen that the return current takes place near the surface, both during S.W. and N.E. winds, and it is to be noted that the place of observation is during a S.W. wind near the windward end of the lake, and during a N.E. wind near the lee end. The observations on 3rd September are of interest, as although the wind was light the currents were strong. On 2nd September there was also little wind, and there were no appreciable currents. But it will be noted that on 3rd September there was a very strongly marked temperature seiche, and the currents recorded 1908-9.] Observations with a Current Meter in Loch Ness. 627 may be due to this. The temperature was rapidly changing at the hour of observation, and, as already shown, the currents due to this cause may be of considerable amplitude. On 6th August a strong S.W. wind was blowing, and also on 8th and 9th August. On 7th and 10th August the wind was of moderate strength, and possibly the strong currents observed are the result of the previous day’s storms. On 27th and 28tli August also the wind was very strong. The discon- tinuity in temperature was at this time at a depth of 125 feet to 150 feet. The only other days during this period on which the wind was of considerable strength and on which observations were made were 3rd and 22nd August. On the 3rd no observations were made between 6 and 50 feet, but at 50 feet there was a current from N. 52 W. of 8 cm. secs. On the 22nd there was at 15 feet a current of 2 2 cm. sec. from N. 60 E. ; 1*6 cm. secs, from N. 40 E. at 75 feet and 2-9 cm. secs, from N. 80 E. at 90 feet. This was after a week of prevailing N.E. winds, and the currents are probably due to the progress of a reversion of the temperature distribution from the N.E. to the S.W. type. On 21st August the currents were very undecided in direction. Frequently cross currents were observed at right angles to the direction of the wind, and during the strong S.W. winds on 3rd and 8th they were well marked, viz. : — On 3rd August 8'0 cm. sec. from N. 52 W. at 50 feet. On 8th August 9’7 cm. sec. from N. 42 W. at 15 feet. In fact, the observations on 8th August show directions at various depths all round the compass ; e.g. : — S. 88 W. near surface. N. 42 W. at 15 feet. S. 23 E. „ 30 „ N. 45 E. „ 60 „ On 28th August a high-current velocity of 15 2 cm. sec. was recorded at 60 feet. Unfortunately on this occasion the compass needle was found to be off its pivot when the meter was brought to the surface, so that the direction of the current is uncertain. The observation is nevertheless interesting, as the velocity is the greatest recorded during this period at any depth with the exception of an observation on 4th August of 15*5 cm. sec. at 24 feet, and on 5th August 16’9 at 6 feet. A contrast between the observations on 5th August during a N.E. wind 628 Proceedings of the Royal Society of Edinburgh. [Sess. with those on 28th August during a S.W. wind is instructive. At Inver- moriston the N.E. winds have much more “ gather ” than the S.W. winds. As a matter of fact, during strong N.E. winds observation was impossible, owing to the size and character of the waves. On the 5th, then, it is seen that although the wind was not strong (force 1 on scale of 1 to 10) the velocities of the currents measured ranged from 3‘2 to 16’9 cm. secs, from the surface down to 60 feet, all with a north-easterly direction. At 100 feet and 200 feet the directions were N. 8 W. and N. 10 W. respectively. On the morning of the 6tli, a day of variable breezes, there was a current of 3’9 cm. sec. from S. 39 W. at the surface, and the current at 30 feet was very variable. On the 28th there was a very strong S.W. wind, so that waves were breaking into the boat, yet as near the surface as 15 feet we have a current velocity of 11 2 cm. sec. from the N.E. and of 12 3 cm. sec. at 30 feet from the same quarter. The surface was too rough for an observation to be made there ; but a curious effect was noticed during a temperature observation : when the thermometer was sunk to a considerable depth the displacement of the line from the vertical was very marked in a direction opposite to that of the wind. The observation on 5th August above referred to was made during an isolated day of N.E. winds. From 14th to 20th August, however, there were continuous easterly winds, variable in strength. In no case is there a trace of a south-westerly current nearer the surface than 30 feet, and, save for a single observation on 17 th August, none nearer than 90 feet. All night observations from 14th to 15tli August show an average current of 1*5 cm. sec. from N. 40 E. at 120 feet, and from 15th to 16th of 1*0 cm. sec. from N. 31 E. at 180 feet. But it is evident that the latter observation was made on the upper margin of the return current, for while ten balls indicated a N.E. current, there were also three indications of currents N. 60 W., S., S. 40 W. Two days later, on the 17th, there are indications of a return current from 30 to 60 feet. The rising of the return current during the continuance of N.E. winds is clearly shown by the overnight observations commenced on 15th and 17th August, viz. : — Date. Depth. Average Current Velocity. Directions. Aug. 15-16 180 feet DO cm. sec. 10N. 31 E.70 ; jN. 60 W. jS. ; LS. 40 W. „ 17-18 150 „ 1*2 „ „s. 10 W.60 ; XN. 20 E. ; ,N. 20 W. ; ,N. 40 E. 1908-9.] Observations with a Current Meter in Loch Ness. 629 The loch was nearly calm on the evening of the 17th, but the wind rose again the next day, and north-easterly currents of 112 cm. sec. at the surface, 8 cm. sec. at 30 feet, 3*5 cm. sec. at 80 feet, and 7*4 cm. sec. at 90 feet, were observed. The directions at 90 feet were not, however, very consistent, and at 96 feet a southerly current of 1 cm. sec. was observed, and at 102 feet a N.W. current of 1*6 cm. sec. The general conclusions to be drawn from these observations during N.E. winds would seem to be that at the station of observation, i.e. near the lee end of the lake, for moderate winds the return current confines itself to the deeper water and takes place in the neighbourhood of the temperature discon- tinuity. The return current seldom penetrates to the cold water below the discontinuity. The effect of very strong winds can only be guessed at, as observation was impossible with the boats and apparatus at our disposal. On one occasion the meter happened to be suspended at 180 feet from the buoy during a strong N.E. wind, viz. on 1st September, when a N.E. gale was sandwiched between two days of calm. The overnight observa- tion showed a slow current (1 cm. sec.) with variable direction. (There were thirteen balls indicating direction, and while one was in the N.E. quadrant the remaining twelve were equally distributed over the other three quadrants.) This isolated observation is not inconsistent with the above conclusion. It should, however, be mentioned that although the return current does not appear to descend below the discontinuity, direct currents do appear to penetrate to considerable depths at the commencement of the north-east winds, and only after the wind has continued for some time does the return current displace the direct current and force it to be confined to a less depth. An examination of the results of south-westerly winds does not appear to give the same conclusions, but they are not inconsistent therewith. The general rule is that strong return currents are met with very near the surface, no matter what is the strength of the wind. This may be due either to the fact that the observation station was near the windward end of the lake, or to the sheltered position of the buoy. The position was slightly sheltered by Portclair Point, which forms the western side of Invermoriston Bay. It was more than once suggested that the return current might be felt very deep on the exposed side of the station, and that Portclair Point caused subsidiary return currents near the surface. Whatever the cause, there is not the same consistency about the results during S.W. winds as during N.E. winds. But it is clear, especially with strong winds, that the return current at the point of observation took place near the surface (cp. observa- tions on 27th and 28th August). With a S.W. wind succeeding a day of calm or N.E. winds, S.W. currents are set up at considerable depths — e.g., at 630 Proceedings of the Royal Society of Edinburgh. [Sess. 90 feet on 12th August and 12th September — but this deep direct current does not continue long. With a moderate breeze the return current makes its appearance with small velocity comparatively near the surface. With a strong wind it is met with very near the surface, and sometimes with a considerable velocity. The period from 30th July to 5th September contained no continuous spell of steady S.W. winds, so that deductions from the results are difficult. But from 12th to 19th September there was a fairly steady wind. Starting on the 12th there is a S.W. current down to 90 feet at least, and a balance in favour of a N.E. current at 210 feet. By the 14th the N.E. current is seen at 30 feet and strongly at 60 feet. On the 15th a N.E. current is registered at 25 feet. On the 17th there was a strong wind, and, as on 27th-28th August, there is a strong N.E. return current just below the surface. The loch was too stormy to use the current meter at the surface, but the velocity of the surface current was estimated from the drift of particles floating in the water at about 13 cm. sec. On the 17th the indications of direction are rather variable, but they indicate — At the surface a current from S.W. of 13 cm. sec. From 2 to 30 feet „ „ N.E. „ 4 to 5 ,, „ 30 „ 150 „ „ „ N.E. „ 3 „ 4 „ Below 150 feet the tendency of the current is from the S.W. This may be due to the existence of a secondary current in the same direction as the wind below the return current. There are also indications of this on 12th and 19th September, but the evidence is too slender to draw any sure inference. A point of difference between the observations from 12th to 19th September and the earlier observations is the greater strength of currents in deep water. Velocities of from 2 to 4'5 cm. sec. were not met with in deep water in August. This may either be due to the prevalence of a S.W. wind or to the fact that the temperature discontinuity was then at a greater depth. Fort Augustus Observations. The observations from 23rd September till 21st October 1908 were taken at a point near the head of Loch Ness, about 1 mile from Fort Augustus, and 400 yards from the east shore, nearly opposite Glendoe pier (C on Sketch Map). As the canal authorities considered that mooring a large buoy in that position was a menace to shipping, we had recourse to other means, and a 1908-9.] Observations with a Current Meter in Loch Ness. 631 series of empty petrol tins, etc., proved very successful, and was probably more efficient than the large buoy, which had a considerable area exposed to the wind, and swayed slightly in consequence. The depth of the loch at the point of observation was found by sounding to be 465 feet, or about twice the depth of the Invermoriston station. During the period of observation at Fort Augustus the prevailing wind was westerly, and as a matter of fact continuous easterly winds of any considerable strength would have made observation impossible. The currents observed seemed very complicated, and this may be attri- buted to a number of causes. With a westerly wind Fort Augustus is the windward end of the lake, and small variations in the direction of the wind are more felt than further down the lake, for the steep mountains which rise all along the lake tend to stereotype the direction of the wind. Cross currents may therefore be set up more easily at Fort Augustus than else- where. When an easterly wind is blowing, the depth of the lake is rapidly decreasing in the direction of the direct surface current, and this must have a disturbing effect on the currents setting in towards the shallowing shore. As evidence of the confusion which exists, two points may be mentioned : (l)the great variation in the direction of the currents registered during observations of only an hour’s duration, which means that in a large number of cases there was no steady direction for even an hour on end ; (2) compared with Invermoriston the velocities measured were small. The following are all the occasions on which velocities above 5 cm. sec. were observed : — Depth in Feet. Velocity. Cm. secs. Date. Direction. Wind. 0 8-0 Sept. 24 N.E. N.E. 1-2. 0 5-0 55 24 N.E. N.E. 1-2. j 0 93 55 29 S.W. S.W. 3-4. 30 9-0 55 29 s.w. S.W. 3-4. 120 5-0 55 29 N.E. S.W. 3-4. 0 5-1 Oct. 1 S.W. S.W. 0-1. 30 5-1 55 1 s.w. Variable. 0 54 55 3 s.w. S.W. 1-4. 90 5-6 55 9 s.w. S.W. 1-4. 120 6*7 55 10 s.w. S.W. 3-4. 0 10-0 55 13 N.E. S.W. 1-3. 0 9-8 55 16 N.E. N.E. 3-4. 30 5-1 55 16 N.E. 3-4. 0 51 55 19 S.W. S.W. 0-1. 0 7-4 55 21 S.E. Variable. Here there are fifteen cases, and in nine of these the observation is at the surface. The most curious fact of all is that the largest velocity recorded was 632 Proceedings of the Royal Society of Edinburgh. [Sess. only 1(H) cm. sec., and that was a return current at the surface, setting in as a S.W. gale died away. At the more sheltered position at Invermoriston velocities were registered up to 17 cm. sec. on several occasions, and in a con- siderable number of cases there were observations of velocities exceeding 10 cm. sec. The slowness of the currents is probably due to the proximity of the head of the lake and to the shallowing of the basin, for there must obviously be at each end of a lake a certain amount of water which does not partake of the general circulation of the lake. The comparative shallowness of the water at Invermoriston may also, by confining the depth through which the currents could move, have increased their velocity ; but this is unlikely, as it is really the depth of the temperature discontinuity which determines the depth to which the currents descend. No velocity above 5 cm. sec. was observed below 120 feet, but at that depth there are two observations of a current velocity of 5 cm. sec., both during S.W. gales. Curiously, one was a direct current (10th October) and the other a return current (29th September). There are only observations on two days with N.E. winds from which reliable conclusions can be drawn, viz. 24th September and 15th October. On the former date the easterly current was decidedly felt at 180 feet about midday, but three hours later the return current has had time to set in, and, with practically the same velocity as the direct current had at 180 feet, it appears at 150 feet. On the 15th October, when the easterly wind had been blowing for not more than twelve hours, the return current is taking place steadily between 60 and 120 feet. On the following day the currents are again confused. There is a tendency for the return current to appear near the surface, while direct currents are also recorded at considerable depths. In consequence, there are indications of currents of all directions at 60 feet. Unfortunately in the other observations the compass needle was displaced. In spite of the variable conditions there are a sufficient number of observations taken on days when the currents were comparatively steady to warrant our drawing the same general conclusions as regards S.W. winds as at Invermoriston, viz., that the return current tends to appear very near the surface. The return current appeared at 30 feet on the 3rd, 7th, and 9th October, at 60 feet on 28th September and 19th October, and at 90 feet on 29th September. The observations on 7th October are especially clear. They show a S.W. current at the surface, a N.E. current from 30 to 120 feet, and a S.W. current at 300 feet. These observations strongly resemble the Invermoriston observations of 17th September in showing a deep water current in the same direction as the surface current. A similar observation made on 20th October, in which some method of distinguishing the order in / 1908-9.] Observations with a Current Meter in Loch Ness. 633 which the balls reached the compass, would have been helpful. The observa- tion on afternoon of the 20th shows a N.E. return current at 150 feet, with a velocity of 3'5 cm. sec. An all-night observation beginning immediately after shows a small current with directions N. 80 E., 4S. 50 W.100. Had the balls been distinguishable, and had it been seen that the N. 80 E. ball was the first indication of direction, less doubt would have been felt in making the statement that there is a tendency for the return current to rise towards the surface, and for this secondary current to appear. It was mentioned in connection with the Invermoriston observations that as the season progressed currents penetrated to greater depths. The observations at Fort Augustus show the same thing, and all the observations go to show that the surface current and the return current are chiefly con- fined to the water above the temperature discontinuity. There are small currents deeper down, but they are negligible in comparison to the upper currents. During the season of the year within which the observations were made the temperature discontinuity is gradually sinking, and therefore it is found (1) currents are appreciable to greater depths, and (2) the velo- cities in individual cases are less, owing to the larger mass of water affected. This confinement of the appreciable currents to the upper layer may be seen at once from the Fort Augustus observations. From 23rd September till 21st October there are eighteen observations at depths below 250 feet, and in only one case did the velocity exceed 1 cm. sec., viz. during a N.E. wind on 24th September. In several of the other observations the meters gave no indication at all. In this connection it is interesting to refer to Forel’s description of “les eaux troubles du Rhone ” ( Le Leman, vol. ii. p. 280). During a strong north wind when the surface of Lake Geneva is viewed from a height the lake appears to be separated into two compartments. For a mile or two from the shore of the lake the water is greenish, while the rest of the lake appears a deep blue. The line of demarcation is quite distinct but does not run parallel to the shore, and varies from time to time. Examined closely it is seen that the blue water is quite clear, while the greenish water is opaline with a low transparency, which is not due to matter in suspension. This greenish water Forel thinks is the water from the depths of the lake brought to the surface by the return current. The extent of the lake which takes on this greenish appearance indicates that the rise of the return current may be felt at a considerable distance from the windward end of the lake, and it is not surprising that one mile from Fort Augustus, or even at Invermoriston, there should appear to be inconsistencies in the current systems during S.W. winds. 634 Proceedings of the Royal Society of Edinburgh. [Sess. For with different strengths of wind the return current must come to the surface at different points. Fig. 4 shows the typical direction of isotherms in a thermally stratified lake during a moderately strong wind whose direction is shown by the arrow, and it is easy to imagine from it that the return current may take place very near the surface at the windward end of the lake, and also that slight variations in the intensity of the wind, or the rise and fall of the temperature seiche, may cause variations, not only in the strength of the return current, but also in the depth at which it is found. To gain further knowledge of the behaviour of currents when the lake was of uniform temperature, arrangements were made for Mr Wm. DIRECTION OF WIND Macdonald to observe during January and February 1909. The observa- tions were not taken with any very definite object in view. Mr Macdonald was instructed to make observations at stated depths and intervals. Had there been any change of wind during the period he worked, better results might have been obtained. As it was, the wind blew persistently from the S.W. of all strengths to a gale, and in practically all cases the observations show greater velocities in the very deep water than at intermediate depths, and persistently in a S.W. direction, with numerous cross-currents. The following examples will serve to show how consistently S.W. the currents in the deep water were. This must have been an accident, due to the point at which the observations were made. The position of the return current was not detected at all, and the presumption is that it has been forced up into shallow water by the shallowing of the lake, as indicated on page 631. 1908-9.] Observations with a Current Meter in Locli Ness. 635 The examples referred to above are as follows : — Date. Velocity. Cm. sec. Depth Feet. Directions. 1909 Jan. 11 37 300 15S. 54 V .50 „ 18 3-3 150 GS. 41 W,90 „ 20 3T 450 18S. 50 "YY .120 „ 21 3 3 450 / 108* 80 W.190 \ XN. 60 E. 55 5? 4-2 200 15S. 31 W.110 „ 23 7-7 (?) 400 8S. 55 W.20 „ 25 37 400 f io8* 61 V .100 t XN. 60 E. „ 26 3 7 465 13S. 50 W.80 „ 27 4*6 465 i0S. 48 W.40 95 55 4-4 400 f 158- 70 W.110 l 52 A¥ .140 95 99 3T 300 4N. 60 E. Feb. 12 6*4 465 22S. 55 W.60 Summary of Results. From observations so complicated and, at times, apparently conflicting, it is difficult and dangerous to draw general conclusions, but it is thought that the following deductions are justified with regard to the currents in Loch Ness: — 1. When the lake is of uniform temperature, then the direct current produced by wind is felt to considerable depths, and the return current is also felt in the deepest parts of the lake. 2. When the lake has become stratified and the temperature discon- tinuity has appeared, the return current is nearly always found to be above the discontinuity, although there are indications of secondary currents in the same direction as the surface current below the discontinuity. 3. When a wind follows a calm, or when the direction of the wind changes, the direct surface current is felt to a considerable depth ; but when the wind has been blowing for about twelve hours the return current asserts itself and the surface current is restricted to a narrower zone. 4. When a calm follows a strong wind the isotherms tend to assume a hori- zontal position, and in consequence there is in the upper layers a current in an opposite direction to that of the wind which has previously been blowing. 5. Towards the windward end of the lake the return current may take place very close to the surface. Towards the lee end it is found in deeper water. 6. At the windward end of the lake there is complexity in the current coming to the surface. 7. There are indications of secondary currents in the same direction as the wind below the temperature discontinuity when the lake is stratified. 8. Cross currents are frequent and form part of the circulation of the lake, reducing the strength of the main return current. Temperature Observations at Invermoriston. 636 Proceedings of the Royal Society of Edinburgh. [Sess o CO o L' rH F • o o CO o tO • CM tO CO CM FTfOHOCOCOFbiO 00 CM CM 05 CO F O iO .hCOhF CM 05 CM CM CM CM * * • ft * * * # m a a ft ft ft CO F ft ft CO F F ft CM ft ft ft ft V f ft :ftftftft ft CO CO CO F F F F F F F F F F F F F F FFFFFF FFFF F F F F o F tO o CM 00 to to 05 r-H ft ft CO tO iO rH 00 CO 00 F tO CO O CO F F O 05 00 F F .005000 rr rH rH r- o CM T— H T“ H CM * F F ft to F F co ib ft •/ F ft F CO CO F F tO iO tO F CO ft F CO ft ft ft : to lb F CO F tb F co F F F F F F F \F F F F F F F F F F F F F F F F F FFFFFF FFFF F F F F tO rH tOOOOO 00 CO CM O CM r-H F CO F O I>- <— i 00 OFOOJC^O .00CMOO00C0CMIM • * * * * * tb ft tb tb F to ib tb tb lO ft ft tb tO CO CO ft ft ft toFcotoFco :concof ft 00 iO F F F F F F F F F F F F F F F F F F F F ftftFFFF FFFF F F F F o ■4* to CM CO r-H I>05005'FC505C01>0 tO OOWftOCO CO ft CO 05 CO h h h 00 .FOhoOCO F 05 CO tO rH rH CM 1>- CO J>* 00 00 ft tb tO to CO CO CO tb ib ft CO iO 05 1> ft ft ft ft ft ft tb ft ft : ft oo oo ft 00 05 ft ft F F F F F F F F F F F F F F F F F F F F F F F F F FFFFFF FFFF F F F F to 1- 00 CO O O CO 00 CO F 00 CO 00 CM 00 F CO O O CMO(MCMOC005C0t0 00(MH CM CM rH 2 * • * * • m 05 05 03 t— i>- CO 03 oo r- co ft ft I> CO O (M r-H 00 05 00 05NC01>0000000500500005 F F F F F F F F F F F F F F tO tO tO F F FFiOfFFFFFiOF tO tO tO F o tO co co f CM rH rH F F 05 CO O F 05 CM CO r- 00 F ft 00 ft i — i COFCOOC5J>NCOtO!>OiO to O 00 00 o l H CM 05 COOOCOOC50000 CM o O^) OC> OC> 00 O CM CM CM CM C0(MFOh05 05OFi — i O r-H CM rH t-H F F F F to tO tO to F F F tO to to F F F tO F tO tO tO tO tO tOtOiOtOtOFFtOtOtOtO tO tO tO tO to # # # . cp tO FOCOF r-H CO rH cp F CM opftPPpcMOcxiipipcppcoipic-Gpipftcocoipcp l~ • • • . CO o o CO CO rH r-H O CO F ft CO CO CO CM i — i O CM CO CO COCOFFFCOCOCOCOCOCOi — i CO CO CO CO F to tO to to tO tO to tO to to to to to tO tO tO tO to to tO tOtOtOiOtOtOtOtOtOtOtO lO iO o o o F 05 CO O CM © CM ■— H CO CM OOF CM ft CM ip CP 00 O 1— 1 03 O r-H 0(M050FC50005J^OOI»00005COOQ o H rH CM CM O rH rH CO CO CM CM rH CO F F ft ft CO CO CO —1 CM CO F F FFtOCOCOCOCOCOCOCOCDl> co CO co F F F tO to tO tO to to tO iO tO to tO to to to to to tO iO lO to tO to lOiOiOtOtOiOiOOOiOiO to iO tO tO to . jp . CM r-H O 05 oo F r- CM 00 l.r. 00 00 cp CO F 1— 1 FOQtOOFiQOCOONOONft # CM • • CM • • • i— H ft F CM CM CM CO ft ft ft CO CO ft ft — ft CO to to CO CO CO CO 1^ CO CO CO . ft ft ft F tO tO to tO to to to tO to to tO lO to tO tO tO to to to lO lO to lO lO to to to to to to tO tO tO o rH F I'- F to F e-H rH CM ft co ft r-H rH CO F CO CO CM F F CO CO to to F F CM CO CO to tocot'NcojHiHiHCO^oor^ I i> CO I> o f F F to to to tO tO tO to tO to to tO to to to to to tO tO tO to to to 10 00000*00000 lO to to in o o o o CO © © CO © © ft tb CO* ft ft ft ooqqqoqoqqqqoqoqq ft CM ft ft CM* ft ft CO* ft CO* O pH Jft- rH iO 1 I>- rH CO Noon o o o ft ft ft M rH rH r-H r-H rH H rH rH r-H rH rH rH rH rH rH rH t-H t-H r-H t-H £ rH rH rH r-H rH r-H r-H rH r-H rH r-H r-H rH rH . Tf rH rH 05 O rH r-H t-H CO F F to tO u 9 9 t>» 00 00 O rH rH CM CM C0C0Fi0iOJ>N00C00505OOhh 00 r-H r-H CM rc co co r-H — H rH rH r-H t-H r-H rH rH rH rH r-H rH rH i-H rH CM CM CM CM 0) 4-3 o • 03 b r*"i ft hn bb . i— 1 P- p 03 H £ #- p £ £££££££££££ CN •" H ^ ft <1 ■H H ^ ht> <4 1908-9.] Observations with a Current Meter in Loch Ness. 637 CO iD q 05 iD O CM r-H o 1^ rH CM P CD rH ID CO iD O rH iD iD iD CM rH rH CM O O CO CO CO CO rH CD CO OO * iD rH rH rH * CM CD CD rH iD CO CD rH CD rH rH rH CO CO iD I- iD rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH 00 iD ip CO cp 00 O O O ip O CO 00 iD pH O iD O CM 00 O i^ 00 © O 0- CO i-H 00 CO CO rH rH ib rH rH rH * i^ CD ib rH CO CM ir- cc iD iD rH CD CD 00 iD ib CD rH rH 05 05 b rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH o o CM oo CM o O l£5 O CO © CM o cp CO O 1 - O CM O r— H rH rH CO r-H rH CD 05 rH rH bn CD ib CD CD iD bn * 00 I' CD ib b CM oo CM CD CD CD r- 00 00 1- r- i- ib ID i—H i-H 05 rH rH rH rH rH rH rH rH rH rH rH rH rH rH iD rH rH rH rH rH rH rH rH rH rH rH iD iO rH lD Cp r-H p (M iD Ip CM O pH O O O r-H 05 O 05 I- pH ip P ip O 00 CO iD CO -H CD o rH rH ib CD CD 00 i> CD CD ib 05 oo oo 00 o (M 05 CM 00 CD CD do 05 r-H 05 05 05 IT" CD i—H CM O rH rH rH rH rH rH rH rH rH rH rH rH rH iD rH rH iD rH rH rH rH rH iD rH rH rH rH rH iD iD iD i5» o iD o o 00 O rH O 00 rH pH o O O O O rH O O iD CO O tp r-H I-H O 00 i^ O CO CD CD O 05 cb r-H rH 05 CM 05 6 rH CM CM CD 6 CO CM CM 05 r-H O i— H 6 rH rH CO 00 r-H CM , 1 rH rH iO rH iD iD iD rH iD rH id iD iD iD rH *D iD iD iD rH iD iD iD O iD iD rH rH iD iD iD rH o o O P O 00 CO r- O ID O 00 O O rH iD O O O O iD CO pH i~ pH rH O ip O O CD CM CM CM ffc 5 CO CM CM CM rH o ib CD ib iD rH CM CM * CO CO rH rH rH CO CO I l I r-H D1 * r-H i—H * CM id lO iD iD iD iD iD iD iD iD iD iD iD iD iD iD ID IO iD ID iD iD iD O O O O rH O 00 O O 00 05 CO CO CO CO CO CO CM CO CO CM CM rH rH rH rH rH rH rH rH rH rH rH r-H CO CM 1- 00 O 00 CO o O cb CO cb ! rH CO CO CO CO CO CO rH rH rH rH rH rH rH rH rH rH pH I I I l rH * * rH pH L” I- p pH CD rH rH CD rH r-H rH rH rH rH CD CD CO 1^ iD co rH rH rH rH rH rH rH rH rH rH rH rH r-H O CO O i-H iD r-H CM iD t-H CO ib r-H i- L- cc 05 rH 05 05 rH CD rH iD rH rH rH rH rH rH rH rH rH Qwwowoooooffiai O O iO O ^ O iO ^ ^ ip . : : : : : cd : : rH m ► — ■> t— ' H rJl & O b CTMqOipClO^no^H i>i n w (k 6 h h 6 6 iO Ci O iO iO o O uO iO iQ o H P? O H <1 cpOWMClOHOQO^p bbcbdobdocbcbrncMdo CCiOCiOOiOCiOiOiO . CD O J> (N M © 9 jt' ICobbbrHrHrHCOCM COCiQiOiOiOiOlO CTiO^O^-ipWOHO CM CM CM t~h t— i t-h CM CO CO lOiOOCCiOiOiOiOiO © O 05 O O CO rp CM CM I- 1 iD MM^MMMCTCOMC-lH lOOiOCiOOiCiOCCliQ o q o o o o o o o o o q o o o © © © © © © o © © © © © © © © © r-H CO r— H CO r-H CO i-H CO r*H i— H rH 1>* ?— H CO . ^ P"H CO r-H CO r-H r-H ^ r— H CO rH CO i—H CO r-H CO r™H r— I r— I i-H rH r—> rH r— I r-H rH rH r-H r— < rH r-H rH rH rH rH rH r-H r-H rH rH r-H rH r-H r-H rH rH oo Soooo o o o o W S O O CO H CD O H CO C5 rH rH rH rH rH rH ^ rH rH WCM^^OOCOCDl>QOaiOiHrH(MCOM^'cl(iOW^OiO©COr^J>GOOO® CMCMCMCMCMCMD-ICCitMCMGClCMCOCO r— I r— I rH r— i i— i i — ! r— Ip— Ip— I r-H p-H U1 CMCO^^OCDCDQOaOiO CM CM CM CM s ® .-s > o CO o OS d T-H o +3 rH • H £ Q £ >4 ^ ,-e >■ ® o M o w !> G o ffi G o o a> ,2 >s ® .13 o X -t-3 o OS o »“H as > -4-3 OJ Oi 'N 1> H (M COO ^ ^ >o 40 o io CO 05 40 SO 40 rG 1-3 -+J . • SD OHH o 40 xn o SO cd OS 05 05 cs CO OU3 4J so t-h Hi CO so m C4 OS I I I rH. © O CO CO rH CO ^ ^ CO O SO SO 40 SO -rtf TjH o cip (N rt -p • o 5>* 5>» CO w 05 so w © 40 a w o o 40 05 40 SO m m • rH m Cl os CO os 05 OO CO l— I 05 CO I i '' J>. O rtf -if o rtf w rtf CO CO SO -1-3 Xfl o m c3 a a o o TJ1 QJ S3 o o rH rO rO .2 c3 m o> CS3 o . rH rtf I 05 c3 G cr1 xn H - X SO G m rtf 05 o 40 o o o o rtf o o 40 o o so o o 5>- Station 1908-9.] Observations with a Current Meter in Loch Ness. 639 PQ oo 0 01 r— I -1-3 m 3 bO 3 -+-3 02 OO o 03 T— I p— 5 3 •“5 -1-3 02 r— l CO 00 o 03 +3 o CO oo o 03 3 •—3 03 03 3 o E ,5 N a> > o 3 O e o CD .2 n ® -t3 > ® 03 T— i I o Ttl £ m 03 ?H 3 O E 16.42-17.15 17.57-18.8 17.23-17.50 10.52-11.22 11.35-11.57 20 10 30 o • H p4 E E 4-3 o : oi 52 ^ : : : : • OO ^ rH s : ^ CO : 1-H : 1 l p- o v'-“y— H rH CO 03 t>- ^+i 03 r-H 03 OO 3 rH r— 1 rH * | o • • * • oi • • E t-H © r-H rH CO rH rH rH O O d 9 • - -03 -CO " th ' CO 61 CO i 03 £ m CO m © © i oo £ o E 3 3 cr1 03 02 9s co Hco©©©©©©©© 3 CO 30 © Q 03 OP © m ^ 03 © © © T— T N © rH . . rH • rH l o O ° • * I (M * • 7A © 03 CO ©‘ © r-4 03* © rH rH H Oi • rH -+i O 05 in CM r“l m &JD & £ © . • © • © CO * ■ rn © © © CO 03 CO HT1 rH © H4 03 03 IN rH rH 03 © rH rH • H • rH rH H 00 CO • 1 co rH CO -HI 03 © © 00 r-4 ©' H oi 03 © © rH ?-H rH rH rH rH Oi r-H Hi O O C4 . © . rH rH rH rH l • • T“ H • ■ hH o IO CO • ' • 1 • rH CO ©i CO OO i— < w rH O © © © r-H rH rH rH rH rH 03 O e 1 in H Oi rH 3 biO NN E £ • : io • • • <1 . o Hfl • rH * • # • m rCl Hi m 02 o\ . © © Oi Oi • ° • • • • # • • e • r— l © 3>. • - rH • pH © © © © iO tH H 03 H rH rH • 1 ® • • i • l O o • © • •- 03 • • • rH CO OO ©* rH 03 © H rH rH © 1 — 1 Hi O © © i in 05 rH CO 3 feO £ > . E 03 £ “ Tf* I * * © • 03 CO : • 02 T3 rH co ID E co m © ■ . © . © © ' ©„, • oo 03 © H ©CO © © © CO © in 03 CO Tf © © © © © - 02 rH 03 Station B — continued. 640 Proceedings of the Royal Society of Edinburgh. [Sess. oo O' 05 bfi 0 <1 OO o 05 bO 0 -M o 00 o 05 w 0 bfl <1 tX +5 00 O o w _o +3 o o> il) -4-4 >’o o ffi rd ^ > o t-i 0 O ft •ft o a> o r® ft (M ft CO CM r—t cm’ rH . • rX 1 * * ’ * 1 ft VO CO I CM © ft I O ft ft £ o o ft ,© c3 • rH 3 > CM • o o I — < i-P I o ft ft CM CO ft CM CO id a o CO ox o i £ 05 OO ft I OO (M ft CM CO rH CM rH Cl r— I rH rH i i i CO ft ft ft ft TJX CM ft I 05 CM • oo ' oo m ^a a ’ (M CO iO Ol ft 03 bO rS 4-5 !>. o ft o CO 05 ft 00 05 ft rft rft ; I i ft 1^ co co J> *H vO Ci • ft TJX CM* id (=! o • rH o £ 02' P> o o CM rtx H • ft CO 00 b. ■ CO CO 'cf HCKN ft ft O O O O O d ft i— X CO ft 05 O 00 m ^ ^ oo o 05 m 0 to 4-5 TJX 00 0 05 ft -ft CO 0 bfi 0 ■<\ 01 -ft CO 00 o 05 CO 0 bO ft CM ft 00 ft ft tjx o ft CM CO VO ft CM r— i cm' r—i rp t" o' rH | ; ; rH rH rH rH . rH o • r^- co Htn 0 Hi OO o Tf rH TJX CO ft 0 cm’ o' cm' id id CQ 05 rH rH rH j-H rH rH rH VI O CO &J0 S > • rH T3 t- x - o g CM O ft CM jp > e« GO T" nO CM O no o OO HO co W 55 55 {5 55 .a ^ sc . . m rH no . C5 no i-c 0) +4) • • • fc> ’o 3^ if CM rH rH r-H co CO OO ?“H CO no CO no CO CM 05 rH co co" i~4 r-H M no 73 rH • r-H rH rH l-H • rH i-l o 1 1 CO 1 1 1 1 1 hH rH CO 30 CO HH co CO 05 o oi 'CtH -Ctl oo o' no co t— i— i CM cm" p o r-H r-H i — 1 rH 1 — 1 rH l-H l-H 05 l-H +45 C/2 So o & O 55 • pH Q 55* 55 05 -f l-H i >, 3>- no o 05 CO no rH 'd rH r-H rH rH l-H co rH Th CO oo no oo 00 CO CM CM co CM r-H rH rd rH cm' CO id o' 2 l-H rH • r-H • r-r r—i l-H r-H o i i • • i • 1 oo i i : i , W Tp no 05 no no CM if CO co CO TP CO 3^ O rH no "N CO i- o rH T— H rH l-H r-H r-H l-H 05 l-H O cm" O o C IO | m b£ c +5 50 p4 no -H W co CD H O r K co m & o rH W < a CD oo no : : : CM : CO no : o (M 55 OO • i— > Q 55 r— 5z* H< 55 05 55 I> 55 co i-H r2 >3 CM o no o CO rH 00 • * CO l-H rH . 5> o rH co CO CO 05 it- 05 no CO HJH CO id l-H l-H cm' tP* 1^ p rH rH rH rH r-H . • l-H . • • • 1-4 o 1 1 1 CM 'OH i i • i • 1 ffi 05 CO 3 00 CM 05 CO CM CM CM ® 4-3 • • • • • • • • 5> 'o rH l-H l-H CM r-H r-H r-H p o no O co no o Tji o co CM o O rj co Tp so CO 00 00 05 05 O IO O in rH r— ' CM M o o CO no O loo CM rH no no |m r-H T—i M 03 no" no p r-H rH rH r-H rH . l-H • r-H . 1' — IO 1 o 1 • co oo * CL. . i . . GO • 55* 55* H £ ° : ^ .co . c 1 £ . CO "fl r—l 'tfl co o 03 I — C 4-3 m 73 bfl 73 CM CO o o 1 — ' HT 1 — l-H r-H CO l-H r—l r—l I I I co oo no nT5 r—i r—l o i-4 cm' 00 CO nO CO r-H t— I I I 1*1 I/— r-H i — i CO no 3=fi“ s “3 “ oi«i“ 01 I O no CO GC I CM CO g I ■H O . o : : : : : : : : : • no m w N. 3^. nO • O CO if i— 1 ‘ t— O CO M CO rH 05 CO O Tf CO M M CM rH rH (M CM no CO P o' l-H rH rH . rH rH T-H l-H • i-H ’ — (M . 1 1 o rH CO • CM , lO rH CO 4ti nO 4*1 CO M CO O I-H rH CM CM* no' co' r4 05 r— < rH rH l-H r—l rH l-H 1-1 rH +D C/2 08 OH O o 3 CD co bJD W W W <1 ;sg • 2 • • OO ^ * o 00 o 1^. 3 • ; H 04 55* 03 C4 CO <55 CO o 55 I> M no M ^ • O co • Oi . # 05 no M M ■ (M l-H M rH O rH T — co rH rH o rH rp rH 4*1 4+ C/2 rH GO Cl M rH CO no o r-H CO M i-l • r-H r-H rH • VnOOnOOnOcMOO 03 COO SHCCTttCONOOOJIM CO IO OOO ^C r-H i — I rH t-h CM VOL. XXIX, 41 Station B. — continued. 642 Proceedings of the Koyal Society of Edinburgh. [Sess. 00 o 05 &0 p H +5) 05 CM OO O 05 K P ££ p CC CM CO o 05 i— I ■+53 m P &0 P < -55) I'-. CM OO O 05 rH +53 CC p P < rP 4-5 50 5 4-3 o > 'o o w G o • rH -H o CD £ >3 ® .13 !> o G O E > o o W G o • rH d-d o CD L • rH > O CO kO rH 00 O to rH rH tH i i i rH O O tMQ (N o' id co" i— i ig co j— I Tfl ^ rH (M rH • i— I i— l i-H : i i i 10 0 50 lO lO H |iO I CO I lO CM W +3 . o p CM >• m i o 00 OO O 05 H lO . 00 lO CO O i — I 50 -5 Ed j4 • O o * ! oo t£> cG o HtH 'P 05 05 Ed Ed O IG I CO ^05 ^ £ m o o CM CO rH 1 id o rH rH rH . rH • • ; • rH 00 ■ o * • • CO CO CM IG CO o’ IG 50 rH td o tH rH rH rH rH a' o § ° © c3 Cl r co © © O fco Ed o iG 10 w 40 W. > . : o : CO ; i : Ed o 7h rt C3 O S3 Q ^ >3 > u 40 CD CD (30 | 1 l 1 pi CO rH CO £ CD CM* rH CM* o’ cd rH rH i — 1 rH < # | 1 X^ * CO rH 1 r~ j CM 04 rH pi 4>. -+—> CO CD CM r-H rH x^I rH rH rH rH rH rH o o cd o oo pi - CM 40 • 40 • • • or Hi • rH o rH rH X^ rH £ CO* pi rH oo CO OX OX o o* rH no CO r— | H I rH 1 rH l rH * 1 O 1 CO • • 1 * 1 HT» • 1 • x>. K 1 — 1 CO CO OX o* o rH rH I pi CO co* o 50 CO o o rH 'rtf cd cd S3 l> O *4-3 05 05 *00 ; <•? : •* CM pi CO P< pi U cS > c3 v CM PI O C 13 oo O 05 03 P a 03 -4-3 p4 03 co 05 OO O 05 03 -O a 03 -4-3 P*4 03 CO 4-3 CO co o 05 03 P a 03 -P> Pi 03 CO 445 !>. CO o C5 03 P a 03 4-3 P 03 CO rP -43 CD CM CO oo 140 CM 40 CM* |rP rH i • >7 ■ • oo CO CO rH CM o pi : : : : : : : h pi cd 'Tl CM ; ; ; ; ; ; ; H ; CM CO * * t“H r-4 O pi I O pi o CM 40 I o CO ID (M 40 rH rH rH c3 >5 rr* e4 W s -p c n o . . o CD • : £ . . HP £ rH ^4 H 05 • • • OO oo • OO . co — ■ CO CO pi rH 40 17 CD (M* 1-i rH 40 © 1—1 i — 1 1 — 1 1 1 1 rH i : 7 : : 1 ‘7 1 1 CO CO T— 1 • • CO CO H pi N rH CO l — H 1—4 O OX* to r-4 i — 1 i— 1 r-H rH rH ■sw O 40 co oi > • 40 o o • • Ol : cm " 40 pc pi CO CO rH o CD 00 |o- CM 40 O CM r-H 7 CM* CD* CM* co id o rH rH rH . rH rH . 7 • - • so so 1 1 r- HH O pi CO CO H 04 CO OX iO rH CD CM CD* rH rH rH rH rH rH © © £ : : o 40 * • co • c3 • • * * rH ,— | rH > * cd fd F-I IM CO iO 05 CO CM CM A- CM 0O CM 40 pi 4-3 7b *p a > o too a o pi i CO £ cd CM I F— 4 £ cd dj io o o o 5 CM CO 40 CO CO O O O O O 40 05 CM CO 40 1— l CM rH rH rH C'X OX V’lNiOO O r- 1— I CO CO CO o o 05 CM O 40 O O 40 00 >— I CO r-4 CM CM Station B -continued. FORT AUGUSTUS— STATION 644 Proceedings of the Royal Society of Edinburgh. [Sess. d oo o 05 05 JO £ 4-4 00 00 OO CM R o w o o OO VO vO 1-4 i — I I I o o CM 00 vO vo o o o o i — vO r— I CM OO CM VO cm’ t— < r— C i—4 i — i I I I I vo O O VO vO OO rH 00 CM CM pH O I'O ;r i VO J-4 O OO* CO a o • r-H 4-3 O CD H (M P3W vo o co co W ^ W : vo ® _ vo . •^C° ^ dcd ^ 0 ^ ^ £ vo CO GO rJ 01 CZi CM W 2; o +4 p4 r£ >5 ®.-S > « 00 vo . rfl *0> 00 r-t ■ CM CM OO CM 3 O w o CO o iO vo’ rH vo • : o *"H rG >4 05 44 <*■ ’o vo <04 00 O 05 *4 05 rQ P4 05 TJ1 O CM O ffi vO CM R O • rH 4-3 o o c3 2 >3 4-3 go : o ^ : : § «o : cd ^ 05 IO v — • — ' VO • rH vO vO o o VO r—H HIC o CM o' co co’ kC co’ r— i rH 1 | r-i r-H ’-p VO vO 1 O o 1 o : < kO rH TJH -T cm 05* r-H C rH i-- ° 1 IvO kO Ico oi VO |05 t-H 1 r-H 1 1 CO 00 CM • G CM CM • • co c3 cm’ CO Ph rH rH H • rH . O H O *4 C-l X> •rH S § u co a I O CM £ GO O vo 05 CM CO © CO (M! o o o o IO CM CO CO Tfl 1 H g3 r-> s3 ?> ® £ > o 4)1 CM • 1> vO co I-H O CO vO • i-H CO r— T— H I-H 00 i— 1 l i . | : i ® VO o • lO • co EG V oi f-H CM O I-H CO* co ' r-H i-H © ~ o ^ sa >' 43 o O VO : o : : . ‘ rH t> EG m A & i-H o (X) 4-3 E> © VO rH o EG 4-5 © © ® .t3 © O EG s o • rH H-3 o p • f—H Q 0> 4^ 'o c3 i> o tG • o CO o CO t^. I CO t>» tG o o CO *o OO 05 I I o o • uT5 OO . oo co CM o' t»h ^ CO ^ zr cc EG CM 4f -)1 I CO m vo vo © o o 44 © O 4-5 05 OO O 05 © r2 o 4-5 © O 4=1 4-5 OO 00 o 05 o 45 © o 00 o C5 © 42 o 45 © O Tin -4 1 O CO to vO o 6 I EG S ? ? I EG 0^00 ° 4)1 *2 to to 20 C/2 E^l Hr £0 ■n 04^ 4 C' 00 M . CO H CO r- (M 1— I 4)1 rH vO CO CM • CO CM oo O I o • 4)1 o j . I-H ICO I " I o o rG M. I-H CO VO CO 1 & > EG ^ O O 4)1 co £ ^ co o CO C+H o o o o o VO O o o o o o o o CO CO 05 (M 00 -M o o CO 05 Cl o o r— H rH CM CO 4)1 m 1—H CO 4)1 o 45 £ m £ o cS &c ‘5b r-j C$ r3 o T— I EG o 45 EG o -45 &J0 CO • rH f-i d c3 a rcS © 02 £ £ TJ O 45 CO 02 s o 10th October 1908. 12th October 1908. 14th October 1908. 15th October 1908. 646 Proceedings of the Royal Society of Edinburgh [Sess, o ft 44> o o> 03 -1-5 !> o R o ft a o • r— < o a> >2 o ft a o • r—* O O Sp £ ^ 43 -tf >• « R O 3C R O • ^ O a> !> o CM hH W CD (N CO CO o o • • • . . H (M CO ID GO Oi t— i I — I | — I r— ' I I I ! I I 0 ift o O 1ft O ^ ^ CO ^ sc tX ^ go, go’ go go’ io 09 a O 0)0 Tf fN - 00 ^ (M lft ift lft CO I'— f — i l-H i-H l-H CM CO 00 CM CO CO I CM £ GO* R r— H c3 0 HH> CO 1 £ 02 Oi I lft co so 3 i CO £ lft GC o lft 02* go be £ 02* CM * ’ • SO 'V'OOOOOOO O O O R CO CO Oi CM lft OO ift O lft o 02 rH i-H i-H CM CO CO H* 00 0 01 03 rfl o 441 o o o CM 00 © 01 rH Si 03 R o 4-3 so 0 -R 4-3 01 OO 0 01 03 R o 44) o o 00 0 01 t-h Si 03 |-R o 441 03 o 44 so O CO O CO OO © CO 1ft l-H CM CO IO . i — I (M lft SO Oi l-H l-H rH rH i— ' 1 I I I I I O O CO O CO OO lft CO lft r-H CM CO 00 O l-H CO H lft I'M lft ISO I £ CO T3 03 £ GO* H 00 lft CO -hH TfC CM CM 00 1 SO lft to CO 3 | Ko • ■ • r-H lft i i-H i-H * I 1 ... * ■ i o . ||... * 3’ O) CM O* CM* CO* rH i—i i-H I I I lft Oi 1ft hj< ■ (M Oi CM ift HJC lft Htl CO w. o ' t4. > Htc I CO w sts o 43 -3 03 43 a CO 'll o3 a S o o 00 IH IJT -CO 01 lft Ml 1— I o o o o o CO SO Oi (M lft m o o O lft CO CO Station C — continued. 1908-9.] Observations with a Current Meter in Loch Ness. 647 co 00 rH r-H LQ rH i CO CO 3 1 l-H rH l \ | l-H : i : . . O w CO • Ol • oo • • • m rH rH cm m oo © rH CO • rH c3 o rH >5 03 r-H CD CD r^ rC r~j H3 o 4-3 _o o O -4-3 • . • .... G o o CD o H F-i 4-3 4-3 s s > o • o o • GO • • • . ‘ ’3 i-H KG O e- in in in cm H CO 1° • CO e o CO CM co m • G O w l-H 1 VO "7 7 : o cm • i— t * — 1 : i : : i • t>. • • m 105 1 O B • in °. r4 rH CO a o CO 05 nT3 rH Ol CO rH o rH rH rH o 03 4H k CM 'S | » CM . m 00 • O 00 • 05 if , > o r-H l-H r-H os in co r-H Ht- CO O 1© o e • • o 7 e O CO CM HP G 05 . r-H _ rH ?-H r-H . l°p O M o 05 • in oo o no . 00 rH rfl CO • . . . CO rH Hfi oo 05 m O rH i-l o o rH rH 4-3 05 m G3 f-H O 50 50 0 120 30 : c3 > -1-3 C/3 r-H rH • rH Q GO* go' br‘ , 05 ^ ”2^ 4-3 co Ol CM d 1 o Velo- city. : : : 05 • CO CO OO : GO w CO * rH 04 rH o o o o o o m o o o r* CO 05 CM m oo o cm in o o m rH rH rH Ol Ol Ol CO -Hi Cl o Cl 648 Proceedings of the Royal Society of Edinburgh. [Sess. XXXIX. — Hydrolysis of Salts of Amphoteric Electrolytes. By Miss Heather Henderson Beveridge, B.Sc., Carnegie Research Scholar. Communicated by Professor James Walker. (MS. received June 12, 1909. Read June 21, 1909.) Different experimenters on the degree of hydrolysis of amphoteric electrolytes in acid solution have obtained very discordant results, according to the method they employed. Winkelblech,* for instance, from his work on the rate of catalysis of methyl acetate by ortho-amidobenzoic acid hydrochloride at 25° C., estimates the hydrolysis constant ^ at 120. From the electrical conductivity of the same solution at ^ = 16 he gives the value 180 for The calculation of the hydrolysis constant in these two cases rests on quite a different basis. The rate of catalysis depends simply on the con- centration of hydrion in the solution, and therefore should give as directly as possible the amount of free acid present, and so the hydrolysis. The conductivity of the solution, on the other hand, is the sum of the molecular conductivities of all the substances present. It depends, therefore, on various factors, any of which may conceivably exert a disturbing influence on the others. There are present in the solution — (1) The Salt, of the general formula HRC1, probably largely dissociated into its ions, HR and Cl. (2) Hydrochloric acid, formed by the hydrolytic action of waf er, and also highly ionised. (3) The amphoteric base HROH, equivalent in amount to the free acid. It probably contributes but little to the total conductivity, as it is only slightly dissociated. (4) Water practically un-ionised. It was thought, in view of these results, that some effort should be made to find out what values are given by methods independent of these, in order to be in a position to judge which of the original methods is at fault, and, if possible, for what reason. * Zeitschrift fur Physikal. Chem ., vol. xxxvi. p. 546. 1908-9.] Hydrolysis of Salts of Amphoteric Electrolytes. 649 Ortho-amidobenzoic acid was chosen as the most convenient example of an amphoteric base whose hydrolysis in acid solution was neither too great nor too small at the temperature and dilutions examined, and therefore most typical of the class. Electrical Conductivity. The conductivity experiments were all carried out in a thermostat at 25° C. The water used was distilled in the open air, using a block tin condenser, and its conductivity at 25° varied from *8 to 1*3 X 10-6. The degree of hydrolysis, x, was obtained from the formula x = — — / Mhci Mv where Mv is the observed molecular conductivity and juv the molecular conductivity of the unhydrolysed salt. The values for juv were taken from Winkelblech. His numbers in Siemens mercury units were recalculated into reciprocal ohms. V. fXV' 16 102-6 32 106-8 64 109-9 128 113-2 256 115-4 . . N The values for ju HC1 were found by experiment. The original solution for each set of observations was made up by weighing out the required amount of o-amidobenzoic acid, adding the corresponding quantity of N . . N . — HC1, of which a large stock was kept, and making up to -- with con- 8 16 ductivity water. The subsequent dilutions were sometimes carried out by means of Arrhenius’ pipettes, sometimes by mixing equal quantities of water and solution in resistance-glass bottles. V. MHCI]. ftv. M, X. kb ( 1 - x)v K" a* Winkelblech. 16 392 102-6 173-6 •245 201 32 400 106-8 207-2 •34 180 177 64 407 109-9 246-7 •46 163 164 128 413 1132 288-0 •58 158 155 256 417 115-4 327T •70 155 150 * Bredig, Zeit. Physikal. Chem., vol. xiii. p. 321. 650 Proceedings of the Royal Society of Edinburgh. [Sess. The conductivity was also taken of a series of solutions in which the concentration of acid was kept constant, but the concentration of the base was varied. The hydrolysis in this case was calculated from the specific N conductivity. In the case of the — solution, for example, the calculation 16 was as follows : — S = Specific conductivity of salt = H= „ „ of HC1 = M = Observed specific conductivity. x — Amount of base hydrolysed. 102*6 ~rir~ 392 16“ = 6-4. = 24-5. When acid and base are in equivalent proportions, M— (1 — x) S + rH. When the concentration of base is half that of the acid, M — (‘5 — x) S + ('5 -\-x) H. When the concentration of base is *25, that of the acid M = (*25 — x) S + (*75 + cc) H. The hydrolysis is of course at a maximum when acid and base are equivalent ; and it will also be noted, although it does not follow from the foregoing, that ^ is at a minimum with equivalent proportions of acid and base. The variation from the mean becomes less and less as the acid used is more dilute. (1) Constant Concentration of Acid — — . 16 Concentration of Base. M., Specific Conductivity. X. rO |Vj |-3 16 173-1 10-82 •244 200 32 262-2 16-4 •053 256 With smaller concentrations of base, becomes still greater. Constant Concentration of Acid = — . J 32 Concentration of Base. M„. Specific Conductivity. X. kb K' 16 141-5 4-421 •1180 213-9 32 206-5 6-452 •3398 182-7 64 284-0 8-876 •2086 200-9 Mean 199-2 1908-9.] Hydrolysis of Salts of Amphoteric Electrolytes. 651 (3) Constant Concentration of Acid = — . w J 64 Concentration of Base. M,. Specific Conductivity. X. kb IT 32 178-0 2-781 •2290 175-1 64 246-2 3-848 •4590 164-3 128 310-6 4-852 •3508 175-4 256 353-9 5-530 •2856 190-5 Mean 176-3 (4) Constant Concentration of Acid — . J 128 Concentration of Base. M,. Specific Conductivity. X. kj) IT 32 170-0 1 -328 •1913 169-5 64 222-3 1-737 •3678 160-8 128 284-7 2-224 •5780 161-7 256 335-6 2622 •4994 171-1 Mean 165-8 In order to be sure that the nitrate of anthranilic acid would have acted in the same way as the hydrochloride, its hydrolysis was calculated both from its electrical conductivity and rate of catalysis. The results are seen to differ in just the same way as those of the hydrochloride. Conductivity of Anthranilic Nitrate. /ulv was taken as being roughly the same as for the hydrochloride, and the conductivity of nitric acid was taken for /aHN03. V. n-v. Mhno3. M„. X. kf, K 8 96 379-4 138-7 •1507 299 16 102 385 169 •2352 221 652 Proceedings of the Royal Society of Edinburgh. [Sess. Rate of Catalysis of Methyl Acetate by Anthranilic Nitrate. For comparison, a solution was catalysed at the same time by nitric acid of the same strength approximately as the nitrate solution. 20 e.c. — Anthranilic Nitrate. 8 1 c.c. Methyl Acetate. 5 c.c. ^ HNOo, 15 c.c. - KNOo. 8 3 8 3 1 c.c. Methyl Acetate. t. X. A- x. k. X. A — x. k 16-3 3-65 19'45 102-7 3-68 18-22 (140-0) 88-3 14-0 9-1 104-9 14-9 8-0 119-0 144-0 17-9 5-2 103-1 18-8 4-1 119-3 2100 20-6 2-5 105-5 20-8 2-1 113-6 Mean 104-0 Mean . 117-3 Hydrolysis at ~ x -25 = ”2222. 8 1 1 ( *o It was thought possible that the apparently anomalous behaviour was not caused entirely by the amphoteric character of the base, but was due perhaps to the fact that in the example taken the hydrolysis was neither very great nor very small, and therefore more affected by errors in calcula- tion caused by flaws in the theory. It was therefore necessary to test a non-amphoteric base also, with about the same degree of hydrolysis. The most convenient one answering to this description was thiazole,* C3H3NS, and accordingly experiments were made on the rate of catalysis of methyl acetate and conductivity of thiazole hydrochloride. Conductivity . — In order to obtain a value for julv — the molecular con- ductivity of the unhydrolysed salt — the conductivity was taken of a solution in which thiazole was molecular-normal, and hydrochloric acid sixteenth-normal. In this way the hydrolysis of the sixteenth-normal hydrochloride present was reduced very considerably. (This device f could not be adopted in the case of anthranilic hydrochloride on account of the very slight solubility of the base.) But Bredig’s plan is not applicable here in its simple form, because the hydrolysis is so great * Walker, Zeit. Physikal. Clhemt , vol. iv. p. 332. t Bredig, loc. cit ., p. 214. 1908-9.] Hydrolysis of Salts of Amphoteric Electrolytes. 653 that it cannot be reduced to a negligible quantity merely by the presence of an excess of base. As the presence of so much thiazole would increase the viscosity of the solution quite appreciably, a check experiment was carried out, using KC1 instead of HC1, in order to find the approximate correction which must be applied on this account. N 16 — KC1 in water 16 — HCi in thiazole 16 KC1 in N. thiazole [xv= 112*7 = 1297 = 9M N iuv for — thiazole hydrochloride in pure water instead of in thiazole will 129-7 therefore be approximately 91*1 X ^—^ = 104*8. But the amount of hydrolysis still not eliminated must be corrected for by a double approximation. Using the value ^,= 104-8 we find the . . N hydrolysis in — solution to be — - Pv 176 - 104*8 fx jjqi fx.v 392 — 104 8 = •248. We must therefore subtract for the conductivity of the HCI present (supposing the hydrolysis to he reduced to one-sixteenth of what it would N be in equivalent — solution) — 16 (392- 104-8)2^ = 4-4. This gives us for the second approximation to julv 104*8 — 4*4= 100-4. The hydrolysis will now be — Mv — fxv 1 76 — 100‘4 _ /xhci ~ Vv 392 — 100 '4 Using this value in finding the correction for the HCI present, we have •26 (392-100-4) -fT = 4*7. 16 The most probable value for /xv at v = 16 is therefore 104*8-4-7 = 100T. Now, assuming /mv to increase with dilution at the same rate as Winkelblech’s values for o-amidobenzoic acid, we have t = 2o'0° C. 654 Proceedings of the Royal Society of Edinburgh. [Sess V. V-V. ^HCl. M*. X. & b K‘ 16 100 392 176*1 •26 174-8 32 104 400 201-4 •33 198-2 Rate of Catalysis by Thiazole Hydrochloride. t = 25‘0° C. 20 c.c. Thiazole Hydrochloride. 1 c.c. Methyl Acetate. r N 5 c.c. — 16 1 c.c. HC1, 15 c.c. ^ KC1. ’ 16 Methyl Acetate. t. X. A-x. k. Another Cata- lysis. t. X. A-x. h Another Cata- lysis. 360 •85 21-60 1067 1041 360 •82 21-63 1028 1067 1500 3-25 19-20 1041 1059 1500 3-12 19-33 995 1009 3090 6-17 16-28 1039 1051 3090 5-95 16-50 995 1021 5990 10-53 11-92 1055 1097 5990 10-27 12-18 1020 1023 7260 12-20 10-25 1079 1086 7260 11-72 10-73 1016 1023 Mean = = 1060 Mean = 1015 Hydrolysis at v= 16 is x '25 = '2160 4= 173. J 1015 IC vr 20 c.c. — Thiazole Hydrochloride. 32 J 1 c.c. Methyl Acetate. 6-7 c.c. — HC1, 13-3 c.c. — KC1. 32 ’ 32 1 c.c. Methyl Acetate. t. X. A-x. h t. X. A -- x. h 1500 2T3 20-32 6639 2880 3-90 18-55 6610 2880 3-95 18-50 6707 4050 5-25 17-20 6569 6840 8-38 14-07 6825 6840 8-65 14-20 6688 8620 9-95 12-50 6784 8620 9-90 12-55 6739 Mean = 6739 Mean = 6707 If Hydrolysis at v — 32 is x -3 = *3348 = 190. J J 6707 K 1908-9.] Hydrolysis of Salts of Amphoteric Electrolytes. 655 The values for the hydrolysis constant of a non-amphoteric electrolyte as obtained from the two methods are thus seen to agree comparatively well with each other. V. Conductivity. g Catalysis. 16 174-8 173-6 32 198-2 190 Evidently the theory holds good so long as the base is non-amphoteric, and either method is equally good as a gauge of the hydrolysis. The Ratio of Distribution of a base between two solvents has been used by Farmer * as a method of estimating the basic constant. His value for o-amidobenzoic acid at 25° corresponds very well with that obtained from the rate of catalysis of methyl acetate, viz. ^- = 118. The Solubility of the amphoteric base in water and in acid of different concentrations was then investigated, as giving a measure of the hydrolysis. Bottles of resistance-glass were used for these estimations. They were almost filled with the solvent, the air above which was replaced by nitrogen in order to preclude oxidation. The liquids were shaken up with recrystallised anthranilic acid in a thermostat at 25° C. At intervals of some hours portions of the liquids were siphoned off through a filter into weighed flasks and titrated against twentieth-normal caustic soda solution. In the acid solutions it is assumed that the concentration of free base is the same as the concentration of the saturated aqueous solution, and that the extra base dissolved is therefore all in the form of combined hydro- chloride. The values obtained in this way for ^ are not constant for the different strengths of acid used, but at v = 16 especially seems to approximate most closely to the catalysis value. The solutions containing hydrochloric acid became saturated compara- tively quickly, but the o.-amidobenzoic acid dissolved in the water very slowly, the acidity still increasing slightly after several days’ shaking. * Journal Chem. Soc., vol. 79, p. 863 ; vol. 85, p. 1713. 656 Proceedings of the Koyal Society of Edinburgh. [Sess. Solubility in Water at 25-2°. Total acidity = Free base = Salt = Free HCI - ki, I. Water. In ■04137 N. •04137 Total HCI - Salt — x -0515 — HCI. 16 1554 N. •04137 •0515 •0110 N. 113-2. K •0110 x -0413 7 i— i i— i III. N N N Water. 16 HC1- Water. 25 HCL 16 HCI- Total acidity . -04315 N. •1551 N. •03723 T106 T493 Free base • • . • •04315 • • • •03723 •03723 Salt • • • • •05110 ... •0317 •04957 Free HCi • • • •00975 •01007 •01293 • 121-4 85-2 103-0 K • N 32 HC1 was also used in this way and gave still lower values of h K' The Rate of Catalysis of Diazo-acetic ester by nitric acid is a possible method of estimating the concentration of liydrion, and there- fore the hydrolysis in a solution.* It was found on investigation to give quite reliable results, and was therefore used to estimate the hydrolysis of anthranilic nitrate solution. The hydrochloride could not be used for this catalysis on account of secondary reactions with the ester. About T of a gram of diazo-acetic ester was weighed out and dis- solved in a known volume of water in a small flask. A small quantity of the acid or nitrate solution was put into the flask in a small test-tube to avoid any mixing of the liquids. The flask was immersed in a thermostat at 25° C. and connected to a gas-burette in a water-jacket at room temperature. When the volume of the contained air was steady, the liquids in the flask were mixed, and readings of the volume were taken every few minutes. The velocity constant was calculated for a reaction of the first degree. In the nitric acid catalysis, enough potassium nitrate was dissolved in the water to reproduce the conditions in the solution of anthranilic nitrate. * Bredig and Fraenkel, Zeit. fur Electrochemie , vol. xi. p. 525. 1908-9.] Hydrolysis of Salts of Amphoteric Electrolytes. 657 I. — Catalysis by A-L Nitric Acid. 320 37 c.c. Water, 2 c.c. — KNO,, 1 c.c. — HNO. ’ 16 d 8 in tube. •100 grm. Ester. ‘102 grm. Ester. t. X. A - x. k k 0 0 20-2 5 8-4 11*8 (•1074) 6 9-8 10-4 •1105 1096 7 10-9 9-3 •1107 1090 8 11*9 8-3 •1110 1074 9 12-8 7-4 •1115 1076 11 14-0 6-2 (•1073) (1023) 13 151 5-1 (•1058) Mean 1109 1084 II. — Catalysis by — Anthranilic Nitrate. 160 38 c.c. Water, 2 c.c. N — Anthranilic Nitrate 8 in tube. •100 grm. Ester. •102 grm. Ester. t. X. A - x. k k 6 12-0 8*2 1501 1537 7 13-2 7-0 1512 1545 8 14-2 6-0 1516 1522 9 15-1 5-1 1528 (1555) 10 15-9 43 (1545) (1567) Mean 1514 1534 1514 Hydrolysis at v — 160 is x *5 = '683. J 1109 *» = 108-7. Iv VOL. XXIX. 42 658 Proceedings of the Royal Society of Edinburgh. [Sess. The constant obtained in this way agrees fairly well with that obtained J, from the ordinary catalysis of methyl acetate by anthranilic nitrate ^ = 126. As another means of determining the hydrolysis of anthranilic hydro- chloride, the hydrion concentration in its solution was estimated by the electro -motive force method. The difference of potential between a hydrogen electrode immersed in the solution and a normal calomel electrode was measured. Then a solution of hydrochloric acid giving nearly the same E.M.F. was substituted for the hydrochloride, and the hydrion concentration c in the latter calculated from the formula d — ' 0572 log , where c is the C2 hydrion concentration of the two solutions, and d the difference between the observed electro-motive forces.* A moving-coil galvanometer with mirror and scale was used as zero instrument, and by an arrangement of resistances at each end of a metre bridge the length of wire available for measurement was about 10 metres. The solutions whose difference of potential was being measured were immersed in a thermostat at 25° C., and were connected by side tubes dipping into saturated ammonium nitrate solution. This has been found by Gumming f to be the most effectual eliminator of liquid surface potential. The hydrogen used was generated from zinc and sulphuric acid, passed through permanganate acidulated with sulphuric acid, and then washed with pure water. It was led into the liquid in the cell through the rubber stopper, and the excess escaped by a side tube with a water-trap. The hydrogen-platinum electrode was prepared by coating a glass tube with a film of burnt-in platinum, which was then lightly platinised. The hydrogen had to be passed through the liquid for about twenty minutes before the E.M.F. exhibited any degree of constancy. The current was then stopped and a reading immediately taken, the stream of hydrogen again passed for five minutes and another reading taken, and so on till the E.M.F. did not vary more than '2 of a millivolt. The potential of a normal calomel electrode was taken in this way alternately against hydrochloric acid and anthranilic hydrochloride solu- tions. After every reading of the unknown E.M.F., that of a standard cadmium cell was measured. Jc . . . The values for obtained in this way are seen to agree fairly well Iv with the results of catalysis experiments. * Nernst, Zeit. Physikal. Ghem., vol. iv. p. 129 (1889). t Trans. Faraday Soc., ii. p. 213 (1907). 1908-9.] Hydrolysis of Salts of Amphoteric Electrolytes. E.M.F. of the combination : — N. Calomel. — HCl/HoPt. A II N. Calomel. N Antliranilic 16 Hydrochloride HaPt. Difference. 659 volt. '3832 1 > '3817 •3773 volt. •0044 volt. •3803 | 1 •3822 ) > *3821 "3789 „ •0032 „ '3820 \ l f •3851 ) > -3845 '3794 „ '0051 „ '3839 j 1 '3834 | j l '3834 •3777 „ •0057 „ '3834 J 1 •3834'| l -3833 '3792 „ •0041 „ •3832 J 1 Mean difference •0045 volt. The ratio corresponding to this difference is calculated from the co formula d = '05*J2 log H. For a difference of ’0045 volt ^ = 1*199. is ® r r 0 °o o the concentration of hydrion in the hydrochloric acid solution, therefore — c i = (•015625 x *9692) x 1T99 = *01816 N. Hydrolysis at v— 16 is - *2904. *Ut) •jO Whence —=134*6. K E.M.F. of combination : N. Calomel. HCl/H2Pt. N. Calomel. N Anthranilic / 32 Hydrochloride/ H2Pt. Difference. volt. •3839 ) > ’3836 *3898 volt. '0062 volt. '3833 ) •3833 ) } '3834 '3894 „ '0060 „ '3835 Mean difference *0061 volt. 660 Proceedings of the Royal Society of Edinburgh. [Sess. -° for *0061 volt - M27. = (*015625 x -9692) x _ L =-01192. 1 *2 7 Hydrolysis at v = 32 is 32 + ’01192 = '3815, and ^=136-0. E.M.F. of combination N. Calomel. A HCl/HoPt. 1 OQ 1 N. Calomel. N Antliranilic /„ p 64 Hydrochloride/ 2 ' Difference. •4001 volt. -3996 volt. ’0005 volt. £l for -0005 volt = 1-02. co c, = (-0078125 X -9835) x 1-02 = '007839 IST. Hydrolysis at v = 64 is 64 x -007839 = -5017, and g = 127 '6. These values for the hydrolysis constant are much nearer the results of catalysis than those of conductivity experiments. The Depression of the Freezing-Point by solutions of o-amidobenzoic acid as compared with the depression caused by the same concentration of hydrochloric acid was then considered as a measure of the number of molecules in the solution. The degree of ionisation of the hydrochloride was assumed to be the same as that of the same concentration of hydrochloric acid. Any extra depression must therefore be caused by the free base present, which was considered to be un-ionised. Its concentration, and thus the hydrolysis of the solution, was then easily obtained from the normal molecular depression caused by an un-ionised substance. The freezing-point of o-amidobenzoic acid itself proved to be quite normal : — Concentration. Depression. Corresponding Molecular Depression. •01717 N. •032° 1-864° •0214 •040 1-869 *02205 •041 1-860 Mean 1-864° C. 1908-9.] Hydrolysis of Balts of Amphoteric Electrolytes. 661 For one set of experiments the method of Walker and Robertson* was used. About 80 c.c. of distilled water were cooled to zero in a Dewar bulb surrounded by a jacket of ice and water. The mouth of the inside vessel was closed by a rubber stopper with three holes, for the thermometer, stirring tube, and filter tube respectively. A block of ice was frozen from distilled water and then planed finely. 50-60 grams of this wet ice were put into the cooled water in the vessel and the apparatus closed. When the zero of the thermometer had been determined, the water was siphoned off by the filter tube without moving the thermometer, and the same quantity of solution cooled to zero was introduced through the stirring tube and rinsed down with cooled distilled water. When the mercury was again steady, the solution was filtered off and analysed. Hydrochloric Acid : — Concentration. Depression. Depression calcu- lated for *05 1ST. •05359 N. •1935° •1805° C. •03954 •1410 For *04 N. *1427° C. Anthranilic Hydrochloride : — Concentration. Depression. Hydrolysis. hb K’ •04891 N. •195° •2033 394 •05545 •218 •1735 495 •04282 . •173 •2335 328 A variation of this method was tried by adding a few c.c. of concentrated solution to the water instead of siphoning it off and adding dilute solution. Hydrochloric Acid : — Concentration. Depression. Depression for ‘05 FT. •0494 N. •1725° •1756° •05417 •190 •1772 •0562 •194 •1728 •0619 *213 •1721 * Proc. Roy. Soc. Edin ., vol. xxiv. p. 363. 662 Proceedings of the Poyal Society of Edinburgh. [Sess. Anthranilic Hydrochloride : — Concentration. Depression. Hydrolysis. h K* *0412 N. •1615° •226 367 *0426 •1630 •177 617 •04636 •1800 •207 399 •0537 •2035 •158 628 •05453 •2055 •152 673 •05586 •2140 •186 421 •0596 •2240 •146 672 •0598 •2250 •148 650 The convergence temperature method of Nernst and Abegg* was also used for some freezing-point determinations. The apparatus consisted of a Jena glass beaker stirred mechanically by a circular silver disc just fitting into it, with a central hole for the thermometer. The beaker was supported inside a brass cylinder fitted with a lid, and this, again, was surrounded by a freezing mixture of ice and salt solution. The convergence temperature of the apparatus was found, and the outside bath kept at the required distance below zero. 200 c.c. of water were overcooled in the beaker 2-2*5° C. It was then put in position and the lids closed. When the temperature (observed through a reading tele- scope) had become steady, the stirring was commenced, and this froze out the ice while the temperature rose to zero. The freezing-point was noted, and enough of a cooled concentrated solution added to make the whole quantity about twentieth-normal, when the new freezing-point could be observed. Hydrochloric Acid : — Concentration. Depression. Depression for '05 N. •04818 N. •171° •1775° •04822 •172 •1783 •04827 •171 1771 •04827 •173 •1792 Mean o o 00 l * Zeit. Physikal. Ghem ., vol. xv. p. 681. 1908-9.] Hydrolysis of Salts of Amphoteric Electrolytes. 663 Anthranilic Hydrochloride : — Concentration. Depression. Hydrolysis. K' •0438 N. •173° •211 404 •0450 •177 •202 434 •04456 •173 •1733 618 (•0490 •187 •139 909) •0500 •198 •216 336 •05082 •202 •223 307 The values for lcb K obtained in this way are consistently very much higher even than the results of the conductivity method. For a fair comparison with them, the conductivity was measured at zero, and the hydrolysis constant calculated for that temperature. The value for Mv at 25° C. had also to be reduced to zero, and in order to find its approximate coefficient the conductivity of cinchonin hydrochloride was taken at 25° and at 0° C. Cinchonin was chosen as a base whose positive ion had about the same speed as the ion of anthranilic acid.* Conductivity of Cinchonin Hydrochloride. 25° C. 0 = 16 m = 76-4 0°C. 0 = 16 ^ = 39-9 The temperature coefficient was taken as being approximately *5, and /nv for anthranilic hydrochloride at zero calculated from the formula — ^o = /%{l-(25 x-0 5/r) } .*. at v= 16 /x0= 102-6 (1 — *625) = 38-62. Conductivity of Anthranilic Hydrochloride at Zero. 0. MHC1. Mu. M.(, X. h K' 16 247 38-6 93-5 •2634 169-8 20 249 39-0 98-3 •2824 180-0 We see that the depression of the freezing-point gives values for the hydrolysis constant which differ very widely from the conductivity values, * Bredig, loc. cit., p. 231. 664 Proceedings of the Royal Society of Edinburgh. [Sess. and still more from the results of catalysis. We find, however, that those methods of ascertaining the hydrolysis of o-amidobenzoic salts which depend directly on the concentration of liydrion in the solution agree fairly well with each other, i.e. catalysis of methyl acetate by the hydrochloride, and of diazoacetic ester by the nitrate, and the electro-motive force. The solubility and distribution between two solvents also point to the same value being correct, The question is, then, why should not the more indirect methods — conductivity and freezing-point — lead to the same result ? The molecular conductivity of a sixteenth normal solution of antlira- nilic hydrochloride is 173. The amount contributed to this by the liydrion present is, according to the catalysis value for the hydrolysis, 392 •313 X X 352 — 102*7. Then, assuming the chloride to be ionised to about the same extent, the conductivity supplied by chloridion is *9x68 = 6T2. Thus there is left for the anthranilic ion M = 173 — (102-7 + 6T2) = 9, which is not nearly enough to correspond with 68‘7 per cent, of chloridion. Or we can account for the specific conductivity of the solution in this way. The total specific conductivity is 173 16 10*8. The hydrochloric acid present supplies *313 x 392 16 = 7*6. This leaves a specific conductivity for the salt of 32, i.e. a molecular conductivity of 51 ‘2 — not nearly enough for the 68 ‘7 per cent, of anthranilic hydrochloride. Evidently the method of calculating the hydrolysis from conductivity and freezing-point data is not legitimate, on account of some factor being overlooked, or perhaps unknown. We assume, for example, that the degrees of ionisation of the acid and salt, and the speeds of their ions, are quite normal, and that the water itself acts quite normally even in presence of the large quantities of ions formed from the strong electrolytes present. In accounting for the conductivity, the small amount left for the hydro- chloride seems to point to its ionisation being abnormally small. If this were so in the comparatively dilute sixteenth-normal solution, it would show up much more in a more concentrated, say half-normal, solution, where the ionisation would probably be reduced to zero, and the hydrolysis, as calculated from the conductivity at that concentration, would therefore appear to differ still more from the catalysis value. 1908-9.] Hydrolysis of Salts of Amphoteric Electrolytes. 665 N Conductivity of — Anthranilic Hydrochloride. 2 Mv observed = 122*7. P-hci jj =332*4. fiv approximately = 95. x= = *117. — = 129*0. ^HCl ~ f^v ^ From this result, however, we see that the ionisation cannot diverge very widely from the normal value, as the hydrolysis in half-normal solution is quite what one would expect it to be. The speed of the ions is another factor in the calculation which is assumed to he quite normal without any particular justification. The viscosities of sixteenth- and of half-normal anthranilic solutions were there- fore compared with those of solutions of hydrochloride acid at the same dilution. Time taken in seconds for the same volume of liquid to run through the capillary. Thermostat 24*9° C. : — Water. - HC1. 16 N Anthranilic 16 Hydrochloride. 125*5 128*0 127*2 126*6 128*0 128*5 126*0 127*6 127*8 125*4 127*4 127*0 Mean 125*9 127*75 127*6 Water. N - HC1. 2 1ST Anthranilic ~2 Hydrochloride. 124*6 127*2 143*0 124*8 126*0 142*5 124*8 127*0 124*8 127*0 Mean 124*8 126*8 142*7 Even in half -normal solution we see that the difference is not nearly enough to account for the great reduction in the conductivity. It may 666 Proceedings of the Royal Society of Edinburgh. [Sess. therefore be assumed in calculation that the speed of the ions is normal. Another possibility which was considered was that the ionising power of the water might be altered in presence of the strong electrolytes in the solution. To test this supposition, the conductivity of a series of solutions of hydrochloric acid diluted with N 8 acetic acid was compared with the con- ductivity of a series diluted with water. With the same object, solutions of KC1 were diluted with water and NH4OH, and solutions of NaCl with water and dimethylamine, respectively, and the conductivity of the resulting solutions taken. The pairs of substances were chosen with positive ions of as nearly as possible the same speed, so that double decomposition alone would not affect the conductivity. I. — 24*9° C. Conductivity of Hydrochloric Acid, diluted with — V. (1) Water. (2) — Acetic Acid. v ' 8 16 391-7 392-3 387-4 389-3 32 401 399-2 398-5 397-8 64 407-7 405-8 403-4 404-8 128 413-6 412-2 410-6 410-1 Molecular conductivity of the acetic acid = 4'65. IT. — 25° C. — Potassium Chloride diluted to — with — 8 16 (1) Water. (2) - NH4OH. 8 fi = 131-6. 135-2. N N III.—— Sodium Chloride diluted to — with — 8 16 (1) Water. (2) Dimethylamine ’0578 N. 110-2. 131-5. Molecular conductivity of the dimethylamine = 21. In every case we see the resulting conductivity to be just what would be expected from the ordinary dissociation theory, so that no abnormality need be looked for in this respect. We are forced to conclude that there are fewer molecules in the solution of the salt of an amphoteric electrolyte than there would be in the 1908-9.] Hydrolysis of Salts of Amphoteric Electrolytes. 667 case of a non-amphoteric substance. This may be accounted for by some kind of association of molecules or ions. A molecule of free base may associate with the positive ion of the salt to form a complete ion — HR, OH + H R1 = HR i + Ho0. From the normal depression of the freezing-point, we see that in solutions of anthranilic acid itself there is no such association, hut it is quite possible that the ion may have a more strongly associative tendency than the complete molecule. For, in the formation of the ion HR1 from a molecule of base R or HROH, a hydroxyl group is taken away, leaving a still possible hydrogen ion. This makes the ion HR of an acidic nature, and it would naturally tend to form an internal salt with a fresh basic molecule. (Issued separately October 14, 1909.) 668 Proceedings of the Koyal Society of Edinburgh. [Sess. XL. — The Superadjugate Determinant and Skew Determinants having a Univarial Diagonal. By Thomas Muir, LL.D. (MS. received June 21, 1909. Read July 12, 1909.) 1. The object of the present paper is to make some advance in the theory of those skew determinants that have the elements of the diagonal all equal. A few results on determinants of more general form and on related subjects are given incidentally. 2. It is recalled as a preliminary that Cayley’s first paper on skew determinants ( Crelles Journ., xxxii., 1846, pp. 119-123) really concerned something else, namely, the construction of a general orthogonant. Taking a skew determinant | ana22 . . . ann i , or A say, having 1 for each of its diagonal elements, he formed a square array with 2cissKrs -n j.jie p}ace ^ and ~('h'r^rr - 1 in the (r,r)th place , and affirmed that these n- elements satisfied the conditions laid down for the coefficients of an orthogonal substitution. As a result it followed, of course, that 2a22A12 2a33Ai3 .... 2cq^A2i 2a22A22 - A 2<%A23 .... = Aw 2anA3i 2a22A32 2a33A33 — A .... < %rs — - Ctsr CLrr— 1 Now, there is nothing in Cayley’s construction that limits its application to a unit-axial skew determinant, and it is therefore suggested to inquire what the construction leads to when the elements of the originating deter- minant | ana22 . . . ann | have no conditions whatever attached to them. In other words, the determinant just written at length, and found in the particular case specified to be equal to An, is like the adjugate a derivative of any determinant, and as such is worthy of investigation apart altogether from the peculiar circumstances under which it first made its appearance. In fact, as each element of it is a degree higher than each element of the 669 1908-9.] Superadjugate and Skew Determinants. adjugate, it may be approximately spoken of as the superadjugate. It may also be convenient to denote it by S, and its (p,q)th element by spq. 3. The product of the 1C column of the superadjugate by the \dh column of the original determinant A is — a]lkA if h be different from k, and is + ahhA if h and k be the same. (i.) For ClTi j ^2/i ) • • ■ > $nh 0 d'lk 3 ^2 k } • ■ • } ^nk) 3 A27 1 j • • • j An;( ) CL j 3 • • • 3 ^ nk ) ~ ® /ifc A f 2$/^ • 0 CL] t*A it h =%= h , \ 2cihh . A — c^fcA if = k . From this it follows that ffiiA S . A = “ a2lA -«31A - «12A - a13A . . . . a22A - a23A . . . . - a32A tt33A . . . . and thence we conclude that The superadjugate of any determinant A is equal to An-1A , where A is what A becomes on changing the sign of all the non-diagonal elements. (ii.) If, then, A be any skew determinant, that is to say, a skew determinant with any kind of diagonal whatever, A is obtainable from A by merely changing rows into columns. We are thus led to affirm that The super- adjugate of any skew determinant A is equal to An. (iii.) The case of this where the diagonal elements of A are all 1 is the property of Cayley’s orthogonant with which we started. It may be noted that this particular case can also be established independently by multi- plying S and A together row- wise. 4. The condition that the superadjugate may be the nth power of the original is seen from (ii.) to be A = A . But by expressing A as a series arranged according to products of the diagonal elements there is obtained d,y, + (^11^22 ' ' ’ ^"n-2,n-‘2 + (^11^22 - ‘ ^n—o , n—3 O'n— 1 , n—l^nn l()/ 2 , n—‘f^n—l , n—l^nn !(jy + + | cl^cl^ • • • ann |q , where the subscript zero is used to indicate that the determinant to which it is attached has had all its diagonal elements changed to 0 : and treating A in the same way we have A - aiia22 ar. + 2 yCL\\CL‘. 22 a. a n— 1 n_l CLn ( n Ifl) 670 Proceedings of the Royal Society of Edinburgh. [Sess. the two expansions thus reached differing only in the signs of the terms which involve zero-suffixed determinants of odd order. The consequence is that for equality of A and A as a condition we may substitute the vanish- ing of the sum of the said terms. Hence The super adjugate of A will be An when and only when 2/ I ffiia22a33 lo ‘ ft44a55a66 • • •) + I ^11^22^33^44^55 lo * a66 • • • ) + • * * = 0 . (iv.) Thus, the superadjugate of | a1b2c3 1 is | a1b2c3 13 if laAcsl0 = 0. i.e. if a2b3c1 + cizbYc2 = 0; and the superadjugate of | af}2c3d± | is | a-fb2c3d± |4 if I C1^2C3 lo ^4 + I lo C3 + I |0 ^2 + I ^2C3^4 loffi = 6 > i.e. if (a2^3c1 + af>Ycf)d^ + (ajb^dx + aAbld2)c3 + (a3c4d1 + aAc1d3)b2 + (b3cAd2 + b4c2d^)al = 0 . 5. Since the pth row of | aL1a22 . . . ann | is O' pi > C^‘2 j . . . , eipp , • • • , &pn > and the pth column is ®\p 5 ^2 p j • • ■ > ^pp j • • • j ® np ) it follows that In any shew determinant the sum of any row and the cor- responding column is twice their common element , (v.) or, say, rowp + coli( = (0,0,..., 2 app , 0 , . . . ) . From this we can prove that If A be skeiv, any element spq of the super- adjugate of A is (rowy of adjug. of A $ colg of A). (vi.) For from (v.) we have (row2 of A + col3 of A$row^ of adjug. of A) (0,0,..., , 0 , . . . $ A^ , Api , . . . , Apn) ^dqqApq , and from the fundamental property of the adjugate (rowg of A $ roWp of adjug. of A) = therefore by subtraction (eol, of A § row,, of adjug. of A) = { f f P * _ 0 if P=¥q, A if p = q ; as was to be proved. 6. From (vi.) it follows immediately that the superadjugate of A, when A is skew, is the product of A by its adjugate, and therefore is An as we have already seen in (iii.). Further, we have only to think of the case of 671 1908-9.] Superadjugate and Skew Determinants. this where A besides being skew is unit-axial to see that Cayley s orthogo- nant is resolvable into determinant factors — that, in fact, it is the row-by- column product of A-1 and A, where A is the basic determinant, and A-1 is in the form which is got from the adjugate of A by dividing each element by A- (vii.) 7. Confining ourselves now to skew determinants which have a univarial diagonal, let us denote the repeated element of the diagonal by a, so that, A being | ana22 . . . ann | , it is understood that ars = — asr and arr = ass = . . . = a. The first property we note is that In any skew determinant with uni- varial diagonal the product of any two rows is the same as the product of the corresponding columns. (viii.) This is seen on writing the pth and qth rows ctpi > eCp 2 ? • • • ? eipp , ... , ctqq , ... , ctpn ®>q\ 5 ^qi j • • • > ®qp J • • • j d'qq j • • • ) ™ qn and the pth and qth columns d\p 5 \p 5 • • • 5 ^pp » • • • j O'qp ®np q •> Ct.qq , ... , CLpq , ... , CLqq , ... . (Vnq and then noting (1) that apr. aqr — arp . arq because of the skewness, and (2) that G/pp.Giqp -j- CLpq.Gjqq CLpp.Llpq -1- Ctqp.C^qq because each of them = a(apq + aqp) = 0. 8. In any skew determinant with a univarial diagonal the conjugate of any m -line minor is got from the latter by changing the signs of the elements of it that belong to the or iginal d iagonal and prefixing to it the sign ( — l)m. (ix.) For we can multiply the given minor by ( — l)m by changing the signs of all its elements, and we can change all the said signs by altering the elements of the form apq into aqp, and those of the form a into —a, that is to say, by taking the conjugate minor and altering the signs of the elements that belong to the original diagonal. The number of 2-line minors of A that are independent of the diagonal element is 3Cn>4. (x.) For there are \n(n— 1) pairs of rows to be considered, each pair having n — 2 ){n — 3) minors of the kind mentioned, and each minor occurring twice. 9. If A be skew and have a univarial diagonal, the product of the p-7t row of the superadjugate of A by the (fh row of A is apqA whether p and q be different or the same. (xi.) 672 Proceedings of the Royal Society of Edinburgh. [Sess. This is supplementary to (i.) and can be proved in the same way. From the two theorems it follows that, when A is skew and has a univarial diagonal, the product of the pth row of S by the qth row of A differs only in sign from the product of the corresponding columns if p and q be different, and does not differ at all if p and q be the same. 10. If | ana22 . . . ann | , or A say, be a skew determinant with univarial diagonal, the product of the pf/' row of A by the sum of the qf/l row , and cf column of the adjugate of A is 2aApq. (xii.) This theorem is due to Torelli (see Giornale di Mat., iii., 1864, pp. 7-10). It may be written : a. 'p\ ? 5 Q’pn $ Ag2 "t" A2q J A A \ _ ■‘^■qn ~ nq ) 2aA ■pq 5 and as, because of the skewness of A, (c#i Ci p , cl^p , ... , cipn "1 ctnp $ Aqi + A , Aq2 1- A 2q , ... , Aqn + Anq) — 2dpp(A.qp + hpq) it follows bv subtraction that (cj p j ct^p , , &np $ Aql + Aqi , Aq2 “I- A 2q , ... , Aqn + A„q) 2cAq^ , in other words, if for “ pth row ” in (xii.) we substitute “ pth column,” we must at the same time alter 2aApq into 2aAqp . Further, since from (v.) we have (Ap! j Apq , • • • A pn $ CLqi *1" U,\q , Clq.y A C2q , . . . , Ctqn "1“ d'nq) -‘^,qqApq , there results by comparison with (xii.) the curious fact that (ctpi , Ctp2 ) . • • 5 $ Aqi + A iq , A q2 + A 2q j • . . , Aqn + Anf is not altered by interchanging the as and As. (xiii.) 11. It will be convenient to insert here two properties of general determinants, for which no proof is necessary. The product of the p77i row of the acljugate of an n -line determinant A by any n elements whatever is the determinant obtained from A by substituting for its p77* row the said new elements. (xiv.) The product of the \)th and c(h rows of the adjugate of a determinant A is obtained from A by substituting for its p77t row the q77t row of the adju- gate, or for its q77i row the p77i row of the adjugate. (xv.) 12. If | aua22 . . . ann | , or A say, be a skew determinant with univarial diagonal, then (Api , Ap , J Apn $ Aqi 5 A q2 , ... , A^?i) 2 ( Apq I* Agp) a 'whether p and q be different or the same. (xvi.) This was originally announced for the case where a = 1 by Spottiswoode in 1853 (see Crelle’s Journ., li. p. 261) as a deduction from the corre- 673 1908-9.] Superadjugate and Skew Determinants. sponding property of Cayley’s orthogonant. Following Torelli, we have from (xii.), on putting p — 1, 2, , n, an(A-i3 + A2i) + + A22) + . • • “I- ®1 ni-h-nq 4" A qf) 2 «Ala ] %l(Ai2 n(^-nq 4” A g?i) 2aA2g 1 am( Ai q + Agl) + an2( A2q + Aq2) + . . . 4“ Ct/nn( Anq 4~ A gf '2aAns , and solving we obtain, with the help of (xv.), -^pq 4~ A qp 2&(-A-ig , A2 q , . . . , Ang $ A^ p > J ' * ' ) A np ) ~ A j which is essentially what was to be proved. 13. If, instead of using (xii.) in the preceding paragraph, we were to use the altered form of it referred to in § 10, we should obtain for + another expression entitling us to assert that In the case of a shew determinant with a nnivarial diagonal the product of any two rows of the adjugate is the same as the product of the corresponding columns. (xvii.) In conjunction with this it is important to recall (viii.) ; also careful note should be taken of the complete diversity of the reasoning now employed to establish the same property. 14. Taking the square of the adjugate of A, we have from (xvi.) (A""1)2 = A 11 2(^12 + ^21) 2(^12 + ^21) A 22 2 (Ain + Anl) 2 (A‘>n "4* Aw2) 2^A in + Awl) |(A2m 4* An2) whence, as Cremona noted, A \tt a ) An + An A12 + A21 .... A\n 4” Anl -A- 12 4* A2i A-22 4“ A22 .... A 2n 4* Am2 = (2a)nAn~\ (xviii.) A in “1“ Anl A*2n "4" An2 .... A . A -cx-nn _r r*-nn By dividing every row of the determinant on the left here by 2 a we obtain an expression for A”-2, that is to say, for A, A2, A3, .... in the case of the 3rd, 4th, 5th, .... orders respectively ; and as these expressions for A, A2, A3, .... are not the ordinary expressions, there results by comparison a series of interesting identities. For example : 3 X a b — a2 + x2 ab ac - a X c ab b2 + x2 be -b - c X ac be e 2 + x X a b c 2 x2 + d2 + e2+f2 - bd - ce ad — cf ae 4- bf - a X cl e - bd - ee x2 4- b 2 4- e2 +f2 — ab - ef - ac 4- df -b -cl X f ad — cf — ab — pf v2 4- a2 + e2 4- e2 -be - de - c — e -f X ae 4- bf - ae 4- df - be - de x2 4- a2 4- b2 4- d2 vol. xxix. 43 674 Proceedings - of the Royal Society of Edinburgh. [Sess. As in the latter example the non-diagonal elements on the right hand are - rxr2 , - rxr3 , - rxr4 , “ r2? 3 > ~ r2r4 > (rq being used for the qth row), we should expect the diagonal elements to be ~ riri » - V2r2 » ~r3r3’ - r4r4 , i.e. - (x2 + a2 + b2 + c2) , - (x2 + a2 + d2 + e2) , . . . The explanation of the apparent anomaly is that the determinant which is squared on the left being equal to x 4 + x2(a2 + b2 + c2 + d2 + e2 +f2) + (af - be 4- cd)2 is not altered by the interchange fa b c\ -i / e d / > for if this change be made on the right we have only got further to alter the signs in the 1st and 3rd rows and then in the 2nd and 4th columns in order to evolve the familiar result. 15. Denoting the pth row of A by rp and thej9th row of the adjugate by Ri;, we know (§ 11, xv.) that R^R^ is expressible as a determinant which is obtainable from A by deleting rq and inserting R^. As a result of multi- plying this determinant by A we obtain RpRq • A rlrl rp-2 r2ri r2r2 7\rp .... ?\rn r2rp .... r2rn rq~ 1^2 Wi t'q+d'o y y y y ' q—V p • • • • ' q—v n A .... ^ q+ dp • ■ • • ^ q-\-d n (-!)>'« A. (A(SA(„), y y y y ^ p y y 1 n' 1 7 iv 2 • • • • 7 n1 p • • • • 7 n' n where A{p means the array got from A by deleting the pth row. But from (xvi.) we have R?;Rg 2^( Apg + Agp) } CL and thus by comparison there results AoAg = ( - ip+2 • KAps + Ki) - 1 CL so that In the case of a skew determinant with univarial diagonal the product of any n — 1 rows by the same or any other n — 1 rows contains the determinant as a factor. (xix.) 1908-9.] Superadj ugate and Skew Determinants. 675 16. For the purposes of (xviii.) the most suitable expression for Apq is as a series of terms arranged according to powers of a, it being then possible to make, by the application of (x.), an immediate simplification of the expression for \(Apq + Aqp). To obtain the former expression let us pass the pth and qth rows over all the others so as to become the 1st and 2nd, and then do the like with the pth and qth columns. The result | ClppClqqCL^^'22 ‘ ' ’ %>-l , P— 1%>+1 .2H-1 • ’ • a which is known to be still a skew determinant with univarial diagonal, has the element apq the place (1, 2), and its cofactor Apq is seen to be — | (XqpdyP 22 • • • * * • ®q—\ , q—\®$jr\ , 2+1 • • * | • We thus learn that If \ ana22 . . . ann | be a skew determinant with univarial diagonal, any primary minor of it is expressible as the result of “ bordering ” a skew determinant of like kind ; or, more definitely, is the determinant obtained by prefixing to the secondary coaxial minor the row I ^11^22 ' - . • • • aq-l,q-\aq+l .2+1 • • • ^nn 1 Clqp , Oq-y , (Zq2 , • • • 5 ^q,p— 1 ) ^q,p+ 1 5 • • • 3 ®q , g-1 5 , q+\ > • • • i %n column O'qp j ^1 p •) ^2 P ’ • * • 5 ^p— 1 ,p ) @Jp+ 1 ,p } • ' • » ^q — 1 ,p > ®q+ 1 ,p 5 • • • j ® np king the sign - . (xx.) From this it follows that in APq the terms containing the product of all the original diagonal elements is - aqp . an~ 2 , i.e. apq . an_2 ; and that the cofactor of the product of any other number of the said elements is a “ bordered ” zero-axial skew determinant, and therefore is expressible as the product of two Pfaffians. Thus the cofactor of is * • • ap~l ,P~\®P+\ ,P+1 • • • ®q-l , q-l^q+l , 2+1 • • • ann l.G. Cty^fcty^Ctq^ Qj2pClq y H- CtqpCt^y) j Ctqp Mql ^22 a IP a 12 (1*2 p and the cofactor of is a44: • ■ • Mp—ltP- ■l^P+l ,2>+l • • aa-i,123]. The rather striking result to which after some difficulty we are finally led is that If | ana22 . . . ann | be a skew determinant with univarial diagonal, then -V/ = an-‘.[pq\ - + an~i. 2 |>ga/?][a/3] - a”-5. 2 y][iaM +••••» where a, ft, y, . . . are any of the integers 1, 2, 3, . . . , n other than p and q. (xxi.) Thus, when n — 5 we have A23 = «3[23] - a2([21][31] + [24][34] + [25][35]) + a([2314][14] + [231 5][ 1 5] + [2345][45]) - [2145][3145] ; so that if | ana22 . . . a55 | be given in the form X a.2 CO 3 a4 - a2 X h -h X C4 -a4 ~C4 X ~a5 -h ~C5 — d5 we know that B3 - x3.b3 - x2(a2r/3 + b4c4 + b5c5) + x / a4 | a2 a3 ct4 + a5 | a2 a3 aF) + db\b3 b4 bb h K ^3 ^5 C4 C5 1 C5 d5 a., a4 ab b d \ h a3 a4 a5 C4 C5 d c Further, it deserves to be noted that an alternative for the coefficient of in (xxi.) is rprq ; also that when n is odd there appear in the develop- ed n— 3 ment n Pfaffians of the highest possible degree, and that when n is even there is only one Pfaffian of highest degree. The latter unique Pfaffian may be conveniently denoted by F, and the former set of n by F1? F2, . . . , Fw, wliere F,- is got by deleting the rth frame-line of 677 1908-9.] Superadjugate and Skew Determinants. Thus the above expression for B3 may also be written b^.x^ — 7'^T^.X" + + — Fgh 3 . D. If I ana22 • • • ann | be a skew determinant with univarial ■ diagonal , then i(A^ + A qp) = ~ an~5-^[pa(3y][ • • • j A qk) ~ A (j!(iA.qp + lu App , and therefore by (xvi.) = 4«2. J(A.P2 + Aqp)— - 2aA(A^ + AM) = 0; CL and when p and q are the same the product = 4«2(Ai,i + Ay, + . . . + Apl) — 4:(iAppA + A2 and therefore by (xvi.) = 4a2.A?)„- - 4a A™, A + A2 a = A2, as was to be proved. The theorem is Cayley’s for the case where a — 1. From it we have S2 A2 0 0 . . . 0 A2 0 0 0 A2 . . . A2n , which agrees with (iii.) and § 6. 19. If | ana22 . . . ann I, or A say, be a skew determinant with univarial diagonal, rprq the product of its p//( and (ff rows, and F the Pfaffan of the elements on the right of the diagonal, then - a2 rp 2 .... rpn *7i rnr2 rnrn - a 2 | 0 when n is odd. J (xxiv.) I F4 when n is even. 678 Proceedings of the Royal Society of Edinburgh. [Sess. By way of proof we have only to note that the subtraction of a2 from the diagonal elements of the determinant | r1r1 r2r2 . . . rnrn | is equivalent to putting a = 0 in the said determinant, and that | 1 2? 2 . • . rni n la=o (A )a= o — (A ~ vp\.a? + ( — a34f 5 — «35F4 — a451 3).a — F2F4 , A22 = cP 4- (a432 + a14’ + -}- «34" + ck352 4- ^452)a“ 4- F22, A23 = ^03. a3 — rqr^.a2 4- (<3q4F5 + ai5F4 "F ^45-^1)*^ — F2F3 » A24 = a2ra3 - r2rra2 + ( - a13F5 + a15F3 - a^F^.a - F2F4, A25 = a25‘a'i ” V2r5'a2 "t ( ~ ai3F4 — ^14F3 + a34Fl)-^ ~ F2F 5 so that in A2]Fi ~ A22F2 + a23f3 — A24F4 4- A25F 5 the cofactor of a4 is — F2 ; the cofactor of a3, as we see from § 22 (xxvii.), is 0 ; the cofactor of a 2 is rp ■ F - {aif "t ^14* + * • • + V)F2 - 7 W ^ 3 r2r4-F4 - r>r_p,.Fr which, if increased by r2r2.F2 — r2r2.F2, is seen from (xxviii.) to be = a2F2 - r2r2 . F2 - (a132 + a142 4- . . . + a452)F2 = ~ (r2r2 ~ «2 + a\f + aU + • • • + «452)F2 = - b2 • 2i2 ; the cofactor of a1 is 0 ; the term independent of a is -f2(F12+f22+ . . . + F52) ; and the whole expression is - F,(<*4 + a- . 20!2 + 2 ••• of theorem (xxi.), then (P^-m j P^m J • • • j P'H'm $ 1 1 > ~ I 2 ’ F3 J — 1 4 5 * • • ) “I” ( — 1 Y • PPm • Fp ^ 0 when m is odd. | \paYa2 . . . a^^j]2 when m is even. (xxxi.) In the left-hand member, it should be noted, there is no term contain- ing Fp, the means taken to indicate this being first to include a term 682 Proceedings of the Royal Society of Edinburgh. [Sess. ( — lp-1. ppm . Fp as one of a group, and then annex a cancelling term ( — l)p. ppm . ¥p. Thus, taking the case where n = 7 , p = 2, m — 4, what we have to simplify is 214.F4 + 234.F8 - 244.F4 + 254.F6 - 264.Fe + 274.F7 , where 21 d = y'i\2g/3yj la/3y ] and where generally the cofactor of each F is the sum of 10 products of two Pfaffians of the 2nd degree, the first Pfafhan of each product having p (i.e. 2) as an umbra, that is to say, being of the form [2 a/3y]. As there are only 20 (i.e. 6. 5. 4/1. 2.3) Pfaffians of this form, it is clear that each of them must occur thrice. For example, a little examination will show that [2134] cannot occur in 214.FX, 234.F3, or 244.F4, but occurs in each of the other terms of the given expression, its full cofactor being [5134]. F5 - [6134]. Ffi + [7131].F7. Now we know from (xxvii.) that [21][5671] - [51][2671] + [61][2571] - [71][2561] - 0, from which there follows by “ extension ” [21 34][567 1 34] - [5 1 34][267 1 34] + [6 1 34][257 1 34] - [7134][256134] = 0 , i.e. - [2134]. F2 + [5134]. F5 - [6134]. F6 + [7134]. F7 = 0, so that the cofactor of [2134] above found is seen to be [2134]F2. In like manner it can be shown that every other Pfaffian of the form [2a/3y] has [2 a/3y] . F2 as cofactor ; and thus we conclude that 214.F, + 234.F3 - 244.F4 + 254.F5 - 264.F6 + 274.Fr = where a, /3, y are any three of the six integers 1, 3, 4, 5, 6, 7. 26. From theorem xiv. we know that the left-hand member of (xxx.) is equal to the determinant got by substituting Fx , — F2 , Fs , — F4 , . . . in place of the pth row of A. Multiplying this determinant row-wise by A, and utilising theorem xxvii., we obtain the determinant which, on being divided by (-lp- la , is the determinant got by substituting F4 , — F2, F3, — F4 , . . . in place of the pth row of A2. There is thus reached the curious theorem that If | ana22 . . . ann |, or A say, be an odd-ordered skew determinant with univarial diagonal, the determinant obtained by inserting F4 , — F2 , F3 , — F4 , . . . in place of the pWl row of Am is ( - :■ • F P’ (xxxii.) This could also be established by proving that the product of F4 , — F2 , F3 , — F4 , . . .by the p*ft row of Am is ( — l)p_1amFr , — a theorem which has for its first two cases theorem xxviii. and a corollary to theorem xxvii. 683 1908-9.] Superadjugate and Skew Determinants. 27. We have already used (§ 24) the fact that if A be an 'a-line skew determinant with univarial diagonal A - an + an~ 2.2 [«/5]2 + a71-4. ^ [«/5yS]2 + where a 8 is any pair of the lirst n integers, a(3yS any set of four, and so on. By adding to 2 the suffix —p to signify that a, (3, y, . . . are not to be taken from 1, 2, . . . , n, but from 1, 2, . . . , p — 1, p + 1, . . . , n, we can readily give expression to the like development of any primary coaxial minor of A : for example, An = an~l + an~3.'^[afi]2 + an~5. y [a/jyg]2 + . . . - -1 With the same notation we have riri = ^2 + Ztla]2’ -i and therefore by multiplication — An.rp*! = an-h an~'2 j ^[a8Y + Z.Da13 l a I -i -i J + an~4 { Z laYy8Y + ZM^-Z^]2 \ i -i -i -i ) + Comparing this development with that of A, we see that on subtraction the coefficients of an and an~‘ 2 would vanish, that the coefficient of an_4 would be Z [a/5yS]2 + Z[laP2W]2 “ Z[« -i -i i.e. 2[la]22ta^]2 _ Z[la^l2* -1 -1 and that as a collective result we should have kj.r.-A = a I -i -i J 1-1 -1 j + (xxxiii.) 28. The simplification, however, does not end here, there being connected with the coefficients on the right a rather remarkable theorem which enables us to substitute for each of them a sum of squares. To illustrate the nature of this, let us examine the coefficient of *1!-2W - = Z([i“]M + [i«^]+[iy]-M+ -i -l -l -l where a, /3, y, . . . on the right is any set of n — 2 integers taken from 2, 3, ... , n, and r is the remaining integer. Although this is the most appropriate form in the present connection, it is better for general purposes to transfer 2[i a/3yf to the right-hand side, when it will be seen that we -i may formulate the result by saying that, A triangular number of elements avl a 13 a In a 23 (xxxvi.) where on the right a, f3, y, ... is a set of n — 6 integers forming with r, s, t , u, v the full set 2, 3, ... , n ; and so on. The general proposition thus derivable regarding quadrate numbers is that The product of the sum of n — 1 squares by the sum of Cn_1> 2m squares is expressible as the sum of Cn_li2m+i + Cn_li2m_1 squares. (xxxvii.) 30. Returning to the result of § 27 and making the substitutions now possible, we have the important theorem that If | ana22 . . . ann |, or An say, be a shew determinant with a univarial diagonal, then ”Airriri “ • Z { [lalar] + \.1PlPr]+ ••• } + an~& . 2 | [la][ars£] + [\/3][f3rst] + . . . | 4 an_8 . ^ | [la][a rstuv] 4 [1 [3][/3rstuv] 4 . . . j + where, under the first 2, r is any one integer taken from 2, 3, ... , n, and, a, /3, ... . are those remaining ; under the second 2, rst is any set of three integers taken from 2, 3, . . . n, and a, /3, .. . are those remaining, and so on. (xxxviii.) Since the number of integers a, /3, .. . under the first 2 is n — 2, under the second 2 n — 4, and so on, the number of terms in the expressions to be squared in any case is 2 more than the index of the attached power of a. When n is even the last term is independent of a, and is a sum of squares of binomials for which there is an alternative mode of expression. This is due to the fact that the cofactors of [la], [1/3], . . . are then primary minors of [123 . . . ri\ and can be denoted by A12, — A13, A14, — A15, . . . , the term thus being (ai2AI3 ~ **13^-12)" 4- (^12A14 — tt14A12k + ■ • • For example, putting n — Q we have — An.nr, - A, = x .2 f (a. >9 ) a ui-'l'l ‘-*6 — ^ 1 (rir2)“ "t • • • + dvtk [ + ai2al3 • • • a\6 Ai2A]3 . ■ A16! When n is odd, the last term is { [!«][««* • • • J 686 Proceedings of the Royal Society of Edinburgh. [Sess. where rst ... is any set of n — 2 integers taken from 2, 3, ... , n, and a is the one remaining. The term therefore is -L | [12]'2[23 . . . n]2 + [13j-’[324 . . . nf + t i.e. i [23 . . . ?if . | al2' 2 + «132 + . . . + aln2 | . Thus, taking n = 7 we have - A7 = (¥!>2+ ••• + } + aj| [[12][2567] + [13][3567] + [14][4567]yJ . . . 1 + —[23 . . . 7 + a13 + ... + a,--) . X From (xxxviii.) it follows directly that If | a11a22 . . . ann |, or A say, be a skew determinant with nnivarial diagonal, then when n is odd An . rxrx and aA are both positive, and when n is even — A11.r1r1 and A are both 'positive, the former in each case being the greater . (xxxix.) ( Issued separately October 15, 1909.) 1908-9.] The Skeleton of a Sowerby’s Whale. 687 XLI. — The Skeleton of a Sowerby’s Whale (Mesoplodon bidens) stranded at St Andrews, and the Morphology of the Manus in Mesoplodon, Hyperoodon and the Delphinidse. By Sir Will. Turner, K.C.B., D.C.L., F.R.S., President of the Society. (Read July 5, 1909. MS. received July 28, 1909.) In May 1908 an adult female Sowerby’s whale, Mesoplodon bidens, was stranded in St Andrews Bay, about a mile from the clubhouse. Its capture and external characters were recorded by Professor W. C. MTntosh in the Annals and Magazine of Natural History, December 1908. The skeleton was obtained by him for the Gatty Marine Laboratory, and at his request I have examined and prepared this report on its characters. The first observation on this interesting cetacean as a Scottish species was made by Mr James Sowerby * * * § on an animal stranded in the Moray Firth near Elgin in 1800 ; no record existed of another example in Scotland until 1872, when I described]* the skull of a female in the Museum of Science and Art, now the Royal Scottish Museum. In 1881 I obtained from Messrs Anderson of Hillswick an imperfect skeleton J of a male stranded in April in Urafirth Yoe, North Mavine, Shetland, and in May 1885 the same gentlemen sent me the carcase of another male § captured at Voxter Yoe, Delting, Shetland. In October 1888 a male was stranded in Dalgety Bay, on the north shore of the Firth of Forth, the characters of which I described at the time.|| In April 1895 another male was captured in the Firth of Forth, at Morrison’s Haven, Prestonpans, and its skull, some bones, and a limb were secured by my late assistant, Mr James Simpson, H for the Anatomical Museum of the University. In drawing up the notes on the St Andrews animal, I have compared the skull and skeleton with the 1881, 1885, 1888 and 1895 specimens in the Anatomical Museum. * The British Miscellany, 1804-1806, vol. i., pi. i. t Trans. Roy. Soc. Edin., vol. xxvi. p. 759, 1872. J Journal of Anat. and Phys ., vol. xvi., April 1882 ; Proc. Roy. Soc. Edin., Jan. 1882. § “ The Anatomy of a Second Specimen of Sowerby’s Whale,” Journal of Anat. and Phys., vol. xx. p. 144, October 1885 ; Proc. Roy. Soc. Edin., vol. xiii. p. 279. || Proc. Roy. Phys. Soc. Edin., vol. x., 1888-1889. IT Annals of Scottish Natural History, October 1895, p. 250. 688 Proceedings of the Hoyal Society of Edinburgh. [Sess. Measurements of Skulls. Royal Scottish Museum, 1872, P. Shetland, 1881, Shetland, 1885, 8- Dalgety, Firth of Forth, 1888, 8- Morrison’s Haven, 1895, g . St Andrews, 1908, Greatest length of skull in straight ]ine 75 cm. broken 76 77-3 broken 82-8 Length of rostrum . 49 broken 5L2 51 51 59 Height from vertex to ptery- goids ..... 24 26 27 27 broken 25-4 Breadth between upper mid- orbital borders 28-5 28-5 28-4 29 290 Breadth across occipital condyls 11 10 1M 10-3 10*5 11*2 Breadth between ant-orbital notches .... 20 18*5 17-3 17-5 20-5 19-8 Premaxillae, width behind anterior nares 13 11-5 11-8 12-3 12-5 12*3 Premax illae, width in front of anterior nares 10 10 11 9-2 10-5 9-9 Premaxillae, width opposite anterior nares 11 10 10*4 10 10*6 11 Width of anterior nares . 4-5 5-5 5-6 5*4 4-8 6-2 Mandible, length of . 69 65 67 65'5 broken 73-8 „ „ symphysis 24 broken 23-3 21 22-8 27-6 ,, height of ramus 11 10 10-7 11 broken 11-2 Skull . — The skull of the St Andrews specimen had the characteristic elongated, slender beak, and other general characters of the species. It was 82-8 cm. (32J inches) in maximum length, and was the longest skull in the Table of measurements. The rostrum was not broken, and the slender tips of the superior and premaxillary bones as well as the mesial cartilage of the beak reached its free end. The length of the beak was 59 cm. (23f inches). The mes-ethmoid septum was prolonged into the upper end of the medio-rostral gutter for 8 cm., and was embraced anteriorly by the medio- (meso-) rostral bone, which occupied the gutter for 21 cm. This bone was divided on its upper surface into two lateral halves by a longitudinal groove, and in front of it the unossified medio-rostral cartilage extended to the tip of the beak. In the 1881 specimen from Shetland, the mes-ethmoid was embraced by the medio-rostral bone, which was divided by a longitudinal groove into two distinct lateral halves as far as 24 mm. from the anterior pointed end, near which the surface of the bone was tuberculated. In the skull from Morrison’s Haven the halves were fused together for 154 mm. from the pointed end, and the surface of the bone was smooth. The free end of the rostrum of this skull was somewhat curved to the right, and a 689 1908-9.] The Skeleton of a Sowerby’s Whale. similar deflection was present in the tip of the mandible. In the Dalgety Bay cranium the longitudinal groove was present in the middle third and the lateral halves were distinct, the posterior and anterior thirds were not grooved, the surface of the medio-rostral bone was smooth and the anterior end was pointed. In a paper on the development of the rostrum in Mesoplodon, H. O. Forbes regarded * the meso-rostral consolidation as an upgrowth formed by the proliferation of the osseous tissue of part of the vomer and perhaps of the premaxillaries, and not as an ossification of the meso-rostral cartilage. The presence of a longitudinal groove, and the consequent indication of two lateral halves to the medio-rostral bone, favour to some extent, as regards its sides, this view, but I think that ossification of the mesial cartilage also participates in the production of the consolidated structure which occupies the medio-rostral gutter both in Ziphius and Mesoplodon. In the female skull which I described in 1872 the medio-rostral gutter did not contain the corresponding bone, which I thought might be a female character, but its extensive ossification in the adult female now described showed that the absence of the bone in the previous specimen was an age, and not a sexual feature. The two halves of the St Andrews mandible were not fused at the symphysis ; the alveolus for the tooth was situated immediately in front of the hinder end of the symphysis, and the apex of the tooth projected for only 9 mm. beyond the alveolus ; the retention of the crown within the alveolus indicated the female sex. In the mandible of the skull from Morrison’s Haven the two halves were in process of fusion, the teeth were lost, but the large sockets extended for about half their extent behind the symphysis. Ear Bones. — In the St Andrews specimen the tympanic bullse and petrous bones were lodged in the hollow near the mastoid. The bulla was bilobed interiorly and posteriorly, characteristic of the genus Mesoplodon. j* Hyoid Apparatus. — The hyoid proper consisted of a body with which the two great cornua were fused. At its anterior border was a notch bounded by a pair of short processes, each with an articular facet, to which the cerato-liyals had doubtless been attached. A well-marked pair of stylo-hyals was anterior to and separated by an interval from the thyro-hyals. Spine, — As the epiphyses were fully anchylosed to their respective * Proc. Zool. Soc. Load., 28th Feb. 1893. t See my account of the tympano-petrous bones in the Odontoceti, Proc. Roy. Soc. Edin., vol. xxiv. p. 423, 1903. VOL. XXIX. 44 690 Proceedings of the Koyal Society of Edinburgh. [Sess. vertebrae, the specimen was an adult. The column consisted of forty-seven vertebrae. Cervical vertebra from the 1st to the 4th were fused together, and formed a massive bone, but the laminae of the 4th were distinct and did not meet to form a neural spine. The 5th, 6th and 7th were separate and with flattened bodies ; in the 5th and 6th the neural arches were incomplete and without spines, but the 7th had a short spine. The transverse processes were distinct ; in the atlas and axis no foramen was present at the root of each process ; in the 3rd to the 6th the transverse process was formed by the junction of the diapophysis and the parapophysis, between which was the vertebrarterial foramen; in the 7th these two processes had not joined and the boundary of the foramen was incomplete. Dorsal V ertebrce. — The 1st and the 5th to the last were separate bones, but the bodies of the 2nd, 3rd and 4th were tied together by a strong bar of bone fused with the ventral surface of their bodies. The body of the 1st dorsal was flattened, as in the last cervicals, but behind it the bodies gradually increased in antero-posterior diameter until the last, which measured 109 cm. and possessed a median ridge on its ventral surface. From the lower part of the side of the body of the 1st dorsal a tubercle projected which resembled the parapophysis of a cervical. The laminae and spines were complete in all the dorsals and increased in size from before backwards. The 1st dorsal, where it gave rise to the parapophysis (inferior tubercle), had a large costal facet for the head of the 1st rib, on the posterior surface of the tubercle which extended on to the body, but no costal facet was seen on the short pointed transverse process. The body of each vertebra from the 2nd to the 7tli had a costal facet on each side at its junction with the pedicle. From the 1st to the 8th vertebra, and close to tli£ anterior zygapophysis, a transverse process sprang from the neural arch, which, except in the 1st, had a large costal facet for the tubercle of a rib. In the terminal dorsals the transverse process did not project from the neural arch, but from the anterior part of the side of the body ; zygapophyses were present in the 1st to the 8th dorsal ; strong metapophyses projected from the laminae of the terminal dorsals which overlapped the laminae of the vertebra immediately anterior, and short metapophyses were present in the 7th and 8th vertebrae. In this spine and in those of the two Shetland and the Dalgety Bay animals the 7th vertebra was the last to show costal facets for both head and tubercle ; the dorsal vertebrae behind it had a facet only on the transverse process for the tubercle of the rib. Lumbar vertebrce had no facets for articulation with the chevron bones. They were the largest of the vertebrae, and were characteristic of the 691 1908-9.] The Skeleton of a Sowerby’s Whale. region. The body was keeled on its ventral surface ; the transverse pro- cesses were spatulate and sprang from about the middle of the sides of the bodies ; the spines were long, flattened plates of bone. Caudal Vertebra. — Eighteen vertebrae followed the last lumbar. They diminished in size from before backwards ; the eight most posterior consisted only of a body, and that of the terminal vertebra measured only 20 mm. in its antero-posterior and 18 mm. in its transverse diameter. The ten anterior had facets on the ventral surface for the nine chevron bones, which had articulated with them and with the intervertebral discs. Ribs. — There were ten pairs of ribs. The 1st and the 10th were the shortest; they increased in length from the 1st (32 cm.) to the 6th (62 cm.) and then diminished to the last (16 cm.). The 1st, the broadest and most flattened, had a facet on the head and one on the tubercle ; the right was marked by an oblique roughened groove on its surfaces, as if it had been fractured and afterwards repaired. The 2nd to the 7 th had also vertebral facets on the head and tubercle, but the 8th and 9th had no head and articulated only with a vertebral transverse process. The 10th was an elongated flat bone 30 mm. in greatest width, pointed at both ends, and without head and tubercle. The opportunity which I have had through the courtesy of Professor MTntosh of studying the skeleton of the St Andrews Mesoplodon has led me to re-examine the skeletons of the two Shetland and the Dalgety Bay animals and to reconsider the mode of articulation of the ribs with the spinal column. In each skeleton the head or capitular process of the 1st rib was jointed to the body of the 1st dorsal vertebra, the transverse process of which was so slender and pointed that the large articular facet on the tubercle of the rib could not be adapted to it. In approximating the 1st rib to the spine its tubercle came into contact with the transverse process of the 2nd dorsal, with which it obviously had articulated. It consequently followed that from the 1st to the 7th rib the tubercle articulated with the transverse process of the vertebra immediately behind the body to which the head was jointed, and with which it was in numerical correspondence. As the tubercle of the 7th rib therefore articulated with the transverse process of the 8th dorsal, the 8th, 9th and 10th ribs, which had no capitular processes, articulated with the transverse processes of the 9th, 10th and 11th post-cervical vertebras. It required therefore eleven vertebrae to articulate with ten pairs of ribs. In the St Andrews skeleton the transverse processes of the 11th post- cervical vertebra were broken, but they were entire in the corresponding- vertebra in the other three skeletons, in each of which the free outer border 692 Proceedings of the Royal Society of Edinburgh. [Sess. was marked by a distinct facet, so that provision existed for the articulation of the 10th rib with the 11th post-cervical vertebra. Vertebral Formula. — The St Andrews skeleton had 47 vertebrae, and a similar number was found in the 1885 Shetland and the Dalgety Bay specimens, but the spines in the 1881 and 1895 animals were incomplete. The complete skeletons had 7 cervicals; 11 post-cervicals articulating with 10 ribs which were therefore dorsal vertebrae; 29 lumbo-caudal vertebrae, of which 11 may be termed lumbar and 18 caudal. The formula may be written C7D11L11Cd18 = 47. Variations in the relative number of lumbar and caudal vertebrae may without doubt from time to time occur. The length of the spine in the St Andrews skeleton, without allowing for the thickness of the intervertebral discs, was 12 feet 5 inches, and the length of the skull was 2 feet 8| inches, together 15 feet 3i inches. Professor MTntosh estimated that the carcase was over 16 feet, and the length of the skeleton, allowance being made for the thickness of the discs, corresponded with this measurement. The Mesoplodon stranded in Dalgety Bay was 15 feet 1 inch in length ; but, as the epiphysial plates of the vertebrae were not completely fused with the bodies, the animal was not fully grown, and although a male, the mandibular teeth projected only 2'6 cm. beyond the alveolus. The Shetland specimen, 1885, measured 15 feet 8 inches, the epiphysial plates were fused with the bodies, and the mandibular teeth projected 4’5 cm. beyond the alveolus. About 16 feet may therefore be regarded as the usual length of the adult Sowerby’s whale. Sternum. — It consisted of five transverse segments with four large intersegmental holes. The 1st, much the largest, 22 cm. long, was a broad plate, with two cornua in front, between which was a deep presternal notch. The two lateral halves of the 2nd segment were united mesially by a suture ; the 5th or terminal segment was incomplete, and the hole between it and the 4th had an imperfect boundary behind ; the 3rd and 4th segments were completely fused in the middle line. Each lateral border had articular facets for five costal cartilages : that for the 1st cartilage marked the anterior part of the 1st segment; those for 2nd, 3rd, 4th and 5th were opposite the line of articulation between the 1st and 2nd, 2nd and 3rd, 3rd and 4th, 4th and 5th sternal segments. Pelvic Bones. — These bones were rudimentary ; each consisted of a slender bar, 61 mm. long and 10 mm. in greatest width, faintly curved at the ends, which were attenuated. There was no sign of a rudimentary femur. Anterior Extremity. — The Scapula were plate-like, 32 cm. in diameter between the anterior and posterior angles, and 22 cm. between the glenoid 693 1908-9.] The Skeleton of a Sowerby’s Whale. and vertebral borders. The coracoid was 10'6 cm. in length. The post- spinous fossa formed so large a proportion of the outer surface that the pre-spinous fossa was a mere groove. The spine was a sharp low ridge, but the large plate-like acromion was 11*2 cm. long and 4'6 cm. wide. The Humerus was a short thick bone, only 15'5 cm. long. The head, neck and tuberosity were distinct ; the shaft was somewhat flattened on its two surfaces, on the inner of which was a roughened dejDression, stronger in the left bone ; the lower end had definite facets separated by a sharp ridge for the radius and ulna, and a concave surface on the inner border of the bone received the articular facet of the olecranon process. The Radius and Ulna were parallel and not movable on each other. The radius was 16‘5 cm. long, the shaft was 4*5 cm. wide at the middle, its surfaces were flattened. The humeral epiphysis was blended with the shaft ; the carpal one was ossified, though not fused with the shaft. The ulna was almost the same length as the radius, the shaft was 3'2 cm. wide ; the carpal epiphysis was ossified but not fused ; the olecranon epiphysis was ossified but movable on the shaft, and in this respect it differed from the bone in the 1885 and 1888 specimens, in which the olecranon was completely fused with the ulna, though in them the carpal epiphysis was distinct. Manus. — The manus was pentadactylous. It consisted of carpus, meta- carpus and phalanges enclosed in a common tegumentary covering. The Carpus had a proximal row , procarpus, a distal row, sometimes called meso- carpus, a pisiform and an os centrale or ossa centralia. In the proximal and distal rows the bones were flattened on the palmar and dorsal surfaces and the cartilage between them was thin. The procarpus consisted of the three bones usually found in this row of the cetacean carpus, the relative position of which is indicated by their names, radiale, the smallest ; intermedium, the largest; and the ulnare. The intermedium had a longitudinal groove on the palmar surface for the flexor digitorum ulnaris, and its upper border sent an angular prolongation between the carpal epiphyses of the radius and ulna. In my memoir on the Sowerby’s whale captured in 1885,* I described its carpus and showed that the distal carpalia were only three in number, which I designated as follows : the smallest was carpale x , next to which was a large bone which represented carpalia2 + 3, and on the ulnar side a large bone which represented carpalia4 + 5. In the St Andrews example a similar arrangement existed. Cl5 21 mm. in transverse diameter, articulated distally with the metacarpal of the pollex, MI; also with Mu, and with the radiale, centrale and the conjoined C2-f-C3. Carpalia2 + 3 formed a * Journal of Anat. and Phys., vol. xx. p. 180. 694 Proceedings of the Boyal Society of Edinburgh. [Sess. bone 37 mm. in transverse diameter, which was grooved for the flexor digitorum, and articulated with Mu on one side of the groove and with Mm on the other, also with CT, centrale, intermedium and C4 + 5. Car- palia4 + 5 formed a bone 42 mm. in transverse diameter, which articulated by its distal border with MIV and My ; opposite the interval between these metacarpals its distal and proximal borders and the dorsal surface were notched as if the two halves of the bone were imperfectly united, so that Fig. 1. — Riglit manus, palmar surface, Sowerby’s Whale, St Andrews. In this and other figures R means radius ; U, ulna ; r, radiale ; i, inter- medium ; u, ulnare ; c is a distal carpal, and the numeral associated with it is its number in the distal row ; C is os centrale ; the roman numerals are the meta- carpal bones ; P is pollex ; p is the pisiform element. it appeared that one part belonged to Mjy, the other to My ; it also articulated with C3, ulnare and the pisiform cartilage. Both in the St Andrews and 1885 animals the three distal carpalia represented the five distinct elements found in Hyperoodon, in which a distal carpal occurs for the metacarpal bone of each digit. It is likely that the two elements which formed the bone C 2 + 3 , as well as those of C4 + 5 had, as in Hyperoodon, been developed independently in the carpal cartilage, but thereafter became conjoined. In the St Andrews animal a narrow bar of cartilage formed the ulnar border of the carpus and a nodule of bone, the 695 1908-9.] The Skeleton of a Sowerby’s Whale. size of a small pea, situated in its mid-part, represented the pisiform. In the interval between the proximal and distal rows a bone on the palmar surface of each manus articulated with the radiale, intermedium, CY and a part of the adjoining bone which represented C2. It was 13 mm. in transverse and 12 mm. in antero-posterior diameter, and was from its position the os centrale (C, fig. 1), but it was not visible on the dorsal aspect. The carpus of the right manus contained also a second os centrale, 8 mm. in transverse and 9 mm. in antero-posterior diameter, which articulated with Fig. 2. — Eight manus, dorsal surface, Sowerby’s Whale, St Andrews. the angles of the intermedium, ulnare, C3 and C4, and was more visible on the dorsal aspect (fig. 2). In its constitution the carpus closely corre- sponded with that of the 1885 specimen previously described, with the addition in the right manus of a second os centrale. The carpus of the Mesoplodon from Dalgety Bay differed in the following points from those above described: — No os centrale existed as a separate bone, but the angle of the right radiale, which projected towards the bone designated C 2 + C 3 , was partially separated by a constriction which might indicate an os centrale fused with the radiale. The transverse diameter of the distal carpalia was as follows: C1? 22 mm.; C2 + 3, 36 mm.; whilst the internal carpale was only 25 mm., considerably less therefore than in 696 Proceedings of the Royal Society of Edinburgh. [Sess. the St Andrews and 1885 specimens. Owing to its small transverse diameter the internal carpale articulated by its distal border only with Mrv, whilst My was jointed to its ulnar border and to the ulnare in the proxi- mal row through an intermediate band of pisiform cartilage. The internal carpale represented perhaps only C4, whilst C5 was not differentiated in the carpal cartilage, nor was a pisiform bone ossified in the cartilaginous inner border of the carpus. Digits. — Each of the five digits of the St Andrews animal consisted of a metacarpal bone M, and one or more phalanges, Ph. The metacarpal of the pollex Mi was a slender cylindriform bone 26 mm. long ; at the free end was a nodule of cartilage which represented the phalanx. The metacarpals of the other digits were flattened ; Mm was the longest, 51 mm., My was only 25 mm. long, and was set at an angle to and articulated with the distal border of the carpale, which represented C5. As some of the phalanges had been lost their exact number cannot be stated, but they were probably the same as in the 1885 specimen, viz.: Dn, five phalanges; Dm, four; DIV, three ; Dy, two, and the longest digit was the index. In the Dalgety Bay specimen, however, Dm had five phalanges in one manus though only four in the other, and Diy had four phalanges, of which the terminal was no bigger than a small shot. The constitution of the manus in the St Andrews and Dalgety Mesoplodons may be expressed by the following formulae, the number of phalanges in the St Andrews specimen being taken from the 1885 specimen: — St Andrews. Dalgety Bay. Min. Ann. Med. Ind. Pollex. Min. Ann. Med. Ind. Pollex. Ph2 Ph3 PlR Ph! PI h Pli4 ?5 Ph5 ph, My MIV MIn Mu Mi i :vx Miv Mm Mn M, | / | / 1 \i 1 / pis. and also with the smaller disto-carpal ; it was obviously carpale2 + s fused together. The intermedium and the larger carpale were marked by a shallow groove on both palmar and dorsal surfaces, which was in line with the interosseous space in the forearm and with the interval between Mu and Mm ; the groove was doubtless for a tendon, or an artery. The smaller carpale was 24 mm. wide and articulated with intermedium, ulnare, almost equally with Mm and MIV, and with the larger disto-carpal e ; to its ulnar side a piece of unossified cartilage separated it from Mv ; it is marked C4 in fig. 6, and the unossified cartilage may represent an undeveloped C5. A plate of pisiform cartilage was at the ulnar border of the carpus, and extended from the lower end of the ulna 705 1908-9.] The Skeleton of a Sowerby’s Whale. to the base of My. No ossihc nodule had been formed in it. The carpus did not contain an os centrale. In digit I, the pollex, the metacarpal was elongated and somewhat conical ; it articulated directly with the radiale, for carpale x was not developed, and also with carpale2 + 3 ; the phalanx was not ossified. In the other digits the metacarpals were flattened. Metacarpain articulated for more than a third with radiale and the rest with carpale2 + 3 ; it had nine osseous phalanges. Metacarpalni articulated almost equally with car- palia2 + 3 and C4; it had seven osseous phalanges. Metacarpaliy articulated with carpale 4 and with the cartilage between it and the ulnare ; it had three osseous phalanges. Metacarpaly was marked by a groove on the dorsal surface which passed obliquely between the two lateral borders ; the bone projected at the ulnar border of the manus, and was set at an angle to MIV ; it articulated with ulnare and MIV and it joined the pisiform cartilage ; two rudimentary osseous phalanges were embedded in cartilage. Max Weber gave figures of the manus in two specimens of Lagenorhynchus alhirostris. In the older the three bones of the procarpus were represented, whilst only two disto-carpalia were figured, which he interpreted as C2 +C3 and C4, giving a significance like that which I have also attached to them. His conception of the metacarpus and phalanx of digit V corresponded with the conclusion to which I have subsequently arrived. From the figure of the carpus in the younger specimen it would seem that he recognised in it three distinct disto-carpalia, whilst a fourth was to be found in a bone occupying the position of the ulnare : the ulnare proper had either disappeared or become blended with the intermedium. I suggest the following formula for L. alhirostris : — Min. Ann. Med. hid. Pollex. Pli2 Ph3 Ph7 Ph9 Ph My Mjy Mm Mu Mi Ulna Radius Phocgena communis (Delphinus phocoena). The manus of the common porpoise was dissected in an adult female in December 1892, and has also been examined in other specimens. In the adult the radial and ulnar carpal epiphyses were united with the vol. xxix. 45 706 Proceedings of the Royal Society of Edinburgh. [Sess. shafts. The procarpus contained the three customary bones. The radiale, 14 mm. in transverse diameter, articulated with radius, intermedium, the carpal cartilage associated with the pollex and with Mn. The intermedium was 14 mm. wide, grooved on the palmar surface, and articulated with radius, ulna, radiale, ulnare and the two distal carpalia. The ulnare was 7 mm. wide and articulated with ulna, intermedium, the more ulnar distal carpale, My, and with the pisiform cartilage. This cartilage was only 5 mm. wide and 7 mm. long, and extended from the ulnar epiphysis to Mv ; it did not contain an ossified nucleus. No os centrale was seen. Two distal-carpalia were situated in the mesocarpus. The more radial was a small bone 9 mm. wide, with a groove in line with that on the intermedium opposite the interval between Mn and Mm, with both of which the nodule articulated, as well as with the radiale, intermedium, and the more ulnar distal carpal. The last-named bone was 12 mm. wide, and articulated with ulnare, intermedium, the radial distal carpal, and Mm, Mjy and My. The more radial bone apparently represented C2 + 3, and the more ulnar C4, or it may be C4 + 5. Both CT and C5 were absent as independent units. The hand was pentadactylous. Digit I, the pollex, was so close to the radial border and so slender that it might easily have been overlooked. It was connected with a band of cartilage on the radial border of the carpus extending to the radiale, which, though no ossific nodule was found in it, might perhaps represent carpale Mi, 12 mm. long, was very slender, and had at its distal end an unossified phalanx. Digit II, the longest, consisted of Mn, 21 mm. long, and six small osseous phalanges, the terminal of which was no bigger than a very small shot ; it was connected with the carpal cartilage of the pollex, the radiale, and the outermost distal carpal. Digit III had a metacarpal 20 mm. long and five small phalanges ; Mm articulated with both distal carpals. Digit IV had a metacarpal 13 mm. long and three small phalanges. Digit V projected from the ulnar side of the carpus ; My, 8 mm. long and 11 mm. wide, was connected with Miy, the ulnar distal carpal, the ulnare and the pisiform cartilage. The presence of three bones in the procarpus of the porpoise and of only two disto-carpalia has been generally described by anatomists. Both Weber and Kiikenthal numbered them as Cx and C2. Ktikenthal con- sidered that Cl5 as described in this memoir on the radial border of the carpus, was either absent or blended with Mi, or with the radiale ; his CY would therefore represent my C2-fC3 conjoined, whilst his C2 might be the conjoined C4 + C5, though more likely from its position only C4, whilst C5 had either not developed or had blended with the ulnare. 707 1908-9.] The Skeleton of a Sowerby’s Whale. The following formula is given for Phocoena communis : — Min. Ann. Med. Index. Pollex. Ph Ph3 Ph, Ph6 Pli M [v ^ Miv Mm Mu J\ h / \ / ulnare intermedium radiale Ulna Radius Globicephalus melas ( Pilot Whale). In my previous memoir on Mesoplodon,* so frequently referred to, I gave a short description of the carpus of Globicephalus melas. I have again studied this specimen, compared it with the descriptions which were subsequently published by Max Weber and by Kilkenthal, and have been led to modify the opinion which I had previously expressed on the morphology of certain of its disto-carpalia. In the two hands of my specimen the radial and ulnar epiphyses were ossified, but not fused with the shafts. The bony elements of the carpus were well formed and dominated the cartilaginous matrix. The radiale was 47 mm. in transverse diameter, the intermedium 40 mm. and the ulnare 24 mm. The bone on the radial border of the carpus, which I had previously spoken of as carpale 2, I now regard as carpale x , which necessarily modifies the numerical order of the other disto-carpalia, so that the former carpale 3 now becomes C2, and the former C4 becomes carpale 3. Again, the bone situated in the plane of the proximal ends of the metacar pals, which from its rounded form and roughened surface I had regarded as distal carpal C x , is now described as the metacarpal of the pollex. This change in opinion of the morphology of these bones is based on a fuller recognition of the position of the os cent rale, which in the original description was regarded as placed between carpalia 2 and 3, whereas its true position is between carpale 1? C2, the radiale and the intermedium. The present description follows, there- fore, the amended view of the morphology of the bones. Carpale Y , 34 mm. in transverse diameter, articulated with radiale, an os centrale in right carpus, and about equally with and Mn : carpale 2 , the bone of which was 33 mm. wide, articulated with intermedium, os centrale in right carpus, radiale in left, carpale 3, and about equally with Mn and Mm : carpale 3, the bony part 31 mm. wide, articulated in right carpus with inter- * Journ. Anat. and Phys ., Oct. 1885, vol. xx. p. 185. 708 Proceedings of the Royal Society of Edinburgh. [Sess. medium, ulna, ulnare, carpale2, and about equally with Mm and Miy; in this carpus it was distinct from the ulnare, but in the left hand it was fused with it and formed a conjoined bone (compare fig. 7 with fig. 8). No separate carpale 4 or 5 existed, though possibly C3 may contain the element C4, and carpale5 may potentially be present as a part of My, for the ulnare was relatively small, so that C5 could scarcely be regarded as fused with it. In the interval between carpale 2 , C 2 , the radiale and the intermedium was shrunken cartilage containing in the right carpus a small osseous nodule, which may be regarded as an os centrale, but in the left carpus the correspond- ing cartilage was unossified. Unossified and shrunken pisiform cartilage Fig. 7 — The right carpus of G. melas. Fig. 8. — The left carpus of G. melcis. formed the ulnar border of the carpus. In their articulations the metacarpals were arranged as follows : — Mi, the rounded bone with roughened surface for the pollex above referred to, articulated with carpale!: Mu with Cl and C2 about equally, and with the cartilage of the os centrale : Mm with C2 and C3 about equally : the carpal ends of Mu and Mm were bif aceted, the facets separated by a mesial ridge were inclined laterally, so that the corre- sponding distal carpalia were not opposite to the ridge, but to the lateral facets and to the interval between two metacarpals: Miy with carpale 3 and the ulnare : My with ulnare, the ulna and the pisiform cartilage. In Max Weber’s figure of the hand of Globicephalns melas three distinct disto-carpaliawere recognised: — carpale l , the most radial, jointed with MT and Mn : a bone which he regarded as representing carpale2 + 3 jointed with the bases of Mu and MnI : next to it a bone lettered C4 which articulated 1908-9.] 709 The Skeleton of a Sowerby’s Whale. with Mm and Miv. No carpale5 was present, and both MIV and Mv articu- lated with the ulnare and the latter also with the ulna. An os centrale occupied the position described above in my specimen. Kukenthal had the opportunity of studying several embryos of G. melas. He recognised only three separate distal carpalia. Carpale 3 in the larger embryos was the biggest and had a short metacarpah ; carpale 2 was associated with Mn and Min, though principally with Mu; carpale 3 with Mm and Miv; whilst carpale 5 was directly fused with the ulnare with which Mv articulated. He referred to an os centrale described by me as present in the well-grown G. melas, but in the majority of the hands of his embryos the centrale was not visible. He stated that the foetal carpus corresponded in the number and position of its elements with that of the well-grown animal. The pisiform cartilage was well formed in the embryos, and in all a small, rounded piece of cartilage projecting from the radial border of the radiale represented the prgepollex of von Bardeleben. As is well known, G. melas is distinguished by the number of the phalanges in the second and third digits and by the great length of the digits, the index beino; the longest. The formulse of the carpus in my specimen are appended, and that in the right hand corresponds with formula No. 2 in Kukenthal’s memoir, p. 34. Right Rand. Ma pis. cart. Ann. Med. Index. Pli2 Ph8 Phi2 Mm Mm Mn / \ / \ / x / c3 C 2 Cen. Ph2 | Mi A ulnare intermedium radiale Ulna Radius Left Hand. Min. Ann. Med. Index. Pollex. Ph Ph Ph Ph Pli My Miv Mm Mu Mi ulnare intermedium radiale Ulna Radius Grampus griseijs ( Risso’s Dolphin). In September 1899 a school of Risso’s dolphin was captured near Hillswick, Shetland, and specimens were sent to me by Dr Charles Anderson.* I dissected the hands in two animals. From the state of the ossification neither had reached maturity, though one was more advanced than the other : the radio-ulnar epiphyses were ossified, though not fused with the shafts. * See my account in Proc. Roy. Phys. Soc. Edin., vol. xi. p. 192, 1891-92 ; also my description of the Viscera in Journ. Anat. and Pliys., vol. xxvi. p. 258, 1892. Two of the skeletons are mounted in the Anatomical Museum of the University. 710 Proceedings of the Royal Society of Edinburgh. [Sess. In the more advanced specimen the carpal hones were well ossified, but in the other the cartilage was more abundant. The rprocarpus had radiale, intermedium and ulnare. In the older animal the radiale was 33 mm. in transverse diameter, the intermedium 40 mm. and the ulnare 28 mm. The radiale articulated with radius, intermedium, carpalia x and 2. The inter- medium was grooved on its palmar surface ; its proximal border mostly articulated with radius and only slightly with ulna ; it also articulated with radiale, C2 and C3+4,the latter of which intervened between intermedium Fig. 9. — Dorsal surface, left manus, Grampus griseus. and ulnare. The ulnare articulated with the inner half of the ulnar epiphysis, with C3+4, with MIV and My, and with the pisiform cartilage, which contained no osseous nodule. The distal row had three separate carpalia. Carpale1 was 25 mm. wide and articulated with radiale, C2 and the epiphysis of Mj. Carpale2 was 31 mm. wide and articulated with radiale, intermedium, C3, largely with Mn and slightly with Mm. Carpale3, 29 mm. wide, was grooved on palmar surface, and articulated with intermedium, ulnare, epiphysis of ulna, largely 1908-9.] 711 The Skeleton of a Sowerby’s Whale. with Mm and less so with Miy ; carpale4 was probably fused with it. No os centrale was present, and the pisiform cartilage extended from ulna to 5th metacarpal. The manus was pentadactylous. Digit I had its metacarpal 25 mm. long, somewhat conical and articulating by its proximal epiphysis with carpale l , whilst distally it was continuous with an unossified phalanx. The other metacarpals were flattened bones, which as well as the phalanges had proximal and distal epiphyses. The second metacarpal articulated with C 2 and very slightly with C l ; its digit was the longest and had eight phalanges. The third articulated with carpalia 2 and 3, and had six phalanges. The fourth, whilst 31 mm. in transverse diameter, was only 20 mm. long ; it articu- lated with carpale 3 and with the ulnare ; its two phalanges were short and flattened. The fifth metacarpal consisted of a bony nodule 24 mm. wide and 13 mm. long, which was imbedded in cartilage continuous with the pisiform, and there was no bony phalanx. A feature in this manus was the rudimentary condition of the fifth digit, the absence of carpale 5, and no separate C4, though this element may have blended with the ulnare, or rather with carpale 3 (fig. 9), which articulated with both Mm and Miy. From the close relation of the fifth metacarpal with the ulnare, C5 had either never been developed or had disappeared very early, either by atrophy, or by fusion with the ulnare or with My. So rudimentary was the fifth digit that in the manus of the younger of the two dolphins it was scarcely recognisable, and the manus almost seemed as if it were tetradactylous. The formula in the well-ossified manus of Risso’s dolphin was as follows : — Min. Ann. Med. Ind, Pollex. Ph Pli2 Ph6 i Pli8 Pip Mv Miy 1 Mm Mu Mi pis. cart. |k intermedium radiale Radius Delphinapterus leucas (Beluga or White Whale). In his memoir “ On the Hand in the Cetacea,” W. Kiikenthal described and figured the characters in an adult Beluga and in a number of embryos at various stages of development. The procarpus was typical. The mesocarpus was variable. In the youngest embryo five cartilaginous disto- carpalia C 2 to C 5 were recognisable. Carpale 5 however disappeared early, 712 Proceedings of the Koyal Society of Edinburgh. [Sess. so that at a later stage only four cartilaginous distal carpalia were present. A fusion of carpale3 with C4 might also occur and the number be reduced to three carpalia, C1? C2, C3 + 4. He thought that carpale5 probably became a part of the ulnare. He saw sometimes two centralia, one of which might remain, though usually both fused with adjoining bones. In an important memoir on the Anatomy of a Beluga the late Sir John Struthers gave a detailed account with figures * of the structure of the manus. The procarpus consisted of the three customary bones, whilst the other bones were regarded as four distal carpalia C Y to C4, a small os centrale, and a pisiform, the ulnare, centrale, C3 and pisiform not being ossified. As Sir John Struthers had presented to me for the Anatomical Museum this and other specimens from his collection of cetacea, I have examined the manus, and I concur in his interpretation of the carpal elements. Thus carpale Y belonged to the pollex : C 2 was mainly for Mn, though with a slight articulation with Mm : C3 was for Mm, though C4 was divided equally between Mm and MIV and its distal angle intervened between these two metacar pals : no independent C 5 existed, for My articulated directly with the ulnare, which was relatively large and probably included, though still in the cartilaginous stage, C5, and its dorsal angle also reached the base of MIV. The area of cartilage interposed between radiale, intermedium, C x and C2, which Struthers regarded as an os centrale, holds the position of that carpal element and may be regarded as its unossified representative. The formula of this carpus corresponds with No. 4 of the formulae of Beluga given by Klikenthal on p. 28 of his memoir, except that there is only one os centrale. Min. Ann. Med. hid. Pollex. Ph3 Ph3 Ph4 P'v, 1 Ph4 I rly Miv Mm Mn i Mi pis. Mm, and MIV, also with a piece of cartilage on its disto-ulnar border Fig. 10. — Radiogram of manus of adult Monodon monoceros. which was situated between the ulnare, MIV and Mv, and may possibly represent an unossified C5. Projecting from the disto-radial border of the intermedium, and continuous with it by a narrow neck, was a nodule of bone 7 mm. in transverse diameter, which articulated with the radiale, C 2 + 3 , and the cartilage with its nodule described as Cx; it was obviously an os centrale fused with the intermedium ; in its relations and intimate association with that bone it corresponded with the arrangement in the foetus B in the Leboucq collection. Mx articulated with the probable Cx and with the radiale ; Mn with Cx and C2 + 3 ; MIn with C2 + 3 and C4 ; 1908-9.] 715 The Skeleton of a Sowerbv’s Whale. MIV with CIV and the cartilage of the possible Cv ; Mv slightly with that cartilage, but mostly with the ulnare. The two less advanced specimens had in the distal row the bony carpalia which I have designated C2 + 3 and C4 ; no ossific nodule was seen in the radiograms in the cartilage between the radiale and MI? or in that between the ulnare and Mv. In both a process of bone projected from the disto- radial border of the intermedium, like that which I have interpreted in the adult as an os centrale. The formula of Monodon monoceros is as follows : — Min. Ann. Med. Ind. Pollex. Ph, ff Ph3 j PP4 PIP Ph2 M y Miv Mm Mu i Mi c5 ? o4 c, I +2 k i Cen. I ulnare intermedium i ’adiale / \ / / Ulna Radius Morphological Summary. It will have been seen from the foregoing description that in the Ziphioid whales, Hyperoodon and Mesoplodon, and in the Helphinidse, whilst the three bones of the proximal row of the carpus, and the pisiform cartilage either unossihed or only partially so, are constant in number and correspond generally in their arrangement, yet that the distal carpalia vary in number, and in their articulations with the procarpus and with the metacarpal bones ; also that the ossa centralia are inconstant. Hyperoodon should, as I stated in 1885, be regarded as the type in which each of the five digits has its corresponding distal carpal, for articulation with the metacarpal of the digit to which it belongs. In other genera and species, however, a smaller number of distal carpalia are present, and the question naturally arises which members of the type-number have remained and which have disappeared as independent units. The range in number varies from five in Hyperoodon to four, or three, or even two in other, species. In my memoir on the Shetland Mesoplodon, 1885, I discussed the question of the diminution in the type-number from five distal carpalia, and stated that it “ may be due either to one or more centres of ossification not having formed in the carpal cartilage, or to the fusion with each other of ossific nuclei which were distinct in the younger con- dition of the same carpus.” The terminology of the carpal bones introduced 716 Proceedings of the Royal Society of Edinburgh. [Sess. by Gegenbaur, and their substitution for the older descriptive terms (adopted from human anatomy in the writings of anatomists as eminent as Owen, van Beneden and Flower), have greatly facilitated the description of this region ; the graphic formulae employed by Leboucq, Max Weber, and Ktikenthal, which I have also used in this memoir, enable the eye to follow the description and assist one in recognising the morphology of the carpal bones in the manus of the Cetacea. The guide to the solution of this problem is to be found in a manus in which the number of disto-carpalia corresponds with that of the digits ; whilst in specimens in which some carpalia are wanting, it is important to study the articulations of those which are present with the metacarpal bones. As previously stated, Hyperoodon provides us with the necessary key, for in this carpus each metacarpal, in the majority of specimens examined, has a definite disto-carpal for articulation with it. The researches of Ktikenthal and Leboucq into the development of embryos of several species of Cetacea have shown that, in the early stages of Beluga and Monodon, a fifth differentiated cartilage existed in the distal row, which was not represented by a bony C5 in the fully formed carpus, so that in the progress towards ossification this carpal element had disappeared.* A similar defect has also been observed in the carpus of a few specimens of Hyperoodon ; the missing bone was carpale 5 , and the formula of the distal row was reduced in them to carpalia 1, 2, 3, 4- Are we to assume that either five carpalia constitute in the Cetacea generally the normal number of elements in the distal row in the very early stages of development ; or that a carpus may be formed at its initial develop- ment in which the elements of the disto-carpalia are fewer than five ? In the latter instance the diminution in number would be a fundamental develop- mental defect, and could only be satisfactorily determined by the study in a given species of a sufficient number of specimens at the commencement of and in the early stages of cartilaginous differentiation in the carpus. In the former case the deficiency would be due to the disappearance of the cartila- ginous precursors of the bones, either by atrophy in the early stages of development, or by fusion between adjoining cartilages or bones at somewhat later stages. The fusion might take place : a, between cartilages or bones in the same row ; b, between cartilages or bones in the distal with those in the proximal row ; c, between the disto-carpalia and the metacarpals. * Gervais, in his part of the great Osteographie des Cetaces by Van Beneden and himself, figured the manus of a foetal Hyperoodon in which five cartilages were present in the distal row, but he regarded the fifth of these as a pisiform. 717 1908-9.] The Skeleton of a Sowerby’s Whale. Examples of fusion in the same row are not uncommon in the cetacean carpus, and their articulation with the metacarpals should be carefully noted in determining which of the bones are fused together. Of the species described in this communication there can be no doubt that the rule in Mesoplodon bidens is for C2 to fuse with C3, and to articulate with Mn and MnI ; usually also C4 fuses with C5 and articulates with MIV and Mv. The fusion of C2 and C3 constitutes the zipliius type of carpus of Klikenthal. In the Dalgety Bay Mesoplodon the small size of the most ulnar disto-carpal led me to think that it represented only C4 for articula- tion with MIV ; whilst Mv was displaced from the proper distal border of C4, and articulated with the ulnare ; C5 was, on this view, possibly absent. In Lagenorynchus cdbirostris C2 and C3 were fused, and the conjoined bone articulated with Mn and MIrI; C4 was small, articulated with MIV and not with Mv ; C l and C 5 were absent as separate bones or were perhaps combined with others. In Grampus griseus C3 and C4 were fused and articulated with MIIX and MIV, whilst C2 remained as a separate bone for Mn, and articulated with the pollex. In Delphinus acutus and Monodon monoceros C2 and C3 were fused and articulated with Mn and MIIX ; C4 was present, and articulated princi- pally with MIV ; C l was also present, but C 5 did not exist as a separate bone. Phocoena communis had only two disto-carpals, being the minimum number found in the Odontoceti ; of these one apparently represented C2 fused with C3, whilst the other was C4 ; CT and C5 were not visible as independent units. As a distinct example of fusion of a distal with a proximal carpal I may refer to fig. 8, the left carpus of Globicephalus melas , in which C3 had fused with the ulnare. The question of fusion between bones of the distal and proximal rows, or of the distal with the metacarpals, arises also in con- nection with the condition of Ca and C5 of the distal carpalia, which bones may in several species be absent as independent units ; the possibility of fusion either with a bone of the proximal row or with a metacarpal has to be considered. C5 is the element which most frequently has no separate representative, and which cannot definitely be regarded as fused with C4. In Belpliinus delphis and acutus , Grampus griseus , Lagenorynchus cdbirostris, Globicephalus melas, Phocoena communis, Delphinapterus leucas (Beluga), Monodon monoceros, Mv articulated directly with the ulnare without the interposition of a separate disto-carpale. Klikenthal regarded this as the Beluga type of carpus common in the Odontoceti. It might arise from fusion of the cartilaginous C5 with the ulnare, or from 718 Proceedings of the Royal Society of Edinburgh. [Sess. fusion of C 5 with Mv , or from an early atrophy and disappearance of the cartilaginous C5. The question whether Cx is present or absent in some species of cetacea has been a matter of discussion. There can be no doubt of its presence in Mesoplodon, Hyperoodon, Beluga and Grampus. In Lageno- rynchus and Phocoena it was absent, and Mr articulated directly with the radiale, with which C x might have fused ; though, as Leboucq has shown in Monodon monoceros, the fusion of C x with Mj does at times undoubtedly take place. In Delphinus, again, the question has arisen whether the bone immediately distal to the radiale is to be regarded as Mx or C1. If the former, then the pollex would possess two phalanges, and its metacarpal would articulate directly with the radiale. If the latter, Cx would be interposed between the radiale and Ml5 and the carpus would possess three disto-carpals. I have adopted the latter interpretation and applied it also to the carpus of Globicephalus. As regards the os centrale, Mesoplodon and Globicephalus furnished examples of the presence of an os centrale as an independent bone ; in the right manus of the St Andrews Mesoplodon a second centrale had been developed, and in that from Dalgety Bay an os centrale had fused with the radiale. In Monodon the centrale was fused with the intermedium. In the Struthers collection of cetacea, already referred to, is the dissected hand of an adult cetacean which, though not marked, is I believe that of Hyperoodon A The carpus consisted of ten bones and cartilages, three in the proximal row; live separate disto-carpalia, of which Cx and C4 were well ossified, C2 and C3 partially so, whilst C5 and the pisiform were unossified. An almond-shaped unossiiied os centrale, 21 mm. in transverse and 14 mm. in vertical diameter, was intercalated on the palmar surface between the radiale, intermedium, carpalia l and 2. In the presence of an os centrale this specimen corresponded with specimens of Hyperoodon, two well grown and a foetus, as described by Ktikenthal. In Beluga an unossified piece of cartilage probably represented the centrale. Ktikenthal came to the conclusion from his observations on embryos that centralia are not unfrequently present in the early stages, but that they commence to disappear when other elements in the carpus lose their * This limb probably belonged to the Hyperoodon which Professor Struthers obtained in 1871, and the finger muscles of which he described in the Journal of Anat. and Phys ., vol. vi. p. 115. At the Aberdeen meeting of the British Association, 1885, he exhibited the carpus of Hyperoodon along with those of other cetacea, but no description was published. Report , p. 1056. The radio-ulnar epiphyses were fused with their shafts. The radiale, intermedium, and ulnare were respectively 43, 58 and 45 mm. wide ; the disto- carpalia 1 to 5 were 39, 33, 35, 27, 30 mm. respectively. 719 1908-9.] The Skeleton of a Sowerby’s Whale. independence. The disappearance may perhaps in some cases be due to atrophy of the cartilaginous centrale, or, as in Mesoplodon and Monodon, to its fusion with an adjoining carpal bone. The pisiform element of the carpus seems to be constant in the cartila- ginous stage, but in my specimens it was undergoing ossification only in Hyperoodon and the St Andrews Mesoplodon. From the observations of Leboucq and Kiikenthal on the development of the phalanges, their number in the adult is less than in that of the embryo of the same species, apparently by fusion with each other of pieces originally distinct, a condition which applies also to diminution in the number of pieces originally present in the carpus. In this memoir I have purposely restricted myself to the consideration of the carpus in those Odontoceti that I have personally examined. The principles which have guided me in ascertaining the morphology of the bones can be applied to their determination in other species of whales ; but as this paper has reached a length more than I had originally intended, I must leave for another occasion their further application. As supplementary to my description and figures of the carpus of Mesoplodon I append a radiogram of the manus of that animal, which shows Fig. 11. — Radiogram of hand of Mesoplodon bidens from Morrison’s Haven. distinctly, in the undissected carpus, carpale1 as a separate bone associated with the pollex ; carpale 2 fused with C 3 , as indicated by the notch opposite the interval between Mn and Mm; carpale 4 fused with C5 for MIV and Mv. 720 Proceedings of the Royal Society of Edinburgh. [Sess. The radio-ulnar epiphyses, though ossified, are not fused with the shafts of their bones. All the illustrations, with the exception of fig. 3, are from photographs of the specimens made in the Anatomical Department of the University by the Museum assistants, Mr Ernest Henderson and Mr William Gill, to whom I would express my indebtedness. For convenience of reference the lettering of the figures is as follows : — R, radius ; U, ulna ; r, radiale ; i, intermedium ; u, ulnare ; c, with arabic numerals disto-carpalia ; the roman numerals are the metacarpals ; C, the os centrale ; P, pollex ; rp, the pisiform element. INDEX. PAGE Mesoplodon bidens , Sowerby’s whale, ...... 687-720 Morphology of manus in Hyperoodon and in the Delpliinidpe, . . . 697 Hyperoodon rostratus , ......... 698 Delphinidse, .......... 700 Delphinus delphis, common dolphin, ....... 700 „ acutus , white-sided dolphin, . . . . . . .702 Lagenorynchus albirostris , white-beaked dolphin, . . . . .703 Pliocoena communis , common porpoise, . . . . . .705 Globicephalus melas, pilot whale, . . . . . . .707 Grampus gfiseus , Risso’s dolphin, . . . . . . .709 Delphinapterus leucas, Beluga or white whale, . . . . . .711 Monodon monoceros, Narwhal, . . . . . . . .712 Morphological Summary, . . . . . . . .715 {Issued separately October 14, 1909.) the printer is not responsible, the expense of such proofs and corrections will be charged against the author. All proofs must, if possible, be returned within one week, addressed to The Secretary , Royal Society, Mound, Edinburgh, and not to the printer. To prevent delay, authors residing abroad should appoint some one residing in this country to correct their proofs. 4. Additions to a Paper after it has been finally handed in for publication, if accepted by the Council, will be treated and dated as separate communications, and may, or may not, be printed immediately after the original paper. 5. Brief Abstracts of Transactions Papers will be published in the Proceedings, provided they are sent along with the original paper. 6. Separate Issue of Reprints; Author’s Free and Additional Copies. — As soon as the final revise of a Transactions paper has been returned, or as soon as the sheet in which the last part of a Proceedings paper appears is ready for press, a certain number of separate copies or reprints, in covers bearing the title of the paper and the name of the author, are printed off and placed on sale. The date of such separate publication will be printed on each paper. The author receives fifty of these reprints free, and may have any reasonable number of additional copies at a fixed scale of prices which will be furnished by the printer, who will charge him with the cost. To prevent disappointment, especially if the paper contains plates, the author should, immediately after receiving his first proof, .notify to the printer the number of additional copies required. 7. Index Slips. — In order to facilitate the compilation of Subject Indices, and to secure that due attention to the important points in a paper shall be given in General Catalogues of Scientific Literature and in Abstracts by Periodicals, every author is requested to return to the Secretary, along with his final proof, a brief index (on the model given below), of the points in it which he considers new or important. These indices will be edited by the Secretary, and incorporated in Separate Index Slips, to be issued with each part of the Proceedings and Transactions. MODEL INDEX. Schafer, E. A.- -On the Existence within the Liver Cells of Channels which can be directly injected from the Blood-vessels. Proc. Roy. Soc. Edin., vol, 1902, pp. Cells, Liver, — Intra-cellular Canaliculi in. E. A. Schafer. Proc. Roy. Soc. Edin., vol. Liver, — Injection within Cells of. E. A. Schafer. Proc. Roy. Soc. Edin., vol. , 1902, pp. , 1902, pp. IV The Paupers published in this Part of the Proceedings may be had separately , on application to the Publishers , at the follow- ing prices: — No. XXXVITI., No. XXXIX., No. XL., No. XLL, . Price Is. 8d. ,, Is. 2d. ,, Is. 2d. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SESSION 1908-9. Part VIII ] YOL. XXIX. [Pp. 721-799. CONTENTS. NO. PAGE XLII. The Atomic Weight of Platinum. By E. H. Archibald. ( Communicated by Professor J. G. MacGregor), . .721 {Issued separately December 2, 1909.) XLIII. On the Development of Mixed Cultures of Bacteria and Lower Fungi in Liquid and Solid Media. By Emil Westergaard, Lecturer on Technical Mycology, Heriot- Watt College, Edinburgh. ( Preliminary Notice), . 748 {Issued separately December 2, 1909.) Obituary Notice, . . . . . . .749 Appendix — Proceedings of the Statutory Meeting, 1908, . . .753 Proceedings of the Ordinary Meetings, Session 1908-1909, . 754 Laws of the Society, . . . . . .759 The Keith, Makdougall -Brisbane, Neill, and Gunning Victoria Jubilee Prizes, . . . . . .764 [ Continued on page iv. of Cover. EDINBURGH : Published by ROBERT GRANT & SON, 107 Princes Street, and WILLIAMS & NORGATE, 14 Henrietta Street, Covent Garden, London, MDCCCCIX. Price Two Shillings. 3 D EC 181 REGULATIONS REGARDING THE PUBLICATION OF PAPERS IN THE PROCEEDINGS AND TRANSACTIONS OF TPIE SOCIETY. The Council beg to direct the attention of authors of communications to the Society to the following Regulations, which have been drawn up in order to accelerate the publication of the Proceedings and Transactions, and to utilise as widely and as fairly as possible the funds which the Society devotes to the publication of Scientific and Literary Researches. 1. Manuscript of Papers. — As soon as any paper has been passed for publication, either in its original or in any altered form, and has been made ready for publication by the author, it is sent to the printer, whether it has been read or not. The ‘ copy ’ should be written on large sheets of paper, on one side only, and the pages should be clearly numbered. The MS. must be easily legible, preferably typewritten, and must be absolutely in its final form for printing ; so that corrections in proof shall be as few as possible, and shall not cause overrunning in the lines or pages of the proof. All tables of contents, references to plates, or illustrations in the text, etc., must be in their proper places, with the page numbers left blank; and spaces must be indicated for the insertion of illustrations that are to appear in the text. 2. Illustrations. — All illustrations must be drawn in a form im- mediately suitable for reproduction; and such illustrations as can be reproduced by photographic processes should, so far as possible, be preferred. Drawings to be reproduced as line blocks should be made with Indian ink (deadened with yellow if of bluish tone), preferably on fine white bristol board, free from folds or creases; smooth, clean lines, or sharp dots, but no washes or colours, should be used. If the drawings are done on a large scale, to be afterwards reduced by photography, any lettering or other legend must be on a corresponding scale. If an author finds it inconvenient to furnish such drawings, the Society will have the figures re-drawn at his expense ; but this will cause delay. When the illustrations are to form plates, a scheme for the arrangement of the figures (in quarto plates for the Transactions, in octavo for the Proceedings) must be given, and numbering and lettering indicated. 3. Proofs. — In general, a first proof and a revise of each paper will be sent to the author, whose address should be indicated on the MS. If further proofs are required, owing to corrections or alterations for which [' Continued on page iii of Cover. 1908-9.] The Atomic Weight of Platinum. 721 XLII. — The Atomic Weight of Platinum. By E. H. Archibald. Communicated by Professor MacGregor. (MS. received March 10, 1909. Read June 7, 1909.) Twenty-two years have passed since the atomic weight of platinum was studied by Dittmar and M£ Arthur .* This is the last investigation recorded which has been concerned with the value of this constant. During the intervening period, as the result of many investigations carried on by Professor T. W. Richards and his students,]* the accuracy with which many of the manipulations incident to atomic weight investiga- tions can be executed has been greatly increased. Perhaps of still greater importance, methods for the preparation of many compounds of undoubted purity have been devised, and the principles underlying the preparation of pure substances have been clearly set forth.j In the case of the atomic weight of platinum, the different investigations, which are comparatively few in number, have seldom given results which show even fair agreement ; and even in these cases, as will be shown later, the agreement between the mean values obtained by different ratios leaves much to be desired. It seems unfortunate that many of the ratios used in calculating the value at present accepted were obtained by weighing a salt, which, after being precipitated from a water solution, was heated to a temperature of only 150 for the purpose of expelling the water. The observations of Precht § have shed a great deal of light upon the difficulties involved in the preparation of pure halogen compounds of platinum. In view of the above considerations, and particularly as the atomic weight of platinum is constantly being used in the estimation of potash, a * Trans. Roy. Soc. Edin., xxxiii. 561 (1887). + Richards, Proc. Am. Acad., xxii. 342 (1887), xxiii. 177 (1888), xxv. 195 (1890), xxvi. 240 (1891), xxviii. 1 (1893), xxix. 369 (1894) ; Richards and Rogers, ibid., xxviii. 200 (1893) ; Richards and Parker, ibid., xxxii. 55 (1896) ; Richards and Cushman, ibid., xxxiii. 97 (1897) ; Richards and Baxter, ibid., xxxiii. 115 (1897) ; Richards and Marigold, ibid., xxxvii. 365 (1902) ; Richards and Archibald, ibid., xxxviii. 443 (1903) ; Richards and Wells, Jour. Am. Chem. Soc., xxvii. 475 (1905) ; Richards, Staehler, Forbes, Mueller, and Jones, Carnegie Inst, of Washington, Publication 69. I Richards, Proc. Amer. Phil. Soc., xlii. 28 (1903). § Precht, Zeit. Anal. Chem., xviii. 509 (1879). VOL. XXIX. 46 722 Proceedings of the Royal Society of Edinburgh. [Sess. critical study of the constant in question seemed altogether desirable. The work recorded in the following pages has extended over a period of four years. Historical. Berzelius * was the first to work upon the atomic weight of platinum. As early as 1826 he determined the per cent, of platinum in platinous chloride, and from these analyses a value of 193T6 is obtained for the atomic weight. Two years later, j- by decomposing potassium chloro- platinate in hydrogen, he obtained data from which the atomic weight of platinum can be calculated by several ratios. The values calculated from these ratios vary between 195*4 and 196*6, giving a mean of 195*90. A report of some work by Andrews f appeared in 1852, but a detailed statment of his experiments is lacking. He worked with potassium chloroplatinate, decomposing it by means of zinc and water. After dis- solving the excess of zinc and filtering, the chlorine in the filtrate was estimated and the platinum was dried and weighed. From three determina- tions we have the values 197*9, 197*7, and 198*1 for the atomic weight, or a mean value of 197*9. Previous to the publication of Seubert’s § determinations in 1881 the atomic weight of platinum was supposed to lie above that of gold. This investigation, however, showed that platinum had an atomic weight several units below that of gold. He studied both potassium and ammonium chloro- platinate, preparing these salts with great care, and decomposing them in a stream of hydrogen. The resulting hydrochloric acid was in some cases absorbed in water or silver nitrate solution, and the chlorine estimated as silver chloride. From the weight of the original salt, the weight of platinum residue, of potassium chloride, and of chlorine lost upon ignition, several independent ratios are obtained, from which the value sought can be calculated. Three different samples of ammonium chloroplatinate gave the following mean values, reducing the weight to the vacuum standard, and assuming that chlorine = 35*46, nitrogen — 14*01, hydrogen = 1*008, bromine = 79*92, silver = 107*88, and potassium = 39*11. I. From the ratio (NH4)2C16 : Pt . . . . 195*12 II. „ „ (NH4)2C16 : Pt . . . . 194*47 III. „ „ (NH4)2C16 : Pt . . . . 195*47 * Poggend, Annalen , viii. 177 (1826). t Ibid., xiii. 468 (1828). X British Assoc. Report , 1852. § Ber. JUeutsch. Ghem. Gesell., xiv. 865 (1881). 723 1908-9.] The Atomic Weight of Platinum. Here is a difference of one unit in the mean values. Another series of analyses where the total chlorine was determined as silver chloride gave : From the ratio (NH4)2C16 : Pt . . . . 194 62 „ „ 6AgCl : Pt . . . . 195-80 6AgCl : (NH4)2 PtCl6 . . 197*20 It seems very likely that the high result in the case of the last ratio was due to the presence of water in the salt weighed. For the potassium chloroplatinate we have the following mean values: From the ratio K2C16 : Pt . . . . 194*81 „ „ 2KC1 : Pt 194-82 „ „ 2KC1 : K2PtCl6 .... 195-00 From another series of analyses, where the chlorine lost upon ignition was determined as well as the platinum, we have: From the ratio K2C16 : Pt . . . . 194-72 „ „ 4AgCl : Pt 195 05 „ „ 4AgCl : K,PtCl6 .... 195-51 In 1884 Halberstadt * published the results of a very complete study of the chi oroplatinates of ammonium and potassium. He also made some analyses of platinic bromide. The platinum was estimated both by weigh- ing the metal left after reducing the salt in hydrogen and by weighing the metal electrolytically. The mean values calculated from his ratios are given below. From the ratio Br4 Pt 99 „ (NH4)2b|6 Pt 99 „ K2Br6 Pt 99 „ 2KBr Pt 99 2KBr PtBr 99 (NH4)2C16 Pt 99 k2ci6 Pt 99 2KC1 Pt 99 „ 2KC1 Pt . 194-51 . 194*82 . 195-05 . 195-19 . 195-89 . 195-05 . 194-75 . 194-90 . 195-33 The extreme values among these results can be explained if we assume that the original salt in each case contained some water which had not been driven out before it was weighed. Thus in the ratio Br4 : Pt any water in the PtBr4 weighed makes the weight for the Br4 too great ; likewise in the ratio 2KBr : PtBr4 the water in the original K2PtBr6 weighed gives too high a value to the PtBr4. It should be remembered that the above * Ber. Deutsch. Ghem. Gesell. , xvii. 2962 (1884). 724 Proceedings of the Koyal Society of Edinburgh. [Sess. are all average values from a number of determinations ; individual de- terminations would show considerably greater variation. In 1887 Dittmar and M‘ Arthur * published an account of a critical examination of potassium chloroplatinate. They concluded that the salt is seldom if ever prepared pure ; that hydrolysis invariably takes place, some chlorine being replaced by hydroxyl, and also that some potassium is always replaced by hydrogen. In the light of these considerations, they apply corrections to a number of determinations which they made of the ratio 2KC1 : Pt. The results which they found give a mean value of 195*50. These authors at the same time criticised the work of Seubert, and concluded that if the proper corrections were applied to his results a value above 195*00 would be obtained. Dittmar and M‘ Arthur have made some timely suggestions regarding the preparation of pure potassium chloroplatinate. The strong tendency of the salt to hydrolyse in water solutions seems to have been generally dis- regarded by others, while the difficulty of getting rid of nitric acid by evaporating with excess of hydrochloric acid after dissolving the platinum in aqua regia was not fully appreciated. Seubert f replied to the criticisms of Dittmar and M‘ Arthur, claiming that the close agreement of the values calculated from the different ratios given by his analyses showed that the impurities mentioned by these authors could not have been present in the material he worked with. In view of the values shown above, this claim should be more or less modified. The different investigations mentioned above give us the following values for the atomic weight of platinum. From the work of Berzelius ..... . 195*90 Andrews ..... . 197*88 Seubert ..... . 195*22 Halberstadt .... . 195*05 Dittmar and M‘ Arthur . 195*50 When selecting a method for the determination of the atomic weight of platinum, one naturally turns to the analysis of the double salts of pottasium chloride, or ammonium chloride and platinic chloride. These salts, when pure, are among the most stable salts of platinum. From their analysis they allow of several ratios being formed, from which not only can the atomic weight of platinum be calculated, but one can at the same time gain a most complete knowledge of the purity of the salts. In addition to these points, the determination of chlorine as silver chloride is among the t Ber. Deutsch. Chem. Gesell. , xxi. 2179 (1888). * Loc. cit. 725 1908-9.] The Atomic Weight of Platinum. most accurate of our analytical operations. While it would be very interesting and most instructive, if it were feasible, to determine the ratio of platinum to oxygen or to silver directly, a few analyses, by means of a reliable method, are of more value than any number carried out according to methods which have been insufficiently studied to reveal their possibly large constant errors. The present investigation covers a study of the potassium and ammonium salts of chloroplatinic acid, and the corresponding salts of bromoplatinic acid. The method of analysis necessitated the preparation of the pure salt, the determination of its weight in a perfectly dry condition, its reduction in a stream of hydrogen, with the absorption in water of the hydrochloric acid formed, and subsequently the weighing of the platinum residue, and the determination of the potassium chloride left behind, and the hydrochloric acid formed, by precipitating and weighing the chlorine of each separately as silver chloride. Preparation of Pure Materials. Potassium Chloride. — Chemically pure potassium chloride was twice precipitated from an almost saturated solution with gaseous hydrogen chloride, prepared by boiling a solution of pure hydrochloric acid. After each of these precipitations, the salt was washed and dried in a centrifugal apparatus, as recommended by Richards.*' This treatment was usually resorted to for the purpose of removing the mother liquor from a mass of crystals. The value of the process of crystallisation as a means of purifying a substance is greatly enhanced by removing the mother liquor from the crystals as completely as possible. Consequently this point received a great deal of attention throughout this work. The potassium chloride from the second precipitation was once recrystallised from water. The above operations were carried out in platinum vessels. The product thus obtained was used in precipitating some platinum as potassium chloro- platinate. This platinum was very pure, having been through all but the last stage of its purification. The platinum salt was now reduced in pure hydrogen gas at a low temperature. The potassium chloride set free was dissolved in water, and twice precipitated in platinum vessels by means of gaseous hydrogen chloride. This product was employed in the preparation of the potassium chloroplatinate used in the analyses described below. Ammonium Chloride. — The method of preparing pure ammonium chloride was analogous to that used in the case of the potassium salt. After * Richards, Jour. Am. Chem. Soc., xxvii. 104 (1905). 726 Proceedings of the Royal Society of Edinburgh. [Sess. precipitating from the acid solution and recrystallising from water, the salt was added to pure chloroplatinic acid solution. The chloroplatinate formed was reduced in pure hydrogen gas, and the ammonium chloride resulting dissolved in water. After precipitating the salt twice with hydrogen chloride gas and throughly washing in each case, it was ready to be used in the preparation of the pure ammonium chloroplatinate. It should be noted that the precipitation of these chlorides from a strongly acid solution should remove all foreign acid radicles, while other metallic radicles would be most effectually removed by the precipitation as the chloroplatinate. Potassium Bromide. — In preparing pure potassium bromide the method adopted by Richards and Mueller * was used. A specimen of potassium oxalate, already very pure, was four times recrystallised in platinum, the crystals being well washed each time. This oxalate was then converted into bromide by treating it with pure bromide in a quartz dish. After recrystallising the bromide from an acid solution, it was used in the preparation of the pure potassium bromoplatinate. Ammonium Bromide. — This salt was prepared by distilling some pure hydrobromic acid directly into redistilled ammonium hydroxide contained in a platinum vessel. Bromine and Hydrobromic Acid. — Chemically pure bromine of com- merce was redistilled three times, rejecting in each case the first and last portions of the distillate. This treatment would remove all but a trace of chlorine present. The bromine was now dissolved in pure calcium bromide and distilled from this solution. The solution and distillation from a fresh portion of the calcium bromide was carried out a second time. The hydro- bromic acid was prepared from this pure bromine by means of thoroughly washed red phosphorus. The solution of hydrobromic acid formed was then redistilled twice, after adding an excess of pure bromine, rejecting each time the first and last parts of the distillate. Every care was taken to exclude chlorine or hydrochloric acid from the laboratory where the bromine and hydrobromic acid were being prepared. Hydrochloric and Nitric Acids. — These acids were prepared from the chemically pure acids by redistilling from platinum and condensing the vapours in platinum. The first and last portions of the distillate were always rejected. The absence of chlorine from the nitric acid was further assured by testing a portion of each sample in the nephelometer *j* before using it. * Loc. cit ., p. 29. t Richards, Proc. Am. Acad., xxx. 385 (1894) ; Richards and Wells, Am. Ghem. Jour. xxx i. 235 (1904). 727 1908-9. J The Atomic Weight of Platinum. Chloroplatinic Acid. — Four samples of chloroplatinic acid were prepared. The material for three of these was platinum scrap. The scrap was first boiled with hydrochloric and nitric acids separately to remove surface impurities. It was then dissolved in aqua regia. The nitric acid was then almost, if not entirely, removed by repeated evaporation with hydrochloric acid. The solution was now diluted to a concentration corresponding to a 5 per cent, solution of platinum. One-third of this solution was set aside for separate treatment. In order to remove the iridium and any iron present, the remaining two-thirds were treated with enough of a dilute solution of pure ammonium chloride to precipitate about 98 per cent, of the platinum. The precipitate was thoroughly washed and dried. It was then reduced in a current of pure hydrogen. The ammonium chloride set free was washed out of the platinum black, and the latter was boiled with successive portions of concentrated hydrochloride acid to dissolve out a possible trace of iron. The platinum was now ready to be again dissolved in aqua regia and subjected to the above treatment a second time. It was found very difficult to remove the last traces of iron from the platinum. Treating it repeatedly with concentrated hydrochloric acid failed to do it, but after a number of precipitations as ammonium chloro- platinate, followed each time with the boiling in the presence of hydro- chloric acid, no iron could be found in the platinum. The elimination of the iridium could be plainly followed from the colour of the residue left upon evaporating the mother liquor from a pre- cipitation. The characteristic dark red colour of the iridium compounds is in evidence when only a very small amount of iridium is present. All indications of iridium had vanished after the above operations had been repeated three times. After the platinum ammonium salt had been precipitated and reduced in hydrogen for the fifth time, a portion of the platinum was set aside, which eventually was used to prepare sample I. of the potassium chloroplatinate. The remainder was redissolved and the above procedure of precipitation and reduction repeated four times more. This treatment gave the platinum which was used to prepare sample II. of the potassium chloroplatinate. The portion of chloroplatinic acid set aside at the beginning of the purification process was treated for the removal of other platinum metals, as well as any iron, according to the method of Schneider and Seubert.* The precipitations were carried out in very dilute solutions in the presence of some alcohol, the more effectually to remove any gold that might be present. The reductions of the platinum salt were effected in the case * Graham Otto’s Lehrbuch, 5th eel., iv. 1153. 728 Proceedings of the Royal Society of Edinburgh. [Sess. of this portion with ammonium formate, prepared by passing ammonia vapour, from a platinum still and condenser, directly into freshly distilled formic acid. This portion of platinum was subjected to five precipitations and reductions. It was then used in the preparation of the third sample of potassium chloroplatinate. The fourth sample of chloroplatinic acid was prepared from 150 grams of osmo-iridium ore supplied by Baker and Company of Newark, N.J. This ore contained about 35 per cent, of platinum. It was first boiled with concentrated hydrochloric acid to dissolve a small per cent, of iron present. This treatment was repeated several times. The ore was then well washed, and afterward boiled with successive portions of nitric acid. To dissolve out the free platinum, the ore was boiled with successive portions of aqua regia until nothing more appeared to go into solution. These several platinum solutions were now combined and evaporated with a large excess of hydrochloric acid. After the nitric acid had been expelled in this way, the solution was diluted to correspond to a 5 per cent, solution of platinum, a considerable amount of alcohol was added, and the platinum then precipitated with ammonium chloride. The mother liquor from this precipitation showed, upon evaporation, that an appreciable amount of iridium had been dissolved along with the platinum. The precipitate of ammonium chloroplatinate, after being throughly washed, was reduced with ammonium formate. The finely divided platinum was now boiled with nitric and hydrochloric acid separately to remove any metal soluble in these acids. It was found practically impossible to remove all the iron in this way, as, after being treated with eight different portions of 50 c.c. each of hydrochloric acid, the boiling being continued for two hours in each case, iron was still found in the last portion. The platinum was now dissolved in aqua regia and subjected to the treatment recommended by Schneider and Seubert,* precipitated, and again reduced. The treatment with nitric and hydrochloride acid was now repeated. This time only a trace of iron was found. The process of precipitation and reduction was repeated until the platinum had been precipitated four times. The salt was then reduced and dissolved as usual in aqua regia, and this solution was electrolysed, at as a low a voltage as possible, until about 90 per cent, of the platinum had been deposited. The platinum anode used here was thickly coated with electrolytic platinum before being used. As, according to Classen, j* the iridium requires a much higher voltage for its * Loc. cit. t Ber. Deutsch. Ghem. Gesell., xvii. 2467 (1884). 72 9 1908-9.] The Atomic Weight of Platinum. deposition than the platinum, this treatment should free the platinum most effectually from iridium. That the pure metal might not again he con- taminated with iridium or iron from the electrode only about 75 per cent, of the deposit was dissolved off. This was again precipitated as the ammonium double salt, and after being reduced, was ready to be used in preparing sample IV. of potassium chloroplatinate. Professor F. A. Saunders has very kindly photographed the arc spectrum from the orange to the end of the ultra-violet of a portion of sample No. I. of the platinum, using a concave grating, and finds no indication of the presence of iridium, osmium, palladium, Rhodium, Ruthenium, or iron in the platinum. The strongest lines of iridium are entirely absent, as indicated in a portion of the spectrum, enlarged and reproduced below. If the iridium has been so effectually removed from this sample of platinum, we are surety warranted in assuming the other samples which were subjected to even more severe treatment for purposes of purification to be equally pure. I wish here to record my appreciation of the kindness of Professor Saunders in making this test. Small part of platinum arc spectrum (in ultra-violet) photographed with concave grating. Enlarged x 2. Place marked : strong Ir line might occur ; | Pd line ditto, but does not. It has been shown by Precht,* that it is almost impossible to remove the last trace of nitric acid from a solution of chloroplatinic acid prepared by dissolving platinum in aqua regia. This point has also been emphasised by Noyes and Weber,]* and, according to the latter’s statement, they never succeeded in preparing perfectly pure potassium chloroplatinate from acid made by this method. It was thought safer, in the present instance, to avoid the use of nitric acid altogether in the preparation of the chloroplatinic acid, from which the potassium chloroplatinate for the analyses was to be prepared. In order to dissolve the platinum, recourse was had to the electrolytic method described by Weber. J According to this method, the platinum to be dissolved rests upon the platinum anode B in the tube A, fig. 1 ; the anode being in * Loc. cit. t Jour. Am. Ghem. Soc ., xxx. 13 (1908). | Jour. Am. Ghem. Soc., xxx. 29 (1908). 730 Proceedings of the Royal Society of Edinburgh. [Sess. turn supported by glass beads which till the lower part of the tube. The cathode is of platinum, and is placed inside the porous cell D. The tube is now filled to the point e with concentrated hydrochloric acid. Upon passing a current of, say, 8 amperes, through the cell from the regular 110 volt circuit, the platinum goes rapidly into solution, and the chloroplatinic acid formed can be siphoned off at F. Fig. 2. This apparatus was somewhat modified for the present purpose. In the first place, as it was desirable to have as small a surface of glass as possible in contact with the solution, the glass beads as a support for the anode were not used. Instead of these, several depressions were made in the tube at the points e e, as shown in fig. 2, and the anode supported by these. Secondly, it was found impossible to obtain a porous cup from which some impurities 731 1908-9.] The Atomic Weight of Platinum. would not be dissolved by the concentrated hydrochloric acid. The cleanest appearing ones to which we had access, and which appeared perfectly white, after being boiled with hydrochloric acid for weeks, still gave off traces of iron to a fresh portion of concentrated acid. The porous cup diaphragm was therefore discarded. In the next place, as it seemed possible that traces of the platinum anode might be dissolved, along with the finely divided platinum in contact with it, and as this might result in the contamination of the solution, a thick coating of platinum was deposited electrolytically upon the anode, from a solution of pure platinum. This apparatus was steamed out for several hours before it was used. In order to still further diminish the action of the solution upon the glass, the tube, while being used, was immersed in a bath of cold water. The current used was a weak one, never more than 4 amperes. Potassium Chloroplatinate.— -After each portion of platinum had been separately dissolved in this apparatus, by means of the electric current, chlorine generated from pure hydrochloric acid and potassium perman- ganate was passed through each solution. If a considerable excess of hydrochloric acid was not already present, more was added in order to neutralise any tendency to hydrolyse on the part of the platinic chloride. The several solutions were now diluted to a concentration corresponding to about 1J per cent, of platinum, and each was precipitated separately by adding it slowly, with constant agitation, to a dilute solution of pure potassium chloride. The precipitates were thoroughly washed with water and alcohol, and after drying as completely as possible, were kept in porcelain over calcium chloride. In this manner samples of potassium chloroplatinate Nos. I., II., III., and IV. were prepared from the above samples of platinum. Ammonium Chloroplatinate. — For the preparation of the ammonium double salt, the platinum resulting from the analysis of samples I. and III. of the potassium salt was combined and dissolved in the manner described above ; the platinum from sample IV. was likewise dissolved separately, and the platinum in each precipitated in exactly the same way as in the case of the potassium salt. These precipitates gave the samples of ammonium chloroplatinate I. and II. Potassium and Ammonium Bromoplatinates. — The platinum which remained from the analysis of the chloroplatinates was used in preparing the corresponding salts of bromoplatinic acid. It was dissolved in pure hydrobromic acid, by aid of the electric current, in the apparatus described above. The potassium and ammonium bromide solutions used in pre- 732 Proceedings of the Royal Society of Edinburgh. [Sess. cipitating the platinum were both very dilute, and the platinum solution was added as before to the bromide solution slowly and with constant stirring. The several solutions from which the above platinates were precipitated were so dilute, and precipitation took place so slowly, that it was thought to be impossible for an appreciable amount of potassium chloride or bromide, or the corresponding ammonium salt, to be occluded by the precipitate. That considerable amounts of these are carried down, as contended by Dittmar and McArthur,* when the platinum salts are formed in solutions at all concentrated, has been found for a number of cases. When carrying out some preliminary work on these salts, it was found that as much as 05 per cent, in excess of the potassium salt may be present in a precipitate formed in a 25 per cent, solution of potassium bromide. Silver. — The mode of preparing pure silver followed closely the admirable methods developed by Professor Richards, which have proved so satisfactory. Briefly stated, C.P. silver nitrate was dissolved in pure water and precipitated, from a very dilute solution, with pure hydro- chloric acid. This precipitate was well washed and reduced, in a strongly alkaline solution, with invert sugar. The sugar used here had been dissolved, filtered, and recrystallised in the laboratory. The caustic soda used had been electrolysed, in order to remove a possible trace of iron. The reduced silver, after a thorough washing, was dissolved in pure nitric acid, and this solution was divided into three portions ; these portions giving eventually three samples of silver. The first portion was again precipitated with hydrochloric acid. Reduction by means of invert sugar followed, and the reduced metal, after washing, was fused on pure lime before the blowpipe. This lime was prepared from calcium nitrate, which had been recrystallised several times, and then precipitated as carbonate with pure ammonium carbonate. The lumps of silver obtained from the fusion were now electrolysed, with a very weak current, in a solution of nitrate prepared from one of these pellets of silver and pure nitric acid. The crystals of silver deposited were well washed, and were then fused on a boat of pure lime, in an atmosphere of hydrogen, at a pressure of 40 mm. The second portion of silver nitrate solution was recrystallised twice from platinum. It was then reduced with ammonium formate prepared by passing ammonia vapor, from platinum still and condenser, directly into freshly distilled formic acid. The reduced metal, after being washed, was fused on lime and electrolysed as in the case of the first portion ; this was * Loc. cit. 733 1908-9.] The Atomic Weight of Platinum. followed also by fusion in hydrogen on a lime boat under a pressure of 40 mm. The treatment of the third portion of silver nitrate solution was the same in principle as in the case of the second sample, but here the silver solutions were not allowed at any time to come in contact with glass vessels. The reductions were carried out in a silver dish, while the electrolysis was effected in a quartz basin. The final fusion took place under the same conditions as in the above cases. The pellets of silver resulting from the fusions in hydrogen were now scrubbed with sand and cut into pieces of the proper size with a clean piece of hard steel. They were then warmed with diluted nitric acid until well etched. After washing and drying, they were kept in a desiccator until used. The above preparations gave samples of silver Nos. I., II., and III. The arc spectrum, from the orange to the ultra-violet, of a portion of sample II. of the silver, has also been photographed by Professor Saunders, under very favourable conditions, using the concave grating. The results indicate the entire absence of copper and iron from this sample of silver. Considerable attention was paid to the water used in this research. It was twice distilled, the second time in the presence of a trace only of sodium hydroxide and potassium permanganate. It was condensed in block tin, received and stored in Jena glass stoppered bottles. Every care was taken to exclude dust, and it was always used soon after distilling. To make certain of the absence of chlorine ions, every sample was tested in the nephelometer before using. The balance used was made by Christian Becker of New York. It was procured especially for this work, and was not used for any other purpose. It is a gold-plated short-arm balance sensitive to 002 mg. with a load of 40 gms. This was looked upon as being quite accurate enough for the purpose in hand. It cannot be too strongly emphasised that even in atomic weight work the errors of a chemical nature are likely to far exceed the errors made in weighing. There is little to be gained in weighing to a few thousandths of a mg., when there may be several hundredths of a mg. of unknown impurity in the portion of substance weighed. The weights used were new ones of the Sartorius make, gold-plated. They were standardised according to the method suggested by Richards,* and have not been used in any other work. * Jour. Am,. Ghem,. Soc ., xxii. 144 (1900). 734 Proceedings of the Royal Society of Edinburgh. [Sess. The Analysts of Potassium Chloroplatinate. From a complete analysis of potassium chloroplatinate, one should be able to gain considerable information concerning the purity of the com- pound. If the salt at the beginning can be weighed free from water, and if, after being reduced in hydrogen, the platinum left behind can be weighed and the potassium chloride and the chlorine set free estimated separately, we can from the relations between these constituents tell which, if any, has been present in excess, or has been replaced by some impurity. Only with a pure salt, having the exact composition represented by the formula, will the several ratios found between these constituents give the same value for the atomic weight. Unfortunately, we are here confronted at once with the knowledge that as the salt has been precipitated from a water solution, it must inevitably have enclosed within the crystals some of the mother liquor, and complete expulsion of this water will only be brought about, as pointed out by Richards,* by the entire disintegration of the crystal. It remains to be considered whether or not the salt in question can be freed, before weighing, from all but an inappreciable quantity of moisture. In the first place, we are dealing here with a salt which can be obtained, as a precipitate, in an exceedingly fine state of division. As it is very soft, it can be ground to a still finer powder without danger of contaminating it with pieces of the pestle or mortar. After such treatment, it would seem as if all but the most minute of the crystal cells must be broken. Further, as pointed out below, we are able to heat the salt in this fine state of division to a temperature but little short of 400° C. and bottle it in a current of pure dry air. It does not seem as if, under these conditions, a very large amount of moisture can be left in the salt. Nevertheless, although the results of the weighings of the salt are given, and are useful as a check upon its purity, the atomic weights calculated from ratios in which the weight of original salt appears are not used in determining the final value. The analytical procedure is now about as follows : — Two weighing- bottles, not differing in weight by more than two or three tenths of a gram, and two porcelain boats fulfilling the same condition, are selected : the one bottle to hold the boat containing the salt to be weighed, the other bottle and boat to act as a tare ; thus doing away with the necessity of making buoyancy corrections, except for the salt weighed. We can also assume, as the bottles are made of the same kind of glass, that the moisture on the surface of one, when being weighed, is practically equal to the moisture on * Proc. Am. Phil. Soc xlii. 28 (1903). 735 1908-9.] The Atomic AVeight of Platinum. the surface of the other. After carefully drying and desiccating for a long time, the difference in weight between these two sets of apparatus is accurately determined. One boat is now filled with the salt to be analysed, and placed in the combustion tube of the Richards * bottling apparatus. The bottle and stopper belonging to this boat are also placed in position. A current of pure dry air (dried by passing over 18 inches of phosphorous pentoxide) is passed through the apparatus, and the combustion tube, which passes through an asbestos oven, is carefully heated. The apparatus through which the air passes, while being purified and dried, is entirely of glass, the pure air not coming in contact with any rubber whatever. The temperature of the asbestos oven is now gradually raised to 380°- 400°. By passing the escaping air through a solution of silver nitrate, and then examining this solution in the nephelometer, it was shown that a little hydrochloric acid was given off between 100° and 150°. All the hydrochloric acid seemed to be expelled between these temperatures. The observation of Noyes and Weber, f in regard to the stability of pure potassium chloroplatinate at high temperatures was confirmed, as it was found that the salt could be heated to 400° in dry air without any de- composition taking place. The salt was kept at a temperature between 380° and 400 for about two hours. The boat and contents were then allowed to cool, and with the stream of air still passing through the apparatus, they were bottled and transferred to the desiccator. After desiccating for two hours the salt is weighed in its bottle and is now ready to be reduced. In order to make sure that nothing more could be expelled from the salt by further heating, it was upon several occasions reheated, bottled, desiccated and weighed as before ; but no change in weight was found to have taken place. The results from one such experiment will suffice. Weight of salt after first heating . . . 2 20469 „ after heating again for three hours . 2 '20468 The silver nitrate solution, through which the escaping air was bubbling, showed no sign of the presence of any chlorine ions. It is evident that nothing appreciable is volatilised from the salt, while it is being heated at this high temperature. The weighed salt is now placed in the combustion tube of the reducing apparatus and carefully heated in a stream of pure hydrogen. The hydrogen for this purpose was prepared by electrolysing a solution of * Proc. Am. Acad xxxii. 55 (1896). t Loc. cit. 736 Proceedings of the Royal Society of Edinburgh. [Sess. barium hydroxide. The gas first passed over heated platinum sponge, where any oxygen would be burned. It was then passed through an 18-inch tube, closely packed with fused potassium hydroxide, then through a tube filled with pure phosphorous pentoxide to the combustion tube. As the apparatus was of glass throughout, the hydrogen did not come in contact anywhere with rubber. The hydrochloric acid formed upon reduc- ing the salt passes first into the tube A, fig. 3, which contains about J a c.c. of water. The purpose of the water here is to absorb any potassium chloride which might be volatilised during the reduction. From here the gas passes to two bottles placed in series, containing water, where the hydrochloric acid is completely absorbed. The temperature at which the reduction takes place in hydrogen is comparatively low for the more exposed portions of salt. It always required a much higher temperature, however, to carry the reaction to •-A Fig. 3. completion. This temperature was about 350 for the potassium salt. Even at this temperature a very little potassium chloride was usually volatilised and condensed on the upper parts of the tube. It was never necessary to continue the heating long enough to change any of the platinum black to spongy platinum. It was of course much more easily washed in the more porous form of platinum black than in the form of sponge. When the reduction of the salt appeared to be complete, the mass of platinum black and potassium chloride was allowed to cool with the stream of hydrogen still passing through the apparatus. While cooling, the platinum will of course absorb a great deal of the hydrogen. After it had cooled, it was reheated until a great deal of this hydrogen had been expelled. This treatment ensures complete reduction of the salt, as it brings the hydrogen into intimate contact with the whole mass, and at the same time serves as it were to wash the platinum black free from any gaseous hydrogen chloride, that might otherwise be retained even at a high temperature. After this treatment has ensured the complete reduction of the chloro- 737 1908-9.] The Atomic Weight of Platinum. platinate, and the removal of all hydrogen chloride, the water in the bulb A is carefully evaporated into the absorbers, and any residue left is cautiously heated. The platinum black has now to be washed free from potassium chloride, and this proved to be one of the most difficult parts of the whole analysis. The platinum and chloride were washed into a platinum dish, and here heated to boiling with successive portions of distilled water. As already pointed out by Seubert,* if the platinum has been reduced at the lowest possible temperature, it will be in so fine a condition as scarcely to be retained by the filter ; on the other hand we find that when heated to such a temperature that it clings together and filters readily, it parts with the potassium chloride so reluctantly that a great many treatments with the boiling water are necessary. If, again, this treatment is continued too long, the platinum becomes more or less colloidal and will not be retained by the filter. It was found that the presence of a little potassium nitrate in the wash water greatly retarded this formation of colloidal platinum, and permitted the boiling with water to be carried on to a much greater extent. When the platinum has been washed free from potassium chloride in this way, it is put in a tared platinum boat, and this is placed in the combustion tube of the apparatus in which it had been reduced. There it is heated in a stream of hydrogen to a red heat, which converts it entirely into the form of spongy platinum. After cooling in the hydrogen it is desiccated and weighed. This ignition and conversion of the platinum black into sponge in the atmosphere of hydrogen was thought to be necessary, in order to make certain that no oxidation of the platinum in this finely divided state took place. At higher temperatures, it seems likely that platinum even in its most coherent form is slowly oxidised, and in a finely divided condition this would probably take place at a much lower temperature. A second weighing of the platinum was made after it had been heated in the air, to the highest heat of the bunsen burner. These two weighings always gave identical results, as the following data will show : — - No. 1. After heating in hydrogen 1st weighing add to tare 0’85094 „ „ in air to approximately 950 C. „ 0’85092 No. 2. „ „ in hydrogen 1st weighing „ 0'61483 „ „ in air to 950° C. „ „ 0’61483 From an examination of the work already done on the occlusion of gases by the different forms of platinum, it appears by no means certain that an * Loc. cit. VOL. XXIX. 47 738 Proceedings of the Royal Society of Edinburgh. [Sess. amount of gas, appreciable in atomic weight work, might not be absorbed by platinum sponge cooled at atmosjDheric pressure. A great many experimenters have investigated this phenomenon. The work of Graham,* Smith, -j* Gladstone and Tribe, J Berthelot, § Traube, || Berliner, IT Neumann and Streintz,** Wilmf-j* and Mond, Ramsay and Shields JJ should be cited. The latter authors, Mond, Ramsay and Shields, concluded from a very careful piece of work, that platinum black upon being heated to a red heat in a vacuum gave up all of the occluded gases. In order to ascertain whether it would be necessary to heat and weigh the platinum sponge in a vacuum, the following experiments were carried out. A few grams of platinum sponge were placed in a platinum boat and carefully weighed. The boat and sponge were then placed in a hard glass tube, and this connected by means of a stopper and a mercury seal with a Topler pump. The tube was then evacuated to a few tenths of a mm. pressure, and the tube containing the boat and sponge heated until the glass began to soften. The pump was again evacuated while the tube was being heated, and all the gas which could be driven off was pumped away. The boat and sponge were now allowed to cool, and the tube sealed off at a point which had been drawn out. After desiccating a long while, the tube containing the boat and sponge was weighed, using as tare a tube of the same kind of glass, and of the same diameter, as the tube which had been heated, and sealed off under the same pressure. The first tube was now broken under conditions which ensured no loss of glass, at a scratch made on it before heating ; the platinum boat and sponge were withdrawn and the glass weighed. As the tube used as tare had been broken for this weighing, only a small buoyancy correction has to be applied if the two tubes have been carefully chosen. We have now all the data necessary for finding the difference in weight of the platinum when heated, cooled and weighed in air, and when the same operations are carried out in a vacuum. Several such experiments were carried out, and they all gave negative results, showing that the difference in weight of the platinum under these different conditions was not larger than the experimental error of the determination. * Proc. Roy. Soc., xvi. 422 (1868). t Ghem. News, xxxi. 55 (1875). j. Jour. Ghem. Soc., xxxv. 172 (1879). § G . R., xciv. 1377 (1882). || Ber. Deutscli. Ghem. Gesell., xv. 2854 (1882). 1 Ann. der. Phys. (Pogg.), [2] xxxiii. 289 (1888). ** Monatsh. Ghem., xii. 642 (1891). tt Jour. Russ. Ghem. Soc., xxiv. I. 241 (1892). f l Proc. Roy. Soc., lviii. 242 (1895). 739 1908-9.] The Atomic Weight of Platinum. In one case it was found that — Platinum boat and sponge cooled in air weighed 4*20520 „ „ „ and weighed in vacuum 4*20516 As we wish to know the amount of silver required for the precipitation, as well as the amount of silver chloride formed, two portions of silver are carefully weighed out, one for the precipitation of the chlorine in the hydrochloric acid, the other for the precipitation of the chlorine in the potassium chloride. A slight excess of silver, amounting to two or three milligrams, is used in each case. The silver is now dissolved in nitric acid, taking every care to prevent any of the silver being carried away mechani- cally with the escaping vapours. All the solutions are diluted to a low concentration before mixing, and the silver nitrate is added very slowly and with constant agitation to the chloride solutions. When precipitation is complete, the silver chloride is shaken up vigorously with the solution for perhaps half an hour, and then allowed to stand for at least ten hours before filtering. Actinic light is of course excluded entirely from the silver chloride. The solutions were filtered on platinum Gooch crucibles, using a good grade of Italian asbestos as a mat. Needless to say that the asbestos had been boiled in nitric and hydrochloric acids, and had been thoroughly washed. After washing, the precipitates were dried first for one hour at 100°, and then for three hours at 150° in an electric drying oven. A platinum crucible, almost equal in weight to the crucibles used in filter- ing, and containing about the same amount of asbestos as one employs for a filtering mat, was always used as a tare when weighing the Gooch crucibles. The moisture which, as shown by Richards and Wells,* is always retained by silver chloride, even when dried at 150°, was determined by placing the pellet of silver chloride, after it had been weighed in the Gooch crucible, without any adhering asbestos, in a tared porcelain crucible ; weighing this combination, then heating until the mass was fused and weighing again. The loss in weight is applied as a correction to the weight of silver chloride previously determined. The small shreds of asbestos which were carried away from the mat while filtering, were collected on a small ashless filter and ignited ; and the weight of these was applied as another correction to the weight of silver chloride. Obviously this is opposite in sign to the previous correction. Unfortunately silver chloride is appreciably soluble in water, and therefore the amount which has dissolved in the water used in washing * Jour. Am. Chew,. Soc., xxvii. 475 (1905). 740 Proceedings of the Royal Society of Edinburgh. [Sess. the precipitate must be determined. The silver chloride in the wash water, as well as the excess of silver over that required for the precipitation, was estimated by means of the nephelometer. The instrument used in this research was supplied by Kny & Scherrer (and proved very satisfactory). Particular attention was paid to having the standard solution correspond as nearly as possible, in every particular, to the solution that was being analysed, and sufficient time was always allowed to elapse before the opalescence of the two solutions was finally compared. In order to reduce the weights of the different substances to the vacuum standard, the specific gravities must be known. For silver, silver chloride and bromide, these constants have been determined with sufficient accuracy. The specific gravity of platinum sponge was redetermined, and a slightly lower value than those already recorded was obtained. In the case of the platinum salts, new measurements were made using toluol as the liquid to be displaced. Kahlbaum’s toluol was dried over sodium and redistilled. 2T5570 grams of this liquid at 24° C. were found to occupy the same volume as 25’0120 grams of water at 4° C. This gives a specific gravity of (18618 for the toluol at 24° C. referred to water at 4° C. It was shown by digesting a portion of each salt with the toluol, and evaporating some of the liquid in a platinum dish, that the salts were not at all soluble in the toluol. The values found are tabulated below, together with the correction to be applied for all the substances weighed. In the case of the platinum salts, each result is the mean of two determinations. Table I. — Specific Gravities. Salt. Weight of Salt. Weight of Toluol displaced. Sp. Gr. of Salt. Correction to be applied to 1 gram, of Sub. K2PtCl6 . . . 1-6712 0-4116 3-499 + 0-00020 (NH4)2PtCl6 . . 1-4563 0-4137 3-034 + 0-00026 K2PtBrfi 1-4787 0-2736 4-658 + 0-00012 (NH4)2PtBr6 1-3210 0-2669 4-265 + 0-00015 Pt 21-16 - 0-00009 ■Ag .... 10-49* - 0*00003 AgCl .... 5‘55t + 0-00007 AgBr .... 6-473J + 0-00004 The results from the analysis of potassium chloroplatinate, together with the ratios obtained from these data, are set forth in the tables below. These are all the analyses made of the potassium salt, after the preliminary * Richards and Wells, Jour. Am. Chem. Soc., xxvii. 459 (1905). t Richards and Wells, ibid. t Baxter and Hines, Amer. Chem. Jour., xxxi. 220 (1904). 741 1908-9.] The Atomic Weight of Platinum. work was finished. Parts of experiments Nos. 5 and 7 are wanting, as these were lost by accident. The atomic weight values for chlorine, silver and potassium used in these calculations were those given above. Table II. — Results of the Analysis of Potassium Chloroplatinate. No. of Experi- ment. Prepar K2PtCl6. ation. Silver. Weight of K2PtCl6 in vacuum. Weight of Pt in vacuum. Weight of 4AgCl in vacuum. Weight of 2AgCl in vacuum . Weight of 4Ag in vacuum. Weight of 2Ag in vacuum. 1 I. II. 1-43605 0-57667 1-69324 0-84690 1-27475 0-63722 2 5) I. 1-69914 0-68226 2-00402 1-00172 1-50834 0-75401 3 55 55 2-11830 0-85062 2-49836 1-24894 1-88046 0-93993 4 II. 55 2-49734 1-00287 2-94462 1-47249 2-21626 1-10841 5 )) II. • • • 0-86012 • • • 1-26271 ... 0-95030 6 55 55 2-20619 0-88588 2-60135 1-30106 1-95842 0-97909 7 III. III. 1-70600 0-68486 2-01201 1-00580 ... ... 8 55 55 1 -74397 0-70018 2-05691 1-02820 1-54816 0-77402 9 55 II. 2-06137 0-82789 2-43096 1-21526 1-82982 0-91481 10 > HH 55 2-34095 0-93991 2-76105 1-38034 2-07759 1-03868 11 55 55 1-54787 0-62150 1-82560 0-91266 1-37391 0-68702 12 55 III. 1-95944 0-78694 2-31070 1-15522 1-73902 0-86967 18 55 55 2-28366 0-91697 2-69304 1-34636 2-02640 1-01338 24 55 II. 2-27441 0-91320 2-68244 1-34093 2-01870 1-00924 Table III. — Ratios obtained from the Analysis of Potassium Chloroplatinate. Comparison of Platinum with Potassium Chloroplatinate and with Silver Chloride. Experiment. q-H O aiOu O Pm O i— H Atomic Weight of Platinum. Parts of Pt = 100-00 parts of . 4AgCl. Atomic Weight of Platinum. Parts of Pt = 100-00 parts of 2AgCl. Atomic Weight of Platinum. pi o P-i ^ . to ; tad P^O -e o d i— i Pn II Atomic Weight of Platinum. 3 ° TS go PH IS . C+H O o o <1 OQ O ^ 72 2 a <— Ph || Atomic Weight of Platinum. 1 67-103 195-25 34-057 195-27 68-092 195-20 84-811 195-29 169-57 195-13 2 67-094 195-22 34-045 195-19 68-109 195-25 84-787 195-15 169-62 195-29 3 67T01 195-24 34-047 195-21 68-107 195-25 84-788 195T6 169-61 195-25 4 67-105 195-26 34-058 195-27 68-107 195-24 84-810 195-29 169-60 195-16 5 67-118 195-29 0 • • ... 68T17 19527 ... ... 169-61 195-25 6 67-096 195-23 34-055 195-25 68-089 195-19 84-810 195-28 169-57 195T4 7 67-068 195-15 34-039 195T6 68-091 195*20 84-791 195-18 169-62 195-28 8 67-081 195T8 34-040 195-17 68-098 195-22 84-786 195-15 169-61 195-26 9 67-118 195-29 34-056 195-26 68-125 19529 84-797 195-21 169-62 195-29 10 67-087 195-20 34-042 195-18 68-093 195-20 84-785 195-14 169-59 195-21 11 67-090 195-21 34044 195-19 68-098 195-22 84-787 195T5 169-60 195-23 12 67T16 195-29 34-056 195-26 68T20 195-28 84-799 195-22 169-62 195-28 18 67-094 195-22 34-050 195-22 68-107 195-25 84-799 195-22 169-62 195-28 24 67-087 195-20 34-045 195-19 68-102 195-23 84-789 195T8 169-62 195-27 Average 67-097 195-23 34-049 195-21 68-104 195-24 84-795 195-20 169-61 195-24 742 Proceedings of the Royal Society of Edinburgh. [Sess. Table IV. — Ratios obtained from the Analysis of Potassium Chloroplatinate. Comparison of Silver with Platinum and with Potassium Chloroplatinate. Experi- ment. Parts of Pt = 100-00 parts of 4Ag. Atomic Weight of Pla- tinum. Parts of Pt = 100-00 parts of 2Ag. Atomic Weight of Pla- tinum. Parts of K„PtCL = 100-00 parts of 4Ag. Atomic Weight of Pla- tinum. Parts of KoPtCL = 100-00 parts of 2Ag. Atomic Weight of Pla- tinum. 1 45-238 195-21 90-498 195-25 112'65 195T5 225-36 195-27 2 45-233 195-19 90-484 195-23 112-65 195T4 225-35 195-24 3 45-235 195-20 90-498 195-26 112-65 195-13 225-37 195-28 4 45-251 195-27 90-478 195-22 112-68 195-28 225-31 195-16 5 ... ... 90-510 195-29 ... ... 225-36 195*27 6 45-234 195-20 90-480 195-22 112-65 195-15 225-33 195-20 8 45-227 195-16 90-460 195*18 112-65 195-13 225-31 195-17 9 45-244 195-24 90-499 195-26 112-65 195T6 225-33 195-21 10 45-240 195-22 90-488 195-24 112-68 195-19 225-37 195-29 11 45-236 195-20 90-463 195-18 112-66 195-19 225-30 195-14 12 45-252 195-27 90-487 195-24 112-68 195-25 225-31 195-16 18 45-251 195-25 90-486 195-23 112-70 195-29 225-35 195-25 24 45-237 195-21 90-484 195-23 112-67 195-21 225-36 195-26 Average 45-240 195-22 90-486 195*23 112-66 195-19 225-34 195-22 It appears from the foregoing results that the different methods adopted for the purification of the platinum salt have yielded pro- ducts of a considerable degree of purity, or else some particular im- purity is present to the same extent in each sample — a rather unlikely supposition. The different samples are probably not all equally pure, but the amount of impurity is not large enough to affect the value for the atomic weight beyond what may be regarded as the experimental error. This would seem to be true as well for the different preparations of silver. If we compare the values obtained for different ratios, it does not appear that any particular ratio gives consistently a higher or a lower value than any other, and this seems to be the best argument for the purity of the salt and the exactness of the analysis. If, for instance, potassium chloride was occluded in appreciable amounts during precipitation, the ratio 2AgCl : Pt would always give a low result, or if PtCl4 was occluded, a high result would be obtained. Again, if water still remained in the salt after heating to 380°, the ratio K2PtCl6 : Pt would give a low value for the atomic weight. If some of the chlorine had been replaced by hydroxyl, this ratio would give a high value while the ratio 4AgCl : Pt would be still higher. On the other hand, if, during the analysis, the potassium chloride had not all been washed out of the platinum, the ratio 2AgCl : Pt would 743 1908-9.] The Atomic Weight of Platinum. give a doubly high result, on account of a too small amount of silver chloride, as well as a too great weight for the platinum. If some of the potassium chloride had been driven, during the heating, into the hydro- chloric acid absorbers, the ratio 2AgCl : Pt would give a high value, while the value from the ratio 4AgCl : Pt would be correspondingly low. The Analysis of Ammonium Chloroplatinate and Bromoplatinate. The analysis of the ammonium salts was carried out in much the same way as in the case of the potassium salt, except that here the salt could not be heated to as high a temperature for the purpose of expelling the occluded water. The purest sample that I have been able to prepare would de- compose slightly above 185°. All the hydrochloric or hydrobromic acid seemed to be driven off below 150°. Nevertheless, as the salt might still contain an appreciable amount of water, the values for the atomic weight obtained from ratios in which the weight of original salt appears are not used in estimating the final mean value. On account of the low tempera- ture at which the ammonium chloride or bromide volatilises, and the consequent difficulty of preventing some of this salt from being carried over into the absorption bottles, with the halogen acid, it was thought safer to estimate the ammonium chloride or bromide, and the acid formed, together. The results given by these analyses, together with the ratios obtained, are set forth in the tables below. The atomic weight values for nitrogen, hydrogen, and bromine used in the calculations were those given above. Table V. — Results of the Analysis of Ammonium Chloroplatinate. Experi- ment. Preparation. Weight of (NH4)2PtCl6 in vacuum. Weight of Platinum in vacuum. Weight of 6AgCl in vacuum. Weight of 6Ag in vacuum. (NH4)2PtCl6. Silver. 13 I. II. 1 -75088 0-76976 3-39181 2-55181 14 55 55 1-36500 0-59997 2-64317 1-99014 15 II. I. P15060 0-50585 2-22810 1-67695 16 55 55 1-27475 0-56049 2-46936 1-85794 17 55 55 2-54096 1T1688 4-92047 3-70420 744 Proceedings of the Royal Society of Edinburgh. [Sess. Table VI. — Ratios obtained from the Analysis of Ammonium Chloroplatinate. Comparison of Platinum and Ammonium Chloroplatinate with Silver and Silver Chloride. Experiment. 60 O 7 w £5- «-t— i o o tfl CO -+n M ^H c3 c3 Ph Ph Atomic Weight of Platinum. Parts of Pt = 100-00 parts of 6AgCl. Atomic Weight of Platinum. o o z3 o Pa co yi i T}' # £ o w-o <1 a? o Ph Atomic Weight of Platinum. Parts of Pt = 100-00 parts of 6Ag. Atomic Weight of Platinum. CC 72 o Ph m "Pi ^ l-rT 03 M Ph bjo ZD «+H ^ ° 8 S ii Ph Atomic Weight of Platinum. 13 78-457 19522 22-695 195-18 5P621 195-12 30-165 195-25 68-613 195-29 14 78-424 195-14 22-699 195-22 51-643 195-31 30-147 195-14 68-588 195-13 15 78-457 195-28 22-703 195-25 51-640 195-29 30-165 195-25 68-613 195-29 16 78-471 195-26 22-698 195-21 51-623 195T4 30-167 195-27 68-611 195-28 17 78-428 195-15 22-699 195-22 51-641 195-29 30-152 195-17 68-597 195-19 Average 78-447 195-21 22-699 195-22 51-634 195-23 30-159 195-22 68-604 195-24 Table VII. — Results of the Analysis of Ammonium Bromoplatinate. Experi- ment. Sample of Silver used. Weight of (NH4)2PtBr6 in vacuum. Weight of Pt in vacuum. Weight of 6AgBr in vacuum. Weight of 6Ag in vacuum. 19 I. 1-83860 0-50497 2-91430 1 -67448 20 II. 2-31057 0-63437 3*66269 2T0379 21 55 2-33965 0-64272 3-70900 2-13049 Table VIII. — Ratios obtained from the Analysis of Ammonium Bromoplatinate. Comparison of Platinum and Ammonium Bromoplatinate with Silver and Silver Bromide. Experiment. O o O © PQ o pzt H -t- II ffi HH> JZ PH C7 CM e+H o o CO co H-H Sh b Cl Ph Oh Atomic Weight of Platinum. Parts of Pt= 100-00 parts of 6AgBr. Atomic Weight of Platinum. o ?H co 72 o Ph co ^ rrt a o§S cn 3 I' Ph Atomic Weight of Platinum. Parts of Pt- 100-00 parts of 6Ag. Atomic Weight of Platinum. o pp ‘p 72 o Ph co Z— “N t-* Jz; o=+-1 ^ o CQ 73 g PL, £ etical List of the Ordinary Fellows of the Society. 777 Fraser, Sir Thomas R., M.D., LL.D., F.R.C.P.E. , F.R.S., Professor of Materia Medica in the University of Edinburgh, Honorary Physician to the King in Scotland, 13 Drumsheugh Gardens * Fullarton, J. H., M.A., D.Sc., Brodick, Arran * Fulton, T. Wemyss, M.D. , Scientific Superintendent, Scottish Fishery Board, 417 Great Western Road, Aberdeen 200 * Galbraith , Alexander, Organiser of Continuation Classes in Science, Glasgow and W est of Scotland Technical College, 4 Maxwell Square, Polloksliields, Glasgow * Galt, Alexander, D.Sc., Keeper of the Technological Department, Royal Scottish Museum, Edinburgh Ganguli, Sanjiban, M.A., Principal, Maharaja’s College, and Director of Public Instruction, Jaipur State, Jaipur, India Gatehouse, T. E. , Assoc. Memb. Inst. C.E., Memb. Inst. M. E. , Memb. Inst. E.E.. Tulse Hill Lodge, 100 Tulse Hill, London Gayner, Charles, M.D., F.L.S. 205 Gayton, William, M.D., M.R.C.P.E., Ravensworth, Regent’s Park Road, Finchley, London, 1ST. * Geddes, Auckland C., M.D. , Professor of Anatomy, Royal College of Surgeons in Ireland, Dublin Geddes, Patrick, Professor of Botany in University College, Dundee, and Lecturer on Zoology, Ramsay Garden, University Hall, Edinburgh Geikie, Sir Archibald, K.C.B., D.C.L. Oxf., D.Sc. Camb. Dub., LL.D. St And., Glasg., Aberdeen, Edin., Ph.D. Upsala, Pres. R.S. , Pres. G.S., Foreign Member of the Reale Accad. Lincei, Rome, of the National Acad, of the United States, of the Academies of Stockholm, Christiania, Gottingen, Corresponding Member of the Institute of France and of the Academies of Berlin, Vienna, Munich, Turin, Belgium, Philadelphia, New York, &c., Shepherd’s Down, Haslemere, Surrey Geikie, James, LL.D., D.C.L., F.R.S., F.G.S., Professor of Geology in the University of Edinburgh, Kilmorie, Colinton Road 210 * Gentle, Wm,, B.Sc. , 2 Blackwood Crescent, Edinburgh Gibson, George Alexander, D.Sc., M.D., LL.D., F.R.C.P.E., 3 Drumsheugh Gardens * Gibson, George A., M.A., LL.D., Professor of Mathematics in the University of Glasgow, 8 Sandyford Place, Glasgow Gibson, John, Ph.D., Professor of Chemistry in the Heriot*Watt College, 16 W7ood hall Terrace, Juniper Green Gilchrist, Douglas A., B.Sc., Professor of Agriculture and Rural Economy, Armstrong College, Newcastle-upon-Tyne 215 Gilruth, George Ritchie, Surgeon, 53 Northumberland Street Gilruth, John Anderson, M.R.C.V.S. , Professor, University, Melbourne, Australia * Gladstone, Hugh Steuart, M.A., M.B.O.U., F.Z.S., Capenoch, Thornhill, Dumfriesshire * Glaister, John, M.D., F.F.P.S. Glasgow, D.P.H. Camb., Professor of Forensic Medicine in the University of Glasgow, 3 Newton Place, Glasgow Goodwillie, James, M.A., B.Sc., Liberton, Edinburgh 220 * Goodwin, Thomas S., M.B., C. M., F.C.S., 1 Heron Terrace, St Margaret’s, Middlesex Gordon-Munn, John Gordon, M.D., 34 Dover Street, London, W. * Graham, Richard D. , 1 1 Strathearn Road *Gray, Albert A., M.D., 14 Newton Terrace, Glasgow Gray, Andrew, M.A., LL.D., F.R.S., Professor of Natural Philosophy in the University of Glasgow 225 * Gray, James Gordon, B.Sc., Lecturer in Physics in the University of Glasgow, 11 The University, Glasgow * Greenfield, W. S., M.D., F.R.C.P.E., Professor of General Pathology in the University of Edinburgh, 7 Heriot Row Greenlees, Thomas Duncan, M.D. Edin., Amana, Tulse Hill, London * Gregory, John Walter, D.Sc., F.R.S.. Professor of Geology in the University of Glasgow, 4 Park Quadrant, Glasgow Greig, Edward David Wilson, M.D., B.Sc., Captain, H.M.’s Indian Medical Service, BycullaClub, Bombay, India 230 Greig, Robert Blyth, F.Z.S., Fordyce Lecturer in Agriculture, University of Aberdeen, Torloisk, Cults, Aberdeenshire * Guest, Edward Graham, M.A., B.Sc., 5 Church Hill * Gulliver, Gilbert Henry, B.Sc., A.M.I. x\lech. E., Lecturer in Experimental Engineering in the University of Edinburgh, 10 Stanley Street, Portobello Guppy. Henry Brougham, M.B. , Rosario, Salcombe, Devon 778 Date of Election, 1905 1899 1876 1896 1896 1888 1869 1877 1881 1880 1892 1893 1890 1900 1908 1890 1881 1908 1894 1902 1904 1885 1881 1896 1904 1897 1893 1899 1883 1886 1887 1887 1908 1882 1906 1904 1904 1875 1894 1889 1882 1901 breedings of the Royal Society of Edinburgh. * Halm, Jacob E., Ph.D. , Chief Assistant Astronomer, Royal Observatory, Cape- Town, Cape of Good Hope 235 Hamilton, Allan M'Lane, M.D. , 44 East Twenty-ninth Street, New York Hannay, J. Ballantyne, Cove Castle, Loch Long * Harris, David, Fellow of the Statistical Society, Lyncombe Rise, Prior Park Road,. Bath * Harris, David Fraser, B.Sc. (Lond.), M. D. , F.S.A. Scot., The Physiological Department, The University, Birmingham * Hart, D. Berry, M.D., F.R. C. P.E. , 5 Randolph Cliff 240 Hartley, Sir Charles A., K.C.M.G., Memb. Inst. C.E., 26 Pall Mall, London Hartley, W. N., D.Sc., F.R.S. , F.I.C., Prof, of Chemistry, Royal College of Science for Ireland, Dublin Harvie-Brown, J. A., of Quarter, F.Z.S., Dunipace House, Larbert, Stirlingshire Haycraft, J. Berry, M.D., D.Sc., Professor of Physiology in the University College of South Wales and Monmouthshire, Cardiff' * Heath, Thomas, B.A., Assistant Astronomer, Royal Observatory, Edinburgh 245 Hehir, Patrick, M. D. , F.R.C.S. E. , M.R.C.S.L. , L.R.C. P.E., Surgeon-Captain, Indian Medical Service, Principal Medical Officer, H.H. the Nizam’s Army, Hyderabad, Deccan, India Helme, T. Arthur, M.D., M.R.C.P.L., M.R.C.S., 3 St Peter’s Square, Manchester Henderson, John, D.Sc., Assoc. Inst. E.E., Kinnoul, Warwick’s Bench Rd., Guildford, Surrey * Henderson, William Dawson, M.A., B.Sc., Ph.D., Assistant Professor, Zoological Department, University College, Dundee * Hepburn, David, M.D., Professor of Anatomy in the University College of South Wales and Monmouthshire, Cardiff 250 Herdman, W. A., D.Sc., F.R.S., Pres.L.S., Prof, of Natural History in the- University of Liverpool, Croxteth Lodge, Ullet Road, Liverpool * Hewat, Archibald, F.F.A., F. I.A., 13 Eton Terrace Hill, Alfred, M.D., M.R.C.S., F.I.C., Valentine Mount, Freshwater Bay, Isle of Wight * Hinxman, Lionel W., B.A., Geological Survey Office, 33 George Square Hobday, Frederick T. G. , F.R.C.V. S. , 6 Berkeley Gardens, Kensington, London 255 Hodgkinson, W. R. , Ph.D., F.I.C. , F.C.S., Prof, of Chem. and Physics at the Royal Military Acad, and Royal Artillery Coll., Woolwich, 89 Shooter’s Hill Road, Blackheath, Kent Horne, John, LL.D. , F.R. S., F.G.S., Director of the Geological Survey of Scotland (Vice-President), 33 George Square, Edinburgh Horne, J. Fletcher, M.D., F.R.C.S.E., The Poplars, Barnsley * Horsburgh, Ellice Martin, M.A. , B.Sc., Lecturer in Technical Mathematics, University of Edinburgh, 11 Granville Terrace Houston, Alex. Cruikshanks, M.B., C.M., D.Sc., 19 Fairhazel Gardens, South Hampstead, London, N.W. 260 Howden, Robert, M.A., M.B. , C.M., Professor of Anatomy in the University of Durham, 14 Burdon Terrace, Newcastle-on-Tyne Howie, W. Lamond, F.C.S., 26 Neville Court, Abbey Road, Regent’s Park, London, N.W. Hoyle, William Evans, M.A. , D.Sc., M.R.C. S. , Crowland, Llandaff, Wales Hunt, Rev. H. G. Bonavia, Mus.D. Dub., Mus.B. Oxon., The Vicarage, Burgess Hill, Sussex * Hunter, James, F.R.C.S.E., F.R.A.S., Rosetta, Liberton, Midlothian 265 * Hunter, William, M.D., M.R.C.P.L. and E., M.R.C.S., 54 Harley Street, London Hyslop, Theophilus Bulkeley, M.D. , M.R.C.P.E., Senior Physician, Bethlem Royal Hospital, London, S.E. Inglis, J. W. , Memb. Inst. C.E. , 26 Pitt Street * Innes, Alexander Taylor, LL.D., M.A. , Advocate, 48 Morningside Park Innes, R. T. A., Director, Government Observatory, Johannesburg, Transvaal 270 * Ireland, Alexander Scott, S.S.C., 2 Buckingham Terrace Jack, William, M.A., LL.D., Professor of Mathematics in the University of Glasgow Jackson, Sir John, LL.D., 48 Belgrave Square, London * James, Alexander, M.D., F.R.C.P.E., 14 Randolph Crescent Jamieson, Prof. A., Memb. Inst. C. E., 16 Rosslyn Terrace, Kelvinside, Glasgow 275 * Jardine, Robert, M.D., M.R.C.S. Eng., F.F.P. and S. Glas., 20 Royal Crescent, Glasgow Date of Election, 1906 1900 1895 1903 1902 1874 1888 1905 1907 1909 1908 1892 1903 1891 1908 1886 1907 1877 1880 1883 1878 1901 1907 1880 1886 1907 1878 1885 1894 1905 1903 1874 1905 1889 1870 1903 1903 1898 1884 1888 >etical List of the Ordinary Fellows of the Society. 77 9 * Jehu, Thomas James, M.A., M.D., F.G.S., Lecturer in Geology, University of St Andrews, Strathmartine, Hepburn Gardens, St Andrews * Jerdan, David Smiles, M. A., D.Sc., Ph.D., Temora, Colinton, Midlothian Johnston, Lieutenant-Colonel Henry Halcro, C.B. , R.A.M.S., D.Sc., M.D., F.L.S., Orphir House, Kirkwall, Orkney * Johnston, Thomas Nicol, M.B., G.M., Corstorphine House, Corstorphine 280 Johnstone, George, Lieut. R.N.R. , late Marine Superintendent, British India Steam Navigation Co., 26 Comiston Drive Jones, Francis, M. Sc. , Lecturer on Chemistry, Beaufort House, Alexandra Park, Manchester Jones, John Alfred, Memb. Inst. C.E. , Fellow of the Univ. of Madras, Sanitary Engineer to the Government of Madras, c/o Messrs Parry & Co., 70 Grace- church St. , London Jones, George William, M.A., B.Sc. , LL. B. , Scottish Tutorial Institute, Edinburgh and Glasgow, 25 North Bridge, Coraldene, Kirk Brae, Liberton * Kemp, John, M.A. , Headmaster, High School, Kelso 285 Kenwood, Henry Richard, M.B., Chadwick Professor of Hygiene in the University of London, 150 Bethune Road, Amherst Park, London, N. * Kerr, Andrew William, F.S.A. Scot., Royal Bank House, St Andrew Square * Kerr, Rev. John, M.A., Manse, Dirleton * Kerr, John Graham, M.A., Professor of Zoology in the University of Glasgow Kerr, Joshua Law, M.D., Biddenden Hall, Cranbrook, Kent 290 Kidd, Walter Aubrey, M.D. , F.Z.S. , 12 Montpelier Row, Blackheath, London * Kidston, Robert, LL.D., F.R.S., F.G.S. (Secretary), 12 Clarendon Place, Stirling * King, Archibald, M.A., B.Sc., Rector of the Academy, Castle-Douglas, Hazeldene, Castle-Douglas, Kirkcudbrightshire King, Sir James, of Campsie, Bart., LL.D., 115 Wellington Street, Glasgow King, W. F., Lonend, Russell Place, Trinity 295 Kinnear, The Rt. Hon. Lord, one of the Senators of the College of Justice, 2 Moray Place Kintore, The Right Hon. the Earl of, M.A. Cantab., LL.D., Cambridge, Aberdeen and Adelaide, Keith Hall, Inverurie, Aberdeenshire * Knight, The Rev. G. A. Frank, M.A., St Leonard’s United Free Church, Perth * Knight, James, M.A., D.Sc., F.C.S., F.G.S. , Headmaster, St James School, Glasgow, The Shieling, Uddingston, by Glasgow Knott, C. G., D.Sc., Lecturer on Applied Mathematics in the University of Edinburgh (late Prof, of Physics, Imperial University, Japan) (Secretary), 42 Upper Gray Street, Edinburgh 300 * Laing, Rev. George P. , 17 Buckingham Terrace * Lanchester, William Forster, M.A. , Den of Gryffe, Kilmalcolm Lang, P. R. Scott, M.A., B.Sc., Professor of Mathematics, University of St Andrews Laurie, A. P., M.A., D.Sc., Principal of the Heriot-Watt College, Edinburgh * Laurie, Malcolm, B.A., D.Sc., F.L.S., Royal College of Surgeons, Edinburgh 305 * Lawson, David, M.A. , M.D., L.R.C.P. and S.E., Druimdarroch, Banchory, Kincardineshire * Leighton, Gerald Rowley, M.D., Sunnyside, Russell Place Letts, E. A., Ph.D., F.I.C., F.C.S. , Professor of Chemistry, Queen’s College, Belfast * Lightbody, Forrest Hay, 56 Queen Street * Lindsay, Rev. James, D.D., B.Sc., F.G.S., M.R.A.S., Corresponding Member of the Royal Academy of Sciences, Letters and Arts, of Padua, Associate of the Philosophical Society of Louvain, Annick Lodge, Irvine 310 Lister, The Right Hou. Lord, O.M., P. C., M.D. , F.R.C.S.L., F. R.C.S.E., LL.D., D. C. L. , F. R. S. , Foreign Associate of the Institute of France, Emeritus Professor of Clinical Surgery, King’s College, Surgeon Extraordinary to the King, 12 Park Crescent, Portland Place, London Liston, William Glen, M.D., Captain, Indian Medical Service, c/o Grindlay Groom & Co.. Bombay, India * Littlejohn, Henry Harvey, M.A., M.B., B.Sc., F.R.C.S.E., Professor of Forensic Medicine in the University of Edinburgh, 11 Rutland Street * Lothian, Alexander Yeitch, M.A., B.Sc., Glendoune, Manse Road, Bearsden, Glasgow Low, George M., Actuary, 11 Moray Place 315 * Lowe, D. F. , M.A., LL.D., late Head Master of Heriot’s Hospital School, Lauriston, 19 George Square 780 Proceedings of the Royal Society of Edinburgh. Date of Election. 1904 1900 1894 1887 1907 1891 1888 C. 1883 1903 1899 1905 1894 1897 C. 1904 1886 1904 1886 1901 C. 1888 C. 1878 C. 1885 C. 1897 1878 1886 1880 C. 1903 1869 O. N. 1895 C. 1882 1873 C. B. 1900 C. 1894 1898 1904 1905 1904 1869 C. 1869 C. 1899 1888 C. 1876 1876 1893 * Lowson, Charles Stewart, M.B., C.M., Captain, Indian Medical Service. c/o Messrs Thomas Cook & Son, Bombay, India. Lusk, Graham, Ph.D. , M.A. , Prof, of Physiology, Univ. and Bellevue Medical College, N.Y. * Mabbott, Walter John, M.A., Rector of County High School, Duns, Berwick- shire M‘Aldowie, Alexander M., M.D., Glengarriff, Leckhampton, Cheltenham 320 MacAlister, Donald Alexander, A. R.S. M., F. G. S., 20 Hanover Square, London, W. Macallan, John, F. I.C. , 3 Rutland Terrace, Clontarf, Dublin M ‘Arthur, John, F.C.S. , 196 Trinity Road, Wandsworth Common, London M‘Bride, P., M.D., F.R.C.P.E., 16 Chester Street * M‘Cormick, W. S., M. A., LL.D., 13 Douglas Crescent 325 * M‘Cubbin, James, B.A., Rector of the Burgh Academy, Kilsyth * Macdonald, Hector Munro, M. A., F.R.S., Professor of Mathematics, University of Aberdeen, 52 College Bounds, Aberdeen * Macdonald, James, Secretary of the Highland and Agricultural Society of Scotland, 2 Garscube Terrace * Macdonald, James A., M.A., B.Sc., H.M. Inspector of Schools, Glengarry, Dingwall * Macdonald, John A., M.A., B.Sc., High School, Stellenbosch, Cape Colony 330 * Macdonald, The Rt. Hon. Sir J. H. A., K.C.B., K.C., LL.D., F.R.S., M.I.E.E., Lord Justice- Clerk, and Lord President of the Second Division of the Court of Session, 15 Abercromby Place Macdonald, William, B.Sc., M. Sc. , Agriculturist, Editor Transvaal Agricultural Journal , Department of Agriculture, Pretoria Club, Pretoria, Transvaal * Macdonald, William J., M. A., 15 Comiston Drive * MacDougal, R. Stewart, M.A., D.Sc., 13 Archibald Place * M‘Fadyean, Sir John, M.B., B.Sc., LL.D., Principal, and Professor of Comparative Pathology in the Royal Veterinary College, Camden Town, London 335 Macfarlane, Alexander, M.A., D.Sc., LL.D., Lecturer in Physics in Lehigh University, Pennsylvania, Gowrie Grove, Chatham, Ontario, Canada Macfarlane, J. M., D.Sc., Professor of Botany and Director of the Botanic Garden, University of Pennsylvania, Philadelphia, Pennsylvania, U.S.A. * MacGillivray, Angus, C.M., M.D., South Tay Street, Dundee M'Gowan, George, F. I.C., Ph.D., 21 Montpelier Road, Ealing, Middlesex * MacGregor, The Very Rev. James, D. D., 3 Eton Terrace 340 MacGregor, James Gordon, M.A. , D.Sc., LL.D., F.R.S., Prof, of Natural Philosophy in the University of Edinburgh, 24 Dalrymple Crescent * M‘Intosh, D. C. , M.A., B.Sc., 3 Glenisla Gardens M‘Intosh, William Carmichael, M.D., LL.D. , F.R.S., F.L.S., Professor of Natural History in the University of St Andrews, 2 Abbotsford Crescent, St Andrews * Macintyre, John, M.D., 179 Bath Street, Glasgow Mackay, John Sturgeon, M.A. , LL.D., late Mathematical Master in the Edinburgh Academy, 69 Northumberland Street 345 M ‘Kendrick, John G., M.D., F.R.C.P.E., LL.D., F.R.S., Emeritus Professor of Physiology in the University of Glasgow, Maxieburn, Stonehaven * M ‘Kendrick, John Souttar, M.D., F.F.P.S.G., 2 Buckingham Terrace, Glasgow * Mackenzie, Robert, M. D., Napier, Nairn Mackenzie, W. Cossar, D.Sc., Alderston, Haddington * Mackenzie, W. Leslie, M.A., M.D., D.P.H., Medical Member of the Local Government Board for Scotland, 1 Stirling Road, Trinity 350 Mackenzie, William Colin, M. D. , F. R.C.S., Demonstrator of Anatomy in the University of Melbourne, Elizabeth Street North, Melbourne, Victoria * Mackintosh, Donald James, M.V.O., M.B. , Supt. Western Infirmary, Glasgow Maclagan, R. C., M.D., F.R.C.P.E., 5 Coates Crescent M‘Laren, The Hon. Lord, LL.D., Edin. & Glasg., F.R.A.S., one of the Senators of the College of Justice, 46 Moray Place Maclean, Ewan John, M.D., M.R.C.P. London, 12 Park Place, Cardiff 355 * Maclean, Magnus, M.A., D.Sc., Memb. Inst. E.E. , Prof, of Electrical Engineering in the Glasgow and West of Scotland Technical College, 51 Kerrsland Terrace, Hillhead, Glasgow Macleod, Very Rev. Norman, D.D. , 74 Murrayfield Gardens Macmillan, John, M.A., D.Sc., M.B., C.M., F.R.C.P.E., 48 George Square * M‘Murtrie, The Very Rev. John, M. A., D.D., 13 Inverleith Place . Date of Election 1906 1907 1890 1898 1908 1880 1909 1882 1901 1888 1892 1903 1885 1898 1906 1902 1901 1888 1902 1885 1908 1905 1909 1905 1904 1886 1899 1889 1897 1900 1899 1906 1890 1887 1896 1892 1901 ►etical List of the Ordinary Fellows of the Society. 781 * Maciiair, Duncan Scott, Ph.D., B.Sc., H.M. Inspector of Schools, 67 Braid Avenue 360 * Macnair, Peter, Curator of the Natural History Collections in the Glasgow Museums, Kelvingrove Museum, Glasgow * M‘Vail, John C., M.D., LL.D., 20 Eton Place, Hillhead, Glasgow Mahalanobis, S. C., B.Sc., Professor of Physiology, Presidency College, Calcutta, India Mallik, Devendranath, B.A., B.Sc., Professor of Physics and Mathematics, Patna College, Bankipur, Bengal, India Marsden, R. Sydney, M.D. , C.M., D.Sc., M.R.I.A., F.I.C, F.C.S., Rowallan House, Cearns Road, and Town Hall, Birkenhead 365 * Marshall, C. R., M.D., M.A., Professor of Materia-Medica and Therapeutics, University of St Andrews, Fairmount, Blackness Avenue, Dundee Marshall, D. H. , M.A., Professor of Physics in Queen’s University and College, Kingston, Ontario, Canada * Marshall, F. H. A., M.A. , D.Sc., Lecturer on Agricultural Physiology in the University of Cambridge, Christ’s College, Cambridge * Marshall, Hugh, D.Sc., F.R.S., Professor of Chemistry in the University College, Dundee * Martin, Francis John, W.S., 17 Rothesay Place 370 Martin, Nicholas Henry, F.L.S. , F.C.S., Ravenswood, Low Fell, Gates- head Masson, Orme, D.Sc., F. R.S., Professor of Chemistry in the University of Melbourne * Masterman, Arthur Thomas, M.A., D.Sc., Inspector of Fisheries, Board of Agriculture, Whitehall, London * Mathieson, Robert, F. C.S. , Rillbank, Innerleithen Matthews, Ernest Romney, Assoc. Memb. Inst. C.E. , F.G.S., Bessemer Prizeman, Soc. Engineers, Bridlington, Yorkshire 375 * Menzies, Alan W. C. , M. A., B.Sc., F.C.S., Kent Chemical Laboratory, University, Chicago, U.S.A. * Methven, Cathcart W., Memb. Inst. C.E., F.R.I.B.A., Durban, Natal, S. Africa Metzler, William H., A.B., Ph.D., Corresponding Fellow of the Royal Society of Canada, Professor of Mathematics, Syracuse University, Syracuse, N.Y. Mill, Hugh Robert, D.Sc., LL.D., 62 Camden Square, London * Miller, Alexander Cameron, M.D., F.S.A. Scot., Craig Linnhe, Fort-William, Inverness-shire 380 * Miller-Milne, C. H.. M.A., Rector, The High School, Arbroath, 8 Dalhousie Place A.rbro8»tii Mills, Bernard Langley, M.D., F.R.C.S.E., M.R.C.S.L., D.P.H., Lt.-Col. R.A.M. C. , late Army Specialist in Hygiene, 4 Palmerston Road, Broomhill, Sheffield * Milne, Archibald, M.A., B.Sc., Lecturer on Mathematics and Science, Edinburgh Provincial Training College, 108 Comiston Drive * Milne, James Robert, D.Sc., 56 Manor Place * Milne, William, M.A., B.Sc., 70 Beechgrove Terrace, Aberdeen 385 * Milroy, T. H., M. D., B.Sc., Professor of Physiology in Queen’s College, Belfast, Thomlea, Malone Park, Belfast Mitchell, A. Crichton, D.Sc., Director of Public Instruction in Travancore, India * Mitchell, George Arthur, M.A., 9 Lowther Terrace, Kelvinside, Glasgow * Mitchell, James, M.A., B.Sc., 4 Manse Street, Kilmarnock * Mitchell-Thomson, Sir Mitchell, Bart., 6 Charlotte Square 390 Moffat, The Rev. Alexander, M.A., B.Sc., Professor of Physical Science, Christian College, Madras, India Mond, R. L. , M.A., Cantab., F.C. S., The Poplars, 20 Avenue Road, Regent’s Park, London Moos, N. A. F. , L.C.E., B.Sc., Professor of Physics, Elpliinstone College, and Director of the Government Observatory, Colaba, Bombay * Morgan, Alexander, M. A., D.Sc., Principal, Edinburgh Provincial Training College, 1 Midmar Gardens Morrison, J. T. . M.A , B.Sc., Professor of Physics and Chemistry, Victoria College, Stellenbosch, Cape Colony 395 Moses, O. St John, M. D., B.Sc., F. R.C.S.E., Captain, Indian Medical Service, 8 Lansdowne Road, Calcutta, India 782 Proceedings of the Royal Society of Edinburgh. Date of Election. 1892 1874 C. C. K. 1888 1907 1887 C. 1894 1891 C. 1896 1892 1907 1877 C. c. c. B. N. 1907 1887 1902 1888 1897 1906 1898 1884 1880 1878 C. 1906 1888 1888 1886 1895 C. 1884 1908 C. K. 1905 1892 1901 1886 C. 1889 1892 1881 C. N. 1907 1904 Mossman, Robert C,, Superintendent of Publications, Argentine Meteorological Office, Cuyo 947, Buenos Ayres Muir, Thomas, C.M.G., M.A. , LL.D., F.R.S., Superintendent-General of Educa- tion for Cape Colony, Education Office, Cape Town, and Mowbray Hall, Rosebank, Cape Colony * Muirliead, George, Commissioner to His Grace the Duke of Richmond and Gordon, K.G., Spey bank, Fochabers Muirhead, James M. P. , Bredisholm, Claremont, near Cape Town, Cape Colony 400 Mukhopadhyay, Asutosh, ML. A., LL.D., F.R.A.S. , M. R.I.A., Professor of Mathe- matics at the Indian Association for the Cultivation of Science, 77 Russa Road North, Bhowanipore, Calcutta * Munro, J. M. M., Memb. Inst. E. E., 136 Bothwell Street, Glasgow * Munro, Robert, M.A., M.D., LL.D., Hon. Memb. R.I. A., Hon. Memb. Royal Soc. of Antiquaries of Ireland, Elmbank, Largs, Ayrshire * Murray, Alfred A., M.A., LL. B. , 20 Warriston Crescent * Murray, George Robert Milne, F.R.S., F. L. S., 32 Market Square, Stonehaven 405 * Murray, James, Park Road, Maxwelltown, Dumfries Murray, Sir John, K.C.B., LL.D., D.C.L., Ph.D., D.Sc., F.R.S., Member of the Prussian Order Pour le Merite, Director of the Challenger Expedition Publications. Office, Villa Medusa, Boswell Road. House, Challenger Lodge, Wardie, and United Service Club * Musgrove, James, M.D., F.R.C.S. Edin. and Eng., Bute Professor of Anatomy, University of St Andrews, 56 South Street, St Andrews Muter, John, M.A., F.C.S., South London Central Public Laboratory, 325 Kennington Road, London Mylne, The Rev. R. S., M.A., B.C.L. Oxford, F.S.A. Lond. , Great Amwell, Herts 410 Napier, A. D. Leith, M.D., C.M., M.R.O.P.L., 28 Angas Street, Adelaide, S. Australia Nash, Alfred George, C. E., B.Sc. , Engineer, Department of Public Works, Jamaica, Belretiro, Mandeville, Jamaica, A\7.I. * Newington, Frank A., Memb. Inst. C.E., Memb. Inst. E.E., 4 Osborne Terrace Newman, George, M.D., D.P.H. Cambridge, Lecturer on Preventive Medicine, St Bartholomew’s Hospital, University of London : Dene, Hatch End, Middlesex Nicholson, J. Shield, M.A., D.Sc., Professor of Political Economy in the University of Edinburgh, 3 Belford Park 415 Nicol, W. W. J., M.A., D.Sc., 15 Blacket Place Norris, Richard, M.D., M.R. C. S. Eng., 3 Walsall Road, Birchfield, Birmingham * O’Connor, Henry, C.E., Assoc. Memb. Inst. C.E., 1 Drummond Place * Ogilvie, F. Grant, C.B., M.A., B.Sc., Principal Assistant Secretary for Science, Art, and Technology, Board of Education, South Kensington, London * Oliphant, James, M.A., 11 Heathfield Park. Willesden, London 420 Oliver, James, M.D., F. L.S., Physician to the London Hospital for Women, 18 Gordon Square, London Oliver, Sir Thomas, M.D. , LL.D., F. R.C.P., Professor of Physiology in the University of Durham, 7 Ellison Place, Newcastle-upon-Tyne Omond, R. Traill, 3 Church Hill Page, William Davidge. F.C.S. , F.G.S. , M. Inst. M. E.. 10 Clifton Dale, York Pallin, William Alfred, F.R.C.V.S., Captain in the Army Veterinary Department, c/o Messrs Holt k Co., 3 Whitehall Place, London 425 Parker, Thomas, Memb. Inst. C. E., Severn House, Iron Bridge, Salop * Paterson, David, F.C.S., Lea Bank, Rosslyn, Midlothian * Paton, D. Noel, M.D., B.Sc., F. R.C.P.E., Professor of Physiology in the Univer- sity of Glasgow, University, Glasgow * Patrick, David, M.A., LL.D., c/o W. & R. Chambers, 339 High Street * Paulin, Sir David, Actuary, 6 Forres Street 430 Peach, Benjamin N., LL.D., F.R.S., F.G.S., late District Superintendent and Acting Palaeontologist of the Geological Survey of Scotland, 72 Grange Loan * Pearce, John Thomson, B. A. . B.Sc., School House, Tranent * Peck, James Wallace, M.A. , Principal Assistant to Executive Officer (Education) of the London County Council, Stanfield House, High Street, Hampstead, London Date of Election. 1889 1887 1900 1893 1889 1907 1905 1908 1906 1886 1888 1902 1892 1875 1908 1885 1903 1880 1898 1897 1899 1884 1891 1904 1900 1883 1889 1902 1902 1908 1908 1875 1906 1898 1880 1900 1896 1902 1896 1881 1909 1880 itical List of the Ordinary Fellows of the Society. 783 Peck, William, F.R.A.S. , Town’s Astronomer, City Observatory, Calton Hill, Edinburgh Peddie, Wm. , D.Sc., Professor of Natural Philosophy in University College, Dundee, Rosemount, Forthill Road, Brough ty Ferry 435 Penny, John, M.B., C.M., D.Sc., Great Broughton, near Cockermouth, Cumberland Perkin, Arthur George, F.R.S., 8 Montpellier Terrace, Hyde Park, Leeds Philip, R. W. , M.A., M.D., F.R.C.P.E., 45 Charlotte Square Phillips, Charles E. S., Castle House, Shooter’s Hill, Kent Pinkerton, Peter, M.A., D.Sc., Head Mathematical Master, George Watson’s College, Edinburgh, 36 Morningside Grove 440 Pirie, James Hunter Harvey, B.Sc. , M.D., M. R.C.P.E., 13 Alva Street Pitcliford, Herbert Watkins, F.R.C.V.S., Bacteriologist and Analyst, Natal Government, The Laboratory, Pietermaritzburg, Natal Pollock, Charles Frederick, M.D., F.R.C S.E., 1 Buckingham Terrace, Hillhead, Glasgow Prain, David, Lt.-Col., Indian Medical Service, M.A., M.B. , LL.D., F. L.S. , F.R.S., Hon. Memb. Soc. Lett, ed Arti d. Zelanti, Acireale ; Corr. Memb. Pharm. Soc. Gt. Britain, etc. ; Director, Royal Botanic Gardens, Kew (late Director, Botanical Survey of India, Calcutta), Botanic Gardens, Kew Preller, Charles Du Riche, M.A. , Ph.D., Assoc. Memb. Inst. C.E., 61 Melville Street 445 Pressland, Arthur, J., M.A. Camb. , Edinburgh Academy Prevost, E. W., Ph.D., Weston, Ross, Herefordshire Pringle, George Cossar, M. A. , Rector of Peebles Burgh and County High School, Bloomfield, Peebles Pullar, J. F. , Rosebank, Perth Pullar, Laurence, The Lea, Bridge of Allan 450 Pullar, Sir Robert, LL.D., M.P. for the City of Perth, Tayside, Perth Purves, John Archibald, D.Sc., 13 Albany Street Rainy, Harry, M.B., C.M., F.R.C. P. Ed., 16 Gt. Stuart Street Ramage, Alexander G., 8 Western Terrace, Murray field Ramsay, E. Peirson, M.R. I.A., F.L.S., C.M.Z.S. , F. R.G.S., F.G.S., Fellow of the Imperial and Royal Zoological and Botanical Society of Vienna, Curator of Australian Museum, Sydney, N.S. W. 455 * Rankine, John, M.A., LL.D., K.C., Professor of the Law of Scotland in the University of Edinburgh, 23 Ainslie Place Ratcliffe, Joseph Riley, M. B., C.M., c/o The Librarian, The University, Birmingham Raw, Nathan, M.D., 66 Rodney Street, Liverpool Readman, J. B., D.Sc., F.C.S., Staffield Hall, Kirkoswald, R.S.O., Cumberland Redwood, Sir Boverton, D.Sc. (Hon.), F. I.C., F.C.S., Assoc. Inst. C.E., Wadham Lodge, Wadham Gardens, London 460 Rees-Roberts, John Vernon, M. D. , D.Sc., D.P.H., Barrister-at-Law, National Liberal Club, Whitehall Place, London Reid, George Archdall O’Brien, M.B., C. M. , 9 Victoria Road South, Southsea, Hants * Rennie, John, D.Sc., Lecturer on Parasitology, and Assistant to the Professor of Natural History, University of Aberdeen, 60 Desswood Place, Aberdeen Richardson, Linsdall, F.G.S., F. L.S., Director, Cheltenham School of Science and Technology, 10 Oxford Parade, Cheltenham Richardson, Ralph, W.S., 10 Magdala Place 465 * Ritchie, William Thomas, M.D., F.R. C.P.E., 9 Atholl Place Roberts, Alexander William, D.Sc., F.R. A.S., Lovedale, South Africa Roberts, D. Lloyd, M.D., F.R.C.P.L., 23 St John Street, Manchester * Robertson, Joseph M‘Gregor, M.B., C.M., 26 Buckingham Terrace, Glasgow * Robertson, Robert, M.A., 25 Mansionhouse Road 470 * Robertson, Robert A., M.A., B.Sc., Lecturer on Botany in the University of St Andrews * Robertson, W. G. Aitchison, D.Sc., M. D., F.R. C.P.E., 2 Mayfield Gardens Rosebery, The Right Hon. the Earl of, K.G., K.T., LL.D., D.C.L. , F.R.S., Dalmeny Park, Edinburgh * Ross, Alex. David, M.A. , B.Sc., Assistant to the Professor of Natural Philosophy in the University of Glasgow, 7 Queen’s Terrace, Glasgow Rowland, L. L., M.A., M.D., President of the Oregon State Medical Society, and Professor of Physiology and Microscopy in Williamette University, Salem, Oregon 475 784 Date of Election. 1906 1902 1880 1904 1906 1903 1903 1891 1900 1885 1880 1905 1902 1897 ] 894 1871 1908 1900 1900 1903 1901 1891 1882 1885 1871 1904 1907 1880 1899 1880 1889 1882 1896 1874 1906 1891 1886 1884 1888 1904 Proceedings of the Royal Society of Edinburgh. * Russell, Alexander Durie, B.Sc., Mathematical Master, Falkirk High School, Dunaura, Heugh Street, Falkirk * Russell, James, 12 Argyll Place Russell, Sir James A., M.A., B.Sc.,M.B., F.R.C.P.E., LL.D., Woodville, Canaan Lane Sachs, Edwin 0., Architect, 7 Waterloo Place, Pall Mall, London, S.W. Saleeby, Caleb William, M.D., 13 Greville Place, London 480 * Samuel, John S. , 8 Park Avenue, Glasgow * Sarolea, Charles, Ph.D., D.Litt., Lecturer on French Language, Literature, and Romance Philology, University of Edinburgh, 21 Royal Terrace Sawyer, Sir James, Knt. , M.D., F. R.C.P. , F. S. A., J.P. , Consulting Physician to the Queen’s Hospital, 31 Temple Row, Birmingham * Schafer, Edward Albert, M. R.C.S. , LL.D., F.R.S., Professor of Physiology in the University of Edinburgh Scott, Alexander, M.A. , D.Sc., F. R. S., The Davy-Faraday Research Laboratory of the Royal Institution, London 485 Scott, J. H., M.B., C.M., M.R.C.S., Prof, of Anatomy in the University of Otago, New Zealand Scougal, A. E., M.A., LL.D., H.M. Senior Chief Inspector of Schools and Inspector of Training Colleges, 1 Wester Coates Avenue Senn, Nicholas, M.D., LL.D., Professor of Surgery, Rush Medical College, Chicago, U.S. A. * Shepherd, John William, Carrickarden, Bearsden, Glasgow * Shield, Wm., Memb. Inst. C.E., 33 Old Queen Street, Westminster, London 490 Simpson, Sir A. R., M.D., Emeritus Professor of Midwifery in the University of Edinburgh. 52 Queen Street * Simpson, George Freeland Barbour, M.D., F.R.C.P.E., F.R.C.S.E., 43 Manor Place * Simpson, James Young, M.A., D.Sc., Professor of Natural Science in the New College, Edinburgh, 25 Chester Street Sinhjee, Sir Bhagvat, G.C.I.E., M.D., LL.D. Edin., H. H. The Thakur Sahib of Gondal, Gondal, Kathiawar, Bombay * Skinner, Robert Taylor, M.A., Governor and Headmaster, Donaldson’s Hospital, Edinburgh 495 * Smart, Edward, B.A., B.Sc., Tillyloss, Tullylumb Terrace, Perth * Smith, Alexander, B.Sc., Ph.D., Professor of General Chemistry, University of Chicago, Ills., U.S. Smith, C. Michie, B.Sc., F.R.A.S., Director of the Kodaikanal and Madras Obser- vatories, The Observatory, Kodaikanal, South India Smith, George, F.C.S., Polmont Station Smith, John, M.D., F.R.C.S.E., LL.D., 11 Wemyss Place 500 * Smith, William Charles, K.C., M.A., LL.B. , Advocate, 10 Doune Terrace Smith, William Ramsay, D.Sc., M.B. , C.M., Permanent Head of the Health Department, South Australia, Winchester Street, East Adelaide, South Australia Smith, William Robert, M.D., D.Sc., Barrister- at- Law, Professor of Forensic Medicine in King’s College, 74 Great Russell Street, Bloomsbury Square, London Snell, Ernest Hugh, M.D., B.Sc., D.P.H. Camb., Coventry Sollas, W. J., M.A., D.Sc., LL.D., F.R.S., late Fellow of St John’s College, Cambridge, and Professor of Geology and Palaeontology in the University of Oxford 505 Somerville, AVm., M.A., D.Sc., D.Oec., Sibthorpian Professor of Rural Economy in the University of Oxford, 121 Banbury Road, Oxford Sorley, James, F.I.A., F. F.A., C. A.., 82 Onslow Gardens, London * Spence, Frank, M.A., B.Sc., 25 Craiglea Drive Sprague, T. B., M.A,. LL.D., Actuary, 29 Buckingham Terrace Squance, Thomas Coke, M.D. , Physician and Pathologist in the Sunderland Infirmary, 15 Grange Crescent, Sunderland 510 * Stanfield, Richard, Professor of Mechanics and Engineering in the Heriot-Watt College * Stevenson, Charles A., B.Sc., Memb. Inst. C.E., 28 Douglas Crescent Stevenson, David Alan, B.Sc., Memb. Inst. C. E., 45 Melville Street * Stewart, Charles Hunter, D.Sc., M.B., C.M., Professor of Public Health in the University of Edinburgh, 9 Learmonth Gardens * Stewart, Thomas W. . M.A., B.Sc., Science Master, Edinburgh Ladies’ College, 29 Bruntsfield Gardens 515 Alphabetical List of the Ordinary Fellows of the Society. 785 Date of Election. 1877 1902 1889 1906 1907 1903 1896 1905 1885 1904 1898 1895 1890 1870 1899 1892 1885 1907 1905 1887 1896 1903 1906 1887 1906 1880 1899 1870 1882 1876 1874 1874 1888 1905 1906 1861 1895 1898 1889 C. C. c. c. c. c. c. B. N c. K. N C. c. Stirling, William, D.Sc., M.D., LL.D, , Brackenbury Professor of Physiology and Histology in Owens College and Victoria University, Manchester * Stockdale, Herbert Fitton, Clairinch, Upper Helensburgh, Dumbartonshire * Stockman, Ralph, M.D., F.R.C.P.E., Professor of Materia Medica and Therapeutics in the University of Glasgow Story, Fraser, Lecturer in Forestry, University College, Bangor, North Wales * Strong, John, B.A. , Rector of Montrose Academy, 11 Union Place, Montrose 520 Sutherland, David W., M.D., M.R.C.P. Lond., Captain, Indian Medical Service, Professor of Pathology and Materia Medica, Medical College, Lahore, India * Sutherland, John Francis, M.D, , Dep. Com. in Lunacy for Scotland, Scotsburn Road, Tain, Ross -shire Swithinbank, Harold William, Denham Court, Denham, Bucks Symington, Johnson, M.D., F.R.C.S.E. , F.R.S. , Prof, of Anatomy in Queen’s College, Belfast * Tait, John YV., B.Sc., Rector of Leith Academy, 18 Netherby Road, Leith 525 Tait, William Archer, B.Sc., Memb. Inst. C. E., 38 George Square Talmage, James Edward, D.Sc., Pli.D., F.R.M.S., F.G.S., Professor of Geology, Univ. of Utah, Salt Lake City, Utah Tanakadate, Aikitu, Prof, of Nat. Phil, in the Imperial University of Japan, Tokyo, Japan Tatlock, Robert R., F.C.S. , City^ Analyst’s Office, 156 Bath Street, Glasgow * Taylor, James, M. A. , Mathematical Master in the Edinburgh Academy, Edinburgh Academy 530% Thackwell, J. B. , M.B., C.M. Thompson, D’Arcy W. , C.B., B. A., F. L. S. , Professor of Natural History in University College, Dundee * Thompson, John Hannay, M. Inst. C. E., M. Inst. Mech. E., Engineer to the Dundee Harbour Trust, Earlville, Brough ty Ferry * Thoms, Alexander, 7 Playfair Terrace, St Andrews * Thomson, Andrew, M.A., D.Sc., F.I.C., Rector, Perth Academy, Ardenlea, Pitcullen, Perth 535 * Thomson, George Ritchie, M.B., C. M., Cumberland House, Von Brandis Square, Johannesburg, Transvaal Thomson, George S., F.C.S. , Dairy Commissioner for Queensland, Department of Agriculture, Brisbane, Queensland * Thomson, Gilbert, C.E., 164 Bath Street, Glasgow * Thomson, J. Arthur, M.A., Regius Prof, of Natural History in the Univ. of Aberdeen Thomson, James Stuart, F.L.S. (Assistant Professor of Zoology, South African College, Cape Town), 24 Briickfeldstrasse, Bern, Switzerland 540 Thomson, John Millar, LL.D., F.R.S., Prof, of Chem. in King’s College, Lond., 9 Campden Hill Gardens, London * Thomson, R. Tatlock, F.C.S., 156 Bath Street, Glasgow' Thomson, Spencer C., Actuary, 10 Eglinton Crescent Thomson, Wm., M.A., B.Sc., LL.D., Registrar, University of the Cape of Good Hope. University Buildings, Cape Town Thomson, William, Royal Institution, Manchester 545 Traquair, R. H., M.D. , LL.D., F. R.S., F.G.S., late Keeper of the Natural History Collections in the Royal Scottish Museum, Edinburgh (Vice-President), The Bush, Colinton Tuke, Sir J. Batty, M.D., D.Sc., LL.D., F.R.C.P.E., M.P. for the Universities of Edinburgh and St Andrews, 20 Charlotte Square * Turnbull, Andrew H., Actuary, The Elms, Wliitehouse Loan * Turner, Arthur Logan, M.D., F.R.C.S.E., 27 Walker Street * Turner, Daw-son F. D., B.A., M.D., F.R.C.P.E., M.R.C.P. Lond., Lecturer on Physics, Surgeon’s Hall, and Physician in charge of Electrical Department, Royal Infirmary, Edinburgh, 37 George Square 550 Turner, Sir William, K.C.B., M.B., F.R.C.S.E., LL.D., D.C.L., D.Sc. Dub., F.R.S., Principal of the University of Edinburgh (President), 6 Eton Terrace Turton. Albert H., M.I.M.M., 18 Harrow Road, Bowenbrook, Birmingham * Tweedie, Charles, M.A., B.Sc., Lecturer on Mathematics in the University of Edinburgh, 40 Gillespie Crescent Underhill, T. Edgar, M.D., F.R.C.S.E., Dunedin, Barnt Green, Worcester- shire VOL. XXIX. 50 786 Date of Election, 1906 1888 1891 1873 1902 1886 1898 1891 1907 1901 1904 1862 1900 1907 1896 « 1907 1903 1904 1896 1909 1896 1890 1881 1894 1879 1897 1908 1900 1879 1902 1895 1882 1891 1902 1908 1886 1884 1890 breedings of the Royal Society of Edinburgh. Yandenbergh, William J., Barrister-at-Law, S.S.C., F.R.S.L., F.R.M.S., 29-32 Exchange Buildings, Pirie Street, Adelaide, S. Australia 555 Walker, James, Memb. Inst. C.E., Engineer’s Office, Tyne Improvement Commission, Newcastle-on-Tyne * Walker, James, D.Sc., Ph.D., LL.D., F.R.S., Professor of Chemistry in the University of Edinburgh, 5 Wester Coates Road Walker, Robert, M.A., LL.D., University, Aberdeen * Wallace, Alexander G., M.A., 56 Fonthill Road, Aberdeen * Wallace, R. , F.L.S. , Professor of Agriculture and Rural Economy in the University of Edinburgh 560 Wallace, Wm., M. A., Belvedere, Alta, Canada * Walmsley, R. Mullineux, D.Sc., Prin. of the Northampton Inst., Clerkenwell, London Waters, E. Wynston, Medical Officer, H.B.M. Administration, E. Africa, Malindi, British East Africa Protectorate, via Mombasa * Waterston, David, M.A., M .D., F. R.C.S. E. , Lecturer on Regional Anatomy in the University of Edinburgh, 1 Coates Place * Watson, Charles B. Boog, Huntly Lodge, 1 Napier Road 565 Watson, Rev. Robert Boog, B.A., LL.D., F.L.S., Past President of the Concho- logical Society, 11 Stratliearn Place * Watson, Thomas P. , M.A., B.Sc., Principal, Keighley Institute, Keighley * Watt, Andrew, M.A., Secretary to the Scottish Meteorological Society, 6 Woodburn Terrace Webster, John Clarence, B.A., M.D., F.R.C.P.E., Professor of Obstetrics and Gynaecology, Rush Medical College, Chicago, 706 Reliance Buildings, 100 State Street, Chicago * Wedderburn, Ernest Maclagan, M.A., LL.B., 6 Succoth Gardens 570 * Wedderburn, J. H. Maclagan, M.A., D.Sc., 11 Alexander Street, Princeton, N.J., U.S.A. Wedderspoon, William Gibson, M.A., LL.D., Indian Educational Service, Senior Inspector of Schools, Burma, The Education Office, Rangoon, Burma Wenley, Robert Mark, M.A., D.Sc., D.Phil. , Litt.D., LL.D., Professor of Philosophy in the University of Michigan, Ann Arbor, Mich., U.S.A. * Westergaard, Reginald Ludovic Andreas Emil, Lecturer in Technical Mycology, Heriot Watt College, 6 Suffolk Road, Edinburgh White, Philip J., M.B., Prof, of Zoology in University College, Bangor, North Wales 575 White, Sir William Henry, K.C.B. , Memb. Inst. C. E., LL.D., F.R.S. , late Assistant Controller of the Navy, and Director of Naval Construction, Cedarscroft. Putney Heath, London Whitehead, Walter, F. R.C.S. E., late Professor of Clinical Surgery, Owens College and Victoria University, Birchfield, Rusholme, Manchester Whymper, Edward, F. R.G.S., Holmwood, Waldegrave Road, Teddington, Middlesex Will, John Charles Ogilvie, of Newton of Pitfodels, M.D., 17 Bon- Accord Square, Aberdeen * Williams, W. Owen, F.R.C.Y.S., Professor of Veterinary Medicine and Surgery, University of Liverpool, The Veterinary School, The University, Liverpool 580 * Williamson, Henry Charles, M.A., D.Sc., Naturalist to the Fishery Board for Scotland, 28 Polmuir Road, Aberdeen Wilson, Alfred C., F.C.S., Voewood Croft, Stockton-on-Tees Wilson, Andrew, Ph.D., F.L.S. , Lecturer on Zoology and Comparative Anatomy, 110 Gilmore Place * Wilson, Charles T. R., M.A., F.R.S. , Glencorse House, Peebles, and Sidney Sussex College, Cambridge Wilson-Barker, David, F. R.G.S., Captain-Superintendent Thames Nautical Training College, H.M.S. “ Worcester,” Greenhithe, Kent 585 Wilson, George, M. A. , M.D., LL.D., 7 Avon Place, Warwick * Wilson, John Hardie, D.Sc., University of St Andrews, 39 South Street, St Andrews Wilson, William Wright, F.R.C.S.E., M. R.C.S. Eng., Cottesbrook House, Acock’s Green, Birmingham * Wood, Thomas, M.D. , Eastwood, 182 Ferry Road, Bonnington, Leith * Woodliead, German Sims, M.D. , F.R. C.P.E., Professor of Pathology in the University of Cambridge 590 Woods, G. A., M. R.C.S., Eversleigh, 1 Newstead Road, Lee, Kent * Wright, Johnstone Christie, Northfield, Colinton Alphabetical List of the Ordinary Fellows of the Society. 787 Date of Election. 1896 1882 1892 i 1896 ! C. 1900 1904 * Wright, Robert Patrick, Professor of Agriculture, West of Scotland Agricultural College, 6 Blythswood Square, Glasgow Young, Frank W., F.C.S. , H.M. Inspector of Science and Art Schools, 32 Buckingham Terrace, Botanic Gardens, Glasgow Young, George, Ph.D. , 79 Harvard Court Mansions, Honeybourne Road, West Hampstead, London, N.W. 595 * Young, James Buchanan, M. B. , D. Sc., Dalveen, Braeside, Liberton * Young, J. M‘LauchIan, F.R.C.V.S., Lecturer on Veterinary Hygiene, University of Aberdeen Young, R. B., M.A., B.Sc. , Transvaal Technical Institute, Johannesburg, Transvaal 788 Proceedings of the Royal Society of Edinburgh. LIST OF HONORARY FELLOWS OF THE SOCIETY At October 1909. HIS MOST GRACIOUS MAJESTY THE KING. Foreigners (limited to thirty-six by Law X.). Elected 1897 Alexander Agassiz, Cambridge {Mass. ). 1897 E.-H. Amagat, Paris. 1900 Arthur Auwers, Berlin. 1900 Adolf Ritter von Baeyer, 1905 Waldemar Chr. Brogger, Munich. Christiania. 1897 Stanislao Cannizzaro, Rome. 1905 Moritz Cantor, Heidelberg . 1902 Jean Gaston Darboux, Paris. 1905 Paul Ehrlich, Frankfurt-a. -M. 1908 Emil Fischer, Berlin. 1902 Albert Gaudry, Paris. 1905 Paul Heinrich Grotli, Munich. 1888 Ernst Haeckel, Jena. 1883 Julius Hann, Graz. 1908 George William Hill, New York. 1879 Jules Janssen, Paris. 1908 Friedrich Wilhelm Georg Kohlrauscli, Charlottenburg. 1897 Gabriel Lippmann, Paris. 1895 Eleuthere-Elie-Nicolas Mascart, Paris. 1895 Carl Menger, Vienna. 1897 Fridtjof Nansen, Christiania. 1908 Henry Fairfield Osborn, New York. 1908 Iwan P. Pawlov, St Petersburg. 1905 Eduard Pfluger, Bonn. 1895 Jules Henri Poincare, 1889 Georg Hermann Quincke, Paris. Heidelberg. 1908 Gustaf Retzius, Stockholm. 1908 Augusto Righi, 1897 Giovanni V. Schiaparelli, Bologna. Milan. 1905 Eduard Suess, Vienna. 1908 Louis Joseph Troost, Paris. 1905 Wilhelm Waldeyer, Berlin. 1905 Wilhelm Wundt, Leipzig. 1897 Ferdinand Zirkel, Bonn am Rhein. Total, 34. British Subjects (limited to twenty by Law X.). Elected 1889 Sir Robert Stawell Ball, Kt., LL.D. , F.R. S., M.R.I.A. , Lowndean Professor of Astronomy in the University of Cambridge, 1892 Colonel Alexander Ross Clarke, C.B., R.E., F. R. S., 1897 Sir George Howard Darwin, K.C.B., M.A., LL.D., F.R.S., Plumian Professor of Astronomy in the University of Cambridge, 1900 David Ferrier, M.D. , LL.D., F.R.S. , Professor of Neuro- Pathology, King’s College, London, 1900 Andrew Russell Forsyth, D.Sc., F.R.S. , Sadlerian Professor of Pure Mathematics in the University of Cambridge, 1892 Sir David Gill, K.C.B., LL.D., F.R.S., formerly His Majesty’s Astronomer at the Cape of Good Hope, 1895 Albert C. L. G. Gunther, Ph.D., F.R.S., 1883 Sir Joseph Dalton Hooker, K.C.S.I., M.D., LL.D., D.C.L., F.R.S., Corresp. Mem. Inst, of France, Cambridge. RedJiill, Surrey . Cambridge. London. Cambridge. London. London. London. 789 List of Honorary Fellows, etc. 1884 Sir William Huggins, K.C.B., LL.D., D.C L. , P.R.S., Corresp. Mem. Inst, of France, 1908 Sir Alexander B. W. Kennedy, LL.D., F.R.S., Past Pres. Inst. C.E., 1908 Sir Edwin Ray Lankester, K.C.B., LL.D., F.R.S. , 1900 Archibald Liversidge, LL.D., F.R.S., Professor of Chemistry in the University of Sydney, 1908 Sir James A. H. Murray, LL.D., D.C.L., Editor of the Oxford English Dictionary, 1905 Sir William Ramsay, K. C.B., LL.D., F.R.S., Professor of Chemistry in the University College, London, 1886 The Lord Rayleigh, D.C.L., LL.D., D.Sc. Dub., F.R.S. , Corresp. Mem. Inst, of France, 1908 Charles S. Sherrington, M.A., M.D., LL.D., F.R.S., Holt Professor of Physiology in the University of Liverpool, 1905 Sir Joseph John Thomson, D.Sc., LL.D., F.R.S., Cavendish Professor of Experimental Physics, University of Cambridge, 1900 Thomas Edward Thorpe, D.Sc., LL.D., F.R.S., Principal of the Govern- ment Laboratories, London, 1895 Sir Charles Todd, K.C.M.G., F.R.S., Government Astronomer, South Australia, London. London. London. Sydney. Oxford. London. London. Liverpool. Cambridge. London. Adelaide. Total, 19. ORDINARY FELLOWS OF THE SOCIETY ELECTED During Session 190S-9. (Arranged according to the date of their election.) 21 st December 1908. William Gentle, B.Sc. 18^ January 1909. James Gordon Gray, B.Sc. Henry Richard Kenwood, M.B. Alex. David Ross, M.A. , B.Sc. C. R. Marshall, M.D. , M.A. 15 th February 1909. John Brownlee, M.A., M.D. Arthur G. S. Mitchell. Bernard Langley Mills, M.D., F.R.C.S.E. Reginald L. A. E. Westergaard. 15 th March 1909. Peter Comrie, M.A., B.Sc. WJi May 1909. Thomas Morrison Clayton, M.D. D.Hy. Aucland Campbell Geddes, M.D. 12 th July 1909. Hugh Steuart Gladstone, M.A. 790 Proceedings of the Royal Society of Edinburgh. ORDINARY FELLOWS DECEASED AND RESIGNED During Session 1908-9. DECEASED. George Seton, M. A. Professor Thomas Gray, B.Sc. D. M. C. L. Argyll Robertson, M.D. Francis Elgar, M.Inst. C.E., LL.D. Rev. Professor Duns, D.D. Walter Stewart. Robert Henry Bow, C.E. Professor D. J. Hamilton, LL.D. Em. ProfessorS. S. Laurie, M.A., LL.D. George Broadrick, Memb. Inst. C.E. Professor D. J. Cunningham, M.D. , LL.D. John A. W. Dollar, M.R.C.V.S. Andrew Fuller Hargreaves, F.C.S. Em. Professor Hugh Blackburn, M.A., LL.D. Sir Arthur Mitchell, K.C.B. Patrick Doyle, C.E. T. G. Has myth, M.D. RESIGHED. Henry Coates. FOREIGN HONORARY FELLOWS DECEASED. Simon Heavcomb (Washington, U.S.A.). Anton Dohrn (Haples). BRITISH HONORARY FELLOW DECEASED. Edward Caird, LL.D. (Oxford). Abstract of Accounts. 791 ABSTRACT OF THE ACCOUNTS OF JAMES CURRIE, ESQ., As Treasurer of the Royal Society of Edinburgh. SESSION 190S-1909. I. ACCOUNT OF THE GENERAL FUND. CHARGE. 1. Arrears of Contributions at 1st October 1908 Contributions for present Session : — 1. 162 Fellows at £2, 2s. each ...... £340 4 0 133 Fellows at £3, 3s. each ...... 418 19 0 £759 3 0 Less included in payments in lieu of future contributions 2 2 0 £757 1 0 2. Commutation Fee in lieu of Future Contributions of one Fellow .......... 21 0 0 3. Fees of Admission and Contributions of nine new Resident Fellows at £5, 5s. each ....... 47 5 0 4. Fees of Admission of three new Non-Resident Fellows at £26, 5s. each ........ 78 15 0 3. Interest received — Interest, less Tax ........ £372 4 8 Annuity from Edinburgh and District Water Trust, less Tax 49 16 7 4. Transactions and Proceedings sold ......... 5. Annual Grant from Government .......... Amount of the Charge DISCHARGE. 1. Rent of Society’s Apartments for Half-year to Martinmas 1908, less Tax 2. Taxes, Insurance, Coal and Lighting : — Property Tax ..... Insurance ...... Coal ....... Gas ....... Electric Light ..... 3. Salaries: — General Secretary . . . . . . . . . £10000 Librarian . . . . . . . . . . 100 0 0 Assistant Librarian . . . . . . . . 62100 Office Keeper (S. Heddle) ....... 65 0 6 Do. (Mrs Hay) ....... 8 14 5 Doorkeeper .......... 5 15 8 Treasurer’s Clerk . . . . . . . . . 2500 Allowance to Widow of Mr Hardy, late Librarian . . . 62 10 0 £7 10 0 11 1 6 13 8 9 0 13 9 2 9 7 £219 9 0 904 1 0 422 1 3 143 2 0 600 0 0 £2288 13 3 £142 10 0 35 3 7 429 10 7 Carry forward £607 4 2 792 Proceedings of the Royal Society of Edinburgh. 4. Brought forward Expenses of Transactions : — Neill & Co., Ltd., Printers ....... Less Received from Scottish National Antarctic Expedition, per Whitson & Methuen ...... Neill k Co., Ltd., Printers, for illustrations . Do. (Ben Nevis) Less Received from the Carnegie Trust per the Meteorological Society of Scotland M‘Farlane k Erskine, Lithographers Less Received from the Scottish National Antarctic Expedition, per Whitson k Methuen ...... Janies Green, Lithographer .... G. Waterston k Sons, do. .... [J. Bartholomew & Co., do. .... Hislop & Day, Engravers .... Orrock k Son, Bookbinders .... 5. Expenses of Proceedings : — Neill & Co., Ltd., Printers .... Do. (for illustrations) M'Farlane & Erskine, Lithographers Hislop k Day, Engravers .... 6. Books, Periodicals, Newspapers, etc. : — Otto Schulze k Co., Booksellers James Thin, do. R. Grant & Son, do. Wm. Green k Sons, do. ... International Catalogue of Scientific Literature Robertson k Scott, News Agents . Egypt Exploration Funds Subscription . Ray Society do. Palseontographical Society do. Journal de Concliyliologie .... Orrock k Son, Bookbinders .... 7. Other Payments : — Neill & Co. , Ltd., Printers .... R. Blair k Son, Confectioners .... S. Duncan, Tailor (uniforms) Lantern Exhibitions, etc., at Lectures . Lindsay, Jamieson k Haldane National Telephone Co. ..... Tods, Murray & Jamieson, W.S. Petty Expenses, Postages, Carriage, etc. . 8. Special Expenses Consequent on Removal : — A. Dishington, Assistant at Removal J. F. Ellis, do. Edinburgh Corporation, Electric Light . Morison k Co., Upholsterers .... J. k T. Scott, Cabinetmakers .... C. H. Woolford, Artist, Cleaning Pictures Aitken, Dott k Son, do. Drummond, Young k Watson, Photographers J. Cavagnari, Cleaning Busts A. k J. M‘Nab, Cleaners .... £155 ' 2 11 100 0 0 £134 13 0 58 0 0 £262 1 o 25 0 0 £237 1 2 34 14 0 55 2 11 76 13 0 33 12 0 5 7 6 3 5 0 17 16 0 70 2 6 £603 6 11 56 18 6 4 5 6 3 19 0 £119 2 2 52 n O 9 7 6 4 0 15 6 17 0 0 5 6 6 3 3 0 1 1 0 1 1 0 0 15 0 16 12 3 £65 8 0 30 14 2 11 18 0 6 10 0 6 6 0 9 10 0 11 6 0 65 16 7 £49 0 0 30 10 0 12 3 3 21 12 6 13 6 9 32 10 0 23 19 6 5 17 0 3 0 0 2 5 9 9. Irrecoverable Arrears of Contributions written off £607 4 2 533 14 1 668 9 11 224 6 6 207 8 9 194 4 9 9 9 0 Carry forward £2444 17 2 Abstract of Accounts. 793 Brought forward 10. Arrears of Contributions outstanding at 1st October 1909 : — Present Session, per list ....... £102 18 Previous Session, per list ....... 166 19 Amount of the Discharge Amount of the Discharge Amount of the Charge Excess of the Discharge Floating Balance due by the Society at 1st October 1908 A eld Excess of Discharge as above . . Floating Balance due by the Society at 1st October 1909 Being — Balance due to Union Bank on Current Account . £2444 17 2 0 0 269 17 0 £2714 : 14 2 £2714 14 2 2288 13 3 £426 O 11 . £202 7 3 426 0 11 . £628 8 2 £628 8 2 II. ACCOUNT OF THE KEITH FUND To 1st October 1909. CHARGE. 1. Balance due by Union Bank at 1st October 1908 ...... £24 18 10 2. Interest Received : — On £896, 19s. Id. North British Railway Company 3 per cent. Debenture Stock for year to Whitsunday 1909, less Tax , £25 10 11 On £211, 4s. North British Railway Company 3 per cent. Lien Stock for year to Lammas 1909, less Tax .... 600 31 10 11 DISCHARGE. £56 9 9 Nil. 1. Balance due by Union Bank at 1st October 1909 £56 9 9 III. ACCOUNT OF THE NEILL FUND To 1st October 1909. « CHARGE. 1. Balance on hand — Uncashed Dividend Warrants, less sum due to the Union Bank at 1st October 1908 £30 16 2 2. Interest Received : — On £355 London, Chatham and Dover Railway 4^ per cent. Arbitration Debenture Stock for year to 30th June 1909, less Tax £15 2 10 Less Interest paid to Union Bank ...... 049 14 18 1 £45 14 3 DISCHARGE. Nil. Balance due by Union Bank at 1st October 1909 £45 14 3 794 Proceedings of the Royal Society of Edinburgh. IV. ACCOUNT OF THE MAKDOU GALL -BRISBANE FUND To 1st October 1908. CHARGE. 1. Balance due at 1st October 1908 : — By Union Bank of Scotland on Deposit Receipt . . . £135 0 0 By Union Bank of Scotland on Current Account . . . 46 17 11 £181 17 11 2. Interest Received on £365 Caledonian Railway Company 4 per cent. Consolidated Preference Stock No. 2 for year to 30th June 1909, less Tax ........ £13 16 7 On Deposit Receipt with Union Bank ..... 198 15 6 3 £197 4 2' DISCHARGE. Nil. 3. Balance due at 1st October 1909 : — By Union Bank of Scotland on Deposit Receipt . . . £135 0 0 By Union Bank of Scotland on Current Account . . . 62 4 2 £197 4 2 V. ACCOUNT OF THE MAKERSTOUN MAGNETIC METEOROLOGICAL OBSERVATION FUND To 1st October 1909. CHARGE. Sum on Deposit Receipt with the Union Bank of Scotland at 1st October 1908 . £212 10 3 Interest thereon 268 £214 16 11 DISCHARGE. Nil. Above Sum on Deposit Receipt with the Union Bank of Scotland at 1st October 1909 £214 16 11 VI. ACCOUNT OF THE GUNNING-VICTORIA JUBILEE PRIZE FUND To 1st October 1909. (Instituted by Dr R. H. Gunning of Edinburgh and Rio de Janeiro.) CHARGE. 1. Balance due by Union Bank at 1st October 1908 ...... £102 17 10 2. Interest received on £1000 North British Railway Company Consolidated Lien Stock for year to Lammas 1909, less Tax ....... 28 8 5 £131 6 3 DISCHARGE. Nil Balance due by the Union Bank of Scotland on Current Account at 1st October 1909 £131 6 3 Abstract of Accounts. 795 STATE OF THE FUNDS BELONGING TO THE ROYAL SOCIETY OF EDINBURGH As at 1st October 1909. 1. GENERAL FUND— 1. £2090, 9s. 4d. three per cent. Lien Stock of the North British Railway Company at 82§ per cent., the selling price at 1st October 1909 2. £8519, 14s. 3d. three per cent. Debenture Stock of do. at 85^ per cent., do. 3. £52, 10s. Annuity of the Edinburgh and District Water Trust, equivalent to £875 at 172 per cent. , do. ......... 4. £1811 four per cent. Debenture Stock of the Caledonian Railway Company at 113| per cent. , do. .......... 5. £35 four and a half per cent. Arbitration Debenture Stock of the London, Chatham and Dover Railway Company at 117| per cent., do. . 6. Arrears of Contributions, as per preceding Abstract of Accounts . £1732 7 7 7284 7 10 1505 0 0 2060 2 0 40 19 10 269 17 0 £12,892 12 5 Deduct Floating Balance due by the Society, as per preceding Abstract of Accounts ............ 628 8 2 Amount . . £12,264 4 3 Exclusive of Library, Museum, Pictures, etc., Furniture of the Society’s Rooms at George Street. 2. KEITH FUND— 1. £896, 19s. Id. three per cent. Debenture Stock of the North British Railway Company at 85 \ per cent., the selling price at 1st October 1909 £766 18 8 2. £211, 4s. three per cent. Lien Stock of do. at 82§ per cent., do. . . . 175 1 2 3. Balance due by the Union Bank of Scotland ...... 56 9 9 Amount . . . £998 9 7 3. NEILL FUND— 1. £355 four and a half per cent. Arbitration Debenture Stock of the London, Chatham and Dover Railway Company at 117^ per cent., the selling price at 1st October 1 909 .......... £415 15 5 2. Balance due by Union Bank of Scotland . . . . . . . 45 14 3 Amount . . . £461 9 8 4. MAKDOUGALL-BRISBANE FUND— 1. £365 four per cent. Consolidated Preference Stock No. 2 of the Caledonian Railway Company at 104^ per cent., the selling price at 1st October 1909 £381 8 6 2. Sum on Deposit Receipt with the Union Bank of Scotland .... 135 0 0 3. Balance due by do. on Current Account . . . . . . . 62 4 2 Amount . . . £578 12 8 5. MAKERSTOUN MAGNETIC METEOROLOGICAL OBSERVATION FUND— Sum on Deposit Receipt with the Union Bank of Scotland at 1st October 1909 £214 16 11 6. GUNNING-VICTORIA JUBILEE PRIZE FUND— Instituted by Dr Gunning of Edinburgh and Rio de Janeiro — 1. £1000 three per cent. Consolidated Lien Stock of the North British Railway Company at 82-| per cent., the selling price at 1st October 1909 . . £828 16 0 2. Balance due by the Union Bank of Scotland on Current Account . . 131 6 3 Amount . . . £960 2 3 Edinburgh, 20th October 1909. —We have examined the six preceding Accounts of the Treasurer of the Royal Society of Edinburgh for the Session 1908-1909, and have found them to be correct. The securities of the various Investments at 1st October 1909, as noted in the above Statement of Funds, have been exhibited to us. LINDSAY, JAMIESON & HALDANE, Auditors. / 796 Proceedings of the Poyal Society of Edinburgh. VIDIMUS of ESTIMATED INCOME of THE GENERAL FUND FOR SESSION 1909-1910. I. Interest: — On £8519, 14s. 3d. Railway Debenture Stock at 3 per cent. .... £255 11 10 On £2090, 9s. 4d. Railway Lien Stock at 3 per cent. .... 62 14 4 On £1811 Railway Debenture Stock at 4 per cent. . . , , 72 8 8 On £35 Kailway Debenture Stock at 4| per cent. • 1 11 6 £392 6 4 2. Annuity from the Edinburgh and District Water Trust . 52 10 0 £444 16 4 Deduct Income Tax at Is. 2d. per £ . . 25 18 10 £418 17 6 3. Annual Contributions : — Of 161 Fellows at £2, 2s. each ..... £338 2 0 Of 130 Fellows at £3, 3s. each ..... 409 10 0 — 747 12 0 4. Annual Grant from Government . 600 0 0 5. Sales of Society’s Transactions ...... . 30 0 0 Total Estimated Income, £1796 9 6 Exclusive of Fees of Admission and Contributions of New Fellows who may be admitted during the Year. INDEX. Absorption. On a Question in Absorption Spectroscopy, by Robert A. Houstoun and Alex. S. Russell, 68-74. Aitken (John). On a Simple Radioscope and a Radiometer for showing and measuring Radioactivity, 471-487. Amphoteric Bases, Hydrolysis of Solution of Salts of, by Heather H. Beveridge, 648-667. Anschutz (Richard). Life and Chemical Work of Archibald Scott Oouper. Translated and communicated by Emeritus-Professor A. Crum Brown, 193-273. Archibald (E. H.). The Atomic Weight of Platinum, 721-747. Arsenious and Arsenic Acids, Reducing Action of Electrolytic Hydrogen in, when liberated from the Surfaces of Different Metals, by Wm. Thomson, 84-95. Auditory Ossicles. The possible Homologues amongst the Lower Vertebra ta of the Auditory Ossicles of the Horse, by Ray F. Coyle, 582- 601. Their Development in the Horse, by Ray F. Coyle, 582-601. Bacteria, Mixed Cultures of, by E. Westergaard, 748. Beveridge (Heather H. ). The Hydrolysis of Salts of Amphoteric Electrolytes, 648-667. Brown (A. Crum), and G. E. Gibson. Pre- liminary Note on the Action of Nitric Anhy- dride on Mucic Acid, 96-97. Camera, A Special Form of, for Recording the Readings of the Scales of Scientific Instru- ments, by J. R. M ilne, 176-181. Chloroform administered by Different Channels, Histological Changes in the Liver and Kidney after, by G. Herbert Clark, 418-426. Circular Weirs and Orifices, Discharge of Water from, by G. H. Gulliver, 295-303. Clark (G. Herbert). On the Histological Changes in the Liver and Kidney after Chloroform administered by Different Channels, 418-426. Copper Alloys, Magnetic Properties of, A. D. Ross and R. C. Gray, 274-286. Couper (Archibald Scott), Life and Chemical Work of, by R. Anschutz, 193-273. Coyle (Ray F.). The Development of the Auditory Ossicles in the Horse, with a Note on their possible Homologues in the Lower Vertebrata, 582-601. Crushing Tests of Materials, by G. H. Gulliver, 432-444. Current Observations in Loch Garry, by E. M. Wedderburn, 98-135. in Loch Ness, by E. M. Wedderburn and W. Watson, 619-647. Cynomacrurus Piriei , by L. Dollo, 316-326. Determinant, Superadjugate, and Skew Deter- minants having a Univarial Diagonal, by Thomas Muir, 668-686. Differentiated Sex, Mendelian Action on, by D. Berry Hart, 607-618. Differentiation, Partial. New Conditions for Reversibility of Order, by W. F. Young, 136- 164. Dini-Schwarz Conditions for Reversibility of Order of Partial Differentiation, Modified form of, by W. F. Young, 136-164. Dissymmetrical Separations, Cases in the Zeeman Effect in Tungsten and Molybdenum showing, by R. Jack, 75-83. Dollo (L. ). Cynomacrurus Piriei , Poisson abyssal nouveau recueilli par l’Expedition Antarctique Nationale Ecossaise. Note Pre- liminaire, 316-326. Nematonurus Lecointei, Poisson abyssal de la “Belgica” retrouve par l’Expedition Antarctique Nationale Ecossaise, 488-498. Dyson (F. W. ). Systematic Motions of the Stars. (Second Paper), 376-392. Electric Oscillations superposed upon Cyclic Magnetisation in Iron, by James Russell, 1-37. Electromotive Force of Iodine Concentration Cells, etc., by A. P. Laurie, 304-315. Energy Accelerations. On Energy Accelerations and Partition of Energy, by O. W. Follett, 349-375. Ewan (A. F. ). Laboratory Note on the Study of Polarisation by means of the Dolezalek Electrometer, 1 65-1 7 5. § Eyre (John). The Pathogenesis of Micrococcus melitensis, 537-581. Flexural Vibrations of Thin Rods, by George Green, 393-400. Fluorescence Absorption, A Negative Attempt to Detect, by R. A. Houstoun, 401-413. Follett (C. W. ). On Energy Accelerations and Partition of Energy, 349-375. Fraser (Sir Thomas R.), and A. T. Mackenzie. On Strophanthus sarmentosus : its Pharmaco- logical Action and its Use as an Arrow Poison. (Abstract), 415-417. 798 Index. Friction, Crushing Strength affected by End, by G. H. Gulliver, 432-444. Internal, in Pieces subjected to Com- pound Loading, by G. H. Gulliver, 427-431. Garry, Temperature Observations in Loch, with Notes on Currents and Seiches, by E. M. Wedderburn, 98-135. Gibb, David. Motion of Neptune’s Satellite, 517-536. Gibson (G. E. ), and A. Crum Brown. — Pre- liminary Note on the Action of Nitric Anhydride on Mucic Acid, 96-97. Gray (Andrew). On Lagrange’s Equations of Motion, and on Elementary Solutions of Gyrostatic Problems, 327-348. Gray (J. G.), and Hugh Higgins. Low Tem- perature Experiments in Magnetism, 287-294. and A. D. Ross. On an Improved Form of Magnetometer and Accessories for the testing of Magnetic Materials at Different Temperatures, 182-192. Green (George). Flexural Vibrations of Thin Rods, 393-400. On Group- Velocity and on the Propaga- tion of Waves in a Dispersive Medium, 445-470. Group- Velocity, and on the Propagation of Waves in a Dispersive Medium, by George Green, 445-470. Gulliver (G. H.). On the Discharge of Water from Circular Weirs and Orifices, 295-303. On the Effect of Internal Friction in Cases of Compound Stress, 427-431. On the Friction at the Extremities of a Short Bar subjected to a Crushing Load, and its Influence upon the Apparent Compressive Strength of the Material, 432-444. Gyrostatic Problems, Elementary Solutions of, by A. Gray, 327-348. Hardy (John). Obituary Notice of, 749. Hart (D. Berry). Mendelian Action on Differ- entiated Sex, 607-618. Heusler Alloy, Magnetism of, by A. D. Ross and R. C. Gray, 274-286. Holonomous and Non-Holonomous Systems, Equations of Motion for, by A. Gray, 327-348. Houstoun (R. A.). A Negative Attempt to Detect Fluorescence Absorption, 401-413. and Alex. S. Russell. On a Question in Absorption Spectroscopy, 68-74. Hydrogen, On the Reducing Action of Electro- lytic, on Arsenious and Arsenic Acids when liberated from the Surfaces of Different Metals, by Wm, Thomson, 84-95. Hydrolysis. Salts of Amphoteric Electrolytes, by Heather H. Beveridge, 648-667. Iodine Concentration Cells, The Electromotive Force of, with one Electrode saturated with Iodine, by A. P. Laurie, 304-315. Iron, Crushing Tests of, by G. H. Gulliver, 432-444. Jack (R. ). Dissymmetrical Separations in the Zeeman Effect in Tungsten and Molybdenum, 75-83. Jacobians, Theory of, in the Historical Order of Development up to 1860, by Thomas Muir, 499-516. Kidney and Liver, Histological Changes in, after Chloroform administered by Different Channels, by G. Herbert Clark, 418-426. Lagrange’s Equations of Motion, by A. Gray, 327-348. Lakes, Currents in, by E. M. Wedderburn and W. Watson, 619-647. Laurie (A. P. ). The Electromotive Force of Iodine Concentration Cells with One Electrode saturated with Iodide, 304-315. Lindsay (T. A. ). On the Recalescence Tempera- tures of Nickel, 57-67. Liver and Kidney, Histological Changes in, after Chloroform administered by Different Channels, by G. Herbert Clark, 418-426. Loch Ness, Currents in, by E. M. Wedderburn and W. Watson, 619-647. Magnetic Properties of certain Copper Alloys, by A. D. Ross and R. C. Gray, 274-286. Magnetisation in Iron, Vibrations and Oscilla- tions superposed upon Cyclic, by James Russell, 1-37. Magnetism in Nickel, Effect of Load and Vibrations upon, by James Russell, 38-56. Magnetism, Low Temperature Experiments in, by Messrs Gray and Higgins, 287-294. Magnetometer for Testing of Magnetic Materials, by J. G. Gray and A. D. Ross, 182-192. Manus in Mesoplodon, Hyperoodon and the Delphinidse, Morphology of the, by Sir Wm. Turner, 687-720. Mendelian Action on Differentiated Sex, by D. Berry Hart, 607-618. Micrococcus melitensis, Pathogenesis of, by John Eyre, 537-581. Milne (J. R. ). A Special Form of Photographic Camera for Recording the Readings of the Scales of Scientific Instruments, 176-181. Mixed Cultures, Development of, by E. Wester- gaard, 748. Morphology of the Manus in Mesoplodon, Hyperoodon and the Delphinidse, by Sir Wm. Turner, 687-720. Muir (Thomas). The Theory of Jacobians in the Historical Order of Development up to 1860, 499-516. The superadjugate Determinant and Skew Determinants having a Univarial Diagonal, 668-686. Nematonurus Lecointei , by Louis Dollo, 488-498. Neptune’s Satellite, Motion of, by David Gibb, 517-536. Nickel, Effect of Load and Vibrations upon Magnetism in, by James Russell, 38-56. Recalescence Temperatures of, by T. A. Lindsay, 57-67. Nitric Anhydride, Action of, on Mucic Acid, by A. Crum Brown and G. E. Gibson, 96-97. Obituary Notice of John Hardy, late librarian, R.S.E., 749. Index. 799 Occlusion. Occlusion of Gases by Platinum Sponge, by E. H. Archibald, 721-747. Orifices, Circular, Discharge of Water from, by G. H. Gulliver, 295-303. Pathogenesis of Micrococcus melitensis, by John Eyre, 537-581. Pettersson’s Observations on Deep Water Oscil- lations, by E. M. Wedderburn, 602-606, Platinum Salts. Preparation of Pure Platinum Salts, by E. H. Archibald, 721-747. Polarisation, Electromotive Force of. Varia- tion during the Flow of the Current, by A. F. Ewan, 165-175. Polarisation of a Cell, Variation of, with Potential Difference between the Electrodes, by A. F. Ewan, 165-175. Radioactivity, Radioscope and Radiometer for showing and measuring, by John Aitken, 471— 487. Radiometer for measuring Radioactivity, by John Aitken, 471-487. Radioscope for showing Radioactivity, by John Aitken, 471-487. Recalescence in Nickel, by T. A. Lindsay, 57- 67. Recording the Readings of the Scales of Scien- tific Instruments, A Special Camera for, J. R. Milne, 176-181. Repeated Derivates and Differential Co-efficient, Properties of, by W. F. Young, 136-164. Rods, Thin, Flexural Vibrations of, by George Green, 393-400. Ross (A. D. ), and J. G. Gray. On an Improved Form of Magnetometer and Accessories for the Testing of Magnetic Materials at Different Temperatures, 182-192. and R. C. Gray. On the Magnetic Properties of certain Copper Alloys, 274-286. Russell (Alex. S.), and Robert A. Houstoun. On a Question in Absorption Spectroscopy, 68-74. Russell (James). The Shift of the Neutral Points due to Variation of the Intensity of Mechanical Vibrations or Electric Oscillations superposed upon Cyclic Magnetisation in Iron, 1-37. The Effect of Load and Vibrations upon Magnetism in Nickel, 38-56. Seiche in Skagerak, by E. M. Wedderburn, 602- 606. Seiches in Loch Garry, by E. M. Wedderburn, 98-135. Skew Determinants having a Univarial Diagonal, by Thomas Muir, 668-686. Sowerby’s Whale, The Skeleton of a, by Sir Wm. Turner, 687-720. Spark Gap, Experiment with, of an Induction Coil, by Dawson F. D. Turner, 414. Spectroscopy. On a Question in Absorption Spectroscopy, by Robert A. Houstoun and Alex S. Russell, 68-74. Steel, Crushing Tests of, by G. H. Gulliver, 432-444. Stones, Crushing Tests of, by G. H. Gulliver, 432-444. Strength, Compressive, of Materials, by G. H. Gulliver, 432-444. Stress, Compound, Internal Friction in Cases of, by G. H. Gulliver, 427-431. Strophanthus scirmentosus : its Pharmacological Action and its Use as an Arrow Poison, by Sir Thomas R. Fraser and A. T. Mackenzie. (Abstract), 415-417. Superadjugate Determinant and Skew Determin- ants having a Univarial Diagonal, by Thomas Muir, 668-686. Systematic Motions of the Stars, by F, W. Dyson, 376. Temperature Observations in Loch Garry, by E. M. Wedderburn, 98-135. Temperature Seiche in Skagerak, by E. M. Wedderburn, 602-606. Thomson (William). On the Reducing Action of Electrolytic Hydrogen on Arsenious and Arsenic Acids when liberated from the Surface of Different Elements, 84-95. Turner (Dawson F. D. ). Experiment with the Spark Gap of an Induction Coil, 414. Turner (Sir Wm. ). The Skeleton of a Sowerby’s Whale ( Mesoploden bidens) stranded at St Andrews, and the Morphology of the Manus in Mesoplodon, Hyperoodon, and the Del- phinidse, 687-720. Vibrational Neutral Points in Cyclically Magnetised Iron, by James Russell, 1-37. Water discharged from Circular Weirs and Orifices, by G. H. Gulliver, 295-303. Watson ( W. ), and E. M. Wedderburn. Observa- tions with a Current Meter in Loch Ness, 619-647. Waves, Propagation of, in a Dispersive Medium, by George Green, 445-470. Wedderburn (E. M.). Temperature Observa- tions in Loch Garry (Inverness-shire), with Notes on Currents and Seiches, 98-135. Oscillations in Deep Water of Skagerak, Pettersson’s Observations on, 602-606. and W. Watson. Observations with a Current Meter in Loch Ness, 619-647. Westergaard, (E. ). On the Development of Mixed Cultures of Bacteria and Lower Fungi in Liquid and Solid Media, 748. Whale, Sowerby’s, The Skeleton of a, by Sir Wm. Turner, 687-720. Young, W. F. On the Conditions for the Reversibility of the Order of Partial Differ- entiation, 136-164. Zeeman Triplet, Influence of the Rotation of the Plane of Polarisation on the, by R. Jack, 75-83. PRINTED BY NEILL AND CO., LTD., EDINBURGH. the printer is not responsible, the expense of such proofs and corrections will be charged against the author. All proofs must, if possible, be returned within one week, addressed to The Secretary , Royal Society , Mound , Edinburgh , and not to the printer. To prevent delay, authors residing abroad should appoint some one residing in this country to correct their proofs. 4. Additions to a Paper after it has been finally handed in for publication, if accepted by the Counci], will be treated and dated as separate communications, and may, or may not, be printed immediately after the original paper. 5. Brief Abstracts of Transactions Papers will be published in the Proceedings, provided they are sent along with the original paper. 6. Separate Issue of Reprints; Author’s Free and Additional Copies. — As soon as the final revise of a Transactions paper has been returned, or as soon as the sheet in which the last part of a Proceedings paper appears is ready for press, a certain number of separate copies or reprints, in covers bearing the title of the paper and the name of the author, are printed off and placed on sale. The date of such separate publication will be printed on each paper. The author receives fifty of these reprints free, and may have any reasonable number of additional copies at a fixed scale of prices which will be furnished by the printer, who will charge him with the cost. To prevent disappointment, especially if the paper contains plates, the author should, immediately after receiving his first proof, notify to the printer the number of additional copies required. 7. Index Slips. — In order to facilitate the compilation of Subject Indices, and to secure that due attention to the important points in a paper shall be given in General Catalogues of Scientific Literature and in Abstracts by Periodicals, every author is requested to return to the Secretary, along with his final proof, a brief index (on the model given below), of the points in it which he considers new or important. These indices will be edited by the Secretary, and incorporated in Separate Index Slips, to be issued with each part of the Proceedings and Transactions. MODEL INDEX.* Schafer, E. A. — On the Existence within the Liver Cells of Channels which can be directly injected from the Blood-vessels. Proc. Roy. Soc. Edin., vol, 1902, pp. Cells, Liver, — Intra-cellular Canaliculi in. E. A. Schafer. Proc. Roy. Soc. Edin., vol. , 1902, pp. Liver, — Injection within Cells of. E. A. Schafer. Proc. Roy. Soc. Edin., vol. , 1902, pp. PAGE Awards of the Keith, Makdougall-Brisbane, Neill, and Gunning Victoria Jubilee Prizes, . . . . .766 The Council of the Society, 1909-1910, .... 771 Alphabetical List of the Ordinary Fellows of the Society, . 772 List of Honorary Fellows of the Society, . . . .788 y j=~— ~ List of Ordinary Fellows of the Society elected during Session 1908-1909, ....... 789 Ordinary Fellows deceased and resigned during Session 1908- 1909, . . ^ . . . . . .790 Foreign Honorary Fellows deceased, . . . .790 British Honorary Fellow deceased, . . . . 790 Abstract of Accounts of the Society, Session 1908-1909, . 791 Index, . . . . . . . . .797 The Papers published in this Part of the Proceedings may be had separately, on application to the Publishers, at the follow- ing prices: — . Price Is. 6d. No. XLII., . No. KLIII., . i